Free Access
Issue
A&A
Volume 528, April 2011
Article Number A14
Number of page(s) 9
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201015605
Published online 18 February 2011

© ESO, 2011

1. Introduction

Studying QSOs and their host galaxies at high redshift (z > 6) is important to gain deeper insight into the formation and evolution of galaxies, the origin of dust production, and the build up of stellar bulge masses in coevolution with supermassive black holes (SMBHs).

While the most distant known QSO, J114816.64+525150.3 (Fan et al. 2003, herafter J1148+5251), is at z = 6.4, several tens of QSOs have been discovered at z ~ 6 (e.g., Fan et al. 2004, 2006; Willott et al. 2007; Jiang et al. 2010). Most of the observed QSOs at this redshift, where the epoch of cosmic evolution is ~1 Gyr, exhibit extreme physical properties such as very high far-infrared (FIR) luminosities which imply large dust masses (e.g., Omont et al. 2001, 2003; Carilli et al. 2001; Bertoldi & Cox 2002), and SMBHs with masses >109 M (e.g., Barth et al. 2003; Willott et al. 2003; Vestergaard 2004).

Observations of QSOs have shown that dust emission at near-infrared (NIR) wavelengths arise from warm and hot dust (T ≲ 1000 K) assembled within a few parsec (e.g., Hines et al. 2006; Jiang et al. 2006). The NIR emission is believed to be powered by the active galactic nucleus and related to the QSO activity (e.g., Polletta et al. 2000). However, two QSOs at z ~ 6 without detectable emission from hot dust have been found (Jiang et al. 2006, 2010). It has been proposed that these QSOs are at a too early evolutionary stage to have built up significant amounts of hot dust. Alternative scenarios including for example the destruction of the hot dust or dust misalignments from the SMBH have also been discussed (Hao et al. 2010a,b; Guedes et al. 2010).

The FIR luminosity of LFIR ~ 1012−13 L is attributed to cold dust (T ~ 30–60 K) (e.g., Wang et al. 2008) which is probably distributed over kilo-parsec scales throughout the host galaxy (Leipski et al. 2010). The amount of cold dust inferred is about a few times 108 M (e.g., Bertoldi et al. 2003a; Robson et al. 2004; Beelen et al. 2006; Michałowski et al. 2010). The dominant source of the high FIR luminosity is believed to be dust heated 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 μm (Maiolino et al. 2005) within a central region with radius ~750 pc of the host galaxy of J1148+5251 also implies a high star formation rate surface density of 1000 M yr-1 kpc-2 (Walter et al. 2009). Wang et al. (2010) derived SFRs between 530–2300 M yr-1 from observations of a sample of QSOs at redshift z > 5. Observations of strong metal emission of high-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 the QSO hosts and solar or supersolar metallicity (e.g., Fan et al. 2003; Freudling et al. 2003; Juarez et al. 2009). Theoretical studies of the gas metallicity of QSO hosts also predict supersolar metallicities for z = 5–6 QSOs (e.g., Di Matteo et al. 2004).

The high inferred SFRs imply short timescales (≤108 yr) of the starburst (e.g. Bertoldi et al. 2003a; Walter et al. 2004; Dwek et al. 2007; Riechers et al. 2009), and consequently a young age of the QSOs. An early evolutionary stage of z > 4 QSOs has also been suggested from studies of extinction curves of broad absorption line QSOs (e.g., Gallerani et al. 2010) which turned out to be best fitted with extinction curves for SN-like dust (e.g., Maiolino et al. 2004, 2006; Gallerani et al. 2010). This suggests SNe as the preferential source of dust at early epochs (e.g., Dwek 1998; Morgan & Edmunds 2003; Hirashita et al. 2005; Dwek et al. 2007; Dwek & Cherchneff 2011), even though the dust productivity of SNe is poorly constrained (for a review see Gall et al. in prep). The dust in high-z QSOs could also be grown in the ISM (e.g., Draine 2009; Michałowski et al. 2010; Pipino et al. 2011). Finally, a dominant dust production by asymptotic giant branch stars has been claimed (Valiante et al. 2009).

Molecular gas masses of the order of ~1–2.5 × 1010 M have been inferred from detections of high excitation CO line emission in QSOs at z > 5 within a ~2.5 kpc radius region (e.g., Bertoldi et al. 2003b; Walter et al. 2003, 2004; Wang et al. 2010). The dynamical masses inferred from these CO observations are a few times ~1010−11 M which sets an upper limit on stellar bulge masses. These however are roughly two orders of magnitude lower than required from the present day black hole-bulge relation (e.g., Marconi & Hunt 2003). It therefore has been proposed that the formation of the SMBH occurs prior to the formation of the stellar bulge. QSOs will then have to accrete additional material to build up the required bulge mass (e.g., Walter et al. 2004; Riechers et al. 2009; Wang et al. 2010). For QSOs at z > 6 super-Eddington growth on timescales shorter than ~108 yr seem to be required to form a SMBH > 109 M (e.g., Kawakatu & Wada 2009). It has also been predicted that QSOs at z ~ 6 likely have formed in dark matter halos of 1012−13 M (e.g., Li et al. 2007; Kawakatu & Wada 2009).

