# Effects of feedback on galaxies in the VELA simulations: elongation, clumps
and compaction

Daniel Ceverino1,2, Nir Mandelker3,4, Gregory F. Snyder5, Sharon Lapiner3,
Avishai Dekel3,6, Joel Primack7, Omri Ginzburg3, Sean Larkin7
1Departamento de Fisica Teorica, Modulo 8, Facultad de Ciencias, Universidad
Autonoma de Madrid, 28049 Madrid, Spain
2CIAFF, Facultad de Ciencias, Universidad Autonoma de Madrid, 28049 Madrid,
Spain
3Centre for Astrophysics and Planetary Science, Racah Institute of Physics,
The Hebrew University, Jerusalem 91904, Israel
4Kavli Institute for Theoretical Physics, Kohn Hall, Santa Barbara, CA 93106,
USA
5Space Telescope Science Institute, 3700 San Martin Dr, Baltimore, MD 21218,
USA
6SCIPP, University of California, Santa Cruz, CA 95064, USA
7Department of Physics, University of California, Santa Cruz, CA, 95064, USA
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The evolution of star-forming galaxies at high redshifts is very sensitive to
the strength and nature of stellar feedback. Using two sets of cosmological,
zoom-in simulations from the VELA suite, we compare the effects of two
different models of feedback: with and without kinetic feedback. At a fixed
halo mass and redshift, the stellar mass is reduced by a factor of $\sim$1-3
in the models with stronger feedback, so the stellar-mass-halo-mass relation
is in better agreement with abundance matching results. On the other hand,
galaxy elongation is robust against feedback strength. At a fixed stellar
mass, $M_{*}<10^{10}\ {\rm M}_{\odot}$, galaxies are more elongated in the
strong-feedback case. More massive, star-forming discs with high surface
densities form giant clumps. However, the population of round, compact, old
(age${}_{c}>300\ {\rm Myr}$), quenched, stellar (or gas-poor) clumps is absent
in the model with strong feedback. On the other hand, giant star-forming
clumps with intermediate ages (age${}_{c}=100-300\ {\rm Myr}$) can survive for
several disc dynamical times, independently of feedback strength. The
evolution through compaction followed by quenching in the plane of central
surface density and specific star-formation rate is similar under the two
feedback models.

###### keywords:

galaxies: evolution – galaxies: formation – galaxies: high-redshift

††pubyear: 2020††pagerange: Effects of feedback on galaxies in the VELA
simulations: elongation, clumps and compaction–Effects of feedback on galaxies
in the VELA simulations: elongation, clumps and compaction

##  1 Introduction

Galaxies at high redshifts, $z\geq 1$, generate high levels of star formation,
especially during the cosmic noon era, $z\simeq 1-4$ (e.g., Whitaker et al.,
2012; Madau & Dickinson, 2014; Förster Schreiber & Wuyts, 2020). The
importance of stellar feedback from massive stars on galaxy-wide properties
reaches a maximum during this epoch. The injection of energy, momentum, mass
and metals has important consequences for the self-regulation of star
formation (Dekel & Silk, 1986; Governato et al., 2007; Ceverino et al., 2014;
Hopkins et al., 2014; Agertz & Kravtsov, 2015), galactic outflows (Oppenheimer
& Davé, 2008; Hopkins et al., 2012a; Muratov et al., 2015; Ceverino et al.,
2016b), and metal enrichment inside and outside galaxies (Oppenheimer & Davé,
2006; Ceverino et al., 2016a; Langan et al., 2020). Other important phenomena
related to galaxy formation at high-z may also be sensitive to feedback:
galaxy elongation, the formation and evolution of giant clumps within massive
star-forming discs, and the compaction and quenching of compact galaxies.

Observations that estimate the intrinsic shapes of the stellar components of
high-z galaxies find that the distribution of projected axis ratios of high-z
samples at $z=1.5-4$ is inconsistent with a population of randomly oriented
disc galaxies (Law et al., 2012; van der Wel et al., 2014; Zhang et al.,
2019). They conclude that the intrinsic shapes of low-mass galaxies,
$M_{*}<10^{10}\ M_{\odot}$, are strongly triaxial. Therefore, galaxies evolve
from prolate to oblate as they build their stellar mass. This build-up is
regulated by feedback. Therefore, this morphological transformation may depend
on the feedback strength.

From the theoretical side, elongated galaxies are predicted within the current
$\Lambda$ cold dark matter ($\Lambda$CDM) paradigm (Ceverino et al., 2015;
Tomassetti et al., 2016; Meng et al., 2019; Pillepich et al., 2019).
Prolateness or triaxiality are common properties of dark matter (DM) halos in
N-body-only simulations (Jing & Suto, 2002; Allgood et al., 2006; Schneider et
al., 2012, and references therein). A general result is that halos at a given
mass scale are more prolate at earlier times. At the same time, the shape of
the inner DM halo could influence the shape of the central galaxy (Dekel &
Shlosman, 1983) through the gravitational potential. If the galaxy is
dominated by a non-axisymmetric, non-rotating potential, the stellar orbits
are elongated along the major axis of the triaxial halo (Binney & Tremaine,
2008, sections 3.3.1 and 3.4.1). Therefore, the degree and evolution of
elongation depend on the relative contribution of dark matter to the inner
gravitational potential. This is related to the galactic stellar-to-DM
fraction, which is sensitive to feedback.

A large fraction of massive, baryon-dominated galaxies at high-z are confirmed
to be rotating but turbulent discs (Genzel et al., 2006; Förster Schreiber et
al., 2009; Wisnioski et al., 2015). Many of these discs are broken into UV-
bright giant clumps that each account for a few percent of the disc mass and
at least 8% of the UV light (Elmegreen & Elmegreen, 2005; Genzel et al., 2008;
Guo et al., 2015, 2018). They are massive starburst regions, $M_{*}\simeq
10^{7}-10^{9}\ M_{\odot}$, with stellar ages of around 100-200 Myr, consistent
with recent episodes of star-formation (Wuyts et al., 2012). However
observational estimates of the basic properties of clumps are still uncertain
and they require a careful consideration of the systematic errors, using for
example tools from machine learning (Huertas-Company et al., 2020; Ginzburg et
al., 2021).

According to our understanding of high-z galaxy formation, these turbulent
discs suffer violent disc instabilities (VDI), in which the strong inflow of
cold gas (Dekel et al., 2009a) maintains high disc surface densities and
marginally-unstable discs (Dekel et al., 2009b). In this scenario, the disc
fragments into giant clumps around the Toomre mass scale (Toomre, 1964; Inoue
et al., 2016). This has been simulated in idealized conditions (Noguchi, 1999;
Bournaud & Elmegreen, 2009; Hopkins et al., 2012b), and in cosmological
simulations of galaxy formation (Agertz et al., 2009; Ceverino et al., 2010).

The lifetime of giant clumps is very sensitive to the strength and nature of
stellar feedback. This has generated a debate about the final fate of these
clumps. Simulations of moderate feedback have shown a population of clumps
that live for many orbital periods, with lifetimes upto 1 Gyr (Ceverino et
al., 2010; Mandelker et al., 2014, M17). On the other hand, simulations with
stronger feedback disrupt clumps in much shorter times scales, 10-50 Myr
(Genel et al., 2012; Oklopčić et al., 2017; Buck et al., 2017). These
simulations use very different models of feedback, acting on different spatial
and temporal scales. Therefore, their comparison is not straightforward.

VDI induces gas inflow within the disc, although clump migration accounts for
less than 25% of the inflow (Zolotov et al., 2015). If the gas inflow rate,
mostly from wet mergers and counter-rotating streams is much higher than the
disc star-formation rate (SFR), this dissipative process leads to wet
compaction (Dekel & Burkert, 2014). This is a characteristic evolution pattern
of high-z galaxies, composed by different phases (Zolotov et al., 2015).
First, galaxies perturbed by gas-rich mergers, VDI or counter-rotating streams
undergo a dissipative contraction into compact, star-forming galaxies (Barro
et al., 2013) or massive bulges (Costantin et al., 2021). The increase of the
stellar surface density within the inner 1-kpc radius, $\Sigma_{1}$, occurs at
roughly constant specific SFR. Secondly, after compaction, there is a inside-
out quenching of star formation into a compact, quiescent galaxy (Tacchella et
al., 2016b). This is driven by a fast gas consumption and strong outflows and
it occurs at constant $\Sigma_{1}$. Finally, a long-term suppression of gas
supply is needed to maintain quenching, through halo quenching (Birnboim &
Dekel, 2003) or AGN maintenance mode (Croton et al., 2006; Cattaneo et al.,
2009; Fabian, 2012). These processes are all sensitive to the strength and
timescales of stellar feedback.

