The physics of galaxy formation

P. Monaco, University of Trieste & INAF-OATs

PhD School of Astrophysics Francesco Lucchin

June 2013

LambdaCDM model

Cosmicmicrowavebackground

Large-scale structure

Inter-galactic medium

Galaxy clusters &

gravitational lensing

Distant supernovae

Cosmology

gravitational

collapse

Galaxies

“gastrophysics”

z=5.7 (t=1.0 Gyr)z=5.7 (t=1.0 Gyr)

z=1.4 (t=4.7 Gyr)z=1.4 (t=4.7 Gyr)

z=0 (t=13.6 Gyr)z=0 (t=13.6 Gyr)

Springel et al. 2006Springel et al. 2006

Dark matter

Theoretical tools(within the LambdaCDM cosmogony)

Semi-analytic models

N-body + hydrodynamical simulations

Halo Occupation Distribution models

Abundance matching models

The physics of galaxy formation

1. Dark matter

ρ(r )=ρc (z)const

cx(1+cx)2

c≡rhr s, x≡ r

rh, cx= r

r sρ(rh)=200ρc (z )

Density profile:Navarro, Frenk & White (1997, ApJ 490, 493)

Dark-matter halos

Mass function of DM halos

Warren et al. (2006, ApJ 646, 881)

Lacey & Cole (1993, MNRAS 262, 627)

Merger trees

●dynamical friction●tidal stripping●tidal shocks/harrassment●orbit decay (merging)●binary mergers

Dynamicalfriction

ddtvorb=

−4G 2 ln M sat host v orbv orbvorb

3

tmerge=1.17f dfln

orb

M host

M sat

Boylan-Kolchin, Ma & Quataert (2008, MNRAS, 383, 93)

Coulomb logarithm

Parameter Orbital parameter

The physics of galaxy formation

1. Dark matter

2. Shock heating and cooling

Gas infall into DM halos

vinfall∼V c=√GM /R

T igm∼103−104K

vinfall≫cs

=> shock heating to the virial T

Massive halos (>1012 Msun

):cooling is slower than infallgas is shock- heated at T

vir

and is in roughly hydrostatic equilibrium

Small halos (<1011 Msun

):cooling is faster than infallcold gas falls directly to the centrethe shock energy is quickly dissipated

White & Frenk (1991, ApJ 379, 52), Keres et al. (2005, MNRAS 363, 2), Dekel & Birnboim (2006, MNRAS 368, 2)

Shock heating and cold flows

t coolt dyn t coolt dyn

Galaxy clusters show such hot gas

Hot baryons in DM halos

NFW profile for the total mass

halo concentration

hydrostatic equilibrium

polytropic equation of state (γp~1.2)

solution for the density

=crit c

r / r s1r /r s2

c=r h/r s

dPg

dr=−G

g M r r 2

P g∝g p

g r =g0 [1−a1− ln 1r /r sr /r s ]

1/ p−1

a=aT g0 /T vir , p , cKomatsu & Seljak (2001, MNRAS 327, 1353)

Radiative cooling of an optically thin plasma: primordial composition

log T (K)

L=n ine , T

t cool=∣d lnTdt ∣

−1

=E th

L= 3nkT

2ne ni

Katz, Weinberg & Hernquist (1996, ApJS, 105, 19)

Assumptions:● collisional ionisation equilibrium● thermal distribution of e- and ions● no external ionising radiation

z=2, average density 1000 times average

Radiative cooling in presence of UV heating

Radiative cooling of an optically thin plasma: solar abundance ratios

Log T (K)

(1993, ApJS, 88, 253)

metal lines dominate cooling

The "classical" cooling model in SAMs

The cooling radius:

Bertschinger's (1989) self-similar solutions:

The "classical" cooling model (White & Frenk 1991):

Total cooling time of a mass element:

The classical model implies that:

r cool t : t cool r =t

M cool∝4g r cool r cool2 dr cool

dt

M cool=4 g rcool r cool2 drcool

dt

t total :T t total≪T t=0

t cool r =t total r

The physics of galaxy formation

1. Dark matter

2. Shock heating and cooling

3. Star formation

Star formation and Jeans mass

E tot = U+Ω = 32kT

M J

μm p

−GM J

2

R=0

M J∼15.4( T1 K )3/2

( n

1 cm−3 )−1 /2

M sun

Warm phase

Cold phase

Molecular phase

Cooling below 104 K

Maio et al. (2007, MNRAS 379, 963)

fraction of ions that are metals

Star formation

Kennicutt (1998, ApJ 498, 541)

DATA:

THINGS (VLA): 21 cm -> HI

BIMA-SONG + HERACLES: CO → H2

SINGS (Spitzer): 24 μm

GALEX: UV

24 μm + UV -> SFR

resolution: 750 pc, 5.2 km/s

atomic molecular

total

The Kennicutt relation(s) for spirals

Bigiel et al. (2008, AJ 136, 2846)

Two relations at high redshift?

