MOLECULAR GAS IN z ∼ 6 QUASAR HOST GALAXIES

There are 33 quasars at z ∼ 6 that have published observations of dust continuum at 250 GHz that were made with the Max-Planck Millimeter Bolometer Array (MAMBO; Kreysa et al. 1998) on the IRAM 30 m telescope, and 10 of these have been detected (Bertoldi et al. 2003a; Petric et al. 2003; Willott et al. 2007; Wang et al. 2007, 2008b). The two brightest MAMBO detections (i.e., S_250 GHz ∼ 5 mJy, L_FIR ∼ 10¹³ L_☉), J1148+5251 and J0927+2001, have all been detected in strong molecular CO line emission (J1148+5251: CO (3–2), Walter et al. 2003; CO (7–6) and (6–5), Bertoldi et al. 2003b; J0927+2001: CO (6–5) and (5–4), Carilli et al. 2007). In this work, we present new observations of CO (6–5) and/or (5–4) line emission in another six z ∼ 6 quasars (J0840+5624, J1044 − 0125, J1048+4637, J1335+3533, J1425+3254, J2054 − 0005) using the Plateau de Bure Interferometer (PdBI). They all have 250 GHz flux density of S_250 GHz ⩾ 1.8 mJy and corresponding FIR luminosities of L_FIR > 5 × 10¹² L_☉ (using the estimation given in Wang et al. 2008a, 2008b). We also report our observations of the CO (2–1) line in J0840+5624 and J0927+2001 with the Green Bank Telescope (GBT), CO (3–2) in J1048+4637 with the VLA, and 350 μm dust continuum in J0840+5624, J0927+2001, J1044 − 0125, J1335+3533, and J1425+3254 with the SHARC-II bolometer camera at the Caltech Submillimeter Observatory (CSO).

We list the basic information of all the eight FIR luminous z ∼ 6 quasars in Table 1, including their redshifts from the discovery papers (Fan et al. 2000, 2003, 2006b; Jiang et al. 2008; Cool et al. 2006), optical magnitudes, continuum flux densities at 250 GHz and 1.4 GHz (Bertoldi et al. 2003a; Carilli et al. 2004; Wang et al. 2007, 2008b), as well as available measurements of the black hole masses and AGN bolometric luminosities (Jiang et al. 2006). These objects are mainly optically selected with rest-frame 1450 Å (m₁₄₅₀) absolute magnitude of −27.8 < M₁₄₅₀ < −26.0, indicating AGN bolometric luminosity of L_bol > 10¹³ L_☉ (Jiang et al. 2006), which are among the brightest objects in the quasar population. The black hole masses of J1148+5251 and J1044 − 0125 have been determined from the measurements of the AGN UV broad line emission (Willott et al. 2003; Jiang et al. 2006) which are a few 10⁹ M_☉, indicating Eddington ratios of 0.5–1.0 (Jiang et al. 2006).

The observations of the CO (6–5) and (5–4) lines were carried out with the new generation 3 mm receiver on the PdBI, which provides a bandwidth of 1 GHz in dual polarization. The sources were observed between 2007 and 2009, in the compact D configuration (FWHM resolution ∼5''). We generally used two frequency setups for the first two tracks on each target to cover a continuous bandwidth of 1.8 GHz, to account for the possible uncertainties between the optical and systemic (CO) redshifts. In the case of marginal detections, we added one more track with both polarization bands centered at the likely line frequency to confirm the line at >3σ significance. The original frequency resolution is 2.5 MHz which was subsequently binned to 23 MHz (∼70 km s⁻¹). Phase calibration was performed every 20 minutes with observations of 0954+658, 1055+018, 1150+497, 1308+326, and 2134+004. We observed MWC 349 as the flux calibrator. The typical rms after 8 hr of observing time is about 0.5 mJy beam⁻¹ per 70 km s⁻¹ wide bin. The data were reduced with the IRAM GILDAS software package (Guilloteau & Lucas 2000).

We also conducted observations of CO (2–1) line emission in two of the CO-detected z ∼ 6 quasars, J0840+5624 and J0927+2001, during the winter months of 2007–2008, using the Ka-band receiver on the 100 m GBT. The observations employed the subreflector nodding mode with half-cycle times between 9.0 and 22.5 s. The tunings were based on the CO (6–5)/(5–4) redshifts (Bertoldi et al. 2003b; Carilli et al. 2007). We set up the spectrometer in low resolution mode with two single-polarization 800 MHz windows centered at offsets of −100 MHz and +100 MHz from the observed line frequency. Thus, the two polarizations cover the redshifted CO (2–1) line with a bandwidth of 600 MHz simultaneously.