In Gall et al. (2011, herafter Paper I we developed a chemical evolution model to elucidate the conditions required for generating large dust masses in high-z starburst galaxies. We showed that galaxies with masses of 1–5 ×  1011 M are suitable for enabling the production of large amounts of dust within ~400 Myr. In the present paper we apply this model to QSOs at z ≳ 6. We perform more detailed comparison between model results and values inferred from observations of z ≳ 6 QSOs to identify the most likely scenario. Furthermore, we consult additional parameters such as the H2 mass and the CO conversion factor for more refined evaluations. In particular, calculations with higher SFRs than in Paper I are considered. We aim to determine the earliest epochs at which the model results are in agreement with those from observations.

The structure of the paper is as follows: in Sect. 2 we briefly review the model developed in Paper I. A detailed analysis of the results is presented in Sect. 3 followed by a discussion in Sect. 4.

2. The model

The galactic chemical evolution model from Paper I is self-consistent, numerically solved and has been developed to ascertain the temporal progression of dust, gas, metals, and diverse physical properties of starburst galaxies. The incorporated stellar sources are AGB stars in the mass range 3–8 M and SNe. A differentiation between diverse SN subtypes has been implemented. Their roles as sources of dust production, dust destruction or suppliers of gas and heavy elements are taken into account. The lifetime dependent yield injection by the stellar sources, as well as dust destruction in the ISM due to SN shocks are also taken into account. Moreover, the formation of a SMBH is considered. Due to the very high SFRs of the starbursts, infall of neutral gas will only effect the system for comparable high infall rates. Thus, gas infall and outflows are neglected. Possible caveats of such an approach are discussed in Paper I. The model allows investigations of a broad range of physical properties of galaxies.

The prime parameters are summarized in the following.

  • Three different possible prescriptions for the stellar yields ofSNe are implemented, i.e., (i) stellar evolutionmodels by Eldridge et al. (2008)(referred to as “EIT08M”); (ii) rotating stellar models by Georgyet al. (2009); or (iii)nucleosynthesis models by either Woosley &Weaver (1995) or Nomotoet al. (2006). The stellar yields forAGB stars are taken from van den Hoek &Groenewegen (1997).

  • We differentiate between five different IMFs. These are a Salpeter (1955) IMF, a top-heavy, and a mass-heavy IMF, as well as IMFs (Larson 1998) with characteristic masses of either mch = 0.35 (Larson 1) or mch = 10 (Larson 2).

  • The SFR at a certain epoch is given by the Kennicutt law (Kennicutt 1998) as ψ(t) = ψini   (MISM(t)/Mini)k, where ψini is the initial SFR of the starburst, MISM(t) is the initial gas mass of the galaxy and k = 1.5.

  • The amount of dust produced by SNe and AGB stars is calculated using the dust formation efficiencies discussed in Paper I. For SNe three different dust production efficiency limits are determined, i.e. a “maximum” SN efficiency, a “high” SN efficiency, and a “low” SN efficiency. The “maximum” SN efficiency originates from theoretical SN dust formation models, and corresponds to dust masses of approximately 3–10 × 10-1 M. Similar dust masses have been observed in SN remnants such as Cas A (e.g., Dunne et al. 2009) or Kepler (e.g., Gomez et al. 2009). Dust destruction in reverse shock interaction of about 93% has been applied to the “maximum” SN efficiency, to obtain the “high” SN efficiency. The amount of dust for instance is ~2–6 × 10-2 M, which is also comparable to some observations of older SN remnants (Paper I, see references therein). The “low” SN efficiency is based on SN dust yields (on average about 3 × 10-3 M) inferred from observations of SN ejecta.

  • Dust destruction in the ISM is implemented in terms of the mass of ISM material, Mcl, swept up by a single SN shock and cleared of the containing dust.

For calculations in this paper most parameters have the same settings as defined in Paper I. We apply the models where the formation of a SMBH has been included. A constant growth rate has been estimated based on the final mass of the SMBH and the considered growth timescale. In this paper the SMBH growth is considered with a shorter growth timescale and calculations are performed with higher initial SFRs. For the SN yields we only consider the case of EIT08M. The parameters which differ from those used in Paper I are listed in Table 1.

Table 1

Model parameters.

thumbnail Fig. 1

Relation between dust mass and stellar mass at an epoch of 30 Myr, for various initial gas masses and IMFs. Calculations are performed for a “maximum” SN efficiency and dust destruction in the ISM with Mcl = 100   M (left panel) and Mcl = 0 (right panel). The colored symbols are obtained for different initial gas masses, Mini, SFRs, and IMFs. The size of the symbols is scaled by Mini. Calculations are made for Mini = 1.3 × 1012 M (largest symbol), Mini = 5 × 1011 M, Mini = 3 × 1011 M, Mini = 1 × 1011 M, and Mini = 5 × 1010 M (smallest symbol). The crosses correspond to calculations for a initial SFR ψini = 103 M yr-1, the filled circles to ψini = 3 × 103 M yr-1, and the stars to ψini = 104 M yr-1. 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 derived from 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 > 5 and accounts for uncertainties in the derived quantities. The horizontal dashed lines mark the lower and upper mass limit of the derived dust masses.

