Hydrodynamics of high-redshift galaxy collisions: From gas-rich disks to dispersion-dominated mergers and compact spheroids

0.51 MB·English

by  Frederic Bournaud

Draftversion January14,2011
PreprinttypesetusingLATEXstyleemulateapjv.11/10/09
HYDRODYNAMICS OF HIGH-REDSHIFT GALAXY COLLISIONS:
FROM GAS-RICH DISKS TO DISPERSION-DOMINATED MERGERS AND COMPACT SPHEROIDS
Fr´ed´eric Bournaud, Damien Chapon, Romain Teyssier, Leila C. Powell
LaboratoireAIMParis-Saclay,CEA/IRFU/SAp–CNRS–Universit´eParisDiderot,91191Gif-sur-YvetteCedex,France.
[email protected]
Bruce G. Elmegreen
1
IBMT.J.WatsonResearchCenter,1101KitchawanRoad,YorktownHeights,NewYork10598USA,[email protected]
1
0
2 Debra Meloy Elmegreen
n VassarCollege,Dept. ofPhysics&Astronomy,Poughkeepsie, NY12604,[email protected]
a
J
Pierre-Alain Duc
3
LaboratoireAIMParis-Saclay,CEA/IRFU/SAp–CNRS–Universit´eParisDiderot,91191Gif-sur-YvetteCedex,France.
1

] Thierry Contini, Benoit Epinat
O
Laboratoired’AstrophysiquedeToulouse-Tarbes,Universit´edeToulouse,CNRS,14AvenueEdouardBelin,31400Toulouse,France.
C
h. Kristen L. Shapiro
p DepartmentofAstronomy,CampbellHall,UniversityofCalifornia,Berkeley,CA94720.
AerospaceResearchLaboratories,NorthropGrummanAerospaceSystems,RedondoBeach, CA90278, USA.
-
o Draft version January 14, 2011
r
t ABSTRACT
s
a Disk galaxies at high redshift (z 2) are characterized by high fractions of cold gas, strong tur-
[ ∼
bulence, and giant star-forming clumps. Major mergers of disk galaxies at high redshift should
4 then generally involve such turbulent clumpy disks. Merger simulations, however, model the ISM
v as a stable, homogeneous, and thermally pressurized medium. We present the first merger simula-
2 tions with high fractions of cold, turbulent, and clumpy gas. We discuss the major new features of
8 these models compared to models where the gas is artificially stabilized and warmed. Gas turbu-
7 lence, which is already strong in high-redshift disks, is further enhanced in mergers. Some phases
4 are dispersion-dominated, with most of the gas kinetic energy in the form of velocity dispersion and
. verychaoticvelocityfields, unlike mergermodels using athermally stabilizedgas. These mergerscan
6
reach very high star formation rates, and have multi-component gas spectra consistent with SubMil-
0
limeter Galaxies. Major mergers with high fractions of cold turbulent gas are also characterized by
0
1 highly dissipative gas collapse to the center of mass, with the stellar component following in a global
: contraction. The final galaxies are early-type with relatively small radii and high Sersic indices, like
v high-redshift compact spheroids. The mass fraction in a disk component that survives or re-forms
i
X after a merger is severely reduced compared to models with stabilized gas, and the formation of a
massive disk component would require significant accretion of external baryons afterwards. Merg-
r
a ers thus appear to destroy extended disks even when the gas fraction is high, and this lends further
support to smooth infall as the main formation mechanism for massive disk galaxies.
Subject headings: galaxies: formation — galaxies: interactions — galaxies: high-redshift — galaxies:
elliptical and lenticular, cD — galaxies: structure
1. INTRODUCTION Bournaud & Elmegreen 2009; Conroy & Wechsler 2009;
Genel et al.2010), aboutone-thirdofagalaxy’sbaryons
In the Λ-CDM cosmological model, collisions and
are still expected to be provided by significant mergers
mergersareanimportantgrowthmechanismforgalaxies,
(e.g., Dekel et al. 2009; Brooks et al. 2009).
and most of them should have occurred at high redshift
The effect of the merger of two disks galaxies has
(z >1,e.g.,Stewart et al.2009). Majormergers,where
been largely explored in the low-redshift context, where
the ratio of the baryonic masses of the involved galax-
galacticdisksaremostlymadeupofstarswithrelatively
ies is close to one, are in particular important for the
modest fractions of cold gas. In such conditions, it
build-upofmassivegalaxies(Hopkins et al.2010). Even
is known that a major merger of two spiral galaxies
if recent models and high-redshift observations suggest
typically produces a remnant resembling an ellipti-
that the growth of galaxies near L is largely through
∗ cal or early-type galaxy (ETG) (Barnes & Hernquist
relatively smooth and cold accretion (Dekel et al. 2009;
2
1996; Mihos & Hernquist 1996; Naab & Burkert proposal that high-redshift merger remnants could be
2003; Bournaud et al. 2004a; Naab et al. 2006, 2007; dominated by large rotating disk components rather
Bournaud et al. 2007b; Hoffman et al. 2010). There are than bulges and spheroids (Springel & Hernquist 2005;
still some differences between the predictions of merger Robertson et al.2006). Therehavebeenclaimsthatsuch
models and observations (Burkert et al. 2008) but there disky merger remnants cannot account for the observed
is, overall,an ample consensusthat hierarchicalmerging properties of high-redshift disk galaxies (Shapiro et al.
is the main formation channel for present-day ETGs. 2008; Bournaud & Elmegreen 2009) but this remains
At high redshift, the role of major mergers in the actively debated in simulations (Robertson & Bullock
formation of particular galaxies and in the growth 2008) and in observations (Hammer et al. 2009).
of galaxies in general remains much more debated. Thus, at least three major unknowns remain: the
First, determinations of the merger rate from high- frequency and observational signatures of high-redshift
redshift surveys are usually based on irregular struc- mergers, their role in forming the high-redshift popula-
tures or disturbed kinematics (e.g., Conselice et al. tionsofETGs,andtheabilityofmassivedisk-dominated
2003; Lotz et al. 2006, 2008; Overzier et al. 2010; galaxies to survive these events.
