Genesis and evolution of dust in galaxies in the early Universe II. Rapid dust evolution in quasars at z > 6
aa r X i v : . [ a s t r o - ph . C O ] M a r Astronomy&Astrophysicsmanuscript no. gallc15605 c (cid:13)
ESO 2018June 16, 2018
Genesis and evolution of dust in galaxies in the early Universe
II. Rapid dust evolution in quasars at z & C. Gall , A. C. Andersen , and J. Hjorth Dark Cosmology Centre, University of Copenhagen, Niels Bohr Institute, Juliane Maries Vej 30, DK-2100 Copenhagen, DenmarkReceived January 07, 2011
ABSTRACT
Aims.
We intend to assess the most plausible scenarios for generating large amounts of dust in high- z quasars (QSOs) on the basis ofobservationally derived physical properties of QSOs at z & Methods.
We use a chemical evolution model to compute the temporal progression of quantities such as the amount of dust and gas,stellar masses, star formation rates (SFRs) and the metallicity for various combinations of the initial mass function (IMF), the massof the galaxy, dust production efficiencies, and the degree of dust destruction in the ISM. We investigate the influence of the SFR onthe evolution of these quantities, and determine the earliest epochs at which agreement with observations can be achieved. We applythe obtained results to individual QSOs at z & Results.
We find that large quantities of dust can be generated rapidly as early as 30 Myr after the onset of the starburst when theSFR of the starburst is & M ⊙ yr − . The amount of dust and several other physical quantities of individual QSOs at z & × M ⊙ . Thebest agreement with observations is obtained with top-heavy IMFs. A sizable dust contribution from supernovae (SNe) is howeverrequired, while at these epochs dust production by asymptotic giant branch (AGB) stars is negligible. Moderate dust destruction inthe ISM can be accommodated. Key words. galaxies: high-redshift – galaxies: starburst – galaxies: evolution – ISM: evolution – quasars: general – stars: massive
1. Introduction
Studying QSOs and their host galaxies at high redshift ( z > z = 6.4, severaltens of QSOs have been discovered at z ∼ ∼ > M ⊙ (e.g.,Barth et al. 2003; Willott et al. 2003; Vestergaard 2004).Observations of QSOs have shown that dust emission atnear-infrared (NIR) wavelengths arise from warm and hot dust( T . z ∼ L FIR ∼ − L ⊙ is attributed to colddust ( T ∼ M ⊙ (e.g., Bertoldi et al. 2003a; Robson et al.2004; Beelen et al. 2006; Michałowski et al. 2010). The domi-nant source of the high FIR luminosity is believed to be dustheated by intense star formation in the circumnuclear region(e.g., Carilli et al. 2004; Riechers et al. 2007; Wang et al. 2008).Detection of [C II ] line emission at 158 µ m (Maiolino et al.2005) within a central region with radius ∼
750 pc of the hostgalaxy of J1148+5251 also implies a high star formation ratesurface density of 1000 M ⊙ yr − kpc − (Walter et al. 2009).Wang et al. (2010) derived SFRs between 530–2300 M ⊙ yr − from observations of a sample of QSOs at redshift z > z QSOs (e.g.,Barth et al. 2003; Dietrich et al. 2003; Maiolino et al. 2003;Becker et al. 2006) indicate strong star forming activity in theQSO hosts and solar or supersolar metallicity (e.g., Fan et al.2003; Freudling et al. 2003; Juarez et al. 2009). Theoreticalstudies of the gas metallicity of QSO hosts also predict superso-lar metallicities for z = 5–6 QSOs (e.g., Di Matteo et al. 2004).The high inferred SFRs imply short timescales ( ≤ yr)of the starburst (e.g. Bertoldi et al. 2003a; Walter et al. 2004;Dwek et al. 2007; Riechers et al. 2009), and consequently ayoung age of the QSOs. An early evolutionary stage of z > z QSOs could also be grown in the ISM (e.g., Draine 2009;Michałowski et al. 2010; Pipino et al. 2011). Finally, a domi-nant dust production by asymptotic giant branch stars has beenclaimed (Valiante et al. 2009).Molecular gas masses of the order of ∼ × M ⊙ have been inferred from detections of high excitation CO lineemission in QSOs at z > ∼ ∼ − M ⊙ which sets an upper limit onstellar bulge masses. These however are roughly two orders ofmagnitude lower than required from the present day black hole-bulge relation (e.g., Marconi & Hunt 2003). It therefore has beenproposed that the formation of the SMBH occurs prior to theformation of the stellar bulge. QSOs will then have to accreteadditional material to build up the required bulge mass (e.g.,Walter et al. 2004; Riechers et al. 2009; Wang et al. 2010). ForQSOs at z > ∼ yr seem to be required to form a SMBH > M ⊙ (e.g., Kawakatu & Wada 2009). It has also been predicted thatQSOs at z ∼ − M ⊙ (e.g., Li et al. 2007; Kawakatu & Wada 2009).In Gall et al. (2011, herafter Paper I) we developed a chemi-cal evolution model to elucidate the conditions required for gen-erating large dust masses in high- z starburst galaxies. We showedthat galaxies with masses of 1–5 × M ⊙ are suitable for en-abling the production of large amounts of dust within ∼
400 Myr.In the present paper we apply this model to QSOs at z &
6. Weperform more detailed comparison between model results andvalues inferred from observations of z & mass and the CO conversion factor for morerefined evaluations. In particular, calculations with higher SFRsthan in Paper I are considered. We aim to determine the earliestepochs at which the model results are in agreement with thosefrom observations.The structure of the paper is as follows: In Sec. 2 we brieflyreview the model developed in Paper I. A detailed analysis of theresults is presented in Sec. 3 followed by a discussion in Sec. 4.