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3. Results

In this section we present the results of models calculated within short timescales after the starburst.

A short enrichment timescale of a few times 107 yr for an intense starburst with a SFR of ~3 × 103 M yr-1 has been proposed by e.g., Bertoldi et al. (2003a), Walter et al. (2004), Dwek et al. (2007), Riechers et al. (2009). Owing to this suggestion we are interested in whether the observed large dust masses in excess of 108 M can be reached within about 100 Myr. Consequently we performed calculations with an initial SFR for the starburst with ψini = 3 × 103 M yr-1 for galaxies with initial gas masses Mini = 5 × 1010 M, Mini = 1 × 1011 M, Mini = 3 × 1011 M, and Mini = 5 × 1011 M. For the most massive system with Mini = 1.3 × 1012 M an initial SFR ψini = 1 × 104 M yr-1 is adopted. We included the results for a lower initial SFR of 103 M yr-1 from models computed in Paper I for comparison.

In Paper I we analyzed the evolution of the amount of dust and various physical properties, and found that these are strongly dependent on the mass of the galaxy. Moreover, for a given initial SFR all quantities evolve faster in less massive galaxies. In this paper we perform detailed comparisons between calculated and observed values of the total dust mass, Md, the stellar mass, M, the SFR, ψ, and the metallicity, Z. We identified the shortest epoch, where some model results are in accordance with observations to be 30 Myr. Furthermore, we discuss quantities such as the CO conversion factor, the gas-to-H2 mass ratio, and the possible amount of molecular hydrogen.

3.1. Dust and stellar mass

In Fig. 1 we present the results for the mass of dust versus the stellar mass for galaxies with different initial gas masses and initial SFRs at an epoch of 30 Myr. The displayed models are computed for a “maximum” SN efficiency. Dust destruction in the ISM is considered for values of Mcl = 100   M (left panel) and Mcl = 0 (right panel).

The dark grey region represents the mass ranges of the stellar mass and dust mass derived from observations of QSOs at z > 6. The lower and upper limits of the stellar mass are estimated by subtracting the molecular gas masses, MH2 from the total dynamical masses, Mdyn. Values for Mdyn and MH2 are based on data from Wang et al. (2010, and references therein) for three QSOs at z > 6. For an estimation of Mdyn an inclination angle i = 65° of the gas disk is taken for QSO J1148+5251 (Walter et al. 2004), while i = 40° similar to Wang et al. (2010) is applied to the remaining 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 stellar masses and dust masses from observations of QSOs > 5 (Wang et al. 2010; Michałowski et al. 2010). The boundaries for the stellar masses are estimated similar to the QSOs at z > 6 (with i = 40° for deriving Mdyn). We set the lower dust limit to 108 M to account for the uncertainties of derived dust masses from observations.

thumbnail Fig. 2

Relation between dust mass and stellar mass at an epoch of 100 Myr for various initial gas masses and IMFs. Calculations are performed for a “maximum” SN efficiency (top row) and a “high” SN efficiency (bottom row). Dust destruction in the ISM is considered for a Mcl = 800 M (left column), Mcl = 100 M (middle column), and Mcl = 0 (right column). The colored symbols are obtained for different initial gas masses, Mini, SFRs, and IMFs. The size of the symbols is scaled by Mini. Calculations are made for Mini = 1.3 × 1012 M (largest symbol), Mini = 5 × 1011 M, Mini = 3 × 1011 M, Mini = 1 × 1011 M and Mini = 5 × 1010 M (smallest symbol). The crosses correspond to calculations for a initial SFR ψini = 103 M yr-1, the filled circles to ψini = 3 × 103 M yr-1, and the stars to ψini = 104 M yr-1. 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 derived from 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 > 5 and accounts for uncertainties in the derived quantities. The horizontal dashed lines mark the lower and upper mass limit of the derived dust masses.

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Despite the short time span of 30 Myr, it is evident that most models are within the plausible mass ranges illustrated by the light and dark grey regions. This signifies a rapid build-up of a large amount of dust, provided SNe produced dust with a “maximum” SN efficiency. For galaxies with Mini = 1–5 × 1011 M all models with an initial SFR of 3 × 103 M yr-1 are in agreement with the observed values for the stellar masses for QSOs at z > 6. The requirements for Md are best accomplished with either a top-heavy, mass-heavy or Larson 1 IMF for both values of Mcl. In a galaxy with Mini = 1 × 1011 M the amount of dust reached with a Larson 2 IMF and Mcl = 100   M also matches with the dark grey region. Models for either a “high” or “low” SN efficiency did not reach 108 M of dust. Only in the most massive galaxy (Mini = 1.3 × 1012 M) and for top-heavy IMFs with a ‘high’ SN efficiency an amount of dust >108 M is obtained.

In Fig. 2 we illustrate the results for dust and stellar masses at an epoch of 100 Myr. We present models for a “maximum” SN efficiency (top row) and a “high” SN efficiency (bottom row), while dust destruction in the ISM is considered for a Mcl = 800 M (left column), Mcl = 100 M (middle column), and Mcl = 0 (right column). We carried out calculations for a “low” SN efficiency, but the obtained dust masses of these models remained below 108 M.

