Evolution of Cosmic Molecular Gas Mass Density From z ~ 0 to z = 1 -1.5
aa r X i v : . [ a s t r o - ph . GA ] D ec Draft version October 17, 2018
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EVOLUTION OF COSMIC MOLECULAR GAS MASS DENSITY FROM Z ∼ Z = 1 − . Fumiya Maeda, Kouji Ohta, and Akifumi Seko
Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-Cho, Sakyo-ku, Kyoto, 606-8502, Japan;[email protected]
ABSTRACTWe try to constrain the cosmic molecular gas mass density at z = 1 − . ρ H = (6 . − . × M ⊙ Mpc − at z = 1 − . . × M ⊙ Mpc − at z ∼ . M ∗ . Although the values have various uncertainties, the cosmicmolecular gas mass density at z = 1 − . z ∼ − z = 1 − . z ∼ − Keywords: galaxy: evolution - galaxy: ISM - galaxy: star formation INTRODUCTIONCosmic star formation rate density (CSFRD) at z ∼ − z ∼ − z ∼
0. However, the molecular gas mass de-pends on prescriptions (such as pressure based, metal-licity based) to evaluate the molecular gas mass fractionamong various phases of the gas. Hence, observationalconstraints are desirable.In order to assess the CMGDs at the redshifts, amost straightforward way would be to derive the molec-ular gas mass function in the local universe and at z ∼ −
2, and to integrate them. The molecular gasmass in a galaxy can be derived from its CO(1-0) lu-minosity. For the local universe, the measurements ofthe CMGD using CO(1-0) luminosity were made (e.g.,Keres et al. 2003; Obreschkow & Rawlings 2009). Us- ing an FIR- and a B -band selected sample of galaxiesincluded in the Five College Radio Astronomy Observa-tory (FCRAO) Extragalactic CO survey, Keres et al.(2003) derived a CO luminosity function and a CMGDby adopting a constant CO-to-H conversion factor.Obreschkow & Rawlings (2009) applied variable CO-to-H conversion factor (depending on CO luminosity and B -band luminosity) to the CO luminosity function byKeres et al. (2003).For normal star-forming galaxies at z ∼ −
2, COobservations of them have been very much time con-suming and have been hard to be achieved. Such a trywas made by Walter et al. (2014) as a blank sky surveyin the Hubble Deep Field North using IRAM Plateaude Bure interferometer (PdBI); they obtained CO lu-minosity functions at z = 0.34(CO(1-0)), 1.52(CO(2-1))and 2.75(CO(3-2)) and derived the CMGD at each red-shift. Although they depicted the cosmological evolutionof the CMGD, the uncertainty is very much large dueto a small number of galaxies from which CO emissionlines are detected. More recently, Decarli et al. (2016a)conducted a spectroscopic survey with Atacama LargeMillimeter/submillimeter Array (ALMA) in the HubbleUltra Deep Field and the situation is improved.As an alternative approach to the CMGD,Berta et al. (2013) derived the molecular gas mass inmain sequence galaxies at z = 0 . − . z ∼ − z ∼ z ∼ − z ∼ − . z ∼ . z ∼ − . M ⊙ and 0 . M ⊙ , respectively.Stellar mass, star formation rate (SFR) and moleculargas mass fraction [ f mol = M mol /M star ] appear beloware corrected to those with Salpeter IMF; M Salpeter (orSFR
Salpeter ) = 1 . × M Chabrier (or SFR
Chabrier ). Weadopt cosmology parameters of H = 70 km s − Mpc − , Ω M = 0 .
3, and Ω Λ = 0 . AVERAGE MOLECULAR GAS MASSFRACTION AND STELLAR MASS FUNCTION2.1.