Stellar feedback is a mix of many different processes, from supernova
explosions to radiation pressure. By adding new mechanisms, we can increase
the strength of feedback and quantify its effect on the above processes of
high-z galaxy formation: galaxy elongation (Ceverino et al., 2015, C15
hereafter), giant clumps (Mandelker et al., 2017, M17 hereafter), and
compaction (Zolotov et al., 2015, Z15 hereafter). In this numerical
experiment, we are going to compare two sets of cosmological simulations from
the VELA suite with different models of feedback. This comparison can give us
some insights about the trends with feedback strength.

Our first set of 35 simulated galaxies to be studied in detail was introduced
in Ceverino et al. (2014) and Z15 and it is here renamed as VELA-3. The second
set, dubbed VELA-6, includes the injection of momentum from the expansion of
supernovae shells from clustered supernovae (Ceverino et al., 2017a). Section
§2 summarises both models in detail. Section §3 describes the effect of
feedback on the stellar-mass-halo-mass relation. Sections §4, §5 and §6 are
devoted to galaxy elongation, clumps and compaction respectively. Finally,
Section §7 ends with the summary and discussion.

##  2 Simulations

Table 1: Properties of the main progenitors in VELA-3 and VELA-6 simulations at $z=2$ and $z_{\rm last}$. The unit for virial radius, $R_{\rm v}$ is proper kpc. Virial masses, $M_{\rm vir}$, have units of $10^{12}\ {\rm M}_{\odot}$ and stellar masses, $M_{*}$, have units of $10^{10}\ {\rm M}_{\odot}$. At a fixed halo mass and redshift, the stellar mass is reduced by a factor of $\sim$1-3 in models with stronger feedback.  |  |  |  |  | VELA-3 |  |  |  |  |  |  | VELA-6 |  |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
Run | $z_{\rm last}$ | $R_{\rm v}$ | $M_{\rm vir}$ | $M_{*}$ | $R_{\rm v}(z=2)$ | $M_{\rm vir}(z=2)$ | $M_{*}(z=2)$ | $z_{\rm last}$ | $R_{\rm v}$ | $M_{\rm vir}$ | $M_{*}$ | $R_{\rm v}(z=2)$ | $M_{\rm vir}(z=2)$ | $M_{*}(z=2)$
V01 | 1 | 124 | 0.48 | 1.5 | 58 | 0.16 | 0.2 | 1 | 122 | 0.46 | 0.79 | 57 | 0.15 | 0.057
V02 | 1 | 115 | 0.39 | 0.95 | 55 | 0.13 | 0.16 | 1 | 113 | 0.37 | 0.70 | 54 | 0.13 | 0.067
V03 | 1 | 108 | 0.32 | 1.0 | 56 | 0.13 | 0.38 | 1 | 108 | 0.32 | 0.49 | 55 | 0.13 | 0.10
V04 | 1 | 90 | 0.18 | 0.35 | 53 | 0.12 | 0.082 | 1 | 88 | 0.17 | 0.14 | 53 | 0.12 | 0.046
V05 | 1 | 83 | 0.14 | 0.27 | 44 | 0.070 | 0.072 | 1 | 83 | 0.15 | 0.095 | 43 | 0.063 | 0.032
V06 | 1.7 | 109 | 0.74 | 2.6 | 88 | 0.54 | 2.1 | 1 | 200 | 1.9 | 4.4 | 93 | 0.63 | 0.81
V07 | 1.5 | 145 | 1.4 | 7.3 | 104 | 0.89 | 5.7 | 1.5 | 150 | 1.5 | 7.4 | 107 | 0.97 | 4.6
V08 | 0.9 | 182 | 1.3 | 4.4 | 71 | 0.28 | 0.35 | 0.9 | 183 | 1.3 | 2.9 | 71 | 0.28 | 0.11
V09 | 1.5 | 121 | 0.83 | 4.3 | 71 | 0.28 | 1.0 | 0.8 | 209 | 1.7 | 5.1 | 64 | 0.21 | 0.50
V10 | 0.8 | 159 | 0.76 | 3.4 | 55 | 0.13 | 0.60 | 0.8 | 182 | 1.14 | 1.7 | 55 | 0.13 | 0.37
V11 | 0.8 | 106 | 0.37 | 1.6 | 70 | 0.27 | 0.76 | 0.8 | 158 | 0.74 | 0.73 | 68 | 0.25 | 0.37
V12 | 1.5 | 86 | 0.29 | 2.1 | 69 | 0.26 | 1.9 | 0.8 | 159 | 0.76 | 2.8 | 76 | 0.35 | 1.5
V13 | 1.5 | 108 | 0.59 | 2.2 | 73 | 0.30 | 0.57 | 0.8 | 169 | 0.92 | 3.5 | 72 | 0.29 | 0.30
V14 | 1.8 | 86 | 0.39 | 2.3 | 76 | 0.36 | 1.3 | 0.8 | 145 | 0.58 | 2.3 | 76 | 0.34 | 0.47
V15 | 0.8 | 123 | 0.35 | 1.5 | 53 | 0.12 | 0.51 | 0.8 | 125 | 0.37 | 0.52 | 53 | 0.12 | 0.18
V16 | 3.2 | 63 | 0.50 | 4.1 | - | - | - | 2.3 | 84 | 0.62 | 3.6 | - | - | -
V17 | 2.2 | 106 | 1.1 | 8.4 | - | - | - | 2.2 | 108 | 1.2 | 4.7 | - | - | -
V18 | - | - | - | - | - | - | - | 2.2 | 79 | 4.8 | 2.2 | - | - | -
V19 | 2.4 | 91 | 0.87 | 4.4 | - | - | - | 2.3 | 96 | 0.92 | 4.1 | - | - | -
V20 | 1.3 | 146 | 1.1 | 7.5 | 87 | 0.53 | 3.5 | 1.3 | 148 | 1.1 | 5.6 | 101 | 0.82 | 4.0
V21 | 1 | 151 | 0.88 | 6.5 | 92 | 0.62 | 4.0 | 1 | 156 | 0.98 | 5.7 | 94 | 0.65 | 3.3
V22 | 1 | 136 | 0.63 | 4.6 | 85 | 0.50 | 4.4 | 1 | 150 | 0.86 | 4.4 | 88 | 0.54 | 3.4
V23 | 1 | 123 | 0.47 | 2.5 | 57 | 0.15 | 0.76 | 1 | 122 | 0.46 | 1.4 | 57 | 0.15 | 0.47
V24 | 1.1 | 108 | 0.36 | 2.1 | 70 | 0.28 | 0.87 | 1 | 117 | 0.41 | 1.5 | 69 | 0.27 | 0.65
V25 | 1 | 108 | 0.32 | 1.4 | 65 | 0.22 | 0.68 | 1 | 107 | 0.31 | 0.62 | 68 | 0.25 | 0.19
V26 | 1 | 120 | 0.44 | 2.2 | 77 | 0.36 | 1.6 | 1 | 120 | 0.44 | 1.6 | 76 | 0.35 | 1.1
V27 | 1 | 114 | 0.38 | 2.0 | 75 | 0.34 | 0.71 | 1 | 114 | 0.37 | 1.3 | 75 | 0.34 | 0.48
V28 | 1 | 96 | 0.22 | 0.49 | 63 | 0.20 | 0.18 | 1 | 94 | 0.21 | 0.30 | 63 | 0.20 | 0.082
V29 | 1 | 152 | 0.90 | 0.37 | 84 | 0.52 | 0.20 | 1 | 153 | 0.91 | 3.2 | 87 | 0.52 | 1.8
V30 | 1.9 | 76 | 0.32 | 1.6 | 73 | 0.31 | 1.6 | 1.8 | 80 | 0.34 | 1.2 | 73 | 0.32 | 1.1
V31 | 4.3 | 38 | 0.22 | 0.8 | - | - | - | 1.8 | 117 | 1.1 | 4.1 | 105 | 0.93 | 3.8
V32 | 2 | 90 | 0.6 | 2.7 | 90 | 0.6 | 2.7 | 2 | 101 | 0.82 | 2.2 | 101 | 0.82 | 2.2
V33 | 1.6 | 144 | 1.5 | 9.4 | 101 | 0.83 | 4.8 | 1.5 | 148 | 1.5 | 6.9 | 107 | 0.98 | 2.5
V34 | 1.8 | 97 | 0.62 | 1.9 | 86 | 0.34 | 0.76 | 2.4 | 66 | 0.34 | 0.32 | - | - | -
V35 | 3.5 | 37 | 0.14 | 0.49 | - | - | - | 3 | 48 | 0.2 | 0.23 | - | - | -
Figure 1: Ratio between stellar mass and virial mass at different redshifts.
At the same virial mass, VELA-6 (blue) have a factor $\sim$1-3 lower stellar
mass than VELA-3 (red), in better agreement with the results from abundance
matching (AM: Moster et al., 2013; Behroozi et al., 2013; Rodríguez-Puebla et
al., 2017; Moster et al., 2018; Behroozi et al., 2019) and other empirical
models at high redshift (BS15: Behroozi & Silk, 2015). Figure 2: Elongation
parameter (eq. 1) versus stellar mass for VELA-3 and VELA-6 at $z=1-3$, color
coded by the star-to-DM mass ratio within the half-mass radius. The elongation
decreases with increasing mass and mass ratio but the trend is weaker for
VELA-6. Galaxies are preferentially elongated (e>0.5) at
$M_{*}<10^{10}M_{\odot}$. More massive galaxies are not shown as they are
preferentially axialsymmetric.  Figure 3:  Three ortogonal projections (XY, XZ
and ZY) of the stellar surface density of the same galaxy (V04) in the VELA-6
(top two panels) and VELA-3 (bottom two panels) at $z=1$. The size of each
image is 20 kpc. VELA-6 galaxies are significantly more elongated, $a>b$, than
the VELA-3 counterparts. Figure 4: Two examples of face-on views of the same
galaxy (V11) in VELA-3 (top) and VELA-6 (bottom) datasets with the same
stellar mass, $M_{*}\simeq 6\times 10^{9}\ {\rm M}_{\odot}$, but at two
different redshifts. The VELA-3 example shows a small axysimmetric disc while
the VELA-6 case shows an elongated galaxy surrounded by a star-forming ring.
The size of the images is 100 kpc. The mock HST images (right) are roughly
rest-frame U-B-V bands.