2. The model
The galactic chemical evolution model from Paper I is self-consistent, numerically solved and has been developed to as-certain the temporal progression of dust, gas, metals, and di-verse physical properties of starburst galaxies. The incorporatedstellar sources are AGB stars in the mass range 3–8 M ⊙ andSNe. A differentiation between diverse SN subtypes has beenimplemented. Their roles as sources of dust production, dust de-struction or suppliers of gas and heavy elements are taken intoaccount. The lifetime dependent yield injection by the stellarsources, as well as dust destruction in the ISM due to SN shocksare also taken into account. Moreover, the formation of a SMBHis considered. Due to the very high SFRs of the starbursts, infallof neutral gas will only effect the system for comparable highinfall rates. Thus, gas infall and outflows are neglected. Possiblecaveats of such an approach are discussed in Paper I. The modelallows investigations of a broad range of physical properties ofgalaxies.The prime parameters are summarized in the following. Table 1.
Model parameters
Parameters Value Unit Description ψ ini × , 1 × M ⊙ yr − Star formation rate M SMBH × M ⊙ Mass of the SMBH t SMBH × yr Growth timscalefor the SMBH – Three different possible prescriptions for the stellar yieldsof SNe are implemented, i.e., (i) stellar evolution modelsby Eldridge et al. (2008) (referred to as ‘EIT08M’), (ii) ro-tating stellar models by Georgy et al. (2009), or (iii) nucle-osynthesis models by either Woosley & Weaver (1995) orNomoto et al. (2006). The stellar yields for AGB stars aretaken from van den Hoek & Groenewegen (1997). – We differentiate between five different IMFs. These are aSalpeter (1955) IMF, a top-heavy, and a mass-heavy IMF,as well as IMFs (Larson 1998) with characteristic masses ofeither m ch = 0.35 (Larson 1) or m ch = 10 (Larson 2). – The SFR at a certain epoch is given by the Kennicutt law(Kennicutt 1998) as ψ ( t ) = ψ ini ( M ISM ( t ) / M ini ) k , where ψ ini is the initial SFR of the starburst, M ISM ( t ) is the initial gasmass of the galaxy and k = 1.5. – The amount of dust produced by SNe and AGB stars is cal-culated using the dust formation efficiencies discussed inPaper I. For SNe three different dust production efficiencylimits are determined, i.e. a ‘maximum’ SN efficiency, a‘high’ SN efficiency, and a ‘low’ SN efficiency. The ‘maxi-mum’ SN efficiency originates from theoretical SN dust for-mation models, and corresponds to dust masses of approx-imately 3–10 × − M ⊙ . Similar dust masses have beenobserved in SN remnants such as Cas A (e.g., Dunne et al.2009) or Kepler (e.g., Gomez et al. 2009). Dust destructionin reverse shock interaction of about 93 % has been appliedto the ‘maximum’ SN efficiency, to obtain the ‘high’ SN ef-ficiency. The amount of dust for instance is ∼ × − M ⊙ , which is also comparable to some observations of olderSN remnants (Paper I, see references therein). The ‘low’ SNefficiency is based on SN dust yields (on average about 3 × − M ⊙ ) inferred from observations of SN ejecta. – Dust destruction in the ISM is implemented in terms of themass of ISM material, M cl , swept up by a single SN shockand cleared of the containing dust.For calculations in this paper most parameters have the samesettings as defined in Paper I. We apply the models where theformation of a SMBH has been included. A constant growth ratehas been estimated based on the final mass of the SMBH and theconsidered growth timescale. In this paper the SMBH growth isconsidered with a shorter growth timescale and calculations areperformed with higher initial SFRs. For the SN yields we onlyconsider the case of EIT08M. The parameters which differ fromthose used in Paper I are listed in Table 1.
3. Results
In this section we present the results of models calculated withinshort timescales after the starburst.A short enrichment timescale of a few times 10 yr for anintense starburst with a SFR of ∼ × M ⊙ yr − has beenproposed by e.g., Bertoldi et al. (2003a), Walter et al. (2004),Dwek et al. (2007), Riechers et al. (2009). Owing to this sugges-tion we are interested in whether the observed large dust masses M * [M O • ]10 M d [ M O • ] M cl = 100 M O • Maximum SN efficiency
Epoch: 30 Myr M cl = 0 M O • Maximum SN efficiency
Fig. 1.
