# Delayed Massive-Star Mechanical Feedback at Low Metallicity

Michelle C. Jecmen  Department of Astronomy, University of Michigan, 1085 S.
University Ave, Ann Arbor, MI 48109-1107  M. S. Oey  Department of Astronomy,
University of Michigan, 1085 S. University Ave, Ann Arbor, MI 48109-1107

(Received May 8, 2023; Revised September 19, 2023; Accepted October 12, 2023)

###### Abstract

The classical model of massive-star mechanical feedback is based on effects at
solar metallicity $(\rm Z_{\odot})$, yet feedback parameters are very
different at low metallicity. Metal-poor stellar winds are much weaker, and
more massive supernova progenitors likely collapse directly to black holes
without exploding. Thus, for $\sim 0.4\ \rm Z_{\odot}$ we find reductions in
the total integrated mechanical energy and momentum of $\sim 40$% and 75%,
respectively, compared to values classically expected at solar metallicity.
But in particular, these changes effectively delay the onset of mechanical
feedback until ages of $\sim 10$ Myr. Feedback from high-mass X-ray binaries
could slightly increase mechanical luminosity between ages 5–10 Myr, but it is
stochastic and unlikely to be significant on this timescale. Stellar dynamical
mechanisms remove most massive stars from clusters well before 10 Myr, which
would further promote this effect; this process is exacerbated by gas
retention implied by weak feedback. Delayed mechanical feedback implies that
radiation feedback therefore dominates at early ages, which is consistent with
the observed absence of superwinds in some extreme starbursts. This scenario
may lead to higher star-formation efficiencies, multiple stellar populations
in clusters, and higher Lyman continuum escape. This could explain the giant
star-forming complexes in metal-poor galaxies and the small sizes of OB
superbubble shells relative to their inferred ages. It could also drive modest
effects on galactic chemical evolution, including on oxygen abundances. Thus,
delayed low-metallicity mechanical feedback may have broad implications,
including for early cosmic epochs.

Stellar Feedback (1602) — Starburst Galaxies (1570) — Massive Stars (732) —
Metallicity (1031) — Dwarf Irregular Galaxies (417) — Lyman-Alpha Galaxies
(978) — Interstellar Medium Wind (848) — Young Massive Clusters (2049) —
Galaxy winds (626)

††journal: AAS

##  1 Introduction

Mechanical feedback from massive stars and young star clusters plays a pivotal
role in the evolution of star-forming galaxies. Supersonic stellar winds from
OB stars and their supernovae (SNe) release large amounts of mechanical energy
($\sim 3\times 10^{38}$ erg s-1 per solar mass of stars (Keller et al., 2014)
which strongly affect the surrounding interstellar medium (ISM). The shocks
generate superbubbles that are pressure-driven by a hot ($>10^{6}$ K), low-
density component which piles up cooler ISM into large, ionized and/or neutral
shells. In starbursts, the super star clusters (SSC) drive galactic superwinds
that blow hot gas and newly synthesized supernova products into the
circumgalactic medium (CGM). Thus, massive-star feedback can be responsible
for the morphology, kinematics, ionization balance, and metallicity of the ISM
and CGM. Furthermore, expanding superbubbles and superwinds can trigger
second, and even third, waves of star formation as they interact with
surrounding ISM (e.g., Oey et al., 2005).

This classical model for mechanical feedback was formulated for effects at
solar metallicity and is approximately constant over the cluster lifetime.
However, this is not the case at low metallicity, as the initial mechanical
feedback of a low metallicity cluster is at least an order of magnitude lower
than its maximum value well into the cluster lifetime (Leitherer et al.,
2014). In this work, we show that this effect is likely to be important and
could fundamentally impact galaxy evolution in multiple ways.

It is well understood that low metallicity mechanical feedback is decreased
for the first $\sim$3 Myr due to weak stellar winds (see, e.g., the review by
Vink, 2022). Recent observational and theoretical evidence suggest that widely
used low-metallicity stellar wind mass-loss rates are too high. Mass-loss
rates obtained from H$\alpha$ and UV absorption features reveal values that
are smaller than theoretical mass-loss rates from, e.g., Vink et al. (2001) by
a factor of $\sim$3 (Bouret et al., 2012; Šurlan et al., 2013; Puls et al.,
2008). Recent numerical models continue to support this moderate decrease
(e.g., Gormaz-Matamala et al., 2022; Vink & Sander, 2021). However, recent
studies which account for wind micro-clumping and weak winds show a much more
dramatic decrease from Vink’s (2001) formula of up to one, or even two, orders
of magnitude (Björklund et al., 2022; Rickard et al., 2022; Ramachandran et
al., 2019). Observations in the Small Magellanic Cloud also support much
weaker winds (Ramachandran et al., 2019) than expected.

Another major effect at low metallicity is that SNe start later than at solar
values. The classical paradigm is that all massive stars above $\sim$8
$M_{\odot}$ explode, starting at an age of $\sim$3 Myr and continuing steadily
until the low-mass limit for core collapse is reached around 45 Myr. However,
core-collapse supernova (CCSN) models find that many potential progenitors do
not explode but instead form black holes (BH). This effect is well established
for low metallicity (Zhang et al., 2008; O’Connor & Ott, 2011; Patton &
Sukhbold, 2020). There is no strong consensus on the maximum progenitor mass
for SN explosions. Sukhbold et al. (2016) find that only 10% of stars more
massive than 20 $\rm M_{\odot}$ successfully explode, and O’Connor & Ott
(2011) find a strict upper limit of 30 $M_{\odot}$ at very low metallicities.