Average molecular gas mass fraction againststellar mass
Tacconi et al. (2010, 2013) used a sample ofmain sequence star-forming galaxies with M star ≥ . × M ⊙ and SFR ≥ M ⊙ yr − at z = 1 − . conversion factor of 4 . M ⊙ (K km s − pc ) − .They also derived molecular gas mass fraction againstthe stellar mass for which CO emission is significantlydetected. Since the CO detected sample biases to higherspecific SFR, they derived the average molecular gasmass fraction in a stellar mass bin by correcting forthe specific SFR of observed galaxies. Resulting gasmass fraction at z = 1 − . ∼ .
14 at M star ∼ × M ⊙ to ∼ .
34 at M star ∼ × M ⊙ .Seko et al. (2016a) used a sample of 18 randomly se-lected main sequence star-forming galaxies at z ∼ . M star ≥ . × M ⊙ and SFR ≥ M ⊙ yr − , respectively, expanding to thelower stellar mass. Further, gas metallicity of the tar-get galaxies was obtained with N2 method (Yabe et al.2012, 2014). CO(5-4) observations were made withALMA. The molecular gas mass was derived by adoptingthe CO(5-4) to CO(1-0) luminosity ratio of 0.23 basedon observations of main sequence star-forming galaxies(sBzK) of z = 1 . conversion factor (equation(7) by Genzel et al. 2012). To obtain the average valueof the fraction at a stellar mass bin, Seko et al. (2016a)made stacking analysis including non-CO detected sam-ple galaxies. The fraction amounts to ∼ .
72 at thelowest stellar mass bin of 2 × M ⊙ .For the local star-forming galaxies, several surveyswere conducted. CO Legacy Database for Galex AreciboSDSS Survey (COLD GASS: Saintonge et al. 2011a)measured the CO(1-0) luminosity for a sample of 350nearby galaxies ( M star & . × M ⊙ ) using the IRAM30-m telescope. CO(1-0) line was detected towards 222galaxies, and they derived the molecular gas mass andits fraction against the stellar mass by adopting the CO-to-H conversion factor of 3 . M ⊙ (K km s − pc ) − .The CO detected galaxies are likely to consist mostlyof late-type galaxies, by considering their distributionsin color, concentration, and stellar mass surface density(Saintonge et al. 2011a); they are considered to be mainsequence galaxies. The average gas mass fraction amongthe galaxies in a stellar mass bin ranges from 0.03 to0.06; a slight tendency that the fraction increases withdecreasing stellar mass is seen.In Herschel
Reference Survey (HRS: Boselli et al.2014), they extended to lower stellar mass ( M star & . × M ⊙ )). They also measured the CO(1-0) lu-minosity for a sample of 225 galaxies consisting of 57E-S0a type galaxies and 168 Sa-Im-BCD type galaxies.The detection rate is very low for early-type galaxies(16%) and high for late-type galaxies (80%). They de-rived the molecular gas mass and its fraction against thestellar mass by adopting the CO-to-H conversion fac-tor of 3 . M ⊙ (K km s − pc ) − . The fraction is 0.19at M star ∼ . × M ⊙ . There is the same tendencyas seen in Saintonge et al. (2011a) that the fraction in-creases with decreasing stellar mass.The gas mass fractions against the stellar mass aresummarized in Figure 1. Since different CO-to-H con-version factors are used to derive the molecular gas massin the data mentioned above, we recalculated them byadopting the metallicity dependent CO-to-H conver-sion factor by Leroy et al. (2011, their Figure 6) andGenzel et al. (2012) at z ∼ z = 1 − .
5, respec-tively. (Hereafter, we do not include the helium in themolecular gas mass.) To do this, we estimated the gasmetallicity from the mass-metallicity relation at z ∼ . z ∼ . f mol ( M star ) = M mol M star = 1exp((log M star − A ) /B ) , (1)where A and B are constant parameters. This func-tion form was designed to match the molecular gas massfractions against the stellar mass at 0 . < z < . A, B ) = (6 . , .
36) and (
A, B ) =(10 . , .
51) at z ∼ z = 1 − .
