Millimeter and Radio Observations of z$\sim$6 Quasars

The tight correlation between the mass of supermassive black holes (SMBH) in the centers of galaxies and the bulge mass/velocity dispersion is well documented in the local universe (Magorrian et al. 1998; Marconi & Hunt 2003; Ferrarese & Merritt 2000; Gebhardt et al. 2000; Tremaine et al. 2002) and suggests that the evolution of SMBH and spheroidal galaxies is coupled even at high redshift. Due to the negative K-correction, submillimeter and millimeter ((sub)mm) observations become an efficient way to study the host galaxies of high redshift quasars (Blain & Longair 1993). Such observations probe the rest frame FIR emission from the dust components in the interstellar medium (ISM) of these objects, and thus provide a unique chance to test co-eval black hole and bulge formation by searching for massive starbursts in the host galaxies of high redshift optically bright quasars.

The (sub)mm and radio properties of some optically bright quasars at high redshift are discussed in a number of papers. Observations of large samples of optically selected quasars from z$\sim$1.5 to 5 (Omont 2001, 2003; Carilli et al. 2001; Isaak et al. 2002; Priddey et al. 2003a; Beelen et al. 2004) result in a (sub)mm detection rate of about 30% at mJy sensitivity. The derived far-infrared (FIR) luminosities of the (sub)mm detections are typically $\sim {10}^{13}{L}_{\odot }$ and imply dust masses $\ge {10}^8{M}_{\odot }$. Comparing samples observed with the Max-Planck Millimeter Bolometer (MAMBO) at the 30-meter IRAM telescope at redshift 2 and 4, Omont et al. (2003) found that the FIR luminosities of the optically bright quasars in these samples do not evolve with redshift. Statistical tests for these (sub)mm observed quasars show a weak correlation between the optical and FIR luminosities (Omont et al. 2003; Beelen 2004; Cox et al. 2005), which is argued as an evidence for FIR emission from warm dust heated by star formation. The inferred star formation rate is $\sim {10}^3{M}_{\odot }y{r}^{-1}$ when assuming a normal initial mass function (IMF). This interpretation is supported by the fact that the radio-to-FIR ratios for the FIR-luminous sources are consistent with the range spanned by star forming galaxies (Carilli et al. 2001; Petric et al. 2006).

The Sloan Digital Sky Survey (SDSS, York et al. 2000) has identified 19 bright quasars at z$\sim$6 (Fan et al. 2000, 2001, 2003, 2004, 2006a). These quasars are unique, in that they are undergoing rapid accretion onto SMBHs with masses $\gtrsim {10}^9{M}_{\odot }$, within 1 Gyr of the Big Bang, an epoch approaching cosmic reionization (Fan et al. 2006c). These z$\sim$6 quasars have been observed at all wavelengths from the X-ray to the radio (eg. Bechtold et al. 2003; Pentericci et al. 2003; Shemmer et al. 2006; Jiang et al. 2006a; Petric et al. 2003). The X-ray to near-infrared (NIR) observations imply Spectral Energy distributions (SEDs) similar to those of local quasars. The integrated bolometric luminosities exceed $\gtrsim {10}^{13}{L}_{\odot }$, and the black hole masses are $\gtrsim {10}^9{M}_{\odot }$ (Willott et al. 2003; Iwamuro et al. 2004; Jiang et al. 2006a). Seven z$\sim$6 SDSS quasars (Fan et al. 2000, 2001, 2003) were observed at 350 GHz with the SCUBA camera at the James Clerk Maxwell Telescope or at 250 GHz with MAMBO. Three are detected by SCUBA (Priddey et al. 2003b; Robson et al. 2004) and two are detected by MAMBO (Bertoldi et al. 2003a). Deep VLA observations at 1.4 GHz were made for six sources, resulting in detections of two of them (Petric et al. 2003; Carilli et al. 2004).