Additionally, mechanical feedback models overlook dynamical processes, which
remove stars, particularly massive stars, before they contribute to the total
mechanical feedback of the cluster. These processes are driven by massive
binaries, which are more prevalent at low metallicity. When star formation
ends, a cluster is not in dynamical equilibrium. As it re-virializes, a
significant number of stars will naturally evaporate (e.g., Brinkmann et al.,
2017). In addition, the massive stars segregated in the dense cluster core are
likely to be dynamically ejected (e.g., Oh et al., 2015; Oh & Kroupa, 2016).
If ejected early enough or fast enough, the stars can travel to distances
where their mechanical feedback no longer contributes to the aggregate as
manifested by a superbubble or superwind.

Taken together, these effects imply that mechanical feedback is profoundly
different at low metallicity than assumed by the classical paradigm. In this
paper we show that the combination of weak stellar winds, fewer supernovae,
and the removal of stars by dynamical processes effectively delays the onset
of mechanical feedback until cluster ages of $\sim 10$ Myr. This has profound
effects on the character of massive-star feedback and implies that radiation
dominates over mechanical feedback at early ages, which has significant
consequences, many of which remain to be understood.

##  2 Starburst99 Models

We use Starburst99, a well-established evolutionary synthesis code, to model
the mechanical feedback of star-forming galaxies with varying SN progenitor
masses (Leitherer et al., 2014). It was previously thought that all stars
between 8 and 120 $M_{\odot}$ end their lives as SNe. However, it is now
believed that many low-metallicity progenitors with extended core structure
experience direct core collapse without SNe (e.g., O’Connor & Ott, 2011; Zhang
et al., 2008; Heger et al., 2003; Sukhbold et al., 2016). The explodability of
a progenitor depends on its stellar structure, which is a function of mass and
metallicity.

To explore the effect of limiting SNe from massive progenitors, we calculate
the mechanical luminosity and momentum injection rate over time for three
cluster models with varying SN progenitor masses and metallicities. In what
follows, the “classical model” has a maximum SN progenitor mass of 120 $\rm
M_{\odot}$ and solar metallicity. The “unrestricted SNe model” is identical to
the classical model but has subsolar metallicity. The “restricted SNe model”
has a maximum SN progenitor mass of 20 $\rm M_{\odot}$, in line with the
predictions of Sukhbold et al. (2016), and has subsolar metallicity.

For all models we retain the typical minimum SN progenitor mass of 8 $\rm
M_{\odot}$, and assume that all stars with masses between the minimum and
maximum values explode. We use two stellar evolutionary models published by
the Geneva group: one excluding stellar rotation and one with a rotational
velocity of 40% of break-up velocity (Georgy et al., 2013; Ekström et al.,
2012). All models include stellar rotation unless stated otherwise. The models
at subsolar metallicity have heavy-element abundances of $Z=0.002$ and
$Z=0.004$ for their evolutionary model (Georgy et al., 2013) and atmospheric
model (Meynet et al., 1994), respectively. All models use instantaneous star
formation with a Kroupa initial mass function for a 106 $\rm M_{\odot}$
cluster.

###  2.1 Mechanical Feedback

Figure 1: Starburst99 models of mechanical luminosity (left) and momentum
injection rate (right) from winds and SNe for a 10${}^{6}\ \rm M_{\odot}$
cluster (cf. Leitherer et al., 2014). The classical (blue) and subsolar
unrestricted SNe (red) models have SN progenitor masses 8 – 120 $\rm
M_{\odot}$. The subsolar, restricted SNe (black) model has SN progenitor
masses of 8 – 20 $\rm M_{\odot}$. The stellar evolutionary tracks include
rotation for both solar (Ekström et al., 2012) and subsolar (Georgy et al.,
2013) metallicity. The green dotted lines in the left panel show mechanical
feedback for the binary population synthesis models of Rappaport et al. (2005)
for an HMXB population of $10\ \rm M_{\odot}$ black holes with secondary stars
drawn from a Salpeter (1955) IMF. Models S and B show $L_{\rm mech}=L_{\rm
Edd}$ and $10L_{\rm Edd}$, respectively (see text).

Figure 1 shows the mechanical luminosity (left) and momentum injection rate
(right) over time due to stellar winds and SNe for different limits on
explodability and metallicity. The dashed blue line shows the classical
mechanical feedback scenario where strong stellar winds dominate until SNe
start at $\sim$3 Myr. The magnitude of the stellar wind contribution roughly
equals that of the SNe contribution, thereby generating a fairly constant
value with time. This is not the case for the subsolar models. The solid red
and black lines show the subsolar restricted and unrestricted SNe models,
respectively. Since stellar winds are significantly weaker at low metallicity,
the start of SNe is clearly identifiable by a sharp increase of an order of
magnitude or more in both plots. Since the restricted SNe model limits the SN
progenitor range to masses $<20\ \rm M_{\odot}$, the onset of SNe is delayed
to an age of $\sim$10 Myr. Stellar winds now dominate the mechanical
luminosity and the momentum injection rate for this much longer initial
period. This causes a great reduction in both the mechanical luminosity and
momentum injection rate because, not only are low metallicity stellar winds
less powerful than SNe, but also after $\sim$3 Myr, as massive stars begin to
expire, the remaining lower-mass stars have exponentially weaker stellar
winds. Furthermore, we expect the mechanical feedback from stellar winds to be
even lower than estimated here, since the adopted mass-loss rates are now
thought to be too high (e.g., Vink, 2022; Björklund et al., 2022; Gormaz-
Matamala et al., 2022; Rickard et al., 2022; Ramachandran et al., 2019).

