GOODS-HERSCHEL: GAS-TO-DUST MASS RATIOS AND CO-TO-H₂ CONVERSION FACTORS IN NORMAL AND STARBURSTING GALAXIES AT HIGH-z

The determination of the conversion factor from CO luminosities to the molecular gas mass (M_gas) of a galaxy (α_CO¹¹ = M_gas/L'_CO) remains an open issue as there is evidence that it varies considerably as a function of metallicity and intensity of the radiation field. Downes & Solomon (1998) showed that α_CO is a factor of ∼6 smaller for local ultra-luminous infrared galaxies (ULIRGs; L_IR > 10¹² L_☉) than for local spiral galaxies. A similar picture seems to emerge at high redshift, with a fraction of submillimeter galaxies (SMGs) playing the role of local starbursts, having lower α_CO values and exhibiting enhanced star formation efficiencies (defined as L_IR/M_gas), when compared to normal¹² star-forming galaxies selected by their rest-frame UV or optical light (Tacconi et al. 2008; Daddi et al. 2010a, 2010b; Genzel et al. 2010; Narayanan et al. 2011). Daddi et al. (2010a, 2010b) used a kinematic analysis of star-forming disk galaxies at z ≈ 1.5 to argue that they have CO conversion factors α_CO = 3.6 ± 0.8, similar to that in the Milky Way. Instead, Tacconi et al. (2008) and Carilli et al. (2010) placed an upper limit of ∼0.8 on the α_CO value of high-z SMGs. Together with a variety of other evidence, these results support the existence of two distinct star formation regimes: a long-lasting mode for normal-disk galaxies and a more rapid mode for local starbursts and SMGs (Daddi et al. 2008, 2010a; Genzel et al. 2010). Nevertheless, excitation biases introduced by the use of different molecular lines, along with substantial uncertainties on the α_CO values, raise potential concerns about the role of SMGs in this picture (e.g., Ivison et al. 2011).

Several studies in the local universe have tried to tackle this question by measuring the total dust mass of a galaxy (M_dust) and assuming that it is proportional to M_gas (e.g., Leroy et al. 2011). However, determining M_dust is a complex task. In order to break degeneracies inherent in current models, a proper characterization of the peak of the spectral energy distribution (SED) of the source as well as of the Rayleigh–Jeans emission tail is required. With the wide wavelength coverage (70–500 μm) of the Herschel Space Observatory (Pilbratt et al. 2010), we can now directly observe the peak of the IR emission of high-z galaxies. Together with ground-based millimeter (mm) observations that probe the Rayleigh–Jeans emission, this allows us to properly quantify M_dust, and explore possible differences between the shape of the SEDs, the M_gas/M_d ratios, and the α_CO values of normal and starburst galaxies at high redshift.

As a test case, we combine Herschel PACS and SPIRE data, from the GOODS-Herschel program with (sub)mm observations for two of the best-studied high-z galaxies in the Great Observatories Origins Deep Survey North field (GOODS-N), the SMG GN20 at z = 4.05, and the normal star-forming galaxy, BzK-21000, at z = 1.521. The uniqueness of these sources relies on the detailed sampling of their Rayleigh–Jeans emission via ground-based mm interferometry (1.1–6.6 mm). Our aim is to derive M_gas/M_d ratio estimates, investigate the slope of their SED in the Rayleigh–Jeans tail, and put constraints on the α_CO values. Throughout this Letter we assume Ω_m = 0.3, H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.7, and Chabrier initial mass function.

We use deep 100 and 160 μm PACS and 250, 350, and 500 μm SPIRE observations of GOODS-N from the GOODS-H program. Details about the observations are given in Elbaz et al. (2011). Herschel fluxes are derived from point-spread function (PSF) fitting using galfit (Peng et al. 2002). A very extensive set of priors is used for 100, 160 and 250 μm, including all galaxies detected in the ultra-deep Spitzer Multiband Imaging Photometer (MIPS) 24 μm imaging, which effectively allow us to obtain robust flux estimates for relatively isolated sources, even beyond formal confusion limits at 250 μm. For 350 and 500 μm, this approach does not allow accurate measurements due to the increasingly large PSFs. Hence, we use a reduced set of priors based on Very Large Array (VLA) radio detections, resulting in flux uncertainties consistent with the confusion noise at these wavelengths. We note that in GN20, the radio priors also include the nearby GN20.2 objects (both"a" and "b" components; Daddi et al. 2009). A detailed description of the flux measurements and Monte Carlo (MC) derivations of the uncertainties will be presented elsewhere (E. Daddi et al. 2011, in preparation).