SDSS J114816.64+525150.3 at $z=6.42$ is the best studied FIR luminous source at z$\sim$6. It was detected with SHARC II, the bolometer camera at the Caltech Submillimeter Observatory at 350 $\mu$m, SCUBA at 450 $\mu$m and 850 $\mu$m, MAMBO at 1.2 mm, and the VLA at 1.4GHz (Beelen et al. 2006; Robson et al. 2004; Bertoldi et al. 2003a; Carilli et al. 2004). Fits to the SED from the FIR to radio imply a warm dust component with a temperature of 55K (Beelen et al. 2006). The corresponding FIR luminosity is $2.2\times {10}^{13}{L}_{\odot }$ with an inferred dust mass of $4.5\times {10}^8{M}_{\odot }$. It is also the only z$\sim$6 source that has been detected in the CO and [C II] 158 $\mu$m emission lines (Bertoldi et al. 2003b; Walter et al. 2003; Walter et al. 2004; Maiolino et al. 2005). These CO observations reveal a large mass of molecular gas ($\sim 2\times {10}^{10}{M}_{\odot }$) in the host galaxy.

The (sub)mm through radio observations of J114816.64+525150.3 argue for a massive starburst in its host galaxy, because (i) the FIR to radio ratio of this source follows that of typical star forming galaxies in the local universe (Yun et al. 2001; Carilli et al. 2004), (ii) the huge amount of molecular gas in its host galaxy can provide the required fuel for massive star formation, and (iii) the star formation rates indicated by both FIR luminosity and [C II] 158$\mu$m line luminosity are $\sim {10}^3$ M${}_{\odot }$ yr${}^{-1}$ (Bertoldi et al. 2003a; Maiolino et al. 2005).

Nineteen z$\sim$6 SDSS quasars have been published to date (Fan et al. 2006b). These are an optically selected sample at the highest redshift. We are pursuing a series of (sub)mm through radio studies on this sample in order to (i) find the general dust and gas properties in the host galaxies of these highest redshift quasars, and (ii) search for star formation activity co-eval with the rapid growth of SMBHs in the early universe.

In this paper, we present new MAMBO-2 250 GHz observations of eleven, and VLA 1.4GHz observations of thirteen, z$\sim$6 SDSS quasars. Then, together with previously published results, we discuss the general far-infrared and radio properties of the optically selected quasars at z$\sim$6, focusing on luminosity correlations and evolution. We will also discuss the radio loud fraction of quasars. We will present further analysis of the FIR to radio SEDs and discuss possible star forming activity in a second paper (paper II). The sample and observations are described in section 2, and results are presented in section 3. In section 4 and 5, we analyse and discuss the general properties of FIR and radio luminosities for the entire sample and give the conclusion in section 6. We adopt a concordance cosmology with $H_0=71km{s}^{-1}Mp{c}^{-1}$, ${\Omega }_m=0.27$ and ${\Omega }_{\lambda }=0.73$ throughout this paper.

The sample of z$\sim$6 quasars are selected from about 6600 $de{g}^2$ of imaging data from the Sloan Digital Sky Survey (Fan et al. 2006b). Fan et al. (2000, 2001, 2003, 2004, 2006a) selected sources with very red $i-zcolors$ as z$\ge 5.7$ quasar candidates. These candidate sources were followed up with high quality spectroscopy. Nineteen z$\sim$6 quasars have been published by the SDSS survey (Fan et al. 2000, 2001, 2003, 2004, 2006a) with redshifts ranging from 5.74 to 6.42 and rest frame B band optical luminosities¹¹1$L_B\equiv \nu L_{\nu ,4400\text{AA}}$: $L_{\nu ,4400\text{AA}}$ is the luminosity density at rest frame $4400\text{AA}$. we calculate $L_{\nu ,4400\text{AA}}$ and $L_B$ from the AB magnitude at rest frame $1450\text{AA}$ in the discovering papers (Fan et al. 2000, 2001, 2003, 2004, 2006a), assuming an optical spectral index of -0.5. from ${10}^{12.5}{L}_{\odot }$ to ${10}^{13.3}{L}_{\odot }$. Most of the 13 objects we observed in this work were discovered in the past two years (Fan et al. 2004; 2006a) and have not been observed in the (sub)mm or radio bands before.