Thus, these combined effects delay the start of strong, SN mechanical feedback
until a cluster age of $\sim 10$ Myr. The effect of varying the maximum SN
progenitor mass is shown in Figure 2 for mechanical luminosity and momentum
injection rate, for subsolar models. The models with less massive maximum SN
progenitors have exponentially larger delays in the onset of SN feedback, and
explodability is also stochastic. Thus, we should take 10 Myr as a nominal
value for the feedback delay.

Figure 2: Mechanical luminosity (left) and momentum injection rate (right)
over time for a subsolar 10${}^{6}\ \rm M_{\odot}$ cluster. Models with
varying maximum SN progenitor masses are shown with different colors as
indicated, in increments of 10 $\rm M_{\odot}$. The model with a maximum SN
progenitor of 20 $\rm M_{\odot}$ (dashed line) corresponds to the default
subsolar, restricted SNe model in Figure 1.

Figure 3: Total cumulative integrated energy (left) and total momentum
injected (right) from winds and SNe. Models are the same as in Figure 1.

Figure 3 shows the total integrated energy (left) and cumulative momentum
(right) for the models in Figure 1. The effect from weak, low metallicity
stellar winds is shown by the difference between the classical model (blue)
and the subsolar, unrestricted SNe model (red). The effect from only
restricting SN progenitor masses is shown by the difference between the
subsolar, unrestricted SNe model (red) and the restricted SNe model (black).
These differences are apparent in the total integrated energy of the cluster
at early ages and become less differentiated as the cluster ages. However, for
the total momentum injected, the difference between the models remains large
over the duration of mechanical feedback input, since, as seen in Figure 1,
the momentum injection rate decreases significantly, and more steeply than,
the energy injection rate. Thus, the initial momentum loss due to the absence
of early SNe causes a significant decrease in the total, cumulative momentum
feedback that the system never recovers.

Figure 4: The total cumulative integrated energy (left) and total momentum
injected (right) for the subsolar, restricted SNe model normalized by the
classical, solar model (blue) and unrestricted, subsolar model (red). The
solid and dotted lines show models including and excluding stellar rotation,
respectively.

Figure 4 gives the cumulative energy ($E$) and cumulative momentum ($p$) for
the restricted SNe model at subsolar metallicity, normalized by the classical
model (blue) and subsolar unrestricted SNe model (red). For the first $\sim$10
Myr, both the cumulative energy and momentum of the restricted SNe model are
only $\sim 10$% that of the classical model. Ultimately, the cumulative energy
of the restricted SNe model reaches $\sim$ 60% of the classically expected
energy. In comparison, the cumulative momentum of the restricted SNe model
only reaches $\sim$ 25% of the classically expected momentum. Figure 4 also
shows models that assume non-rotating stars. Rotation increases the stellar
wind power, but it also extends stellar evolution and therefore effectively
shifts the maximum SN progenitor to slightly lower masses. The overall effect
is a slight reduction in total energy injection.

##  3 Additional Mechanisms

###  3.1 Accretion Driven Feedback

Justham & Schawinski (2012) also noted the expected delay in SN feedback due
to the most massive stars collapsing directly to black holes. They therefore
suggest that mechanical feedback from high-mass X-ray binaries (HMXBs)
generated by some of these black holes could potentially be important at times
before SN feedback dominates. However, the binary population synthesis models
of Rappaport et al. (2005), predict that the total expected mechanical
luminosity from HMXBs at ages $<10^{7}$ yr is only on the order of $\log
L_{\rm mech}/\hbox{erg\,s${}^{-1}$}\sim 38-39$ for a $10^{6}\ \rm M_{\odot}$
stellar populations. The left panel of Figure 1 shows mechanical feedback from
the Rappaport et al. models overplotted, normalized to the $10^{4}$ core-
collapse events in our Starburst99 models. We assume that the X-ray luminosity
$L_{X}\sim L_{\rm mech}$ is on the order of the Eddington luminosity $L_{\rm
Edd}$ (e.g., Pinto & Kosec, 2022; Justham & Schawinski, 2012). Predictions
(e.g., King & Muldrew, 2016) and observations (e.g., Kosec et al., 2018; Tao
et al., 2019) suggest that $L_{\rm mech}$ could also be $10-100\times L_{\rm
Edd}$, while on the other hand, $L_{\rm Edd}$ may be a substantial upper limit
to $L_{X}$ (e.g., Kosec et al., 2018). The figure shows models where $L_{\rm
mech}=L_{\rm Edd}$ (S) and $10L_{\rm Edd}$ (B).

We see that HMXB feedback could increase $L_{\rm mech}$ in the minima of the
troughs at age 5 – 10 Myr seen in Figure 1, and the effect also would be
slightly enhanced at low metallicity (e.g., Renzo et al., 2019). It is
important to note that both HMXB feedback and SNe are stochastic. But in
general, the order-of-magnitude reduction in $L_{\rm mech}$ preceding the
onset of SNe remains.