Flux calibration was performed using 3C147, and pointing was checked regularly on known radio sources. Data were analyzed using the data reduction routines in the GBTIDL software package. The uncertainties of the flux calibration are typically 10%–20%. We have spent 17.7 hr of observing time (including overhead due to subreflector movement) on J0840+5624, leading to an rms noise of about 0.13 mJy per 50 km s⁻¹ wide channel, measured from the line-free channels. However, there is a small-scale baseline structure close to the observed line frequency, which cannot be removed in the calibration, and thus, precluded detection of weak line emission with peak flux density of a few hundred μJy (see Wagg et al. 2008). We also spent 10.7 hr on J0927+2001, and the CO (2–1) line is not detected with a 1σ rms sensitivity of 0.15 mJy per 50 km s⁻¹ channel.

Finally, we report a tentative VLA Q-band detection of CO (3–2) line emission from J1048+4637. These observations were conducted in 2004 in BC, C, and CD configurations. The source was observed in continuum mode, i.e., two polarizations, two intermediate frequency bands "IFs," and 50 MHz bandwidth (∼310 km s⁻¹ in velocity) per IF for each frequency setup. We searched the CO (3–2) line emission in the frequency range from 47.715 GHz to 48.165 GHz (corresponding to 6.179–6.247 in redshift) by observing the source repeatedly with different frequency setups.

We reduced the data and made images using the standard VLA wide field data reduction software AIPS and the source is detected in the 50 MHz channel centered at 47.865 GHz (z = 6.224, Δz = 0.008) at ≳4σ with a 1σ rms of 70 μJy beam⁻¹. The spatial resolution on the final map is 05 (FWHM). The 1σ rms values for the other channels are much higher, i.e., from 120 to 200 μJy beam⁻¹ (due to less observing time) and no signal is detected at the quasar position. We excluded the data observed at 47.865 GHz and 47.815 GHz which are close to the CO (3–2) line frequency for z = 6.2284 (i.e., the redshift determined with the PdBI CO (6–5) detection), and merged the data of all the other channels to constrain the source continuum at 48 GHz. The 1σ rms noise on the combined image is 65 μJy beam⁻¹ and no continuum emission is detected.

We obtained new 350 μm observations of the dust continuum emission from five z ∼ 6 quasars, using the SHARC-II bolometer camera on the CSO 10.4 m telescope. The SHARC-II camera is a 12 × 32 element array with a field of view of 26 × 10 and a beam size of 85. The observations were conducted in 2008 February during excellent weather conditions on Mauna Kea (opacity at 225 GHz < 0.06). We adopted a scan pattern similar to our previous SHARC-II observations of z ∼ 6 quasars, i.e., a Lissajous pattern with amplitudes of ±45'' and ±12'' in azimuth and elevation, respectively. This provides a uniform coverage of ∼65'' × 34''. Pointing, focus, and flux calibrations were done on Mars, Saturn, and a number of secondary calibrators (OH 231.8+4.2, CRL 618, IRC 10216, Arp 220, and 3C345). The final calibration uncertainties are within 20%.

The on-source integration time for each of the five objects is listed in Table 2. Data reduction was performed with the CRUSH data reduction package version 1.63 (Kovács 2006) and the rms noise values in the final maps are <5 mJy beam⁻¹ for all targets. With these new observations, we confirm a previous 350 μm detection of J0927+2001 and marginally detect the dust continuum toward J0840+5624 (2.9σ). The measurements and upper limits for the other three sources are listed in the next section.

J0840+5624. Both the CO (6–5) and (5–4) transitions were detected, peaking at 08^h40^m3508, +56°24'205, 06 from the optical quasar position. The integrated line flux densities are 0.60 ± 0.07 Jy km s⁻¹ and 0.72 ± 0.15 Jy km s⁻¹, respectively. A single Gaussian line profile fitted to the combined spectrum of the two CO transitions yields a host galaxy redshift of 5.8441 ± 0.0013 and a FWHM line width of 860 ± 190 km s⁻¹. This is the largest CO line width that we have detected among the z ∼ 6 quasars, and the line profile is double peaked. A fit with two Gaussian components to the combined spectrum gives peak velocity offsets of −300 km s⁻¹ and 230 km s⁻¹, and FWHM line widths of ∼300 km s⁻¹ and 410 km s⁻¹ for the two components, respectively. Continuum is not detected in the line-free channels and the 3σ upper limits are 0.15 mJy at 85 GHz and 0.30 mJy at 101 GHz.

The GBT observation of the CO (2–1) transition gives an rms of about 0.13 mJy per 50 km s⁻¹ channel. Assuming a velocity range similar to the CO (5–4) line, We estimated a 3σ line flux upper limit of about 0.1 Jy km s⁻¹ for this object.¹³ However, we emphasize that there are large uncertainties in this measurement due to a small-scale baseline structure close to the expected line frequency (Wagg et al. 2008).