Jogee et al. 2009; Lo´pez-Sanjuan et al. 2009; Puech
Thedynamicsandoutcomeofmergershaveneverbeen
2010). However, primordial galaxy disks can have
modeled for realistic, high-redshift galaxies. Simula-
irregular morphologies and disturbed kinematics even
tions by Cox (2004), Springel & Hernquist (2005), and
when they are mostly isolated, not undergo-
Robertson et al.(2006)consideredhighgasfractionsand
ing strong interactions (Elmegreen et al. 2007, 2009;
concluded that disks could survive or re-form after a
Genzel et al. 2008; Bournaud et al. 2007a; Genzel et al.
merger. However, these simulations had high thermal
2008; Bournaud et al. 2008; Dekel et al. 2009), so
pressuresupportintheISM(temperature>104K),which
the actual merger rate remains unknown. Also,
forces the gas to be smooth and stable in the isolated
high-redshift disk galaxies have typical morphologies
galaxies and in the colliding pairs as well.
that differ from nearby spirals (Cowie et al. 1996;
Star-forming galaxies at high redshift (z = 1
Elmegreen & Elmegreen 2005; Elmegreen et al. 2007;
−
5) are very different from such models. They
Genzel et al.2008),andtheirmergerscouldalsohavedif-
are generally gassy, clumpy, and turbulent, with
ferent morphologies and kinematics compared to nearby
50% of their baryons in cold molecular gas
mergers,potentiallymakingtheidentificationofmergers
∼
(Daddi et al. 2010a; Tacconi et al. 2010), giant star-
more ambiguous: for instance, asymetries and clumpi-
ness in optical imaging are often attributed to merg- forming clumps of 107 109 M⊙ (Elmegreen et al.
−
ers (Conselice et al. 2003; Lotz et al. 2008), but high- 2004, 2007, 2009), and velocity dispersions of sev-
redshift disk galaxies seem to frequently form massive eral tens of km s−1 (F¨orster Schreiber et al. 2009;
clumps just by internal instabilities that do not require Shapiro et al. 2008; Genzel et al. 2008; Epinat et al.
interactions (Elmegreen et al. 2007, 2009; Genzel et al. 2009; Queyrel et al. 2009). Associated star formation
2008). Even in cosmological simulations, the galaxy rates (SFRs) are around 100 M⊙ yr−1. While
merger rate is continuously revised (e.g., Genel et al. most observations of high-redshift star forming galaxies
2008,2010,andreferencestherein). Inparticular,merg- concerned only very massive galaxies (above the crit-
ers of dark halos do not necessarily lead to the merging ical mass L ), recent studies of z > 1 lensed galax-
∗
of their central galaxies, and the baryonic mass ratio of ies find that gravitational instabilities and turbulent
galaxymergerscansignificantlydifferfromthedarkmat- clumps could also be dominant in lower-mass galax-
ter mass ratio of their host haloes (Hopkins et al. 2010). ies (Jones et al. 2010; Swinbank et al. 2010). The
Second, the outcome of major mergers is usually con- morphology and dynamics of the disks suggest that
sideredtobeearly-typegalaxies(ETGs). However,high- the observed clumps form by gravitational instabilities
redshiftETGsareoftenunexpectedlycompactcompared (Elmegreen et al. 2004; Elmegreen & Elmegreen 2005;
tonearbyellipticalsandmergersimulations(Daddi et al. Shapiro et al. 2008; Bournaud et al. 2008; Daddi et al.
2005;Trujillo et al.2006;van Dokkum et al.2009,2008; 2010a). Simulations of this process require cosmological
Kriek et al. 2009). The role of mergers in forming codes that allow for highly supersonic turbulent speeds
these ETGs has been questioned: while their evolu- (Agertz et al. 2009; Ceverino et al. 2010). Even low-
tion into modern, more extended elliptical galaxies can redshift spiral galaxies have an unstable, cloudy ISM
be explained through continuous hierarchical merging supported mostly by supersonic turbulence rather than
(Naab et al. 2009), the emergence of compact ellipticals thermal pressure (e.g., Burkert 2006). Recent simula-
at high redshift remains more mysterious. tionsshowedthataspatialresolutionof10%ofthe scale
Third, the most general issue is the ability of disk- heightwithfulltrackingofturbulentmotionsisrequired
dominated galaxies to survive violent mergers. While to reproduce the three-dimensionalinertial range of tur-
it is known that mergers of disk galaxies can produce bulence inside a modern galaxy (Bournaud et al. 2010).
ETGs with no or little residual disk component (ref- A typical wet merger at high redshift should involve
erences above), whether all mergers even with very the interaction of such clumpy, turbulent disks. The
high gas fractions destroy disk galaxies and transform outcome could differ from previously modeled merg-
them into ETGs, or whether disk-dominated galax- ers using thermally-stabilized gas. Recent studies have
ies could survive major mergers in high-redshift con- shown that ISM turbulence and clumpiness have a sub-
ditions, remain more uncertain. The frequency of vi- stantial effect in mergers of present-day spirals with
olent mergers could indeed call into question the sur- just a few percent of gas, with significant differences
vival of disk-dominated galaxies (Weinzirl et al. 2009). bothinthe star-formationhistoryduringthe interaction
Some models of mergers, however, have led to the (Teyssier et al. 2010; Saitoh et al. 2009) and the prop-
3
erties of the relaxed post-merger ETG (Bournaud et al. Our clumpy disk simulations were performed with a
2008; Bois et al. 2010). The effect could presumably be barotropic cooling model (Bournaud et al. 2010), nat-
more dramatic in high-redshift mergers involving high urally producing a cloudy and turbulent ISM, with a
fractions of cold gas. temperature floor around 103 K. We refer to these as
In this paper, we present hydrodynamical AMR sim- the cooling models. For comparison, the same gas-rich
ulations of major mergers between galaxies with high mergers were modeled with a thermally pressurized and
fractions of cold, turbulent and clumpy gas, like typical Toomre-stableISM,usinganadiabaticEquationofState
z 2 star-forming galaxies. Gas cooling below 104 K is (EoS) with an exponent of γ = 5/3 for densities above
all∼owed,supersonic ISM turbulence is captured, and the 1 cm−3, and T=104 K for lower densities. This EoS
main star-forming complexes are directly resolved. We maintains a Toomre parameterQ 1.5 2 in the initial
≃ −
compare with models using artificially stabilized disks, disks and stabilizes the gas against axisymmetric per-
as in traditional high-redshift studies. turbations. These will be called the stabilized models.