Daddi et al. (2010, ApJ 714, L118)

The physics of galaxy formation

1. Dark matter

2. Shock heating and cooling

3. Star formation

4. Energetic feedback

Feedback sources

Supernova explosions

UV from massive stars

Star winds

AGN

1051 erg each >8 Msun

star + type Iaup to ~1050 erg

each >10 Msun

star

up to ~1050 erg each >10 M

sun star

up to ~1047 erg s-1 for ~107 yr

SuperNova Remnant (SNR)

(1) Free expansion

(2) Adiabatic stage

(3) Pressure-driven snowplow stage

(4) Momentum conserving stage

SN energy feedback

Energy is injected through blastwaves

The ISM is heated in the adiabatic stage

The ISM is cooled if the blast goes into the “snowplough” stage

McKee & Ostriker 1977Cioffi, McKee & Berschinger 1988Ostriker & McKee 1988

The efficiency of feedback

It is determined by the energy radiated away before the blast stops propagating.

Blasts stop by:

merging with the ISM

blowing out of the galaxy

merging with other blasts

v s=cs0

R s=H eff

Q bubbles=1

Feedback in DM halos

thermalenergy

kineticenergy

hot/cold gas metals

Feedback in DM halos

galactic fountain

outflow

Simple model of feedback

The properties of dwarf galaxies require that gas is efficiently removed from small halos.

Condition for removal:

Energy from (tII) SNe:

Star formation:

Critical Vc:

E inj=ϵ E aval≥M gasV c2

(Dekel & Silk 1986)

Eaval=E SN SN M star

M star=M gas / t ff

V c≈100km /sParameters: E

SN ( E

51), η

SN (IMF), ε, τ (computed)

A simple energetic argument

ϵE SN M star

M star , SN

=M outflow vSN2

vSN≃√ϵ 750 km /sif

M outflow=M star

The physics of galaxy formation

1. Dark matter

2. Shock heating and cooling

3. Star formation

4. Energetic feedback

5. Morphology

Angular momentum of halos

J = ∫V L

a3ax−a xcm ×v d3 x

J i= −a D ijk T jl I lk ∝ t1 /3M 5 /3

tidal tensor inertia tensorWhite (1984, ApJ 286, 38)

=∣E∣1 /2∣ J h∣

G M h5/2 ≃

V rot

V c

V c= GM h

r h

Spin parameter

Bett et al. (2007, MNRAS, 376 215)

Formation of discs

Dissipation of all random motions

The size of discs

Assuming that(1) a fraction m

d of the halo baryonic mass settles on the disc

(2) a fraction jd of the angular momentum is conserved

(3) the disc has an exponential profile(4) the disc has negligible mass

(5) the halo has a singular isothermal profile

Rd =G M h

3/2

2Vc∣E∣1/2 j dmd

Rd =1

2 j dmd r h

Mo, Mao & White (1998, MNRAS 295, 319)

r=0 exp − rRd

r∝r−2

Complications

(1) NFW halo

(2) disc mass not negligible

(3) adiabatic contraction of the DM halo

(4) central bulge

iterative solution!

GM r r=const

J d

M d

= j dmd J h

M h

J d = ∫0

rhV rot r rr 2 r dr

V rot2 =V dm

2 V d2V b

2

V d2=

G M d

Rd

y2 [ I 0 y K 0 y− I 1 y K 1 y ] , y= 12rRd

Galaxy mergers

Bar instabilityThin discs are unstable to bar formation, unless they are surrounded by a DM halo (Ostriker & Peebles 1973)

≡V d Rd

G M d

limit~1

limit :

Stability condition:

(Efstathiou et al. 1982, Christodoudou et al. 1995)

disc is unstable to m=2 modes

Disc instability

Bournaud et al. (2008, A&A 486, 741)

2r=2V d2

r 2 V d

r

dV d

dr if V d~V c then ~2

V c

r

Q r≡cs

G gas

Q1 : disc is unstable to axisymmetric modes

Toomre criterion for a gas disc

Bar instability(secular evolution)

Mergers

pseudo-bulges

bulges/ellipticals

Kormeny & Kennicutt (2004, ARA&A 42, 603)

Morphology at high redshift

Förster Schreiber, N. M., et al. 2009 ApJ, 706, 1364

Problems in galaxy formation

1. Massive galaxies are red and dead

A problem with cooling flowsin Galaxy Clusters

Peterson & Fabian (2006)

X-ray observations of galaxy clusters allow us to estimate density and temperature, and then cooling time, of the hot gas.

Some clusters should be sites of strong cooling flows

...from cooling flow clustersto cool core clusters...

De Grandi & Molendi (2002, ApJ 567, 163)

Massive (cD) elliptical galaxies reside at the centre of galaxy clusters

Brinchmann et al. (2004, MNRAS 351, 1151)

Why are massive galaxies red & dead? sp

eci

fic s

tar

form

atio

n ra

te

stellar mass

The mass deposited into the galaxy is 10-1 or 10-2 times that suggested by the cooling flow

Why are massive ellipticals so old?

(proxy for stellar mass)Nelan et al. (2005, ApJ 632, 137)

A possible answer: AGN feedback

(proxy for stellar mass)

Every elliptical galaxy hosts a super-massive black hole at its centre

These black holes may be reactivated by the cooling gas

Ferrarese & Merritt 2000Gebhardt et al. 2000

AGN feedback in action?

