# Survival in the Neptune desert: LTT 9779 b kept its atmosphere thanks to an
unusually X-ray faint host star

Jorge Fernández Fernández,1,2 Peter J. Wheatley1,2 George W. King3,1,2 James
S. Jenkins4,5
1Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4
7AL, UK
2Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill
Road, Coventry CV4 7AL, UK
3Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA
4Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias,
Universidad Diego Portales, Av. Ejército 441, Santiago, Chile
5Centro de Astrofísica y Tecnologías Afines (CATA), Casilla 36-D, Santiago,
Chile
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The Neptunian desert is a region in period-radius parameter space with very
few Neptune-sized planets at short orbital periods. Amongst these, LTT 9779 b
is the only known Neptune with a period shorter than one day to retain a
significant H-He atmosphere. If the Neptune desert is the result of X-ray/EUV-
driven photoevaporation, it is surprising that the atmosphere of LTT 9779 b
survived the intense bombardment of high energy photons from its young host
star. However, the star has low measured rotational broadening, which points
to the possibility of an anomalously slow spin period and hence a faint X-ray
emission history that may have failed to evaporate the planet’s atmosphere. We
observed LTT 9779 with XMM-Newton and measured an upper limit for its X-ray
luminosity that is a factor of fifteen lower than expected for its age. We
also simulated the evaporation past of LTT 9779 b and found that the survival
of its atmosphere to the present day is consistent with an unusually faint XUV
irradiation history that matches both the X-ray and rotation velocity
measurements. We conclude that the anomalously low X-ray irradiation of the
one Neptune seen to survive in Neptunian desert supports the interpretation of
the desert as primarily a result of photoevaporation.

###### keywords:

stars: individual: LTT 9779 – stars: activity – X-rays: stars – planets &
satellites: atmospheres – planet-star interactions

††pubyear: 2023††pagerange: Survival in the Neptune desert: LTT 9779 b kept
its atmosphere thanks to an unusually X-ray faint host star–Survival in the
Neptune desert: LTT 9779 b kept its atmosphere thanks to an unusually X-ray
faint host star

##  1 Introduction

The Kepler space telescope uncovered thousands of exoplanets during its 9
years of operation, many of them without an analogue in our Solar System. This
included super-Earths and sub-Neptunes in tightly packed systems (Borucki et
al., 2011).

These discoveries have revealed a scarcity of Neptune to Saturn sized planets
(3–10 R${}_{\text{E}}$) at short orbital periods of $<3$ days. This region,
known as the sub-Jovian or Neptunian desert, has become more statistically
significant with further planet discoveries by the K2 and TESS missions (e.g.
Szabó & Kiss, 2011; Benítez-Llambay et al., 2011; Sanchis-Ojeda et al., 2014;
Mazeh et al., 2016).

Since close-in planets are easier to detect in transit surveys, with many
detections of hot Jupiters and even Earth-sized worlds with periods under two
days (Murray-Clay et al., 2009; Mazeh et al., 2016), the Neptunian desert
cannot be explained as an observational bias alone, and must be caused by
underlying physical mechanisms affecting these planets during their formation
and/or evolution.

The origin of the Neptunian desert has been attributed to the inability of
planets in this region to hold onto their gaseous envelopes due to atmospheric
escape (Kurokawa & Kaltenegger, 2013; Kurokawa & Nakamoto, 2014; Ionov et al.,
2018; Owen & Lai, 2018), a phenomenon that is also thought to give rise to the
period-radius valley (Lopez et al., 2012; Owen & Wu, 2013; Fulton et al.,
2017; Owen & Wu, 2017).

Neptune-sized planets that formed in the desert, or migrated there in their
youth, would be stripped of their H/He envelopes joining the more abundant
population of hot rocky worlds with smaller radii. Hot Jupiters (>10
R${}_{\text{E}}$), on the other hand, are thought to be stable against
atmospheric loss thanks to their deep gravitational potentials (Yelle, 2004;
Murray-Clay et al., 2009; Vissapragada et al., 2022). The underlying
mechanisms that drive atmospheric escape, however, are still unclear, and
several have been proposed.

One such mechanism, photoevaporation, derives the energy for atmospheric
escape from the X-ray and extreme ultraviolet radiation (together, XUV)
originating in the host star’s corona. These high energy photons are readily
absorbed by the upper layers of large H/He-rich atmospheres, heating and
expanding the gas, and driving a hydrodynamic wind that escapes the planet
(Lecavelier Des Etangs, 2007; Owen & Wu, 2013; Lopez & Fortney, 2014).