We compare the (sub)mm properties of the z$\sim$6 objects with luminous ($L_B\ge {10}^{12.5}{L}_{\odot }$) quasars at lower redshifts from the literature. We define a low redshift group, $1.5\le z\le 3.0$, using a sample from Omont et al. (2003) containing radio-quiet quasars with B-band absolute magnitude $-29.5\le M_B\le -27.0$ and redshift $1.8\le z\le 2.8$ observed by MAMBO at 250GHz, and a sample from Priddey et al. (2003a) of radio-quiet quasars with $-29.2\le M_B\le -27.5$ and $1.5\le z\le 3.0$. Our higher redshift group ($3.6\le z\le 5.0$) is drawn from the the Palomar Sky Survey (PSS) selected sample of Omont et al. (2001) ($M_B\le -27.0$; $3.9\le z\le 4.6$) and the SDSS sample of Carilli et al. (2001) ($-28.8\le M_B\le -26.1$; $3.6\le z\le 5.0$), both observed with MAMBO at 250 GHz. The 3$\sigma$ detection limits of the MAMBO observations by Omont et al. (2001) and (2003) are $\sim$1.5 to 4 mJy, and $\sim$1.4 mJy by Carilli et al. (2001). The typical 3$\sigma$ detection limit of SCUBA observations reported by Priddey et al. (2003a) is $\sim 10$ mJy at 350 GHz, which corresponds to an upper limit of $\sim$4 mJy at 250 GHz (assuming a warm dust SED with temperature $T_d=47K$ and emissivity index $\beta =1.6$).

A total of 13 z$\sim$6 SDSS quasars were observed in the course of the work presented here, all with the VLA at 1.4GHz and eleven (all but J000552.34-000655.8 and J104845.05+463718.3) with MAMBO-2 at 250GHz (See Table 1 for the source list). J104845.05+463718.3 was a published detection by MAMBO (Bertoldi et al. 2003a) and was observed by the VLA with a signal at 2.2$\sigma$ (Carilli et al. 2004). We re-observed it with the VLA, and combined all the data.

MAMBO-2 at the IRAM 30m telescope is a 117-channel bolometer array. The Half Power Beamwidth (HPBW) of each pixel is ${11}^{\prime \prime }$ and the spacing between horns is about ${20}^{\prime \prime }$. The effective sensitivity is about 40 mJy$s^{1/2}$. The new observations were made in the winters of 2004-2005 and 2005-2006 during pooled observations using the on-off mode, wobbling by ${32}^{\prime \prime }-{46}^{\prime \prime }$ in azimuth and at a rate of 2 Hz. The target sources are positioned on the most sensitive bolometer and the correlated sky noise is determined from the other bolometers and subtracted from the source bolometer. The median rms is $\sim$0.8 mJy (Table 1). We reduced the data with the MOPSIC software package (Zylka 1998) and standard scripts for on-off observation data.

The VLA observations were made with the A array, of which the maximum baseline is 30 km. The sources were observed at 1.4 GHz with two Intermediate Frequency bands ”IFs” and 50MHz bandwidth per IF. The corresponding Full Width at Half Maximum (FWHM) resolution is about ${1.4}^{\prime \prime }$. We observed each source for two to four hours to a typical rms noise level of $\sim$16 $\mu Jybea{m}^{-1}$ (Table 1). The data were reduced and images were made using the standard VLA wide field data reduction software AIPS.

We present our MAMBO-2 results of 11 sources and the VLA results of 13 sources in Table 1. The optical properties are taken from Fan et al. (2006b) and presented in Col. (1): the SDSS name, Col. (2): the redshift, and Col. (3): the AB magnitude at 1450$\text{AA}$. Col. (4) lists the radio 1.4GHz surface brightness at the optical position. Col. (5), (6), and (7) list the nearest radio peak position and peak surface brightness for detected sources. Col. (8) presents the 250GHz flux densities in mJy. We mark detections in bold face. For the source J000552.34-000655.8, there is a strong ($\sim$Jy) radio source in the field which precludes deep VLA radio imaging. The rms on the 1.4GHz map is 130 $\mu$Jy, which is an order of magnitude higher than the others, yielding an extremely high upper limit of $\sim$390 $\mu$Jy. Thus, we exclude this source in all of our analyses in this paper.