The 350 μm dust continuum emission is marginally detected in this object at ∼2.9σ. The continuum source is unresolved and peaks at R.A. = 08^h40^m3532, decl. = 56d24'175, which is 31 away from the optical quasar (the left panel of Figure 2). The peak value is 9.3 ± 3.2 mJy beam⁻¹ on the final map and we adopt this as the tentative 350 μm flux density. Further 350 μm observations with better sensitivity are necessary to confirm this tentative detection. On the SHARC-II map, there is also a 4σ peak (14.8 ± 3.7 mJy) at the position of R.A. = 08^h40^m3435, decl. = 56d24'450 (i.e., northwest to the quasar, see the left panel of Figure 2). We checked our previous VLA 1.4 GHz continuum observation (observed in A array with a resolution of FWHM ∼14; Wang et al. 2007) and there is a radio source with S_1.4 GHz = 44 ± 9 μJy close to this position, i.e., at R.A. = 08^h40^m3425, decl. = 56d24'447. The offset is only 09, well within the position uncertainty of the SHARC-II observation. There is no further identification information for this field source yet.

J1044 − 0125. We detected the CO (6–5) line in this source, peaking at the position of 10^h44^m33.02, −01°25'023, 03 away from the optical quasar. The FWHM of the CO line fitted with a single Gaussian profile is 160 ± 60 km s⁻¹, which represents the narrowest CO line width among all the CO-detected z ∼ 6 quasars. The integrated line flux is 0.21 ± 0.04 Jy km s⁻¹. The 3σ upper limit on the continuum emission is 0.15 mJy at 102 GHz.

The 350 μm dust continuum emission has not been detected in our SHARC-II observations, and the 1σ rms is 4.5 mJy beam⁻¹. This yields a 3σ flux density upper limit of 13.5 mJy.

J1048+4637. We detected the CO (6–5) line emission in this source, peaking at 10^h48^m45.08, 46°37'187, 05 away from the optical quasar position. The CO redshift is 6.2284 ± 0.0017, which is close to the value of 6.23 estimated from the Lyα+NV emission in the quasar rest-frame UV spectrum (Fan et al. 2003), but higher than the value of 6.19–6.20 measured from the Mg ii λ2798 Å emission (Iwamuro et al. 2004; Maiolino et al. 2004b). The 3 mm dust continuum emission is detected along with the CO line emission. A simultaneous fit of the CO lines and the continuum gives a continuum flux density of 0.13 ± 0.03 mJy at 96 GHz. The integrated line flux is 0.27 ± 0.05 Jy km s⁻¹, and the FWHM line width from single Gaussian fit is 370 ± 130 km s⁻¹. We have also detected CO (6–5) line emission from a source ∼28'' away, to the northeast of the quasar (J1048NE). The CO spectrum yields a redshift of 6.2259 ± 0.0019 for this NE source, indicating the presence of a companion galaxy ∼160 kpc away from the optical quasar. The observed peak flux density is 0.53 ± 0.14 mJy, which gives an integrated flux of 0.23 ± 0.05 Jy km s⁻¹. Considering an attenuation factor of ∼0.4 for the primary beam (FWHM ∼ 52'') at the source position, we estimate the intrinsic line flux to be 0.58 ± 0.13 Jy km s⁻¹ (see Figure 1).

The CO (3–2) line emission from this object was searched using the Q-band receiver on the VLA, and we detected the source at 0.30 ± 0.07 mJy in a 50 MHz wide channel centered at 47.865 GHz. The data averaged over the other channels present a 3σ upper limit of 0.195 mJy for the continuum emission at 48 GHz, indicating that the 0.3 mJy detection at 47.865 GHz are not due to nonthermal quasar continuum emission. An optically thin graybody model with a dust temperature of T_dust = 47 K and an emissivity index of β = 1.6 (Beelen et al. 2006; Wang et al. 2008b) fitted to the continuum measurements at 250 GHz and 96 GHz suggests a continuum flux density of only 0.017 mJy at the observed frequency of 47.865 GHz. Thus, the 0.30 mJy detection in this channel is likely to be from the CO (3–2) line emission. The source on the VLA image is marginally resolved by the 05 × 05 synthesized beam, and a fit to a two-dimensional-Gaussian component yields a source size of 09 × 04. The integrated line intensity detected in the channel is 0.09 ± 0.02 Jy km s⁻¹. According to the line profile and source redshift of z = 6.2284 ± 0.0017 determined from the CO (6–5) transition, the VLA observation is likely to be centered at the blue part of the CO (3–2) line emission and covers a bandwidth of 310 km s⁻¹ in velocity. Thus, we adopt the measurement as a lower limit of the CO (3–2) line flux for this object.

