# When and how does ram pressure stripping in low-mass satellite galaxies
enhance star formation

Jingyao Zhu  Department of Astronomy, Columbia University, New York, NY 10027,
USA  Stephanie Tonnesen  Center for Computational Astrophysics, Flatiron
Institute, New York, NY 10010, USA  Greg L Bryan  Department of Astronomy,
Columbia University, New York, NY 10027, USA  Center for Computational
Astrophysics, Flatiron Institute, New York, NY 10010, USA

###### Abstract

We investigate how a satellite’s star formation rate (SFR) and surviving gas
respond to ram pressure stripping in various environments. Using a suite of
high-resolution “wind-tunnel” simulations with radiative cooling, star
formation, and supernovae feedback, we model the first infall orbit of a low-
mass disk galaxy ($M_{*}=10^{9.7}$ $M_{\odot}$) in different host halos,
ranging from Milky Way-like to cluster hosts. When the ram pressure is
moderate, we find that the stripping satellite shows an enhanced SFR relative
to the isolated control case, despite gas loss due to stripping. The SFR
enhancement is caused, not directly by compression, but by ram pressure-driven
mass flows, which can increase the dense gas fraction in the central disk
regions. The spatially-resolved star formation main sequence and Kennicutt-
Schmidt relations in our simulations are consistent with recent findings of
the VERTICO and GASP surveys. Our results predict the environmental signals of
RPS in future multiwavelength, high-angular resolution observations: the star
formation and gas surface densities will be centralized, and symmetrically
enhanced within the stripping radius.

hydrodynamical simulations — star formation — galaxy interactions —
interstellar medium

##  1 Introduction

A galaxy can either be star-forming or quenched, depending on internal and
environmental processes (Kauffmann et al., 2004; Baldry et al., 2006; Peng et
al., 2010). For the central galaxies within halos, internal processes such as
supernova and AGN feedback are the main star formation regulators (Croton et
al., 2006; Dalla Vecchia & Schaye, 2008). This explains the “main sequence” of
star formation over cosmic time: a tight correlation between the star
formation rate (SFR) and stellar mass ($M_{*}$) of galaxies (Speagle et al.,
2014). For satellite galaxies, environmental factors from the interactions
with a central halo become significant: satellites show a strong observational
bias to be ‘red’, or star formation quenched, compared with their central
counterparts at the same stellar masses (Peng et al., 2012; Wetzel et al.,
2012; Phillips et al., 2014). The environmental quenching of satellite
galaxies is also ubiquitous in cosmological simulations (Tremmel et al., 2019;
Wright et al., 2019; Appleby et al., 2020; Donnari et al., 2021a, b).

Despite the consensus of environmental quenching in observations and
simulations, uncertainties remain in the mass dependence and the scatter of
the quenching effectiveness (Donnari et al., 2021a). The uncertainties likely
arise from the complex physical processes during the satellite-environment
interactions (see recent review by Cortese et al. 2021), of which the dominant
is ram pressure stripping (RPS; Gunn & Gott 1972), the direct removal of the
satellite’s interstellar medium (ISM) by a host halo medium. RPS galaxies,
identified by unidirectional gas tails and little stellar disk deformation,
have been observed in several clusters (van Gorkom, 2004; Boselli et al.,
2006; Sun et al., 2007; Poggianti et al., 2016; Deb et al., 2022) as well as
in both idealized (e.g., Abadi et al. 1999; Quilis et al. 2000; Schulz &
Struck 2001; Roediger & Brüggen 2006; Jáchym et al. 2007; McCarthy et al.
2008) and cosmological simulations (Bahé et al., 2012; Yun et al., 2019; Rohr
et al., 2023). Although the hallmark of RPS is gas removal and, therefore, the
eventual quenching of star formation (Boselli et al., 2006; Crowl & Kenney,
2008), recent detailed observations have shown that the early stages of RPS
may have complex effects on both the ISM phase distribution and SFRs. Under
RPS, the satellite’s star formation can be triggered (Ebeling et al., 2014;
Jáchym et al., 2019; Poggianti et al., 2019), the SFR globally (Vulcani et
al., 2018; Roberts et al., 2021; Kolcu et al., 2022; Molnár et al., 2022) or
locally (Vulcani et al., 2020) enhanced, and the molecular-to-atomic gas ratio
boosted (Moretti et al., 2020).

The interplay between RPS and star formation is key to understanding
environmental quenching, and has been explored in various controlled
hydrodynamical simulations. Multiple simulations analyzed the star formation
triggering- or enhancing-potential of RPS (Schulz & Struck, 2001; Kapferer et
al., 2009; Tonnesen & Bryan, 2012; Roediger et al., 2014; Bekki, 2014;
Steinhauser et al., 2016; Ruggiero & Lima Neto, 2017; Lee et al., 2020), but
the physical reasons behind the enhancement are unclear. Ram pressure-driven
shock passages can trigger local boosts to the SFR, but have little global
effects (Roediger et al., 2014); pressure enhancement in the wind-leading
halves of the galaxies undergoing stripping suggests that compression likely
enhances the star formation efficiency (Troncoso-Iribarren et al., 2020); ram
pressure-induced radial gas inflows can modify the star formation morphology,
shifting it to the central regions with higher SFR (Schulz & Struck, 2001;
Tonnesen & Bryan, 2012; Lee et al., 2020). There is a need to examine the
physical causes of RPS-enhanced star formation in simulations, and to directly
compare with recent observations.

In this work, we study the complicated effects of RPS on the ISM distribution
and SFRs. (i) We simulate a low-mass spiral galaxy (lowest resolved in Donnari
et al. 2021a, with tension in the quenched fractions) undergoing RPS in
different environments, from a Milky Way-like to a cluster halo, and examine
the galaxy’s gas and SFR response; (ii) For each host halo, we model a
realistic infall orbit with time-varying ram pressure profiles; (iii) We
analyze the local SFR-mass relations at comparable spatial resolutions with
recent high angular resolution observations (Vulcani et al., 2020; Jiménez-
Donaire et al., 2023); and finally (iv) We compare and identify key physical
causes of RPS-enhanced star formation.

The structure of this paper is as follows. In §2 we introduce the methodology,
with §2.1 on the satellite galaxy model, §2.2 on the infall orbits, and §2.3
the simulation initial conditions. We present the simulation global results in
§3: the time evolution of star formation and the surviving gas (§3.1), and the
gas morphology and kinematics (§3.2). Then, §4 compares the spatially resolved
SFR-mass relations ($\Sigma_{\rm SFR}-\Sigma_{\rm gas}$ and $\Sigma_{\rm
SFR}-\Sigma_{*}$) between the stripping and isolated galaxy sets. We discuss
our results in §5: the impact of RPS on star formation (§5.1), predictions for
observations (§5.2), and limitations of our methodology (§5.3). §6 summarizes
the key findings.

##  2 Methodology

We run a suite of three-dimensional “wind-tunnel” simulations using the
adaptive mesh refinement (AMR) code Enzo (Bryan et al., 2014). The simulation
volume is a $162^{3}$ kpc cube with a $128^{3}$ root grid resolution. We allow
up to five levels of refinement, giving a highest spatial resolution of $39$
pc (marginally resolving giant molecular clouds). To model the radiative
cooling of the multiphase gas, we use the Grackle chemistry and cooling
library111https://grackle.readthedocs.io/ (Smith et al., 2017), which
calculates photoheating and photoionization from the UV background of Haardt &
Madau (2012). We use the star formation recipe of Goldbaum et al. (2015) with
the following parameters: Once a gas cell reaches the Jeans criterion with a
number density threshold of $n_{\rm min}=10$ $\rm cm^{-3}$, it forms star
particles (including regular stars and Type II supernovae) with a $5\%$
efficiency. The star particles, now followed in our simulations as active
particles, subsequently deposit energy into the gas in the forms of stellar
and supernovae feedback, under the Goldbaum et al. (2016) feedback model,
which includes the terminal momentum input from the number of supernovae
expected to go off during a given timestep, adding any additional energy in
the form of thermal energy.

We use yt, a multi-code toolkit for analyzing and visualizing astrophysical
simulation data (Turk et al., 2011), to create slices and projections, and to
select the disk gas and the active star particles for subsequent analyses.

###  2.1 The galaxy

Our galaxy is placed at the center of the $162$-kpc cubical simulation volume
at (81, 81, 81) kpc. We choose a galaxy of low stellar mass $M_{*}=10^{9.7}$
$M_{\odot}$, motivated by the lowest satellite $M_{*}$ examined in Donnari et
al. (2021a) using the IllustrisTNG cosmological simulations (Weinberger et
al., 2017; Pillepich et al., 2018). Table 1 summarizes the global parameters
of the satellite galaxy.

Table 1: Global Parameters of the Low-mass Galaxy Stellar Disk | Dark Matter | Gas Disk
---|---|---
$M_{*}$ | $a_{*}$ | $b_{*}$ | $\rho_{d0}$ | $r_{0}$ | $M_{\rm gas}$ | $a_{\rm gas}$ | $b_{\rm gas}$
($M_{\odot}$) | (kpc) | (kpc) | ($\rm g~{}cm^{-3}$) | (kpc) | ($M_{\odot}$) | (kpc) | (kpc)
$10^{9.7}$ | 2.5 | 0.5 | 5.93e-25 | 11.87 | $10^{9.7}$ | 3.75 | 0.75

Among the three components in Table 1, our simulations model the stellar disk
and dark matter as static gravitational potential fields. The static stellar
disk potential is under the Plummer-Kuzmin model (Miyamoto & Nagai, 1975) with
the scale length ($a_{*}$) and height ($b_{*}$) of $2.5$ and $0.5$ kpc,
respectively (from the baryonic mass-stellar disk size scaling relation; Wu
2018). We model the cold dark matter potential under the spherical Burkert
model (Burkert, 1995; Mori & Burkert, 2000), which is selected to better match
the observational rotation curves of low-mass galaxies (Salucci & Burkert,
2000; Blok et al., 2008). Given the stellar mass (Table 1), we obtain the
circular velocity $V_{\rm circ}\approx 120$ $\rm km~{}s^{-1}$ from the
observational baryonic Tully-Fisher relation (Lelli et al., 2019; McGaugh et
al., 2021), which gives the dark matter central density $\rho_{d0}$ and scale
radius $r_{0}$ (Table 1).

The gas disk in Table 1 is followed in our simulations with AMR. We adopt the
gas mass from observed gas-(H i and H2 combined) to-stellar mass ratio $M_{\rm
gas}/M_{*}\approx 1$ (Calette et al., 2018), and the disk size from the size
ratio $R_{\rm gas}/R_{\rm optical}\approx 1.25$ (Swaters et al., 2002). This
ensures that the resulting galaxy model is consistent with the $z\approx 0$
observed scaling relations. The gas density is distributed under a softened
exponential disk model (see Tonnesen & Bryan, 2009, 2010, eqn. 1), and the
temperature and pressure are calculated to maintain hydrostatic equilibrium in
the disk with the surrounding ICM. The rotational velocity is then calculated
to balance the gravitational force and the combination of the centrifugal
force and the pressure gradient.

###  2.2 The orbits

We model the time-varying infalling orbits — satellites travelling from the
host’s virial radius $R_{200}$ to the pericenter location $R_{\rm peri}$ — of
three host halos: a “Milky Way-like” host halo of $M_{200}=10^{12}$
$M_{\odot}$, a “group” halo of $M_{200}=10^{13}$ $M_{\odot}$, and a “cluster”
halo of $M_{200}=10^{14}$ $M_{\odot}$. The host mass selection is motivated by
the mass-dependent quenched fraction disagreements in Donnari et al. (2021a):
a satellite of $M_{*}=10^{9.7}$ $M_{\odot}$ tends to be under-quenched in the
TNG300 simulations compared with SDSS observations for the low-mass hosts
$M_{200,\rm host}<10^{13.5}$ $M_{\odot}$, but over-quenched in simulations for
the higher-mass hosts (see Donnari et al., 2021a, Fig 9). Our host mass
sampling ($M_{200,\rm host}\in[10^{12},10^{14}]$ $M_{\odot}$) is to span the
mass range over which the Donnari et al. (2021a) turnover in quenching
effectiveness happens for the satellite of $M_{*}=10^{9.7}$ $M_{\odot}$.

In this subsection, we describe our two-step orbit modeling process: (1)
Satellite orbit kinematics (Table 2), which gives the position and velocity of
the satellite galaxy as a function of infalling time; and (2) Host halo radial
profiles (Table 3), which gives the density and temperature of the host’s
gaseous halo medium as a function of radius.

Table 2: Parameters of the Satellite Galaxy Infalling Orbits

$M_{200}$ | Case(1) | $c^{(2)}$ | $R_{200}^{(3)}$ | $R_{\rm peri}^{(3)}$ | $V_{200}^{(4)}$ | $(|V_{\phi,0}|,|V_{r,0}|)^{(5)}/V_{200}$ | $V_{\rm peri}^{(3)}$ | $e^{(6)}$ | $\tau_{\rm infall}^{(7)}$
---|---|---|---|---|---|---|---|---|---
($M_{\odot}$) |  |  | (kpc) | (kpc) | ($\rm km~{}s^{-1}$) |  | ($\rm km~{}s^{-1}$) |  | (Mpc)
$10^{12}$ | Milky-Way | 8.81 | 211 | 75 | 143 | (0.655, 0.832) | 265 | 0.674 | 1127
$10^{13}$ | Group | 7.08 | 455 | 149 | 308 | (0.603, 0.786) | 565 | 0.666 | 1165
$10^{14}$ | Cluster | 5.62 | 949 | 278 | 663 | (0.53, 0.782) | 1236 | 0.692 | 1164

Note. — (1) The case names represent the physical context of the central
halos. (2) The present-day (redshift-zero) concentration values $c$ from
Ludlow et al. (2014). (3) The virial radii ($R_{200}$), and the pericentric
radii ($R_{\rm peri}$) and velocities ($V_{\rm peri}$) from the Gala-generated
orbits, see §2.2. (4) The virial velocities defined as
$V_{200}\equiv\sqrt{G\cdot M_{200}/R_{200}}$, following Wetzel (2011). (5) The
tangential ($|V_{\phi,0}|$) and radial ($|V_{r,0}|$) velocity magnitudes at
$R_{200}$ in units of the virial velocity ($V_{200}$; see note 4) from Wetzel
(2011), used as velocity initial conditions for the orbit integration. (6) The
resulting orbital eccentricities. (7) The infalling time from $R_{200}$ to
$R_{\rm peri}$.