Owen & Lai (2018) argued that two separate mechanisms are responsible for the
formation of the two boundaries of the Neptune desert. Its lower boundary is
sculpted by the photoevaporation of the atmospheres of Neptune-sized planets.
The upper boundary of the desert, over which hot Jupiters lie, is the result
of a tidal disruption barrier that interrupts the high-eccentricity migration
of gas giants.

Alternatively, it has been suggested the Neptunian desert may arise due to the
effects of Roche Lobe Overflow (RLO) on hot Neptunes (Jackson et al., 2017;
Koskinen et al., 2022), or as a result of high-eccentricity migration
(Matsakos & Königl, 2016).

In Figure 1 we plot all validated exoplanets from the NASA Exoplanet
Archive111The NASA Exoplanet Archive can be accessed at
https://exoplanetarchive.ipac.caltech.edu/. as of July 2023. The Neptune
desert is delimited by the boundaries proposed by Mazeh et al. (2016), who
defined the lower and upper edges by finding the boundaries of maximum
contrast of planet number density.

Figure 1: Plot of orbital period against planet radius, with LTT 9779 b marked
as a red star. The upper and lower bounds of the Neptune desert are shown as
black dashed lines, following Mazeh et al. (2016). Data points represent
confirmed exoplanets source from the NASA Exoplanet Archive, with ultra-short
period Neptunes shown as green circles.

In the past few years, a handful of ultra-short period Neptunes have been
discovered, a group of planets distinct from the larger exoplanet population,
plotted as green points on Figure 1. Some of these ultra-short period Neptunes
are consistent with a rocky density and hence a high-mass core (TOI-849 b,
Armstrong et al. (2020); TOI-332 b, Osborn et al. (2023)) and whose origins
are still unknown; others lack mass measurements (K2-399 b, Christiansen et
al., 2022) or the necessary precision in mass measurement to constrain their
densities and internal structures (K2-266 b, Rodriguez et al., 2018). There is
also a growing population of low density sub-Neptunes in the desert at periods
of 1–3 days, such as NGTS-4 b (West et al., 2019) and GJ 1214 b (Cloutier et
al., 2021).

Finally, LTT 9779 b (marked in red on Fig. 1) is a hot Neptune in an extremely
short orbit around a G7V star with a period of just 0.79 days (about 19 hours,
Jenkins et al., 2020). Its measured mass ($29.30^{+0.78}_{-0.81}$
M${}_{\text{E}}$) and radius ($4.72\pm 0.23$ R${}_{\text{E}}$) require a very
low density ($1.53\pm 0.23$ g cm-3) characteristic of a volatile-rich planet.

The presence of a large gaseous atmosphere has been confirmed by Crossfield et
al. (2020) and Dragomir et al. (2020) with infrared observations from Spitzer,
Edwards et al. (2023) with HST/WFC3 transmission spectroscopy, and by Hoyer et
al. (2023) with CHEOPS occultation measurements. The existence of a
substantial H/He-rich atmosphere makes LTT 9779 b a one-of-a-kind planet and
its survival deep in the Neptune desert puzzling. If the Neptune desert is the
result of X-ray driven evaporation, one would expect that a highly irradiated
Neptune-sized planet, such as LTT 9779 b, should have already been stripped of
its envelope.

We list the stellar parameters of LTT 9779 in Table 1 and note that the star
has very low measured rotational broadening ($v\sin{i}$). Assuming the
rotation axis of the star is not pointing towards the Earth, this implies a
spin period of around 45 d, which is unusually long for a star of its type and
age (Johnstone et al., 2021). Since stellar activity and X-ray emission are
strongly correlated with spin period (e.g Wright et al., 2011) the slow spin
of LTT 9779 suggests diminished XUV emission that might have failed to remove
the planet’s atmosphere.

In this paper, we test this scenario for the survival of LTT 9779 b. We
observed LTT 9779 with XMM-Newton and placed a limit on its X-ray luminosity
(Sect. 2). We then modelled the rotation and X-ray emission history of the
star (Sect. 3) and the possible evaporation histories of LTT 9779 b (Sects. 4
& 5). In Sect. 6, we conclude that the survival of LTT 9779 b in the Neptunian
can indeed be explained by an unusually low X-ray emission history of its host
star, adding weight to the suggestion that the wider Neptunian desert
originates from photoevaporation.