We find that mergers of high-redshift disks can un- In all cases, a density-dependent pressure floor ensures
dergo a very clumpy and chaotic phase, during which that the Jeans length is resolved by at least 4 cells to
the kinematics is dispersion-dominated even for the gas avoid artificial fragmentation, as initially proposed by
component. The gas kinematics appears consistent with Machacek et al. (2003) (see Teyssier et al. 2010 for the
the observed properties of some “dispersion-dominated implementation details).
galaxies” as well as the spectral properties of SubMil- In the cooling models, star formation is assumed to
limeter Galaxies (SMGs). A large part of the total mass proceed above a density threshold of 300 cm−3 with an
is thus supported by supersonic turbulence, which is a efficiency of 7%, i.e. 7% of the gas in a given cell forms
dissipativesupport,hencethemergingsystemundergoes stars per local free-fall time. This gives a star formation
a rapid dissipational collapse into a compact ETG. The rate (SFR) of 120 M⊙ yr−1 in the isolated disk model,
massfractioninasurvivingorre-formeddiskcomponent realistic for such gas-rich z 2 systems. In the stabi-
is much lower for supersonically turbulent high-redshift lizedmodels, the starformat∼ionthresholdis 3cm−3 and
mergers than for models with artificially warmed gas. the efficiency is 4%, giving the same SFR in the isolated
Thisdoesnotmeanthatmergersofgas-richgalaxiescan disks: we compare the two sets of models with the same
never re-form a disk: a large enough far-outer reservoir SFR in pre-merger disks. The resulting star formation
of gas could recollect into a new disk, or continuous in- historyinthemergermodelswithcooling/stabilizedEoS
fall of fresh gas could build a new disk. Some orbital is relatively similar (see Section 3.4).
parameters not modeled here might also be more favor- All simulations use the kinetic feedback model de-
ableto disksurvival(e.g.Hopkins et al.2009). Still, our scribed in Dubois & Teyssier (2008), with 20% of the
main conclusion is that mergers between gas-richturbu- energy from each supernovae re-injected in the form of
lent and clumpy galaxies are qualitatively different than an expanding bubble of initial radius 100 pc (assuming
mergers between gas-rich smooth galaxies with artificial thattherestofthesupernovaeenergywasradiatedaway
pressure support, and can better explain resolved obser- before propagating up to scales of 100 pc). Some mod-
vations of high-redshift systems. els have increased feedback with 100% of the supernova
energy injected into the ISM (models labeled ”F”) and
2. SIMULATIONS
some have a supernova feedback efficiency set to 500%
This paper studies idealized models of disk galaxies. (models labeled ”F5”, discussed only in Section 3.4).
The initial conditions are not cosmological, and there is Our simulations start with disk galaxies, each having
no cosmologically-motivatedboundary condition model- a stellar mass of 4 1010 M⊙, an initial gas fraction of
ing mass infall or extended gas reservoirs. Instead, the 70%,adiskscalelen×gthof5kpcwithatruncationradius
initialconditionsaredesignedtoberepresentativeofgas- of12kpc,andaninitialscaleheightof800pc. Aninitial
rich major mergers of redshift z 2 galaxies, based on bulgecontaining15%ofthestellarmassisassumed,with
∼
their main observedcharacteristics. We model collisions aHernquistprofileandascalelengthof500pc. Thedark
and mergers between two such galaxies and study the matter halo has a Burkert profile with a core radius of
effect of this merger,by comparisonto the modeled evo- 8 kpc, and a mass fraction (dark/total) inside the disk
lution of a single isolated galaxy. radius of 30%. The circular velocity in the outer disk is
The simulations were performed with the AMR code 245 km s−1.
RAMSES (Teyssier 2002). The technique is fully de- In the cooling models, the initial disks spontaneously
scribed elsewhere and shown to model realistic inter- become clumpy and turbulent, with V/σ 5 (for rota-
stellar gas in low-redshift mergers and isolated disks tionspeedV andturbulentspeedσ). Whe≃n the mergers
(Teyssier et al. 2010; Bournaud et al. 2010). The main occur, at the first pericenter, gas fractions are around
parameters adopted for the present simulations are in 50% after some early gas consumption (see Table 2):
Table 1. thisseemstypicalfordiskgalaxiesatz 2(Daddi et al.
Theboxsizeforthesimulationis200kpc. Thecoarsest 2010a;Tacconi et al.2010),andhencee∼xpectedforawet
level of the AMR grid is l = 8, which corresponds to a merger at z 2.
2563 Cartesian grid with a cell size of 781 pc. A cell Our merge∼r models start with relatively massive disk
thatcontainsa gasmasslargerthanmres =8 104 M⊙, galaxies, so as to compare with existing models, e.g.
×
or a number of particles larger than 15, is refined, until in Robertson et al. (2006). There are galaxies like
the maximal level l = 11 is reached. At that point, the this in z 2 samples (for instance in the sample
cellsizecorrespondsto 97pc. Starsanddarkmatterare of F¨orster S∼chreiber et al. 2009). Also, our pre-merger
described with 2 105 collisionless particles each in the disks are not extreme in terms of gas clumpiness and
×
initial galaxies.
4
TABLE 1
Parameter used for the simulations.