We use the Galactic Dynamics package Gala (Price-Whelan, 2017; Price-Whelan et
al., 2020) to perform time integration of the satellite orbits. First, we use
Gala to construct the three host halos’ gravitational potential profiles,
adopting an NFW halo structure (Navarro et al., 1996), and redshift-zero
concentration values ($c$ in Table 2; Ludlow et al. 2014). For simplicity, we
assume that the satellite travels as a point mass when orbiting the host
halos. The orbital integration begins at the host’s virial radius $R_{200}$
(from the Gala-generated NFW profiles), and takes the best-fit values of
Wetzel (2011) as velocity initial conditions, see
$(|V_{\phi,0}|,|V_{r,0}|)/V_{200}$ in Table 2. With the position and velocity
initial inputs, we then use the Gala orbital integrator to integrate for a
sufficient time (e.g., 100 Gyr) to ensure we capture many stable orbits, and
focus on the branch from $R_{200}$ to pericenter $R_{\rm peri}$. The resulting
orbits contain the satellite’s position and velocity as a function of
infalling time, as summarized in Table 2.

We model the extended, diffuse gaseous halos of the hosts as an isothermal
sphere with a $\beta$-profile in density (Cavaliere & Fusco-Femiano, 1976;
Arnaud, 2009). The spherical $\beta$ model is a relatively simple three-
parameter model capable of reproducing the X-ray surface brightness
observations for a range of galaxies (Makino et al., 1998; O’Sullivan et al.,
2003; Anderson & Bregman, 2011; Dai et al., 2012). It gives the gaseous halo
density at a distance $r$ from the center as,

$n(r)=n_{0}\cdot[1+(\frac{r}{r_{c}})^{2}]^{-3\beta/2},$ (1)

where $n_{0}$ is the core density, $r_{c}$ is the core radius, and $\beta$ is
the density slope at large radii. Among our three host cases, we apply the
generic $\beta$-modeling for the group and cluster cases, but it breaks down
at the low mass of $10^{12}$ $M_{\odot}$, where we instead use observational
data of the Milky Way (Miller & Bregman, 2013, 2015; Salem et al., 2015; Voit,
2019). The parameters of the halo models are summarized in Table 3 below.

Table 3: Parameters of the Hosts’ Gaseous Halo Profiles

Case(1) | $n_{0}r_{c}^{3\beta~{}(2)}$ | $C^{(3)}$ | $\beta$ | $T$ | Refs(4)
---|---|---|---|---|---
| ($10^{-2}\rm cm^{-3}kpc^{3\beta}$) | (kpc) |  | (K) |
Milky-Way | 1.35 | 2.73 | 0.5 | 2.51E6 | MB15
Case(1) | $n_{0}$ | $r_{c}$ | $\beta$ | $T$ | Refs(4)
| ($\rm cm^{-3}$) | (kpc) |  | (K) |
Group | 0.0121 | 25 | 0.655 | 5.53e6 | KS01
Cluster | 0.0071 | 76 | 0.675 | 2.02e7 | KS01

Note. — (1). Case names as in Table 2. We list the Milky Way case separately
from the group and cluster cases because of the different methods; see §2.2.
(2). Best fit parameter $n_{0}r_{c}^{3\beta}$ for the modified $\beta$ profile
of Miller & Bregman (2015), which fits $n_{0}$ and $r_{c}$ of a $\beta$
profile together (equations 1 and 2). (3). The constant factor $C$ in equation
2 to match with the LMC-constrained pericentric conditions of the Milky Way
halo (Salem et al., 2015). (4). References for our adopted $\beta$-profile (or
modified in the Milky Way case) parameters, $\beta$, $r_{c}$, and the
isothermal gas halo temperatures $T$. MB15: Miller & Bregman (2015); KS01:
Komatsu & Seljak (2001).

For the “Milky Way” host case, we refer to the Miller & Bregman (2015)
parameterization of a modified $\beta$ profile,

$n(r)\approx\frac{n_{0}r_{c}^{3\beta}}{r^{3\beta}},$ (2)

where $n_{0}$, $r_{c}$, and $\beta$ are defined as in equation 1 above (see
Miller & Bregman, 2015, eqn. 2). However, this profile becomes less
constrained at the large radii of our satellite’s orbit (Table 2), and tends
to underestimate densities compared with other studies (see Voit, 2019, Fig.
3). To address this density underestimation at large radii, we boost the best-
fit Miller & Bregman (2015) model by a constant factor $C\approx 2.73$,
obtained by matching the LMC-constrained pericentric (at 48.2 kpc) density
from Salem et al. (2015).

For the galaxy group and cluster cases, we obtain the three parameters in the
$\beta$ model (equation 1) as follows: We adopt $r_{c}$ and $\beta$ from the
gas halo profiles of Komatsu & Seljak (2001), and solve for $n_{0}$ as an
integration constant by assuming the gas-to-total mass fraction at $R_{500}$
is $\approx 10\%$ (Lovisari et al. 2015; $f_{\rm gas,500}=M_{\rm
gas,500}/M_{\rm tot,500}\approx 10\%$). The gas mass within $R_{500}$ under a
$\beta$-profile in density (equation 1) can be written as,

$\begin{split}M_{\rm gas,500}&=4\pi\rho_{\rm
gas,0}\int_{0}^{R_{500}}[1+(\frac{r}{r_{c}})^{2}]^{-3\beta/2}r^{2}dr\\\
&\approx 10\%\cdot M_{\rm tot,500}\end{split}$ (3)

where we supply $r_{c}$, $\beta$ from Komatsu & Seljak (2001), $M_{\rm
tot,500}$ and $R_{500}$ from the Gala-generated host NFW halos, and the
$f_{\rm gas,500}\approx 10\%$ relation from Lovisari et al. (2015). Solving
equation 3 for the integration constant $\rho_{\rm gas,0}$ gives the central
mass density and hence the number density $n_{0}$.

Figure 1 shows the density profiles of the three gaseous halo cases shown in
Table 3, where we annotate the infall orbits’ initial (virial radius) and
final (pericenter) locations from Table 2. At a given time $t$ of an infall
orbit, the orbital density is given by the density profiles $\rho(r)$ in
Figure 1, taking the radius $r(t)$ from the Gala-generated orbits. The
resulting orbital density ranges (densities between the solid and empty
circles in Figure 1) for the group and the cluster cases are relatively
similar, but the cluster case has a higher pericentric velocity (Table 2),
which leads to about five times the ram pressure of the group case at the
pericenter, see Section 2.3 below for details.

Figure 1: The radial density profiles of the three gaseous host halos in this
study (Table 3). Solid and empty circles show the virial radii ($R_{200}$) and
pericenter radii ($R_{\rm peri}$), respectively, which mark the initial and
final locations of the satellite infall orbits (see Table 2). The y-axis on
each side shows the same information in mass density (left: $\rho$) and number
density (right: $n$).

###  2.3 The simulations

Our suite of four simulations includes three “wind-tunnel” runs and one
“isolated galaxy” run. In each of the “wind-tunnel” runs, we introduce a
45-degree-inclined boundary inflow (velocity normal vector $\hat{v}_{\rm
wind(x,y,z)}=(0,\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$) from the $y=0$, $z=0$
corner of the simulation box. Instead of a purely face-on or edge-on wind, we
choose the 45∘ inclination angle to investigate the ram pressure effects both
perpendicular and parallel to the disk. The inflow is modeling the ram
pressure ‘wind’, which carries the time-varying orbital conditions (gas
density, temperature, and velocities) set in §2.2. The metallicities of the
inflow gas (the ‘wind’) and the initial galaxy gas disk (see §2.1) are set as
$Z_{\rm wind}=0.1Z_{\odot}$, $Z_{\rm galaxy}=0.3Z_{\odot}$, respectively,
which are subsequently used as tracers for galactic versus wind material. The
isolated galaxy run is a control case without inflow, but otherwise has the
same setup of galaxy structure, radiative cooling, star formation, and
feedback as in the wind runs.

We summarize key aspects of the simulations in Table 4 and Figure 2. The time-
dependent ram pressure is defined as $P_{\rm ram}(t)=\rho_{\rm host}(t)\cdot
v_{\rm sat}(t)^{2}$, where the host halo medium density (Figure 1) $\rho_{\rm
host}(t)$ is evaluated at the satellite location $r_{\rm sat}(t)$; and the
satellite location and velocity, $r_{\rm sat}(t)$ and $v_{\rm sat}(t)$, are
from the gala-generated orbits (§2.2 and Table 2). For the three wind runs
(hereafter 12W, 13W, and 14W), we list the initial and final ram pressure
values from the orbits described in §2.2, and show their time evolution in
Figure 2. We initialize the 13W run from a snapshot in the 12W run where the
ram pressure matches the 13W initial conditions, and similarly start the 14W
run from a 13W snapshot; see the relevant time frames in Figure 2. This
results in the initial galaxy disk in the 13W and 14W runs being “pre-
processed”: it has been orbiting in smaller host halos prior to their
accretion onto the more massive group- or cluster-host, a highly probable
process for low-mass galaxies that has abundant observational and theoretical
evidence (Zabludoff et al., 1996; Wetzel et al., 2013; Haines et al., 2015;
Jung et al., 2018; Bahé et al., 2019; Donnari et al., 2021b). For the masses
modeled in this paper, TNG simulations find $\approx 50\%$ of satellites below
$M_{*}=10^{10}$ $M_{\odot}$ have been pre-processed in hosts of
$M_{200}=10^{12}$ $M_{\odot}$ or above, if they reside in a cluster of
$M_{200}=10^{14}$ $M_{\odot}$ at $z=0$ (Donnari et al., 2021b).

Initializing the simulations from a previous snapshot effectively avoids the
numerical artifacts in the initial few hundred Myr, like an unstable outburst
of star formation (Tasker & Bryan, 2006) and significant transient ringing
(Goldbaum et al., 2015) in the gas disk. Previous works such as Tonnesen &
Bryan (2012) addressed these artifacts by delaying the wind and allowing for a
thermal relaxation phase of at least 200 Myr to stabilize the disk. For our
12W run (the only wind simulation that begins at $t=0$), however, the wind
delay is unnecessary. Because of the Milky Way wind’s initial slow speed
($|v_{\rm wind}|\approx 151$ $\rm km~{}s^{-1}$; Table 2), it takes the first
shock wave (of Mach number 2) generated by the initial inflow more than 300
Myr to reach the galaxy disk, and longer for the stable inflow, see Figure 2.
The location of the sampling box for ram pressure values (right panel of
Figure 2) is chosen to be relatively close to the galactic disk, while
avoiding the bow shock in front of the galaxy after the thermal relaxation
phase.

The three wind runs cover over three orders of magnitude in ram pressure
(solid lines in Figure 2), which generally follow the input orbit conditions
(dashed lines). We attach a constant ram pressure value at the end of each
wind run to ensure the pericentric inflow from the corner of the simulation
box reaches the galactic disk, and the attached time periods are relatively
short ($<$300 Myr). We annotate the input ICM thermal pressure of the isolated
case as the dash-dotted line in Figure 2, which is lower than the weakest ram
pressure input of the wind runs ($t=0$ of 12W). The sampled ram pressure of
12W (blue solid line) is low during $0-300$ Myr because it shows the initial
collapse of the gas before the wind reaches the sampling box; then during
$\sim$$300-700$ Myr, its stochasticity reflects an interplay between the
feedback outflows and ram pressure of a comparable strength. The two short
peaks in ram pressure at $\sim$1250 (13W) and 1700 Myr (14W) are due to shock
waves generated when we stack the ram pressure profiles; they have no global
effects on the simulations.

Table 4: Overview of the Simulation Suite

Simulation | $P_{\rm ram,i}$ | $P_{\rm ram,f}$ | $t_{i}$
---|---|---|---
| ($\rm g/(cm\cdot s^{2})$) | ($\rm g/(cm\cdot s^{2})$) | (Myr)
12W | 4.6e-15 | 6.7e-14 | 0
13W | 6.4e-14 | 1.9e-12 | 1060
14W | 2.6e-13 | 1.2e-11 | 1600
iso |  $\cdots$ |  $\cdots$ | 0

Note. — (1) Simulation short names, used throughout this paper. 12W: “Milky
Way” halo ($10^{12}$ $M_{\odot}$) wind; 13W: “group” halo ($10^{13}$
$M_{\odot}$) wind; and 14W: “cluster” halo ($10^{14}$ $M_{\odot}$) wind; iso:
isolated galaxy (no wind). (2) and (3) The initial and final ram pressure
values of the wind orbits (§2.2), also see Figure 2. (4) The initial time of
each simulation. 12W and iso both begin at $t=0$, but the 13W and 14W runs are
each continued from a lower halo mass case’s evolved snapshot with matching
ram pressures. For example, the 13W run is a continuation from the $t=1060$
Myr snapshot of 12W, where the initial ram pressure $P_{\rm ram,i(13W)}$
matches the 12W run’s $P_{\rm ram,t=1060(12W)}$, see Figure 2.