At these early epochs the stellar mass, M, is higher for models with an initially larger SFR (at fixed IMF and Mini). The stellar mass is also larger for IMFs biased towards low mass stars (at fixed Mini and ψini). It is interesting to note that in the less massive galaxies (0.5–1 × 1011 M) dust masses obtained for the higher initial SFR (ψini = 3 × 103 M yr-1) are lower than dust masses obtained for the lower SFR (ψini = 103 M yr-1). Moreover, in these galaxies the amount of dust reached at an epoch of 30 Myr (see Fig. 1) and for Mcl = 100–800 M is also higher than that seen at the epoch of 100 Myr for same Mcl.

We find that the stellar masses for models with an initial SFR ψini = 1–3 × 103 M yr-1 are within the observed region for z > 5 QSOs. For some models with ψini = 3 × 103 M yr-1, stellar masses are within the mass range for z > 6 QSOs. This in particular applies to systems with either Mini = 0.5–1 × 1011 M (all IMFs) or Mini = 3–5 × 1011 M with top heavy IMFs. Stellar masses within the dark grey area are also found with ψini = 103 M yr-1 for galaxies with either Mini = 3–13 × 1011 M and top heavy IMFs or for the less massive galaxies in combination with IMFs favoring low mass stars.

In the case of Mcl = 800 M and for a “maximum” SN efficiency most models with Mini = 3–13 × 1011 M and ψini = 103 M yr-1 fit within the dark grey region. However for the higher initial SFR Md is within or close to this zone only for galaxies with Mini = 3–5 × 1011 M and top-heavy IMFs. For Mcl = 100 M and a “maximum” SN efficiency the dust mass obtained in a galaxy with Mini = 1 ×  1011 M, ψini = 3 × 103 M yr-1 and for top-heavy IMFs is in agreement with observations, while the dust masses in the more massive galaxies for some IMFs and SFRs are higher than required. In the case of no dust destruction the dust masses reached for some IMFs and SFRs are able to match within the dark grey area also in the least massive galaxy.

We find that in case of a “high” SN efficiency and for ψini = 3 × 103 M yr-1 in galaxies with initial masses 3–5 × 1011 M and top-heavy IMFs high dust masses are possible, even if dust destruction is included (i.e., Mcl = 0–100 M).

3.2. Metallicity and SFR

thumbnail Fig. 3

Relation between metallicity and SFR at epochs of 30 Myr (left panel) and 100 Myr (right panel). The colored symbols are obtained for different initial gas masses, Mini, SFRs, and IMFs. The size of the symbols is scaled by Mini. Calculations are made for Mini = 1.3 × 1012 M (largest symbol), Mini = 5 × 1011 M, Mini = 3 × 1011 M, Mini = 1 × 1011 M, and Mini = 5 × 1010 M (smallest symbol). The crosses correspond to calculations for a initial SFR ψini = 103 M yr-1, the filled circles to ψini = 3 × 103 M yr-1 and the stars to ψini = 104 M yr-1. 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 shaded region indicates the range of the metallicity and SFR based on observations of QSOs at z > 6. The vertical dashed lines represent the lower and upper limits of the observationally derived SFRs. The light grey shaded area accounts for the uncertainty of the upper limit of the metallicity. The horizontal dashed lines mark the lower and possibly upper limit of the metallicity.

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We next present the obtained metallicities and SFRs at the time of observation for the models discussed above.

Figure 3 depicts the metallicity versus SFR at epochs of 30 Myr (left panel) and 100 Myr (right panel). With respect to observations of QSOs > (5) 6 we marked the range of derived values as a dark grey shaded zone. The lower and upper limits of the SFR are based on observations by Bertoldi et al. (2003a) and Wang et al. (2010). We set the lower limit for the metallicity at the solar value and the upper limit at 5 Z. This is based on the inferred solar or supersolar metallicities in 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 limit and therefore the zone above 5 Z is marked as light grey shaded region to account for the uncertainty.

We find that at an epoch of 30 Myr high metallicities in the less massive galaxies are already reached. The best result is attained by a system with Mini = 1 × 1011 M, ψini = 3 × 103 M yr-1, and IMFs biased towards higher masses. For a galaxy with Mini = 5 × 1010 M all models with either the same ψini or with the lower initial SFR, and top-heavy IMFs are within the dark grey shaded region as well.

At an epoch of 100 Myr the metallicity has increased in all models, while the SFR in the less massive galaxies has significantly decreased. The models for Mini = 3–5 × 1011 M, ψini = 3 × 103 M yr-1, and top heavy IMFs constitute the best results. In galaxies with Mini = 3 × 1011 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. The metallicities in the low mass galaxies which give the best agreement at 30 Myr are now shifted above the upper limit, while the SFRs remain in the observed range. The models for a galaxy with Mini = 1 × 1011 M, a lower initial SFR of 103 M yr-1, and top-heavy IMFs at this epoch (100 Myr) reach sufficiently high metallicities, while high enough SFRs are sustained.