Individual ultraluminous X-ray sources (ULXs) have larger $\log
L_{X}/\hbox{erg\,s${}^{-1}$}\sim 39-40$, which is $L_{\rm Edd}$ of black holes
with masses up to $\sim 100\ \rm M_{\odot}$. Thus, individual objects could be
important, but due to their stochasticity and unknown $L_{\rm mech}$, it is
unclear whether they are an important systematic effect (Justham & Schawinski,
2012).

###  3.2 Cluster Evaporation

Another mechanism that affects the output of mechanical feedback from a given
cluster is the removal of stars by dynamical processes. Dynamical evolution
can remove massive stars before they explode as SNe, thereby further reducing
mechanical feedback. Massive stars are more likely to be ejected, and if
ejected early and fast enough, their stellar winds and possible SNe will be
located outside the cluster’s sphere of influence, nominally the superbubble
or outflow radius. Dynamical processes which remove stars are dependent on
several key initial conditions (see e.g., review by Portegies Zwart et al.,
2010), including the initial parameters for cluster density, star formation
efficiency, mass segregation, cluster mass, and binary population (e.g., Oh &
Kroupa, 2016; Brinkmann et al., 2017).

Oh & Kroupa (2016) find that the initial cluster density is the most
influential parameter in their study, with the densest clusters ejecting 50%
of their O stars by age 3 Myr while the least dense ones eject only 4.5% at 3
Myr. Primordial mass segregation enhances this effect, since such clusters
already have a pre-existing dense core of massive stars where most dynamical
ejections occur (e.g., Oh & Kroupa, 2016). However, the amount and timescale
of gas dispersal significantly affects the stellar density, which in turn
strongly affects the stellar ejection rate (Pfalzner & Kaczmarek, 2013).
Similarly, Brinkmann et al. (2017) find that clusters with the same initial
density can have widely differing bound fractions depending on gas dispersal
parameters. Thus, weak early feedback promotes stellar dynamical ejections,
further removing sources of mechanical feedback.

The stellar ejection fraction peaks at moderately massive clusters ($10^{3.5}\
M_{\odot}$), including for models with different initial radii (Oh et al.,
2015). Brinkmann et al. (2017) find that massive clusters ($>10^{5}\ \rm
M_{\odot}$) have an 80% bound fraction while moderately massive clusters
($5\times 10^{3}\ \rm M_{\odot}$) have only a 20% bound fraction for currently
expected gas expulsion parameters. As noted above, the most massive stars tend
to sink to the cluster center, promoting their ejection.

Numerical simulations by, e.g., Oh et al. (2015); Oh & Kroupa (2016);
Brinkmann et al. (2017) suggest that most massive stars are ejected within the
first 5 Myr. Furthermore, the efficiency of dynamical ejections peaks after 1
Myr for all moderately massive, mass segregated models simulated by Oh &
Kroupa (2016). These massive ejected stars must be outside the superbubble
radius to not contribute to the mechanical feedback of the cluster. Velocity
distributions of Oh & Kroupa (2016) show that $<~{}25$% of ejected O-stars and
B-stars will remain bound at 3 Myr. If SNe do not start until an age of 10
Myr, the remaining ejected yet local SN progenitors have another 7 Myr to
escape the cluster. Ejected stars could easily travel 50 – 100 pc in only a
few Myr.

Therefore, the overall effect of dynamical ejections is to enhance the delay
in the onset of massive-star mechanical feedback at low metallicity.
Accounting for dynamical ejections would further decrease, and potentially
extend, the weak mechanical feedback at ages $\lesssim 10$ Myr.

##  4 Discussion

###  4.1 Evidence and Implications

Thus, at early times $<10$ Myr in low-$Z$ systems, we expect only very weak
mechanical feedback from metal-poor stellar winds in gas-rich environments.
These conditions promote catastrophic cooling (e.g., Silich et al., 2004;
Wünsch et al., 2008; Krumholz et al., 2017), pressure-confinement (e.g.,
Silich et al., 2007; Oey & García-Segura, 2004; Smith et al., 2006), or
delayed launching (Danehkar et al., 2021) of any adiabatic mechanical feedback
or superwinds. Observational evidence for missing or suppressed superwinds is
building; nearby starbursts such as NGC 5253 (Turner et al., 2017), M82 (Smith
et al., 2006; Westmoquette et al., 2013), and Mrk 71 (Oey et al., 2017;
Komarova et al., 2021) show no evidence of classical, energy-driven
superwinds, and instead show giant molecular clouds within a few pc of the
super star clusters, with evidence of metal retention in one instance
(Westmoquette et al., 2013). High nebular ionization seen in species like He
ii, C iv, and O vi observed in such systems may be evidence that superwinds
are being suppressed by weak mechanical input and/or catastrophic cooling
(e.g., Danehkar et al., 2021, 2022; Oey et al., 2023). Moreover, some of the
most extreme, metal-poor, Green Pea galaxies, a population including many
Lyman-continuum emitters (Flury et al., 2022), show the lowest superwind
velocities (Jaskot et al., 2017).