Figure 2: Left: Ram pressure time evolution for the three wind simulations.
Dashed lines show the input from the orbits (§2.2 and §2.3), solid lines are
the simulation values ($\rho\cdot v_{\rm gas}^{2}$ in the wind direction
$\hat{v}_{\rm wind}$) read in at a sampling box (see right panel). The dash-
dotted gray line shows the ambient gas thermal pressure in the isolated run
for reference. The three shaded vertical bars denote important time frames we
will later refer to in Figure 3 and §3. Right: A density slice of the 12W
“Milky Way” case, annotating in-plane gas velocities. The inflow wind from the
lower left corner travels at low velocities (Table 2), taking 200-300 Myr to
reach the sampling box (white circle; at (0, -25, -25) kpc), and another
100-200 Myr to reach the disk (domain center). The inflow is about to reach
the sampling box at this snapshot.

##  3 Global Results: Gas Stripping and Star Formation Rate Response

We present our simulation results as follows: §3.1 summarizes the global
evolution of baryonic mass, star formation rate (SFR), and star forming
location; §3.2 describes the wind-driven gas morphology and kinematics, which
explains the global evolution in §3.1.

###  3.1 The Fate of the Ram Pressure Stripped Galaxy

The global effects of RPS on the disk mass and SFR are demonstrated in Figure
3, comparing the three wind cases and the iso case. The upper panel shows the
galactic disk masses: gas as solid lines and gas plus formed stars as dashed
lines, versus simulation time. We apply a spatial disk cut ($R_{\rm disk}=18$
kpc, $z_{\rm disk}=\pm 2$ kpc) and a metallicity cut ($Z_{\rm gas}\geq
0.25Z_{\odot}$) to select the gas in the galactic disk, and place the same
spatial cut when calculating masses of the formed stars. We verified that
varying these selection criteria to include more gas (e.g., using $z_{\rm
disk}=\pm 5$ kpc and $Z_{\rm gas}\geq 0.2Z_{\odot}$) does not change the
trends. The gas fuels star formation and decreases in mass in all four cases.
Without RPS, star formation accounts for most of the gas mass loss, as shown
by the iso case’s gas plus formed stellar mass (dashed gray line), which
remains at $\sim 98.5\%$ its initial value — almost conserved after $\sim$3
Gyr of evolution over which time nearly $45\%$ of the initial gas mass is
converted to stars.

In the wind runs, in addition to forming stars, the gas can gain or lose mass
due to interactions with the wind, depending on the ram pressure strength. In
12W, there is no stripping-induced mass loss compared to the iso case due to
the weak ram pressure (Figure 2). Instead, there is a mild mass excess at
$t\sim 750$ Myr, because ram pressure pushes part of the feedback outflows
back to the disk (this will be discussed in §3.2). Both 13W and 14W experience
the onset of the stripping phase at $t\sim 2150-2250$ Myr, seen from the
steepened gas mass slopes in Figure 3 (leftmost vertical bar; see Figure 2 for
the corresponding $P_{\rm ram}$). The stripping only lasts for $\sim$200 Myr
in 13W, after which the gas mass slope flattens as the ram pressure is kept
constant (Figure 2). But in 14W, as the ram pressure continues to increase,
the stripping continues until nearly the entire gas disk is removed.

The lower panel of Figure 3 shows the SFR evolution, manifesting both the SFR
enhancing and quenching potential of the wind. The first $\sim$500 Myr is the
thermal relaxation phase where star formation is still stabilizing, and the
12W wind has yet to reach the galaxy (Figure 2 and §2.3). This period will be
omitted in subsequent plots and analyses. After the relaxation phase, the SFR
steadily decreases in the iso case throughout the $\sim$3 Gyr of evolution, as
its gas density steadily decreases due to starvation without cosmological
inflow replenishing the disk. The SFR of 12W remains similar to the iso case
throughout its orbit. In 13W and 14W, the SFR remains approximately constant
at $\sim 0.6$ $M_{\odot}/\rm yr$ until $t\sim 2450$ Myr, which is a relative
enhancement compared with iso. The SFR then mildly increases in 13W as the gas
mass remains almost constant, resulting in a 2.5 times SFR enhancement
relative to iso at the first-infall pericenter (middle vertical bar). In 14W
during the final $480$ Myr, the SFR decreases by $\sim 65\%$, dropping to
below iso at the cluster pericenter (rightmost vertical bar), as the gas is
rapidly removed from the disk (from $\sim 2.2\times 10^{9}$ $M_{\odot}$ to
$\sim 3.8\times 10^{8}$ $M_{\odot}$). The 14W galaxy will ultimately be
quenched judging from the rapid, almost complete gas removal.

Figure 3: Upper panel: The time evolution of the galaxy disk’s ISM mass (solid
lines), where the ISM is specified by a combined spatial and metallicity
selection (§3.1). The dashed lines are the ISM mass in solid lines added with
the total mass of formed stars under the same spatial selection. Lower panel:
The SFR time evolution. The first $\sim$500 Myr is the thermal relaxation
phase (§2.3), where the disk cools and collapses, leading to an initial burst
in star formation, and gradually stabilizes. This unstable phase ($0-500$ Myr)
is shaded and will be omitted in plots hereafter. To aid visual comparison, we
denote three 100 Myr time periods with vertical bars showing the onset of
effective stripping, 13W pericenter, and 14W pericenter from left to right;
see §3.1.

Combining the ram pressure, the disk mass, and SFR (Figures 2 and 3) gives the
direct effect of ram pressure on these star-forming disks’ global evolution.
The turning point at $t\sim 2200$ Myr, where the effective gas stripping takes
place in 13W and 14W, corresponds to a total 45∘-angled ram pressure of
$P_{\rm ram}\approx 1.5\times 10^{-12}$ g/($\mathrm{cm}\cdot\mathrm{s}^{2}$).
Before this critical ram pressure is reached, the gas plus formed stellar
masses in the disks (dashed lines in Figure 3) remain conserved with respect
to ram pressure for all wind runs. Unlike gas stripping, which is a direct
consequence of strong ram pressure, the SFR shows no immediate correlation to
ram pressure. The SFR turning points in 13W and 14W appear $\sim$300 Myr
delayed compared to the gas mass change (Figure 3), likely because it takes
time for the wind-driven mass flows around the disk to affect the global SFR.

As the wind interacts with the galactic disk, the location of star formation
changes, as shown in Figure 4. We select stars newly formed within 100 Myr of
each given time and obtain their distribution in cylindrical/disk radius
($R_{\rm disk}$) and height ($z_{\rm disk}$). These stars’ radial distribution
has a power-law tail, and Figure 4 shows their $95\%$ percentile values as
solid lines. The height distribution characterizes a thin disk of cold gas —
symmetrically peaked around $z=0$ kpc without wind impact, or skewed towards
$+z$ under a wind that has a $+z$ component, and Figure 4 shows their $5-95\%$
percentiles as colored bands.

The radial ringing in Figure 4 results from epicyclic oscillations triggered
by rapid radiative cooling disturbing the initial equilibrium disk (Goldbaum
et al., 2015), and has no global effect on our results. In the iso case, the
radius of star formation in an undisturbed disk shows a slow and steady
increase and asymptotes to $\sim$11 kpc at the final stage of evolution, and
the height remains symmetric within $\pm 0.5$ kpc, which 12W closely follows
throughout its orbit. In 13W and 14W, when the gas stripping begins at $t\sim
2200$ Myr (Figure 3), their radii of star formation begin to deviate from the
iso case, with the 13W radius decreasing slightly faster and its $z_{\rm
disk}$ symmetrically thickening, while the 14W radius decreasing relatively
slowly to $\sim$6 kpc and its $z_{\rm disk}$ extending to $+4$ kpc, highly
skewed towards the wind direction. The star formation radius in 13W decreases
faster than in 14W, where ram pressure is higher, which seems to contradict
the Gunn & Gott (1972) face-on stripping picture. But this is because of the
wind inclination: more 14W gas is stripped into an extensive tail inclined to
the disk (see Figure 5 below), forming stars in the tail, which skews the 14W
star formation to higher cylindrical radii.

Figure 4: The evolution of star forming locations in terms of the
cylindrical/disk radius $R_{\rm disk}$ and height $z_{\rm disk}$ versus
simulation time. The radii shown here as solid lines are the $95$ percentile
values, and the heights as colored bands are $5-95$ percentile values. We
select new stars formed within 100 Myr to match the typical timescales of UV
observations (§3.1). Higher ram pressures lead to more central star formation.

We selected the 100 Myr timescale in Figure 4 in order to match the typical
timescales in UV observations of star formation (e.g., Leroy et al. 2012;
Kennicutt & Evans 2012). We also experimented with 10 Myr (typical H$\alpha$
timescale), 30 Myr, and all formed stars within the simulations (1-3 Gyr,
roughly matching the timescales in optical observations, see Tasker & Bryan
2006), and found the temporal trends agree for the 10, 30, 100 Myr selections.
If using all formed stars, however, the radial distributions in all cases
asymptote to $R_{\rm disk}\approx 10-11$ kpc, characterizing a steady stellar
disk (rather than recent star formation); the similar radius across all cases
is expected as RPS has no direct effect on the stellar disk.

###  3.2 Wind-driven Gas Morphology and Kinematics

The global results in §3.1 show that RPS directly affects the gas mass and,
although the global SFR is eventually affected, that impact occurs a few
hundred Myr after the onset of gas stripping. We find the impact on star
formation can evolve in opposite directions: enhance or quench (Figure 3). In
this section, we examine the wind-driven gas flows to determine the physical
reasons behind the bimodal effects on star formation.

We first show the different morphology of the gas via density slices along the
$x=0$ plane in Figure 5, comparing the iso case to each wind run when the ram
pressure has reached its peak value at the galaxy position. The three lower
panels show that, without RPS, the isolated galactic disk remains
cylindrically symmetric and drives an outflow above and below the disk via
star formation feedback, which decays in strength as the SFR decreases with
time (Figure 3). The three wind runs demonstrate different interactions
between the wind and the galactic gas, as summarized below.

  * •

12W: There is no clear signal of RPS within the gas disk. Ram pressure appears
to interact with the feedback-driven outflows, likely suppressing those
outflows below the disk (against the wind direction).

  * •

13W: Gas is being stripped and forms an outer ring that, in this slice, looks
like two tails. The feedback-launched gas below the disk in the iso and 12W
runs is missing because of the higher ram pressure.

  * •

14W: Gas is being stripped relatively uniformly from all radii of a shrunken
and highly fragmented disk, forming a single extended tail tracing the wind
direction. The 14W wind has a similar density but $>$2 times higher velocity
compared with 13W, leading to its $>$4 times higher pericentric ram pressure
(Tables 2 and 4).

Figure 5: Gas density “edge-on” slices, zoomed in to $40$ kpc. The 45∘ winds
introduced as boundary inflows are in the $\hat{v}_{\rm
wind(y,z)}=(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$ direction (§2.3). The
selected time frames, as annotated on the upper left corners, correspond to
the pericentric conditions of the 12W, 13W, and 14W orbits (Figures 2 and 3).
The upper panels show the wind cases, and the lower panels show the isolated
case at the same time for comparison.

Moving from 12W to 13W and finally to 14W, we see a clear progression from
negligible stripping to outer gas removal to nearly complete stripping.
However, the 13W gas morphology in Figure 5 demonstrates a unique complexity:
within the stripping radius (characterized by the outer ring of stripped gas),
there is high-density gas above the disk. We zoom in and examine the gas
kinematics of 13W in Figure 6. The $v_{z}$ slice (left; not mass-weighted)
shows that much of the gas above the disk has a $\sim$0 or negative z-velocity
— falling back to the disk. The stripped material from the leading side
($y<0$), initially traveling at 45∘ ($\hat{v}_{\rm wind}$), experiences
gravitational forces toward the disk center where the potential well is
deepest (perpendicular to the contour lines, Figure 6). This fallback
phenomenon is confirmed by the mass-weighted gas velocity streamlines,
indicating the paths of motion, in the edge-on projection map of gas that
originated in the galaxy (middle panel). Fallback happens for the relatively
dense stripped gas at the wind leading edge ($y\approx-6$ kpc) onto the
leading half of the disk, and also for the more diffuse stripped gas in the
tail ($z\gtrsim 5$ kpc), which occurs on a larger spatial scale.

Figure 6: Gas z-velocity slice and projected density maps of 13W at the
pericenter (as in Figure 5), zoomed in to $30$ kpc. Left panel: Gas $v_{z}$
slice map, annotating gravitational potential contours in white lines. The
potential includes the static stellar and dark matter components (§2.1), self-
gravity of the gas, and of the newly formed stars. The in-plane velocity
vectors ($v_{y,z}$) are marked by black arrows. Middle and right panels: Gas
density projection maps (edge-on and face-on) with a metallicity selection for
the galactic ISM ($Z_{\rm gas}\geq 0.25$ $Z_{\odot}$; largely unmixed with the
ICM). The streamlines show the mass-weighted gas velocities.