J1335+3533. The CO (6–5) line was detected in this source, peaking at the position of 13^h35^m5075, 35°33'158, 07 away from the optical quasar position. The CO FWHM fitted with a single Gaussian profile is 310 ± 50 km s⁻¹. The integrated line intensity is 0.53 ± 0.07 Jy km s⁻¹, and the 3σ upper limit on the continuum emission is 0.15 mJy at 100 GHz.

No 350 μm dust continuum is detected in our SHARC-II observations of this object. The 1σ rms on the final map is 4.4 mJy beam⁻¹, and the corresponding 3σ upper limit is 13.2 mJy for the 350 μm flux density.

J1425+3254. The CO (6–5) line was detected, peaking at the position of 14^h25^m1626, 32°54'093, 06 away from the optical quasar. The CO FWHM fitted with a single Gaussian profile is 690 ± 180 km s⁻¹, and the line flux of 0.59 ± 0.11 Jy km s⁻¹. The 3σ upper limit for the continuum at 101 GHz is 0.12 mJy.

This source was not detected in our SHARC-II observations of the 350 μm dust continuum with a 1σ rms of 2.6 mJy beam⁻¹. This yields a 3σ upper limit of 7.8 mJy for the 350 μm flux density.

J2054 − 0005. The CO (6–5) line was detected in this source, peaking at the position of 20^h54^m0645, −00°05'131, 18 away from the optical quasar. The CO line FWHM obtained from a fit to a single-Gaussian line profile is 360 ± 110 km s⁻¹. The derived integrated intensity is 0.34 ± 0.07 Jy km s⁻¹, and the 3σ upper limit on the continuum emission at 98 GHz is 0.15 mJy.

J0927+2001. We have observed the CO (2–1) line in this object for 10.7 hr with the GBT, and the final rms is 0.15 mJy per 50 km s⁻¹ channel. We adopt a line width of ∼900 km s⁻¹ (full width at zero intensity) based on the previous PdBI detections of the CO (6–5) and (5–4) transitions (Carilli et al. 2007), and derive a 3σ upper-limit to the integrated line intensity of ∼0.1 Jy km s⁻¹.

The 350 μm dust continuum emission from this object was previously detected by our SHARC-II observations in 2007 (17.7 ± 5.7 mJy; Wang et al. 2008a). The new data we presented here confirm the detection with better sensitivity, i.e., a 350 μm flux density of 11.7 ± 2.4 mJy. This 350 μm dust continuum peak is quite consistent with the optical quasar position (offset of <1''). We cannot confirm the ∼3σ peak 15'' away from the quasar position reported in our previous work (Wang et al. 2008a).

We compare the redshifts determined from CO and UV emission lines in Table 3 for all CO detected z ∼ 6 quasars, including the previous CO-detections in J1148+5251 and J0927+2001 (Bertoldi et al. 2003b, Carilli et al. 2007). The C iv λ1549 Å redshifts of J0840+5624 and J1044 − 0125 are blueshifted by about 3000 and 1600 km s⁻¹ compared to the values determined from the CO lines, respectively. This is consistent with the fact that the C iv emission is typically blueshifted from the quasar systematic redshift by up to a few thousand km s⁻¹ (Richards et al. 2002; Goodrich et al. 2001; Ryan-Weber et al. 2009). There is no systematic offset between the CO redshifts and those determined from other UV emission lines. In particular, the CO redshifts of J1044 − 0125 and J1148+5251 are in good agreement with the values derived from the C iii] λ1909 Å and Si iv λ1400 Å broad emission lines with high-quality near-infrared spectroscopy (Jiang et al. 2007; Ryan-Weber et al. 2009). The largest offset between CO and Lyα redshifts is ∼0.04, which is reasonable since the Lyα redshifts are always poorly constrained (with uncertainties of 0.02–0.05).¹⁴ Three objects have redshifts determined from the Mg ii λ2798 Å line. The CO redshifts of J1044 − 0125 and J1148+5251 are consistent with the Mg ii measurements within the uncertainties, while a large offset of ∼0.03 is seen in J1048+4637 between the CO redshift and the Mg ii ones quoted in Iwamuro et al. (2004b) and Maiolino et al. (2004b).

