Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 24 October 2011 (MN LATEX style file v2.2)
Stellar Feedback in Galaxies and the Origin of Galaxy-scale Winds
Philip F. Hopkins1, Eliot Quataert1, & Norman Murray2;3
1Department of Astronomy and Theoretical Astrophysics Center, University of California Berkeley, Berkeley, CA 94720
2Canadian Institute for Theoretical Astrophysics, 60 St. George Street, University of Toronto, ON M5S 3H8, Canada
3Canada Research Chair in Astrophysics
Submitted to MNRAS, September, 2011
ABSTRACT
Feedback from massive stars is believed to play a critical role in driving galactic super-
winds that enrich the intergalactic medium and shape the galaxy mass function, mass-
metallicity relation, and other global galaxy properties. In previous papers, we have intro-
duced new numerical methods for implementing stellar feedback on sub-GMC through galac-
tic scales in numerical simulations of galaxies; the key physical processes include radiation
pressure in the UV through IR, supernovae (Type-I & II), stellar winds (“fast” O star through
“slow” AGB winds), and HII photoionization. Here, we show that these feedback mechanisms
drive galactic winds with outflow rates as high as  10 20 times the galaxy star formation
rate. The mass-loading efficiency (wind mass loss rate divided by the star formation rate)
scales roughly as _Mwind= _M /V1c (where Vc is the galaxy circular velocity), consistent with
simple momentum-conservation expectations. We use our suite of simulations to study the rel-
ative contribution of each feedback mechanism to the generation of galactic winds in a range
of galaxy models, from SMC-like dwarfs and Milky-way analogues to z 2 clumpy disks. In
massive, gas-rich systems (local starbursts and high-z galaxies), radiation pressure dominates
the wind generation. By contrast, for MW-like spirals and dwarf galaxies the gas densities
are much lower and sources of shock-heated gas such as supernovae and stellar winds dom-
inate the production of large-scale outflows. In all of our models, however, the winds have
a complex multi-phase structure that depends on the interaction between multiple feedback
mechanisms operating on different spatial and time scales: any single feedback mechanism
fails to reproduce the winds observed. We use our simulations to provide fitting functions to
the wind mass-loading and velocities as a function of galaxy properties, for use in cosmo-
logical simulations and semi-analytic models. These differ from typically-adopted formulae
with an explicit dependence on the gas surface density that can be very important in both
low-density dwarf galaxies and high-density gas-rich galaxies.
Key words: galaxies: formation — star formation: general — galaxies: evolution — galaxies:
active — cosmology: theory
1 INTRODUCTION
Feedback from massive stars is critical to the evolution of galaxies.
In cosmological models of galaxy evolution without strong stellar
feedback, gas rapidly cools and turns into stars, leading to galax-
ies with star formation rates much higher than observed, and  ten
times the stellar mass found in real galaxies (e.g. Katz et al. 1996;
Somerville & Primack 1999; Cole et al. 2000; Springel & Hern-
quist 2003b; Kereš et al. 2009a, and references therein). Simply
suppressing the rate of star formation does not solve the problem:
the amount of baryons in real galactic disks is much lower than the
amount of cool gas in disks found in cosmological simulations, es-
 E-mail:phopkins@astro.berkeley.edu
pecially in low-mass galaxies (White & Frenk 1991; for a recent re-
view see Kereš et al. 2009b). Constraints from the mass-metallicity
relation and enrichment of the IGM also imply that the baryons
cannot simply be prevented from entering galaxy halos along with
dark matter (Tremonti et al. 2004; Erb et al. 2006; Aguirre et al.
2001; Pettini et al. 2003; Songaila 2005). Some process must very
efficiently remove baryons from galaxies.
Related problems appear on smaller spatial and time scales.
The Kennicutt-Schmidt (KS) law implies that star formation is very
slow within galaxies, with a gas consumption time of 50 dynam-
ical times (Kennicutt 1998). Moreover, the integrated fraction of
mass turned into stars in GMCs over their lifetime is only a few
to several percent (Zuckerman & Evans 1974; Williams & McKee
1997; Evans 1999; Evans et al. 2009). Without strong stellar feed-
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2 Hopkins et al.
back, however, self-gravitating collapse leads to most of the gas
turning into stars in just a few dynamical times.
The problem, then, on both galactic and sub-galactic scales,
is twofold. First, star formation must be “slowed down” at a given
global/local gas surface density. But this alone would still violate
integral constraints, producing galaxies and star clusters more mas-
sive than observed by an order of magnitude. Thus the second prob-
lem: on small scales gas must be expelled from GMCs, and on
galactic scales either prevented from entering, or, more likely in
our judgment, removed from, the host galaxy. In other words, local
outflows and global super-winds must be generated that can remove
gas at a rate rapid compared to the star formation rate.
Because low-mass galaxies are preferentially baryon-poor,
matching the faint end of the observed galaxy mass function in cos-
mological simulations requires that the global efficiency of galactic
super-winds scales as a declining power of galaxy mass or circu-
lar velocity. Oppenheimer & Davé (2006) and Oppenheimer et al.
(2010) find that an average scaling _Mwind= _M / V1c produces
good agreement with the observed mass functions at different red-
shifts,1 with a normalization such that an SMC-mass dwarf has a
mass loading _Mwind= _M  10. Large mass-loading factors of sev-
eral times the SFR are also estimated in even relatively massive
local galaxies and massive star-forming regions at z 23 (Mar-
tin 1999, 2006; Heckman et al. 2000; Newman et al. 2011; Sato
et al. 2009; Chen et al. 2010; Steidel et al. 2010; Coil et al. 2011).