Table 1: Stellar parameters of LTT 9779.

Parameter | Units | Value | Reference
---|---|---|---
Astrometric
RA (J2000) | hh:mm:ss | $23:54:40.21$ | Gaia DR3c
Dec (J2000) | dd:mm:ss | $-37:37:40.52$ | Gaia DR3c
$\mu_{\text{RA}}$ | mas yr-1 | $247.634\pm 0.013$ | Gaia DR3c
$\mu_{\text{Dec}}$ | mas yr-1 | $-69.752\pm 0.014$ | Gaia DR3c
Parallax | mas | $12.338\pm 0.017$ | Gaia DR3c
Distance | pc | $81.050\pm 0.011$ | Gaia DR3c
Physical
Spectral type | — | G7V | J20a
V | mag | $9.76\pm 0.03$ | UCAC4b
T${}_{\text{eff}}$ | K | $5480\pm 42$ | J20a
M∗ | M⊙ | $1.02^{+0.02}_{-0.03}$ | J20a
R∗ | R⊙ | $0.949\pm 0.006$ | J20a
L∗ | L⊙ | $0.708\pm 0.016$ | J20a
[Fe/H] | dex | $0.25\pm 0.04$ | J20a
$v\sin{i}$ | km s-1 | $1.06\pm 0.37$ | J20a
P${}_{\text{rot}}$ | days | $<45$ | J20a
Age | Gyr | $2.0^{+1.3}_{-0.9}$ | J20a
$\log{\text{R}^{\prime}}_{\text{HK}}$ | dex | $-5.10\pm 0.04$ | J20a

  * a

J20: Jenkins et al. (2020)

  * b

UCAC4: Zacharias et al. (2012)

  * c

Gaia DR3: Gaia Collaboration et al. (2022)

  * d

2MASS: Cutri et al. (2003)

Table 2: Upper limit count rates for the PN and MOS1+2 instruments. Instrument | Energy range | Exposure | Source | Expected background | 90% upper limit | Upper limit rate
---|---|---|---|---|---|---
| keV | ks | counts | counts | source counts | counts ks-1
pn | 0.15 – 2.0 | 31.7 | 91 | 69.6 | 37.3 | $1.177$
MOS1+2 | 0.20 – 2.0 | 42.3 | 32 | 34.3 | 9.64 | $0.228$
Table 3: Upper limit X-ray fluxes and luminosities predicted by the APEC model from pn and MOS count rates. Energy range | Instrument | X-ray flux | Luminosity
---|---|---|---
(keV) |  | ($10^{-15}$ erg cm-2 s-1) | ($10^{27}$ erg s-1)
0.1 – 2.4 | pn | 2.87 | 2.26
| MOS1+2 | 2.83 | 2.23
0.2 – 2.4 | pn | 2.07 | 1.63
| MOS1+2 | 2.04 | 1.60

##  2 X-ray observations & analysis

LTT 9779 was observed with the XMM-Newton spacecraft on May 27th and 28th 2021
for a continuous exposure of 52 ks (ObsID: 0884250101, PI: Wheatley). The
star, however, was not detected in the standard pipeline outputs. We inspected
the data from the the EPIC pn (Strüder et al., 2001) and MOS (Turner et al.,
2001) detectors using the proper-motion corrected coordinates of the star on
the pipeline-processed event list, adopting both wide and narrow standard
energy bands. Nevertheless, we found no evidence of a detection of our target.

We also found that the particle background in the detectors increased
significantly towards the end of the observation, and hence we decided to
remove these noisy sections by dropping the time intervals with count rates
higher than $0.5\rm\,s^{-1}$ for pn and $0.35\rm\,s^{-1}$ for MOS in the band
10-12 keV across the full area of the detector. The remaining data amounted to
31.7 ks for pn and 42.3 ks for each MOS. The target star, however, remained
undetected after this removal of noisy data.

In the absence of a detection, we estimated an upper limit X-ray flux from LTT
9779 using the method described by Farihi et al. (2018). This analysis is also
based on the standard data analysis threads using the XMM Science Analysis
Software (SAS)222Users Guide to the XMM-Newton Science Analysis System”, Issue
17.0, 2022 (ESA: XMM-Newton SOC), https://www.cosmos.esa.int/web/xmm-
newton/sas-threads version 19.