Relation between dust mass and stellar mass at an epoch of 30 Myr, for various initial gas masses and IMFs. Calculationsare performed for a ‘maximum’ SN efficiency and dust destruction in the ISM with M cl = 100 M ⊙ (left panel) and M cl = 0 (rightpanel). The colored symbols are obtained for different initial gas masses, M ini , SFRs, and IMFs. The size of the symbols is scaledby M ini . Calculations are made for M ini = 1.3 × M ⊙ (largest symbol), M ini = 5 × M ⊙ , M ini = 3 × M ⊙ , M ini = 1 × M ⊙ , and M ini = 5 × M ⊙ (smallest symbol). The crosses correspond to calculations for a initial SFR ψ ini = 10 M ⊙ yr − , the filledcircles to ψ ini = 3 × M ⊙ yr − , and the stars to ψ ini = 10 M ⊙ yr − . The black, green, cyan, magenta, and blue colors denote theSalpeter, mass-heavy, top-heavy, Larson 1, and Larson 2 IMF, respectively. The dark grey region indicates the mass range of stellarmasses and dust masses derived from observations of QSOs at z >
6. The vertical dashed lines represent the lower and upper limitsof the observed stellar masses. The light grey area illustrates the whole mass ranges derived from observations of QSOs > M ⊙ can be reached within about 100 Myr.Consequently we performed calculations with an initial SFR forthe starburst with ψ ini = 3 × M ⊙ yr − for galaxies with initialgas masses M ini = 5 × M ⊙ , M ini = 1 × M ⊙ , M ini = 3 × M ⊙ , and M ini = 5 × M ⊙ . For the most massive systemwith M ini = 1.3 × M ⊙ an initial SFR ψ ini = 1 × M ⊙ yr − is adopted. We included the results for a lower initial SFR of 10 M ⊙ yr − from models computed in Paper I for comparison.In Paper I we analyzed the evolution of the amount of dustand various physical properties, and found that these are stronglydependent on the mass of the galaxy. Moreover, for a given ini-tial SFR all quantities evolve faster in less massive galaxies. Inthis paper we perform detailed comparisons between calculatedand observed values of the total dust mass, M d , the stellar mass, M ∗ , the SFR, ψ , and the metallicity, Z . We identified the shortestepoch, where some model results are in accordance with obser-vations to be 30 Myr. Furthermore, we discuss quantities suchas the CO conversion factor, the gas-to-H mass ratio, and thepossible amount of molecular hydrogen. In Fig. 1 we present the results for the mass of dust versus thestellar mass for galaxies with different initial gas masses andinitial SFRs at an epoch of 30 Myr. The displayed models arecomputed for a ‘maximum’ SN efficiency. Dust destruction inthe ISM is considered for values of M cl = 100 M ⊙ (left panel)and M cl = 0 (right panel).The dark grey region represents the mass ranges of the stellarmass and dust mass derived from observations of QSOs at z > M H from the total dynam-ical masses, M dyn . Values for M dyn and M H are based on datafrom Wang et al. (2010, and references therein) for three QSOsat z >
6. For an estimation of M dyn an inclination angle i = ◦ ofthe gas disk is taken for QSO J1148+5251 (Walter et al. 2004),while i = ◦ similar to Wang et al. (2010) is applied to theremaining two QSOs. We adopt the lower and upper limits for the dust masses from Beelen et al. (2006) and Michałowski et al.(2010). The light grey region covers the range of derived stel-lar masses and dust masses from observations of QSOs > z > i = ◦ for deriving M dyn ). We set the lower dust limit to10 M ⊙ to account for the uncertainties of derived dust massesfrom observations.Despite the short time span of 30 Myr, it is evident that mostmodels are within the plausible mass ranges illustrated by thelight and dark grey regions. This signifies a rapid build-up of alarge amount of dust, provided SNe produced dust with a ‘maxi-mum’ SN efficiency. For galaxies with M ini = 1–5 × M ⊙ allmodels with an initial SFR of 3 × M ⊙ yr − are in agreementwith the observed values for the stellar masses for QSOs at z >
6. The requirements for M d are best accomplished with either atop-heavy, mass-heavy or Larson 1 IMF for both values of M cl .In a galaxy with M ini = 1 × M ⊙ the amount of dust reachedwith a Larson 2 IMF and M cl = 100 M ⊙ also matches with thedark grey region. Models for either a ‘high’ or ‘low’ SN effi-ciency did not reach 10 M ⊙ of dust. Only in the most massivegalaxy ( M ini = 1.3 × M ⊙ ) and for top-heavy IMFs with a‘high’ SN efficiency an amount of dust > M ⊙ is obtained.In Fig. 2 we illustrate the results for dust and stellar masses atan epoch of 100 Myr. We present models for a ‘maximum’ SNefficiency (top row) and a ‘high’ SN efficiency (bottom row),while dust destruction in the ISM is considered for a M cl = 800M ⊙ (left column), M cl = 100 M ⊙ (middle column), and M cl = 0(right column). We carried out calculations for a ‘low’ SN effi-ciency, but the obtained dust masses of these models remainedbelow 10 M ⊙ .At these early epochs the stellar mass, M ∗ , is higher for mod-els with an initially larger SFR (at fixed IMF and M ini ). The stel-lar mass is also larger for IMFs biased towards low mass stars(at fixed M ini and ψ ini ). It is interesting to note that in the lessmassive galaxies (0.5–1 × M ⊙ ) dust masses obtained forthe higher initial SFR ( ψ ini = 3 × M ⊙ yr − ) are lower thandust masses obtained for the lower SFR ( ψ ini = 10 M ⊙ yr − ). M cl = 800 M O • Maximum SN efficiency
Epoch: 100 Myr M cl = 100 M O • Maximum SN efficiency M cl = 0 M O • Maximum SN efficiency M d [ M O • ] M cl = 800 M O • High SN efficiency M * [M O • ] M cl = 100 M O • High SN efficiency M cl = 0 M O • High SN efficiency
Fig. 2.