We show the radio 1.4GHz continuum images of the 12 remaining sources in Figure 1. We searched for $\ge 3\sigma$ peaks within a $0^{{}^{\prime \prime }}.6$ radius from the optical quasar position in the radio map. This is a combination of the positional uncertainty of $0^{{}^{\prime \prime }}.3$ between the radio and optical reference frames (Deutsch 1999) and the radio observation uncertainty of ${\sigma }_{pos}\sim \frac{FWHM}{SNR}\sim 0^{{}^{\prime \prime }}.5$²²2We require a signal to noise ratio (SNR) of 3 for detections here.. Six sources are detected at the $\ge 3\sigma$ level. According to the 1.4 GHz radio source counts (Fomalont et al. 2006, in prep.), we expect 0.003 detections with $S_{1.4GHz}\ge 50\mu Jy$ by chance, within the total search area around the 12 quasars.

We obtain four detections among the 11 sources with MAMBO. Three of the detections, J084035.09+562419.9 J092721.82+200123.7 and J133550.81+353315.8, are detected at $>4\sigma$. The fourth source, J081827.40+172251.8, is marginally detected at the $\sim 3\sigma$ level. As a comparison, the cumulative number counts of 250 GHz source is about 400 deg${}^{-2}$ with flux density $S_{250GHz}\ge 2.4mJy$ (Greve et al. 2004; Voss et al. 2006) which is the typical 3$\sigma$ limit of our observations. Thus we should expect 0.03 detections in our 11 fields by chance, given the ${11}^{\prime \prime }$ beam size of the MAMBO bolometer elements.

We summarize the (sub)mm and radio observations of the six previously observed quasars in the z$\sim$6 SDSS sample (Petric et al. 2003; Priddey et al. 2003b; Bertoldi et al. 2003a; Robson et al. 2004; Carilli et al. 2004) in Table 2. Col. (1), (2), and (3) give the name, redshift, and 1450$\text{AA}$ AB magnitude, and Col. (4), (5), (6), and (7) the flux densities at 250 GHz, 350 GHz, 667 GHz and 1.4 GHz.

Combining Tables 1 and 2, there are seventeen z$\sim$6 quasars that have been observed with MAMBO. Together with the results from SCUBA at 850 $\mu$m, there are eighteen z$\sim$6 SDSS quasars that have (sub)mm observations at the 1 mJy sensitivity level and 8 of them are detected at $\gtrsim 3\sigma$. The detection rate is $44\pm 16\%$. The detection rate of optically bright quasar samples at redshifts 2 and 4 is $\sim 30\%$ in Omont et al. (2001, 2003) with an rms level of $>1.5mJy$, and $\sim 39\%$ in Carilli et al. (2001) with a lower rms level of $\sim 1.4mJy$. Thus our detection rate at z$\sim$6 is slightly higher compared to these observations at lower redshifts, but is consistent within the errors.

Seventeen sources in the z$\sim$6 SDSS quasar sample have deep observations with the VLA at 1.4 GHz and 8 are detected at the $\gtrsim 3\sigma$ level. J083643.85+005453.3 is the only $>$1 mJy radio source at 1.4 GHz among them. It was detected by Petric et al. (2003), as well as in the FIRST survey (White et al. 1997), leading to a weighted average flux density of 1.74$\pm$0.04 mJy³³3The 1.4 GHz flux density for J083643.85+005453.3 is $1750\pm 40\mu Jy$ in Petric et al. (2003) and $1530\pm 150\mu Jy$ in the FIRST catalog. . Another source, J163033.90+401209.6, has not been observed with the VLA yet, and the FIRST catalog yields an upper limit of 0.44 mJy at the optical position (Bertoldi et al. 2003). We thus exclude this source in the analysis of radio properties in the next section.