The face-on projection map (Figure 6 right panel), on the other hand, shows
the interplay between ram pressure and disk rotation within the disk plane. On
the $x>0$ side of the disk where the ram pressure in-plane component ($+y$)
counters disk rotation, the disk gas can lose its angular momentum, manifested
in radial inflows towards the disk center. This is clearly distinct from the
$x<0$ side, where ram pressure aligns with disk rotation, and the in-plane gas
kinematics transforms into radial outflows in the wind-trailing end of the
disk ($y>0$). Gas that is pushed above the disk while losing angular momentum,
as illustrated in the third panel, will be more able to fall back along the
streamlines shown in the middle panel.

We now focus on RPS-driven mass losses using the gas motions perpendicular to
the disk (Roediger & Brüggen, 2006; Bekki, 2014). In our simulations, this
corresponds to flows in the z-direction, $\dot{M}_{z}=\int_{\rm
surface}\rho~{}\vec{v}\cdot d\vec{A}=\int_{\rm surface}\rho~{}v_{z}\cdot
dA_{(x,y)}$, where the surfaces are selected to be $z_{\rm disk}=\pm 2$ kpc
for the gas with metallicity $Z\geq 0.25Z_{\odot}$222The metallicity selection
excludes the ICM inflows (§2.3)., consistent with our disk ISM selection
(Figure 3). In addition, the mass flows are expected to have radial
dependence, because gas removal typically begins at larger disk radii where
the local gravity is weakest, and migrates radially inward as the ram pressure
increases (Gunn & Gott 1972, also see Figure 4). To characterize the radial
dependence, we further distinguish the mass flows across the full planes
($z_{\rm disk}=\pm 2$ kpc) versus only the central 5 kpc regions of the planes
($R_{\rm disk}\leq 5$ kpc, $z_{\rm disk}=\pm 2$ kpc). The resulting
$\dot{M}_{z}$ of the full and central planes are shown in Figure 7, together
with the gas mass and SFR time evolution (similar to Figure 3) of the central
plane.

Figure 7: Left: Gas mass loss rate perpendicular to the disk ($\dot{M}_{\rm
gas,z}$, where positive values indicate outflows), evaluated at disk heights
$z=\pm 2$ kpc, for the full plane (upper left) and the central 5 kpc regions
(lower left). Right: The central 5 kpc gas mass (upper right) and SFR (lower
right) time evolution as solid lines (similar to Figure 3, here for the
central disk), and the central-to-full disk ratio (“c/f ratio”) as dashed
lines on the right-hand y axes. In all panels, we show the three 100 Myr
reference time frames as in Figure 3.

The mass loss rates in Figure 7’s left two panels are obtained by summing
$\dot{M}_{\rm gas,z}$ above and below the disk (at $z=+2$ and $-2$ kpc), where
a positive value is outflow/mass loss by definition. For the iso case, the
mass loss rate demonstrates galactic fountain flows driven by the stochastic
star formation feedback alone: in the central plane where the star formation
and feedback is strongest, $\dot{M}_{\rm gas,z}$ remains an outflow (lower
left panel); but the full plane $\dot{M}_{\rm gas,z}$ oscillates around 0
(upper left panel), and results in $\sim$0 net baryonic mass loss throughout
the 3 Gyr iso simulation (gray dashed line, Figure 3). The fountain flows’ (or
central plane feedback outflows’) amplitudes decay as the SFR decreases with
time (Figure 3). The mass loss rate of 12W overall follows iso, except for a
mildly enhanced inflow within its full plane (upper left panel) at $t\sim
600-800$ Myr, which explains the mild 12W gas mass excess around this time
(Figure 3). We verified that the 12W enhanced inflow relative to iso is via
the $z=-2$ kpc surface, indicating that the ram pressure, although not yet
sufficient to strip the gas disk, transfers momentum with the diffuse fountain
flows below the disk.

For 13W and 14W, the mass loss rates are dominated by RPS. Across the full
plane, the first peak of mass loss occurs at $t\sim 2150-2250$ Myr (leftmost
vertical bar, Figure 7), corresponding to the onset of effective stripping in
both 13W and 14W (Figure 3). After that, the 13W mass loss rate steadily
decreases to $\sim$0 at its pericenter, as the ram pressure becomes constant
(Figure 2), and the 14W mass loss rate keeps increasing for another $\sim$400
Myr with its still increasing ram pressure. For the central plane, however,
there is a clear dichotomy: 13W shows a central inflow ($\dot{M}_{\rm
gas,z}<0$) with increasing amplitude, while 14W shows a (slightly delayed)
central outflow. During the onset of effective stripping, the stripping radius
is greater than the selected central region (5 kpc), so $\dot{M}_{\rm
gas,z}\sim 0$ for both cases. At $t\sim 2500$ Myr, the 14W stripping radius
reaches the inner 5 kpc, and hence the central outflows begin. But for 13W,
ram pressure was never sufficient to strip the inner disk; instead, the
gravitational fallback of the stripped material (as described in Figure 6)
replenishes the central disk.

The right-hand two panels of Figure 7 show the central disk gas mass and SFR
time evolution and the central-to-full disk ratios (“c/f ratio”; see Figure 3
for the full disk). For all four simulations, the central gas mass evolution
tightly correlates with the central SFR evolution. The temporal oscillations
arise from the radial ringing discussed previously in Figure 4. In the absence
of effective RPS, the iso and 12W cases maintain an almost constant c/f ratio
throughout the simulations (gray and blue dashed lines). Effective RPS (13W
and 14W) leads to a radial redistribution of the gas and SFR: (i) the profiles
are more radially centralized (enhanced c/f ratios), and (ii) the inner disk
$\rm M_{gas}$ and SFR values (solid lines) are both enhanced relative to iso.
Although (i) partially results from the removal of outer disk gas, (ii)
directly reflects the star formation enhancement potential of RPS.

Figure 8: The cumulative mass loss ($\Delta\rm M_{gas}$) over time for the
central 5 kpc disk as driven by mass transport, comparing 13W, 14W, and iso.
Left: the cylindrical radial ($\Delta M_{\varpi}$; solid lines) versus
vertical ($\Delta M_{z}$; see Figure 7 for $\dot{M}_{z}$, here dashed lines)
mass loss components. Right: the total kinetic mass loss by summing the two
components. As in Figure 7, positive $\Delta\rm M_{gas}$ values denote
outflows, and the vertical bars show the three reference time frames. Key
physical processes that explain the trends are annotated on the right panel.

The gas motions perpendicular to the disk (Figure 7) demonstrated an indirect
mode of radial mass transfer in 13W: gas is lifted by RPS from the edge of the
disk, and falls back to the central disk a few 100 Myr later, replenishing
star formation there (also see Figure 6, middle panel). Another mode of radial
mass transfer is directly via the (cylindrical) radial direction,
$\dot{M_{\varpi}}=\int_{\rm surface}\rho~{}\vec{v}\cdot d\vec{A}=\int_{\rm
surface}\rho~{}v_{\varpi}~{}dA$, where $\hat{\varpi}$ is the cylindrical
radial vector, and the surface can be approximated by a thin cylindrical shell
of average width $\bar{h}$, such that
$\dot{M}_{\varpi}\approx(1/\bar{h})~{}\sum_{i}^{\rm
shell}(m_{i}~{}v_{\varpi,i})$. We evaluated the radial mass flow rate for the
central disk in Figure 8 ($R_{\rm disk}\leq 5$ kpc, $|z_{\rm disk}|\leq 2$
kpc)333The shell width $\bar{h}$ is obtained by $\bar{h}=(1/A_{\rm
shell})\sum_{i}^{\rm shell}V_{i}$, where $V_{i}$ is the individual cell
volume, and $A_{\rm shell}=2\pi R_{\rm disk}\cdot(2z_{\rm disk})$ is the shell
area. We tested a range of shell widths, $\bar{h}\in[39,156]$ pc, which
corresponds to 1 to 4 times the highest-refined cell length (§2), and
$\dot{M}_{\varpi}$ is approximately constant over these $\bar{h}$. After
obtaining $\bar{h}$, we evaluate $\dot{M}_{\varpi}(\bar{h})$ for the cells in
the thin shell that satisfy the ISM metallicity selection $Z\geq
0.25Z_{\odot}$. The final $\dot{M}_{\varpi}$ is an average of
$\dot{M}_{\varpi}(\bar{h})$ over $\bar{h}\in[39,156]$ pc.. Because
$\dot{M_{\varpi}}$ characterizes mass transfer within the galaxy, its
amplitude is particularly susceptible to radial oscillations (Figure 4).
Therefore, we show the time cumulative ($\Delta M=\sum\dot{M}(t)\Delta t$;
frequent temporal oscillations cancel out) mass flows in Figure 8: the left
panel compares the radial and vertical (perpendicular to the disk) components,
the right shows the total kinetic flows (the sum of the two).

The dashed lines in Figure 8’s left panel is the time integration of the
central plane $\dot{M}_{\rm gas,z}$ (Figure 7 lower left panel). As described
above, in the central plane there is a consistent feedback outflow in iso,
fallback replenishment in 13W, and stripping in 14W when $P_{\rm ram}$ becomes
sufficient to affect the inner disk ($R_{\rm disk}\leq 5$ kpc). In the radial
direction (solid lines, Figure 8 left panel), however, both 13W and 14W show
an excess of inflow relative to iso, with peak amplitudes ($\Delta M_{\rm
inflow}\approx 2\times 10^{8}$ $M_{\odot}$) comparable to the net fallback
inflow in 13W. These radial inflows can be explained by an interplay between
the edge-on ram pressure component and disk rotation (right panel of Figure
6). Rotating gas in the disk, when countered by ram pressure (where $x>0$;
Figure 6), can lose angular momentum and migrate radially inward. For 14W,
this radial inflow eventually decreases to 0 as stripping proceeds into the
central region of the disk with increasing $P_{\rm ram}$.

The right panel of Figure 8 shows the sum of the radial and vertical
components: the total kinetic mass transport across all surfaces of the
central disk. We summarize the key physical processes at play in the figure.
For iso, the gradual mass loss is dominated by the central plane’s star
formation feedback. For 13W, there is a combination of replenishment from
fallback and from direct radial inflow, resulting in its highest central plane
gas mass and SFR (Figure 7 right panels). For 14W, because the ram pressure
keeps increasing, there is net replenishment from radial inflow but little to
no fallback around the group pericentric time (middle vertical bar), which
eventually becomes a net outflow as the stripping radius reaches within the
selected central disk ($R_{\rm disk}=5$ kpc) at the cluster pericenter
(rightmost vertical bar). Collectively, the kinetic mass transport (Figure 8)
explains the central plane $M_{\rm gas}$ and SFR evolution (Figure 7). We
found RPS-driven direct radial inflows, in agreement with literature results
(Schulz & Struck, 2001; Tonnesen & Bryan, 2009; Akerman et al., 2023), can
replenish the central star-forming disk; and we identified fallback as an
indirect mode of radial mass transport (Figures 6, 7, and 8) that can add to
the enhancement for certain orbits.

We emphasize that as long as the $P_{\rm ram}(t)$ profiles are consistent,
even with different $\rho_{\rm ICM}$, $v_{\rm sat}$ components (§2.3), the
galaxy undergoes a similar global evolution. For example, at $t\sim 2200$ Myr
(leftmost vertical bar), the global properties and the mass loss rates of 13W
and 14W closely match (Figures 3, 7, and 8) as their $P_{\rm ram}$ values are
comparable (Figure 2), despite the 14W orbit consisting of a higher $v_{\rm
sat}$ and a lower $\rho_{\rm ICM}$. Importantly, the galaxy’s global evolution
is also sensitive to the time derivative of ram pressure, $dP_{\rm ram}/dt$.
When the 13W ram pressure stops increasing as the galaxy reaches the group
pericenter ($dP_{\rm ram}/dt=0$, Figure 2 leftmost to middle vertical bar),
the stripping radius is kept at constant and the remaining gas disk acts as a
“shield” for the stripped gas above it, such that gravity outweighs ram
pressure in shielded regions and causes the central plane fallback
($\dot{M}_{z}$, Figure 7). Conversely, in 14W where $dP_{\rm ram}/dt$ keeps
increasing after $t\sim 2200$ Myr for $\sim$500 Myr, the stripping radius
decreases, so the shielded region shrinks (Figure 5); without shielding the
stripped gas above the disk is unable to fall back.

The global evolution described in §3.1 and 3.2 can be summarized as follows.
In the iso run, the gas disk primarily loses mass to steady star formation,
which drives feedback fountain flows that decrease in magnitude with
decreasing SFR. In 12W with weak $P_{\rm ram}$, the global properties are
overall consistent with iso, other than the additional interactions between
the wind and the low-density fountain flows. In 13W with moderate $P_{\rm
ram}$, RPS in the disk outskirts dominates the mass loss, and actually
enhances the SFR in the remaining disk. Because the pericentric $P_{\rm ram}$
is insufficient to remove the entire gas disk, gas can migrate radially inward
via fallback and direct radial inflows, both replenishing the central disk’s
star formation. In 14W, $P_{\rm ram}$ is sufficient to strip the gas first in
the outskirts and then in the center, ultimately resulting in a rapid decline
in the galaxy’s SFR.

##  4 Spatially Resolved Star Formation Rate-Mass Relation

In the previous section, we found that RPS can enhance the satellite galaxy’s
global SFR while removing its gas (Figure 3), and the wind-enhanced star
formation favors central disk regions (Figures 4 and 7). In this section, we
evaluate the spatially-resolved SFR-mass relations — a direct clue to the star
formation microphysics (e.g., Kennicutt & Evans 2012). We compare the
relations between the RPS and isolated cases to characterize the physical
conditions of ram pressure-enhanced star formation.