Relation between dust mass and stellar mass at an epoch of 100 Myr for various initial gas masses and IMFs. Calculationsare performed for a ‘maximum’ SN efficiency (top row) and a ‘high’ SN efficiency (bottom row). Dust destruction in the ISM isconsidered for a M cl = 800 M ⊙ (left column), M cl = 100 M ⊙ (middle column), and M cl = 0 (right column). The colored symbols areobtained for different initial gas masses, M ini , SFRs, and IMFs. The size of the symbols is scaled by M ini . Calculations are made for M ini = 1.3 × M ⊙ (largest symbol), M ini = 5 × M ⊙ , M ini = 3 × M ⊙ , M ini = 1 × M ⊙ and M ini = 5 × M ⊙ (smallestsymbol). The crosses correspond to calculations for a initial SFR ψ ini = 10 M ⊙ yr − , the filled circles to ψ ini = 3 × M ⊙ yr − ,and the stars to ψ ini = 10 M ⊙ yr − . The black, green, cyan, magenta, and blue colors denote the Salpeter, mass-heavy, top-heavy,Larson 1, and Larson 2 IMF, respectively. The dark grey region indicates the mass range of stellar masses and dust masses derivedfrom observations of QSOs at z >
6. The vertical dashed lines represent the lower and upper limits of the observed stellar masses.The light grey area illustrates the whole mass ranges derived from observations of QSOs > M cl = 100–800 M ⊙ is alsohigher than that seen at the epoch of 100 Myr for same M cl .We find that the stellar masses for models with an initial SFR ψ ini = 1–3 × M ⊙ yr − are within the observed region for z > ψ ini = 3 × M ⊙ yr − ,stellar masses are within the mass range for z > M ini = 0.5–1 × M ⊙ (all IMFs) or M ini = 3–5 × M ⊙ with top heavy IMFs. Stellarmasses within the dark grey area are also found with ψ ini = 10 M ⊙ yr − for galaxies with either M ini = 3–13 × M ⊙ and topheavy IMFs or for the less massive galaxies in combination withIMFs favoring low mass stars.In the case of M cl = 800 M ⊙ and for a ‘maximum’ SN effi-ciency most models with M ini = 3–13 × M ⊙ and ψ ini = 10 M ⊙ yr − fit within the dark grey region. However for the higherinitial SFR M d is within or close to this zone only for galaxieswith M ini = 3–5 × M ⊙ and top-heavy IMFs. For M cl = 100M ⊙ and a ‘maximum’ SN efficiency the dust mass obtained ina galaxy with M ini = 1 × M ⊙ , ψ ini = 3 × M ⊙ yr − andfor top-heavy IMFs is in agreement with observations, while thedust masses in the more massive galaxies for some IMFs andSFRs are higher than required. In the case of no dust destructionthe dust masses reached for some IMFs and SFRs are able tomatch within the dark grey area also in the least massive galaxy.We find that in case of a ‘high’ SN efficiency and for ψ ini =3 × M ⊙ yr − in galaxies with initial masses 3–5 × M ⊙ and top-heavy IMFs high dust masses are possible, even if dustdestruction is included (i.e., M cl = 0–100 M ⊙ ). We next present the obtained metallicities and SFRs at the timeof observation for the models discussed above.Fig. 3 depicts the metallicity versus SFR at epochs of 30Myr (left panel) and 100 Myr (right panel). With respect toobservations of QSOs > (5) 6 we marked the range of de-rived values as a dark grey shaded zone. The lower and upperlimits of the SFR are based on observations by Bertoldi et al.(2003a) and Wang et al. (2010). We set the lower limit forthe metallicity at the solar value and the upper limit at 5 Z ⊙ .This is based on the inferred solar or supersolar metallicitiesin high- z QSOs (e.g., Barth et al. 2003; Dietrich et al. 2003;Fan et al. 2003; Freudling et al. 2003; Maiolino et al. 2003;Di Matteo et al. 2004; Becker et al. 2006; Juarez et al. 2009).We note that there are no strong constraints on the upper limitand therefore the zone above 5 Z ⊙ is marked as light grey shadedregion to account for the uncertainty.We find that at an epoch of 30 Myr high metallicities in theless massive galaxies are already reached. The best result is at-tained by a system with M ini = 1 × M ⊙ , ψ ini = 3 × M ⊙ yr − , and IMFs biased towards higher masses. For a galaxy with M ini = 5 × M ⊙ all models with either the same ψ ini or with
100 1000 ψ [M O • /yr] Z Epoch: 30 Myr
Z = Z O •
100 1000 10000
Epoch: 100 Myr
Fig. 3.