The heating sources of the FIR emitting dust in quasars are studied and the contributions from host galaxy star formation are discussed in a number of papers (eg. Haas et al. 2003; Omont et al. 2003; Schweitzer et al. 2006). Star formation is believed to be the dominated dust heating resource in the local infrared luminous quasars that are located in ULIRGs (Hao et al. 2005). Schweitzer et al. (2006) studied the connection between FIR emission and PAH/low excitation fine-structure emission lines of the local PG quasars. Their results suggest that star formation is responsible for at least 30% to the average local quasar FIR emission and that this contribution tends to increase with FIR luminosity. The z$\sim$6 SDSS quasars we discussed in this paper belong to the population of the brightest quasars in the optical. About $1/3$ of them are detected at (sub)mm wavelength. According to Figure 4, most of these detections have FIR luminosities stronger than the predictions from local quasar templates, indicating extra emission from warm dust in these sources compared to the typical optical quasar emission. Moreover, the relationship between the FIR and B band optical emission is non-linear and significantly scattered, only manifesting itself when a larger luminosity range is considered (See Section 4.1). Beelen (2004) studied a number of optically bright quasar samples at $z>1.5$ that had (sub)mm observations, and first report this weak correlation between FIR and B band optical emission, namely $log{L}_{FIR}=(8.36\pm 0.90)+(0.33\pm 0.07)\times log{L}_B$ (See also Cox et al. 2005). The results are consistent when we include our new observations at z$\sim$6. Additionally, most of the (sub)mm detections at z$\sim$6 have FIR-to-radio ratios or upper limits within the range occupied by star forming galaxies (See Table 4 and Figure 6).

One possible explanation for all of these facts is that star formation is happening on a massive scale in the host galaxies of these FIR luminous z$\sim$6 quasars and dominating the heating process of the FIR emitting warm dust. The implied star formation rate is $\sim {10}^3{M}_{\odot }y{r}^{-1}$. This idea is supported by the detections of CO in the high-redshift quasars that have strong FIR emission ($L_{FIR}\gtrsim {10}^{13}{L}_{\odot }$). CO line emission was detected in several FIR luminous quasars at z$\gtrsim$4, including the highest redshift quasar J114816.64+525150.2 (eg. Riechers et al. 2006; Bertoldi et al. 2003b; Walter et al. 2003, 2004). The CO detections indicate huge amount of molecular gas in the host galaxies of these FIR luminous quasars which are the requisite fuel for star formation. Moreover, Riechers et al. (2006) found that the FIR-to-CO relation of the high-redshift FIR luminous quasars are consistent with that defined by ULIRGs, starforming galaxies and submillimeter galaxies.

One may argue that the strong FIR emission can be also processed by the AGN power since the dust torus geometry of these sources are still unkown. This possibility cannot be rule out given the limited data we have for these sources, but detailed dust models are required to explain the results we list above. One fact is that the hot dust emission of the SDSS z$\sim$6 quasars probed by recent Spitzer observation are similar to those of the local quasar templates as we mentioned in Section 1 (Jiang et al. 2006a). Four (sub)mm detections are included in this Spitzer observed sample, and no different properties are found in the optical to near infrared SEDs of these sources. This may not support the idea of a quite different geometry of the dust torus.

However, we should mention that there are still large uncertainties in the estimations of the FIR luminosities for these (sub)mm detected z$\sim$6 quasars. The FIR luminosities for some of the sources can be overestimated given the poor data at (sub)mm wavelengths. Thus further studies on these (sub)mm detected z$\sim$6 quasars are required, including observations of the submm continuum at higher frequencies and emission lines of CO and other molecules, such as HCN, as well as the C and $C^{+}$ fine structure lines.

Another interesting question is how the current radio observations constrain the radio loud fraction (RLF) at z$\sim$6. The RLF of optically selected quasar samples is $\sim 10\%$, as quoted in many papers (Kellermann et al. 1989; Ivezi$\acute{c}$ et al. 2002, 2004; Cirasuolo et al. 2003, 2006). Jiang et al. (2006b) studied the FIRST data (Becker et al. 1995) for SDSS quasars with redshifts up to 5, and suggested that the quasar RLF increases with optical luminosity and decreases with redshift, namely $log\left(\right(RLF\left)/\right(1-RLF\left)\right)=(-0.112\pm 0.109)+(-2.196\pm 0.269)log(1+z)+(-0.203\pm 0.026)(M_{2500}+26)$. This result gives an RLF of $\sim 37\%$ at $z=0.5$, $\sim 11\%$ at $z=2$, and $\sim 2\%$ at $z=6$, given the rest frame 2500$\text{AA}$ absolute AB magnitude $M_{2500}=-27.3$ — the typical value of the z$\sim$6 SDSS quasar sample⁶⁶6The $M_{2500}$ is estimated from the absolute AB magnitude at rest frame $1450\text{AA}$ ($M_{1450}$, Fan et al. 2006b). For the current sample of 19 z$\sim$6 SDSS quasars with $M_{1450}$ from -26.2 to -27.9, we adopt a typical value of $M_{1450}=-27.0$ and an optical spectral power law index of -0.5..