The mass of the molecular gas in J1148+5251 is well determined from the CO (3–2) data (Walter et al. 2003, 2004; Riechers et al. 2009). The high-order CO transitions (J ⩾ 5) detected in SMGs and high-redshift quasars are usually not thermalized (e.g., Weiß et al. 2005a, 2007; Riechers et al. 2009). Thus, for the other seven CO-detected z ∼ 6 quasars, we adopt the line ratios of L'_CO(6–5)/L'_CO(1–0) ≈ 0.78 and L'_CO(5–4)/L'_CO(1–0) ≈ 0.88 from the multi-CO transition large velocity gradient (LVG) modeling of J1148+5251 (Riechers et al. 2009) and use these numbers to calculate the CO (1–0) line luminosities (L'_CO(1–0)). We then estimate the molecular gas masses (M_gas = M[H₂ + He]) within the CO emitting region of the quasar host galaxies using M_gas = αL'_CO(1–0). An integrated CO intensity-to-gas mass conversion factor of α = 0.8 M_☉(K km s⁻¹ pc²)⁻¹, appropriate for ULIRGs, is adopted here (Solomon et al. 1997; Downes & Solomon 1998; SV05). The derived molecular gas masses are in the range, 0.7 × 10¹⁰–2.5 × 10¹⁰ M_☉ (Table 4) with a median value of 1.8 × 10¹⁰ M_☉.

We plot the molecular gas mass distribution of the z ∼ 6 quasars, CO-observed SMGs, and 1.4 ⩽ z ⩽ 5 quasars in the left panel of Figure 4. The range of gas masses of the z ∼ 6 quasars (0.7 × 10¹⁰ to 2.5 × 10¹⁰ M_☉) appears narrower but still comparable to the typical values found in the other two samples. We performed the standard Kolmogorov–Smirnov test between the z ∼ 6 quasars and the other two samples. The probabilities that the data are drawn from the same parent population are 19% for the z ∼ 6 and 1.4 ⩽ z ⩽ 5 quasar samples, and 16% for the z ∼ 6 quasar and SMG samples. This agrees with the results from previous studies that the high-z FIR and CO luminous quasars show molecular gas mass distribution similar to that of the SMGs (Carilli & Wang 2006; Coppin et al. 2008a).

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The CO line widths (FWHM) of the z ∼ 6 quasar sample are spread over a wide range, from 160 km s⁻¹ to 860 km s⁻¹, with a median value¹⁵ of 360 km s⁻¹. The broadest CO line detection (J0840+5624) appears to be double-peaked with peak-velocity offsets of ∼270 km s⁻¹ (see Figure 1). Similar line profiles are widely observed in samples of SMGs (Greve et al. 2005; Weiß et al. 2005a; Tacconi et al. 2006), which may be due to either uncoalesced molecular gas components in a galaxy merger or simply reflect a large inclination angle of an extended gas disk relative to the sky plane.

In the right panel of Figure 4, we compare the CO line-width distribution of the z ∼ 6 quasar sample to that of the CO-detected SMGs (Greve et al. 2005; Tacconi et al. 2006) and 1.7 ⩽ z ⩽ 5 quasars (SV05; Coppin et al. 2008a). The Kolmogorov–Smirnov tests return probabilities of 13% for z ∼ 6 quasars and SMGs, and 71% for z ∼ 6 and 1.7 ⩽ z ⩽ 5 quasars, i.e., there is no significant difference in the line-width distributions. This result confirms that the observed line-width distribution of high-z CO and FIR quasars is comparable to that of the SMGs as was found in Coppin et al. (2008a). The systemic difference reported in previous works (Greve et al. 2005; Carilli & Wang 2006) is likely to be due to selection effects and small sample size.

The detection of CO (6–5) line emission in all eight z ∼ 6 quasars in our sample implies highly excited molecular gas in their host galaxies. Four of the CO-detected z ∼ 6 quasars, J0840+5624, J0927+2001, J1048+4637, and J1148+5251, have observations of multiple CO line transitions (Bertoldi et al. 2003b; Carilli et al. 2007; this work). The CO "excitation ladder" of J1148+5251 has been studied by Bertoldi et al. (2003b) and Riechers et al. (2009), and the best LVG model fitted to the data suggests CO emission from a single gas component with kinetic temperature of T_kin = 50 K and a molecular gas density of ρ_gas(H₂) = 10^4.2 cm⁻³. Similar CO excitation conditions are also found in the CO and FIR luminous quasar BR 1202 − 0725 at z = 4.69 (Carilli et al. 2002; Riechers et al. 2006) and some nearby starburst galaxies (e.g., the high excitation component in M82; Weiß et al. 2005b). In Figure 5, we plot the CO excitation ladders of J0840+5624, J0927+2001, and J1048+4637, together with the LVG models of J1148+5251, BR 1202 − 0725, and the high excitation component in M82. The line intensity ratios of I_CO(5–4)/I_CO(6–5) for J0840+5624 and lower limit of I_CO(3–2)/I_CO(6–5) for J1048+4637 are consistent with the model values. J0927+2001 shows a lower value of I_CO(5–4)/I_CO(6–5) compared to the model, which, however, is still marginally consistent given the large uncertainties in the measurements of both transitions. These results suggest that such a warm, highly excited, single component gas model is a reasonable description of the molecular gas in all of these quasar host galaxies. Further observations of additional CO transitions in the CO-detected z ∼ 6 quasars will address how the CO excitation properties vary among these objects.