Originally detected at 850 μm by Pope et al. (2006), GN20 is one of the best-studied SMGs to date, the most luminous and also one of the most distant (z = 4.055; Daddi et al. 2009) in the GOODS-N field. It is detected in all Herschel bands apart from 100 μm. Carilli et al. (2010) reported the detection of the CO[1−0] and CO[2−1] lines with the VLA, and CO[6−5] and CO[5 −4] lines with the Plateau de Bure Interferometer (PdBI) and the Combined Array for Research in Millimeter Astronomy (CARMA), respectively. The source is detected in the Aztec 1.1 mm map and continuum emission is also measured at 2.2, 3.3, and 6.6 mm (Carilli et al. 2011) and at 1.4 GHz with the VLA (Morrison et al. 2010). GN20 is identified in all Infrared Array Camera (IRAC) bands and at 24 μm while it appears as a B-band dropout in the Advanced Camera for Surveys-Hubble Space Telescope image. The stellar mass of the source is 2.3 × 10¹¹ M_☉ (Daddi et al. 2009). A compilation of the photometric data is given in Table 1.

BzK-21000 is a near-IR-selected star-forming galaxy, with a spectroscopic redshift, z = 1.521 (Daddi et al. 2008, 2010a). The source has secure detections in both PACS and in the first two SPIRE bands, while at 500 μm it is only marginally detected. In addition to IRAC and MIPS 24 μm data, the source is seen in the 16 μm InfraRed Spectrograph peak-up image (Teplitz et al. 2011). With follow-up VLA and PdBI observations, Dannerbauer et al. (2009), Aravena et al. (2010), and Daddi et al. (2008) have reported the detection of CO[3−2], CO[1−0], and CO[2−1] emission lines, respectively. Continuum detections and upper limits are also obtained at 1.1, 2.2, and 3.3 mm (Daddi et al. 2010a; Dannerbauer et al. 2009). The stellar mass is 7.8 × 10¹⁰ M_☉ (Daddi et al. 2010a). The UV rest-frame morphology of this galaxy, the double-peaked CO profile, the large spatial extent of the CO reservoir, and the low gas excitation all provide strong evidence that this galaxy is a large, clumpy, rotating disk (Daddi et al. 2010a).

We employ two methods to derive the dust mass of the galaxies: the physically motivated dust models of Draine & Li (2007, hereafter DL07), and a more simplistic, but widely used, modified blackbody model (MBB).

The DL07 models describe the interstellar dust as a mixture of carbonaceous grains and amorphous silicate grains. The properties of these grains are parameterized by the polycyclic aromatic hydrocarbon (PAH) index, q_PAH, defined as the fraction of the dust mass in the form of PAH grains. The majority of the dust is supposed to be located in the diffuse interstellar medium (ISM), heated by a radiation field with a constant intensity U_min. A smaller fraction γ of the dust is exposed to starlight with intensities ranging from U_min to U_max, representing the dust enclosed in photodissociation regions. Following the prescription of DL07, we fit the rest-frame mid-IR to mm data points and search for the best-fit model by minimizing the reduced χ². The total dust mass is derived from the best-fit model and its uncertainty is estimated by the distribution of M_d values that correspond to models with χ² ⩽ χ²_min + 1 (Avni & Bahcall 1976). Although a different grain size distribution would result in different M_dust, we choose to adopt the one prescribed by the DL07 models as they can successfully reproduce the IR and submillimeter emission for a sample of SINGS galaxies (including both normal and starburst galaxies).

We also fit the SEDs of our sources with the standard form of a single-temperature (T_d) modified blackbody, leaving the effective emissivity (β_eff) as a free parameter along with the dust temperature (T_d). For the fit we only consider data points with λ_rest > 40 μm, to avoid emission from very small grains and from the best-fit model we can then estimate the M_dust from the relation:

$$\begin{equation} M_d = \frac{S_\nu D^2_L}{(1+z)\kappa _{{\rm rest}} B_\nu (\lambda _{{\rm rest}}, T_d)}, \end{equation} \tag{ 1 }$$

where S_ν is the observed flux density, D_L is the luminosity distance, and κ_rest = κ₀(λ₀/λ_rest)^β is the rest-frame dust mass absorption coefficient at the observed wavelength (Li & Draine 2001). The uncertainty in M_dust is obtained as for the DL07 models. The photometric data along with the best-fitting DL07 and MBB models are shown in Figure 1, while in Table 2 we summarize the derived parameters.

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The two methods return M_dust estimates that are in broad agreement. In particular, for GN20 we derive M_dust = 2.0^+0.7_−0.6 × 10⁹ M_☉(DL07) and 1.5^+0.4_−0.5 × 10⁹ M_☉ (MBB) while for BzK-21000 the corresponding values are M_dust = 8.6^+0.6_−0.9 × 10⁸ and 7.6^+1.2_−1.3 × 10⁸ M_☉. Best-fit MBB models also indicate T_d = 33 K and 34 K for GN20 and BzK-21000, respectively, and β_eff = 2.1 ± 0.2 and 1.4 ± 0.2. The dependence of M_dust on the other two free parameters of the MBB models,¹³ i.e., T_d and β_eff, along with the 68% and 99% confidence intervals, are shown in Figure 2.