If mechanical feedback effectively starts later at low metallicity than at
solar metallicity, it should have profound effects on the structure and
evolution of starbursts and their host galaxies. In particular, it implies
that radiation feedback dominates over mechanical feedback for the first $\sim
10$ Myr (e.g., Freyer et al., 2003; Krumholz & Matzner, 2009). Weaker stellar
winds and fewer SNe imply increased gas retention and less negative feedback
to disrupt ongoing star formation. This effect may be amplified by the
negative cycle of poor gas expulsion enhancing stellar densities and thus,
stellar ejections, further weakening both radiative and mechanical feedback
(Section 3.2), which thus may be insufficient to suppress ongoing star
formation. This leads to an increase in the star formation efficiency, star
formation rate, and timescale for star formation in a given region (e.g.,
Shima et al., 2017). It is consistent with the higher star formation
efficiencies seen in super star clusters (e.g., Turner et al., 2015; Herrera &
Boulanger, 2017; Oey et al., 2017), and it has been linked to the formation of
multiple stellar populations found in globular clusters (Krause et al., 2012;
Lochhaas & Thompson, 2017; Silich & Tenorio-Tagle, 2018).

Additionally, the standard paradigm for Lyman-continuum (LyC) escape from
starburst regions assumes that mechanically driven superwinds clear channels
in the ISM allowing LyC to travel without being absorbed (e.g., Heckman et
al., 2001). Our new model for delayed superwinds poses a problem for this
scenario of LyC escape, since at age $\sim$ 10 Myr, the emission rate of LyC
photons is $>100\times$ lower than at unevolved times (e.g., Leitherer et al.,
2014). Hence there must be another mechanism to create channels for LyC escape
in young, gas-rich conditions. Jaskot et al. (2019) propose that large
quantities of retained gas naturally cool and clump in the absence of strong
mechanical feedback, and therefore create gaps between the clumps, providing
channels for LyC to escape. This scenario is consistent with the “picket
fence” geometry that is often invoked for LyC emitters (Heckman et al., 2001,
2011; Rivera-Thorsen et al., 2017). It is also consistent with simulatioms by,
e.g., Rogers & Pittard (2013) and Dale et al. (2013), who find that on the
order of 50% or more of LyC photons can escape from star-forming giant
molecular clouds due to their inhomogeneous, clumpy nature and radiation-
dominated feedback. Moreover, Kimm et al. (2019) find that LyC escape is
enhanced in metal-poor clouds, in particular.

Observations of the local starburst Mrk 71-A appear to support this scenario.
This object provides the strongest evidence of catastrophic cooling where
adiabatic mechanical feedback is suppressed, as evidenced by the gas
kinematics (Komarova et al., 2021; Oey et al., 2017) and direct observation of
strong radiative cooling (Oey et al., 2023). Komarova et al. (2021) find that
LyC radiation drives a fast superwind out to hundreds of pc from the parent
SSC in this object. This strongly suggests that the radiation is able to
escape even further beyond this region and is therefore optically thin,
despite the suppression of energy-driven mechanical feedback. Since the SSC is
obscured by high-density gas, including molecular gas (Oey et al., 2017), the
presence of the LyC-driven wind therefore implies that the radiation is able
to escape through gaps in this gas, consistent with the model of Jaskot et al.
(2019).

A more straightforward consequence of delayed mechanical feedback is that the
total mechanical energy from a given cluster will be reduced. In Figure 4 we
show the total cumulative energy of the restricted SN model relative to the
classical solar model and the subsolar, unrestricted SN model. For the first
10 Myr, the energy from the restricted SN model is just 10% of the classically
expected solar model. Around this age, the SNe begin to explode and quickly
dominate the total energy. However, while the total mechanical energy in the
metal-poor models is lower than at $\rm Z_{\odot}$, the reduction is less than
a factor of two, and therefore order-of-magnitude estimates for mechanical
feedback are still valid.

However, the fact that it is effectively delayed for 10 Myr may have
fundamental consequences. For example, delayed SN feedback may resolve the
superbubble growth-rate discrepancy (e.g., Oey, 2009), in which superbubbles
around OB associations in the Magellanic Clouds and the Milky Way appear to be
too small for their observed stellar populations (e.g., Oey, 1995, 1996;
Cooper et al., 2004; Smith & Wang, 2004). This discrepancy could be resolved
if the mechanical luminosity was reduced by a factor of ten (Oey, 1996).
Figure 1 shows that excluding SNe from the first $\sim$ 10 Myr indeed reduces
the mechanical power by about the right amount during this early period when
stellar winds dominate and O stars are prevalent. The cited studies of objects
in the Magellanic Clouds and Milky Way all have ages in this range. Similarly,
if a given cluster’s mechanical power is overestimated, then superbubble ages
are correspondingly underestimated for given observed radii. This is
especially true for objects estimated to be $<15$ Myr old.

On a global scale, the porosity of the neutral ISM will be correspondingly
reduced if superbubbles are smaller (Oey & Clarke, 1997; Clarke & Oey, 2002).
Simplistically, there will be $\sim$ 40% less hot gas generated than expected
from prior models, modestly affecting the phase balance of the ISM.
Interestingly, the observed ISM porosities of Local Group galaxies estimated
by Oey & Clarke (1997) tend to be lower than the predicted values based on the
observed H ii region luminosity function. The reduction in hot gas and
superwinds may be exacerbated by radiative cooling enhanced by weak feedback
(e.g., Danehkar et al., 2022).