We first applied an extraction area around the proper motion corrected
coordinates of the source with a circular aperture of radius 16 arcseconds, as
well as a secondary aperture of radius 80 arcseconds for the background in a
nearby region that contained no X-ray sources. We collected the detected
counts in these regions using the energy ranges 0.15 – 2.0 keV for pn and 0.2
– 2.0 keV for MOS. We discarded counts over 2 keV as coronal emission from
stellar activity is relatively soft (Güdel, 2004). We then scaled the
background counts to the aperture area used for the source region. In the case
of the two MOS detectors, we combined the count rates from both instruments by
making use of common Good Time Intervals (GTI) and adding up the detected
counts.

We then applied the method by Kraft et al. (1991) to estimate 90% confidence
upper limit count rates. They model noise using a Poisson distribution and
adopt a Bayesian approach with the prior that the source count rate cannot be
negative. The results, shown in Table 2, indicate upper limit count rates of
$1.18$ ks-1 for pn and $0.23$ ks-1 for the combined MOS1 and MOS2 detectors
(hereafter MOS1+2).

In order to convert the count rates to X-ray fluxes, we built model spectra
using the software XSPEC version 12.12.1 (Arnaud, 1996), which we then scaled
to match the upper limit count rates in Table 2. In the case of MOS, we loaded
the response and ancillary files for MOS1 only, and scaled the model to half
the combined MOS1+2 count rate. We adopted solar abundances from Asplund et
al. (2009) and accounted for interstellar absorption with the TBABS model by
Wilms et al. (2000). We estimated an interstellar hydrogen column density of
$2.5\times 10^{19}$ cm-2 following Redfield & Linsky (2001), who determined a
hydrogen density of 0.1 cm-3 for the local interstellar medium. We used a
single-temperature APEC model to simulate the spectrum (Smith et al., 2001),
which models the emission spectrum of collisionally-ionized diffuse gas. In
order to determine a plasma temperature for our spectral model, we adopted the
luminosity-temperature relation by Güdel (2004), which shows that average
coronal temperatures increase with X-ray luminosity on Sun-like stars. We
found that their relation is consistent with our choice of model for plasma
temperatures between 0.15 and 0.3 keV. For our upper limit calculation we
selected a temperature of 0.15 keV, since this results in the most
conservative (higher) limit.

Finally, we scaled and integrated the spectral model, and estimated X-ray
fluxes and luminosities for both the pn and MOS1+2 instruments, as shown on
Table 3. The pn and MOS limits are very similar, corresponding to upper limit
X-ray luminosities of $2.2\times 10^{27}$ erg s-1 in the 0.1–2.4 keV energy
range, and $1.6\times 10^{27}$ erg s-1 in the 0.2–2.4 keV band.

The measured rotational velocity $v\sin{i}$ of LTT 9779 implies a spin period
of 45 d, assuming its spin axis is aligned with the planet’s orbit. Using
rotation-activity relations (e.g. Wright et al., 2011), we estimated an X-ray
luminosity of $3.9\times 10^{27}$ erg s-1 in the band 0.1–2.4 keV, which is
within a factor of two of our upper limit – consistent with the $1\sigma$
uncertainty on the measured $v\sin{i}$.

We also verified that the exact value for the hydrogen column density did not
have a strong effect on the spectral model for values of $N_{H}\leq 10^{21}$
cm-2. A change of a factor of two in this quantity resulted in only a
difference of a few percent in the output fluxes.

Figure 2:  Left panel: spin histories for a 1 M⊙ star predicted by Johnstone
et al. (2021), including the population mean, $1\sigma$, and $2\sigma$
spreads, as well as the spin history fitted to the 45-day upper limit spin of
LTT 9779. Right panel: X-ray emission histories in the 0.1–2.4 keV band
corresponding to the spin histories on the left panel. Our X-ray upper limit
measured from XMM-Newton observations is shown as a magenta triangle.

##  3 Stellar rotation and XUV history

In order to model the XUV emission history of LTT 9779, we adopted the
rotation evolution models by Johnstone et al. (2021). Those authors model the
spin evolution of stars of different masses by combining angular momentum
transfer mechanisms within the star (core-envelope coupling) as well as
interactions with its environment (stellar wind and disc-locking), and
constrain the distribution of stellar rotation rates to observations of
clusters of ages 12 Myr to 2.5 Gyr. Their models predict that the average
rotation period for Solar-mass star of 2 Gyr age, such as LTT 9779, is $14$
days, with a $2\sigma$ spread from $12$ to $16$ days. The spin and X-ray
luminosity evolution of a $1\text{M}_{\odot}$ star according to this model are
shown in black in Figure 2, with the the X-ray emission determined from the
spin evolution using rotation-activity relations (Pizzolato et al., 2003;
Wright et al., 2011, 2018).