3.3. CO conversion factor and gas-to-H2 mass ratio

To evaluate the calculated models, we additionally consider the relation between the gas-to-H2 mass ratio and the CO conversion factor 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 × 1010 M of molecular hydrogen (e.g., Bertoldi et al. 2003b; Walter et al. 2003, 2004; Riechers et al. 2009; Wang et al. 2010). This molecular gas mass is derived from the relation , where α is the conversion factor between the low excitation CO J = 1–0 line luminosity and MH2. For spiral galaxies α is typically ~4.6 M (K km s-1 pc2)-1 (e.g., Solomon & Barrett 1991), while for the centre of nearby ultra luminous starburst galaxies a conversion factor of α = 0.8–1   M (K km s-1 pc2)-1 is appropriate (e.g., Downes & Solomon 1998). The latter value of α is usually used for e.g., high-z QSOs (e.g., Bertoldi et al. 2003b; Walter et al. 2003; Wang et al. 2010), Ultra Luminous Infrared Galaxies (ULIRGs) (Yan et al. 2010) or for high-z sub-mm galaxies (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) gas mass MG which remains in the galaxies at a given epoch. The molecular gas mass, MH2, constitutes a certain fraction of the total gas mass, MG. Hence we introduce the gas-to-H2 mass ratio as ηg,H2 = MG/MH2. The CO conversion factor can thereby be expressed as a function of ηg,H2 as (1)where ηg,H2 ≥ 1 is kept as a free parameter. In ULIRGs and SMGs a major fraction of the gas is believed to exist in form of molecular hydrogen (e.g., Sanders & Mirabel 1996). For example a value for ηg,H2 of ~1 has been found for the z = 3 radio galaxy B3 J2330+3927 (De Breuck et al. 2003). This might also be the case for QSOs and suggests a gas-to-H2 ratio between 1 and 2.

thumbnail Fig. 4

CO conversion factor versus gas-to-H2 ratio at epochs 30 Myr (top panel) and 100 Myr (bottom panel). The solid lines correspond to calculations of α as a function of the gas-to-H2 ratio ηg,H2 for a CO line luminosity of  K km s-1 pc2. Calculations are performed for different IMFs and galaxies for a range of different initial gas masses Mini. The thickness of the lines is scaled by Mini as indicated in the upper panel. The black and cyan colors denote the Salpeter and top-heavy IMF, respectively. The arrow indicates the shift of α for calculations with the lower  K km s-1 pc2, and Δα is the difference of α between the higher and lower . Calculations are shown for models with ψini = 3 × 103 M yr-1, except for the model for the most massive galaxy for which ψini = 104 M yr-1. The grey shaded region signifies the possible range of α and ηg,H2. The horizontal black dashed lines mark the values of α = 0.8, 1 and 4.6 M (K km s-1 pc2)-1.

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In Fig. 4 we show the results for α as a function of ηg,H2 with ψini = 3 × 103 M yr-1 for models with Mini ≤ 5 × 1011 M and with ψini = 104 M yr-1 for the most massive galaxy. Calculations are performed for two different epochs; 30 Myr (top panel) and 100 Myr (bottom panel). The IMFs involved are the top-heavy IMF and the Salpeter IMF. We adopt a CO line luminosity  K km s-1 pc2 which is based on 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 (i.e.,  K km s-1 pc2) is indicated by the arrow in Fig. 4. The grey shaded area signifies a possible range for α and ηg,H2 as discussed above.

For a fixed value of α the gas-to-H2 ratio increases with increasing initial mass of the galaxy. This is as a consequence of the larger amounts of gas mass remaining in the more massive galaxies at the epochs of interest (see also Paper I). Conversely, for a fixed ηg,H2, α increases with increasing Mini. The maximum value of α is obtained for ηg,H2 = 1, i.e., MG ≡ MH2. We find that at both epochs, the maximum value of α for the less massive galaxies is lower than ~4.6 M (K km s-1 pc2)-1. For a given Mini, α, and ηg,H2 are lower at later epochs. For a lower , α shifts to higher values for a given ηg,H2.

At an epoch of 30 Myr the values for α and ηg,H2 are similar for all IMFs and galaxies with Mini > 1 × 1011   M, while the difference becomes larger with decreasing Mini. Feasible values of α and ηg,H2 are possible for galaxies with Mini = 1 × 1011 M and the higher value of . For top-heavy IMFs ηg,H2 = 1 results in a maximum α of ~2.3 M (K km s-1 pc2)-1, while for α = 0.8   M (K km s-1 pc2)-1, the fraction of molecular hydrogen is about one third of the total gas mass. In the least massive galaxy (Mini = 5 × 1010 M) and for a top-heavy IMF α  ≈ 0.8 M (K km s-1 pc2)-1 presupposes that all the gas in this system is in the form of molecular hydrogen. In more massive systems with Mini = 1–3 × 1011 M, a value of α ≈ 0.8–1 M (K km s-1 pc2)-1 presumes that the molecular hydrogen constitutes only a small fraction of about 1/10–1/20 of the total gas mass.