Relation between metallicity and SFR at epochs of 30Myr (left panel) and 100 Myr (right panel). The colored sym-bols are obtained for different initial gas masses, M ini , SFRs, andIMFs. The size of the symbols is scaled by M ini . Calculations aremade for M ini = 1.3 × M ⊙ (largest symbol), M ini = 5 × M ⊙ , M ini = 3 × M ⊙ , M ini = 1 × M ⊙ , and M ini = 5 × M ⊙ (smallest symbol). The crosses correspond to calcula-tions for a initial SFR ψ ini = 10 M ⊙ yr − , the filled circles to ψ ini = 3 × M ⊙ yr − and the stars to ψ ini = 10 M ⊙ yr − . The black,green, cyan, magenta, and blue colors denote the Salpeter, mass-heavy, top-heavy, Larson 1, and Larson 2 IMF, respectively. Thedark grey shaded region indicates the range of the metallicityand SFR based on observations of QSOs at z >
6. The verticaldashed lines represent the lower and upper limits of the observa-tionally derived SFRs. The light grey shaded area accounts forthe uncertainty of the upper limit of the metallicity. The horizon-tal dashed lines mark the lower and possibly upper limit of themetallicity.the lower initial SFR, and top-heavy IMFs are within the darkgrey shaded region as well.At an epoch of 100 Myr the metallicity has increased in allmodels, while the SFR in the less massive galaxies has signif-icantly decreased. The models for M ini = 3–5 × M ⊙ , ψ ini = 3 × M ⊙ yr − , and top heavy IMFs constitute the best re-sults. In galaxies with M ini = 3 × M ⊙ , the same initial SFR,and either a mass-heavy or Larson 1 IMF the obtained values for Z and ψ ( t ) are also in agreement with the observed values. Themetallicities in the low mass galaxies which give the best agree-ment at 30 Myr are now shifted above the upper limit, while theSFRs remain in the observed range. The models for a galaxywith M ini = 1 × M ⊙ , a lower initial SFR of 10 M ⊙ yr − ,and top-heavy IMFs at this epoch (100 Myr) reach sufficientlyhigh metallicities, while high enough SFRs are sustained. mass ratio To evaluate the calculated models, we additionally consider therelation between the gas-to-H mass ratio and the CO conversionfactor used to derive the molecular gas mass in a galaxy.Detections of high excitation CO line emission in QSOs at z > (5) 6 indicate the presence of 0.7–2.5 × M ⊙ of molecularhydrogen (e.g., Bertoldi et al. 2003b; Walter et al. 2003, 2004;Riechers et al. 2009; Wang et al. 2010). This molecular gas mass M i n i = . x M O • M i n i = . x M O • M i n i = . x M O • M i n i = . x M O • M i n i = . x M O • Epoch: 30 Myr ∆ α = 1.9 η g,H α Epoch: 100 Myr ∆ α = 1.2 Fig. 4.
CO conversion factor versus gas-to-H ratio at epochs 30Myr (top panel) and 100 Myr (bottom panel). The solid lines cor-respond to calculations of α as a function of the gas-to-H ratio η g , H for a CO line luminosity of L ′ CO(1 − = 2.7 × K km s − pc . Calculations are performed for different IMFs and galax-ies for a range of different initial gas masses M ini . The thicknessof the lines is scaled by M ini as indicated in the upper panel.The black and cyan colors denote the Salpeter and top-heavyIMF, respectively. The arrow indicates the shift of α for calcu-lations with the lower L ′ CO(1 − = 1.5 × K km s − pc , and ∆ α is the difference of α between the higher and lower L ′ CO(1 − .Calculations are shown for models with ψ ini = 3 × M ⊙ yr − ,except for the model for the most massive galaxy for which ψ ini = 10 M ⊙ yr − . The grey shaded region signifies the possiblerange of α and η g , H . The horizontal black dashed lines mark thevalues of α = 0.8, 1 and 4.6 M ⊙ (K km s − pc ) − .is derived from the relation M H = α × L ′ CO(1 − , where α is theconversion factor between the low excitation CO J = 1–0 lineluminosity L ′ CO(1 − and M H . For spiral galaxies α is typically ∼ ⊙ (K km s − pc ) − (e.g., Solomon & Barrett 1991), whilefor the centre of nearby ultra luminous starburst galaxies a con-version factor of α = 0.8–1 M ⊙ (K km s − pc ) − is appropri-ate (e.g., Downes & Solomon 1998). The latter value of α isusually used for e.g., high- z QSOs (e.g., Bertoldi et al. 2003b;Walter et al. 2003; Wang et al. 2010), Ultra Luminous InfraredGalaxies (ULIRGs) (Yan et al. 2010) or for high- z sub-mmgalaxies (SMGs) (Tecza et al. 2004; Greve et al. 2005). However α is not well known in the case of very high excitation. In our models we have computed the total (H + He) gasmass M G which remains in the galaxies at a given epoch. Themolecular gas mass, M H , constitutes a certain fraction of the to-tal gas mass, M G . Hence we introduce the gas-to-H mass ratioas η g , H = M G / M H . The CO conversion factor can thereby beexpressed as a function of η g , H as α = M G η g , H L ′ CO(1 − , (1)where η g , H ≥ η g , H of ∼ z = 3 radiogalaxy B3 J2330+3927 (De Breuck et al. 2003). This might alsobe the case for QSOs and suggests a gas-to-H ratio between 1and 2.In Fig. 4 we show the results for α as a function of η g , H with ψ ini = 3 × M ⊙ yr − for models with M ini ≤ × M ⊙ and with ψ ini = 10 M ⊙ yr − for the most massive galaxy.Calculations are performed for two different epochs; 30 Myr (toppanel) and 100 Myr (bottom panel). The IMFs involved are thetop-heavy IMF and the Salpeter IMF. We adopt a CO line lu-minosity L ′ CO(1 − = 2.7 × K km s − pc which is basedon the derived values of J1148+5251 and J0840+5624 (e.g.,Bertoldi et al. 2003b; Walter et al. 2003; Wang et al. 2010).The