5, respectively.Note that the original function form is for the fittingto the gas mass fraction of M mol / ( M mol + M star ) anddoes not exceed 1.0. Uncertainties (1 σ ) of the best-fitfunctions are shown as shaded region in Figure 1. Wederived the uncertainties by random realizations of thedata points according to their errors.2.2. Stellar mass function of star-forming galaxies
We use the stellar mass functions (SMFs) at z = 1 − . z ∼
0, we adopt the SMF of star-forming galaxies by Moustakas et al. (2013). The SMFsare also corrected for the IMF difference.T14 derived galaxy SMFs over a redshift range of0 . < z < ∼ M star (M ⊙ )0.010.11 f m o l Figure 1 . Gas mass fraction ( f mol = M mol /M star ) againststellar mass. For all sample data, we corrected to SalpeterIMF, adopted the metallicity dependent CO-to-H conver-sion factor by Leroy et al. (2011) and Genzel et al. (2012)at z ∼ z = 1 − .
5, respectively. Filled blue squaresrefer to the average values for the star-forming galaxies at z = 1 − . Galaxy Evolution Survey obtained in the Chandra DeepField South, the Cosmic Evolution Survey, and the Hub-ble Ultra Deep Field. T14 derived the SMF down toabout 1 dex lower stellar mass than those of the previ-ous studies at 0 . < z <
3. T14 reached stellar mass of6 . × M ⊙ at z = 1 . − .
5. They separated the fullgalaxy sample into star-forming and quiescent popula-tions based on a rest-frame U − V vs. V − J diagram,and then derived SMF for respective populations. Theyfitted the SMFs with double-Schechter function asΦ( M ) dM = e − M/M ∗ (cid:18) Φ ∗ (cid:18) MM ∗ (cid:19) α + Φ ∗ (cid:18) MM ∗ (cid:19) α (cid:19) dMM ∗ (2)where M ∗ is the characteristic stellar mass. We deriveda SMF of star-forming galaxies at z = 1 − . z = 1 . − . . − . . < z < .
0) using a combination of the UK InfraredTelescope Infrared Deep Sky Survey (UKIDSS) UltraDeep Survey (UDS), Cosmic Assembly Near-infraredDeep Extragalactic Legacy Survey (CANDELS) UDSand CANDELS the Great Observatories Origins DeepSurvey-South survey data sets. M15 reached stellarmass of 3 . × M ⊙ at z = 1 − .
5. They selectedSF galaxies based on
U V J classification (contaminationby SF galaxies in quiescent population is estimated tothe on average ∼ µ m data), and derivedSMF of star-forming galaxies at z = 1 . − . U V J classification (i.e., contamination due to thecolor classification), the uncertainties in the SED mod-eling, the Poisson uncertainties, and cosmic variance.Moustakas et al. (2013) derived a SMF of nearbygalaxies ( z = 0 . − .
2) using ∼ . × M ⊙ .They separated the galaxies into star-forming and quies-cent populations based on whether they lie on or belowthe main sequence in SFR vs. stellar mass diagram.We fitted the single-Schechter function and obtainedthe best-fit parameters : (log M ∗ /M ⊙ , α, log Φ ∗ ) =(11 . ± . , − . ± . , − . ± . COSMIC MOLECULAR GAS MASS DENSITYCombining the dependence of the molecular gas massfraction on the stellar mass and the SMF, we derivedthe CMGD as ρ mol = Z M max M min f mol M star Φ( M star ) dM star , (3)where Φ( M star ) is the SMF of star-forming galaxies and f mol refers to M mol /M star (equation (1)).Since we intend to compare the cosmic evolution ofthe CMGD with that of the CSFRD, obtaining themolecular gas masses in the galaxies in the same stel-lar mass range as that for the CSFRD is desirable.Madau & Dickinson (2014) derived the CSFRD by in-tegrating luminosity function from 0 . L ∗ where L ∗ isthe characteristic luminosity of the Schechter function.This does not necessarily correspond to stellar mass ex-actly. But considering the correlation between SFR andstellar mass, i.e., main sequence for star-forming galax-ies, it would be reasonable to choose M min as 0 . M ∗ at each redshift. From the best-fit M ∗ , M min in the lo-cal universe is 3 . × M ⊙ and that at z = 1 − . . × M ⊙ (T14) and 2 . × M ⊙ (M15). As for M max , we take 10 M ⊙ .The resulting CMGD at z ∼ . +0 . − . × M ⊙ Mpc − and that at z = 1 − . . +5 . − . × M ⊙ Mpc − (T14) and 6 . +2 . − . × M ⊙ Mpc − (M15). The results are shown in Figure 2. The resultsby adopting T14 and M15 agree with each other withinthe error. Here the uncertainties (1 σ ) shown with soliderror bars to the obtained values are calculated from theuncertainties on the molecular gas mass fraction (equa-tion (1)) and the SMF; we ran 10 realizations assumingthe error distribution for the best-fit values is Gaussian.The CMGD at z = 1 − . z = 1 − .