The VELA-3 and VELA-6 simulations use the same set of initial conditions. They
only differ in their models of stellar feedback. These models have been
developed from a pure thermal feedback model (VELA-2) with the addition of
radiation pressure (VELA-3), photoheating/photoionization (VELA-4), and a
moderate trapping of infrared photons (VELA-5). The last model, VELA-6,
includes thermal, radiation pressure, moderate IR trapping and kinetic
feedback. The comparison between VELA-2 and VELA-3 was discussed in Ceverino
et al. (2014), Moody et al. (2014) and M17. Until now, VELA-3 has been our
standard set of simulations. In addition to the works already mentioned, these
simulations have been used to study metallicity drops (Ceverino et al.,
2016a), the velocities of warm outflows (Ceverino et al., 2016b), the link
between halo and galaxy spin (Jiang et al., 2019), to distinguish between
mergers and discs (Simons et al., 2019), to study star-formation laws (Dekel
et al., 2019), the mass threshold for galactic discs (Dekel et al., 2020a),
the origin of star-forming rings (Dekel et al., 2020b), circumgalactic medium
(Roca-Fàbrega et al., 2019; Strawn et al., 2021), and dynamical masses
estimates (Kretschmer et al., 2021). The comparison between VELA-3, VELA-4 and
VELA-5 yields very similar results. Therefore, in this paper we are going to
focus on the comparison between VELA-3 and VELA-6.

###  2.1 The Initial Conditions of VELA

VELA halos were drawn from N-body simulations with cosmological boxes of 10,
20 or 40 Mpc/h across, assuming a $\Lambda$CDM cosmology with $\Omega_{\rm
m}=0.27$, $\Omega_{\Lambda}=0.73$, $\Omega_{\rm b}=0.045$, $h=0.7$ and
$\sigma_{8}=0.82$. They were selected randomly in log $M_{\rm vir}$ in order
to cover a halo mass range between $M_{\rm vir}\sim 10^{11}$ and $\sim
10^{12}\ {\rm M}_{\odot}$ at $z=1-0.8$. Only ongoing major mergers at $z=1$
were excluded. This only discarded 10% of the halos. The selected halos were
filled with gas and refined to a much higher resolution on an adaptive mesh
within a zoom-in lagrangian volume that encompasses the mass within twice the
virial radius (Klypin et al., 2002). The initial conditions of these runs
contain between 6.4 to 46 $\times 10^{6}$ dark matter particles with a minimum
mass of $8.3\times 10^{4}\ {\rm M}_{\odot}$, while the particles representing
single stellar populations that were formed in the simulation have a minimum
mass of $10^{3}\ {\rm M}_{\odot}$. The best spatial resolution is between
17-35 proper pc. More details can be found in Ceverino et al. (2014) and
Zolotov et al. (2015).

###  2.2 ART

The ART code (Kravtsov et al., 1997; Kravtsov, 2003) accurately follows the
evolution of a gravitating N-body system and the Eulerian gas dynamics using
an AMR approach. Besides gravity and hydrodynamics, the code incorporates many
of the astrophysical processes relevant for galaxy formation. These processes,
representing subgrid physics, include gas cooling due to atomic hydrogen and
helium, metal and molecular hydrogen cooling, photoionisation heating by a
constant cosmological UV background with partial self-shielding, star
formation and feedback, as described in Ceverino & Klypin (2009), Ceverino et
al. (2010), and Ceverino et al. (2014).

###  2.3 Thermal Feedback

The model of thermal feedback assumes that each stellar particle acts as a
single stellar population and injects their mechanical luminosity from
supernovae and stellar winds as thermal heating. The model assumes a constant
heating rate over 40 Myr, motivated by the results from population synthesis
codes, such as STARBURST99 (Leitherer et al., 1999). More details and
discussions can be found in Ceverino & Klypin (2009).

###  2.4 Radiative Feedback

In addition to thermal-energy feedback, the simulations use radiative feedback
(Ceverino et al., 2014). This model adds a non-thermal pressure, radiation
pressure, to the total gas pressure in regions where ionising photons from
massive stars are produced and trapped. In the model used in VELA-3, named
RadPre in Ceverino et al. (2014), radiation pressure is included in the cells
(and their closest neighbours) that contain stellar particles younger than 5
Myr and whose gas column density exceeds $10^{21}\ \,{\rm cm}^{-2}.$ Instead,
VELA-6 uses the model RadPre_IR, which adds a moderate trapping of infrared
photons, only if the gas density in the host cell exceeds a threshold of 300
$\,{\rm cm}^{-3}$. More details can be found in Ceverino et al. (2014).

###  2.5 Kinetic feedback

In addition to radiative feedback, VELA-6 also includes the injection of
momentum coming from the (unresolved) expansion of gaseous shells from
supernovae and stellar winds (Ostriker & Shetty, 2011). A momentum of $10^{6}\
{\rm M}_{\odot}\,{\rm km}\,{\rm s}^{-1}$ per massive star (i.e per star more
massive than 8 ${\rm M}_{\odot}$) is injected at a constant rate over 40 Myr,
the lifetime of the lightest star that explodes as a core-collapsed
supernovae. The model also takes into account a factor 3 boost in the injected
momentum due to the clustering of supernovae (Gentry et al., 2017). The
injection of momentum is implemented in the form of a non-thermal pressure, as
described in Ceverino et al. (2017b).

##  3 Stellar-Mass-Halo-Mass Relation

One of the main effects of feedback is the self-regulation of the galaxy
formation efficiency (Ceverino et al., 2014; Hopkins et al., 2014, and
references therein). That efficiency can be quantified by the stellar-mass-
halo-mass (SMHM) relation. The halo mass is measured as the virial mass (Bryan
& Norman, 1998) and the stellar mass is computed within 10% of the virial
radius. Table 1 shows these properties at $z=2$ and at the last available
snapshot for VELA-3 and VELA-6 respectively. Figure 1 shows the SMHM ratio at
different redshifts. In general, that ratio decreases towards low masses, as
stellar feedback regulates star formation. There is a large scatter of about a
factor 2 around the average ratio, driven by the different mass accretion
histories (Moster et al., 2018). At a fixed halo mass, VELA-6 halos have a
factor $\sim$1-3 lower stellar mass than in VELA-3, due to their stronger
feedback. The biggest difference is concentrated at low masses, $M_{\rm
vir}\leq 10^{11}\ {\rm M}_{\odot}$, where stellar feedback is most efficient
(Dekel & Silk, 1986).