Model Orbit EoS Comment
C1 1 cooling mergerofgas-richclumpydisks
C1F 1 cooling C1withstrongerfeedback
C1F5 1 cooling C1with500%feedback
S1 1 stabilized gas-rich,smooth,stabilizeddisks
S1F 1 stabilized S1withstrongerfeedback
S1F5 1 stabilized S1with500%feedback
C2 2 cooling mergerofgas-richclumpydisks
S2 2 stabilized gas-rich,smooth,stabilizeddisks
C3 3 cooling mergerofgas-richclumpydisks
S3 3 stabilized gas-rich,smooth,stabilizeddisks
I isolated cooling controlrun: high-redshiftdisk
LM-C2 2 cooling lower-massgas-richclumpydisks
LM-C2F 2 cooling C2withstrongerfeedback
LM-S2 2 stabilized lower-mass,smoothstabilizeddisks
TABLE 2
Propertiesof the finalrelaxed systems:
Half-massradiusR1/2 andSersicindexn(bestfitbetween 0.3and3R1/2);gasfractionremainingatthepericenterand400Myrlater;
mass-weigthedaverageofthe1Dlocalgasturbulentspeed<σturb,1D>measured140Myraftereachpericenter;baryonicmassfraction
ofthebaryonsinarotatingdiskfdisk,measuredusingakinematicdisk+spheroiddecompositionasinMartig&Bournaud(2010).
Gasconsumption ISMturbulence Mergerremnantproperties
Model fgas,peri fgas,i+400Myr <σturb,1D>(kms−1) Sersicn R1/2 fdisk
C1 45% 17% 175 4.4 2.8 12%
C1F 54% 22% 186 4.2 3.0 16%
C1F5 58% 21% 204 3.9 3.1 21%
S1 48% 20% 56 2.9 6.1 40%
S1F 52% 22% 59 2.5 6.3 48%
S1F5 56% 23% 65 2.6 6.2 53%
C2 53% 13% 153 4.2 2.9 14%
S2 49% 18% 68 3.2 5.8 37%
C3 53% 19% 164 4.9 2.6 11%
S3 47% 17% 72 3.3 5.6 37%
I – – 59 1.7 5.4 66%
LM-C2 52% 19% 89 3.7 1.2 10%
LM-C2F 58% 21% 96 3.9 1.3 13%
LM-S2 57% 22% 42 2.7 2.0 35%
Fig.1.— Snapshots of the gas mass distribution formodels C1 (cooling) and S1 (stabilized ISM) at similarinstants and under similar
projections. t=0isthefirstpericenterpassageandallmapsareinlogscale.
5
Fig.2.— Snapshots of the stellar mass surface density distribution for models C1 (cooling) and S1 (stabilized ISM) at similarinstants
andundersimilarprojections. t=0isthefirstpericenterpassageandallmapsareinlogscale.
6
Fig.3.—ThreeorthogonalprojectionsofmodelC1showingthe
surface density, velocity and dispersion maps (mass-weighted val-
ues along the line-of-sight, for gas denser than 10 cm−3). A res-
olution of 1 kpc was assumed (FWHM of a gaussian beam). All
snapshots are 44 × 44 kpc. Note that Hα observations would be
mostlysensitivetoemissionfromthedenseclumps.
turbulence: many z 2 disks have even lower V/σ ra-
∼
tios (e.g., F¨orster Schreiber et al. 2009).
Three interaction orbits were used. They are all pro-
grade for one galaxy and retrograde for the other in or-
dertoconsideratypicaltotalangularmomentumrather
than extreme cases with aligned spins1. Orbit 1 has an
impact parameter of 12 kpc and is parabolic. One disk
has an initial inclination of 30◦ from the orbital plane,
and the other has an initial inclination of 50◦. For or-
bit 2, these parameters are: 35 kpc, hyperbolic (total
energy of the galaxy pair is 0.3 times its initial kinetic
energy), and 30◦ and 50◦ degrees, respectively. For or- Fig. 4.—SameasFig.2,withcomparisonofon-goingmergersin
thecoolingandstabilizedISMmodelsatthesameinstantandun-
bit 3, they are 25 kpc, hyperbolic (total energy = 0.2
derthesameprojection,shownhereatfullresolution. Anisolated
the initial kinetic energy), 40◦, and 65◦ degrees, respec×- clumpy turbulent disk is also shown after a similar evolutionary
tively. timeasthemergers.
Three simulations were also run for a merger of lower-
and LM-S2, and LM-C2F with increased feedback.
massgalaxies. Themassesofallinitialcomponents(stel-
lar disk, gaseous disk, bulge, halo) where reduced by a 3. RESULTS
factor of 8 compared to the initial higher-mass models,
3.1. On-going mergers
and all sizes and distances were reduced by a factor of
√8,hencekeepingsurfacedensitiesaboutconstant. The The time evolution of mergers C1 (cooling) and S1
(stabilized ISM) is shown in Figures 1 and 2. The sta-
pre-mergergalaxiesthen had circular velocities of about
150 km s−1 in their outer disks, with a V/σ 3.5 ra- bilized model has relatively homogeneous tidal tails or-
≃ biting around smooth gas disks. The gas in the cooling
tio – somewhat lower than in the more massive disks
model is dominated by numerous star-forming clumps
models, which is in agreement with observed trends
that are somewhat more massive than the clumps were
(F¨orster Schreiber et al. 2009). These merger models
in the pre-mergergalaxies. Visual inspection shows that
were performed using Orbit 2 with our cooling and sta-
some of the pre-existing clumps survived and some have
bilizedISMmodels,andarerespectivelydenotedLM-C2
disrupted and re-formed. Numerous filaments form in
1 Aligned spins would not necessarily result in higher angular many directions, instead of a main pair of continuous
momentumormorediskcomponentinthefinalresult,becauseof tidal tails. Other projections (Fig. 3) show that the gas
tidalremovaloftheangularmomentum (Robertsonetal.2006) distribution during the merger forms a very irregular
7
Fig.5.—Radial profilesof the stellarsurfacedensities infinal mergedandrelaxedsystems, and theisolateddiskmodel afterthe same
evolutionarytime. Severalprojectionswereaveragedforeachmodel. Ellipse-fittingwasperformedwiththeellipse taskinIRAF.