difference of α from calculations with a lower L ′ CO(1 − (i.e., L ′ CO(1 − = 1.5 × K km s − pc ) is indicated by thearrow in Fig. 4. The grey shaded area signifies a possible rangefor α and η g , H as discussed above.For a fixed value of α the gas-to-H ratio increases with in-creasing initial mass of the galaxy. This is as a consequence ofthe larger amounts of gas mass remaining in the more massivegalaxies at the epochs of interest (see also Paper I). Conversely,for a fixed η g , H , α increases with increasing M ini . The maximumvalue of α is obtained for η g , H = 1, i.e., M G ≡ M H . We find thatat both epochs, the maximum value of α for the less massivegalaxies is lower than ∼ ⊙ (K km s − pc ) − . For a given M ini , α , and η g , H are lower at later epochs. For a lower L ′ CO(1 − , α shifts to higher values for a given η g , H .At an epoch of 30 Myr the values for α and η g , H are similarfor all IMFs and galaxies with M ini > × M ⊙ , while thedifference becomes larger with decreasing M ini . Feasible valuesof α and η g , H are possible for galaxies with M ini = 1 × M ⊙ and the higher value of L ′ CO(1 − . For top-heavy IMFs η g , H = 1 results in a maximum α of ∼ ⊙ (K km s − pc ) − ,while for α = 0.8 M ⊙ (K km s − pc ) − , the fraction of molecularhydrogen is about one third of the total gas mass. In the leastmassive galaxy ( M ini = 5 × M ⊙ ) and for a top-heavy IMF α ≈ ⊙ (K km s − pc ) − presupposes that all the gas in thissystem is in the form of molecular hydrogen. In more massivesystems with M ini = 1–3 × M ⊙ , a value of α ≈ ⊙ (Kkm s − pc ) − presumes that the molecular hydrogen constitutesonly a small fraction of about 1/10–1/20 of the total gas mass.At an epoch of 100 Myr a clear separation between theIMFs is noticeable. For a Salpeter IMF the galaxies underwent astronger gas exhaustion than for a top-heavy IMF, which is moresignificant for the less massive galaxies. As for the epoch at 30Myr the system with M ini = 1 × M ⊙ and top-heavy IMFis plausible , i.e., for α ∼ ⊙ (K km s − pc ) − the gas-to-H ratio η g , H = 2. For the galaxies with M ini = 3–5 × M ⊙ and top-heavy IMF we obtain α = 1.4–1.5 for a correspondinggas-to-H ratio η g , H = 5–10, resulting in a molecular mass of M H ∼ × M ⊙ . Alternatively, a higher value for α up to4.6 results in a lower η g , H = 2–4. It is noteworthy that for the as-sumed L ′ CO(1 − = 2.7 × K km s − pc , α = 4.6 M ⊙ (K km s − pc ) − implies M H = 1.2 × M ⊙ . The likelihood that such ahigh M H could have been built up within a short timescale of30–100 Myr however is unclear.
4. Discussion z & We ascertain plausible scenarios by comparing the model resultsdiscussed in Sect. 3 with the derived values from observationsfor specific quantities of individual QSOs listed in Table 2. Thecalculated values for diverse properties such as M d , M ∗ , M H ,metallicity, and SFR from the models discussed below, whichbest match the QSOs, are listed in Table 3. The correspondingmodel parameters, and all models which match the discussedproperties within the range defined by observations, are summa-rized in Table 4.We find that at an epoch of 30 Myr the models with an initialmass of the galaxy of M ini = 1 × M ⊙ , an initial SFR of ψ ini = 3 × M ⊙ yr − and either a Larson 2 IMF, a top-heavy ora mass-heavy IMF reproduce the observed quantities of someQSOs at z > × M ⊙ for dust destruction in the ISM with M cl = 100–0 M ⊙ . A stellar mass of M ∗ ∼ × M ⊙ is ob-tained. The metallicity in the system is ∼ ⊙ and a SFR of ∼ ⊙ yr − could be sustained. This model is also favoredgiven its values of α and η g , H . The higher H mass of M H = 3.7 × M ⊙ derived by Riechers et al. (2009) leads to η g , H < α ∼ ⊙ (K km s − pc ) − . However, such a galaxy with M ini = 1 × M ⊙ implies that the dynamical mass is largerthan the derived M dyn of ∼ × M ⊙ (for a i = 65 ◦ ) byWalter et al. (2004). While none of the models for M ini = 5 × M ⊙ , which was used by Dwek et al. (2007), can be applied,a lower inclination angle similar to what has been adopted forthe other QSOs might be considered.Another possible match with the properties of J1148+5251is achieved by the same set of values for M ini , ψ ini , SN efficiencyand IMF at an epoch of 100 Myr. The calculated stellar massis within the estimated range from observations and the dustmass is ∼ × M ⊙ , depending on M cl . However, theSFR dropped to ∼ ⊙ yr − , while the metallicity increasedto ∼ ⊙ . In view of the lower SFR reached by these modelsthan suggested by observations at epochs either 30 or 100 Myr,a higher initial SFR than the 3 × M ⊙ yr − might be con-ceivable. In Fig. 3 one notices that a longer evolution with thesame (or lower) initial SFR as used here does not lead to a betteragreement with observations, since this results in an even lowerSFR and higher metallicity.In view of this we find that this scenario at an epoch of 100Myr is more appropriate for the QSOs J1048+4637 (Fan et al.2003) at z = 6.23 and J2054-0005 (Jiang et al. 2008) at z = 6.06.For the latter QSO a fine tuning of the epoch to 70 Myr results ina better match. At this epoch we obtain a SFR of 1150 M ⊙ yr − and a metallicity of ∼ ⊙ . The amount of dust is M d ∼ × M ⊙ (for M cl = 100 M ⊙ ), while the stellar mass is M ∗ ∼ × M ⊙ . The lower derived L ′ CO(1 − leads to η g , H ∼ α = 0.8–1 M ⊙ (K km s − pc ) − is applied, while for η g , H ∼ α of ∼ Table 2.