VELA-6 galaxies agree better with available results from models of abundance
matching (Moster et al., 2013; Behroozi et al., 2013; Rodríguez-Puebla et al.,
2017; Moster et al., 2018; Behroozi et al., 2019), and other empirical models
at high redshifts (Behroozi & Silk, 2015; Tacchella et al., 2018). We added an
uncertainty of a factor 2 in these models that takes into account systematic
differences due to different cosmology and IMF assumptions, as well as
uncertainties in the stellar mass estimates (Leja et al., 2019).

VELA-6 also agrees with the FirstLight simulations at $z\simeq 6$ (Ceverino et
al., 2017b), which use a similar feedback model but have twice better spatial
resolution. Therefore these overall results are independent of numerical
resolution. They are still sensitive to feedback. Only future simulations will
tell us whether we have reached model-independent values.

##  4 Elongation

The degree of intrinsic, 3D elongation of a galaxy can be quantified by the
elongation parameter, as defined in C15,

$e=\sqrt{1-(b/a)^{2}}$ (1)

where $a$ and $b$ are the major and intermediate axes of a 3D ellipsoidal
shell that fits the stellar iso-density surface at the galaxy 3D half-mass
radius, $R_{0.5}\simeq a$. Figure 2 shows elongation versus galaxy mass,
coloured by the stellar-to-DM mass ratio within $R_{0.5}$. The results of
VELA-3 were obtained in C15. These simulations show that a galaxy achieves a
high elongation if DM mass dominates over stellar mass within the galaxy. In
this case, the elongation of the DM halo dominates the gravitational
potential, which sets the galaxy elongation. As galaxy mass and halo mass
increases, the stellar fraction increases and the galaxy elongation decreases.
This is because baryons make rounder halos (Zemp et al., 2012), especially in
the inner parts, where baryons dominate the potential. VELA-6 shows a weaker
trend between elongation and mass, because star formation is less efficient at
a fixed halo mass.

At a fixed stellar mass, the mass fraction in DM is higher in VELA-6.
Therefore, they are more DM dominated and more elongated than VELA-3. That
difference is more striking for masses between $10^{9.5}$ and $10^{10}\ {\rm
M}_{\odot}$, where galaxies are preferentially more elongated ($e>0.5$) in
VELA-6 than in VELA-3.

Figure 3 shows stellar mass projections of the same galaxy (V04) at $z=1$ in
both suites. The XY projection coincides with the face-on view of the galaxy,
according to the angular momentum of the cold gas. The VELA-6 case shows a
typical elongated galaxy ($e=0.7$) of low stellar mass, $M_{*}=1.4\times
10^{9}\ M_{\odot}$. It is DM dominated within $R_{0.5}$,
$M_{*}(R_{0.5})/M_{\rm DM}(R_{0.5})=0.25$. This is similar to the case shown
in C15. The VELA-3 example is more massive, $M_{*}=3.5\times 10^{9}\
M_{\odot}$, and it shows a more oblate shape ($a\simeq b$), typical of a
massive, baryon-dominated galaxy with $M_{*}(R_{0.5})/M_{\rm
DM}(R_{0.5})=1.2$.

Figure 4 compares the same galaxy in the two datasets (V11) but now the galaxy
mass is the same, $M_{*}\simeq 6.5\times 10^{9}\ {\rm M}_{\odot}$. Therefore,
the selected snapshots have different redshifts. Both galaxies have roughly
the same luminosity but the VELA-6 case lives in a halo that is twice more
massive, $M_{\rm vir}=5.6\times 10^{11}\ {\rm M}_{\odot}$, than in the VELA-3
example. This drives a big difference in their stellar-to-DM mass fraction
within $R_{0.5}$. The VELA-6 case is DM-dominated, $M_{*}(R_{0.5})/M_{\rm
DM}(R_{0.5})=0.5$, while the contribution of baryons is much more relevant in
the VELA-3 example ($M_{*}(R_{0.5})/M_{\rm DM}(R_{0.5})=1$).

The galaxy in VELA-3 shows an oblate axysimmetric disc, as also shown in
Tomassetti et al. (2016). This is seen both in the stellar maps as well as in
the mock HST image, obtained with SUNRISE as described in Simons et al. (2019)
and Snyder et al. (2015). The VELA-6 case is far from axysimmetry ($e=0.8$ at
$R_{0.5}\simeq 3\,{\rm kpc}$). The mock data in rest-frame U-B-V bands shows
an elongated galaxy surrounded by a clumpy star-forming ring. The rest-frame
visible bands follow the elongated stellar shape while the rest-frame UV
traces the star-forming gas clumps of the gaseous disc.

##  5 Clumps

Figure 5: Face-on views of cold gas plus young stars, T$<1.5\times 10^{4}$ K
and $\rm{age}<100\,{\rm Myr}$ (top) and all stars (bottom) of V07 at $z\simeq
2$ for VELA-3 (left) and VELA-6 (right). Circles represent the disc radius as
defined in M17. Clumps in VELA-3 are significantly denser and rounder. Gas is
clumpy in both models but the stellar map in VELA-6 is much smoother than in
VELA-3.  Figure 6: Mock images in the HST F606W band (left) and JWST F277W
band (right) for VELA-3 (top) and VELA-6 (bottom) of the same galaxy from
Figure 5. The rest-frame UV is clumpy in both models. However, the rest-frame
near-IR is significantly less clumpy in models with stronger feedback.

Massive, $M_{*}\geq 10^{10}M_{\odot}$, galaxies develop a thick rotating disk,
which undergoes violent disk instability (Dekel et al., 2009b; Ceverino et
al., 2010) and the formation of giant in-situ clumps (Mandelker et al., 2014,
M17). We have used the clump finder described in M17 to generate catalogs of
clumps in VELA-3 and VELA-6. The finder uses a cloud-in-cell interpolation to
deposit mass from star particles and cold ($T<1.5\times 10^{4}$ K) gas cells
into a uniform 3D grid with a cell size of $\Delta=70$ pc. For each component,
it applies a gaussian filter to smooth the density field and it calculates a
density residual in each point, $\delta_{\rho}=(\rho-\rho_{\rm w})/\rho_{\rm
w}$, where $\rho$ and $\rho_{\rm w}$ are the original and smoothed fields.
Finally, it takes the maximum of the two residual values (stars or gas) at
each point. We define clumps as connected regions containing at least 8 grid
cells above a residual threshold, $\delta^{\rm min}_{\rho}=10$. More details
and a discussion of the sensitivity of results to parameter variations can be
found in M17. The final clump catalog contains the properties of regions with
stellar and/or gas densities that are at least 10 times higher than their
local surroundings.

###  5.1 Examples of clumpy galaxies

Figure 5 shows a massive, $M_{*}>10^{10}\ {\rm M}_{\odot}$, baryon-dominated
galaxy in the two datasets. The distribution of cold gas plus young stars
(T$<1.5\times 10^{4}$ K, $\rm{age}<100\,{\rm Myr}$) looks clumpy in both
cases. However, in VELA-3 there is a population of small and compact clumps
that is absent in VELA-6. The clumps with stronger feedback look more
irregular and elongated. The stellar distribution clearly shows dense and
round stellar overdensities in VELA-3. The stellar disc in VELA-6, where
feedback is stronger, is significantly less clumpy and the stellar clumps are
less prominent.