Our study complements the large body of work simulating the effects of SN
feedback on their host galaxies (see, e.g., Keller et al., 2022, and
references therein). Keller & Kruijssen (2022) specifically explore how SN
parameters, including the time of SN onset and the duration of SNe, affect the
regulation of star formation and galactic outflows. They find that longer
delay times indeed enhance the star formation efficiency of individual clouds
as noted above. Based on individualized timing and location of momentum,
energy, and chemical enrichment from stars, Andersson et al. (2023) agree that
reduced mechanical feedback leads to colder and more fragmented disks and thus
much higher star formation rates. Semenov et al. (2021) and Keller et al.
(2022) find similar results for the presence or absence of early, pre-SN
feedback, which have significant effects on the ISM structure, subsequent star
formation, and nature of superwinds. Gutcke et al. (2021) find that allowing
for variable SN feedback reduces the total energy, and thus dwarf galaxies
will expel slightly less gas and metals. They confirm that more spatially
distributed SNe inhibit the development of superwind outflows (Clarke & Oey,
2002) and mass loading; this effect is enhanced when progenitor stars are
ejected from clusters.

We have shown that all of these effects are especially prevalent in metal-
poor, dwarf galaxies, which therefore may explain why dwarf irregular galaxies
have such large star-forming complexes and high specific star-formation rates.
These processes may also be linked to the compactness of blue compact dwarf
galaxies and Green Peas, many of which appear to be responsible for Lyman
continuum emission (e.g., Flury et al., 2022; Jaskot et al., 2019). Weak
mechanical feedback is also suggested to be a driving factor in star formation
observed at cosmic dawn in JWST observations (Dekel et al., 2023).

###  4.2 Element Yields and Abundances

Figure 5:  Production of C, N, O, Mg, Si and Fe by number over time, for the
three model populations of $10^{6}\ \rm M_{\odot}$. Line types are as in
Figure 3.  Figure 6: Cumulative production of C, N, O, and Fe for the models
at subsolar metallicity. Dashed and solid lines show unrestricted and
restricted SN models, respectively.

Table 1: Element YieldsaaValues are for a $10^{6}\ \rm M_{\odot}$ Starburst99 population at the time when SN feedback ends at 46.9 Myr. | Model | C | N | ObbThe total yield of oxygen by number from the subsolar, unrestricted SNe model is 9.14e59; and for the solar, classical model it is 4.84e59. | Mg | Si | S | Fe
---|---|---|---|---|---|---|---|---
$N$(X, res) / $N$(X, unr)ccRatio of yield produced by subsolar, restricted SNe model relative to subsolar, unrestricted SNe model. | Restricted/Unrestricted | 0.492 | 0.582 | 0.209 | 0.207 | 0.459 | 0.498 | 0.856
| Solar, Classical | 0.479 | 0.087 | 1.00 | 0.039 | 0.059 | 0.027 | 0.022
X/O ddTotal yield by number of element X relative to oxygen for each model.  | Subsolar, Unrestricted | 0.181 | 0.013 | 1.00 | 0.038 | 0.045 | 0.018 | 0.028
| Subsolar, Restricted SN | 0.426 | 0.036 | 1.00 | 0.037 | 0.098 | 0.043 | 0.116
| Solar Classical | –0.059 | –0.200 | 0.000 | –0.321 | –0.051 | 0.007 | –0.475
$\mathrm{[X/O]}$eeLogarithmic ratio from above, relative to solar photospheric elemental abundances (Asplund et al., 2009). | Subsolar, Unrestricted | –0.481 | –1.032 | 0.000 | –0.335 | –0.169 | –0.171 | –0.358
| Subsolar Restricted SN | –0.111 | –0.589 | 0.000 | –0.341 | 0.171 | 0.204 | 0.254

Under the restricted SN scenario, the SN nucleosynthesis rate will be somewhat
lower than generally expected, causing galactic chemical evolution to take
place a bit more slowly and with modified element enrichment patterns. In
particular, the $\alpha$/Fe enrichment rate will be slower, since the more
massive stars are those that dominate $\alpha$-element yields. Eliminating SNe
from the upper IMF also affects the relative element yields. Figure 5 shows
the production of C, N, O, Mg, Si, and Fe during the modeled timeframe for our
three models. The Starburst99 SN yields are from Woosley & Weaver (1995), and
stellar wind yields are from the Geneva evolution models. Table 1 gives the
total yields for all elements calculated by Starburst99, relative to O, for
our model populations. The first row shows the yield reduction for the
subsolar-metallicity, restricted SNe model relative to the unrestricted model
where all massive stars explode. Additionally, Figure 6 shows the cumulative
production of C, N, O, and Fe at subsolar metallicity, comparing the
restricted and unrestricted SN models.

The data show that restricting the range of SN progenitors causes significant
changes in production among the shown elements, and these may have noticeable
effects on abundance patterns of $\alpha$-elements and other species due to
massive stars. In particular, O and Mg are produced at only 20% the rate for
full-IMF SNe (Table 1), since they are disproportionately generated by the
most massive stars. This is more than a factor of 2 below the typical
reduction factors for other elements. Interestingly, standard galactic
chemical evolution models for the Milky Way slightly overpredict the solar O
abundance relative to other species (see, e.g., review by Prantzos, 2008). An
underproduction of O might also be relevant to the enhanced N/O ratios seen
for young systems dominated by primary N evolution (see, e.g., review by
Maiolino & Mannucci, 2019), and similar enhancements in C/O at low metallicity
are suggested to be linked to the same processes dominating early N evolution
(e.g., Maiolino & Mannucci, 2019; Berg et al., 2016).

