The UV luminosity density provides an estimate of the total amount of light emitted by galaxies per unit volume. In the present work we compute the UV luminosity density assuming the Schechter form of the luminosity function (Schechter 1976). Once we have the Schechter parameters ↵, M⇤ and ⇤, we can derive the UV luminosity density, by integrating it from the observed bright-end to a fixed faint-end. (Llim=L⇤z=0, where L⇤z=0 is the L⇤ at z=0.)
Fig.14 presents the evolution in the integrated Schechter fit LD from our sample, compared with previous studies. Our errors are standard errors from the fitting procedure.
We compare our results with a compilation from Cucciati et al. (2012), Reddy et al. (2008) and Bouwens et al. (2007). The results of LD from z⇠1 to z⇠3 are consistent with Reddy et al. (2008) and Cucciati et al. (2012). Our results are done for smaller bins compared to previous studies of redshift. The evolution of UV LD from z ⇠ 3 to z ⇠ 1 is a good representation of the evolution of SFR and agrees well with previous studies (Reddy et al.
2008, Bouwens et al. 2007, Cucciati et al. 2012).
Cucciati et al. (2012) use both the Deep and Ultra-Deep surveys obtained in the VVDS-0226-04 field with spectroscopy redshift, over 2200 arcmin2 of sky area. The depth of data is IAB 24.75; Reddy et al (2008), used optical data from LBG selection with typical depth of RAB ⇠27.5 from GOODS-North field, HDF-North field and Westphal field, total area covered almost a square degree; Bouwens et al. (2007), used a high-redshift LBG sample from HUDF, HUDF-Ps, HUDF05, and GOODS fields, with detecting limits i775,AB
> 26.5 (GOODS), i775,AB > 27.3 ( HUDF-Ps/ HUDF05 ), and i775,AB > 28 ( HUDF ), for a total coverage of about 400 arcmin2.
Thanks to our large sample, we can reduce the size of the redshift bins and have consistent method to compare to these previous studies. Because our data is deeper, we
should have better faint-end result. However, the area of other studies can be wider than our, meaning their bright-end should be less biased.
Nevertheless, these results present evidences that the UV LD peak at z ⇠2 (Fig.14).
After an increase from z⇠6 to z⇠2, the UV LD decreases sharply down to z⇠0. It tells us the galaxies number increase very fast in early universe, then the speed of increasing slow down from z⇠ 2. There are two explanation in recent scenario of galaxy evolution from these results: First, the e↵ect of kinetical feedback, we think it is because of gas exhaustion (Tresse et al. 2007) or truncation of the star formation such as through AGN or supernova feedback (e.g., Kriek et al. 2006; Reddy et al. 2006b, 2005; Erb et al. 2006c); In the other hand, the e↵ect of thermal feedback tell us due to heating by some mechanisms gas is unable to cool in galaxies with the largest stellar masses. This includes AGN feedback (Scannapieco et al. 2005; Granato et al. 2004) and dilution of infalling gas due to virial shock ( Dekel & Birnboim 2006). Interestingly, it is around this epoch, z ⇠ 2, that AGN activity appears to peak making AGN feedback a good candidate as potential mechanisms of star formation quenching. (e.g., Hopkins et al. 2007; Fan et al. 2001; Shaver et al.
1996). In order to better constrain these scenario and have a better understanding of galaxy evolution, we can use our results and compare to di↵erent properties of galaxies.
One possible way is to explore LD in di↵erent stellar mass with redshifts, which is done in next section.
Fig. 14.— LD evolution for our data (in red crosses) compared with Reddy et al. (2008) at z ⇠ 2 3 (blue diamons), Cucciati et al. (2012) at z = 0.3-3.0 (black squares) and Bouwens et al. (2007) at z = 4-6 (green triangles)
7. Luminosity Density of Low Stellar Mass System
Thanks to the stellar mass we derived by SED fitting, we select low stellar mass galaxies with 108.5M < M⇤ <1010M to compute their LD. Compare to LD of full sample (M⇤ >108.5M ), we explore preliminarily the contribution of LD from low mass system to total LD. In order to have more obvious trend, we use smaller redshift bins z=0.2 instead of z=0.4 in 1< z <1.8. We also select sample only in redshift range 1< z <2 to avoid malmquist bias at z> 2 (see Fig.8). Our results are in Fig.15, we observe a slight increase of this ratio from high redshift to low redshift. The measurement at z⇠1.7 is surprising low and we guess it is due to a combination of problems of our bright-end and a possible structure at this redshift (see Fig.6). If this structure is real, we are actually expecting a drop of the LD in low mass galaxies due to environment e↵ects. We ignore this measurement when we describe the trend of the ratio evolution. This trend means the LD contribution is dominated by low mass galaxies at low redshift, and higher mass galaxies at high redshift. This is the actually consistent with downsizing scenario, which tells us the locus of SFR migrate from high mass galaxies at high redshift to low mass galaxies at low redshift. Of course due to unaccounted extinction we can’t derive directly the e↵ect on SFR.