Young stars (and indirectly the star-forming gas) can be traced by rest-frame
UV, while the near-IR traces stellar mass. Figure 6 shows mock images of the
same typical $z\simeq 2$ galaxy shown in Figure 5. They are performed using
Sunrise. We created high resolution mock images for both the VELA-3 and VELA-6
simulations using the Sunrise dust radiative transfer code (Jonsson, 2006;
Jonsson et al., 2010). They are a follow up to earlier generations of VELA
mock images presented by Snyder et al. (2015) and Simons et al. (2019), now
publicly available in the Mikulski Archive for Space Telescopes (MAST) 111See
https://archive.stsci.edu/prepds/vela/. These mock images include face-on,
edge-on, and random viewing orientations. We simulated both a Milky-Way-like
dust model and an SMC-like dust model. We created images using a variety of
HST, JWST, and Roman broadband imaging filters, which make them suitable for
comparing with observations. We plan to submit these new mock images to MAST.
Figure 6 uses the HST F606W filter for the rest-frame UV and the JWST F277W
band for the rest-frame near-IR image. The HST image looks clumpy in both
datasets. Clumps show a large variety of sizes and shapes. They all trace the
same dense, star-forming regions seen in Figure 5. The JWST images look very
different. In particular, bright and round clumps in VELA-3 are absent in
VELA-6. Only some clumps associated with large star-forming regions can be
barely seen above the disc background. Therefore, the rest-frame near-IR looks
less clumpy than the rest-frame UV in models with strong feedback. This is
consistent with the trends seen in other simulations (Buck et al., 2017) and
in observations. Images in the rest-frame optical bands look less clumpy than
the UV counterparts (Wuyts et al., 2012; White et al., 2022). JWST’s larger
diameter will allow better resolution of clumps than HST. Our results suggest
that JWST observations that provide rest-frame near-IR images of galaxies at
$z\simeq 2$ will be crucial for mapping the stellar distribution of clumpy
galaxies and they will be able to distinguish between different feedback
scenarios.

###  5.2 Clump statistics

We analyzed clump properties following the methods described in M17. The clump
mass, $M_{c}$, is the total baryonic mass (stars and gas) within the clump
volume. The clump radius, $R_{c}$, is defined as the radius of a sphere with
the same volume as the clump. The shape of this volume is characterized by its
inertia tensor. We define the shape parameter as $S_{c}=I_{3}/I_{1}$, where
$I_{1}$ and $I_{3}$ are the largest and the smallest eigenvalues of the
tensor. A perfect sphere yields $Sc=1$ and a flattened oblate clump has
$Sc\simeq 0.5$.

Clumps are tracked through time in the simulations using their stellar
particles. While tracking the clump throughout its lifetime, we use the same
definition of clump time, t, as used in M17. This is the time since the clump
formation. When a given clump is identified for the first time, we compute $t$
as the stellar age of the clump if this is lower than the time since the
previous snapshot. Otherwise, we set $t=0$. If a clump is identified at later
snapshots, we increase $t$ by the corresponding time interval. $t_{\rm c,max}$
is the clump time at the last snapshot of the clump. We refer to M17 for
further details. We only follow in-situ clumps that formed via VDI in the
central galaxies. Ex-situ clumps, that joined the disc through mergers, are
excluded based on their dark matter content and the birth place of their
stellar particles.

Figure 7 shows the mass-radius plane of clumps, as in Figure 6 from M17, for
VELA-3 and VELA-6 in-situ clumps. The maps are coloured by the shape
parameter, $S_{c}$ and the clump age, $t$, normalized by the disc dynamical
time, $t_{d}$. At low clump masses, the distribution of clumps is similar in
both cases. This regime is dominated by clumps with $t_{\rm c,max}=0$, defined
as zero-lifetime clumps (ZLC) in M17. They are mostly transient features in
the density field. At higher masses, $M_{c}>10^{7}\ M_{\odot}$, the clumps in
VELA-6 have lower baryonic densities in general, as a result of a stronger
feedback.

The distribution of clump shapes is very similar, with the exception of round
clumps, $S_{c}\geq 0.7$. They are not present in the runs with strong
feedback, as seen in Figures 5 and 6. The only oblate clumps with $S_{c}\simeq
0.4-0.6$ seen in VELA-6 correspond to the densest clumps that survive
feedback. These can retain a coherent structure in Jeans equilibrium between
self-gravity, shear and feedback (Dekel et al., 2022b, a).

Figure 7 shows the distribution of clump age at a given snapshot with respect
to the disc dynamical time. In both datasets, there is a large fraction of
transient clumps with very short ages. These clumps are quickly disrupted due
to feedback right after the onset of star formation. Most of them are ZLC as
described in M17. This population is also seen in other simulations with
strong feedback (Genel et al., 2012; Oklopčić et al., 2017) with lifetimes
between 10-50 Myr, much shorter than the disc dynamical time.

Figure 7: Distribution of clumps in the mass-radius plane for VELA-3 (left)
and VELA-6 (right). Top panels are coloured by the shape parameter, $S_{c}$
and bottom panels show the clump age in units of the disc dynamical time.
Clumps with t = 0 were artificially set to dark blue. The red lines represent
constant baryonic density in units of ${\rm cm}^{-3}$. The grey lines
represent a constant circular velocity of $V_{\rm circ}=20$ and 40 km s-1,
while white lines represent a constant baryonic column density of $\Sigma_{\rm
bar}=200$ and $400{\rm M}_{\odot}\,{\rm pc}^{-2}$. VELA-6 clumps are
significantly less round. In VELA-3, migrating clumps with times longer than
the disc dynamical have typically $V_{\rm circ}>20\,{\rm km}\,{\rm s}^{-1}$
and $\Sigma_{\rm bar}>200{\rm M}_{\odot}\,{\rm pc}^{-2}$. The stronger
feedback in VELA-6 pushes migrating clumps to higher values: $V_{\rm
circ}>40\,{\rm km}\,{\rm s}^{-1}$ and $\Sigma_{\rm bar}>400{\rm
M}_{\odot}\,{\rm pc}^{-2}$.  Figure 8: Distributions of clump lifetimes,
$t_{\rm c,max}$, normalized to the mass-weighted clump free-fall time (left)
and clump masses, normalized to the disc mass (right). The number of long-
lived clumps with lifetimes longer than 20 free-fall times is drastically
reduced in VELA-6. They are limited to the most massive clumps with masses
similar to the Toomre mass, log($M_{\rm c}/M_{\rm d})\simeq-1.5$.  Figure 9:
Gradients of clump properties with galactocentric distance for VELA-6 SLC
clumps (yellow points) and LLCs (grey points). Lines represent median values
for VELA-6 (solid) and VELA-3 (dash). Top-left: mass-weighted mean stellar
age; Top-right: gas fraction; bottom left clump sSFR normalized to the disc
sSFR; bottom-right: clump metallicity normalized to the mean disc metallicity.
In-situ clumps in VELA-6 show a steep age gradient with typical clump ages of
100-200 Myr. They are gas-rich, with higher sSFR and lower metallicities than
the disc.

A second population of clumps has ages longer than the disc dynamical time.
These clumps can migrate within the disc and can drive gas inflows towards the
galaxy centre (Dekel et al., 2009b; Ceverino et al., 2010, M17). However, the
properties of the migrating clumps differ in the two datasets. Migrating
clumps in VELA-6 are are rarer and denser than in VELA-3. They usually have
$\Sigma_{\rm bar}\geq 400{\rm M}_{\odot}\,{\rm pc}^{-2}$ and $V_{\rm circ}\geq
40\,{\rm km}\,{\rm s}^{-1}$ in VELA-6, whereas migrating clumps in VELA-3 have
$\Sigma_{\rm bar}\geq 200{\rm M}_{\odot}\,{\rm pc}^{-2}$ and $V_{\rm circ}\geq
20\,{\rm km}\,{\rm s}^{-1}$. It seems that migrating clumps should be denser
in order to survive stronger feedback. With respect to ages, VELA-6 migrating
clumps have shorter ages, $t\leq 10\ t_{d}$, whereas the range of ages in
VELA-3 is much broader, $t=(1-30)t_{d}$. A more detailed analysis of clump
evolution is discussed in a companion paper (Dekel et al., 2022b, a).

As discussed in M17, VELA-3 runs show a bimodality in clump lifetimes, $t_{\rm
c,max}$ with respect to their free-fall times, $t_{\rm ff}$. We keep the same
nomenclature and use the same threshold, $20t_{\rm ff}$, to distinguish
between short-lived clumps (SLCs) and long-lived clumps (LLCs), after
excluding all ZLCs from further analysis ($t_{\rm c,max}$=0). In VELA-6, that
bimodal distribution is absent (Figure 8) and LLCs only account for an
extended tail in the distribution of clump lifetimes. This is consistent with
the results from isolated disc simulations with strong feedback (Hopkins et
al., 2012b). Therefore, the fraction of LLC in VELA-6 is much lower than in
VELA-3. Feedback is limiting the lifetime of clumps but it also decreases the
average clump densities, increasing the clump free-fall times.