###  4.1 Spatial Division Methodology and Radial Profiles

When spatially resolving galactic regions, the sampling scales need to exceed
certain minima for galactic star formation-mass scaling relations to hold
(Kruijssen & Longmore, 2014; Kruijssen et al., 2018); the selected sampling
scales need to account for the incomplete statistical sampling of independent
star-forming regions and the spatial drift between gas and stars. Empirically,
this minimum spatial scale $\Delta x$ works out to be $\sim 1$ kpc for typical
star-forming galaxy disks (see Kruijssen & Longmore, 2014, Fig. 2). Here, we
select the sampling scale to be 1 $\rm kpc^{2}$ to satisfy the validity of the
scaling relations; and to match with typical scales ($0.75-1.2~{}\rm kpc^{2}$)
in high-angular-resolution observations in the local universe (Bigiel et al.,
2008; Vulcani et al., 2019, 2020; Jiménez-Donaire et al., 2023).

For a given simulation snapshot, we divide the satellite disk into 1 $\rm
kpc^{2}$-resolved patches, integrate the patches along the disk-height
direction (for disk height $|z|\leq 2$ kpc), and calculate the projected SFR,
gas, and stellar surface densities ($\Sigma_{\rm SFR}$, $\Sigma_{\rm gas}$,
and $\Sigma_{*}$) of each patch. We focus on the galaxy group and cluster
pericenter time frames, when RPS most effectively enhances/quenches the
satellite star formation (Figure 3), and compare the wind cases with the
isolated galaxy case (iso) at the corresponding times. Using 100 Myr windows
(10 simulation outputs) produces larger samples of 1 kpc2 regions with recent
star formation (10 Myr) across the disk. Changing the number of outputs does
not qualitatively affect our results. Global properties of the selected
patches are summarized in Table 5. Throughout the Section, we will focus on
the four pericentric cases in Table 5: 13W, 14W, iso group, and iso cluster
control, while iso pre-starvation is a special reference case for the star
formation law comparison in §4.2 below.

Table 5: Summary of the 1 $\rm kpc^{2}$ patch selection

Case | $t_{\rm peri}$ | $\rm N_{patch,SF}$ | $\rm SFR_{global}$ | $\tau_{\rm dep}$
---|---|---|---|---
| (Myr) |  | ($M_{\odot}/\rm yr$) | (Gyr)
13W pericenter | 2530-2630 | 1427 | 0.85 | 2.28
iso group control | 2530-2630 | 3016 | 0.38 | 7.12
14W pericenter | 2830-2930 | 447 | 0.21 | 1.70
iso cluster control | 2830-2930 | 2933 | 0.32 | 8.16
iso pre-starvation | 580-680(a) | 2292 | 1.08 | 3.11

Note. — (1) Simulation cases. (2) Simulation time periods that correspond to
13W and 14W pericenter passages. (a) The iso “pre-starvation” time frame is
selected to match the central plane $\rm M_{gas}$ of 13W pericenter (Figure
7), see §4.1. (3) The number of star-forming patches, where star formation is
defined to have $\Sigma_{\rm SFR}>10^{-6}~{}M_{\odot}/(\rm yr\cdot kpc^{2})$
per patch. (4) The total SFR of the star-forming patches averaged over the
selected 100 Myr time period. (5) The gas depletion time defined as $\tau_{\rm
dep}=M_{\rm gas}/\rm SFR$, where $M_{\rm gas}$ is the total gas mass in the
patches, and SFR as in column 4.

Figure 9: The SFR, gas, and stellar surface densities ($\Sigma_{\rm SFR}$,
$\Sigma_{\rm gas}$, and $\Sigma_{*}$) radial profiles of the resolved 1 $\rm
kpc^{2}$ patches. The four cases (Table 5) are 13W and 14W at pericenters
(solid and dashed in blue) and iso group and cluster control cases (same line
styles in red). On the top panel, the open circles show the radii enclosing
95$\%$ of the $\Sigma_{\rm SFR}$. On the bottom panel, $\Sigma_{\rm gas}$
(deeper colors; left-hand y-axis) and $\Sigma_{*}$ (lighter colors; right-hand
y-axis) are shown under the same scale, following the conventional units of
each quantity.

The radial profiles of the resulting patches are shown in Figure 9. The SFR
profiles (top panel) closely resemble the respective gas profiles (bottom
panel) in all cases. In the central few kpc, the wind cases (blue) are
enhanced in both the SFR and gas densities relative to iso (red); at larger
radii, the wind radial profiles show a steeper decrease with radius than iso.
This is expected given our previous finding that ram pressure removes gas in
the outer disk while driving gas into the central disk (Figure 7). The 95$\%$
enclosing radii of the SFR, denoted by the open circles, show that star
formation is more centrally-concentrated with increasing ram pressure, with
the iso cases forming stars within $\sim$9.0 kpc (no ram pressure), 13W within
$\sim$5.4 kpc (moderate ram pressure, enhanced SFR), and 14W within $\sim$2.3
kpc (strong ram pressure, approaching complete stripping). The time evolution
in iso from the group to cluster pericenter times ($\sim$300 Myr duration; red
solid and dashed curves) is due to star formation “starvation”, which has a
relatively small impact on the radial profiles (and reduces the global SFR by
$\sim 16\%$; see Table 5).

The bottom panel of Figure 9 directly compares the gas and stellar surface
density ($\Sigma_{\rm gas}$ and $\Sigma_{*}$) profiles. The y-axes are under
the same physical scale following the conventional units of each quantity, as
will be used in Sections 4.2 and 4.3 and figures therein. In all cases,
$\Sigma_{*}$ profiles (lighter lines) are greater than $\Sigma_{\rm gas}$
(deeper lines) within the inner $\sim$8 kpc region that encloses the majority
of star formation. Unlike $\Sigma_{\rm gas}$ (or $\Sigma_{\rm SFR}$) that
clearly distinguishes wind and iso, the $\Sigma_{*}$ profiles are consistent
among all cases. This is because (i) ram pressure only directly impacts the
gas disk and not the stellar disk; (ii) the formed stellar mass is low
compared with the static stellar potential ($\Delta M_{\rm
formed~{}star}/M_{\rm static~{}disk}<3\%$; Figure 3 and §2), therefore the
static potential is dominated by the total $\Sigma_{*}$ (and dark matter) at
all radii.

###  4.2 SFR$-M_{\rm gas}$: The Kennicutt-Schmidt Relation

We investigate the SFR$-M_{\rm gas}$ relation, also known as the Kennicutt-
Schmidt (KS) relation (Schmidt, 1959; Kennicutt, 1989), for the resolved 1
$\rm kpc^{2}$ patches. The KS relation is an empirical power-law between the
observed SFR and gas surface densities, $\Sigma_{\rm SFR}=A\cdot\Sigma_{\rm
gas}^{N}$. Physically, it is a proxy for how efficiently gas forms stars at
given surface densities. In our suite of simulations, both the stripping and
the isolated galaxy cases follow the same numerical star formation and
feedback recipe (Goldbaum et al. 2015, 2016; see §2), and differences on the
$\Sigma_{\rm SFR}-\Sigma_{\rm gas}$ (KS) phase plane will directly reflect the
impact of RPS.

Figure 10: Spatially resolved SFR$-M_{\rm gas}$ ($\Sigma_{\rm SFR}-\Sigma_{\rm
gas}$; “Kennicutt-Schmidt”) relation within disk height $|z|\leq 2$ kpc. The
left and right panels show the 100 Myr duration of the galaxy group and
cluster pericentric passages (or the corresponding times in iso; Table 5),
respectively. Each panel shows the $\Sigma_{\rm SFR}-\Sigma_{\rm gas}$
bivariate and one-dimensional (1D) distributions of 1 $\rm kpc^{2}$ patches in
the iso (red) and wind (blue) simulations. Solid and dashed black lines show
the spatially resolved KS power-law from Bigiel et al. (2008) over the
observed $\Sigma_{\rm gas}$ ranges for H2 and H i+H2 combined, see §4.2 for
details. Constant depletion time contours $t_{\rm dep}=0.1$, 1, 10 Gyr are
annotated in gray dotted lines. Gray vertical line indicates the atomic-to-
molecular gas density transition at $\Sigma_{\rm gas}\approx 10$
$M_{\odot}/\rm pc^{2}$ (Krumholz et al., 2009).

Figure 10 shows the KS relation in the RPS and isolated galaxy disks at the
group and cluster pericenters (Table 5). For all cases, the gas densities are
tightly correlated with SFR on the resolved scale, but the RPS cases populate
a distinct phase space of high-density, high-SFR gas that is absent in iso. To
quantify this excess, we first identify the 99.85 percentile surface density
thresholds (empirically 3$\sigma$ upper limits) in iso using the 1D histograms
of $\Sigma_{\rm SFR}$ and $\Sigma_{\rm gas}$. For each of these distributions,
these upper limits are nearly identical at both the group and cluster
pericentric times: $\log\Sigma_{\rm gas}/(M_{\odot}~{}\rm pc^{-2})\gtrsim 1.2$
and $\log\Sigma_{\rm SFR}/(M_{\odot}~{}\rm yr^{-1}~{}kpc^{-2})\gtrsim-1.8$.
Many patches in 13W and 14W occupy the KS phase space beyond these upper
limits in iso (blue scatter points; upper right corner of Figure 9); these are
the dense gas excess in the RPS cases and have a significant contribution to
the total SFR ($\sim$58% in both 13W and 14W).

For 13W, star formation from this dense gas (58% or 0.5 $M_{\odot}/\rm yr$) is
comparable with its SFR enhancement relative to iso ($\Delta$SFR${}_{\rm
group}\approx 0.45$ $M_{\odot}/\rm yr$; Table 5). For 14W, ram pressure is
strong enough to remove most of the surviving ISM and leads, ultimately, to a
quenching of star formation. Despite 14W’s dense gas excess, its number of
star-forming patches ($N_{\rm patch,SF}$; Table 5) has decreased to $\sim$30%
of 13W and $\sim$15% of the iso control, resulting in its lowest total SFR of
all cases. We will further discuss why gas and SFR surface densities are
enhanced in the RPS cases in §5.1.

We showed in Figure 10 that the RPS and iso cases populate different
$\Sigma_{\rm gas}$ ranges. At the selected pericentric time frames,
$\Sigma_{\rm gas}$ in iso primarily belongs in the H i-dominated regime (the
left of the dashed vertical line in both panels), while in 13W and 14W, it
populates both H i and H2 regimes (Krumholz et al., 2009). The relatively low
surface densities in iso are a direct result of the gradual gas consumption
due to star formation and the feedback-driven outflows, also known as
“starvation” (Larson et al., 1980; van den Bosch et al., 2008; Trussler et
al., 2020). To evaluate the effect of RPS on the KS relation over a similar
$\Sigma_{\rm gas}$ range, we identified an earlier time frame in iso (iso pre-
starvation; see Table 5), where the central disk gas mass — and hence the
highest $\Sigma_{\rm gas}$ — is comparable to 13W at the pericenter (Figure
7). This comparison will determine if the star formation efficiency at given
gas densities is modified in the RPS cases.

Figure 11: The effects of RPS versus starvation on the KS plane. The red and
blue filled contours and solid 1D distribution lines are iso group control and
13W pericenter, respectively (as in Figure 10), and the red dashed lines are
for iso at an earlier time (prior to $\sim$2 Gyr of starvation; see §4.2). The
constant depletion time contours are shown as in Figure 10.

Figure 11 shows the effect of RPS versus starvation on the KS plane by
comparing three cases: 13W and iso at group pericenter time and iso pre-
starvation. Starvation shifts the isolated galaxy to lower surface densities
along the KS relation (red dashed versus red filled) via gas consumption and
feedback-driven outflows. However, the iso pre-starvation case shares a very
similar KS relation with the RPS case (red dashed versus blue filled), despite
their distinct evolutionary history and gas morphology (Figures 3 and 5).
Judging from the similar KS relation, the star formation efficiency in RPS and
iso cases remains the same at comparable $\Sigma_{\rm gas}$.

Independent of RPS, the resolved patches in our simulations show a KS power-
law slope turnover from the H i to H2 regimes when sufficient dense gas exists
as H2 (Figures 10 and 11). This is a direct reflection of our numerical star
formation recipe (see Goldbaum et al., 2016, Fig 5), which agrees with
observational findings that the KS power-law slope transitions from
superlinear in the atomic regime ($N_{\rm KS,\rm H\,\textsc{i}}>1$ with poor
correlation; Bigiel et al. 2008; Leroy et al. 2008; Kennicutt & Evans 2012) to
approximately linear in the molecular regime ($N_{\rm KS,H_{2}}\approx 1$;
Krumholz et al. 2009; Heiderman et al. 2010; Krumholz et al. 2012; Jiménez-
Donaire et al. 2023; see the solid line in Figure 10). We also annotated the H
i+H2 combined fitting result from Bigiel et al. (2008) in Figure 10 (dashed
line, N${}_{\rm KS}\approx 1.8$); our simulations follow a mildly steeper
slope in the atomic regime (N${}_{\rm KS,\rm H\,\textsc{i}}\approx 2.0$),
still well within the observational scatter (Bigiel et al., 2008). An
exception to the overall consistent KS slope in our simulations is 14W at the
lowest gas surface densities ($\Sigma_{\rm gas}\leq 0$ $M_{\odot}~{}\rm
pc^{-2}$; see Figure 10 right panel), which shows distinctively higher
$\Sigma_{\rm SFR}$ than iso and hence a lower KS slope in the low-density H i
regime. The high $\Sigma_{\rm gas}$ (H2-dominated) regime in 14W is similar to
the other cases. We suspect that the low-density star-forming gas in 14W is
driven by fast gas removal from RPS in recently star-forming regions.