5. There are, however, many uncertaintiesin deriving the CMGD other than the fitting error on themolecular gas mass fraction and the SMF: (1) CO lumi-nosity ratio, (2) CO-to-H conversion factor, (3) f mol inlow stellar mass range, (4) slope of main sequence, and(5) contribution from Ultra-Luminous InfraRed Galax-ies (ULIRGs). We discuss these uncertainties.(1) To obtain CO(1-0) luminosity, Seko et al. (2016a)assumed the ratio of 0.23 for CO(5-4) luminosity byDaddi et al. (2015). Daddi et al. (2015) reported thatCO(5-4) emissions from three main sequence galaxies(sBzK) at z = 1 . J -ladders of z = 1 − . J -ladder is similar to that of M82 (e.g.,Carilly & Walter 2013), the CO(1-0) luminosity wouldbe lower by a factor of ∼
3. If the ladder resemblesto that of our Galaxy, it increases by a factor of ∼ conversion factor of 3 . M ⊙ (K km s − pc ) − (not in-cluding helium mass), the CMGD decreases 23 % (T14)and 25 % (M15) at z = 1 − . z ∼ M star = 1 . × M ⊙ at z = 1 − . . × M ⊙ ≤ M star ≤ . × M ⊙ at z = 1 . − f mol ∼ −
2, supporting our extrapola-tion. However, the average molecular gas mass fractionin star-forming galaxies with the low stellar mass rangemay be smaller, because the low metallicity and the lowgas column density are likely to suppress formation ofmolecular component. Although the CO-to-H conver-sion factors we used are metallicity dependent, we alsocalculated the CMGD assuming f mol = 1 . f mol = 0 . . × M ⊙ < M star < . × M ⊙ . ResultingCMGD is reduced by 25% (44%). Further studies ofthe gas mass fraction in the low stellar mass range aredesirable.(4) If we consider that the slope of the main se-quence is slightly flatter (SFR ∝ M . ), M min would be0 . M ∗ . In this case, the resultant CMGD increases70 −
80% at z = 1 − . z ∼
0, though theuncertainties of the fractions and SMFs are larger thanthose for the case of 0 . M ∗ .(5) SMFs of star-forming galaxies used here do not ex-clude ULIRGs, but here we discuss the contribution to redshift(z) −2.0−1.5−1.0−0.5 l og ρ S F R [ M ⊙ y r − M p c − ] l og ρ m o l [ M ⊙ M p c − ] Popping+14 (metallicity-based)Popping+14 (pressure-based)Lagos+11(metallicity-based)Lagos+11(pressure-based)
Figure 2 . CMGD (left ordinate) and CSFRD (right ordi-nate) against redshift. Filled red circle and square refer tothe CMGD at z ∼ − . z ∼
0. The vertical solid error bars only include fitting un-certainties of the gas mass fraction and SMF. Dashed errorbars at z ∼ − . con-version factor. Box frames show the results by Decarli et al.(2016a) based on the CO luminosity function. They adoptedthe conversion factor of 3 . M ⊙ (K km s − pc ) − . Openblue circle and triangle show the result by Keres et al.(2003) and Obreschkow & Rawlings (2009), respectively.Keres et al. (2003) adopted the conversion factor of4 . M ⊙ (K km s − pc ) − . Obreschkow & Rawlings (2009)used the CO luminosity function by Keres et al. (2003)but adopting the CO luminosity and B -band luminosity de-pendent conversion factor. Semi-analytic model predictionsfor the CMGD by Popping et al. (2014) and Lagos et al.