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# The mass-loss process in dwarf galaxies from 3D hydrodynamical simulations: The role of dark matter and starbursts

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Theoretical $\Lambda$CDM cosmological models predict a much larger number of low mass dark matter haloes than has been observed in the Local Group of galaxies. One possible explanation is the increased difficulty of detecting these haloes if most of the visible matter is lost at early evolutionary phases through galactic winds. In this work we study the current models of triggering galactic winds in dwarf spheroidal galaxies (dSph) from supernovae, and study, based on 3D hydrodynamic numerical simulations, the correlation of the mass loss rates and important physical parameters as the dark matter halo mass and its radial profile, and the star formation rate. We find that the existence of winds is ubiquitous, independent on the gravitational potential. Our simulations revealed that the Rayleigh-Taylor Instability (RTI) may play a major role on pushing matter out of these systems, even for very massive haloes. The instability is responsible for 5 - 40% of the mass loss during the early evolution of the galaxy, being less relevant at $t > 200$Myrs. There is no significant difference in the mass loss rates obtained for the different dark matter profiles studied (NFW and logarithmic). We have also found a correlation between the mass loss rate and both the halo mass and the rate of supernovae, as already reported in previous works. Besides, the epoch in which most of the baryon galactic matter is removed from the galaxy varies depending on the SN rate and gravitational potential. The later, combined to the importance of the RTI in each model, may change our understanding about the chemical evolution of dwarf galaxies, as well as in the heavy element contamination of the intergalactic medium at high redshifts.
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arXiv:1211.4068v1 [astro-ph.CO] 17 Nov 2012
Mon. Not. R. Astron. Soc. 000, 1–?? (2012) Printed 9 January 2014 (MN L
A
T
E
X style ﬁl e v2.2)
The mass loss process in dwarf galaxies from 3D
hydrodynamical simulations: the role of dark matter
and starbur sts
L. O. Ruiz
1
, D. Falceta-Gon¸calves
2
, G. A. Lanfranchi
1
& A. Caproni
1
1
ucleo de Astrof´ısica Torica, Universidade Cruzeiro do Sul - Rua Galv˜ao Bueno 868, CEP 01506-000, ao Paulo, Brazil,
2
EACH, Universidade de ao Paulo, Rua Arlindo Bettio 1000, CEP 03828-000, ao Paulo, Brazil
ABSTRACT
Theoretical ΛCDM cosmological models predict a much larger number of
low mas s dark matter haloe s than has been observed in the Local Group of
galaxies . One possible explanation is the increased diﬃculty of detecting these
haloes if most of the visible matter is lost at early evolutionary phases through
galactic winds. In this work we study the current models of triggering gala c tic
winds in dwarf spheroidal galaxies (dSph) from super novae, and study, based
on 3D hydrodynamic numerical simulations, the correlation of the mass loss
rates and important physical parameters as the dark matter halo mass and its
radial proﬁle, and the star formatio n rate. We ﬁnd that the existence of winds
is ubiquitous, independent on the gravitational potential. Our simulations
revealed that the Rayleigh-Taylor Instability (RTI) may play a major role
on pushing matter out of these systems, even for very massive haloes. The
instability is responsible for 540% of the mass loss during the early evolution
of the galaxy, being le ss relevant at t > 200Myrs. Ther e is no signiﬁcant
diﬀerence in the mass lo ss rates obtained for the diﬀerent da rk matter proﬁles
studied (NFW and logarithmic). We have also found a correlation between
the mass loss rate and both the halo mass and the rate of supernova e, as
already reported in previous works. Besides, the epoch in which most of the
baryon galactic matter is removed from the galaxy varies depending on the
SN rate and gravitational potential. The later, combined to the importance
of the RTI in each model, may change our understanding about the chemical
c
2012 RAS
2 L. O. Ruiz, D. Falceta-Gon¸calves, G. A. La nfranchi & A. Capro ni
evolution of dwarf galaxies, as well as in the heavy element contamination of
the inter galactic medium at high redshifts.
Key words: galaxies: dwarf - galaxies: evolution - cosmo logy: dark matter -
stars: winds - methods: numerical
1 INTRODUCTION
Tens of dwarf spheroidal galaxies (dSph, hereafter) are known to populate the Local Group
of gala xies (Mateo 1998), including the so-called classical dSph (Sculptor, Fornax, Ursa
Minor, Leo I, Leo II, Draco, Sextans, Carina, and Sagittarius) and the recently discovered
ones (normally called ultra faint dwarf s), observed through analysis of the deep multi-colour
photometry fro m the Sloan Digital Sky Survey (SDSS) (Willman et al. 2 005A, 2005B, Zucker
et al. 2006A, 2006B, Belokurov et al. 2006, Belokurov et al. 2007, Irwin et al. 2007, Walsh et
al. 2007, Belokurov et al. 2008, Belokurov et al. 2009, Grillmair 20 09, Watkins et al. 2009,
Belokurov et al. 201 0).
The classical dSph g alaxies are relatively large in size, typically with half light radii within
the range of 100 500pc, but present very low luminosity, M
V
> 11 (Mateo 1998). Their
sizes are related to the large velocity dispersion o f the stars, which indicates the presence
of large amounts of dark matter (Armandroﬀ, Olszewski & Pryor 1995, Mu˜noz et al. 2005,
2006, Walker 2012 and references therein). The dSph gala xies ar e therefore considered dark
matter dominated systems, with mass-to-luminosity ratios M/L > 20. The ultrafaint dwa r fs,
on the other hand, seem to exhibit even larger mass-to-luminosity ratios, with values varying
from hundreds (Kleyna et al. 2005, Muoz et al. 2006, Martin et al. 2007, Simon & Geha
2007) up to M/L
V
3400 , as observed in Segue 1 (Geha et al. 2009, Simon et al. 2011).
Consequent ly, both classical and ultrafaint dSph galaxies must be related to the dark matter
halos associated to our Galaxy as predicted by the Cold Dark Matter (CMD) cosmological
simulations (Moore et al. 1999). However, even with the recent discoveries of faint objects,
the number of dSph associated with the Milky Way ( 26 objects) is much lower than the
theoretical predictions (of hundreds of objects) from the current cosmological paradigm
of the cold dark matter (ΛCDM) Universe (Moore et al. 1999, Kyplin et al. 1999).
A proposed scenario considers a threshold in the dark matter mass of the primordial
haloes which would host a dwarf gala xy, to reconcile the discrepancy between the predictions
E-mail:dfal ceta@usp.br
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 3
of cosmological simulations and observations. The limiting ma ss is deﬁned according to the
capability of the galaxy to retain gas and maintain star format ion despite the destructive
processes during early star formation, such as supernovae (SNe) explosions and heating of the
interstellar medium (ISM) by photoionizing radiation (Somerville 2002, Benson et al. 2002,
Hayashi et al. 200 3, Ka zantzidis et al. 2004). With the mass threshold the number of existing
dwarf galaxies would be considerably lower, close to what is o bserved (Kazantzidis et al.
2004). However, the state-of-ar t cosmological simulations are able to describe the dynamics
of the dark matter component only, being unable to properly describe the contribution and
eﬀects of baryons (Diemand et al. 2007, Springel et al. 2008, Boylan-Kolchin et al. 2012). It
has been shown by several high resolution simulations, for instance, that star forma t ion and
supernovae feedback can alter the distribution and the proﬁle o f the dark matter component
of the galaxy (Read & Gilmore 2005, Mashchenko et al. 2006, Governato et al. 2010, Cloet-
Osselaer et al. 2012, Pontzen & Governat o 2012, Governato et al. 2012). A cuspy dark matter
density proﬁle can be turned into a cored proﬁle after the beginning of t he star formation
(Pasetto et a l. 2010, Governato et al. 2012).