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The FIR luminosities, L_FIR, of the eight CO-detected quasars at z ∼ 6 are derived using the submillimeter and millimeter continuum measurements from the literature and the CO observations in this work (Bertoldi et al. 2003a; Beelen et al. 2006; Wang et al. 2007, 2008a, 2008b; Carilli et al. 2007), as listed in Table 4. A dust emissivity index of β = 1.6 (Beelen et al. 2006) is adopted in these calculations. J1148+5251 has a fitted dust temperature, T_dust, of 56 K (Beelen et al. 2006) and J0927+2001 has T_dust = 46 K, from fits to the submillimeter and millimeter measurements (this work; Wang et al. 2007, 2008a; Carilli et al. 2007; Riechers et al. 2009). We adopt the average dust temperature of 47 K found in high-z quasar host galaxies (Beelen et al. 2006) for the other six objects (see Wang et al. 2008b).

We plot L_FIR versus L'_CO(1–0) for the eight z ∼ 6 quasars in Figure 6 and compare them with the local spiral, infrared luminous galaxies (LIRGs; Gao & Solomon 2004), ULIRGs (Solomon et al. 1997), the 1.4 ⩽ z ⩽ 5 quasars, and SMG samples discussed above. For the high-z samples, L_FIR is re-calculated using (sub)mm measurements from the literature (Smail et al. 2002; Kovács et al. 2006; Chapman et al. 2005; Omont et al. 2003; Benford et al. 1999; Beelen et al. 2006), using the β value mentioned above. We assume T_dust = 47 K for the objects with less than three (sub)mm measurements in the quasar sample (Beelen et al. 2006), while T_dust = 35 K is used for the SMGs, which is typical for the T_dust values found in previous (sub)mm studies (Kovács et al. 2006; Coppin et al. 2008b). The z ∼ 6 quasars fall along the trend defined by all the other samples systems within the scatter (see the open stars in Figure 6).

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A fit to the samples of local spirals, LIRGs, ULIRGs, and SMGs using the ordinary least squares bisector method (Isobe et al. 1990) yields a relationship of log  L_FIR = 1.67 × log  L'_CO(1–0) − 4.87 for these typical star-forming systems, which is consistent with the result of log  L_FIR = 1.7 × log  L'_CO(1–0) − 5 quoted in SV05 with similar samples. We also note that the z ∼ 6 quasars all lie above this relationship. There are a number of undetermined parameters for individual objects, e.g., unknown AGN contributions to the FIR emission, different dust temperatures, and CO line ratios, which may account for the offsets and scatters. Further observations at infrared, submillimeter, and millimeter wavelengths will be important to directly probe the infrared SEDs and better constrain the dust temperatures and AGN contributions for these objects. For a rough estimation, we derive the AGN contributions to the FIR emission for our sample with the quasar rest frame 1450 Å continuum (Table 1) and a FIR-to-1450 Å luminosity ratio of L_FIR/νL_ν,1450 Å = 0.14 from the local radio quiet quasar template (Elvis et al. 1994). The estimated AGN-dominated FIR emission is 0.9–4.4 × 10¹² L_☉ for the eight sources, which account for about 30% of the FIR luminosities we calculated above with the (sub)mm observations on the average. We subtract these from the original L_FIR values (Table 1) and the corrected data points (see the filled stars in Figure 6) show a better agreement with the FIR-to-CO luminosity relationship for the star-forming system.

CO emission has been detected toward the eight z ∼ 6 quasars with published 250 GHz dust continuum flux densities of S_250 GHz ⩾ 1.8 mJy, indicating ≳10¹⁰ M_☉ of molecular gas in the host galaxies of the FIR luminous quasars at the earliest epoch. The derived FIR and CO (1–0) luminosities follow the L_FIR–L'_CO relationship defined by star-forming systems at low and high redshifts, suggesting a star formation origin of a dominant fraction of the FIR emission in most of these objects, i.e., the excess FIR dust emission is powered by star-forming activity in the circumnuclear region, not the central AGNs (Bertoldi et al. 2003a; Wang et al. 2008b; Walter et al. 2009). This is consistent with the idea of co-eval star formation with SMBH accretion in the massive z ∼ 6 quasar systems which are bright at both UV-optical and FIR wavelengths (e.g., Bertoldi et al. 2003a, 2003b; Wang et al. 2007, 2008a, 2008b; Walter et al. 2003, 2004, 2009).