Even though the rotation period of LTT 9779 is unknown, Jenkins et al. (2020)
were able to place an upper limit on the period of 45 days based on a HARPS
$v\sin{i}$ of $1.06\pm 0.37$ km s-1. This 45 d period will correspond to the
true rotation period of the star if its spin axis is aligned with the orbit of
the planet (i.e. $i=90^{\circ}$). The implied period remains well above 14 d
for stellar inclinations greater than 20 deg, and the probability of an
inclination of 20 deg or less is only 6%, even if the stellar inclination is
randomly misaligned with the planet’s orbit. Furthermore, Jenkins et al.
(2020) also measured the strength of the Ca ii HK lines and found a
$\log{R^{\prime}}_{HK}$ value of $-5.10\pm 0.04$ dex, which is indicative of a
very low activity and also supports the star having an unusually slow rotation
period.

In order to model a plausible low XUV emission history, we choose to adopt the
45-day limit as the current rotation period of the star and use the models by
Johnstone et al. (2021) to extrapolate to earlier and later times. The spin
and X-ray luminosity evolution in this scenario are shown in orange in Figure
2.

Our results for a typical star in Figure 2 show a predicted X-ray luminosity
of $3.4\times 10^{28}$ erg s-1 for LTT 9779 at the present time, which is a
factor of 15 brighter than our XMM-Newton upper limit from Sect. 2. In
contrast, our X-ray upper limit is within a factor of 2 of the predicted X-ray
luminosity for the 45 d spin period corresponding to the measured $v\sin{i}$
and an aligned system. Our XMM-Newton upper limit is clearly more consistent
with the anomalously slow rotation scenario.

Figure 3: Emission histories for the X-ray band (solid lines) and EUV band
(dashed lines) for the two stellar models discussed in Section 3: the
predicted history for a solar mass star (blue) and the fainter history
motivated by spin and X-ray measurements (red). The EUV band was estimated
from the X-rays using the scaling law by King et al. (2018).

##  4 Evolution modelling

We used the X-ray luminosity evolution for the different scenarios shown in
Figure 2 to model the evaporation history of the LTT 9779 b in order to
determine the conditions under which the planetary atmosphere will be
stripped.

We used the photoevolver 333The code is available on GitHub at
https://github.com/jorgefz/photoevolver code (Fernández Fernández et al.,
2023), which combines three ingredients: (1) a description of the stellar
X-ray history, using the model by Johnstone et al. (2021) described in Section
3, (2) the envelope structure model by Chen & Rogers (2016, Eqn. 5) based on
MESA hydrodynamic simulations, which links the atmospheric mass to its size,
and (3) the mass loss model by Kubyshkina et al. (2018), which translates
incident X-ray irradiation into atmospheric mass loss rate.

At each simulation time step, the XUV flux incident on the planet is drawn
from the stellar tracks in Figure 2 and then used to remove some mass from the
atmosphere, calculated using the mass loss model. The envelope size is then
recalculated with the new mass, and the age advances one time step forward. We
evolved the planet from the age of 10 Myr, the time at which the
protoplanetary disc has fully dissipated (Fedele et al., 2010) and any boil-
off processes have completed (Lammer et al., 2016; Owen & Wu, 2016), to 5 Gyr,
with a fixed time step of 0.1 Myr. We considered the envelope stripped when
its mass reached a value below 0.01% of the planet’s mass, as it is the lower
limit for which the envelope model by Chen & Rogers (2016) is rated.

We adopted two spin period histories from Figure 2 to find feasible
evaporation pasts for LTT 9779 b: one matching the typical spin period
distribution for a solar-mass star, and another matching the star’s measured
rotation upper limit of 45 days at its current age. We also estimated the
extreme ultraviolet (EUV) stellar emission in the band 0.0136–0.1 keV using
the empirical relations by King et al. (2018), which are based on Solar
TIMED/SEE data. We plot the relative contributions of the X-ray and EUV bands
on Figure 3.