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To evaluate the significance of adding mm data in the derivation of M_dust, we repeat the fitting procedure, this time excluding any data at wavelengths longer than 850 μm. For the DL07 models, the best-fit M_dust are unaffected, but the uncertainties increase by a factor of ∼2. Similar results are presented by several studies in the local universe (e.g., Draine et al. 2007; Galametz et al. 2011), where they find that in the absence of rest-frame (sub)mm data, the derived M_dust estimates are highly uncertain.

We derive a total IR luminosity of L_IR = (1.9 ± 0.4) × 10¹³ L_☉ for GN20 and L_IR = (2.1 ± 0.3) × 10¹² L_☉ for BzK-21000 that correspond to SFRs of ∼2000 and ∼210 M_☉ yr⁻¹ and specific star formation rates (sSFR) of ∼8.6 and ∼2.6 Gyr⁻¹. Several studies have shown that star-forming galaxies at any redshift follow a tight SFR–M_* relation, with outliers being starburst galaxies (e.g., Brinchmann et al. 2004; Elbaz et al. 2007; Daddi et al. 2007, 2009; Magdis et al. 2010a, 2010b). Our results confirm that the sSFR of BzK-21000 is similar to that of main-sequence galaxies defined in the SFR–M_* space at this redshift, while GN20 is located in the starburst regime.

As illustrated in Figure 1, it appears that GN20 has a steeper slope in the Rayleigh–Jeans tail when compared to that of BzK-21000. Despite the large uncertainties, the MBB analysis indicates that the β_eff values of two galaxies are different at a ∼2σ significance level. This difference in β_eff explains the similar effective T_d derived for the two sources despite the fact that the SED of GN20 peaks at ∼90 μm while that of BzK-21000 peaks at ∼100 μm. The best-fitting DL07 models suggest that BzK-21000 has properties similar to those found by Draine et al. (2007) for local spirals, with a larger fraction of dust in PAHs (q_PAH = 3.9%) and a less intense radiation field (U_min = 8) compared to that in GN20 (q_PAH = 1.12%, U_min = 25). Similar results are obtained by Elbaz et al. (2011).

Several studies have shown that there is a correlation between M_gas/M_d and the enrichment of the ISM of a galaxy. In Figure 3 (left), we plot M_gas/M_d versus metallicity for a local sample studied by Leroy et al. (2011). For consistency we have computed all metallicities on the Pettini & Pagel (2004, hereafter PP04) scale. This tight correlation (dispersion of ∼0.15 dex) can be used as a tool to constrain α_CO. In particular, if we know the metallicity of a galaxy and have measured its M_dust, then we can estimate its M_gas and subsequently the α_CO value of the source, if L'_CO is known. In what follows we will attempt to apply this approach to the two galaxies in our sample, under the assumption that the observed M_gas/M_d–metallicity relation for local galaxies holds at high redshift.

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Having derived estimates for the M_dust values of our sources, we need information on their metallicities, for which we have to rely on indirect indicators. One of these is the M_*–metallicity relation of Erb et al. (2006), based on which BzK-21000 has a slightly sub-solar metallicity, Z = 8.65. A similar derivation would follow using the fundamental metallicity relation (FMR) of Mannucci et al. (2010) that relates the SFR and the stellar mass to metallicity.

For GN20, the situation is somewhat more complicated, as the Erb et al. (2006) relation is not sufficiently sampled at the high mass end (>10¹¹ M_☉). Using the FMR, and accounting for the evolution observed for galaxies at z > 2.5 (Mannucci et al. 2010), we derive a metallicity of Z = 8.8. Another metallicity estimate can be obtained by assuming that the huge SFR of GN20 could stem from the final burst of star formation, triggered by a major merger that will eventually transform the galaxy into a massive elliptical. Once star formation ceases, the mass and metallicity of the resulting galaxy will not change further, and one might therefore apply the mass–metallicity relation to present-day elliptical galaxies. In this scenario, the metallicity of GN20 could range between Z = 8.8 and 9.2, although a moderately super-solar metallicity is more probable. For our purposes we will adopt a metallicity of 8.65 ± 0.2 for BzK-21000 and a whole range of Z = 8.8–9.2 for GN20.