spheroid in three dimensions; there are no disks. The smooth velocity gradients along these tails (see exam-
model with stronger feedback (C1F in Fig. 3) is quali- ples in Bournaud et al. 2004b; Chilingarian et al. 2010).
tatively similar: self-gravityis already sufficient to drive Low-redshift merger models with warm stable gas ver-
strong ISM turbulence in massive galaxies at high red- sus colder and unstable gas in cooling models have been
shift (Dekel et al. 2009; Elmegreen & Burkert 2010). compared in Teyssier et al. (2010). While they display
Gasvelocityfieldsandline-of-sightdispersionmapsare substantialdifferencesintheirstarformationproperties,
shown in Figures 3 and 4. The gas velocity fields of our both models are dominated by long tidal tails and have
high-redshift cooling models are very chaotic, and often similar half-mass sizes after the merger. The tails have
lackextendedrotatingcomponents,suchaslargedisksor star-formingclumpsinthecoolingmodel,buttheclumps
long tidal tails with monotonic velocity gradients. The donotdominate the morphologyandkinematicsasthey
gas velocity dispersions are high, especially near dense do at higher redshift.
clumps. In this sense, stabilized ISM models are a more ac-
Interactions at low redshift substantially increase the ceptable recipe for the large-scale gas properties in low-
gasvelocitydispersion,fromtypically10kms−1 in non- redshift mergers than in high-redshift ones. This can
interactingspiralsto30–40kms−1 inmajormergers(see be explained because low-redshift systems have weaker
Elmegreen et al. 1995 for observations, Bournaud et al. gas turbulence and are more stable than high-redshift
2008forsimulations). We find asimilar relativeincrease systems on scales of a kpc. Low-redshift disks are only
here, but starting with disks that are already quite tur- slightlyunstable,andthesizesandmassesofthe clumps
bulent before the merger. This results in systems where that form are much smaller than they are at high red-
the gas component is dispersion-dominated during the shift. Thusthe effectsofISMturbulenceandclumpiness
merger,with V/σ ratios2 of around 2 or even 1 for some are more striking in high-redshift mergers. Resolving
projections and times. The gas dispersions are high in gas turbulence, star forming instabilities and/or shocks
projection on the line-of-sight, and also in direct mea- change the star formation history of these low-redshift
surements of the local three-dimensional motions: we mergers (Barnes 2004; Saitoh et al. 2009; Teyssier et al.
measured the turbulent velocity dispersion in 1 kpc3 2010; Chien & Barnes 2010), but have no major impact
cubes in model C1 at t = 140 Myr; the mass-weighted on the morphology of the merger remnants and only a
average value was < σ > 175 km s−1 (higher limited impact on their kinematics (Bois et al. 2010).
turb,1D
≃
values on projected maps such as Figures 3 and 4 result
fromline-of-sightprojectioneffects,nottoaphysical,lo- 3.2. Merger remnants
cal turbulent motion). Similar measurements are given
Supersonicgasturbulencedissipatesrapidly,whichcan
for all models in Table 2, at the same instant which is
produce a strong contraction of a dispersion-supported
about the peak of turbulent speed in our merger models
gaseous system. Such dissipative collapse is observed in
with cooling. These measures show that the turbulent
Figure1formodelC1. Someclumpsareexpelledbytidal
velocities become much higher during the interactions
interactions,butmostofthegasclumpsandinter-clump
and mergers than in the pre-merger clumpy disks, and
gas coalesce in a compact central object. Because the
that this property is not reproduced in the simulations
gasfractionisinitiallyhigh,alargepartofthefinalstel-
using a stabilizedgas model. The values ofline-of-sight
larcontentformswithinthesamegasclumpsandfollows
velocity dispersions in Figures 3 and 4 will be further
theircoalescence. Oldstellarcomponentscontractdueto
compared to high-redshift observations in Section 4.1.
thedissipationofthegasandyoungstars,whichcontain
Mergers with the stabilized ISM model show velocity
alargefractionofthetotalmass. Thus,themergerleads
dispersions that are lower by a factor 3 for all times.
tothe formationofarelativelycompactstellarspheroid.
∼
Instead of chaotic velocity fields, they have relatively
This spheroid has a low half-mass radius, a high Sersic
smooth and extended rotating gas disks, surrounded by
index, and an extended stellar halo visible as a low sur-
long tidal tails that co-rotate with large-scale velocity
face mass density component beyond radii of 7 kpc
gradients (see examples in Fig. 3). ∼
in Figure 5. Table 2 gives half-mass radii and Sersic
Low-redshift mergers have different signatures, since
indices for all models. Figure 4 shows the correspond-
they typically exhibit long tidal tails with large and
ingstellarmassprofiles. Remnantsofthestabilized-ISM
merger models are more extended3 and have lower Ser-
2 Throughout the paper, σ refers to a one-dimensional disper-
sion. AsystemwithV/σ<2isdispersion-dominatedwith>60% 3 Mergerremnants inthestabilizedmodels aremoreextended
ofitskineticenergysupportisintheformofdispersions. intermsofhalfmassradii: theouter,low-massdensityhaloismore
8
sic indices than remnants of the cooling merger models. tionforthestars,the totalenergyisE =1.5M σ2+
tot gas
The isolated clumpy turbulent disk model has formed a 1.5M V2,assumingthatstellarmotionsareoftheor-
stars
central bulge through internal evolution (as in Noguchi der of the circular velocity V (even if not consisting in
1999, Immeli et al. 2004and Elmegreen et al. 2008 mod- organized rotation). Thus ∆E/E = X/(1+X) where
els), but remains dominated by a rotating exponential X = (M /M ) τ2, with τ =−σ/V. This ratio,
gas stars
disk (Bournaud et al. 2007a). X/(1+X), is also×the relative contraction of the ra-
The merger remnant of a typical high-redshift merger d−ius after all of the initial gas motion dissipates. If f is
g
is not just more compact, but also less disky. Gas disk the disk gas fraction, then X =(f /[1 f ])τ2.