When baryons are not included, coalescence of dark matter haloes, mergers and tidal
interactions with more massive galaxies could, in principle, explain the increase in the mass-
to-luminosity ra t io of these objects. Pe˜narrubia et al. (2008) studied the halo masses of the
Local Group dSphs based on the velocity dispersion of the luminous component. Fitting
Navarro-Frenk-White (Navarro et a l. 1996, NFW hereafter) proﬁles, virial masses of M
V
10
9
M
V
1.5 7.0kpc, with core masses M
c
10
7
M
R
c
0.2 0.4kpc, are found. Besides, Pe ˜narrubia et al. (20 08) state that the velocity
dispersion of the luminous component peaks at radii much lower than the virial radius (see
also the review of Walker 2012). Therefore, stars are usually packed in a region small enough
to be unaﬀected by tidal disruption produced, for instace, by gravitational interaction due
to neighboring galaxies.
Another possibility would be tha t these low luminosity galaxies are the result of quenched
star forma t ion, if the eﬀects of baryons are accounted. Large feedback from starbursts would
work on two ways, ﬁrstly on radiative suppression of star formation (e.g. Andersen & Burkert
2000) and secondly on the ejection of gas in form of galactic winds (e.g. Dekel & Silk 1986,
Somerville & Primack 1999, Ferrara & Tolstoy 2000). Actually, radiative suppression only
retards the star formation to the cooling timescales.
The idea of gala ctic mass-loss from starbursts in galaxies is not new (Matthews & Baker
c
2012 RAS, MNRAS 000, 1–??
4 L. O. Ruiz, D. Falceta-Gon¸calves, G. A. La nfranchi & A. Capro ni
1971, Larson 1974 , Bradamante, Matteucci & D‘Ercole 1998, Mac Low & Ferrara 1999,
Fragile et al. 2003, Sawala et al. 2009, Stringer et al. 2011, Zolotov et al 2012, and many
others). Despite of the great theoretical development of this ﬁeld, open issues still remain as
the results strongly depend on t he modeling itself. As an example, star f ormation eﬃciencies
6 1 0% would be enough to processed gas to leave the gravitational potential (Mor i, Ferrara,
& Madau 2002), but this conclusion was obtained considering a single and localized burst o f
SNe. Fragile et al. (2003) studied the chemical enrichment in dSphs considering the ejection
of processed material by SNe and found that a SNe rate of 10
6
yr
1
is enough to remove half
of the baryonic matter out o f these galaxies, though in their paper cooling eﬀects are treated
inhomogeneously within the computed volume to account for a less eﬃcient cooling in the
SNe. The eﬀects of mass-loss processes in t he evolution of dSphs can also be noticed in the
chemical enrichment of such galaxies (Marcolini et al. 2006, 2008, Lanfranchi & Matteucci
2007, Salvadori, Ferrara & Schneider 2008, Revaz et al. 2009, Okamoto et al. 2010, Sawala
et al. 2010, Kirby, Martin & Finlator 2011, Revaz & Ja blonka 2012, and many others).
Bradamante, Matteucci & D’Ercole (1999) proposed a semi-analytic chemical evolution
model for blue compact galaxies (BCG) and dwarf irregular galaxies (DIG) based on a de-
tailed calculation of winds generated from SNe feedback. In order to explain the observed
abundances of elements the winds should be able to completely remove the ISM gas out of
the galaxies, mostly due to type II SNe. Also, an unrealistic amount of dark matter would
be necessary to avoid this process to occur. Qualitative similar results were obtained by
Recchi, Matteucci & D’Ercole (2001) based on 2D hydrodynamical simulations, with addi-
tional conclusions tha t mostly heavy elements are dragged out of the galaxies by the galac-
tic winds. Kirby, Martin & Finlator (2011) argued that galactic winds aﬀect substantially
the metallicity of Milky Way satellites, since their low observed values are systematically
more metal-poor than expected from “closed-box” chemical evolution models. Lanfranchi
& Matteucci (2007) by adopting a chemical evolution mo del compared to observed stellar
metallicity distributions in Ursa Minor and Draco, claimed that strong galactic winds are
required t o repoduce the observed dat a. Using hydrodynamical simulatio ns, Marcolini et al.
(2006, 2008) predicted weak winds driven by supernovae explosions and suggested the need
of an external mechanism (such as ram pressure or tidal stripping) to account for the low
fraction of gas in dSph galaxies. Revaz et al. (2009) and Reva z & Jablonka (2012) reached
similar conclusions through a SPH code: the chemical properties of local dSph galaxies can
be achieved only if a high rate of gas loss is considered. Salva dori, Ferrara & Schneider (2008)
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 5
with a semi-analytical code also concluded tha t a large fraction of gas can be removed from
dSph galaxies as a result of star format ion feedback. Therefore, the mass-loss process during
the ear ly stages of dSph galaxy formation is fundamental for t he understanding of galaxy
formation as a whole and for comparison o f observations and cosmological simulations of
structure formation. This, however, depends o n bot h the star formation rates at early stages
and the dark matter gravitational potential. These studies however diverge on the precise
mass-loss rates obtained, basically due to the diﬀerent prescription of SNe driven wind used.
The timescales needed for the gas removal is also a matter of debate. Also, the models still
cannot properly predict if these galactic winds a r e more eﬃcient in removing enriched or
the low metallicity portion of the interstellar gas. The current techniques employed can lead
to conclusions quite diﬀerent. Also, the role of diﬀerent dark matt er distributions in the gas
removal eﬃciency has not been addressed yet.
In this wor k we f ocus on modelling the dynamics of the baryonic content of a typical
isolated dSph galaxy, and study the mass loss process in this type of galaxy based on hy-
drodynamical numerical simulations that follow the evolution of the mass content of the
system. We developed a numerical setup for typical dSphs, taking into account the g r avi-
tational potential of the dark matter content and the star format ion activity. The later, in
particular, is tr eat ed in a more consistent way as done in previous works. The theoretical
basis of the model and the numerical setup are described in Section 2. In Section 3 we
present the results, followed by a discussion of the main results and comparison to previous
works. The main conclusions of this work are presented in Section 4.
2 THE MODEL
In this work we simulate the dynamical evolution of the gas component of a typical dSph
galaxy taking into account the energy feedback from SNe, the g r avitational potential of a
given stationary dark matter distribution, and thermal losses of the heated gas, as described
below.
2.1 Numerical Setup
The simulations were performed solving the set of hydrodynamical equations, in conservative
form, as follows:
ρ
t
+ · (ρv) = 0, (1)
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2012 RAS, MNRAS 000, 1–??
6 L. O. Ruiz, D. Falceta-Gon¸calves, G. A. La nfranchi & A. Capro ni
ρv
t
+ · [ρvv + pI] = f , (2)
where ρ, v and p are the plasma density, velocity and pressure, respectively, and f represents
the external source terms (e.g. the dark matter gravity).
The set of equations is complete with an explicit equation for the evolution of the energy.
Fo r the radiative cooling the set of equations is closed calculating
P
t
=
1
(1 γ)
n
2
Λ(T ), (3)
after each timestep, where n is the number density, P is the gas pressure, γ the adiabatic
constant and Λ(T ) is the interpolation function f r om an electron cooling eﬃciency table for
an optically thin gas (see Falceta-Gocalves et al. 2010 a, for details).