At an epoch of 100 Myr a clear separation between the IMFs is noticeable. For a Salpeter IMF the galaxies underwent a stronger gas exhaustion than for a top-heavy IMF, which is more significant for the less massive galaxies. As for the epoch at 30 Myr the system with Mini = 1 × 1011 M and top-heavy IMF is plausible, i.e., for α ~ 0.8   M (K km s-1 pc2)-1 the gas-to-H2 ratio ηg,H2 = 2. For the galaxies with Mini = 3–5 ×  1011 M and top-heavy IMF we obtain α = 1.4–1.5 for a corresponding gas-to-H2 ratio ηg,H2 = 5–10, resulting in a molecular mass of MH2 ~ 3.7 × 1010 M. Alternatively, a higher value for α up to 4.6 results in a lower ηg,H2 = 2–4. It is noteworthy that for the assumed  K km s-1 pc2, α = 4.6   M (K km s-1 pc2)-1 implies MH2 = 1.2  ×  1011 M. The likelihood that such a high MH2 could have been built up within a short timescale of 30–100 Myr however is unclear.

4. Discussion

Table 2

Observed properties of quasars at z ≳ 6.0.

Table 3

Calculated properties from the best matching models of z ≳ 6 QSOs from our sample.

4.1. Individual QSOs at z  ≳  6

We ascertain plausible scenarios by comparing the model results discussed in Sect. 3 with the derived values from observations for specific quantities of individual QSOs listed in Table 2. The calculated values for diverse properties such as Md, M, MH2, metallicity, and SFR from the models discussed below, which best match the QSOs, are listed in Table 3. The corresponding model parameters, and all models which match the discussed properties within the range defined by observations, are summarized in Table 4.

We find that at an epoch of 30 Myr the models with an initial mass of the galaxy of Mini = 1 × 1011 M, an initial SFR of ψini = 3 × 103 M yr-1 and either a Larson 2 IMF, a top-heavy or a mass-heavy IMF reproduce the observed quantities of some QSOs at z > 6 in the case of a “maximum” SN efficiency.

In particular, the model with a top-heavy IMF is best applicable to the QSO J1148+5251. The amount of dust reached is between 3.1–5.1 × 108 M for dust destruction in the ISM with Mcl = 100–0 M. A stellar mass of M ~ 3.5 × 1010 M is obtained. The metallicity in the system is ~2 Z and a SFR of ~1600 M yr-1 could be sustained. This model is also favored given its values of α and ηg,H2. The higher H2 mass of MH2 = 3.7 × 1010 M derived by Riechers et al. (2009) leads to ηg,H2 < 2 and α ~ 1.4 M (K km s-1 pc2)-1. However, such a galaxy with Mini = 1 × 1011 M implies that the dynamical mass is larger than the derived Mdyn of ~5.5 × 1010 M (for a i = 65°) by Walter et al. (2004). While none of the models for Mini = 5 × 1010 M, which was used by Dwek et al. (2007), can be applied, a lower inclination angle similar to what has been adopted for the other QSOs might be considered.

Another possible match with the properties of J1148+5251 is achieved by the same set of values for Mini, ψini, SN efficiency and IMF at an epoch of 100 Myr. The calculated stellar mass is within the estimated range from observations and the dust mass is ~2.4–8.9 × 108 M, depending on Mcl. However, the SFR dropped to ~1000 M yr-1, while the metallicity increased to ~5 Z. In view of the lower SFR reached by these models than suggested by observations at epochs either 30 or 100 Myr, a higher initial SFR than the 3 × 103 M yr-1 might be conceivable. In Fig. 3 one notices that a longer evolution with the same (or lower) initial SFR as used here does not lead to a better agreement with observations, since this results in an even lower SFR and higher metallicity.

In view of this we find that this scenario at an epoch of 100 Myr 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 in a better match. At this epoch we obtain a SFR of 1150 M yr-1 and a metallicity of ~4.4 Z. The amount of dust is Md ~ 2.7 × 108 M (for Mcl = 100 M), while the stellar mass is M ~ 4.7  ×  1010 M. The lower derived leads to ηg,H2 ~ 3–4 in case α = 0.8–1 M (K km s-1 pc2)-1 is applied, while for ηg,H2 ~ 2 a value for α of ~1.6 would be required. For J1048+4637 the model for a lower initial SFR of ψini = 103 M yr-1 might be an option. The SFR is ~610 M yr-1 and the metallicity is ~3.4 Z. While the stellar mass remains low, M ~ 2.8  ×  1010 M, a dust mass of Md ~ 3.5  ×  108 M is obtained for a “maximum” SN efficiency and moderate dust destruction in the ISM. However, for α = 0.8–1 M (K km s-1 pc2)-1 the gas-to-H2 ratio is ~5–6, since for the lower initial SFR the system at this epoch is less exhausted.

At either the same or a later epoch the more massive galaxies with Mini = 3−5 × 1011   M, an initial SFR of ψini = 3 × 103   M yr-1 and IMFs biased towards higher stellar masses are applicable to some z ~ 6 QSOs. The stellar mass, metallicity, and SFR of these systems are in agreement with observations, with either top-heavy IMFs or a mass-heavy IMF leading to the best results. The amount of dust can be produced by SNe with a “high” SN efficiency and Mcl ≤ 100 M, although the dust masses reached are at the lower limit.