Observed properties of quasars at z & Object z L ′ CO(1 − SFR M d M H M dyn sin i Ref.10 K km s − pc M ⊙ yr − M ⊙ M ⊙ M ⊙ J1148+5251 6.42 3.0 ± ± a ± ± ± ± ± ± References. (1) Fan et al. (2003); (2) Wang et al. (2010); (3) Michałowski et al. (2010); (4) Walter et al. (2004); (5) Jiang et al. (2008); (6)Fan et al. (2006)
Notes. ( a ) M H = 3.7 × M ⊙ deduced from [C I ] line detections by Riechers et al. (2009) Table 3.
Calculated properties from the best matching models of z & Object a SFR M d M ∗ Z α b η g , H b M H b M ⊙ yr − M ⊙ M ⊙ Z ⊙ M ⊙ J1148+5251(A) 1600 3.1–5.1 3.5 2 0.8–2.3 3.0–1.0 2.16–6.2J1148+5251(B) 1000 2.4–8.9 5.4 5 0.8–1.55 2.0–1.0 2.10–4.1J1048+4637(A) 1000 2.4–8.9 5.4 5 0.8–2.8 3.4–1.0 1.2–4.2J1048+4637(B) 610 3.5 2.8 3.4 0.8–4.5 5.8–1.0 1.2–6.7J2054-0005 1150 2.7 4.7 4.4 0.8–3.2 3.0–1.0 1.2–4.8J0840+5624(A) 1500 2.1 11.0 4 0.8–4.6 7.0–1.2 2.5–14.7J0840+5624(B) 1400 4.8 20.0 5 0.8–4.6 10–1.8 2.5–14.7
Notes. ( a ) All models are calculated for a top-heavy IMF. Capital letters in brackets (A,B) signify the different models (see corresponding modelsin Table 4) for the same object. ( b ) The ranges of η g , H and M H corresponds to the range of α , which is between the commonly used value of α =0.8 and the possible upper limit. model for a lower initial SFR of ψ ini = 10 M ⊙ yr − might be anoption. The SFR is ∼
610 M ⊙ yr − and the metallicity is ∼ ⊙ . While the stellar mass remains low, M ∗ ∼ × M ⊙ , adust mass of M d ∼ × M ⊙ is obtained for a ‘maximum’ SNefficiency and moderate dust destruction in the ISM. However,for α = 0.8–1 M ⊙ (K km s − pc ) − the gas-to-H ratio is ∼ M ini = 3–5 × M ⊙ , an initial SFR of ψ ini = 3 × M ⊙ yr − and IMFs biased towards higher stellar masses are applica-ble to some z ∼ M cl ≤
100 M ⊙ , although the dust masses reachedare at the lower limit.At an epoch of 170 Myr the system with M ini = 3 × M ⊙ is plausible for the QSO J0840+5624 (Fan et al. 2006) at z = 5.85, if an inclination angle higher than the assumed 40 ◦ isassumed. The SFR is ∼ ⊙ yr − and the metallicity is ∼ ⊙ . The stellar mass is around 1.1 × M ⊙ . The amount ofdust obtained with a ‘high’ SN efficiency is 2.1 × M ⊙ , whilewith the ‘maximum’ SN efficiency the dust mass exceeds a fewtimes 10 M ⊙ (as already at an epoch of 100 Myr). However,for a L ′ CO(1 − = 3.2 × K km s − pc as derived for thisQSO the gas-to-H ratio of η g , H ∼ α = 0.8–1 M ⊙ (Kkm s − pc ) − is higher than for the less massive galaxies. Incase of a lower η g , H of ∼ α ∼ ⊙ (K km s − pc ) − isrequired. The larger galaxy with M ini = 5 × M ⊙ , ψ ini = 3 × M ⊙ yr − and top heavy IMF can account for the observedquantities at an epoch of 400 Myr. The amount of dust reached with a ‘high’ SN efficiency is ∼ × M ⊙ and the SFR is ∼ ⊙ yr − . The metallicity and stellar mass are in agreement,but the fraction of M H is around 1/10 for α = 0.8 M ⊙ (K km s − pc ) − , while α ∼ ⊙ (K km s − pc ) − is needed for η g , H of ∼
2. A higher amount of M H as denoted by the higher value of α in these massive galaxies might be possible. For example, thepresence of large amounts of cold and low-excited molecular gashave been suggested by Papadopoulos et al. (2001) for the QSOAPM 08279+5255 at z = 3.91. Our calculations show that with increasing M ini (and fixed ψ ini ,IMF) the SN dust production efficiencies can either be loweredor the degree of dust destruction increased in order to reach therequired large dust masses. This is best demonstrated by modelsfor the most massive galaxies with M ini = 3–13 × M ⊙ inwhich a ‘high’ SN efficiency is sufficient in case of moderate tono dust destruction.However, the largest system with M ini = 1.3 × M ⊙ ex-ceeds the plausible dynamical masses derived from observationsof QSOs at z & (5) 6 by more than an order of magnitude.Moreover, our computed models show that at least one of theproperties of either SFR, Z or M ∗ are not in agreement with ob-servations at any epoch for any assumption of either the initialSFR or the IMF (see also Paper I). Additionally the values for η g , H remain very high even for α = 4.6 M ⊙ (K km s − pc ) − .We therefore conclude that such a massive system as advocatedby Valiante et al. (2009), cannot be applied to QSOs at z > (5)6. Although systems with M ini = 3–5 × M ⊙ are appropriatefor some QSOs at z <
6, such massive systems can only be ap-
Table 4.