(2011) are also shown. Green solid curve represents the best-fit CSFRD by Madau & Dickinson (2014). the CMGD from the ULIRGs. The gas mass fractionsof ULIRGs at z = 1 . − . − M ⊙ , thenumber density of ULIRGs (Goto et al. 2015) is morethan ten times smaller than that of main sequence galax-ies with M star = 10 − M ⊙ ((T14) and (M15)).Hence, the contribution to the CMGD from ULIRGs isexpected to be small.The largest uncertainty seems to be the CO luminosityratio, and the observations in lower CO transitions aremore desirable. DISCUSSION AND SUMMARYThe CMGD at z = 1 − . z = 1 − . J -ladder by Daddi et al. (2015). Theyalso conclude the CMGD at z = 1 − . − conversion factor used. Since they used the constantconversion factor of 3 . M ⊙ (K km s − pc ) − , we alsouse the same factor to directly compare with their re-sults. Resulting values are 6 . × M ⊙ Mpc − (T14)and 5 . × M ⊙ Mpc − (M15) which are in the range of(3 . − . × M ⊙ Mpc − by Decarli et al. (2016a).It should be note that the CO luminosity correspondingto our M min is close to the lowest CO luminosity usedby Decarli et al. (2016a).The CMGD at z ∼ . ± . × M ⊙ Mpc − ), which is also shown inFigure 2. They derived the CMGD using the CO lumi-nosity function by Keres et al. (2003) and adopting thethe CO luminosity and B -band luminosity dependentCO-to-H conversion factor. Obreschkow & Rawlings(2009) noted that Keres et al. (2003) overestimatedthe CMGD due to the constant CO-to-H conversionfactor. Although the CO luminosity corresponding toour M min is close to the lowest CO luminosity usedby Obreschkow & Rawlings (2009), the CMGD doesnot agree with that by Obreschkow & Rawlings (2009).The cause for this discrepancy is not clear, but itmay be worth noting that if we use f mol only byBoselli et al. (2014), the CMGD agrees with that byObreschkow & Rawlings (2009)We also show the semi-analytic model predictions byLagos et al. (2011) and Popping et al. (2014) of theCMGD in Figure 2. The model predictions roughlyagree with the observational results. However, the in-crease factor of the gas density from z ∼ . z ∼ z ∼ . z = 1 − . − z ∼ . z ∼
0. Thus thelarge CSFRD at z = 1 − ∼ × M ⊙ , which is almost middle of thestellar mass sampled in this study.In this paper, in order to constrain the CMGDat z = 1 − . . M ∗ , the CMGD is derived. The obtainedCMGD at z = 1 − . . − . × M ⊙ Mpc − .Although these values still have various uncertainties, this CMGD at z = 1 − . . × M ⊙ Mpc − ),implying that the large CSFRD at z = 1 − .5 is due tothe large CMGD. The CMGD at the redshift obtainedin this study agrees with that recently obtained fromintegration of CO luminosity function, indicating thatthe approach employed here is effective.We would like to thank the referee for usefulcomments and suggestions. K.O. is supported byGrant-in-Aid for Scientific Research (C) (16K05294)from Japan Society of the Promotion of Science (JSPS).A.S. is supported by Research Fellowship for YoungScientists from JSPS.REFERENCES