At an epoch of 170 Myr the system with Mini = 3 × 1011 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° is assumed. The SFR is ~1500 M yr-1 and the metallicity is ~4 Z. The stellar mass is around 1.1 × 1011 M. The amount of dust obtained with a “high” SN efficiency is 2.1 × 108 M, while with the “maximum” SN efficiency the dust mass exceeds a few times 109 M (as already at an epoch of 100 Myr). However, for a  K km s-1 pc2 as derived for this QSO the gas-to-H2 ratio of ηg,H2 ~ 5–7 for α = 0.8–1 M (K km s-1 pc2)-1 is higher than for the less massive galaxies. In case of a lower ηg,H2 of ~2, α  ~ 2.7 M (K km s-1 pc2)-1 is required. The larger galaxy with Mini = 5  ×  1011 M, ψini = 3 × 103 M yr-1 and top heavy IMF can account for the observed quantities at an epoch of 400 Myr. The amount of dust reached with a “high” SN efficiency is ~4.8 × 108 M and the SFR is ~1400 M yr-1. The metallicity and stellar mass are in agreement, but the fraction of MH2 is around 1/10 for α = 0.8   M (K km s-1 pc2)-1, while α ~ 4 M (K km s-1 pc2)-1 is needed for ηg,H2 of ~2. A higher amount of MH2 as denoted by the higher value of α in these massive galaxies might be possible. For example, the presence of large amounts of cold and low-excited molecular gas have been suggested by Papadopoulos et al. (2001) for the QSO APM 08279+5255 at z = 3.91.

Table 4

Modelsa which match the observed range of properties of z ≥ 5 QSOs.

4.2. SN efficiency and mass of the galaxy

Our calculations show that with increasing Mini (and fixed ψini, IMF) the SN dust production efficiencies can either be lowered or the degree of dust destruction increased in order to reach the required large dust masses. This is best demonstrated by models for the most massive galaxies with Mini = 3–13 × 1011 M in which a “high” SN efficiency is sufficient in case of moderate to no dust destruction.

However, the largest system with Mini = 1.3 × 1012 M exceeds the plausible dynamical masses derived from observations of QSOs at z ≳ (5) 6 by more than an order of magnitude. Moreover, our computed models show that at least one of the properties of either SFR, Z or M are not in agreement with observations at any epoch for any assumption of either the initial SFR or the IMF (see also Paper I). Additionally the values for ηg,H2 remain very high even for α = 4.6   M (K km s-1 pc2)-1. We therefore conclude that such a massive system as advocated by Valiante et al. (2009), cannot be applied to QSOs at z > (5) 6. Although systems with Mini = 3–5 × 1011 M are appropriate for some QSOs at z < 6, such massive systems can only be applied to QSOs > 6 when the inclination angle is lower than the assumed average angle.

The models which best reproduce the observed properties of QSOs > 6 are for a galaxy with Mini = 1 × 1011 M, but necessitate a “maximum” SN efficiency and/or a moderate amount of dust destruction. The overall rapid evolution of dust and some properties in these models indicates that such QSOs could possibly be present at a higher redshift than z > 6.4. An interesting example at a lower redshift of z = 1.135 is the ULIRG SST J1604+4304, which shows properties similar to the considered high-z QSOs. Kawara et al. (2010) reported a dust mass in this ULIRG of 1–2 × 108 M, a metallicity of around 2.5 Z and estimated the age of the stellar population to be 40–200 Myr.

The possibility of moderate dust destruction in the ISM was already discussed in Paper I. We found that the amount of dust for most models better coincide with observations for Mcl ≤ 100   M, which would be in agreement with the values of Mcl of 50–70 M derived for a multiphase ISM (e.g., McKee 1989; Dwek et al. 2007).

The “maximum” SN efficiency might be problematic. There is only little observational evidence that SNe can be very efficient (e.g., Wilson & Batrla 2005; Douvion et al. 2001; Dunne et al. 2009), and theoretical models predict significant dust destruction in reverse shocks of SNe (e.g., Bianchi & Schneider 2007; Nozawa et al. 2007, 2010). On the other hand, these models also show that the effectiveness of dust destruction depends on various properties such as the geometry of the shocks, the density of the ejecta and the ISM, the size and shape of the grains, clumping in the SNe ejecta, and different SN types. In addition there is some observational evidence that type IIn SNe and sources such as luminous blue variables are possibly efficient dust producers (Fox et al. 2009; Smith et al. 2009; Gomez et al. 2010). While dust production and destruction in SNe is yet unresolved, a “maximum” SN efficiency cannot be ruled out (e.g., Gall et al. in prep). Alternatively, either dust formation in the outflowing winds of QSOs or grain growth in the 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 2011) as supplementary or primary dust sources. However it remains to be investigated, if dust grain growth can be as efficient as required under the prevailing conditions of high star formation activity and a short time span. Typical grain growth timescales in molecular clouds are of order 107 yr, but depending on the density and metallicity these can possibly be shorter (e.g., Hirashita 2000; Zhukovska et al. 2008; Draine 2009). The fact that the starburst is assumed to occur in an initially dust free galaxy implies that heavy elements first need to be ejected into the ISM before grain growth can take place. In forthcoming work we will further develop the model to investigate the impact of different infall and outflow scenarios on the evolution of the amount of dust and various properties of a galaxy.