Models a which match the observed range of properties of z ≥ . Epoch M ini ψ ini SN efficiency M cl IMF z & b M ⊙ M ⊙ yr − M ⊙
30 Myr 5 × × J1148+5251(A)3 high 0 Larson 270 Myr 1 × J2054-0005100 Myr 5 × × J1148+5251(B), J1048+4637(A)1 max 100 Larson 2
J1048+4637(B)3 × ×
170 Myr 3 × J0840+5624(A)400 Myr 5 × J0840+5624(B)
Notes. ( a ) All models which match the observed range of all properties of z ≥ ( b ) Capital letters in brackets signifythat different models (A,B) are applicable for the same object plied to QSOs > > M ini = 1 × M ⊙ , but neces-sitate a ‘maximum’ SN efficiency and/or a moderate amount ofdust destruction. The overall rapid evolution of dust and someproperties in these models indicates that such QSOs could pos-sibly be present at a higher redshift than z > z = 1.135 is the ULIRG SSTJ1604+4304, which shows properties similar to the consideredhigh- z QSOs. Kawara et al. (2010) reported a dust mass in thisULIRG of 1–2 × M ⊙ , a metallicity of around 2.5 Z ⊙ andestimated the age of the stellar population to be 40–200 Myr.The possibility of moderate dust destruction in the ISM wasalready discussed in Paper I. We found that the amount of dustfor most models better coincide with observations for M cl ≤
100 M ⊙ , which would be in agreement with the values of M cl of 50–70 M ⊙ derived for a multiphase ISM (e.g., McKee 1989;Dwek et al. 2007).The ‘maximum’ SN efficiency might be problematic. Thereis only little observational evidence that SN can be very efficient(e.g., Wilson & Batrla 2005; Douvion et al. 2001; Dunne et al.2009), and theoretical models predict significant dust destruc-tion in reverse shocks of SNe (e.g., Bianchi & Schneider 2007; Nozawa et al. 2007, 2010). On the other hand, these modelsalso show that the effectiveness of dust destruction dependson various properties such as the geometry of the shocks, thedensity of the ejecta and the ISM, the size and shape of thegrains, clumping in the SNe ejecta, and different SN types.In addition there is some observational evidence that Type IInSNe and sources such as luminous blue variables are possi-bly efficient dust producers (Fox et al. 2009; Smith et al. 2009;Gomez et al. 2010). While dust production and destruction inSNe is yet unresolved, a ‘maximum’ SN efficiency cannot beruled out (e.g., Gall et al. in prep). Alternatively, either dustformation in the outflowing winds of QSOs or grain growth inthe ISM might be an option (e.g., Elvis et al. 2002; Dwek et al.2007; Draine 2009; Michałowski et al. 2010; Pipino et al. 2011;Dwek & Cherchneff 2010) as supplementary or primary dustsources. However it remains to be investigated, if dust graingrowth can be as efficient as required under the prevailing con-ditions of high star formation activity and a short time span.Typical grain growth timescales in molecular clouds are of or-der 10 yr, but depending on the density and metallicity thesecan possibly be shorter (e.g., Hirashita 2000; Zhukovska et al.2008; Draine 2009). The fact that the starburst is assumed to oc-cur in an initially dust free galaxy implies that heavy elementsfirst need to be ejected into the ISM before grain growth can take place. In forthcoming work we will further develop the model toinvestigate the impact of different infall and outflow scenarioson the evolution of the amount of dust and various properties ofa galaxy. Acknowledgements.
We would like to thank Michal Michałowski, DarachWatson, Thomas Greve, and Sabine K¨onig for informative and helpful discus-sions. We also thank the anonymous referee for useful suggestions which helpedimprove the paper. The Dark Cosmology Centre is funded by the DNRF.
References