Problems in galaxy formation

1. Massive galaxies are red and dead

2. The stellar mass function cuts at ~1011 Msun

Benson et al. (2003, ApJ 599, 38)

The luminosity function

stellar feedback

cooling time + AGN feedback

Constraints from abundance matching

Moster et al. (2010, ApJ 710, 903)

stellar feedbackcooling time + AGN feedback

Problems in galaxy formation

1. Massive galaxies are red and dead

2. The stellar mass function cuts at ~1011 Msun

3. Galaxies show several “downsizing” trends

The many manifestations of downsizing: Fontanot et al. (2009, MNRAS 397, 1176)

archaeological DS more massive galaxies host older stellar populations

star formation DS:the mass of the typical SF galaxy grows with z

stellar mass DS:at z≲1 the number density of smaller galaxies evolves faster

chemical DS:the metallicity of smaller galaxies evolves faster

chemo-archaeological DS:more massive ellipticals have higher [α/Fe] ratios

AGN DS:the number density of fainter AGN peaks at lower z

Archaeological downsizing

Gallazzi et al. (2005, MNRAS 362, 41)

Downsizing in star formation

Cowie et al. (1996, AJ 112, 839)

Chemo-archaeological downsizing

Trager et al. (2000, AJ 120, 165); Matteucci (1994, A&A 288, 57)

Downsizing in metallicity

Maiolino et al. (2008, A&A 488, 463)

Downsizing in nuclear activity

Brandt & Hasinger (2005, ARA&A 43, 827)

comparison of three models:Garching-De LuciaMorganaSomerville 08

(assumed error on mass: 0.25 dex)with observational estimates of stellar mass functions by

Panter+ 07, SDSSCole+ 01, 2MASSBell+ 03, 2MASS+SDSSBorch+ 06, COMBO17 PerezGonzalez+ 08, SpitzerBundy+ 06, DEEP2Drory+ 04, MUNICSDrory+ 05, FDF+GOODSFontana+ 06, GOODS-MUSICPozzetti+ 07, VVDSMarchesini+ 08, 3 samples

Stellar mass function

Fontanot et al. (2009)

10

-10

.5

10

.5-1

1

11-

11.5

11.5

-12

in L

og M

*

Log

Ste

llar

mas

s de

nsity

(M

sun M

pc-3)

Downsizing in stellar mass

first best-fit model

second best-fit model

Redshift intervals:3.4 < z < 4.5 (B-drop)

4.5 < z < 5.5 (V-drop)

5.5 < z < 6.5 (i-drop)

Lyman-break galaxies in a SAM

B-drop

i-drop

V-drop

Lo Faro et al. (2009, A&A 399, 827)

“Excess” galaxies

absolute UV magnitude: MUV

~-18

star formation rate: SFR~10 Msun

yr-1

apparent magnitude: z850

~27

stellar mass: M*~108-109 M

sun@z~6 to 109-1010 M

sun@z~4

bimodal metallicity: Z~solar and Z~0.25 solarhosted in halos of: M

h~1011-1012 M

sun

with circular velocities: Vc~120-250 km/s

Important contributors to the IGM pollution

Waiting for ALMA and JWST!

Problems in galaxy formation

1. Massive galaxies are red and dead

2. The stellar mass function cuts at ~1011 Msun

3. Galaxies show several “downsizing” trends

4. Growth of average SFR with z (Daddi)

The evolution of star formation rates

Log

aver

age

SFR

of g

alax

ies

(Msu

n yr

-1)

Fontanot et al. (2009)

Problems in galaxy formation

1. Massive galaxies are red and dead

2. The stellar mass function cuts at ~1011 Msun

3. Galaxies show several “downsizing” trends

4. Growth of average SFR with z (Daddi)

5. Surprises from the cool side of galaxies

Somerville et al. (2012, MNRAS 423, 1992)

Sub-mm number counts with GALFORM

Baugh et al. (2005, MNRAS 356, 1191)

Sub-mm number counts with MORGANA

with a standard Salpeter IMF

Fontanot et al. (2007, MNRAS 382, 903)

Predicted evolution of Far-IR LF

Lacey et al. (2010, MNRAS 405, 2) Somerville et al. (2012, MNRAS 423, 1992)

Herschel-PEP Far-IR LF

Gruppioni et al. (2013, MNRAS 432, 23)

Problems in galaxy formation

1. Massive galaxies are red and dead

2. The stellar mass function cuts at ~1011 Msun

3. Galaxies show several “downsizing” trends

4. Growth of average SFR with z (Daddi)

5. Surprises from the cool side of galaxies

6. Angular momentum loss in hydro simulations

bottom-up formation of DM halo+

overcooling (White & Rees 1978, MNRAS 183, 341)

+segregation of cooled baryons

+dynamical friction and tidal stripping

=angular momentum loss

The Aquila comparison project

Scannapieco et al. (2012, MNRAS 423, 1726)

A successful simulation of spiral galaxy

Murante et al., in preparation