On the other hand, the Fe yield changes the least, with a production rate of
86% that of unrestricted SNe. Since Fe production is dominated by Type Ia SNe,
massive-star production effects on its long-term chemical abundance patterns
is further minimized. We also note that the effects of suppressed feedback are
likely unimportant for the interpretation of abundances in extremely metal-
poor (EMP) stars. Although these are dominated by core-collapse SN production,
the interpretation is that they reflect the products of individual SN events
(e.g., Frebel & Norris, 2015), and therefore the collective production of a
young population, as modeled here, is not relevant. Since the number of SNe is
dominated by the lower-mass range of progenitors according to the IMF, the
effect of changing the maximum SN progenitor mass does not have a strong
effect on galactic chemical evolution. As noted above, it results in changes
on the order of 2 – 3 to some element yields, which is modest relative to
evolutionary abundance patterns. However, as shown in Table 1 and Figure 6,
these effects may still be significant. More comprehensive investigation,
including the production of other elements, is needed to fully understand the
effect of restricting the range of SN progenitors.

###  4.3 Uncertainties

The scenario we have presented is subject to a number of uncertainties that
affect the timescale for the onset of SN feedback and magnitude of preceding
stellar wind feedback. The main source of uncertainty centers on which stars
successfully explode as core-collapse SNe. While there is a consensus that
most metal-poor high-mass stars collapse directly to BHs without SN explosions
(e.g., Zhang et al., 2008; O’Connor & Ott, 2011; Sukhbold et al., 2016; Müller
et al., 2016; Patton & Sukhbold, 2020), exactly which progenitor masses
explode and why has yet to be definitively determined. O’Connor & Ott (2011)
find that a progenitor’s core compactness at bounce determines its final fate.
At low metallicities, this parameter is what causes the failure of stars more
massive than $\sim$20 $\rm M_{\odot}$ to explode. Ertl et al. (2016) find a
related explosion criterion that produces similar results, and finds that only
$\sim$10% of stars more massive than 20 $\rm M_{\odot}$ generate SNe (Sukhbold
et al., 2016). Keller & Kruijssen (2022) also stress the importance of the
minimum-mass SN progenitor, which strongly influences the total energy and
momentum injected by a given IMF. The stellar structure, explosion mechanics,
and progenitor mass range are also important for nucleosynthetic yields (e.g.,
Prantzos, 2008).

There are also certain mass ranges that tend to explode. Sukhbold et al.
(2016) find that SN progenitors less massive than 15 $\rm M_{\odot}$ explode
easily, while those in the ranges 15 – 23 $\rm M_{\odot}$, 27 – 30 $\rm
M_{\odot}$, or $>35\ \rm M_{\odot}$ explode rarely. For their one-dimensional
core-collapse models, the vast majority of SN progenitors having masses $>20\
\rm M_{\odot}$ do not explode. We adopted this value as a threshold for our
simple parameterization above that assumes all stars with higher masses
collapse directly into black holes. On the other hand, 3-D models show higher
turbulence and convection, which may enhance explodability (Fields & Couch,
2021).

Moreover, most models of explodability agree that the masses of exploding
stars are not a continuous distribution. Although not fully understood yet,
the explosion mechanism of core-collapse supernovae is thought to be
inherently stochastic (e.g., Cardall & Budiardja, 2016). This introduces
variance into the explosion timescale, yields, and SN mass threshold, so the
start of CCSN feedback will be more gradual than modeled in Figure 1, and some
SNe are expected to occur before 10 Myr.

In addition, very massive stars are predicted to end their lives in rare,
energetic ($<10^{53}$ erg) pair-instability supernovae (PISNe). Heger &
Woosley (2002) find that stars with helium core masses 64 – 133 $\rm
M_{\odot}$ produce PISNe. This corresponds to initial masses of 140 – 260 $\rm
M_{\odot}$, of which we have $\sim 100$ in our 106 $\rm M_{\odot}$ cluster
(Kasen et al., 2011; Heger et al., 2003; Hirschi, 2017). If these predictions
are correct, this would produce significant mechanical luminosity from the
cluster at early ages. However, a single PISN event has yet to be reliably
identified, even with $>1,000$ SNe detected per year and a relative event rate
of PISNe to CCSNe of 1%. Takahashi (2018) therefore suggests that there may be
fewer PISNe than expected due to shell convection occurring earlier in the
core carbon-burning phase, whereby PISN progenitors can avoid pair-creation
instability.

Moreover, there are still significant uncertainties in stellar wind
parameters, especially at low metallicity. Uncertain mass-loss rates and wind
velocities are a major problem in creating accurate stellar evolution models
and population synthesis models. The most commonly used formula for mass loss
is that of Vink et al. (2001), which is now believed to be an overestimate.
Accounting for clumping and wind hydrodynamics has been shown to lower
theoretical mass-loss rates by at least factor of 2 – 3 (Bouret et al., 2012;
Šurlan et al., 2013; Puls et al., 2008). However, UV spectral observations of
O-stars in the massive young SMC regions NGC 346 and SMC-SGS 1 show even more
dramatic mass-loss rate reductions by factors closer to an order of magnitude
or more (Rickard et al., 2022; Ramachandran et al., 2019) from the theoretical
values of Vink et al. (2001).

