The cosmic star formation
history
沈世银
outline
• Cosmic Star formation history
– UV luminosity function
– Initial mass function
– Dust extinction
• Cosmic stellar mass density
– Stars forming VS stars formed
Cosmic star formation
history(SFH): Madau plot
Madau 1998
Steidel 1999
Cosmic SFH to z=10 Bouwens et al. 2010
GALEX data
z<2
Schiminovich 2005
Lyman break gals
z~2~3
Reddy & Steidel 2009
B,V,i dropouts
z~4,5,6
Bouwens 2009
WFC3/IR HST
z,Y,J dropouts
z~7,8,10
Bouwens 2010
z<2
z~2.5
z~5, i dropout
z~8
Star formation rate(SFR) indicator
(Kennicutt 1998)
• UV luminosity: SFR=1.4x10-28 Lv(erg s-1Hz)
– Nearly flat in Lv (1500-2800Å)
– Contributed by stars M> 5M¯ , time scales of 108 year
– Dust: UV slope 
• Recombination lines: SFR=7.9x10-42 LH(erg s-1)
– M >10M¯ t<20Myr stars contribute to ionizing flux
– Instantaneous measure of SFR
– Dust: line ratio
•
forbidden lines: SFR=1.4x10-41 L[OII](erg s-1)
– to redshift z~1.6, calibrated by H
– Sensitive to abundance and the ionization state
• Far-infrared Continuum: SFR=4.5x10-44 Lv(erg s-1)
– Starburst: high dust opacity; within times cale for the dispersal of
dust(108yr)
– Red gals: dust heating from the old stars
Other SFR indicators
• X-ray luminosity
– High mass X-ray binaries
• Radio luminosity
– Supernova remnants
– Correlated with far-infrared luminosity
• UV + FIR
Key ingredients of SFR: IMF
Initial mass function(IMF)
– Salpeter’s IMF
• dN/dM / M-2.35
– Kroupa(2001) IMF
– Chabrier(2005) IMF
The choice of IMFs
• From Salpeter IMF to Kroupa IMF
– decrease the SFR with a factor of 1.7
– also decrease the stellar mass of a similar factor,
weekly depends on stellar age and SFH
• From Kroup IMF to Chabrier IMF
– Gives similar stellar mass, decrease the SFR of a
factor of 1.8
• From Salpter IMF (0.1-100 M¯) to Salpter
IMF(0.1-125M¯)
– Also decrease the SFR with a factor of 1.7
– Does not change the K-band M/L
Key ingredients of
SFR: dust extinction
• SED fitting: model
SED fold with
reddening curve
See Calzetti(1997) for the
reddening curve of star-busts.
Dust extinction: IRX VS UV slope 
IRX=LIR/LUV f()=
Meurer, 1999
Bouwens 2009
: luminosity depends and redshift evolution
Bouwens 2009
More dust in brighter galaxies
Less dust at higher redshift
Dust: ULIRG
• Ultra luminous infrared
galaxies(ULIRG)
– Invisible in UV bands
– Increase the SFR
density ~20% at z~2.5
and ~10% at z~4
• Estimated from IR
luminosity function
Key ingredients of Cosmic SFH:
UV luminosity function(LF)
Reddy & Steidel 2009
UV LF: luminosity limit Llim
• star formation density: LF integrated to LLim
– LLim=0.3/0.04L*z=3 M(1700)=-19.7/-17.5 mag
• Halo evolution, luminosity evolution
– LLim=0, all, is it safe? dependent on 
• Half the luminosity density below the detection limit (=-1.7)
• Integrated to constant number density (Papovich
et al. 2010)
– In the absence of mergers, the comoving number
density is invariant with time
• Accretion dominate over major merges in the growth of
galaxies (Keres et al. 2009, Wang 2010)
SFH at high z(>2)
• Integrated to
number density
n=2£ 10-4 Mpc-3
– Rising SFH
– If exponential
increasing for
indvidual gals
• Ms=s SFR(t) dt
• Constant
specific SFR
sSFR ~ const
Papovich et al. 2010
Specific SFR of high z galaxies
M/L
Weak dependence of sSFR on redshift and stellar mass at z>4
Gonzalez et al. 2010
SFR  Gas mass gas accretion
•From measured SFR to gas
mass
•Kenicutt law
•size evolution, high z gals
is smaller
•High z gals are gas richer
• gas accretion rate
z>4: gas accretion phase
From halo mass ?
• SAM
– Halo  gas
 SFR 
stellar mass
SFR  stellar mass
rising SFH VS decaying SFH
Part II: Stars forming  stars formed
• Local stellar mass function
– SDSS, 2df
• Stellar mass sample at high redshifts
– Color selected, e.g. DRG, ERO, Bzk, LBG
– Infrared selection: Spitzer 3.6-4.5m
• Photometric redshift
– 3<z<5 UKIDSS ultra deep survey (Caputi 2005)
– 0<z<4 HDF (Perez-Gonzalez et al. 2008)
– z>5, UV selection sample, same as SFR sample
Stellar mass function
Caputi et al. 2010
Increased slope at
higher redshifts
Perez-Gonzalez et al. 2008
 ~1.2 at different z
Sample variance
Photometric error
Cosmic stellar mass density
Infrared selected sample
Caputi et al. 2010
UV selected sample
Labbe et al. 2010
Self-consistence: SMD VS SFR integration
Papovich et al. 2010
Gonzalez et al. 2010
Mismatch between SFR and SMD at high z
• Some galaxies are properly missed in UVselected sample
– Burst mode of SFH
• Duty cycle of the high UV galaxies ~1
– Rising SFH of galaxies predict bluer H160-[3.6] color
than observed (Labbe et al. 2010)
– Halo Occupancy 0.2-0.4, star formation duty cycle=1
(Finlator et al. 2010)
• Momentum driven outflow
• Other systematic uncertainties, e.g. dust, IMF
– From Salpter IMF to Kroupa IMF, the derived stellar
mass decrease about a factor of 2
Self-consistence: SFR VS SMD differential
Perez-Gonzalez et al. 2010
Bouwens et al. 2010
Mismatch between SFR and SMD at low z
• SMD differential SFR is systematical lower
– Chabrier IMF(z<2), top heavy at z>2
– Contradictory to high z results?
• SFR over-estimated at high z, e.g. AGN contain
nation
• 0<z<0.4, SMD differential is higher than SFR
measured
– Stellar mass function evolution governed by dry
mereger
My idea
• Comprehensive self-consistence check of the
SFR and SMD
– IMF, sample selection, dust etc.
• Enhanced self-consistence check
– SMD only constrains the number of stars formed in
past, but not the way they formed
– During the estimation of stellar mass, the information
of the SFH is neglected.
– Can we use the cosmic stellar population at redshift
z0 to constrain/compare the measured SFH at z>z0
Example: SDSS cosmic spectrum