The equations are solved using a second-order shock capturing Godunov-type scheme,
with essentially nonoscillatory spatial reconstruction. The time integration is perfo rmed with
a RungeKutta (R K) method. We used HLLC Riemann solver (see Mignone 2007) to obtain
the numerical ﬂuxes at each step to properly resolve the contact discontinuities and reduce
the numerical difusion at the shocks. The code has been tested extensively in previous work
as tool to study several diﬀerent astrophysical problems (Kowal et al. 2009 , Le˜ao et al
2009, Burkhart et al. 2009, Falceta-Gon¸calves et al. 2010a,b, Falceta-Gon¸calves, Lazarian
& Houde 2010, Kowal, Falceta-Gon¸calves & Lazarian 2011, Falceta-Gon¸calves & Lazarian
2011, Monteiro & Falceta-Gon¸calves 2011, Falceta-Gon¸calves & Abraham 2012).
The code is run in the single ﬂuid approximation and is not able to solve separately the
cooling functions for the initially set ISM (with low metallicity) and for the the metal en-
riched gas ejected by the SNe. For the sake o f simplicity we used a low metallicity abundance
Z = 10
3
Z
for the cooling function in all regions of the computational domain, during the
whole computational time. We also perfomed 2-dimensional tests comparing the evolut ion
of the gas for Z = 10
3
Z
and Z = Z
, and found no signiﬁcant diﬀerences. The major
diﬀerent in cooling rates are given at 10
5
K, where C and O emission lines dominate the
cooling rate for Z = Z
, being approximately one order of magnitude larger than the coo ling
rate for Z = 10
3
Z
. In bot h cases though the cooling timescales are typically similar, when
compared to the dynamical timescales.
The gas is initially set in isothermal hydrostatic equilibrium with the dark matter gravi-
tational pot ential, where we assumed T
gas
= 10
4
K. The density proﬁle peaks at the center of
the box with an assumed density n
gas
c
= 1 or 10 cm
3
, depending on the model (e.g. Mori,
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 7
Ferrara & Mori 2002) , resulting in a total initial gas mass of M
gas
10
6
M
and 10
7
M
,
respectively. The gas to dark matter mass ratio, calculated at the virial radius, is therefore
in the range of 0.001 0.01, but much larger at the half light radii.
We evolve the dynamics of the galactic gas in a 3-dimensional domain of 51 2
3
cells, equally
spaced in an uniform grid, totaling a physical lenght of 1kpc in each cartesian direction. The
grid resolution in physical units is equivalent to 1.95pc/cell. The simulations were run up
to t = 1Gyr.
2.1.1 The injection of SNe energy
The injection of energy in the code should mimic the eﬀects of real SNe explosions in the
ISM. In our model, at a given time t, the density distribution of gas is analyzed and all
cells with densities larger than the thr eshold of 0.1cm
3
are selected as possible sites of
starburst. The ad hoc assumption of a low averag e density limit for star formation is due
to the numerical resolution of our simulations. It is still not possible to completely follow
the turbulent evolution of the ISM, the creation of pa rsec scale dense clouds, and t heir
fragmentation to sub-parsec scales.
The second step is to randomly choose the cells that will have a starburst at tha t timestep,
weighted linearly by the local density, i.e. denser regions have la r ger probability as given
by the Schmidt-Kennicut law. The total number of cells chosen per timestep to present
a starburst is determined by the preset star formation rate of the galaxy. It is worth to
mention that there is no special need fo r deﬁning a speciﬁc range of temperatures in which
star formation would occur. This is basically due to the fact that, if the density is large,
the typical motions of the diﬀuse medium always end up with the creation of a thermally
unstable region that will develop into a molecular cloud, or fragment into ma ny.
Each selected cell is tagged and we inject thermal energy, proport ional to the number of
SNe expected to occur based on the SK law for the local density (see Equations 5 and 8 in
the next section, but with η = 1 and ǫ
51
= 1). Notice that in this prescription the injection
of energy is not ﬁxed spacially, nor in time, i.e. there is no ﬁxed star formation rate for
the galaxy. Depending on the dark matt er mass there will be more or less concentration of
gas in the core, which will naturally result in a larger concentration of SNe in this region.
Also, instead of injecting hundreds o f SNe at once we allow partial evolution of the gas from
the ﬁrst bursts before all energy is released from all SNe. Finally, ano ther advantage of this
c
2012 RAS, MNRAS 000, 1–??
8 L. O. Ruiz, D. Falceta-Gon¸calves, G. A. La nfranchi & A. Capro ni
type of modeling is that if too much gas is removed from the galaxy the sta r formation is
naturally quenched, instead of injecting energy even when voids are created in the simulated
ISM.
2.2 The physics of the galactic mass-loss
Larson (1974) had already proposed a quantitative model to show tha t a fraction of the SNe
energy would be converted into kinetic a nd thermal pressures, which result in galactic winds.
Fo r example, if radiative cooling is not eﬃcient, a simple energy conservation a pproach may
be used, i.e. the energy from SNe is converted into the ISM gas thermal and turbulent kinetic
energies. These may be compared t o the binding energy of the gravitational potential, as
follows (Brada ma nte, Matteucci & D’Ercole 1998):
E
kin,th
(t) > E
b
(t), (4)
where
E
kin,th
(t) =
Z
t
0
ηǫ
SN
R
SN
(t
)dt
, (5)
being η the eﬃciency in the conversion of the SN energy into kinetic-thermal pressure of the
gas
1
, ǫ
SN
the average energy released by a supernova and R
SN
the SN occurrence ra t e, given
by:
R
SN
(t)
Z
120
8
sSF R ( t τ
M
)φ(M)dM, (6)
where sSF R is the speciﬁc star formation rate, i.e. the star formation r ate divided by the
total mass of stars, τ
M
1.2M
1.85
+ 0.003 Gyrs is the evolution lifetime of a star with
a given mass M (Matteucci & Greggio 1986), a nd φ is the adopted initial mass function
(IMF).
Notice that only SNe of type II were taken into account in R
SN
, as calculated above.
Matteucci & Greggio (1 986) calculated the supernova occurrence rates for bo t h types Ia
and II, showing that SNe type II are dominant by an order of magnitude at t < 1 Gyr, and
continues more than a factor of 2 larger even for t 1Gyr. O bviously, even though basically
irrelevant for the energy budget of a galaxy, the type Ia SNe rate must be accounted for the
1
typical eﬃciencies of 1 5% have b een used in both numerical and semi-analytical models (see Bradamante, Matteucci
& D’Ercole 1998). In this work, however, we do not set an ad hoc thermal to kinetic energy eﬃciency since our numerical
prescription follows the thermal evolution of the SN burst self-consistently. Notice that we obtain eﬃciencies as low as 1%,
and as high as 60%, depending on the surrounding density and the evoluti on of the buoyancy instability. The main issue in
modelling the SN-driven wind is not the value of η, but its dependence on the local physical parameters.
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 9
chemical evolution models since most of the Fe group elements of the ISM is origina t ed in
these objects.
Therefore, if only the massive stars (M
> 8M
) are considered the IMF is reduced to
the single-slope form φ(M) 0.17M
2.3
(Kroupa 2001). Finally, in order to obtain R
SN
a
speciﬁc SFR function is needed.
Fo r the case of a delta function SFR in time, i.e. a single a nd very fast starburst, the SN
rate (R
SN
) can b e written as:
R
SN
(t)
Z
120
8
δ(t τ
M
)M
2.3
dM, (7)
which, by changing variables M to τ is reduced to:
R
SN
(t)
Z
δ(t τ
M
)(τ 0.003)
1.0175
(t
Gyr
0.003)
1.0175
. (8)
The rate of type II SNe fo r a single starburst increases with t ime, with a peak at 20Myrs,
as the number of very massive stars that explode at short timescales is much smaller than
of those that explode a t later times.