Fig. 15.— The fraction of luminosity density of low mass system and total luminosity density
8. Conclusion and Summary
The UDS is currently the deepest and most extensive infrared survey ever conducted of the distant Universe. Furthermore, our K-selected study is less biased against dusty galaxies unlike previous I-band or R-band selected studies. We have used the DR8 photometry in combination with CFHT u⇤-band and SXDS optical data to derive the 1700˚A absolute magnitude.
Our LF results shown in section 5 are in good agreements with previous studies (Reddy et al. 2008, Sawicki et al. 2006). The bright-end slope of the LF become steeper from high redshift to low redshift, and M⇤ become fainter from high redshift to low redshift.
Also our UV LD which is a good indicator of SFR agrees very well with previous studies at z > 2 (see Figure 14), also we can better constrain the UV LD because our smaller redshift bin. We confirm that the peak of UV LD is at z⇠2, which implies that star-forming galaxies are forming more actively stars at that epoch, and we can better constrain the UV LD because our smaller redshift bin.
We compute the ratio between LD of low stellar mass as 108.5M < M⇤ <1010M and LD of full sample (M⇤ >108.5M ) with redshifts. We derive a preliminary result on the contribution of LD from low mass system to total LD (Fig.15). We show a trend from lower ratio at high redshift then increase to higher ratio at low redshift. All these results indicate UV luminosity is dominated by low mass system at low redshift and high mass at system.
This is the actually evidence of downsizing scenario, which tells us the SFR dominated by massive system at high redshift but dominated by less mass system.
To explain this trend in individual galaxy, we guess the most luminous and massive galaxies have exhausted their cold gas reservoir during their early intense star formation
which has occured in the early universe, they undergo passive evolution as star formation cease. At z ⇠ 2, AGN activity appears to peak (e.g., Hopkins et al. 2007; Fan et al. 2001;
Shaver et al. 1996) indicating a relation between AGN and evolution of SFR.
As highlighted previously, UV LD is a direct tracer of SFR, but a fraction of luminosity is missed due to dust extinction. Consequently, the proper way is that we have to observe the IR luminosity and combine UV and IR to trace the SFR. Herschel and 24um MIPS data are available on the UDS field, and we are planning to use them to IR LD, then we can bring much better constrain on the star-formation rate history.