g g
re-growth is faster in the models with a stabilized ISM −
Turbulent dissipation should occur in about a cross-
(see Fig 1 at t = 215), and thus forms a more massive
ing time for radialmotions (McLow 1999). The crossing
final stellar disk. For example, the final disk component
time for a whole galaxy is about the orbit time, typ-
in model S1 contains 40% of the baryons and is obvious
ically 100-200 Myr, so most of the non-rotational gas
up to large radius in Figure 1. In cooling model C1,
kinetic energy can be dissipated over the duration of a
moststarformationtakesplaceingasclumpsbeforethey
major merger. After dissipation and galaxy contraction,
coalesce and get a chance to re-form a disk; the final
the gas receives new kinetic energy from the potential
diskinmodelC1iscompact,withadiskfractionofonly
energy, and can then dissipate even more energy. This
12%. Similar differences are found for all merger orbits
cycle of dissipation, contraction, heating and more dis-
(Table 2).
sipation, continues with ever decreasing orbit time until
The increased dissipation and resulting compactness the radial component of the turbulent energy is gone.
in cooling models with a clumpy turbulent gas can be Low-redshift Milky Way-like disks have τ 3
∼ −
explained: clumps interact with each other gravitation- 5%, and their major mergers have a value about 3-
ally, scatter, and develop 3D motions (i.e., high disper- 5 times higher, τ 20% (observations: Irwin 1994;
∼
sions). The gas clumps and holes can then pass by each Elmegreen et al. 1995 – simulations: Bournaud et al.
other. InstabilizedISMmodels,thesmoothdistribution 2008; Teyssier et al. 2010). Together with fg of a few
of the gas does not allow it to pass through itself and percent,thesizeofamergerremnantisnotmuchsmaller
it therefore rapidly settles back into a relatively planar thanthe originalgalaxysize. Thesamewouldbe truein
disk. Gas clumpiness can reduce the ISM cross section high-redshift merger models that have subsonic gas, i.e.,
for self-interaction and thereby increase the dissipation gas without much energy dissipation, even if fg is large.
timescale, but the supersonic turbulence that accompa- High-redshift disk galaxies have τ 20% (e.g.
∼
nies this clumpiness is highly dissipative. For modest F¨orster Schreiber et al. 2009), fg 0.5 (e.g., Daddi et
∼
clump filling factors, the net result is a greater dissipa- al. 2010, Tacconi et al. 2010), and highly dissipative
tionrateforISMkineticenergy. Thisisunlikethesitua- gas. With an increase of gas dispersions of a factor
tioninstabilizedISMmodels,wherethegasissupported three during interactions (conservatively based on the
by a steady thermal pressure. Excess thermal energy knownincreasedatlow-redshift,butalsoconsistentwith
can be radiated away, but the EoS, high temperature high-redshiftmergersspectroscopyin,e.g.,Shapiroetal.
floor,and/orfeedbackrecipe,keepthegaswarminthese 2008), τ would become of the order of 60% for high-
∼
models andmake the thermalsupportnon-dissipativein redshift mergers. Then ∆R/R 0.25. This result im-
∼
practice. Furthermore, the massive clumps that form in plies thatturbulent dissipationfor agas-richsystemcan
highlyturbulentgasrapidlymigrateinwardsthroughdy- cause significant radial contraction of both the gaseous
namical friction, unlike the relatively homogeneous gas and stellar components for every gas dissipation time,
in stabilized models which settles into a circular orbit. i.e. just 100-200 Myr. As the gas continues to dissipate
energy,the systemiccontractionofthe galaxycontinues,
and the total contraction of the merger can be larger if
3.3. Interpretation: increased turbulence and rapid
some massis expulsedfromthe system andcarriesmore
dissipation in mergers
energy away.
The effect of turbulence dissipation on the size evolu-
tion of a merger can also be estimated through simple Another mechanism for galaxy contraction is inward
calculations. A star and gassystem in equilibrium satis- clump migration through dynamical friction. The
fies the Virial Theorem, and then the total energy from timescale for this, given the clump masses and total
self-gravity and motion equals half of the gravitational masses of our models, is typically around 500 Myr (see
potentialenergy,E =0.5E ,bothofwhichareneg- Bournaud et al. 2007). This is slower than gaseous tur-
tot grav
ative. Lossof energy by dissipationleads to a more neg- bulence dissipation, and therefore not as important for
ative E , and so a smaller, more tightly-bound equi- overallshrinkage when the gas fraction is large.
tot
librium. For typical mass distributions in a galaxy, the
Contractionalsooccursifweconsiderthesizeofadisk
gravitational potential energy scales with the inverse of
tobedeterminedbyangularmomentum. Baryonsinthe
the radius, R, in which case the relative contraction is
central few kpcs of interacting galaxies loose significant
∆R/R= ∆E/E =∆E/E .
− | | angular momentum, while baryons initially in the outer
Ifthegasmassis M andthe1Dgasvelocitydisper-
gas
disks carry away a large fraction of the initial angular
sionisσ,then∆E = 1.5M σ2whenasignificantfrac-
− gas momentum in tidal tails (see review in Bournaud 2010).
tion of the gas kinetic energy is lost. With similar nota-
At first order, the angular momentum of baryons near
the corotation region, which is typically about the half
extended in the cooling models, but would be hardly detected in
themajorityofhigh-redshiftobservations,asshownbyManciniet mass radius (a few kpc for the disk masses considered
al. (2010). here) is be roughly conserved.