In r eality, the star fo r ma t ion rate is a f unction o f time. The Schmidt-Kennicutt empirical
law parameterizes the SFR with both local and global properties of the system: the local
density and a dynamical t imescale, respectively, i.e (Schmidt 1956, Kennicutt 1998):
SF R
ρ
k
τ
dyn
, (9)
being k 1.4. For spiral galaxies, such as the Milky Way, this empirical law has the volume
gas density ρ replaced by Σ, the surface gas density, and τ
dyn
by the typical rotation period
around t he center of the galaxy Ω. In a more realistic scenario, in which the SFR is a function
of time, the peak will occur at diﬀerent times. In Figure 1 we show the dependency of the
SNR with time for an exponentially decaying SFR (with τ being the scale of the decay).
Basically, if no energy losses are considered and knowing the star for ma t ion history, Eq.2
may be computed at a given time t and directly compared to the gravitational binding energy.
In a real system however it is not straightforward. This because the kinetic energy is not
simply cumulative fo r large timescales, i.e. the time evolution of E
kin,th
is very complex, and
many processes may take place, such as turbulent dissipation, viscosity, and the radiative
cooling. Finally, kinetic energy is also lost when part o f the ga s is removed through the
winds. This loss is generally disregarded in semi-analytical models. The absence of dissipation
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2012 RAS, MNRAS 000, 1–??
10 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
Figure 1. Type II supernova occurence rate for a single starburst with an exponentially decaying s tar formation rate, i.e.
SF R exp(t/τ). Three SFR decay timescales are considered, τ = 1(solid), 2 (dashed) and 5Gyrs (dash-dotted). Each curve
is normalized to its integral over time.
eﬀects results in an underestimation of the minimum SNe rat e needed to remove the ga s
from galaxies.
2.2.1 The role of radia tive cooli ng
The eﬃciency of SNe in pushing matter out of g alaxies depends strongly on the radiative
cooling. During the early expansion stage of a SN blast the gas temperature of the ejecta
is very high (> 10
6
K), and its expansion speed above v
SN
> 3000km s
1
. Therefore, the
expansion timescale, t
dyn
R/v, being R the radius of the shell, is much shorter than
the coo ling timescale t
cool
kT/nΛ, where Λ stands for the cooling function. As t he shell
expands the temperature decreases a nd the velocity of the ejecta diminishes in a sense that
the cooling becomes faster than the dynamical timescales. At this stage, which occurs af t er
t
c
10
4
1 0
5
ǫ
4/17
51
n
9/17
yr (Cox 1972, Le˜ao et al. 2009), where ǫ
51
represents the energy
released by the SN in units of 10
51
ergs and n is the ISM gas density in cm
3
, the typical
radius of the shell is R
c
2 0 30ǫ
5/17
51
n
7/17
pc. Further expansion of the shell will be greatly
reduced due to the conversion of the kinetic energy of the bla st wave into radiation.
The typical sizes of the SNe shells are, in g eneral, much smaller than the galaxies radii.
Considering then that most of the SNe occur near the center of the galaxies multiple explo-
sions in a short timescale are required in order to generate a gala ctic wind.
A realistic description of the evolution of SNe ejecta, and their interaction with the ISM,
is too complex to be handled analytically. Nonlinear evolution of bubbles, turbulence and
presence multiple asymmetric shocks, at diﬀerent stages of evolution are a few examples
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 11
of the physics that must be taken into account in this problem. For this reason, full 3D
numerical simulations are required.
2.3 Dark matter density proﬁles
Not only the total mass but also the density proﬁles of the dark matter haloes have an impor-
tant role on the physics o f mass loss in dSphs (Falceta-Gon¸calves 2012). The observational
detection of the dark matter haloes in dwarf galaxies is not an easy task. Their intrinsic low
luminosity, absence of diﬀuse X-ray emission and history of tidal interactions makes it even
more complicated. From theoretical point of view, CDM cosmological simulations predict
the existence of cusped pro ﬁles (e.g., Navarro et a l. 1996) , which means the dark mat ter
density diverges formally towards the centre of galaxies. The NFW dark matter proﬁle is
perhaps the most famo us member of cusped dark matter distributions, which is deﬁned as:
ρ
DM
(r) =
200
3
A (c) ρ
crit
(r/r
s
) (1 + r/r
s
)
2
(10)
where
A (c) =
c
3
ln (1 + c) c/ (1 + c)
, (11)
ρ
crit
is the critical density for a closed Universe, c a concentration parameter and r
s
the
distribution length scale.
However, recent observational and numerical wor ks have shown that cusped da r k matter
proﬁles do not ﬁt well the observational line-of-sight velocity dispersions of a large number
of dSph galaxies, as well as many other types of dwar f galaxies, such as the low surface
brightness (LSB) disk galaxies, where the gravitational potential at the centra l regions of
the galaxies tends to be less steep and cored (e.g. Burkert 1995; van den Bosch et al. 2000; de
Blok & Bosma 2002; Kleyna et al. 2003; Simon et al. 20 05; Walker et al. 200 9; Governato et
al. 201 0; Oh et al. 2011 ; Del Popolo 2012 ; Ja rdel & Gebhardt 2012). Many core dark matter
proﬁles have been suggested in the literature to account for the dark matter distribution
in dwarf galaxies (e.g., Begeman 1989; Begeman, Broeils & Sanders 1991; Burkert 199 5; de
Blok et al. 2001; Blais-Ouellette et al. 2001; Simon et al. 2 005; Amorisco & Evans 2012;
Zolotov et al 201 2). A representative of this type of density proﬁle can be derived from a
logarithmic po t ential, as follows:
Φ (r)
V
2
c
2
ln (r
2
+ r
2
c
), (12)
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2012 RAS, MNRAS 000, 1–??
12 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
Table 1. Description of the simulations
DM proﬁle r
s
or r
c
(pc) M
DM,r200
(M
)
a
M
DM,virial
(M
)
a
n
gas
c
(cm
3
)
c
SNr/yr M
gas
/M
gas
0
Log 200 1 × 10
7
1 × 10
9
1.0 1 × 10
6
0.96
Log 200 1 × 10
7
1 × 10
9
1.0 1 × 10
5
0.58
Log 200 1 × 10
7
1 × 10
9
1.0 1 × 10
4
0.23
Log 200 1 × 10
6
1 × 10
8
1.0 1 × 10
6
0.74
Log 200 1 × 10
6
1 × 10
8
1.0 1 × 10
5
0.28
Log 200 1 × 10
7
1 × 10
9
10.0 1 × 10
5
0.44
Log 200 1 × 10
7
1 × 10
9
10.0 1 × 10
4
0.04
NFW 200 1 × 10
7
1 × 10
9
10.0 1 × 10
4
0.11
NFW 500 1 × 10
7
1 × 10
9
10.0 1 × 10
4
0.04
Log 200 1 × 10
7
1 × 10
9
10.0 1 × 10
4
0.03
Log 500 1 × 10
7
1 × 10
9
10.0 1 × 10
4
0.40
a
Dark matter mass enclosed at r = 200, at z = 0.
b
virial mass enclosed the virial radius, deﬁned where the overdensity is ρ
200
= 200ρ
crit
.
c
n
gas
c
is the number density of the gas at the center of the galaxy.
where r
c
is the core radius and V
c
is the circular speed at r , result in density distribu-
tions as follows:
ρ
DM
(r)
V
2
c
4πG
3r
2
c
+ r
2
(r
2
+ r
2
c
)
2
, (13)
which feat ures a ﬂat core and is r
2
for r r
c
, similar to the observations (e.g. Jardel &
Gebhardt 2012).
The inferred discrepancy between the central dark matter distributions in dwarf galaxies
and those predicted from the CDM numerical simulations is known as the cusp/core problem.