###  4.3 SFR$-M_{*}$: Strong Stripping and Disk Truncation

In this section, we investigate the SFR$-M_{*}$ relation, also known as the
star formation main sequence relation (e.g., Schiminovich et al. 2007; Sargent
et al. 2014; Speagle et al. 2014), on the spatially-resolved $\Sigma_{\rm
SFR}-\Sigma_{*}$ plane. We examine the impact of RPS using our simulations and
make comparisons with Vulcani et al. (2020) (from the GAs Stripping Phenomena
in galaxies “GASP” survey; Poggianti et al. 2017). The SFR surface densities
of the resolved simulation patches are identical to those in the KS relation
(§4.2), while the stellar surface densities are a combination of the static
stellar disk and the formed star particles as outlined in §4.1, which turns
out to be highly consistent among all simulations (Figure 9). The Vulcani et
al. (2020) sample contains $\sim$1 $\rm kpc^{2}$ resolved patches within 30
RPS galaxies under various stripping stages in nearby clusters, along with 10
isolated control case galaxies of similar masses (see Vulcani et al. 2019).
Our simulated galaxy with $M_{*}\approx 10^{9.8}$ $M_{\odot}$ lies well within
the GASP sample range and is directly comparable.

Figure 12: Spatially resolved SFR$-M_{*}$ ($\Sigma_{\rm SFR}-\Sigma_{*}$)
relation within disk height $|z|\leq 2$ kpc, in the same style as Figure 10.
The stellar surface densities are a combination of the static Plummer-Kuzmin
potential (§2.1 and Table 1) and the formed stars (as active particles) in the
simulations. The black lines show the best-fit relations for the GASP
stripping (solid; Vulcani et al. 2020) and isolated control (dashed; Vulcani
et al. 2019) samples; both relations are shown over the observed $\Sigma_{\rm
SFR}$, $\Sigma_{*}$ ranges, see Vulcani et al. (2020).

Figure 12 shows the $\Sigma_{\rm SFR}-\Sigma_{*}$ relation for the resolved
patches, comparing 13W, 14W at their pericenters with the respective iso
control cases in the same style as Figure 10. Since $\Sigma_{*}$ is a tight,
monotonic function of disk radius (Figure 9), it is an indicator for star
formation location on the $\Sigma_{\rm SFR}-\Sigma_{*}$ phase plane. Two major
effects of RPS can be identified from the differences between the wind and iso
cases, (i) the truncation of the star-forming disk, shown by the high
$\Sigma_{*}$ cutoffs for star formation, $\Sigma_{*}\approx
10^{6.5}(M_{\odot}~{}\rm kpc^{-2})$ in 13W and $10^{7}(M_{\odot}~{}\rm
kpc^{-2})$ in 14W; (ii) the enhancement of star formation in the central disk
regions, shown by the $\Sigma_{\rm SFR}$ excess at $\Sigma_{*}\gtrsim
10^{7.1}(M_{\odot}~{}\rm kpc^{-2})$ in 13W and $\Sigma_{*}\gtrsim
10^{7.6}(M_{\odot}~{}\rm kpc^{-2})$ in 14W. The disk truncation is more
evident in 14W, where the ram pressure is higher, which is consistent with the
radial profiles (Figure 9).

In Figure 12, we annotated the GASP best-fit power-law lines for the stripping
(solid) and isolated control (dashed) samples (Vulcani et al., 2020), where
the slopes are almost identical, but the stripping sample is $\sim$0.35 dex
higher in $\Sigma_{\rm SFR}$ at all $\Sigma_{*}$. Our result is consistent
with Vulcani et al. (2020) at high $\Sigma_{*}$ (central disk regions) that
the spatially-resolved SFR is enhanced in the stripping cases. But we do not
see a similar SFR enhancement at low $\Sigma_{*}$; instead, the low
$\Sigma_{*}$ phase space is poorly populated in our wind cases due to disk
truncation. We note that, however, the Vulcani et al. (2020) sample contains
an ensemble of galaxies with a range of $M_{*}$, inclinations, and
environments, while our simulations focus on one galaxy under different ram
pressure strengths versus in isolation. The disk truncation and SFR
enhancement in our wind cases are consistent with the “Jstage=3” (strongest
stripping) galaxies in Vulcani et al. (2020), which do have a steeper fitted
$\Sigma_{\rm SFR}$-$\Sigma_{*}$ slope.

We also examined earlier pre-pericenter time frames in our simulations:
qualitatively, the wind cases at earlier times (weaker stripping) show a
similar truncation at lowest $\Sigma_{*}$ (disk edge) and a mild SFR
enhancement at relatively high $\Sigma_{*}$ as those in Figure 12. The
transition $\Sigma_{*}$, where $\Sigma_{\rm SFR}$ in the wind cases becomes
higher than in iso, increases with ram pressure strength, as expected for
outside-in stripping. We will present the “time-stacked” results from various
RPS stages in §5.2.

##  5 Discussion

###  5.1 Impacts of RPS on star formation

Our key results in Sections 3 and 4 are,

  1. 1.

In certain orbits, RPS can lead to an enhanced global star formation rate
(SFR) in relatively gas-deficient galaxies.

  2. 2.

The SFR enhancement is driven by an excess of dense gas in the disk central
regions, while the star formation efficiency at given gas surface densities
(the Kennicutt-Schmidt relation) remains the same.

There are two possible channels through which the SFR is enhanced in the
galaxies undergoing ram pressure stripping: compression and mass transport,
which are usually not separable (Tonnesen & Bryan, 2012; Roediger et al.,
2014; Troncoso-Iribarren et al., 2020; Vulcani et al., 2020). The ISM at the
ram pressure interface can be locally compressed, leading to a higher star
formation rate and efficiency; global mass flows driven by ram pressure can
redistribute gas in the disk and cause SFR enhancement.

Our results show that RPS-driven mass transport, including fallback and radial
inflows (§3.2; Figures 7 and 8), is directly responsible for the central disk
gas mass enhancement relative to iso during the $\sim$Gyr early stripping
stage (Figure 7 upper right panel). The centralized ISM mass distribution in
the RPS galaxies results in enhanced central surface densities ($\Sigma_{\rm
gas}$ and $\Sigma_{\rm SFR}$; Figures 9 and 10), which account for the global
enhancement of SFR in the stripping cases relative to iso (with only
starvation). The signal of relative SFR enhancement exists for longer than Gyr
timescales unless ram pressure becomes sufficient to remove the entire gas
disk and quench the star formation (Figure 3).

The role of compression is more challenging to quantify and is often inferred
indirectly. Roediger et al. (2014) found that compression, indicated by shock
passages, can drive a local, short-lived SFR burst ($\sim$15 Myr), but it only
impacts the low-density outer disk and has only a mild effect on the global
SFR. Choi et al. (2022) modeled a local patch of star-forming galactic disks
under RPS and found a similar short-lived enhancement ($\sim$20 Myr; see their
fig 13(c)) in the dense gas surface density ($\Sigma_{\rm
gas,n_{H}>10~{}cm^{-3}}$), demonstrating vertical gas compression by the
initial ram pressure passage. Compression would increase the gas volume
density ($\rho_{\rm gas}$) without increasing the surface density integrated
throughout the disk ($\Sigma_{\rm gas}$). If such compression happens, at
comparable $\Sigma_{\rm gas}$, $\Sigma_{\rm SFR}$ will be systematically
higher on the KS plane. However, our Figures 10 and 11 show that at the same
gas surface densities, the stripping set follows the same KS relation as the
iso set. This suggests that local compression is insufficient to account for
the galaxy-scale SFR enhancement in our simulations.

Another search for compression in RPS galaxies in simulations was performed by
Troncoso-Iribarren et al. (2020), which spatially divided satellite galaxy
disks from the EAGLE simulations into leading and trailing halves (LH and TH)
separated by the infall velocity vector. Under this LH-TH division, which
maximizes the SFR asymmetry between the two halves of the satellite galaxies,
Troncoso-Iribarren et al. (2020) found that gas in the LH that tends to be
more compressed, as inferred from higher average pressure, also has a higher
star formation efficiency (defined as the total $\rm SFR/M_{\rm gas}$)
compared with the TH. Here, we follow the methodology of Troncoso-Iribarren et
al. (2020) to further test for galaxy-scale effects of compression. We divide
the galaxy disks based on a simple LH: $y<0$ and TH: $y\geq 0$ spatial
criterion, given the infall velocity vector (Figure 5) and that the star-
forming disk is thin throughout the simulations (Figure 4). In the discussion
hereafter, we will assume that the LH is under higher compression than the TH
because of ram pressure. The disparity (or the lack of) in mass and star
formation between the LH and TH will help disentangle the effects of mass
transport and compression.

Figure 13: The SFR and gas surface density radial profiles (described in §4.1)
for the wind-LH and TH of the disks. The simulations are color-coded as in §3,
and we omitted 12W where the ram pressure has negligible impacts on the gas or
SFR (Figure 3). For each wind simulation, we averaged over the 100 Myr closest
to the pericenter (10 outputs), as in Table 5; for iso, we selected the group
pericenter time, which yields a largely consistent profile with the cluster
pericenter time (Figure 9).

Figure 13 shows the SFR and gas radial profiles of the wind and iso runs
(similar to Figure 9), distinguishing the LH (solid lines) and TH (dashed
lines) of the disks. As expected, the surface density profiles for the
isolated galaxy control case are an equal division between the two halves at
all radii. In the wind runs, the surface densities in the LH consistently show
a steeper decrease with disk radius than the TH; the disk radius at which the
two halves diverge decreases with ram pressure. The more extended low
$\Sigma_{\rm SFR}$, $\Sigma_{\rm gas}$ material in the TH is caused by the
asymmetric disk morphology444Our $|z|\leq 2$ kpc disk height selection
excludes tail contamination. under an inclined wind (Figure 5). Within the
central few kpcs of the disk, the surface density profiles show a mild LH
excess in 13W and a stronger excess in 14W. However, we found that the 14W
signal oscillates over time555Figure 14 shows the temporal oscillations of the
LH-TH differences, which can explain the 14W central disk LH excess in Figure
13. If we select, e.g., 100 Myr prior to the pericenter (t=2730-2830 Myr), the
LH densities become lower than the TH in the central disk. But the mild LH
excess in the 13W central disk is independent of the oscillations during the
few hundred Myr approaching the pericenter because the accumulation of
fallback gas mildly favors the LH (Figure 6)., which is likely due to the
orbit of the few dense clouds remaining before complete stripping instead of
compression.

Figure 14: The SFR and gas mass differences between the LH and TH versus
simulation time. The three panels from top to bottom show the differences (LH
minus TH) in SFR, the disk ISM mass, and the dense ISM mass (where number
density exceeds the star formation threshold; see §2), respectively. In each
panel, the solid curves show the running means over $100$ Myr, and the
horizontal dash-dotted lines show the time averages of individual simulations.

Figure 14 shows the time evolution of the LH-TH disparity. The time-dependent
differences in the SFR and gas mass are subject to oscillations due to disk
rotation and epicyclic motions (as previously shown in Figure 4; also see
Tonnesen & Bryan 2009), which always average to $\sim$0 in the absence of ram
pressure; see the time averages of iso (horizontal gray dash-dotted line).
Under ram pressure, the time-averaged SFR remains close to equal between the
two halves (top panel); the disk ISM mass shows a strong excess in the TH
under intermediate and strong ram pressure (middle panel); but the dense,
star-forming ISM (bottom panel) mass is again almost equal between the two
halves. The temporal trends of the SFR generally follow those of the dense
ISM; they are much less sensitive to the total ISM, which acquired the
strongest LH-TH disparity from RPS.

The primary effect of RPS (with an edge-on component) is generating an excess
of low-density gas in the TH that has a low contribution to the global SFR
(Figure 13). The SFR and dense ISM of the two halves, although subject to
temporal oscillations, show close to equal time-averaged values and no trend
with respect to ram pressure (Figure 14). Our finding of the RPS-driven gas
excess in the TH agrees with Troncoso-Iribarren et al. (2020), but our
interpretation of this asymmetry differs. Since Troncoso-Iribarren et al.
(2020) defined the star formation efficiency of each half as the mass-weighted
$\rm SFR/M_{\rm gas}$, the TH efficiency may be biased by the excess of non-
star forming gas, appearing as an efficiency enhancement in the LH. We showed
that the dense ISM responsible for star formation shows no such disparity
(Figure 14), indicating that the likely more compressed LH has the same
efficiency as the TH.

To conclude, compression is not the direct cause of the ram pressure-induced
SFR enhancement in our simulations, judging from two independent tests, (i)
the spatially resolved SFR surface densities ($\Sigma_{\rm SFR}$) in the
stripping set show no systematic enhancement at comparable $\Sigma_{\rm gas}$
(inferred from KS relation; Figures 10 and 11), (ii) galaxy-scale global
properties, SFR and dense ISM mass, show no enhancement in the LH where
compression is stronger. Instead, the RPS-induced mass flows (Figures 7 and 8)
account for the centralized mass and SFR profiles (enhanced central surface
densities; Figures 9 and 13), which supports mass transport as the direct
mechanism for the SFR enhancement.

###  5.2 Predictions for observations

Here we predict RPS observables based on the simulation results, where Section
5.2.1 focuses on the surviving gas in the disk and Section 5.2.2 on the local
SFR-mass relations. We will discuss our predictions in the context of recent
environmental surveys, GASP (Poggianti et al., 2017; Moretti et al., 2020;
Vulcani et al., 2020) and VERTICO (Brown et al., 2021; Jiménez-Donaire et al.,
2023).