Table 4: Planetary parameters and internal structure of LTT 9779 b.

Parameter | Value | Source
---|---|---
Orbital period | P${}_{\text{orb}}$ (days) | $0.792\pm(9.3\times 10^{-6})$ | J20a
Semi-major axis | a (AU) | $0.01679\pm 0.00014$ | J20a
Equilibrium temperature | T${}_{\text{eq}}$ (K) | $1978\pm 19$ | J20a
Mass | M${}_{\text{p}}$ (M${}_{\text{E}}$) | $29.30^{+0.78}_{-0.81}$ | J20a
Radius | R${}_{\text{p}}$ (R${}_{\text{E}}$) | $4.72\pm 0.23$ | J20a
Core radius | R${}_{\text{core}}$ (R${}_{\text{E}}$) | $2.69\pm 0.11$ | This work
Core mass | M${}_{\text{core}}$ (M${}_{\text{E}}$) | $27.30\pm 1.10$ | This work
Envelope radius | R${}_{\text{env}}$ (R${}_{\text{E}}$) | $2.03\pm 0.26$ | This work
Envelope mass fraction | f${}_{\text{env}}$ | $0.067\pm 0.029$ | This work

  * a

J20: Jenkins et al. (2020)

Figure 4:  Evaporation histories of a range of simulated scenarios for LTT
9779 b, with initial envelope mass fractions from 5% to 17%. The panels
present the evolution of the planet radius (top), envelope mass fraction
(middle), and mass loss rate (bottom) under two XUV irradiation histories: (1)
the expected stellar emission history of a solar mass star (left column), and
(2) a fainter emission history consistent with the measured stellar rotation
velocity and our X-ray upper limit from our XMM-Newton observation (right
column). The dashed grey line on the top panels represents the rocky core
radius of LTT 9779 b.

###  4.1 Internal structure

We modelled the internal structure of LTT 9779 b assuming a silicate-iron
(rocky) core surrounded by a large H/He-rich atmosphere, following Rogers &
Owen (2021). This description entails a total of four model parameters: the
core radius R${}_{\text{core}}$, core mass M${}_{\text{core}}$, envelope
radius R${}_{\text{env}}$, and envelope mass fraction $\text{f}_{\text{env}}$
(see Table 4). With knowledge of the planet’s mass and radius alone (together
with orbital and host star parameters), we can deduce values for these
quantities by combining four equations. First we defined planet radius as
$\text{R}_{\text{p}}=\text{R}_{\text{core}}+\text{R}_{\text{env}}$, and
envelope mass fraction as the ratio of envelope and planet masses
$\text{f}_{\text{env}}=\text{M}_{\text{env}}/\text{M}_{\text{p}}=(\text{M}_{\text{p}}-\text{M}_{\text{core}})/\text{M}_{\text{p}}$.
Additionally, we adopted the empirical mass-radius relation for rocky planets
by Otegi et al. (2020, Eqn. 1) to link the core mass $\text{M}_{\text{core}}$
to the core radius $\text{R}_{\text{core}}$. Finally, we adopt the envelope
structure model by Chen & Rogers (2016, Eqn. 5), which links the mass fraction
of the envelope $\text{f}_{\text{env}}$ to its thickness
$\text{R}_{\text{env}}$. We found that LTT 9779 b is consistent with a rocky
core of radius $2.69\pm 0.11$ R${}_{\text{E}}$ and a gaseous envelope of mass
fraction $6.7\pm 2.9\%$ (see Table 4), in good agreement with the mass
fraction of 9% estimated by Jenkins et al. (2020).

Moreover, we estimated that the predicted XUV emission for LTT 9779 induces a
present-day mass loss rate of $3.5\times 10^{11}$ g s-1 using the model by
Kubyshkina et al. (2018). Energy-limited photoevaporation, a simpler model
that accounts only for the energy from incident X-ray photons (Watson et al.,
1981; Lecavelier Des Etangs, 2007), predicts a lower present-day mass loss
rate of $2.8\times 10^{11}$ g s-1 using the same evaporation efficiency as
Kubyshkina et al. (2018) of 15%. On the other hand, the fainter XUV emission
motivated by our XMM-Newton observations yields a present-day mass loss rate
of $1.5\times 10^{11}$ g s-1 using the model by Kubyshkina et al. (2018), and
$0.6\times 10^{11}$ g s-1 with the energy-limited formulation.