Time evolution from an initial cusped distribution (as predicted from the CDM simulations)
to a core-like density proﬁle induced by baryonic feedback from supernovae winds (e.g.,
Governato et al. 2010; de Souza et al. 2011; Pontzen & Governato 2012; G overnato et a l.
2012), and/or tidal stirring of rotationally supported dwarf galaxies (e.g, Mayer et al. 2001a,
2001b; Klimentowski et al. 20 07, 2009; Kazantzidis et al. 2011; Loka s, Karantzidis & Mayer
2012) seem to be the most natural candidates for solving such discrepancy.
The main mechanisms that result in the ejection of matter o ut of the galaxies operate
mainly at within the ga lactic cores, i.e. even for haloes with similar masses, the radial
distribution of dark matter plays a role on the resulting mass loss rates. It is important to
emphasize that this aspect has not been a ddressed from numerical simulations before.
3 RESULTS
Initially, in order to study the energy budget of SNe explosions and the gravitational po-
tential of the dark matter total mass, we run 7 models varying the DM halo masses, for
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 13
Figure 2. Remaining gas mass nor malized by its initial value as a function of time for each of the models described in Table 1.
which we used the logarithmic dark matt er distribution (Eq.13), and star formation rates
as described in Table 1.
The total baryon mass within the simulat ed box for each model as a function of time is
shown in Figure 2. In the plot, each curve correspo nds to the r emaining gas mass at a given
time, normalized by its initial value. Lower values correspond to a larger mass loss during
the simulation, also steeper gr adients correspond to increased mass loss rates. We ﬁnd that
all the models considered in this work present, though at diﬀerent levels, mass loss. The
correlation between the mass loss and the physical prop erties of each model is discussed as
follows.
3.1 Mass loss vs DM halo mass
In order to understand the role of the dark matter potential in the mass loss rate we may
compare the results o f Models 1, 2, 4, and 5. Models 1 and 4 present equal initial physical
conditions, except for the dark matter mass. The same with mo dels 2 and 5.
In Model 1, the SNe driven wind is responsible for removing 4% of the gas after
500Myrs, while in Model 4 the total loss is of 26% considering the same timescale. After
1Gyr, Model 1 shows 9% of mass loss and Model 4 around 65%, as seen in Fig. 2.
Obviously, the gravitational binding energy here is responsible for this diﬀerence, as already
noted previously in former numerical simulations (e.g., Mac-Low & Ferrara 1999). The lower
the dark matter total mass the larger the gas mass lost in winds. However, as seen in the
comparison of these two models, the relationship between the binding energy and the mass
loss eﬃciency is not linear.
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2012 RAS, MNRAS 000, 1–??
14 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
The comparison of Models 2 and 5 results in a similar conclusion, but with some compli-
cations. Model 1 has a large binding energy and a small SN rate that resulted in a lat e and
slow wind. Model 2, which is set with a SN rate one order of magnitude larger, presents a
much stronger wind. Also, the mass loss rate is small up to t 300Myrs but increases fast
after this time, subtly reducing the mass fraction of gas.
This “two stage” proﬁle is detected in most of the models and are related to two processes:
i- the dominant mechanism of wind acceleration, and ii- the migration of the SNe lo cat ion
to outer radii. In the ﬁrst case, the slow wind is caused by the kinetic pressure of the SNe
near the center of the galaxy. The abrupt increase of the mass loss process is a result of
the Rayleigh-Taylor instability (RTI), as will be discussed in the next section. In the second
scenario, the initial bursts generate a cavity of low density gas surro unded by a dense shell.
The star formation keeps going at this shell but no more energy is injected from stars formed
within it. This process results in a temporary decrease in the SFR, which halts the galactic
wind for a short period, until the ga s falls back into the central region of the galaxy and
feeds star formation once again.
After t = 500Myrs of the ﬁrst stars birth, Model 2 presents a total loss o f 42% of the
initial gas mass while Model 5 presents a loss of 72%. Again, this diﬀerence is related
to the gravitational binding energy. However, at t = 1Gyr, the to tal gas mass loss reaches
67% and 88% for Models 2 and 5, respectively. The curves shown in F ig. 2 for these
two models present “multiple stages”, characterized by diﬀerent slopes, i.e. diﬀerent mass
loss rates. Notice that at the end of the simulations the mass loss rate for Model 2 is even
larger than for Model 5 (the slope in Figure 2 is steeper). This could be explained by a mass
loss r ate depending o n the remaining amount of gas in the galaxy. As the system loses gas
in earlier epochs the SFR diminishes and the galactic wind weakens. However, this is not
the case for these two models. Here, the RTI is speeding up the ma ss loss process of Model
2 at later epochs.
3.2 Rayleigh-Taylor instability
The RTI occurs when a low density gas interpenetrates a denser one, as the cavities created
by SNe explosions buoyantly rising up through the denser ISM. The perturbation grows
exp onentially (i.e. δv exp(γt)) at a rate given by ( Ristorcelli & Clark 2004):
γ =
s
gk
ρ
ISM
ρ
cav
ρ
ISM
+ ρ
cav
, (14)
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 15
Figure 3. C olumn density (top), gas density map (center) and thermal energy density (bottom) for t = 0, 50, 100 and 200Myrs,
from left to right, obtained from Model 3.
being k the wavenumber of t he perturbation, g the acceleration of gravity and ρ
cav
and ρ
ISM
the densities of the SNe blown cavity and of the ISM, resp ectively.
Interestingly, the RTI is more important in galaxies with more massive haloes, or in
more concentrated haloes. This result contradicts the basic assumption derived from Eq. 1,
namely the requirement for the kinetic energy to be larger than the gravitatio nal binding
energy. The critical point is that a homogeneous ISM is implicit in Eq. 1, though in reality
SNe explosions create cavities of lower density gas that may be buoyantly unstable, which
will be stronger in more ma ssive haloes.
The RTI also plays a major role in Models 6 and 7. These runs were set with t he same
parameters as Models 2 and 3, respectively, except for the larg er ISM gas density. As we see
in Figure 2, Models 6 and 7 lost more mass compared to the later two. In terms of energy
conservation, for an homogeneous ISM, the galactic wind should only depends on the energy
injected by SNe (i.e. on the SFR ) and on the gravitational potential. However, as mentioned
before, the RTI growth rate depends on the diﬀerence between the cavity and ISM densities,
i.e. denser ISM result in a faster rise o f the low density gas.
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2012 RAS, MNRAS 000, 1–??
16 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
It is possible to estimate the timescales for the RTI to eﬃciently raise the low density
gas out of the galaxy. If the perturbations are large compar ed to the dissipation or injection
scales (i.e. h > 10 20pc) the instability is a ssumed to enter in a self-similar growth phase,
and the mixing length is t hen approximatelly equal to:
h(t) 0 .05gt
2
ρ
ISM
ρ
cav
ρ
ISM
+ ρ
cav
. (15)
Fo r ρ
cav
= 0.5ρ
ISM
, h = R
gal
3 00pc at t = τ
RT
1 00Myrs for M
DM,viri al
= 10
9
M
, a nd
τ
RT
290Myrs for M
DM,viri al
= 10
8
M
. If ρ
ISM
cav
is ten times larger, as we varied in the
simulations, t he timescales will be 2 times shorter.
The buoyant rise of the SNe inﬂated cavities is clearly seen in Figure 3, where we show
the column density (to p), central slice of density (middle) and integrated thermal energy
density (bottom), at diﬀerent evolutionary stages of the run fo r Model 3.
Just few million years after the ﬁrst starburst SNe start the heating and stirring of the
ISM, as shown in the left panel (t = 0) of the thermal energy density projection. Each
bright spot represents a SN explosion. Its further evolution, with cooling taken into account,
results in stalled dense shells surrounding low density cavities. These cavities are seen in
the density map (middle row) for t = 50Myrs, as well as for the column density (top row).