####  5.2.1 Surviving gas in the disk: the dense gas ratio and the gas mass
fraction

We describe the surviving gas using two global quantities: the dense gas ratio
($R_{\Sigma_{10}}$) and the gas mass fraction ($f_{\rm gas}$) within the
simulated disk. The dense gas ratio is an estimate for the H2 to H i mass
ratio, defined as $R_{\Sigma_{10}}\equiv M_{\rm gas(\Sigma_{gas}>10)}/M_{\rm
gas(\Sigma_{gas}\leq 10)}$, where $\Sigma_{\rm gas}=10$ $M_{\odot}/\rm pc^{2}$
is adopted as an empirical atomic-to-molecular transition density (Krumholz et
al. 2009; Kennicutt & Evans 2012; also see §4.2). The ratio $R_{\Sigma_{10}}$
is not direct modeling of $M_{\rm H_{2}}/M_{\rm H\,\textsc{i}}$, but it self-
consistently compares the molecular- and atomic-dominated gas masses in our
simulations. The gas mass fraction is defined as $f_{\rm gas}\equiv M_{\rm
gas}/M_{*}$, where $M_{\rm gas}$ is the total gas mass within the disk and
$M_{*}$ includes the static stellar potential (§2) and the formed star
particles. Figure 15 shows the time evolution of both quantities, for which we
consistently selected disk height $|z|\leq 2$ kpc, hence excluding most of the
unbound gas in the tail.

Figure 15: Time evolution of the dense gas ratio $R_{\Sigma_{10}}$ (left) and
the gas mass fraction $f_{\rm gas}$ (right). For the dense gas ratio, we
employed a simplified $\Sigma_{\rm gas}=10$ $M_{\odot}/\rm pc^{2}$ cut to
distinguish the H i\- and H2-dominated gas; see §5.2. The dash-dotted line on
the left panel shows the average $M_{\rm H_{2}}/M_{\rm H\,\textsc{i}}$ ratio
for the disk regions of the xGASS sample (see Fig 3 of Moretti et al. 2020).
The cyan dashed lines and shadings on both panels show the median and the
first to third quartile ranges of the xGASS sample (Saintonge et al., 2017;
Catinella et al., 2018) at a comparable stellar mass range ($9.6<\log
M_{*}/M_{\odot}<9.9$). All simulation quantities are for the disk only (disk
height $|z|\leq 2$ kpc; excluding the stripping tails).

In Figure 15, we annotated the observational results from the extended GALEX
Arecibo SDSS Survey (xGASS; Catinella et al. 2018) as a reference. The
comparison sample we adopted (cyan on both panels, dashed line for median,
shading for first to three quartiles) is a subset of 21 xGASS galaxies with
comparable stellar masses ($M_{*}\in 10^{9.6-9.9}M_{\odot}$) to our simulated
satellite galaxy, and with detections in both CO and H i (Saintonge et al.,
2017; Catinella et al., 2018). We consistently adopted $M_{\rm H_{2}}/M_{\rm
H\,\textsc{i}}$ as the dense gas ratio (left panel) for the observational
samples. Additionally, we showed the average dense gas ratio of xGASS disk
regions (dashed-dotted line; following Moretti et al. 2020), which has an
additional disk radius selection (Wang et al., 2020) that results in a higher
dense gas ratio.

In our simulations, the dense gas ratio $R_{\Sigma_{10}}$ in the RPS cases is
consistently higher than that in the isolated galaxy case (Figure 15 left
panel). The ratio $R_{\Sigma_{10}}$ increases with time in 13W and 14W, as
opposed to the clearly decreasing trend in iso. The decreasing trend in iso is
a result of starvation (Figure 11): gas depletion due to star formation and
feedback favors the high $\Sigma_{\rm gas}$ regions with high local
$\Sigma_{\rm SFR}$, reducing the ratio of the denser (e.g., $\Sigma_{\rm
gas}>10$ $M_{\odot}/\rm pc^{2}$; H2-dominated) gas. While in the RPS cases,
gas removal favors the low $\Sigma_{\rm gas}$ regions where the gravitational
restoring force is weakest (“outside-in stripping”), and the disk central
regions can be replenished by the ram pressure-driven mass flows like fallback
and radial inflows (§5.1) — both mechanisms increasing the dense gas ratio
within the disk. Compared at the pericenter times (Table 5), $R_{\Sigma_{10}}$
in 13W and 14W are $1.04$ and $0.87$ dex higher than iso (a factor of $11.0$
and $7.5$), respectively.

Our result that RPS can increase the dense gas ratio agrees with Moretti et
al. (2020), which found a factor of 4 to $\sim$100 higher $M_{\rm
H_{2}}/M_{\rm H\,\textsc{i}}$ ratios for three GASP jellyfish galaxies
(undergoing active RPS) than the xGASS disk control sample (dash-dotted line
in Figure 15). Moretti et al. (2020) suggested that a more efficient
conversion of neutral into molecular gas in these jellyfish galaxies can
explain their significantly higher molecular mass ratios. However, the
$R_{\Sigma_{10}}$ trends in our simulations can be explained by the different
gas depletion models under starvation versus RPS described above, independent
of the H i-H2 conversion. Despite the different definitions, our
$R_{\Sigma_{10}}$ values are comparable with the observational $M_{\rm
H_{2}}/M_{\rm H\,\textsc{i}}$ values of the xGASS sample (Figure 15); we do
not see the high $M_{\rm H_{2}}/M_{\rm H\,\textsc{i}}\gtrsim 10$ ($\log
R_{\Sigma_{10}}>1$) of the three jellyfish galaxies in Moretti et al. (2020).

The evolution of the gas mass fraction $f_{\rm gas}$ (Figure 15 right panel)
closely follows that of $M_{\rm gas}$ (Figure 3), because the stellar mass
evolution is relatively minimal throughout the simulations
($M_{*}=10^{9.7-9.8}$ $M_{\odot}$). The initial condition of $\log f_{\rm
gas}\approx 0$ we adopted (§2.1) is $\sim$0.5 dex higher than the xGASS
average value ($0.01<z<0.05$ galaxies, Catinella et al. 2018, but within
1$\sigma$ of Calette et al. 2018), otherwise the $f_{\rm gas}$ evolution
throughout the iso simulation is within the observational scatter of xGASS
(cyan shading in Figure 15). We take $f_{\rm gas}(t)$ in iso as the reference
gas fraction in our simulations: 12W is in overall agreement with iso, 13W at
the group pericenter is mildly lower ($\Delta\log f_{\rm gas}\approx-0.16$
dex), and 14W at the cluster pericenter significantly lower ($-0.84$ dex). As
expected, direct removal by RPS decreases the total $M_{\rm gas}$ and hence
$f_{\rm gas}$ in the group and cluster cases. But in the group case, a $-0.16$
dex deviation from prediction is within the typical observational scatter
($0.2-0.3$ dex) of such relations (see Figure 15 and Cortese et al. 2021 fig
2). The satellite at 13W pericenter has a reduced gas fraction but still
belongs to the gas normal regime, while at 14W, it is gas deficient during the
final $\sim$400 Myr approaching the pericenter.

For the simulation cases with observable gas stripping morphology (13W and
14W), RPS always reduces $f_{\rm gas}$ in the galaxy disks. This means that
under RPS, despite the mass transfer channels that can potentially replenish
the dense/central-disk gas, stripping of the low-density/outer-disk gas
dominates the global mass evolution (see, e.g., Figure 7). But when we account
for the total gas in the disk and tail (tail gas potentially unbound), we
find, similarly to Moretti et al. (2020), that $f_{\rm gas,disk+tail}$ is
similar between the RPS and iso cases.

To summarize §5.2.1, first, RPS with an edge-on component tends to increase
the dense gas ratio in the disk, while starvation decreases it. This could
explain the observed higher molecular-to-atomic gas ratio ($M_{\rm
H_{2}}/M_{\rm H\,\textsc{i}}$) in jellyfish galaxies (Moretti et al., 2020)
without requiring a substantially higher H i-H2 conversion efficiency. Second,
RPS (unsurprisingly) reduces the gas mass fractions in the disk, even where
the global SFR is enhanced. Where ram pressure at the orbital pericenter is
insufficient to remove the densest ISM (13W), the $f_{\rm gas}$ reduction can
be mild, maintaining the stripped galaxy in the gas normal regime ($<\pm 0.3$
dex). The remaining gas in the disk at 13W pericenter will likely be perturbed
by galaxy-galaxy gravitational interactions, which are expected to be
effective in group environments; see §5.3.

####  5.2.2 RPS signatures on the local SFR-mass relations

High angular resolution observations have enabled the direct mapping of
galactic star formation laws on small scales (Bigiel et al., 2008; Leroy et
al., 2008; Kennicutt & Evans, 2012). Some recent programs include the PHANGS
(Physics at High Angular resolution in Nearby GalaxieS) survey for nearby
galaxies (Leroy et al., 2021; Lee et al., 2022), the VERTICO survey for Virgo
cluster galaxies (Brown et al., 2021; Jiménez-Donaire et al., 2023), and the
GASP survey for environmentally selected jellyfish galaxies (Poggianti et al.,
2017; Jaffé et al., 2018; Vulcani et al., 2020; Moretti et al., 2020). RPS is
one of the main environmental processes in the environmentally-selected
samples (e.g., GASP and VERTICO), but the assessment of the RPS impact often
faces several challenges: (i) the inevitable mixture of sample stellar masses
and inclination angles, (ii) the difficulties of constraining the environment
(e.g., ICM densities) and the satellite orbits, and (iii) the complex
gravitational effects that could coexist with RPS. Here, we use our simulation
suite, which focuses on a single galaxy across various environments undergoing
RPS and no tidal effects, to make predictions for the observational “RPS
signatures” on the local SFR-mass relations.

To create mock observational datasets, we selected 900 Myr of simulation data
(90 outputs) that cover more than 3 dex of $P_{\rm ram}$ in the wind runs
(Figure 2), ranging over 1.5 Gyr in simulation time. Stacking the selected
data creates two datasets, the stripping set and the isolated control set.
This is equivalent to observing an ensemble of galaxies at $M_{*}\approx
10^{9.7-9.8}$ $M_{\odot}$ undergoing various stages of RPS (stripping set:
Milky Way-like to cluster pericenter environments) or starvation (isolated
control set: $\sim$1.5 Gyr duration). Figure 16 shows the local SFR-mass
relations for the two sets on 1 kpc2 scale, following the methodology
described in §4. In Figure 16, we shaded the low SFR regions where
$\log\Sigma_{\rm SFR}$ are below observational limits ($\sim$-4 dex, e.g.,
Leroy et al. 2012; Kennicutt & Evans 2012; Vulcani et al. 2020). The over-
densities in the simulation data at certain low $\Sigma_{\rm SFR}$ is a
numerical effect due to our star particle mass resolution (e.g., the lowest
horizontal over-density corresponds to the $\Sigma_{\rm SFR}$ from a single
star particle of $\approx 800$ $M_{\odot}$). To guide observational
comparison, we show the global KS relation for the 61 non-starburst spiral
galaxies from Kennicutt (1998) on the left panel in addition to the resolved
KS relations from Bigiel et al. (2008); also see Figure 10. The discontinuous
sampling at high $\Sigma_{*}$ (right panel) is caused by the limited 1 kpc2
spatial patch number in the disk center.

Figure 16: Spatially resolved SFR-mass relations (KS and star formation main
sequence; see §4), similar to Figures 10 and 12. Here for the observational
predictions, we stacked 900 Myr of simulation data (90 outputs), covering more
than 3 dex of ram pressure strengths in the wind runs (§5.2). The shaded
regions in both panels are where $\log\Sigma_{\rm SFR}$ is below current
observational limits ($\sim$-4 dex). On the left panel, we additionally show
the global KS relation of the non-starburst spiral galaxies from Kennicutt
(1998), see §5.2.2.

The resolved KS relation for the time-stacked stripping and iso sets is
remarkably consistent (Figure 16 left panel). When observed at different
snapshots in time (e.g., in Figures 10 and 11), the galaxy populates different
$\Sigma_{\rm gas}$ ranges, which is closely correlated with the local
$\Sigma_{\rm SFR}$ (§4.2). In the time-stacked view, where the $\Sigma_{\rm
gas}$ ranges become similar between the two sets, the underlying KS relation
is in overall agreement. Our finding is consistent with Jiménez-Donaire et al.
(2023) (VERTICO) results that the local KS relation agrees between an ensemble
of Virgo RPS satellites and their isolated field counterparts, which suggests
that RPS does not directly affect the local star formation efficiency within
the gas.

The main difference between the stripping and isolated control sets is best
seen in the 1D distributions of $\Sigma_{\rm gas}$ and $\Sigma_{\rm SFR}$. The
stripping set reaches higher maximum surface densities and is truncated at low
surface densities; the peaks in both $\Sigma_{\rm gas}$ and $\Sigma_{\rm SFR}$
distribution are at higher values compared with the isolated set. The
difference can be explained by a combination of low-density gas removal and
high-density gas replenishment in the stripping set; see the evolution of the
dense gas ratio (§5.2.1). Another relatively minor difference is that the
stripping set reaches higher $\Sigma_{\rm SFR}$ at low $\Sigma_{\rm gas}$
($<0$ dex), which, as also discussed above, is likely due to fast gas removal
by RPS in still star-forming regions. The signals of high $\Sigma_{\rm SFR}$
at low $\Sigma_{\rm gas}$ only occur shortly before the complete removal of
gas (cluster pericenter in Figure 10).