##  5 Evaporation history

We simulated a range of evolutionary scenarios for LTT 9779 b, all using the
rocky core determined in Table 4, but each starting off at an age of 10 Myr
with a different envelope mass fraction. We used envelope mass fractions of
5%, 10%, and 17%, with the lowest of these values being motivated by the
uncertainty on the planet’s current envelope mass fraction.

The maximum initial envelope is motivated by the maximum radius the planet
could have following its formation. This is set by the radius of its Roche
lobe which we calculate using the expression by Owen & Lai (2018, Eqn. 3) for
low density gaseous planets. This gives a maximum envelope mass fraction of
17% for LTT 9779 b at the beginning of our simulation. Finally, the choice of
initial envelope mass fraction of 10% serves as a mid-point between the two
values above.

###  5.1 Expected XUV history

Firstly, we adopt the XUV luminosity tracks that are expected for a typical
solar-mass star following the model by Johnstone et al. (2021), as shown in
Figure 2 (right hand panel), and evolve LTT 9779 b under photoevaporation for
the three initial envelope mass fractions. The results, shown in Figure 4
(left column) show that none of these scenarios match the mass and radius of
LTT 9779 b at the present time, as they are all stripped of their envelopes
before now. This confirms that a planet of this nature orbiting LTT 9779 with
the expected X-ray emission history would already be a hot rocky world of
radius $2.7$ R${}_{\text{E}}$, joining the population of planets that define
the lower edge of the Neptune desert. We thus rule out this scenario as a
description of the evaporation history of LTT 9779 b.

###  5.2 Faint XUV history

We repeat the analysis in Sect. 5.1 but adopting a stellar XUV history that
respects both the measured stellar rotation velocity and our X-ray upper
limit, as determined with our XMM-Newton observation (Sect. 2). This emission
history, shown in Figure 2 (right hand panel), matches a star that has a
rotation period of 45 days at the age of 2 Gyr.

We find that the planetary atmosphere survives evaporation to the present day
for all three initial envelope fractions, as shown in Figure 4 (right column).
Furthermore, we find that, under these conditions, LTT 9779 b is consistent
with an evaporation history where it started out with an envelope mass
fraction of 10% to 17%. This would make the planet a 6–7 R${}_{\text{E}}$
puffy super-Neptune after disc dispersal.

We find that continued exposure to these low XUV fluxes does end up stripping
the planet of its envelope by the age of 6–7 Gyr (Figure 4). As can be seen in
Figure 2, this is because the low activity track is flat in comparison to the
high activity track, and so the X-ray emission in both histories become
comparable at later ages. This behaviour can be attributed to faster rotators
spinning down more rapidly than slow rotators, leading to the tracks
converging (Johnstone et al., 2021).

In principle, our conclusion that the low activity track is consistent with
the planet retaining its envelope to the present day is sensitive to our
choice of EUV scaling law. This is illustrated in Fig. 3, where it is clear
that the EUV emission is expected to be higher than X-rays throughout the
lifetime of the star. Maggio et al. (2023) compared different X-ray/EUV
scaling laws and confirmed the that the King et al. (2018) relation used here
is in good agreement with available EUV observations. Some other EUV scaling
laws, however, such as that from Sanz-Forcada et al. (2011) predict somewhat
higher EUV emission up to a factor 2 (revised down to 1.5 by Sanz-Forcada et
al., 2022). In order to test whether the choice of scaling relation affects
our conclusions, we re-ran our model with both the Sanz-Forcada et al. (2011)
and Sanz-Forcada et al. (2022) relations. We found that the gaseous envelope
of the planet is still expected survive to the present day for both scaling
relations, demonstrating that our results in practice are not sensitive to
this choice.

##  6 Discussion & Conclusions

We have presented an analysis of X-ray driven photoevaporation of the ultra-
short period Neptune LTT 9779 b: the only known planet deep in the Neptune
desert with a significant gaseous envelope. Since the Neptune desert is
thought to be cleared out by X-ray photoevaporation (e.g. Owen & Lai, 2018),
the existence of this planet at such a short period is puzzling.

Specifically, we have considered the possibility that LTT 9779 b has survived
at its present orbital separation due to anomalously low X-ray emission from
its host star, as suggested by its unusually low rotational velocity (Table 1)
and lack of Ca ii HK emission lines (Jenkins et al., 2020).

