The Scatter in the Relationship between Redshift and the Radio-to-Submm Spectral Index

Transcription

1 University of Massachusetts Amherst From the SelectedWorks of Min S. Yun February 20, 2000 The Scatter in the Relationship between Redshift and the Radio-to-Submm Spectral Index C L Carilli Min S. Yun, University of Massachusetts - Amherst Available at:

2 THE ASTROPHYSICAL JOURNAL, 530:68È624, 2000 February 20 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. THE SCATTER IN THE RELATIONSHIP BETWEEN REDSHIFT AND THE RADIO-TO-SUBMILLIMETER SPECTRAL INDEX C. L. CARILLI National Radio Astronomy Observatory, PO Box O, Socorro, NM 8780; and Max Planck Institute for Radio Astronomy, Auf dem Hu gel 69, Bonn, Germany, D532; ccarilli=nrao.edu AND MIN S. YUN National Radio Astronomy Observatory, PO Box O, Socorro, NM 8780; myun=nrao.edu Received 999 August 3; accepted 999 September 30 ABSTRACT We derive the scatter in the relationship between redshift and the radio-to-submillimeter spectral index, a350, using the observed spectral energy distributions of 7 low-redshift star-forming galaxies. A mean galaxy model is derived, along with the rms scatter in a350. The scatter is roughly constant with redshift. Constant rms scatter, combined with the Ñattening of the mean a350-z relationship with increas- ing redshift, leads to increasing uncertainty for redshift estimates at high redshifts. Normalizing by the dust temperature in the manner proposed by Blain decreases the scatter in a350 for most of the sample, but does not remove outliers, and free-free absorption at rest frequencies above GHz is not likely to be a dominant cause of scatter in the a350-z relationship. We rederive the cumulative redshift distribu- tion of the 4 Ðeld galaxies in a recent submillimeter and radio source sample of Smail et al. The most likely median redshift for the distribution is 2.7, with a conservative lower limit of z \ 2, as was also found by Smail et al. based on the original models. The normalization and shape of the redshift distribution for the faint submillimeter sources are consistent with those expected for forming elliptical galaxies. Subject headings: galaxies: distances and redshifts È galaxies: evolution È galaxies: starburst È infrared: galaxies È radio continuum: galaxies. INTRODUCTION optical (R º 25) and near-ir (K º 2) sources (Smail et al. The sharp rise of observed Ñux density, S, with increas- 999b), in which case obtaining reliable optical redshifts is l ing frequency, l, in the Rayleigh-Jeans portion of the graybody difficult. Moreover, at these faint levels confusion in optical spectrum for thermal dust emission from star-forming Ðelds can be severe. At the limit of the Hubble Deep Field, galaxies (S P l3h4), leads to a dramatic negative K- one expects about Ðve sources in a typical faint submillimeter source error circle of 3A radius (Blain et al. 999c; l correction for observed Ñux density with increasing redshift. Submillimeter surveys thereby provide a uniquely distanceindependent Downes et al. 999; Hughes et al. 998). For comparison, sample of objects in the universe, meaning that the probability of detecting a radio source with S º 50 the observed submillimeter Ñux density of an object of given kjy in this same region is 0.04 (Richards 2000). Even crude intrinsic luminosity is roughly constant for z between and 7 (Blain & Longair 993; Hughes & Dunlop 998). Sensitive estimates of source redshifts that do not rely on identiðcation of the sources in the optical or near-ir are fundamental observations at submillimeter wavelengths are to our understanding of the faint submillimeter source revealing what may be a population of active star-forming galaxies at high redshift that are unseen in deep optical surveys due to dust obscuration (Smail, Ivison, & Blain 997; Barger et al. 998, 999c; Hughes et al. 998; Blain et al. 999a; Eales et al. 999; F. Bertoldi et al., in preparation). Current models suggest that this population may represent the formation of elliptical galaxies and galactic bulges at z between 2 and 5, constituting about half of the total amount of cosmic star formation from the big bang to the present (Barger et al. 999b, 999d; Tan, Silk, & Balland 999; Blain et al. 999b; Trentham, Blain, & Goldader 999; Lilly et al. 999; Smail et al. 2000). The faint submillimeter source counts suggest that a signiðcant population. We recently proposed the technique of using the radioto-submillimeter spectral index as a redshift indicator (Carilli & Yun 999). This technique is based on the universal radio-to-far-infrared (FIR) correlation for star-forming galaxies (Condon 992), with the extrapolation that the spectral shapes may be similar enough to allow us to di erentiate between low- and high-redshift objects. Even a gross indication of the source redshift distribution provides critical constraints on models of the star formation history of the universe using submillimeter source counts (Blain et al. 999b). Carilli & Yun (999) presented empirical models for the relationship between z and the observed spectral index revision is needed to the optically derived star for- between and 350 GHz, a350, based on the spectral mation history of the universe (Steidel et al. 999), with the energy distributions (SEDs) of Arp 220 and M82, plus semianalytic addition of a population of highly reddened active starforming galaxies not seen in deep optical surveys (Chapman et al. 999). However, this conclusion hinges on the currently models based on the equations in Condon (992), assuming a dust spectrum comparable to that of M82 (Gu sten et al. 992). We found that these simple models unknown redshift distribution of the faint submillimeter were in reasonable agreement with the few spectro- sources. Follow-up observations have shown that most faint submillimeter sources are associated with very faint scopically measured redshifts for high-z submillimeter sources, and we discussed possible reasons for the departure 68