There is one marginally radio loud source in this z$\sim$6 sample of 17 sources. This result argues against a high RLF, i.e. $>20\%$, for the current SDSS quasar sample at z$\sim$6. Thus it is roughly consistent with the result of Jiang et al. (2006b). However, the sample size is still too small to set a strict constrain, i.e. differentiate an RLF between $\sim 2\%$ and $\sim 10\%$. Thus to provide a better test of the redshift evolution of the RLF; we would need a sample three times larger to usefully constrain the RLF at z$\sim$6.

We should also mention the recent discovery of a radio loud quasar at z$>$6, FIRST J1427385+331241(McGreer et al. 2006), with a FIRST flux density of 1.73mJy. This source is the most radio luminous quasar known at z$\sim$6, with $R_{1.4}^{\ast }>100$. However, it cannot be included in our radio loud analysis at z$\sim$6, as the selection criteria of this source are quite different from that of the SDSS quasars and its UV/Optical emission is just beyond the SDSS detection limits (McGreer et al. 2006).

In this paper, we present new results of millimeter and radio observations of a sample of z$\sim$6 quasars. These quasars are selected from the SDSS survey and observed with MAMBO-2 at 250 GHz and the VLA at 1.4 GHz. We obtained three $>4\sigma$ detections and one $\sim 3\sigma$ detection out of 11 observed sources by MAMBO-2 and six radio detections out of 13 observed sources by the VLA.

We combine our new millimeter and radio results of the SDSS z$\sim$6 quasars with results from the literature and discuss the FIR and radio properties of the optically selected quasars at z$\sim$6. Our conclusions are as follows.

• Eight out of 18 z$\sim$6 optically selected quasars are detected in the (sub)mm regime. This indicates a (sub)mm detection rate of $44\%$ at z$\sim$6 at mJy sensitivity. Within the errors, this is consistent with the $\sim$30% (sub)mm detection rate at lower reshift (eg. Carilli et al. 2001; Omont et al. 2001; 2003). The observational data imply FIR luminosities $\sim {10}^{13}{L}_{\odot }$ in the (sub)mm detected sources.
  

• We compare the distribution of FIR luminosities and FIR to optical ratios between the z$\sim$6 SDSS sample and (sub)mm observed optically bright quasars ($L_B\ge {10}^{12.5}{L}_{\odot }$) at lower reshifts. The distributions of the FIR-optical ratio are similar for different redshift groups, which suggests that the average optical-to-FIR SED of optically bright quasars is independent of redshift.
  

• We extend the quasar FIR-to-optical correlation study to the z$\sim$6 SDSS sample. No correlation is found with the z$\sim$6 sample only. However, a correlation (albeit with large scatter) can be seen when all the samples extending from z=1.5 to 6.42 are included.
  

• We also discussed the FIR-to-radio ratios of the z$\sim$6 quasars, by comparing them to the typical correlation defined by star forming galaxies. Three of the four sources that are detected in both the millimeter and radio bands have FIR-to-radio ratios within the range defined by star forming galaxies.
  

• We found no strong radio sources with $R_{1.4}^{\ast }\ge 30$ among the new SDSS sources of bright z$\sim$6 quasars. In the whole z$\sim$6 sample, only one radio detection has a radio to optical ratio $R_{1.4}^{\ast }\sim 40$ and no source has $R_{1.4}^{\ast }\gtrsim 100$. These data are consistent with, although do not set strong constraints on, the recent conclusion of a decreasing radio loud quasar fraction with increasing redshift (Jiang et al. 2006b).
  

These results give a view of the general FIR through radio properties of the z$\sim$6 SDSS quasars. The data are consistent with the idea that massive starbursts may exist in the host galaxies of the strong (sub)mm detections at z$\sim$6 and contribute to the FIR and radio emission. These strong (sub)mm sources provide the only candidates to search for CO and $C^{+}$ into the epoch of reionization, and to test the idea of co-eval SMBH and host galaxy formation. We may expect to go an order of magnitude deeper in a few years time with the coming instruments of the Expanded Very Large Array (EVLA) and the Atacama Large Millimeter Array (ALMA).