9. Reference
Arnouts et al. 1999, M N RAS, 310, 540
Bertin & Arnouts 1996, A&A Supplement, 317, 393
Blanton et al. 2003a, AJ, 125, 2348
Bouwens et al. 2007, ApJ, 670, 928
Caputi et al. 2007, ApJ, 660, 97
Coleman et al. 1980, ApJS, 43, 393
Cowie et al. 1996, AJ, 112, 839
Cucciati et al. 2012, A&A, 539, A31
Dekel & Birnboim 2006, M N RAS, 368, 2
Erb et al. 2006c, ApJ, 646, 107
Faber et al. 2007, ApJ, 665, 265
Fan et al. 2001, AJ, 122, 2833
Furusawa et al. 2008, ApJS, 176, 1
Gilli et al. 2007, A&A, 463, 79
Granato et al. 2004, ApJ, 600, 580
Hartley et al. (in prep)
Hirashita et al. 2003, A&A, 410, 83
Hopkins et al. 2006, ApJ, 652, 107
Hopkins et al. 2007, ApJ, 654, 731
Ilbert et al. 2004, M N RAS, 351, 541
Ilbert et al. 2005, A&A, 439, 863
Kinney et al. 1996, ApJ, 467, 38
Kriek et al. 2006, ApJ, 649L, 71
Lawrence et al. 2007, MNRAS, 379 ,1599
Lehmer et al. 2008, ApJ, 681, 1163
Lilly et al. 1995, ApJ, 455, 108
Marshall 1985, ApJ, 289, 457
Norman et al. 2004, ApJ, 607, 721
Oesch et al. 2010, AP J, 725, 150
Oke, J.B. 1974, ApJS, 27, 21
P`erez-Gonz`alez et al. 2005, ApJ, 630, 82
Quadri et al. 2012, ApJ, 744, 88
Reddy et al. 2008, ApJS ,175, 48
Sawicki et al. 2005, ApJ, 635, 100
Sawicki et al. 2006, ApJ, 642, 653
Scannapieco et al. 2005, ApJ, 635, 13
Schechter 1976, ApJ, 203, 297
Schiminovich et al. 2005, ApJ, 619, 47
Shaver et al. 1996, N ature, 384, 439
Simpson et al., 2012, M N RAS, 421, 3060
Steidel et al. 2004, ApJ, 604, 534
Swindle et al. 2011, AJ, 142, 118
Tresse et al. 2002, M N RAS, 337, 369
Tresse et al. 2007, A&A, 472, 403
Zucca et al. 2006, A&A, 455, 879
Appendix A1
To check our calculation for absolute magnitude, we used mock catalogs from Henriques et al. (2012) computed from the semi-analytic modelling (SAM) of galaxy formation based on Millennium N-body simulation. The aim of this work is aim to predict the evolution of population properties, including the distributions of stellar mass, luminosity, star formation rate, size, rotation velocity, morphology, gas content and metallicity, as well as the scaling relations linking these properties. The data set includes redshifts, apparent magnitudes with di↵erent filters, and rest-frame absolute magnitudes with di↵erent colors, etc,.
In order to determine the absolute magnitude, we use CWW + KINNEY templates (Coleman et al. 1980, Kinney et al. 1996) to do SED fitting to derive k-correction. We applied the same method than our data. In addition, we don’t use only one band to trace the intrinsic magnitude because it will be model dependent. We use di↵erent band with redshift instead. Since it is simulation, we know the intrinsic rest-frame absolute magnitude.
We use it to check how good is our calculation by di↵erencing between our results and the given absolute magnitude.
Our UV-LF is computed in a mock top-hat filter at 1700˚A filter with 400˚A width.
For every galaxy, first we shift at each SED template to the observed-frame according to its redshift, then we convolve the SED by all uBVRizJHK filters to get magnitudes.
In addition, we adjust SED in the flux direct to identify its proper scale. Then we use chi-square minimisation to find the best SED template. We convolve intrinsic SED with 1700˚A filter to get the intrinsic magnitudes. Finally, we can get the k-correction by computing the di↵erence between the magnitude from shifted SED and the intrinsic magnitude from intrinsic SED.
Fig.16 shows the dispersion of our computed absolute magnitudes and the absolute
magnitudes given by the Mock, we get a dispersion of the order of 1 mag. And we show the dispersion with redshift in Fig.17, the black points are computed absolute magnitude before k-correction, red points are absolute magnitude after k-correction. This 1 magnitude dispersion cannot a↵ect LF a lot. It tell us that our calculation doing well.
Fig. 16.— The dispersion between our computing absolute magnitude and given absolute magnitude.
Fig. 17.— The dispersion between our computing absolute magnitude and given absolute magnitude with redshift. The black points are computed absolute magnitude before k-correction, red points are absolute magnitude after k-correction.