The measurements of (sub)mm dust continuum and molecular CO line emission from the quasar host galaxies provide the first constraint on the star-forming activities in these objects. Using the AGN contribution-removed FIR luminosities derived in the previous section (Table 1), we estimate the star formation rates (SFRs)¹⁶ for the eight z ∼ 6 quasars to be ∼530–2380 M_☉ yr⁻¹ (Kennicutt 1998). The ratios between SFR and M_gas (i.e., SFR per solar mass of molecular gas) provide a measure of the star formation efficiency, which are about 5 × 10⁻⁸ yr⁻¹–1 × 10⁻⁷ yr⁻¹. This is comparable to that of the SMGs, 1.4 ⩽ z ⩽ 5 CO-detected quasars, and local ULIRGs (SV05), and systematically higher than that of the local normal spiral disks (Kennicutt 1998), and high-z star-forming disk galaxies (e.g., the z ∼ 1.5 BzK galaxies; Daddi et al. 2008, 2010), suggesting a high star formation efficiency in the host galaxies of these FIR and CO luminous z ∼ 6 quasars similar to that of the extreme starburst systems (Tacconi et al. 2006; Walter et al. 2009). The inverse gives the gas depletion timescales of τ_dep = M_gas/SFR ∼ (1–2) × 10⁷ yr.

Massive bursts of star formation are likely to be on-going in these FIR and CO bright quasars at z ∼ 6. In this section, we investigate the possible constraints of the black hole–bulge masses and velocity dispersion relationships in these z ∼ 6 quasar systems using the available CO measurements. The available SMBH masses and AGN bolometric luminosities (L_bol) from the literature are listed in Table 1. For other objects, we adopt the L_bol values estimated in Wang et al. (2008b) from M₁₄₅₀, corrected to the CO redshifts, and estimated the black hole masses assuming L_bol/L_EDD = 1 and M_BH = L_bol(erg s⁻¹)/1.26 × 10³⁸ M_☉. The estimated M_BH values are all of the order of 10⁹ M_☉

5.2.1. M_BH–M_bulge Relationship

The dynamical masses (M_dyn) of the eight z ∼ 6 quasars can be expressed as M_dyn ≈ 2.3 × 10⁵v_cir²R (e.g., Neri et al. 2003; Walter et al. 2004; SV05; Narayanan et al. 2008), where R is the disk radius in kpc and v_cir is the maximum circular velocity of the gas disk in km s⁻¹. High-resolution CO observations of J1148+5251 give a gas disk radius of ∼2.5 kpc and a dynamical mass of 4.5 × 10¹⁰ M_☉. In the absence of spatially resolved measurement for our sample quasars, we here assume a disk radius of 2.5 kpc also for the other seven objects and estimate v_cir using 1/2 of the full width at 20% maximum (Ho 2007a, 2007b), which corresponds to about 3/4 of the CO FWHM for a single-Gaussian profile i.e., v_cir = 3FWHM/4 sin i, where i is the inclination angle of the molecular gas disk. We leave sin i as an unknown factor in these calculations. The derived M_dyn sin²i are from 8.4 × 10⁹ to 2.4 × 10¹¹ M_☉ (Table 4). For 0840+5624, if we adopt the average peak-velocity offset of 270 km s⁻¹ as the disk circular velocity, the M_dyn sin²i will reduce from 2.4 × 10¹¹ M_☉ to 4.2 × 10¹⁰ M_☉.

We then estimate the masses of the stellar components (M_bulge) in the spheroidal bulges as M_bulge = M_dyn − M_gas. We adopt a series of inclination angle values, i.e., i = 1°, 5°, 10°, 20°, 30°, 40°, 50°, 60°, and 90°, and derive M_dyn and M_bulge accordingly. The corresponding black hole–bulge mass ratios (M_BH/M_bulge) versus different inclination angles are plotted in Figure 7, compared to the local mass relationship of M_BH ∼ 0.0014M_bulge. The plot shows that if the sources were falling on the local black hole–bulge mass ratio of 0.0014 this would require inclination angles from <5° to ∼25°, or <5° to 15° when the two broadest line objects are excluded.

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However, the observed distribution of CO line widths of the z ∼ 6 quasar sample is similar to that of the SMGs, which argues against systematically smaller inclination angle values. Moreover, these z ∼ 6 quasars are all among the brightest objects in the quasar population with AGN bolometric luminosities of L_bol ⩾ 10¹³ L_☉. Recent studies showed that the unobscured fraction of quasars is increasing with quasar luminosity, and for objects with L_bol ⩾ 10¹³ L_☉, this fraction is probably larger than 50% (Simpson 2005; Treister et al. 2008). This is consistent with the receding torus model and implies a very large opening angle of the unobscured cone in these most luminous quasars, i.e., the central AGNs can be directly seen over an inclination angel range of i from 0° to probably ⩾60° (Elitzur 2008). Thus, though we cannot rule out small inclination angle values for individual objects, it is highly unlikely that more than half of these CO detected z ∼ 6 quasars are viewed in the extreme inclination angle range of i < 15°. The CO estimated bulge dynamical masses probably reflect intrinsically smaller M_BH/M_bulge for these z ∼ 6 quasars compared to that of the local mature galaxies.