When several explosions occur close to each other a large cavity is created. This low density
bubble becomes convective unstable and rises up, as seen at the density maps and column
density projections between t = 50 and t = 100Myrs. The instability is then responsible fo r
the creation of a tunnel through which gas may scape.
Regarding the gas ﬂows, the enhanced gas velocity t hrough these tunnels is also seen in
Figure 3 as normalized vectors over-plotted to the density maps. For Model 3, it is clear
that the mass lo ss is no t spherically symmetric. However, the tunnels created by the RTI are
short lived. Once the pot ential energy of t he cavities are released, the ﬂow that continues
to rise through them do not present pressure large enough to prevent the ISM to collapse
it. In Figure 3, it is clear the destruction of the diagonal ﬁlament between t = 100 and
t = 200Myrs. In the mean time an another bubble is created and rose up in the vertical
direction, as seen at t = 200 Myrs.
The cyclic process of buoyantly unstable cavities is important to reactiva t e star formation
at the central region of the galaxy. When a large cavity is created the star formation cease
due to the decrease in density below the critical threshold. At this time, the star formation
migrated to the surrounding denser shell. This is clearly seen in the integra t ed energy density
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 17
maps of F igure 3. The bright spots, representing the SN explosions, are concentrated in the
center of the galaxy at t 6 50 but moves to larger radii at t > 100. When the cavity moves
upward due to the RTI, the ISM denser material occupies the center of the galaxy once
again, bringing the local density above the critical value.
The competition between the RTI and kinetic pressure may be estimated by comparing
two timescales. One is the RTI timescale described above, the other is the timescale for the
SNe to release energy into the ISM:
τ
kin
E
b
ηǫ
SN
R
SN
. (16)
If τ
kin
< τ
RT
, the kinetic energy released by the SNe will result in galactic winds before the
RTI is able to rise the buoyancy cavities out of the g alaxy. In other words, for a typical
dSph, the RTI will play a major role in releasing part of the energy injected by SNe if:
R
SN
<
7 × 10
7
η
M
DM,r200
10
7
M
!
3/2
ρ
ISM
ρ
cav
ρ
ISM
+ ρ
cav
!
1/2
SN yr
1
. (17)
The fraction of the mass loss due to the RT instability
˙
M
RT
/
˙
M
tot
may then be estimated.
Numerically, we ﬂag each buoyantly unstable cell of the cub e and track its dynamical evo-
lution outwards (basically the density ρ
RT
and velocity ﬁeld v
RT
.)
˙
M
RT
˙
M
tot
=
R
ρ
RT
(t)v
RT
(t) · dA
R
ρ
gas
(t)v
gas
(t) · dA
, (18)
where A is deﬁned a s the outer boundary of the simulated domain.
In Fig ure 4 we show slices of the ﬂagged unstable cells, overplotted with the corresponding
velocity vectors, fo r Models 1, 2, 5 and 6, at t = 50Myrs. The color scheme corresponds to
the local density of the unstable cells.
The relat ive ma ss loss rate due to the RT instability is also presented in the plots.
Obviously, for Model 1, where the rate of explosions is low, it is more diﬃcult for the
interacting SNe to generate large bubbles. The wind obtained in this model is basically
wave-driven. Model 2, with 10 times more explosions, result in an increased RT-driven
wind. However, the dark matter mass and the local density also play a role. Model 5, with
a dark matter mass 10 times smaller than in Model 2, result in lower RT-driven mass loss
rate. In this case, the explosions push the gas from the centra l region outwards resulting in
increase mass loss rates, but dominated by the direct transfer of momemtum from the SNe
to the gas. Also, as seen for Model 6, the increased local gas density is less inﬂuenced by the
SNe directly, but increases the RT-instability, resulting in a relative impor t ance of 40 %
in the mass loss rate. The muchroom like structures are perfectly recognized in this model.
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2012 RAS, MNRAS 000, 1–??
18 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
Figure 4. Maps of density overplotted to with velocity vectors of Rayleigh-Taylor unstable regions in Models 1, 2, 5 and 6, at
t = 50Myrs. The fr action of the Rayleigh-Taylor excited galactic wind at the given time, relative to the total, is also i ndi cated.
It is also seen from Figure 4 that the rising bubbles are modiﬁed by Kelvin-Helmholtz and
Karman vortex instabilities, which destroy the spherical mo r pho logy of the cavities, excite
turbulence behind them and enhance the gas mixing with the colder external gas.
We obtained a mass loss r ate contribution of 5 40% due to the RT instability for
all models. This eﬀect though is strongly a t t > 200Myrs. Once the quasi-steady wind is
developed, it becomes more diﬃcult to precisely estimate the fraction of the mass loss due
to the RT instability. Basically, most of the g as in the center of the cube is heated and part
of it also gain momemtum from the SNe explosion. In this sense we expect a transition in
the chemical enrichment of the intergalactic medium due to the galactic winds.
3.3 Mass loss vs SNe rate
Despite of the diﬀerent particular mechanisms of galactic wind acceleration (e.g. kinetic
pressure and convective instability), the main source of energy and momentum for all these
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 19
Figure 5. Mass loss rate as a function of time for each of the models described in Table 1.
is still stellar feedback. It is important then to study the relationship between the mass lo ss
rates obtained from the simulat ions and the preset r ate of SNe (R
SN
).
The SNe rate is the only diﬀerence in the initial setup of the Models 1, 2 and 3. The
remaining baryon mass for each model at t = 500Myrs is shown in Table 1. Model 3 presents
the lowest value, which is related to its larger SF R, and R
SN
as a consequence. Model 1, on
the other hand, presents a small mass loss, of only 4%, compared to 42% for Model 2, and
77% for Model 3. At t = 1Gyrs, these values a r e 9%, 70% a nd 85%, respectively. The
correlation between R
SN
and mass loss rate is also clear, as shown in Figure 5. This is also
true for the other models.
As seen in Figure 5, the mass loss process is not stationary, varying in short timescales,
with the presence of peaks of fast mass loss and periods of weak, or even absent winds. As
example, Model 3 presents two events of increased mass loss rates, with
˙
M 0.9% Myr
1
at
t 60Myrs and
˙
M 0.3 5% Myr
1
at t 150Myrs, decreasing slowly with time afterwards,
while Model 2 present a very similar proﬁle, with a single peak (
˙
M 0.3% Myr
1
), but
much later around t 400Myrs. At this stage, the mass loss rate of Model 2 is even larger
than in Model 3.
Fo r Models 4 and 5, and Models 6 and 7, the correlation of mass loss rates with SF R
is even clearer. The peak in mass loss rate for Model 4 is two times smaller, and occur
7 0Myrs later tha n for Model 5. Model 6 presents a peak in mass loss r ate a lmo st 5 times
smaller, and delayed in 300Myrs compared to Model 7. For this case in particular t he RTI
plays a major ro le on this diﬀerence.
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2012 RAS, MNRAS 000, 1–??
20 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
It is worth noticing that the duration of the strong winds is also dependent on R
SN
.
Basically t his is due to the loss o f gas, which in turn supplies further star formation. Once
the ga laxy presents a strong wind most of volume will not present ideal physical conditions
for new starbursts. In some cases, gas will fall back to the core of the galaxy, triggering a
new sequence of SNe, as seen in Models 3 and 7.
3.4 Dark matter density proﬁle
In order to test the role of diﬀerent dark matter distributions in the galactic wind accel-
eration and insta bilities, we additional run 4 models, considering the two diﬀerent density
distributions (namely the NF W and logarithmic), for two diﬀerent concentrations radii, as
described in Table 1 .