Appendix A2
Following is our idl code for computing LF:
pro plotlf_v, z, mab,sh=sh,ldd=ldd,phi=phi,er=er,x=x, $ bin=bin,sh_init=sh_init,fitn=fitn,area=area,ftend=ftend, $
;area: fov (default:0.58 for UDS)
;/cu,/oesch,/reddy,sawicki: comparison
;sh_init: suggustion for schecter parameter
;bin:magnitude bin (e.g. bin=0.5 or bin=0.25 ...;default: 0.5)
;fitn=decreasing data number after cut for schecter function fitting (default:0)
; IF n_elements(area) ne 0 THEN a=area IF n_elements(bin) eq 0 THEN bin=0.5 IF n_elements(ftend) eq 0 THEN ftend=-18
rr=fltarr(100000) phi=fltarr(14d/bin+1) er=fltarr(14d/bin+1) x=fltarr(14d/bin+1) for i=0,14d/bin do begin
rr=where(mab ge i*bin+min(mab) and mab lt (i+1)*bin+min(mab),cn) if rr[0] ne -1 then begin
phi[i]=(1d/bin)*total(1d/ajs_comvol(z[rr],area=a))
er[i]=phi[i]/sqrt(cn) ;(1d/bin)*sqrt(total(1d/(ajs_comvol(z[rr],area=a))^2))
x[i]=min(mab)+(i+0.5)*bin endif
endfor
z_r=round(zr*10)*0.1
IF n_elements(ftend) eq 0 THEN $ ;decide the faint end for plot fd=-18
IF n_elements(ftend) ne 0 THEN $ fd=ftend
IF n_elements(fitn) ne 0 THEN ub=[ub,max(ub)+fitn]
x1=x[ub]
phi1=phi[ub]
er1=er[ub]
IF n_elements(sh_init) ne 0 THEN $
schechter={phistar:sh_init[2], mstar:sh_init[0], alpha:sh_init[1], $ phistar_err:0.d, mstar_err:0.d, alpha_err:0.d}
IF n_elements(sh_init) ne 0 THEN $
lf_fit_schechter, x1,phi1,er1,schechter ;sh_init---phi,M,alpha IF n_elements(sh_init) ne 0 THEN $
sh=schechter
lf_fit_schechter, x1,phi1,er1,sh
;sh_init=[M*,alpha,phi*]
;IF n_elements(sh_init) EQ 0 THEN $
; sh=ajs_schechter_fit(x1,phi1,er1, range=[round(max(mab)),round(min(mab))] )
;
sh=ajs_schechter_fit(x1,phi1,er1,range=[round(max(mab)),round(min(mab))],params_init=
sh_init)
;IF n_elements(ftend) eq 0 THEN $
s=[-24,-23.5,-23,-22.5,-22,-21.5,-21,-20.5,-20,-19.5,-19,-18.5,-18,-17.5,-17,-16.5,-16]
IF ftend eq -14 THEN $ s=[s,-15.5,-15,-14.5,-14]
IF ftend eq -12 THEN $
legend,['This work','Oesch et al. 2010'],charsize=2,box=0,linestyle=[0,2],$
textcolors=[fsc_color('White'),fsc_color('Green')],$
legend,['This work','Sawicki et al. 2006'],charsize=2,box=0,linestyle=[0,2],$
textcolors=[fsc_color('White'),fsc_color('Red')],$
end
legend,['This work','Reddy et al. 2008'],charsize=2,box=0,linestyle=[0,2],$
textcolors=[fsc_color('White'),fsc_color('Blue')],$
legend,['This work','Cucciati et al. 2012'],charsize=2,box=0,linestyle=[0,2],$
textcolors=[fsc_color('White'),fsc_color('Gold')],$
end
Following is our idl code for computing k-correction:
pro kc_fit, z,
u=u,bd=bd,v=v,r=r,i=i,zm=zm,j=j,h=h,kb=kb,kcn=kcn,chi2=chi2,band=band,sedn=sedn,ap m=apm
;purpose: find best sed then do convlution with filter to get rest-frame mag
;
;INPUT
; z: redshift
; u~k: each color, apparent mag
; band: use 'uv' or 'u' or 'b'... to select which band in rest-frame
;
;
;OUTPUT
; amag: rest-frame apparent mag
; chi2: chisquare from best SED
;---;---start
time---t1=systime(/seconds) ;set start for calculating how much time it spend
;---;make gallaxy's all bands data n=n_elements(z)