The clump mass function is very similar among the two models (Figure 8). SLCs
dominate by number in both cases. Only the distribution of LLCs is radically
different. LLCs with low masses, $M_{\rm c}/M_{\rm d}\leq 0.03$, dominate the
LLCs population in VELA-3. That population disappears in VELA-6. Only at high
masses, $M_{\rm c}/M_{\rm d}>0.03$, the fraction of LLCs is roughly similar in
both models. These giant clumps are massive enough to survive feedback, as
steady winds generated by feedback are not expected to unbind giant clumps
(Krumholz & Dekel, 2010).

Figure 10: Example of compaction and quenching of the galaxy V12 in the VELA-3
(top) and VELA-6 (bottom) suite in the $\Sigma_{1}$-sSFR plane. The maps show
the gas surface density at the relevant phases: pre-compaction, compaction and
post-compaction times with a scale of 10 kpc.

Figure 11: Evolution of the mass within 1 kpc, M1, of the different components
of the galaxy V12 in the VELA-3 (top) and VELA-6 (bottom) suite. The increase
in the central gas mass starts a compaction event, weaker by a factor 2
inVELA-6.

###  5.3 Gradients

Figure 9 compares various clump properties as a function of their cylindrical
distance from the galaxy center, referred to as clump gradients, for in-situ
clumps in VELA-3 and VELA-6. This is analogous to Figure 15 in M17. The
gradients of SLCs in VELA-3 and VELA-6 are relatively similar. They show a
steep age gradient with typical clump ages of 100-200 Myr. They are gas-rich,
with higher sSFR and lower metallicities than the disc. The only difference is
that SLC gradients in VELA-6 show slightly lower sSFR, higher gas fraction,
and lower metallicity than the corresponding SLC gradients in VELA-3. The
increase in feedback strength produces a decrease in the star-formation
efficiency within these clumps.

LLCs show very different gradients. The population of old (age${}_{c}>300\
{\rm Myr}$), gas poor ($f_{\rm gas,c}<0.1$) LLCs with sSFR lower than the
underlying disc and high metallicity is absent in VELA-6. In particular, a
population of quenched clumps (log(sSFRc/sSFRd)<-3, where subscripts c and d
refer to clump and disk), which accounts for 40% of the total population of
LLCs in VELA-3 (M17) have disappeared in VELA-6. Feedback may prevent the
formation of these stellar-rich clumps. As a results, typical ages in VELA-6
clumps extend to 100-300 Myr, consistent with observations (Wuyts et al.,
2012; Guo et al., 2015). A more detailed comparison with observations requires
the use of mock observations (Huertas-Company et al., 2020; Ginzburg et al.,
2021) and this will be the focus of future work.

In VELA-6, there are no clumps at low galactocentric distances, $d<0.2R_{d}$.
It seems that clumps in models with stronger feedback are disrupted before
they reach the galaxy centre, delivering gas and stars into the inner 20% of
the disc radius. Clump evolution and its contribution to the growth of the
bulge will be discussed in follow-up papers.

##  6 Compaction and Quenching

Gas inflows within galactic discs, partially driven by VDI and migrating
clumps, naturally trigger wet compaction and inside-out quenching (Dekel &
Burkert, 2014; Zolotov et al., 2015; Tacchella et al., 2016a). Figures 10
shows an example of compaction and quenching in VELA-3 and VELA-6. The overall
behaviour is similar in both models. At high redshifts, the galaxy is star-
forming and diffuse (pre-compaction phase), characterized by a relatively high
sSFR and low surface stellar density in the inner 1 kpc, $\Sigma_{1}$. After
some time, the galaxy reaches a maximum in $\Sigma_{1}$. This happens a little
earlier in VELA-3 and the maximum density is higher. The sSFR remains high
during the peak of the compaction event. After that maximum, the galaxy
reduces its sSFR (quenching) and enters into the post-compaction phase with
roughly constant $\Sigma_{1}$ within a factor of 2. This path in the
$\Sigma_{1}$-sSFR plane, also seen in observations (Barro et al., 2013), seems
robust against variations in the feedback strength.

The evolution of the mass in the different components within the central 1 kpc
is a key feature in compaction events (Figure 11). In the VELA-3 run, the peak
in gas and SFR within 1 kpc is narrower in time than in VELA-6. The maximum
gas mass is also a factor 2 lower in VELA-6. This decreases the maximum of
stellar mass by a factor of 2, because of the self-regulation by feedback.
This maximum of compaction happens after the central mass becomes dominated by
stars in both cases. It seems that feedback weakens compaction and gas inflows
within the galaxy by less than a factor of 2. After that maximum of
compaction, both gas mass and SFR strongly decreases, most probably due to gas
consumption and strong outflows driven by the nuclear starburst. However, in
VELA-6, the stellar mass and dark-matter mass decreases by a factor of 2, most
probably due to fluctuations in the gravitational potential induced by gas
outflows (Pontzen & Governato, 2012). As a result, the stellar mass after
compaction in VELA-6 is 0.5 dex lower than in VELA-3.

The overall evolution of high-z galaxies in the $\Sigma_{1}$-sSFR plane is
insensitive to the strength of feedback once these properties are normalized.
Figure 12 shows this behaviour in the plane between
$\Delta$log(sSFR)$=$log(sSFR)-log(sSFRMS) and
$\Delta$log($\Sigma_{1}$)=log($\Sigma_{1}$)-log($\Sigma_{1,\rm max}$), where
sSFR($z$)MS marks the star-forming main sequence and $\Sigma_{1,\rm max}$ is
the maximum $\Sigma_{1}$ value of each galaxy, as described in Z15. Galaxies
in VELA-6 evolve around the main-sequence (horizontal branch in Figure 12),
with slightly higher deviations than in VELA-3 (Larkin et al. in prep.) After
they reach the point of maximum compaction, they evolve below the main
sequence (vertical branch), initialising a process of quenching that could be
completed and maintained with the aid of AGN feedback (not included in these
simulations).

Figure 12: log(sSFR)-log(sSFR${}_{\rm MS})$ vs
log($\Sigma_{1}$)-log($\Sigma_{1,\rm max}$) for VELA-3 (top) and VELA-6
(bottom) coloured by redshift. The galaxies in both models evolve along a
universal L-shape track, first along a horizontal path, following the star-
forming main sequence, and then, after compaction, along a vertical, quenching
path.

##  7 Conclusions and Discussion

We have compared two sets of cosmological, zoom-in simulations of 35 high-z
galaxies with the same initial conditions but different models of stellar
feedback (with and without kinetic feedback, §2.5). The model with stronger
feedback (VELA-6) gives the following results with respect to the previous
model (VELA-3):

  * •

At a fixed halo mass and redshift, the galaxy stellar mass is reduced by a
factor of $\sim$1-3, making the stellar-mass-halo-mass relation in better
agreement with abundance matching results (Figure 1).

  * •

In agreement with previous works (C15), the degree of 3D elongation in a
galaxy is higher for lower stellar-to-DM mass ratios within the half-light
radius. Therefore, low-mass galaxies, $M_{*}<10^{10}\ {\rm M}_{\odot}$, are
preferentially non-axisymmetric and elongated, $e>0.5$ at $z\geq 1$, and more
so for VELA-6 at a fixed stellar mass (Figure 2).

  * •

The population of dense, round, compact, old (age${}_{c}>300\ {\rm Myr}$),
quenched (log(sSFRc/sSFRd)<-3), stellar (or gas poor) clumps is absent in
VELA-6. Therefore, the distribution of stellar mass, traced by rest-frame
near-IR bands, is significantly less clumpy than the distribution of star
forming regions, traced by rest-frame UV (Figure 6).

  * •

Migrating clumps with clump times longer than the disc dynamical time have
shorter stellar ages (age${}_{c}=100-200\ {\rm Myr}$) and higher baryonic
densities and circular velocities (Figure 7).

  * •

In VELA-6, the rarer long-lived clumps with lifetimes longer than 20 free-fall
times are limited to the most massive clumps ($M_{\rm c}/M_{\rm d}\geq 0.03$)
with masses similar to the Toomre mass (Figure 8).

  * •

The evolution of compaction and quenching in the $\Sigma_{1}$-sSFR plane is
similar in both models (Figure 12).

Our results suggest that JWST observations will be crucial for our
understanding of galaxy evolution at high-z. Rest-frame near-IR images of
galaxies at cosmic noon will be able to map the stellar distribution of clumpy
galaxies in great detail. JWST will also observe low-mass elongated galaxies,
which should dominate the number of galaxies at high-z. The great capabilities
of JWST will allow us to study these processes at even higher redshifts. For
example, recent NIRCam observations of galaxies at $z\simeq 6-8$ have shown
very clumpy morphologies (Chen et al., 2022). We expect that new observational
constrains on clump properties, particularly age and mass distributions, may
help distinguish between different feedback models.