The time-stacked star formation main sequence relation (Figure 16 right panel)
shows a mild $\Sigma_{\rm SFR}$ enhancement over a range of $\Sigma_{*}$ in
the stripping set. Independent of RPS or starvation, the $\Sigma_{*}$ radial
profiles remain monotonic (Figure 9), so the local $\Sigma_{*}$ can be used as
an indicator of disk radii. Under increasing ram pressure, the $\Sigma_{*}$
threshold where the wind SFR exceeds iso SFR increases (corresponding disk
radius decreases), so the time-stacked result here shows a smoother
$\Sigma_{\rm SFR}$ enhancement that extends to lower $\Sigma_{*}$ (larger
radii) compared with the group and cluster pericenter cases (Figure 12). This
agrees with the Vulcani et al. (2020) (GASP) finding that $\Sigma_{\rm SFR}$
can be enhanced over a range of $\Sigma_{*}$ when accounting for various
stripping stages. However, at the lowest $\Sigma_{*}$ end, where Vulcani et
al. (2020) found SFR enhancement in the stripping sample, our simulations
always show disk truncation (lowest $\Sigma_{*}$ not populated in the
stripping set; §4.3), instead of SFR enhancement. We note that since we
focused on the disk region ($|z|\leq 2$ kpc), our sampled patches are free of
star-forming clumps in the tail, which are shown to have a higher $\Sigma_{\rm
SFR}$ than the disk at low $\Sigma_{*}$ (Vulcani et al., 2020).

Our predictions in §5.2.2 can be summarized as follows. When observing a large
ensemble of RPS and isolated galaxies at the same stellar mass, the set of
galaxies undergoing RPS will have the same KS relation with the isolated
control set at comparable gas surface densities. Individual galaxies may
populate different $\Sigma_{\rm gas}$ ranges and hence occupy different
subsets of the ensemble KS relation, which can be caused by both active (RPS-
driven gas flows) and passive (gas consumption due to starvation) mechanisms,
as shown in Figure 11. But there is no evidence of star formation efficiency
change at given $\Sigma_{\rm gas}$ in the RPS cases. On the star formation
main sequence plane ($\Sigma_{\rm SFR}-\Sigma_{*}$), the RPS galaxy disks
(clear of tail contamination and inclination/projection effects) will show
enhanced $\Sigma_{\rm SFR}$ above a certain $\Sigma_{*}$ threshold, and sparse
sampling indicating disk truncation below the $\Sigma_{*}$ threshold. This is
because galaxies undergoing RPS tend to have more centrally concentrated gas
(and SFR) radial profiles than their isolated counterparts under starvation
(e.g., Figure 9). All predictions here assume that RPS is the only active
effect and starvation is the only passive effect. We discuss how these
assumptions are limited and their implications in §5.3 below.

###  5.3 Limitations

We made idealistic simplifications in our modeling choices in order to focus
on the science goals. We adopted a single star formation and feedback recipe
(Goldbaum et al., 2015, 2016) and a static dark matter potential, omitted the
direct modeling of magnetic fields, turbulence, and cosmic rays, and only
sampled a single (most probable; Wetzel 2011) satellite orbit and a 45∘ wind
inclination in each halo, instead of conducting a population study. In
particular, we discuss the following two and their implications.

(i) Gas removal by gravitational mechanisms. Our controlled suite of
hydrodynamical simulations only includes active gas removal by RPS; we are
missing the gravitational mechanisms, including satellite-host and satellite-
satellite interactions (Boselli & Gavazzi, 2006). In clusters, RPS by the ICM
is the dominant mechanism for cold gas stripping (Boselli & Gavazzi, 2006;
Cortese et al., 2021). In galaxy groups (lower relative velocities),
satellite-satellite gravitational interactions are traditionally considered
the primary stripping mechanism based on the observational evidence in various
systems (e.g., Yun et al. 1994; Serra et al. 2013; Lee-Waddell et al. 2019;
Wang et al. 2022). However, the observational selection bias towards gas-rich
galaxies in groups may have favored the gravitational mechanisms (Cortese et
al., 2021); in fact, both simulations (Bekki, 2014; Bahé & McCarthy, 2015;
Marasco et al., 2016) and recent observational work (Roberts et al., 2021;
Putman et al., 2021; Kolcu et al., 2022) have found that RPS can be efficient
in galaxy groups. RPS and gravitational (satellite-satellite) interactions are
likely both effective in groups, and the relative importance depends on
individual environments and satellites.

Missing the aspect of gravitational interactions, we likely overestimated the
final $M_{\rm gas}$ (and $f_{\rm gas}$) in our galaxy group case (13W; Figures
3 and 15), as gravitational encounters can contribute to active gas removal.
As the satellite still retains some ISM at 13W pericenter, gravitational
interactions will additionally perturb the remaining gas, affecting its
morphology and kinematics (Figures 5 and 6), and cause disturbances in the
stellar disk. Such effects may also be present in the Milky Way and cluster
halo cases but will have a weaker impact on the global properties (low
likelihood of massive galaxy-galaxy close encounters in a Milky Way-like halo;
high relative velocities in clusters).

Gravitational interactions will not change our key result of the RPS-induced
star formation enhancement. Gas stripping by gravitational mechanisms is
“outside-in” like RPS and will have a relatively minimal impact on the dense
gas in the disk center, where the SFR enhancement occurs in our simulations
(e.g., Figures 9 and 12). Our result is overall consistent with current
observational evidence of triggered star formation that is of RPS origin,
including global and local SFR enhancement (Vulcani et al., 2018, 2020;
Roberts & Parker, 2020), and star formation in the tail (Hester et al., 2010;
Ebeling et al., 2014; Poggianti et al., 2019).

(ii) Passive gas depletion and accretion. We modeled passive gas depletion
(i.e., free of direct removal) in our isolated galaxy simulation: steady
consumption by star formation and stellar and supernova feedback-driven
outflows. This scenario, however, only applies to a special case of galaxies
where gas accretion has been halted, which we referred to as starvation
following literature conventions (Larson et al., 1980). Accretion flows can
naturally be halted by RPS, but they also likely occur in many of the star-
forming field galaxies today, whose SFR relies on the rejuvenating cold gas
accretion, e.g., via cooling inflows from the circumgalactic medium (CGM;
Tumlinson et al. 2017).

Gas accretion is a fundamental aspect of galaxy evolution that remains poorly
constrained (Fox & Davé, 2017). With the typical inflow rates and redshift
dependence being highly uncertain, direct modeling of accretion is
challenging. But we can infer the impact of accretion by comparing the SFR-
time evolution in our simulated iso case (starvation without accretion), with
the observational SFR-redshift relation (Speagle et al., 2014) at our modeled
stellar mass. The difference in the SFR time evolution will characterize the
star formation fueled by accretion missing in our iso simulation.

Taking the initial and final conditions in iso (Figure 3; $t_{\rm init}=500$
Myr and $t_{\rm final}=2980$ Myr), which converts to $t_{\rm lookback}\approx
2.5$ Gyr and the present day, the best-fit relation from Speagle et al. (2014)
gives $\log\rm SFR_{best-fit}$ of 0.07 and -0.24 dex. While in the iso
simulation (starvation without accretion), the initial and final $\log\rm
SFR_{iso}$ are 0.18 and -0.46 dex, respectively. The simulation values are
still within the expected scatter of $\log\rm SFR_{best-fit}$ ($\pm$0.3 dex;
Speagle et al. 2014), but unsurprisingly decrease faster with time due to the
lack of replenishment. If we use the observational best-fit value as our field
galaxy control case instead, which represents the average of observed star-
forming galaxies at this stellar mass, the galaxy group case (13W) still shows
globally enhanced SFR, although the enhancement becomes mild (a factor of 1.5
instead of $\sim$2.5).

##  6 Summary and Conclusions

In this paper, we present a suite of galaxy-scale “wind-tunnel” simulations
with radiative cooling, star formation, and supernovae feedback, modeling a
low-mass satellite galaxy undergoing RPS in various halo environments. The
input time-varying ram pressure covers over three orders of magnitude (Figure
2), representing realistic satellite infall orbits from a Milky Way-like
halo’s $R_{200}$ to a cluster’s pericenter. We simulate the same satellite
galaxy in isolation for $\sim$3 Gyr as a control case, and compare the
simulations in terms of their global evolution, gas morphology and kinematics,
and the spatially resolved SFR-mass relations. Our key findings can be
summarized as follows.

  1. 1.

RPS has the potential to quench or enhance (up to a factor of $\sim$2.5) the
global SFR of a satellite galaxy while gas is being removed (Figure 3). The
impact on SFR depends on both the strength and the time derivative of the ram
pressure.

  2. 2.

Star formation is radially centralized under a moderate (13W; group halo) or
strong (14W; cluster halo) ram pressure profile, and it occurs in the stripped
tail when the satellite reaches the cluster pericenter (Figure 4). This is
also reflected in a central enhancement of gas density (Figure 9).

  3. 3.

Under an inclined wind (with face-on and edge-on components), stripping in the
disk outskirts dominates the gas mass loss, but when the pericentric ram
pressure is insufficient for complete gas removal (13W), some stripped gas
falls back and replenishes the central disk (Figures 6 and 7). The edge-on
component of ram pressure also drives a direct radial gas inflow (13W and 14W;
Figure 8) where it counters the disk rotation (right panel of Figure 6).

This radial gas transport has the following consequences:

  1. 4.

The stripping set (13W and 14W) shows an excess of high $\Sigma_{\rm
SFR}$-high $\Sigma_{\rm gas}$ material relative to the iso control set on the
spatially resolved KS plane (Figure 10). However, the underlying KS relation
is the same between the two sets when compared at similar $\Sigma_{\rm gas}$
(Figure 11), indicating that RPS has no direct effect on the star formation
efficiency.

  2. 5.

On the spatially resolved SFR-stellar mass plane, the stripping set shows
enhanced $\Sigma_{\rm SFR}$ at high $\Sigma_{*}$ (corresponding to central
disk regions) relative to iso, and is truncated at the lowest $\Sigma_{*}$
(Figure 12).

  3. 6.

The dense gas ratio ($R_{\Sigma_{10}}$; an approximation for $M_{\rm
H_{2}}/M_{\rm H\,\textsc{i}}$) increases with time in the stripping set
because of a combination of low-density gas removal and dense gas
replenishment, as opposed to the decreasing trend in iso due to starvation
(Figure 15).

Several of our findings agree with observational results. First, the RPS-
induced global SFR enhancement is mild, up to a factor of $\sim$2.5 relative
to iso, or $\sim$1.5 relative to the observational SFR-redshift relation
(Speagle et al. 2014; see §5.3). This agrees with the typical enhancement
factor of $<$2 in observational samples of RPS-triggered star formation
(Iglesias-Páramo et al., 2004; Vulcani et al., 2018; Roberts & Parker, 2020).
Second, despite occupying different $\Sigma_{\rm gas}$ ranges, the stripping
and isolated sets follow the same local KS relation, consistent with Jiménez-
Donaire et al. (2023) (the VERTICO survey); the stripping set’s $\Sigma_{\rm
SFR}$ is smoothly enhanced at high $\Sigma_{*}$ — the inner disk, consistent
with Vulcani et al. (2020) (the GASP survey). Third, the stripping set
acquires an enhanced dense gas ratio, which agrees with the high $M_{\rm
H_{2}}/M_{\rm H\,\textsc{i}}$ ratios found for three GASP jellyfish galaxies
(Moretti et al., 2020). Finally, RPS by a galaxy group medium can be effective
for low-mass spiral galaxies and potentially lead to enhanced global SFR
(Roberts et al., 2021; Kolcu et al., 2022).

The radial redistribution of gas in the galaxy is a key result of this work:
gas is stripped from the outskirts and enhanced in the center. It is the
direct cause of the SFR enhancement when $P_{\rm ram}$ is insufficient to
remove the entire gas disk; when $P_{\rm ram}$ is sufficient for central gas
removal, the galaxy is ultimately quenched of star formation. This mass
transport scenario is consistent with the increased dense gas ratio in
jellyfish galaxies (Moretti et al., 2020), the local KS relation agreement
between environmentally selected samples (Jiménez-Donaire et al., 2023), and
the comparable star formation efficiency between the leading and trailing
halves of the disk (Figure 14). We find that this explanation is a better
match to the simulations than compression by ram pressure (§5.1) or a more
efficient H i-H2 conversion (§5.2.1) — as the main driver for potential SFR
enhancement.

We thank Dan Foreman-Mackey, Mary Putman, David Schiminovich, Jacqueline van
Gorkom, and Ann Zabludoff for helpful discussions. We thank the anonymous
referee for useful suggestions that improved the paper. JZ thanks Matthew
Abruzzo, Nina Akerman, and Hui Li for the conversations on the simulations. ST
thanks the GASP collaboration for useful conversations. GLB acknowledges
support from the NSF (AST-2108470, XSEDE), a NASA TCAN award, and the Simons
Foundation through the Learning the Universe Simons Collaboration. The
simulations used in this work were run and analysed on facilities supported by
the Scientific Computing Core at the Flatiron Institute, a division of the
Simons Foundation. We also acknowledge computing resources from Columbia
University’s Shared Research Computing Facility project, which is supported by
NIH Research Facility Improvement Grant 1G20RR030893-01, and associated funds
from the New York State Empire State Development, Division of Science
Technology and Innovation (NYSTAR) Contract C090171, both awarded April 15,
2010. Analyses of this work have made use of NumPy (Harris et al., 2020),
Astropy (Astropy Collaboration et al., 2013, 2018, 2022), yt (Turk et al.,
2011), and Ipython (Perez & Granger, 2007).

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