The scaling _Mwind= _M / V1c is expected from momentum
conservation arguments, given a number of simplifying assump-
tions and sufficient global momentum input from supernovae, stel-
lar winds, radiation pressure, etc. (Murray et al. 2005). Direct ob-
servations, while uncertain, tend to favor velocity and _Mwind scal-
ings similar to this constraint for the bulk of the outflowing gas
(Martin 2005; Rupke et al. 2005; Weiner et al. 2009).
To date, however, numerical simulations have generally not
been able to produce, from an a priori model, winds with either such
large absolute mass loading factors or the scaling of mass-loading
with galaxy mass/velocity. Many simulations, lacking the ability to
directly resolve the relevant feedback processes, put in winds “by
hand” by e.g. forcing an outflow rate that scales in a user-specified
manner with the star formation rate or other parameters (Springel
& Hernquist 2003a; Oppenheimer & Davé 2008; Sales et al. 2010;
Genel et al. 2010). Alternatively, models that self-consistently in-
clude stellar feedback have generally been limited to a small subset
of the relevant processes; the vast majority include only thermal
feedback via supernovae (i.e. thermal energy injection with some
average rate that scales with the mass in young stars). However,
thermal feedback is very inefficient in the dense regions where star
formation occurs, and in the ISM more broadly in gas-rich galaxies.
For this reason, such models require further changes to the physics
in order for thermal energy injection to have a significant effect.
Often cooling (along with star formation and other hydrodynamic
processes) is “turned off” for an extended period of time (Thacker
& Couchman 2000; Governato et al. 2007; Brook et al. 2011). With
or without these adjustments, however, such models generally ob-
tain winds that are weaker than those required to explain the galaxy
mass function, especially at low masses (see e.g. Guo et al. 2010;
1 Note that the agreement we speak of is with the faint sub-L end of the
mass function. It is widely agreed that different physics, perhaps AGN feed-
back, is critical for the regulation of the bright super-L end of the mass
function. We focus here on stellar feedback and star-forming systems.
Powell et al. 2011; Brook et al. 2011; Nagamine 2010, and refer-
ences therein).
In our view, part of the resolution of this difficulty lies in the
treatment of the ISM physics within galaxies. Feedback processes
other than supernovae are critical for suppressing star formation in
dense gas; these include protostellar jets, HII regions, stellar winds,
and radiation pressure from young stars. Including these mecha-
nisms self-consistently maintains a reasonable fraction of the ISM
at densities where the thermal heating from supernovae has a larger
effect. This conclusion implies that (not surprisingly) a realistic
treatment of galactic winds requires a more realistic treatment of
the stellar feedback processes that maintain the multi-phase struc-
ture of the ISM of galaxies.
Motivated by this perspective, in Hopkins et al. (2011a) (Pa-
per I) and Hopkins et al. (2011b) (Paper II) we developed a new set
of numerical models to follow feedback on small scales in GMCs
and star-forming regions, in simulations with pc-scale resolution.2
These simulations include the momentum imparted locally (on sub-
GMC scales) from stellar radiation pressure, radiation pressure on
larger scales via the light that escapes star-forming regions, HII
photoionization heating, as well as the heating, momentum deposi-
tion, and mass loss by SNe (Type-I and Type-II) and stellar winds
(O star and AGB). The feedback is tied to the young stars, with the
energetics and time-dependence taken directly from stellar evolu-
tion models. Our models also include realistic cooling to tempera-
tures< 100K, and a treatment of the molecular/atomic transition in
gas and its effect on star formation (following Krumholz & Gnedin
2011).
We showed in Papers I & II that these feedback mechanisms
produce a quasi-steady ISM in which giant molecular clouds form
and disperse rapidly, after turning just a few percent of their mass
into stars. This leads to an ISM with phase structure, turbulent ve-
locity dispersions, scale heights, and GMC properties (mass func-
tions, sizes, scaling laws) in reasonable agreement with observa-
tions. In this paper, we use these same models of stellar feedback to
quantitatively predict the elusive winds invoked in almost all galaxy
formation models.
The remainder of this paper is organized as follows. In §2 we
summarize the galaxy models we use and our methods of imple-
menting stellar feedback. In § 3 we discuss how each feedback
mechanism affects the morphology, phase structure, and velocity
distribution of galactic winds. In § 4, we discuss the mass-loading
of winds and how the mass loss rate depends on the inclusion of dif-
ferent feedback mechanisms. We further determine how the outflow
rate scales with galaxy properties and use our simulations to derive
more accurate approximations to wind scalings for use in cosmo-
logical simulations and semi-analytic models. In § 5 we summarize
our results and discuss their implications.
2 METHODS
The simulations used here are described in detail in Paper I (see
their Section 2 and Tables 1-3) and Paper II (their Section 2). How-
ever we briefly summarize the most important properties of the
models here. The simulations were performed with the parallel
TreeSPH code GADGET-3 (Springel 2005). They include stars, dark
matter, and gas, with cooling, star formation, and stellar feedback.
Gas follows a standard atomic cooling curve but in addition
2 Movies of these simulations are available at https://www.cfa.
harvard.edu/~phopkins/Site/Research.html
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