The VELA project allows us to compare a large sample of zoom-in simulations
performed with different models of feedback. This unique dataset provides
overall trends with feedback strength. In Ceverino et al. (2014), Moody et al.
(2014) and Mandelker et al. (2017), we compared the effect of feedback in the
previous suites of the VELA simulations: VELA-2 (thermal-only feedback) and
VELA-3 (thermal plus radiative feedback). The addition of radiative feedback
reduces the gas mass in the high-values tail of the density distribution
function. The galaxy stellar mass growth is therefore reduced by a factor
$\sim$2\. The addition of kinetic feedback reduces the stellar mass by another
factor of a few. Radiative feedback also reduces the number of long-lived
clumps with respect to the thermal-only case. This trend continues in VELA-6.
Therefore, there is a threshold for clump disruption that increases with
feedback. In VELA-2, clumps are disolved in a few free-fall times if their
baryonic column density is $\Sigma_{\rm bar}<100\ {\rm M}_{\odot}\,{\rm
pc}^{-2}$. The addition of radiative feedback in VELA-3 increases that
threshold to 200$\ {\rm M}_{\odot}\,{\rm pc}^{-2}$. It becomes 400$\ {\rm
M}_{\odot}\,{\rm pc}^{-2}$ with the inclusion of kinetic feedback in VELA-6.
As feedback strength increases, only denser clumps can survive for a
significant amount of time.

The strength of feedback does not only depend on the amount of energy
deposited (thermally or kinetically) by the mechanisms of feedback. The time-
scales are also important. Both radiative feedback (with a moderate coupling
of IR photons) and supernova shells impart roughly the same amount of momentum
(Agertz et al., 2013), but the time-scales are very different. Radiative
feedback from ionising photons (VELA-3) injects momentum over 5 Myr. On the
other hand, supernova shells are effective over longer time-scales, 40 Myr in
the case of VELA-6. This makes the feedback model in VELA-6 more efficient
than in VELA-3, even when the increase of energy and momentum is just a factor
of a few.

## Acknowledgements

We acknowledge stimulating discussions with Guillermo Tenorio-Tagle, Sergey
Silich and Casiana Muñoz-Tuñón. The VELA simulations were performed at the
National Energy Research Scientific Computing Center (NERSC) at Lawrence
Berkeley National Laboratory, and at NASA Advanced Supercomputing (NAS) at
NASA Ames Research Center. DC is a Ramon-Cajal Researcher and is supported by
the Ministerio de Ciencia, Innovación y Universidades (MICIU/FEDER) under
research grant PGC2018-094975-C21." NM acknowledges support from ISF grant
3061/21, from the Gordon and Betty Moore Foundation through Grant GBMF7392 and
from the National Science Foundation under Grant No. NSF PHY-1748958. AD was
partly supported by ISF 861/20.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