The mass distribution of the modelled dark matt er radial distributions are given in
Figure 6 (upper panel). The plot refers to the total dark mass enclosed as a function of the
radius. Notice that we have assumed all distributions to give same values at r = 200pc. This
follows the result given in Walker (2 012) (see its Figure 18) showing that ﬁts to the velocity
dispersion of stellar population in dSph galaxies predict approximately the same enclosed
mass near the halﬂight radius, regardless the dar k matter distribution tha t is adopted. The
time evolution of the total gas mass in each case is given in the bottom panel of Figure 6.
We ﬁnd that all models give strong winds and large mass loss in the timescales of t 1Gyr.
Model 11, with a logarithmic DM density proﬁle with concentra tion r adius r
c
= 500pc
presents the largest delay in the mass lo ss rate, compared to the other 3 models tha t present
very similar mass loss rates as function of time. The reason for this diﬀerence is the lower
gravity acceleration at lower radii for Model 11. This may be r elat ed to a stronger RT-
instability occuring at models where the dark matter potential is larger at smaller radii. In
this sense, models with NFW dark matter distributions would tend to show stronger RT
instabilities.
4 DISCUSSION
The numerical simulatio ns provided in this work show that galactic winds may have occurred
in the early stages of most of the dwarf g alaxies. Several previous works studied the same
problem, considering similar schemes, namely considering SNe a s the main source of energy
to tr igger the galactic wind. Despite of the numerical resolution, which is r esponsible for
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2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 21
Figure 6. Up: total enclosed dark matter mass as function of radius for Models 8 - 11 (see Table 1). Bottom: total r emaining
gas mass as a function of time.
relatively important changes in the obtained results, the major diﬀerence between these and
the present work relies on the treatment of the SNe as a random event, both in time and
in space. Also, the treatment of the radiative cooling homogeneously in the computational
grid is also diﬀerent to t he prescriptions used in the past.
4.1 Comparison to previous works
Marcolini et al. (2006) studied the SNe feedback in the chemical evolution of the particular
case of the Draco dwarf spheroidal galaxy using a similar scheme. These authors computed
few 3D numerical simulations with a maximum spatial resolution of 13pc per cell, compared
to the 1.95pc per cell in our case. In their scheme, the SNe are supposed to occur in a
sequence o f instantaneous and identical bursts. In contrast to our model, the SN events were
random in space but not random in time. According to the authors, the simultaneous bursts
resulted in a total energy released by t he SNe orders of magnitude larger than the binding
energy of the ISM. Even though, the galactic wind produced was negligible. This was due
to the large eﬃciency of the radiative cooling. We note that, in their model, the assumed
star for ma t ion history resulted in a SNe rate below 10
6
SN yr
1
for the whole simulation
(up to t = 3Gyr). This result is in perfect agreement with our simulations.
As in their speciﬁc case, we found that even when the SNe result in a larger energy
released compared to the gravitational binding energy, the radiative cooling is eﬃcient in
removing most of this energy from the system. The consequence is a much lower net ki-
netic/thermal pressure of the ISM, which inhibits the mass loss. Besides, we provide a more
detailed study of the physical parameters and show that, despite of the eﬃcient cooling
of the SNe heated gas, the galactic wind may be important when r estricted conditions are
fulﬁlled.
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2012 RAS, MNRAS 000, 1–??
22 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
Fragile et al. (2003) also studied the dynamical evolution of the gas component during
the early stages of dwarf galaxies. They have already recognized t hat the results are sensitive
to numerical overcooling of the shocked gas, which leads to an underestimation of the eﬀects
of the supernovae. In order t o prevent this overcooling they did not compute cooling within
the SN-ISM shock until it has already evolved the Sedov phase. Despite o f the unrealistic
treatment of the physics in their scheme, due to the computatio nal limitation at that time,
they have realized that, in the absence of cooling, the hot a nd enriched g as fro m the super-
novae would eventually leave the galaxy because of their buoyancy. They also pointed out
that the numerical overcooling would prevent this eﬀect.
In our work, we calculated the r adiative cooling of the models using a high-order nu-
merical scheme and ﬁner g r id resolution compar ed to the previous works. This allowed a
self-consistent treatment of the dynamical evolution of individual supernovae. We a lso ﬁnd
that radiative cooling plays a maj or role in the dynamical evolution of the ISM ga s. The
cooling timescale τ
cool
kT/nΛ, gives τ
cool
> τ
RT
for the bubbles, but is very short (com-
pared to the dynamical timescales) for the typical ISM. It means that the thermal energy of
the ISM gas is quickly lost by radiation, long before t he thermal/kinetic pr essure is able to
drive the galactic winds. However, the low density cavities present longer coo ling timescales,
which result in eﬃcient RTI dr iven outﬂows.
The star formation history of dSph galaxies strongly depends on the properties of their
winds. We have shown that, depending on the dark matter proﬁle and SN rate, the thermal
and kinetic pressures at the center of the galaxy push the gas outwards. The result is a
low density core gas, and the star formation may be quenched. Once the central region
cools and kinetic pressure is dissipated, the envelope gas falls back into the galaxy and
new stars form. Notice that cyclic starbursts due to episodic galactic winds have also been
obtained in SPH numerical simulations (e.g. Stinson et al. 2007). Numerical tests though
show that the RayleighTaylor instability is poorly resolved by SPH techniques. This because
SPH introduces spurious pressure forces bacause of the smoothing kernel radius, over which
interactions are severely damped (Agertz et al. 2007). In this sense, it is clear that the
RT instability is possibly not the dominant mechanism in quenching sta r formation at the
center of the galaxy, nor in triggering the g alactic wind. However, it may be importa nt in
fast delivering metal enriched gas to the intergalactic medium - long before t he diﬀusion of
the elements at local ISM is possible -, and on the release of thermal energy from the core.
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Mass Loss in Dwarf Galaxies 23
4.2 Winds and the chemical evolution of dwarf galaxies
Mass loss is claimed to be one of t he main mechanisms that controlls the chemical evolution
of dSph galaxies. The removal of a considerable fraction of the gas content of the galaxy
will aﬀect directly the star formation and also the production of new chemical elements and
the enrichment of the ISM. For instance, Recchi, Matteucci & D‘Ercole (2001) studied the
2D-chemodynamical evolution of the gas in a dwarf irregular galaxy ( dIrr) considering the
eﬀects of SNe driven winds. The authors concluded that selective galactic winds, in terms of
elements that are removed, can explain most of the observed abundances in these objects.
This could possible be applicable to the early stages of dSph galaxies as well. If this is t he case
several observational constraints will have their pattern deﬁned by t he mass loss rate. The
assumption of a galactic wind occurring during t he evolution of the galaxy can explain, for
instance, the mass-metallicity and mass-luminosity relations, as well as the relation between
[O/H] and mean velocity dispersions, observed in dSph galaxies. Richer, McCall & Stasinska
(1998) suggested that there is a correlation between [O/H] and mean velocity dispersions
in several types of dynamically ho t g alaxies t hat can be explained naturally if the chemical
evolution proceeded until the energy input from SNe g ave rise to a galactic wind. A similar
scenario was presented by Tamura, Hirashita & Takeuchi (2001), where they explain the
mass-metallicity relation as due to the SF proceeding at a very low ra t e until a galactic
wind develops and expels the gas out of the system.