9
For a mass M encompassed by a radius R, and a cir- merger disk pair (with both the cooling and stabilized
cular velocity V = pGM/R, angular momentum con- EoS). This factor is somewhat higher than the typi-
servation implies that: cal value in larger samples of merger simulations (e.g.
Di Matteo et al. 2007, 2008; Martig & Bournaud 2008;
R 1/VM M−3. Stewart et al. 2008) but not in large disagreement. This
∝ ∝
factorofabout10alsoappearssomewhathigherthan in
If gas initially outside the half-mass radius dissipates
observations of mergers and close pairs (Bergvall et al.
its turbulent energy and moves towards the center, the
2003; Bell et al. 2005; Jogee et al. 2009; Robaina et al.
central mass increases, possibly as much as a factor of
2009). However,theseobservationsindicatethe SFRen-
2. Then the half-mass radius can decrease by a factor of
hancement at a random instant of an interaction, and
8, all the while conserving angular momentum. Further
what they consider to be major mergers are not strictly
shrinkage can be caused by angular momentum removal
equal-mass ones. The factor 10 at the peak SFR in
throughtidallyexpelledbaryons. Onlythistidalremoval
our models, which is reached only for a short period,
is presentin models with a smooth, non-turbulentISM.
is broadly consistent with the factor of 3-4 indicated by
these observational studies. We did not here focus on
3.4. Star formation history
particularly efficient cases where the SFR enhancement
The star formation histories of mergers C1, C1F and inamergercanreachfactorslargerthanahundred(asin
S1 are shown in Figure 6. The efficiency was cali- Mihos & Hernquist 1996 or Springel & Hernquist 2005),
bratedineachmodeltoresultinaSFRofapproximately but rather on random, representative orbits.
100M⊙ yr−1 ineachpre-mergergalaxy,typicalforz 2
∼ The peak in the merger-induced star formation rate
disk galaxies with similar masses. The star formation
begins somewhat earlier in the cooling models than in
rate during the merger reaches a factor of 10 higher
∼ the stabilizedones,just afterthe firstpericenter passage
than in the pre-merger pair in all cases, with peak val-
ues of 1000-2000 M⊙ yr−1. This rate is consistent with (Fig. 6). This earlier gas consumption cannot cause the
lowerdisk fractionofthe mergerremnantsbecause (i) it
the SFRs estimated in SubMillimeter Galaxies (SMGs;
occursonlyoncetheinteractionprocessstarts,sothegas
e.g., Tacconi et al. 2008). The star formation peak can
fractions during the interaction remain quite similar in
occur earlier-on or later-on in various models, but the
bothmodels (Table 2)and(ii) the increasedfeedback in
maximal SFR and the duration of the starburst remain
model C1F delays the peak of star formation until a bit
comparable, leading to globally similar amounts of gas-
later than in model S1, but the final merger remnant is
to-star conversion for the cooling and stabilized models.
almost as compact and disk-free as for the initial model
The fraction of remaining gas at the first pericenter and
C1.
300 Myr later are given in Table 2: no major or system-
The earlier merger-induced star formation activity in
atical differences are found between the cooling and the
the cooling models is consistent with the results ob-
stabilized ISM models for any given orbit.
tained by Teyssier et al. (2010) in low-redshift merger
Both the cooling and the stabilized ISM models reach
models (see also Saitoh et al. 2009, for resolved star-
rates of star formation that are realistic for observed
forming regions in early pahses of galaxy interactions).
z 2 disks and starbursting mergers. The rates are
∼ High-resolutionmodelswithalowtemperaturefloorcan
also consistent with each other. This does not mean
that gas cooling below 104 K in a clumpy turbulent capture ISM turbulence, local dense shocks, and frag-
mentation into star-forming clouds. Stars form in these
ISM has no effect on star formation in mergers. High-
clouds when they are still in the main disk, long be-
resolution models explicitly including gas cooling could,
fore they have accreted to the galaxy center. Such mod-
inprinciple,resolvethedensestgasphasesthatareactu-
ellingisrequiredtoreproducecorrectlytheextentofstar
allystar-forming(Tasker & Tan2009;Agertz et al.2009;
formation in early- and late-stage interactions, which
Bournaud et al. 2010), but models using an artificially
is missed by standard prescriptions (see also Barnes
thermalizedISMdonotreachsuchhighgasdensitiesand
2004; Chien & Barnes 2010). On the other hand, low-
they have to describe star formation as a low-efficiency
resolution or stabilized ISM models get intense star for-
processpervasivelydistributedthroughoutalow-density
mationonly inthe dense centralizedgasthatfollows the
gas. The calibration of the efficiency is subjective when
merger-driven inflow. Dense clouds do not form in the
densecloudsarenotmadeself-consistentlybythemodel.
disk. The delay in star formation for this stabilized case
Herewechooseanefficiency inthe stabilizedISMmodel
is comparable to the rotation period of the entire galax-
that gives the same star formation rate as the cooling
ies.
model for an isolated disk. Had we used the same pre-
scription for star formation in each case, then the cool-
3.5. Feedback and clump evolution in mergers
ing models would have had much higher star formation
rates andtheir collisions wouldhave been more gas-free. Our simulations include a kinetic model for the en-
Whilewecomparethecoolingandstabilizedmodelswith ergy feedback from Type II supernovae. Other sorts of
similarSFRsandresultinggasfractions,theEoSusedto feedback such as Type Ia supernovae, stellar winds, and
model cold gas imposes most of this gas to be relatively massreturnareimportantforhigh-redshiftgalaxyevolu-
cold <104 K. Different feedback models might result in tion (Agertz et al. 2010; Martig & Bournaud 2010), but
higher amounts of hot extended gas, which could poten- the timescalesfor this feedback aretypicallylongerthan
tially cool down later-on and accrete onto a re-formed the timescale for a major merger of massive disk galax-
disk (see discusion in Sections 3.4 and 3.5. ies. Another sort of feedback with a short timescale
Globally, the star formation rate in our merger mod- is radiation pressure from young massive stars. Gi-
els peaks at about 10 times the value of the pre- ant clumps in high-redshift, gas-rich galaxies could be
∼
10
5" 5$ 5%
5"3 2$ 2%
2"
"### "### "###
!",,,,,,,,,,432,,,,,,,,,,,,,-./01,6"## !",,,,,,,,,,432,,,,,,,,,,,,,-./01,6"## !",,,,,,,,,,432,,,,,,,,,,,,,-./01,6"##
"# "# "#
!"## # "## $## %## &## ’## !"## # "## $## %## &## ’## !"## # "## $## %## &## ’##
()*+,-./01 ()*+,-./01 ()*+,-./01
Fig.6.—Starformationhistoryforthemergermodelsalongorbits1,2and3,withvariousEoSandfeedbackparameter. Thepericenter
passagecorresponds tot=0Myrineachcase.