We emphasize that accurate calculations of the bulge dynamical and stellar masses still require high-resolution measurements of the disk size and geometry for each object. To roughly constrain the average black hole–bulge mass ratio of these FIR and CO luminous z ∼ 6 quasars here, we simply adopt an average inclination angle of 40° based on the assumption of uniformly distributed i between 0° and 60°. This results in a median M_BH/M_bulge ratio of 0.022 for our sample, which is about 15 times higher than the present-day value of 0.0014. This is in good agreement with the picture suggested by other high-z M_BH–M_bulge studies (e.g., Walter et al. 2004; Coppin et al. 2008a; Riechers et al. 2008a, 2008b; Peng et al. 2006a, 2006b), i.e., that the SMBH accumulates most its mass before the formation of the stellar bulge.

For further consideration, if these z ∼ 6 quasars will finally evolve into systems with black hole–bulge relationships identical to that in the local universe, the final bulge stellar mass should be around 10¹² M_☉ with black hole masses on the order of 10⁹ M_☉. The M_BH/M_bulge ratio we derived above suggests that only ≲10% of the stellar component has been formed in these FIR and CO bright z ∼ 6 quasars on the average. On the other hand, the detected molecular gas mass of ∼10¹⁰ M_☉ in these objects can only account for <3% of the mature bulge mass if the gas will all be converted to stars. Thus, large amounts of gas supplied from external sources is required to form the 10¹² M_☉ stellar bulge by z = 0.

5.2.2. M_BH–σ Relationship

We investigate the black hole mass–bulge velocity dispersion relation with the eight CO-detected z ∼ 6 quasars in Figure 8. The SMBH mass (M_BH) and bulge velocity dispersion (σ) in local galaxies follow a relationship of log (M_BH/M_☉) = 8.13 + 4.02log(σ/200 km s⁻¹) (Tremaine et al. 2002). We first roughly estimate σ for the eight z ∼ 6 quasars with the CO line widths, using the empirical relation σ ≈ FWHM/2.35 (Shields et al. 2006; Nelson 2000). The results are plotted in Figure 8, together with the local active and inactive galaxies from Tremaine et al. (2002) and CO-detected 1.4 ⩽ z ⩽ 5 quasars that have available SMBH mass measurements (Shields et al. 2006; Coppin et al. 2008a). Most of the high-z CO-detected quasars, especially the objects with M_BH ⩾ 10⁹ M_☉, are above the local M_BH–σ relationship with offsets of more than 1 order of magnitude in black hole mass, as was found in Shields et al. (2006). The median value of the ratios between M_BH and the expected black hole masses from the local M_BH–σ relation (M_BH,σ) for our z ∼ 6 sample is 〈M_BH/M_BH,σ〉_median ∼ 40.

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This is consistent with the high M_BH/M_bulge ratios and the idea of prior SMBH formations we discussed in the previous section (Section 5.2.1). However, the systemic offset between the high-z objects and the local M_BH − σ relation (i.e., 〈M_BH/M_BH,σ〉_median) can be reduced if we include assumptions of inclination angles in our estimations of σ, following the empirical correlations between σ and inclination angle-corrected CO line width from the literature (e.g., Ho 2007a, 2007b; Wu 2007). In particular, if we consider the possible gas disk inclination angle range for these z ∼ 6 quasars and adopt an average value of i = 40° (as was discussed in Section 5.2.1), the derived 〈M_BH/M_BH,σ〉_median will reduce to ∼26 and 4 following the methods described in Wu (2007) and Ho (2007a), respectively.

We also note that our sample exhibits significant scatter on the M_BH–σ plot with derived M_BH/M_BH,σ values over 3 orders of magnitude. This is mainly due to the intrinsic scatter and offset between the real bulge velocity dispersions and the CO estimated values based on the empirical relationships of low-z samples. Indeed, how the observed CO line widths trace the bulge velocity dispersions in the high-z CO-detected quasars is still an open question. These objects are the most massive SMBH–host systems in the universe with SMBH masses of a few 10⁹–10¹⁰ M_☉ and experiencing massive star formation in the central kpc scale regions (Walter et al. 2009). We will expect the sensitive interferometer arrays (such as ALMA and the EVLA) to directly probe the gas properties, e.g., the gas distribution, geometry, dynamics (virialized or not), line profiles, and contributions from turbulence, etc., in their spheroidal hosts and finally address the M_BH–σ correlation in these high-z FIR and CO luminous quasars.