We made an XMM-Newton observation of the host star and measured an upper-limit
to the X-ray luminosity that is a factor of fifteen lower than the expected
X-ray luminosity for a star of this type and age (Sects. 2 & 3). In contrast,
our X-ray upper limit is within a factor of 2 of the luminosity expected for a
star rotating with the much slower 45 d period suggested by the rotational
velocity and an assumed alignment between the stellar spin and planetary
orbital axes.

We also simulated the possible evaporation history of the planet using a range
of initial envelope mass fractions. As expected, we confirm that the planetary
atmosphere would not survive to the present day under the expected X-ray
emission history of a solar mass star like LTT 9779 (Sect. 5.1). However, we
find that a dimmer X-ray past, motivated by the upper limits on the X-ray
luminosity and spin period, allows the planetary atmosphere to survive to the
present day (Sect. 5.2).

We conclude that LTT 9779 most-likely formed as an anomalously slowly rotating
star, and that its close-in Neptune-sized planet LTT 9779 b was thus able to
survive in the Neptune desert to the present day due to unusually low X-ray
irradiation. This scenario is consistent with the planet forming in situ
and/or migrating within the protoplanetary disc, offering an alternative to
the scenario suggested by Jenkins et al. (2020), in which late inward
migration followed by Roche-lobe overflow (RLO) may have eroded a Jupiter-mass
planet down to a hot Neptune like LTT 9779 b.

Moreover, the super-solar ($400\times$) metallicity of its atmosphere together
with its very high albedo, determined by Hoyer et al. (2023), would make the
planet more resistant to evaporation as heavier species require more energy to
remove (Wilson et al., 2022; Owen & Jackson, 2012).

Even though the implied slow 45-day spin of LTT 9779 may be unusual, examples
of long-period (30-45 d) solar-mass stars have been found in the 950 Myr-old
cluster NGC 6811, hinting towards a rare mechanism that yields extremely slow
rotators (Godoy-Rivera et al., 2021).

This unusual feature of the host star is consistent with our interpretation
because of the unique nature of LTT 9779 b within the Neptunian desert. The
strong selection bias in favour of large close-in transiting exoplanets means
that planets like LTT 9779 b must be extremely rare. In contrast, finding
similarly anomalous stars without a hot Neptune is extremely difficult. This
is because their low stellar activity results in low amplitude photometric
modulation that is difficult to detect. Their long periods are also beyond the
reach of most photometric surveys, and we cannot use $v\sin i$ because of
contamination by pole-on faster rotators. Nevertheless, it is known that stars
are formed with a wide range of initial spin periods, at least in part due to
interactions with long-lived protoplanetary discs ($\sim$10 Myr), which can
prevent them from spinning-up during the pre-main sequence stage of their
evolution and allowing slow rotators to maintain their initial spin into the
main sequence (e.g. Moraux et al., 2013; Ribas et al., 2015; Richert et al.,
2018).

Finally, our conclusion that the only known planet deep in the Neptunian
desert with a gasesous envelope is also unusual in having an X-ray faint star,
strongly supports the suggestion that the primary origin of the Neptunian
desert is X-ray driven photoeveporation.

## Acknowledgements

The work presented here was supported by the UK Science and Technology
Facilities (STFC). JFF is supported by the STFC studentship grant
ST/W507908/1. PW acknowledges support under the STFC consolidated grants
ST/T000406/1 and ST/X001121/1. JSJ gratefully acknowledges support by FONDECYT
grant 1201371 and from the ANID BASAL project FB210003. This research made use
of the Python packages  numpy (Harris et al., 2020),  astropy (Astropy
Collaboration et al., 2022),  scipy (Virtanen et al., 2020),  matplotlib
(Hunter, 2007),  Mors (Johnstone et al., 2021), and
uncertainties444Uncertainties: a Python package for calculations with
uncertainties, Eric O. LEBIGOT, http://pythonhosted.org/uncertainties. This
research has made use of the NASA Exoplanet Archive, which is operated by the
California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.
Based on observations obtained with XMM-Newton, an ESA science mission with
instruments and contributions directly funded by ESA Member States and NASA.
We thank the reviewer for their constructive comments which have improved the
quality of this work.

## Data Availability

The XMM-Newton data used in this work is publicly available at the XMM-Newton
Science Archive (XSA) 555https://www.cosmos.esa.int/web/xmm-newton/xsa, under
the observation ID 0884250101 (target: LTT 9779, PI: Wheatley).

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