## References

  * Agertz & Kravtsov (2015) Agertz O., Kravtsov A. V., 2015, ApJ, 804, 18
  * Agertz et al. (2009) Agertz O., Teyssier R., Moore B., 2009, MNRAS, 397, L64
  * Agertz et al. (2013) Agertz O., Kravtsov A. V., Leitner S. N., Gnedin N. Y., 2013, ApJ, 770, 25
  * Allgood et al. (2006) Allgood B., Flores R. A., Primack J. R., Kravtsov A. V., Wechsler R. H., Faltenbacher A., Bullock J. S., 2006, MNRAS, 367, 1781
  * Barro et al. (2013) Barro G., et al., 2013, ApJ, 765, 104
  * Behroozi & Silk (2015) Behroozi P. S., Silk J., 2015, ApJ, 799, 32
  * Behroozi et al. (2013) Behroozi P. S., Wechsler R. H., Conroy C., 2013, ApJ, 770, 57
  * Behroozi et al. (2019) Behroozi P., Wechsler R. H., Hearin A. P., Conroy C., 2019, MNRAS, 488, 3143
  * Binney & Tremaine (2008) Binney J., Tremaine S., 2008, Galactic Dynamics: Second Edition. Princeton University Press
  * Birnboim & Dekel (2003) Birnboim Y., Dekel A., 2003, MNRAS, 345, 349
  * Bournaud & Elmegreen (2009) Bournaud F., Elmegreen B. G., 2009, ApJ, 694, L158
  * Bryan & Norman (1998) Bryan G. L., Norman M. L., 1998, ApJ, 495, 80
  * Buck et al. (2017) Buck T., Macciò A. V., Obreja A., Dutton A. A., Domínguez-Tenreiro R., Granato G. L., 2017, MNRAS, 468, 3628
  * Cattaneo et al. (2009) Cattaneo A., et al., 2009, Nature, 460, 213
  * Ceverino & Klypin (2009) Ceverino D., Klypin A., 2009, ApJ, 695, 292
  * Ceverino et al. (2010) Ceverino D., Dekel A., Bournaud F., 2010, MNRAS, 404, 2151
  * Ceverino et al. (2014) Ceverino D., Klypin A., Klimek E. S., Trujillo-Gomez S., Churchill C. W., Primack J., Dekel A., 2014, MNRAS, 442, 1545
  * Ceverino et al. (2015) Ceverino D., Primack J., Dekel A., 2015, MNRAS, 453, 408
  * Ceverino et al. (2016a) Ceverino D., Sánchez Almeida J., Muñoz Tuñón C., Dekel A., Elmegreen B. G., Elmegreen D. M., Primack J., 2016a, MNRAS, 457, 2605
  * Ceverino et al. (2016b) Ceverino D., Arribas S., Colina L., Rodríguez Del Pino B., Dekel A., Primack J., 2016b, MNRAS, 460, 2731
  * Ceverino et al. (2017a) Ceverino D., Glover S. C. O., Klessen R. S., 2017a, MNRAS, 470, 2791
  * Ceverino et al. (2017b) Ceverino D., Glover S. C. O., Klessen R. S., 2017b, MNRAS, 470, 2791
  * Chen et al. (2022) Chen Z., Stark D. P., Endsley R., Topping M., Whitler L., Charlot S., 2022, arXiv e-prints, p. arXiv:2207.12657
  * Costantin et al. (2021) Costantin L., et al., 2021, ApJ, 913, 125
  * Croton et al. (2006) Croton D. J., et al., 2006, MNRAS, 365, 11
  * Dekel & Burkert (2014) Dekel A., Burkert A., 2014, MNRAS, 438, 1870
  * Dekel & Shlosman (1983) Dekel A., Shlosman I., 1983, in Athanassoula E., ed., IAU Symposium Vol. 100, Internal Kinematics and Dynamics of Galaxies. p. 187
  * Dekel & Silk (1986) Dekel A., Silk J., 1986, ApJ, 303, 39
  * Dekel et al. (2009a) Dekel A., et al., 2009a, Nature, 457, 451
  * Dekel et al. (2009b) Dekel A., Sari R., Ceverino D., 2009b, ApJ, 703, 785
  * Dekel et al. (2019) Dekel A., Sarkar K. C., Jiang F., Bournaud F., Krumholz M. R., Ceverino D., Primack J. R., 2019, MNRAS, 488, 4753
  * Dekel et al. (2020a) Dekel A., Ginzburg O., Jiang F., Freundlich J., Lapiner S., Ceverino D., Primack J., 2020a, MNRAS, 493, 4126
  * Dekel et al. (2020b) Dekel A., et al., 2020b, MNRAS, 496, 5372
  * Dekel et al. (2022a) Dekel A., Tziperman O., Sarkar K., Ginzburg O., Mandelker N., Ceverino D., Primack J., 2022a, arXiv e-prints, p. arXiv:2209.04462
  * Dekel et al. (2022b) Dekel A., Mandelker N., Bournaud F., Ceverino D., Guo Y., Primack J., 2022b, MNRAS, 511, 316
  * Elmegreen & Elmegreen (2005) Elmegreen B. G., Elmegreen D. M., 2005, ApJ, 627, 632
  * Fabian (2012) Fabian A. C., 2012, ARA&A, 50, 455
  * Förster Schreiber & Wuyts (2020) Förster Schreiber N. M., Wuyts S., 2020, ARA&A, 58, 661
  * Förster Schreiber et al. (2009) Förster Schreiber N. M., Genzel R., Bouché N., Cresci G., Davies R., Buschkamp P., Shapiro K., et al., 2009, ApJ, 706, 1364
  * Genel et al. (2012) Genel S., Dekel A., Cacciato M., 2012, MNRAS, 425, 788
  * Gentry et al. (2017) Gentry E. S., Krumholz M. R., Dekel A., Madau P., 2017, MNRAS, 465, 2471
  * Genzel et al. (2006) Genzel R., Tacconi L. J., Eisenhauer F., Förster Schreiber N. M., Cimatti A., et al. 2006, Nature, 442, 786
  * Genzel et al. (2008) Genzel R., et al., 2008, ApJ, 687, 59
  * Ginzburg et al. (2021) Ginzburg O., Huertas-Company M., Dekel A., Mandelker N., Snyder G., Ceverino D., Primack J., 2021, MNRAS, 501, 730
  * Governato et al. (2007) Governato F., Willman B., Mayer L., Brooks A., Stinson G., Valenzuela O., Wadsley J., Quinn T., 2007, MNRAS, 374, 1479
  * Guo et al. (2015) Guo Y., et al., 2015, ApJ, 800, 39
  * Guo et al. (2018) Guo Y., et al., 2018, ApJ, 853, 108
  * Hopkins et al. (2012a) Hopkins P. F., Quataert E., Murray N., 2012a, MNRAS, 421, 3522
  * Hopkins et al. (2012b) Hopkins P. F., Kereš D., Murray N., Quataert E., Hernquist L., 2012b, MNRAS, 427, 968
  * Hopkins et al. (2014) Hopkins P. F., Kereš D., Oñorbe J., Faucher-Giguère C.-A., Quataert E., Murray N., Bullock J. S., 2014, MNRAS, 445, 581
  * Huertas-Company et al. (2020) Huertas-Company M., et al., 2020, MNRAS, 499, 814
  * Inoue et al. (2016) Inoue S., Dekel A., Mandelker N., Ceverino D., Bournaud F., Primack J., 2016, MNRAS, 456, 2052
  * Jiang et al. (2019) Jiang F., et al., 2019, MNRAS, 488, 4801
  * Jing & Suto (2002) Jing Y. P., Suto Y., 2002, ApJ, 574, 538
  * Jonsson (2006) Jonsson P., 2006, MNRAS, 372, 2
  * Jonsson et al. (2010) Jonsson P., Groves B. A., Cox T. J., 2010, MNRAS, 403, 17
  * Klypin et al. (2002) Klypin A., Zhao H., Somerville R. S., 2002, ApJ, 573, 597
  * Kravtsov (2003) Kravtsov A. V., 2003, ApJ, 590, L1
  * Kravtsov et al. (1997) Kravtsov A. V., Klypin A. A., Khokhlov A. M., 1997, ApJS, 111, 73
  * Kretschmer et al. (2021) Kretschmer M., Dekel A., Freundlich J., Lapiner S., Ceverino D., Primack J., 2021, MNRAS, 503, 5238
  * Krumholz & Dekel (2010) Krumholz M. R., Dekel A., 2010, MNRAS, 406, 112
  * Langan et al. (2020) Langan I., Ceverino D., Finlator K., 2020, MNRAS, 494, 1988
  * Law et al. (2012) Law D. R., Steidel C. C., Shapley A. E., Nagy S. R., Reddy N. A., Erb D. K., 2012, ApJ, 745, 85
  * Leitherer et al. (1999) Leitherer C., et al., 1999, ApJS, 123, 3
  * Leja et al. (2019) Leja J., et al., 2019, ApJ, 877, 140
  * Madau & Dickinson (2014) Madau P., Dickinson M., 2014, ARA&A, 52, 415
  * Mandelker et al. (2014) Mandelker N., Dekel A., Ceverino D., Tweed D., Moody C. E., Primack J., 2014, MNRAS, 443, 3675
  * Mandelker et al. (2017) Mandelker N., Dekel A., Ceverino D., DeGraf C., Guo Y., Primack J., 2017, MNRAS, 464, 635
  * Meng et al. (2019) Meng X., Gnedin O. Y., Li H., 2019, MNRAS, 486, 1574
  * Moody et al. (2014) Moody C. E., Guo Y., Mandelker N., Ceverino D., Mozena M., Koo D. C., Dekel A., Primack J., 2014, MNRAS, 444, 1389
  * Moster et al. (2013) Moster B. P., Naab T., White S. D. M., 2013, MNRAS, 428, 3121
  * Moster et al. (2018) Moster B. P., Naab T., White S. D. M., 2018, MNRAS, 477, 1822
  * Muratov et al. (2015) Muratov A. L., Kereš D., Faucher-Giguère C.-A., Hopkins P. F., Quataert E., Murray N., 2015, MNRAS, 454, 2691
  * Noguchi (1999) Noguchi M., 1999, ApJ, 514, 77
  * Oklopčić et al. (2017) Oklopčić A., Hopkins P. F., Feldmann R., Kereš D., Faucher-Giguère C.-A., Murray N., 2017, MNRAS, 465, 952
  * Oppenheimer & Davé (2006) Oppenheimer B. D., Davé R., 2006, MNRAS, 373, 1265
  * Oppenheimer & Davé (2008) Oppenheimer B. D., Davé R., 2008, MNRAS, 387, 577
  * Ostriker & Shetty (2011) Ostriker E. C., Shetty R., 2011, ApJ, 731, 41
  * Pillepich et al. (2019) Pillepich A., et al., 2019, MNRAS, 490, 3196
  * Pontzen & Governato (2012) Pontzen A., Governato F., 2012, MNRAS, 421, 3464
  * Roca-Fàbrega et al. (2019) Roca-Fàbrega S., et al., 2019, MNRAS, 484, 3625
  * Rodríguez-Puebla et al. (2017) Rodríguez-Puebla A., Primack J. R., Avila-Reese V., Faber S. M., 2017, MNRAS, 470, 651
  * Schneider et al. (2012) Schneider M. D., Frenk C. S., Cole S., 2012, J. Cosmology Astropart. Phys., 2012, 030
  * Simons et al. (2019) Simons R. C., et al., 2019, ApJ, 874, 59
  * Snyder et al. (2015) Snyder G. F., Lotz J., Moody C., Peth M., Freeman P., Ceverino D., Primack J., Dekel A., 2015, MNRAS, 451, 4290
  * Strawn et al. (2021) Strawn C., et al., 2021, MNRAS, 501, 4948
  * Suess et al. (2022) Suess K. A., et al., 2022, arXiv e-prints, p. arXiv:2207.10655
  * Tacchella et al. (2016a) Tacchella S., Dekel A., Carollo C. M., Ceverino D., DeGraf C., Lapiner S., Mandelker N., Primack Joel R., 2016a, MNRAS, 457, 2790
  * Tacchella et al. (2016b) Tacchella S., Dekel A., Carollo C. M., Ceverino D., DeGraf C., Lapiner S., Mandelker N., Primack J. R., 2016b, MNRAS, 458, 242
  * Tacchella et al. (2018) Tacchella S., Bose S., Conroy C., Eisenstein D. J., Johnson B. D., 2018, ApJ, 868, 92
  * Tomassetti et al. (2016) Tomassetti M., et al., 2016, MNRAS, 458, 4477
  * Toomre (1964) Toomre A., 1964, ApJ, 139, 1217
  * Whitaker et al. (2012) Whitaker K. E., van Dokkum P. G., Brammer G., Franx M., 2012, ApJ, 754, L29
  * White et al. (2022) White H. A., Fisher D. B., Abraham R. G., Glazebrook K., Obreschkow D., 2022, ApJ, 926, 32
  * Wisnioski et al. (2015) Wisnioski E., Förster Schreiber N. M., Wuyts S., Wuyts E., Bandara K., et al. 2015, ApJ, 799, 209
  * Wuyts et al. (2012) Wuyts S., et al., 2012, ApJ, 753, 114
  * Zemp et al. (2012) Zemp M., Gnedin O. Y., Gnedin N. Y., Kravtsov A. V., 2012, ApJ, 748, 54
  * Zhang et al. (2019) Zhang H., et al., 2019, MNRAS, 484, 5170
  * Zolotov et al. (2015) Zolotov A., et al., 2015, MNRAS, 450, 2327
  * van der Wel et al. (2014) van der Wel A., Chang Y.-Y., Bell E. F., Holden B. P., Ferguson H. C., et al. 2014, ApJ, 792, L6