The fit to the local M_gas/M_d−Z relation (Figure 3, left) indicates a value of M_gas/M_d ∼104 for BzK-21000 and ∼75 (35) for GN20 assuming a metallicity of Z = 8.8(9.2). Santini et al. (2010) report similar M_gas/M_d ∼50 for SMGs. Based on these ratios we first calculate M_gas for each galaxy and find 8.9 × 10¹⁰ M_☉ and 1.5 × 10¹¹ M_☉ (7.0 × 10¹⁰ M_☉) for BzK-21000 and GN20, respectively. Then based on the relation M_gas = α_CO× L'_CO we estimate the corresponding α_CO factors and find α_CO = 4.1^+3.3_−2.7 for BzK-21000 and in the case of GN20 α_CO = 0.9^+0.4_−0.5 for Z = 8.8 and 0.4^+0.2_−0.2 for Z = 9.2. The derived values, along with the estimates of Leroy et al. (2011) for a local sample, are shown in Figure 3 (middle). We also overplot a sample of local ULIRGs from Solomon et al. (1997), for which we were able to compute their metallicities on the PP04 scale. The quoted uncertainties account both for the dispersion of the M_gas/M_d−Z relation and the uncertainties in M_gas/M_d and M_dust.

The derived α_CO values agree with previous independent estimates. In particular, Daddi et al. (2010a), based on the dynamical masses of a sample of z ∼ 1.5–2.0 BzK galaxies (including BzK-21000), argued for an average conversion factor of α_CO = 3.6 for high-z star-forming disks and reported a value of M_gas = (8.1 ± 1.4) × 10¹⁰ M_☉ for BzK-21000 (see also Aravena et al. 2010). Furthermore, Carilli et al. (2010), based on the CO[1 − 0] transition line, estimated the gas mass of GN20 to be M_gas = 1.3 × 10¹¹ × (α_CO/0.8) M_☉, putting a coarse upper limit on the conversion factor of α_CO ∼0.8 from dynamical constraints. This indicates that our α_CO < 1.0 estimate for GN20 is reasonable. Inverting this line of reasoning, placing the sources on the M_gas/M_d–metallicity plane of Figure 3 (left) based on the M_gas estimates from the literature, indicates that BzK-21000 is very close to the relation defined by a linear regression fit to the local sample. Similarly, GN20 appears to broadly follow the local trend. Another way to show that the M_gas/M_d–Z relation holds for high-z galaxies is to plot direct observables, without any assumptions for α_CO. Indeed, in Figure 3 (right), we plot L'_CO/M_dust versus metallicity for our sample and find again that both GN20 and BzK21000 follow the local trend. Finally, recent results from Genzel et al. (2011) seem to verify our assumption.

Despite the substantial uncertainties, the agreement with independent α_CO estimates is reassuring. In the local universe there is observational and theoretical evidence that α_CO in starburst galaxies is significantly smaller than that in the Milky Way disk (Downes & Solomon 1998; Scoville et al. 1997). The derived conversion factor for GN20 is consistent with that of local ULIRGs or even lower, while for BzK-21000 the value is considerably higher and close to that of local spirals. We stress that without the addition of the mm data, the large uncertainties in M_dust would not allow us to derive any meaningful conclusions. Furthermore, although the sources appear to have comparable L_IR/L'_CO ∼100 L_☉ (K km s⁻¹ pc²)⁻¹, their star formation efficiencies (SFEs) are considerably different. In particular, for BzK-21000 we derive an SFE ∼25 while for GN20, SFE ∼100–200 (depending on the assumed metallicity). The two sources also have comparable M_*/M_dust ∼100. This is also the case for local ULIRGs and normal Sloan Digital Sky Survey galaxies (da Cunha et al. 2010), supporting the idea that the property that distinguishes starbursts from normal star-forming galaxies is their enhanced SFR (at fixed M_gas, M_dust, and M_*).

We conclude by noting that our results, although limited to two sources, are in line with previous claims that the star formation mode of BzK-21000 and other high-z galaxies in the main sequence of the SFR–M_* plane is different from that of most SMGs, and more similar to that of local disks, despite their very large infrared luminosities and SFRs. Additionally, we confirm the validity of the widely adopted ULIRG-like α_CO factor for SMGs (e.g., Tacconi et al. 2008). We have also demonstrated that the combination of Herschel with ground-based mm data provides a powerful tool to investigate the dust and gas properties of high-z galaxies. A larger sample is needed to extend this investigation and draw statistically robust conclusions.

We thank Alvio Renzini for useful discussions. G.E.M. acknowledges support from Oxford University. E.D. acknowledges funding support from ERC-StG grant UPGAL 240039 and ANR-08-JCJC- 0008. D.R. acknowledges support from NASA through a Spitzer Space Telescope grant. This work is based on observations made with the Herschel Space Observatory, a European Space Agency Cornerstone Mission with significant participation by NASA.