if sedx eq 'sed1' then sedn[x]=1 if sedx eq 'sed2' then sedn[x]=2 if sedx eq 'sed3' then sedn[x]=3 if sedx eq 'sed4' then sedn[x]=4 if sedx eq 'sed5' then sedn[x]=5 if sedx eq 'sed6' then sedn[x]=6 if sedx eq 'sedc' then sedn[x]=7 if sedx eq 'sedd' then sedn[x]=8 if sedx eq 'sede' then sedn[x]=9 if sedx eq 'sedi' then sedn[x]=10
;obs-frame convlution mag from SED upd=dblarr(13)
zpmag=dblarr(13) for ted=0,12 do begin upd[ted]=ted-5
cvlm_uv, ssed=sedx, cm=cm2,z=z[x],updown=upd[ted]
bandtol = { uv:[170], u:[350], b:[436.641],v:[542.956],r:[622.057],i:[764.124],zm:[914.674],j:
[1252.9],h:[1642.69],k:[2228.63],m36:[3600],m45:[4500] } tag = tag_names(bandtol)
tag1 = strupcase(band) op = where(tag eq tag1) value=(bandtol.(op)*(1+z[x]))
if (value gt 150) and (value le 190 ) then zpmag[ted]=cm2[0]
if (value gt 300) and (value le 400 ) then zpmag[ted]=cm2[1]
if (value gt 400) and (value le 500 ) then zpmag[ted]=cm2[2]
if (value gt 500) and (value le 583) then zpmag[ted]=cm2[3]
if (value gt 583) and (value le 690 ) then zpmag[ted]=cm2[4]
if (value gt 690) and (value le 820 ) then zpmag[ted]=cm2[5]
if (value gt 820) and (value le 1000) then zpmag[ted]=cm2[6]
if (value gt 1000) and (value le 1450) then zpmag[ted]=cm2[7]
if (value gt 1450) and (value le 1900) then zpmag[ted]=cm2[8]
if (value gt 1900) and (value le 2400) then zpmag[ted]=cm2[9]
endfor
best=upd[where(abs(apm[x]-zpmag) eq min(abs(apm[x]-zpmag)))]
zpmag1=zpmag[where(abs(apm[x]-zpmag) eq min(abs(apm[x]-zpmag)))]
;to avoid infinity ...but seems no work if best eq -5 then best=-5
if best eq -4 then best=-4 if best eq -3 then best=-3 if best eq -2 then best=-2 if best eq -1 then best=-1 if best eq 0 then best=0 if best eq 1 then best=1 if best eq 2 then best=2 if best eq 3 then best=3 if best eq 4 then best=4 if best eq 5 then best=5 if best eq 6 then best=6
if best eq 7 then best=7
;rest-frame convlution mag from SED
cvlm_uv, ssed=sedx, cm=cm1 ,updown=best
; to avoid infinity
if cm1[1] gt 100 then cvlm, ssed=sedx, cm=cm1
;choose which band in rest-frame
if strupcase(band) eq strupcase('uv') then pmag=cm1[0]
if strupcase(band) eq strupcase('u') then pmag=cm1[1]
if strupcase(band) eq strupcase('b') then pmag=cm1[2]
if strupcase(band) eq strupcase('v') then pmag=cm1[3]
if strupcase(band) eq strupcase('r') then pmag=cm1[4]
if strupcase(band) eq strupcase('i') then pmag=cm1[5]
if strupcase(band) eq strupcase('zm') then pmag=cm1[6]
if strupcase(band) eq strupcase('j') then pmag=cm1[7]
if strupcase(band) eq strupcase('h') then pmag=cm1[8]
if strupcase(band) eq strupcase('k') then pmag=cm1[9]
;k-correction value = rest-frame mag - obs-frame mag kcn[x]=pmag-zpmag1
if (fix(x/10d)-x/10d) eq 0 then print,'waiting for',hr,'hour',mint,'min',sec,'sec'
pro dr8kc, z1,z2 ,name,rest=rest
;run SED fitting for k-correction vi mobile phone restore,'dr8n.sav'
if n_elements(z1) eq 0 then z1=min(z) if n_elements(z2) eq 0 then z2=max(z)
aa=where(z gt z1 and z le z2 and u le 40 and b le 40 and v le 40 and r le 40 and i le 40
;if n_elements(rest) ne 0 then band=rest gtreb ,rtf=band,zp,u,b,v,r,i,zm,j,h,kb,apm=apm kc_fit, zp,
u=u,bd=b,v=v,r=r,i=i,zm=zm,j=j,h=h,kb=kb,chi2=chi2,band=rest ,kcn=kcn,apm=apm
abmag=gtabs(apm+kcn,zp,o_m=0.25,o_l=0.75,H0=73) if n_elements(name) eq 0 then name='temp.sav'
save,/all,filename=name
exit end