Acknowledgments

We would like to thank Michal Michałowski, Darach Watson, Thomas Greve, and Sabine König for informative and helpful discussions. We also thank the anonymous referee for useful suggestions which helped improve the paper. The Dark Cosmology Centre is funded by the DNRF.

References

All Tables

Table 1

Model parameters.

Table 2

Observed properties of quasars at z ≳ 6.0.

Table 3

Calculated properties from the best matching models of z ≳ 6 QSOs from our sample.

Table 4

Modelsa which match the observed range of properties of z ≥ 5 QSOs.

All Figures

thumbnail Fig. 1

Relation between dust mass and stellar mass at an epoch of 30 Myr, for various initial gas masses and IMFs. Calculations are performed for a “maximum” SN efficiency and dust destruction in the ISM with Mcl = 100   M (left panel) and Mcl = 0 (right panel). The colored symbols are obtained for different initial gas masses, Mini, SFRs, and IMFs. The size of the symbols is scaled by Mini. Calculations are made for Mini = 1.3 × 1012 M (largest symbol), Mini = 5 × 1011 M, Mini = 3 × 1011 M, Mini = 1 × 1011 M, and Mini = 5 × 1010 M (smallest symbol). The crosses correspond to calculations for a initial SFR ψini = 103 M yr-1, the filled circles to ψini = 3 × 103 M yr-1, and the stars to ψini = 104 M yr-1. 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 derived from 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 > 5 and accounts for uncertainties in the derived quantities. The horizontal dashed lines mark the lower and upper mass limit of the derived dust masses.

Open with DEXTER
In the text
thumbnail Fig. 2

Relation between dust mass and stellar mass at an epoch of 100 Myr for various initial gas masses and IMFs. Calculations are performed for a “maximum” SN efficiency (top row) and a “high” SN efficiency (bottom row). Dust destruction in the ISM is considered for a Mcl = 800 M (left column), Mcl = 100 M (middle column), and Mcl = 0 (right column). The colored symbols are obtained for different initial gas masses, Mini, SFRs, and IMFs. The size of the symbols is scaled by Mini. Calculations are made for Mini = 1.3 × 1012 M (largest symbol), Mini = 5 × 1011 M, Mini = 3 × 1011 M, Mini = 1 × 1011 M and Mini = 5 × 1010 M (smallest symbol). The crosses correspond to calculations for a initial SFR ψini = 103 M yr-1, the filled circles to ψini = 3 × 103 M yr-1, and the stars to ψini = 104 M yr-1. 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 derived from 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 > 5 and accounts for uncertainties in the derived quantities. The horizontal dashed lines mark the lower and upper mass limit of the derived dust masses.

Open with DEXTER
In the text
thumbnail Fig. 3

Relation between metallicity and SFR at epochs of 30 Myr (left panel) and 100 Myr (right panel). The colored symbols are obtained for different initial gas masses, Mini, SFRs, and IMFs. The size of the symbols is scaled by Mini. Calculations are made for Mini = 1.3 × 1012 M (largest symbol), Mini = 5 × 1011 M, Mini = 3 × 1011 M, Mini = 1 × 1011 M, and Mini = 5 × 1010 M (smallest symbol). The crosses correspond to calculations for a initial SFR ψini = 103 M yr-1, the filled circles to ψini = 3 × 103 M yr-1 and the stars to ψini = 104 M yr-1. 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 shaded region indicates the range of the metallicity and SFR based on observations of QSOs at z > 6. The vertical dashed lines represent the lower and upper limits of the observationally derived SFRs. The light grey shaded area accounts for the uncertainty of the upper limit of the metallicity. The horizontal dashed lines mark the lower and possibly upper limit of the metallicity.

Open with DEXTER
In the text
thumbnail Fig. 4

CO conversion factor versus gas-to-H2 ratio at epochs 30 Myr (top panel) and 100 Myr (bottom panel). The solid lines correspond to calculations of α as a function of the gas-to-H2 ratio ηg,H2 for a CO line luminosity of  K km s-1 pc2. Calculations are performed for different IMFs and galaxies for a range of different initial gas masses Mini. The thickness of the lines is scaled by Mini as indicated in the upper panel. The black and cyan colors denote the Salpeter and top-heavy IMF, respectively. The arrow indicates the shift of α for calculations with the lower  K km s-1 pc2, and Δα is the difference of α between the higher and lower . Calculations are shown for models with ψini = 3 × 103 M yr-1, except for the model for the most massive galaxy for which ψini = 104 M yr-1. The grey shaded region signifies the possible range of α and ηg,H2. The horizontal black dashed lines mark the values of α = 0.8, 1 and 4.6 M (K km s-1 pc2)-1.

Open with DEXTER
In the text

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