sufficiently massive to self-regulate their star forma- primarilyresultfromastronglyturbulentISM, inwhich
tion so that they “survive” feedback for several hun- massive clumps naturally arise.
dred Myr (Krumholz & Dekel 2010).This however re- We have not explored the modeling of other sources
mainsdebated(Murray et al.2010). The“survival”defi- of stellar feedback (radiation pressure, winds, etc). We
nitionofKrumholz & Dekel(2010)impliesthatabound already discussed models with an efficiency up to 100%
stellar clump remains but not necessarily that the gas in our supernovae feedback scheme, but Agertz et al.
is retained by this clump. Expelled gas could be re- (2010) suggested that higher efficiencies, up to 500%,
accreted by the clump and start forming stars again couldbemorerealistic–presumablytoaccountforother
(Pflamm-Altenburg & Kroupa 2009). sorts of feedback that are not modeled, such as pho-
Theseadditionalfeedbackmechanismsarenotpresent toionization, or radiative feedback, the role of which at
in our models. Nevertheless, we found that varying the high redshift remains debated (e.g. Murray et al. 2010;
efficiency of the supernovae feedback (in runs C1F and Krumholz & Dekel 2010; Genel et al. 2010). Thus, we
LM-C2F) did not result in major changes to the prop- performed tests with SN feedback efficiency increased
erties of the final ETGs. Models C1 and C1F also have to 500%, for the cooling and stabilized models on or-
similarline-of-sightvelocitydispersionsintheirgascom- bit 1. The results (see Table 2) show some variations,
ponent (Fig. 3 and 4). The main source of turbulence in as strongerfeedback fuels more extended and hotter gas
high-redshift disk galaxies is generally considered to be reservoirs in the early phases of the merger, which adds
gravitationalenergyreleasedthroughclumpinginstabili- mass to a re-formed disk component in the post-merger
tiesand/orinwardmassaccretion(Elmegreen & Burkert phases(following the process discussed,e.g., by Springel
2010, Dekel et al. 2009). Observations have sug- & Hernquist 2005 and Governato et al. 2009). Nev-
gested that the local velocity disperion scales with the ertheless these variations are relatively minor compared
local gas density and/or star formation surface den- to the initial discrepancies between models C1 and S1,
sity (Lehnert et al. 2009, see also Green et al. 2010 for both in terms of final disk fraction and final compact-
low-redshift analogues) which could suggest energy in- ness. Furthermore, the differences between models C1F
put from stellar feedback. The local velocity disper- and S1F, or C1F5 and C1F5 respectively, are about of
sion scales with the local surface density also in models thesameamplitudeasthedifferencesbetweentheinitial
dominated by gravity-driventurbulence such as those in models C1 and S1. This suggests that, while a stronger
Bournaud et al. 2009. Gas turbulence can be further in- feedback can moderately increase the disk fraction and
creasedbytidalforcesinmergers(Elmegreen et al.1993; half-massradiusofthefinalETG,thiseffectisdecoupled
Irwin1994;Elmegreen et al.1995;Bournaud et al.2008; fromtheimpactofusingacoolingmodelgeneratingtur-
Teyssier et al. 2010). Stellar feedback is thus not ex- bulent gas rather than a thermally stabilized model. It
pected to be the main energy source of the turbulent doesnotstronglyimpactourpreviousconclusionsonthe
motions. The same appears to be true in local galaxies effectofresolvinggascoolingandstrongISMturbulence
(Bournaud et al. 2010). onthe stellarsize evolutionanddiskfractioninthe final
Whilethepre-mergerdiskgalaxiesarealreadyclumpy, merger remnants.
themaingasclumpsduringthemergertendtobedenser
3.6. Mergers of lower-mass galaxies
and more massive (see for instance the time sequence
on Figure 1): some are pre-existing clumps that accrete Our main set of simulations used galaxy models that
more mass, some new clumps form with high masses al- were relatively massive (without being unrealistic) for
lowed by the high gas densities and velocity dispersions. the typical disks and spheroids observed at z 2.
∼
This maintains a clumpy stellar morphology during and Lower-mass disk galaxies at z 2, with circular ve-
afterthemerger. Mostclumpsareneverthelessnotlong- locities of 100-200 km s−1, also ∼show giant clumps of
livedthroughoutthemergerprocess. Theaveragestellar star formation and gas turbulent speeds of several tens
age of the five largest stellar clumps in the final ETG in of km s−1 (F¨orster Schreiber et al. 2009; Wright et al.
modelC1wasmeasured450Myrafterthepericenterpas- 2009), like the pre-merger galaxies in our models. ISM
sage,which is about 200 Myr after the final coalescence. turbulenceandclumpinessshouldthushavequalitatively
These ages range from 80 Myr to 175 Myr. Hence these similareffectsinhighandlowmassmajormergers. This
clumps arerelativelyyoungcomparedtothe mergerand can be explicitly checked using models LM-C2, LM-S2
formed in the latest phases. This suggests that our re- and LM-C2F.
sultsdonotdirectlyrelyonalowfeedbackefficiency,but The structural parameters of these low-mass mergers
remnant are given in Table 2, and the edge-on stellar