Another important uncertainty originates from the omission of binary stars
from our analysis. Accounting for massive binary evolution will extend the
lives of binary mass gainers and therefore add SNe at later ages. It will also
increase the numbers of HMXBs and ULXs, and their feedback. We suggested above
(Section 3.1) that neither of these effects will significantly change the weak
mechanical feedback at early times, but further study is needed to clarify
their contribution. Massive, interacting binaries lead to increased LyC
emission and stellar winds from stripped stars, possibly increasing both
radiative and mechanical feedback. However binaries also drive ejection of
massive stars from their clusters, which is likely to offset this effect.

Furthermore, binarity is now believed to dominate massive star evolution.
Binaries dominate dynamical processes leading to stellar ejections, and
further work is needed to quantify the loss of mechanical feedback due to this
effect, which, as we argued above, is likely substantial. Binary mass transfer
will greatly increase rotation velocities of mass gainers, while also greatly
reducing the masses of donors. The SB99 models have only two stellar
rotational velocities, 0 and 40% of the ZAMS break-up velocity. As is evident
in Figure 4, faster rotating stars further delay the onset of mechanical
feedback. Binary mass transfer could cause much higher rotation velocities,
which would thus further shift the start of strong mechanical feedback to
somewhat later times. Binary mergers could also affect the mechanics and
likelihood of SN explosions and their nucleosynthetic yields.

##  5 Conclusion

In summary, massive-star feedback at low metallicity differs greatly from the
classical paradigm at solar metallicity. At low metallicity, stellar winds are
weak, and the more massive stars fail to explode as core-collapse SNe. We have
compared the evolution of mechanical luminosity and momentum injection for low
metallicity models to those predicted by the classical, $\rm Z_{\odot}$
feedback paradigm. Our restricted SNe model limits SNe to progenitor masses
$<20\ \rm M_{\odot}$, as compared to the classical, unrestricted limit. We
find that low metallicity Starburst99 models predict that mechanical feedback
is effectively delayed by roughly 10 Myr.

We additionally discussed the contribution of HMXBs to our low metallicity,
delayed feedback model. We found that accretion-driven feedback could slightly
increase the mechanical luminosity of the cluster only between the ages 5-10
Myr, but the order-of-magnitude reduction during this time remains.

Furthermore, dynamical mechanisms remove stars from clusters, reducing their
mechanical feedback contribution. This is often an overlooked, but likely
significant process. The effect is enhanced for clusters that are mass-
segregated, dense, have high binary fractions, and have moderate masses (Oh et
al., 2015). Such clusters at low metallicity will deviate the most from the
classical mechanical feedback paradigm. For example, the moderately massive
and densest cluster modeled by Oh & Kroupa (2016) ejected 50% of its O-stars
by 3 Myr. A potentially important process that remains to be explored is that
gas retention due to weak feedback likely promotes ejection of OB stars,
exacerbating the effect. This occurs because gas retention further promotes
mass segregation and high cluster densities. Accounting for the dynamical
mechanisms that remove stars will thus further decrease the expected total
mechanical feedback of a given cluster.

A delay in the onset of mechanical feedback implies that radiation dominates
over mechanical feedback at early ages. This corresponds to the scenario where
mechanically driven superwinds are suppressed by catastrophic cooling or
pressure confinement, as has been observed in several local starburst systems.
This has a variety of important implications. There is increased gas
retention, which increases rate and timescale of star formation. This is
consistent with the higher star formation efficiencies in super star clusters
and may be linked to the multiple stellar populations in globular clusters.
Delayed feedback may also offer a simple explanation for why metal-poor, dwarf
irregular galaxies have such large star-forming complexes. Retention of dense
gas near super star clusters likely leads to clumping, thereby generating the
picket-fence geometry that may be conducive to LyC escape through inter-clump
regions.

Overestimated early mechanical luminosity can explain why superbubbles are
often found to be too small for their observed parent stellar populations.
Similarly, superbubble ages that are inferred from the observed radii and
stellar populations are therefore too young. The cumulative, large-scale
effect of reduced initial mechanical luminosity is to reduce the total
integrated energy and production of hot gas from clusters by $\sim$40% and to
reduce the total momentum injected by 75% relative to the classical model.
This correspondingly, modestly modifies the phase balance of the ISM and CGM.
It also has a modest effect on galactic chemical evolution by slowing the
$\alpha$/Fe evolution rate, and slightly modifying abundance patterns. In
particular, the production of O is reduced by a factor $\gtrsim 2$ relative to
other elements.

These effects are subject to a number of uncertainties, in particular,
involving the stellar progenitors that successfully explode as core-collapse
SNe; and the myriad effects of binary evolution, which is unaccounted for in
our models. However, this model of delayed mechanical feedback cohesively
explains many observations for metal-poor star-forming regions and starburst
galaxies, including the character of star formation in metal-poor, dwarf
galaxies and starbursts. Since the associated feedback processes play a key
role in our universe, both at early epochs and the present, this effect is
broadly relevant and worth deeper investigation.

We wish to thank Carl Fields, Edmund Hodges-Kluck, Anne Jaskot, Evan Kirby,
Lena Komarova, Claus Leitherer, and Vadim Semenov for helpful comments and
discussions. Additionally, we thank the anonymous referee for valuable
suggestions which improved the depth of the paper. This work was supported by
NASA HST-GO-16261 and the University of Michigan.

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