From the theoretical point of view, galactic winds were also suggested as a necessary
mechanism to explain some chemical properties of local dSph galaxies, even though there is
a controversy regarding the rate of the gas loss. Kirby et al. (2011) claimed that the observed
low metallicities cannot be ﬁtted by a closed box model of chemical evolution (given the long
timescales for the SF in such galaxies) implying that the removal of gas is required to avo id
an abnormal increase in metallicity. Besides, the lowest va lues of the [alpha/Fe], the trends
of the neutron capture elements and the shape of the stellar metallicity distributions can be
very well repro duced by models of chemical evolution that adopted SNe triggered galactic
winds, with a high eﬃciency which is adjusted by hand to ﬁt the da t a (Lanfranchi and
Matteucci 2004, 2007) . The removal of a large fraction of the ga s will decrease substantially
the SFR, almo st ceasing the for ma tion of new stars and the injection o f oxygen and r-
process elements in the ISM. Iron and s- process elements, on the other hand, are produced
and injected in the medium in a much longer timescale (up to some Gyr), giving rise to
c
2012 RAS, MNRAS 000, 1–??
24 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
low abundance ratios after the wind starts. The decrease in the SFR will also prevent the
formation of stars with high metallicities, keeping the mean metallicity of these galaxies low
with a stellar metallicity distribution peaked at [Fe/H] below -1.4 dex.
Diﬀerent kinds of simulat ions, either hydrodynamical (Marcolini et al. 2006 , 2 008) or with
SPH codes (Revaz et al. 2009, Revaz & Jablonka 2012), reach, however, other conclusions
regarding the eﬃciency of gas removal. In the SPH simulatio ns, normally, the hydrodynamics
of the gas is not treated in detail a nd the eﬃciency with which thermal energy is converted
into kinetic energy is a free parameter adj usted ad-hoc. Revaz & Jablonka (2012), in their
analysis of the dynamical and chemical evolution of dSph ga laxies, adopted a low value for
the star formation feedback eﬃciency in their simulations to ﬁt the ﬁnal predicted metallicity
to the observed values. If the feedback eﬃciency is too high, the metallicity would be below
what is observed. In fact, these authors claim that the most sensitive para meter in their
code is this eﬃciency and that the low values adopt ed ( between 0.03 and 0.05) imply that
strong winds are not compatible with the observations. The main causes for the low values
for the feedback eﬃciency are, however, not treated. In the simulations of Marcolini et
al. (2 006, 2008), on the ot her hand, the dynamics of the hot gas was taken into account
carefully, but the ga lactic wind produced was very weak and capable of removing only a
small fra ctio n of the gas. The main reason behind that result, is that the a dopted eﬃciency
of the radiative cooling was large. In none of these cases (nor in any other study) the eﬀects
of the instabilities in the ISM caused by the low density gas that interpenetrates a denser
region due to the SNe explosion is considered. As previously mentioned, the occourence of
RTI can alter signiﬁcantly the scenario for the occurence of the galactic wind, in respect of
both the epoch when the gas starts to be removed and the rate at which the gas is lost.
The epoch when the gas starts to be removed and the rat e of this process a r e crucial in the
models o f chemical evolutio n. The rate of the wind is, in general, a free parameter adjusted
just to ﬁt observational constraints, and the time when it begins depends on the energetics
of the galaxy: it starts when t he kinetic energy of the gas exceeds the binding energy of the
galaxy. The ﬁrst term depends on the SNe rat e and the last one on the mass of the dark halo
(Bradamante et al. 1998, Lanfranchi & Matteucci 2003). The relation between these terms
and t he mass loss is not evident, as shown by the hydrodynamical simulations presented in
this work. As discussed in t he previous sections, gas can be r emoved from the galaxy even if
the kinetic energy is not lar ger than the binding energy, mostly due to the RTI. The cavities
created by SNe explosion carry gas out of the gala xy even in more massive haloes. In fact,
c
2012 RAS, MNRAS 000, 1–??
Mass Loss in Dwarf Galaxies 25
this eﬀect can be stronger in these systems. Besides that, the removal of gas is not uniform,
as seen in Figure 2. The “two stage” proﬁle of the mass loss can aﬀect directly the SFR and
the enrichment of the medium. Following the oscillation of the SFR, the enrichment of the
medium will also vary in time, leading perhaps to a spread in observed abundances. What
is similar in the simulations and chemical evolution models is the dependence of the total
amount of lost mass on the dark matter halo mass and in the SNe rate. Galaxies with more
dark matter tend to present also larger masses for the stellar component, whereas galaxies
with higher SNe rate present smaller gas mass at the end of the simulations. Variations in
these two quantities aﬀect the amount of gas mass loss and the epoch when gas starts to be
removed, giving rise to diﬀerent chemical enrichment histories (see also Revaz & Jablonka
2012). Obviously, the details of the enrichment history due to t he mass loss as predicted by
the simulations can only be fully understood by adopting chemical evolution models that
take into account the results presented here.
A major contrast between a RTI-dominated and a wave/turbulent scenario is the o r igin
of the gas that is being removed out of the galaxy. The kinetic pressure tends to push the
ISM as a whole upwa r ds, thus removing, ﬁrst and mostly, the low metallicity fraction of t he
gas. The RTI, on the other hand, is responsible for the rise of the metal- enriched hot bubbles
of gas, resulting in a selective wind. In this case, a larg e fration of the heavy elements would
be ejected out of the galaxy to the intergalactic medium, while the low metallicity ISM
would remain. This is in special agreement with both the o bservations and the predictions
of semi-analytical models of galactic chemical evolution for the dSph. This process may also
have important cosmological impact since dwarf galaxies are believed to be formed earlier
than the more massive ones.
5 CONCLUSIONS
In this work we presented a number of hydrodynamical numerical simula t ions of the time
evolution of dSph gas component, studying its dependence on the star formation history
and the dark matter mass.
In agreement with previous works, we found a strict, but not trivial, dependence between
the mass loss rate and both the star formatio n rate and the gravitational binding energy of
the system. The galactic winds are easily triggered in most of the galaxies, except for those
with very little supernova occurence rates (R
SN
< 10
6
yr
1
).
c
2012 RAS, MNRAS 000, 1–??
26 L. O. Ruiz, D. Fal ceta-Gon¸calves, G. A. Lanfranchi & A. Caproni
As main results, we conclude that:
the complexity of these dependences arise from the diﬀerent mechanisms that may
trigger the galactic wind, e.g. the kinetic pressure and the RTI. More massive haloes tend
to inhibit the formation of kinetic/thermal pressure driven winds, but on t he other hand
accelerate the rise of the buoyant unstable cavities of ho t gas.
as showed in previous works, the radiative cooling may reduce the eﬃciency of the SNe
in generating galactic winds. However, we found that the RTI may still occur due to the
longer cooling timescales of the cavities.
galactic winds may be selective in terms of the elements ejected to the intergalactic
medium, depending on the dominant acceleration process.
This is particularly important in the sense that the dark matter distribution of dSph
galaxies may severely change during their evolution. As a consequence, the main wind ac-
celeration mechanism, and the type of chemical elements preferred to be driven out of the
galaxy, will be also diﬀ erent.
From the t imescales derived in this work it is possible that the winds of dSph have enriched
the intergalactic medium before the massive galaxies have been formed.
With more computational resources, we plan to extend this work in the near future by
running more simulations covering with better resolution the range of the important physical
parameters, such as the star formation rate and the dark matter halo mass. Also, it will be
interesting to study the diﬀerence between kinetic/thermal and RTI-driven winds in terms
of a multi-ﬂuid hydrodynamical code in order to follow more consistently the dynamical
evolution of the low and high metallicity fractions of the ISM.
ACKN OWLEDGMENTS
LOR t hanks INCT-A/CAPES (573648/2 008-5) for ﬁnancial support. DFG thanks CNPq
(no. 300382/2008-1) and FAPESP (no. 2011/129 09-8) for ﬁnancial support. GAL thanks
CNPq (no. 302112/2009-0) .
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