3 SCATTER IN REDSHIFTÈSPECTRAL INDEX RELATIONSHIP 69 of sources from this relationship, including the presence of a radio-loud active galactic nucleus (AGN) and cooling of the synchrotron-emitting relativistic electrons due to inverse Compton scattering o the microwave background radiation. A subsequent paper by Blain (999) showed that very low dust temperatures (T \ 30 K) can also lead to departures from the standard relations. D In this paper we take a complimentary, empirical approach to the analytic approach of Blain (999), by looking at the mean and scatter in the a350-z relation using the observed SEDs of 7 low-z star-forming galaxies. Note that Blain (999) considered the logarithm of the Ñux density ratio between observed frequencies of 350 and GHz, while we use the spectral index. These quantities are simply related by a scale factor, log (350/) \ 2.4. We use H \ 75 km s~ Mpc~ and q \ ANALYSIS 2.. Scatter in the a350-z Relation Most of the galaxies in our study come from the recent submillimeter study of Lisenfeld, Isaak, & Hills (999), which is a subsample of bright IRAS galaxies observed in CO (È0) by Sanders, Scoville, & Soifer (99). Lisenfeld et al. detected 4 of 9 galaxies at 350 GHz using SCUBA on the James Clerk Maxwell Telescope (JCMT). As discussed in Lisenfeld et al., these galaxies span a wide range in IR luminosity, from luminous (L B 00 L ) to ultralumin- FIR _ ous (L B 02 L ), and in infrared-to-blue luminosity FIR _ ratio, and should be representative of the star-forming galaxy population, although the fact that these are IRASselected galaxies could lead to a bias toward warm dust. We have augmented this sample with three other star-forming galaxies with well-sampled SEDs from to 25,000 GHz (M82, IRAS 0589[2524, and UGC 50). The sources are listed in column () of Table. The process of deriving the redshift evolution of a350 entails Ðtting accurate polynomials to the observed SEDs at centimeter through IR wavelengths, then using these polynomials to predict the change in a350 with redshift (Carilli & Yun 999). Examples of the SEDs, plus polynomial Ðts, TABLE GALAXY SAMPLE L FIR Source a a4.9 a350 (]0 L ) q 0.33 _ () (2) (3) (4) (5) (6) Mrk [0.48 ]0.30 [ Arp [0.5 [0.37 ] Mrk [0.49 [0.27 [ UGC [0.69 [0.56 [ NGC [0.82 [0.70 [ Arp [0.54 [0.52 [ NGC [0.54 [ NGC [0.79 [0.67 [ NGC [0.73 [0.50 [ NGC [0.65 [0.79 [ NGC [0.27 [0.26 ] NGC [0.79 [0.78 ] NGC [0.89 [ NGC [0.56 [0.77 ] M82... [0.34 [0.6 [ IRAS 0589[ [ Zw [0.70 [ TABLE 2 MEAN GALAXY MODEL a350 z z z` mean ~ () (2) (3) (4) [7 for four of the galaxies are shown in Figure. The Ðtting process is required to interpolate the discretely sampled data points to unsampled spectral regions. As with any interpolation process, errors will occur in unsampled regions, and the errors will increase as the sampling decreases. This is particularly true for the six sources in the sample with only one millimeter or submillimeter measurement (NGC 30, 535, 5256, 5653, 5936, and Zw 049). Such errors are difficult to quantify. We have performed the analysis excluding these sources, and Ðnd no substantial changes in the results. Table lists the spectral index between 0.33 and GHz (col. [2]), and 5 GHz (col. [3]), and 350 GHz and GHz (col. [4]), the FIR luminosities (col. [5]), and the radio-to-fir ratio (col. [6]), as quantiðed in the q parameter deðned by Condon (992), q 4 log [(S ] 2.6S )/ S ], where S is the Ñux density at GHz in Jy, and S and S are the Ñux densities at 60 and 00 km, respec tively, in Jy. The sources are ordered in decreasing FIR luminosity. Condon (992) has found for a large sample of nearby spiral galaxies a mean value of q \ 2.3, with an rms scatter of 0.2. The galaxies in our sample generally fall within 2 p of this value. The z \ 0 values for a350 have a mean of B0, and an rms scatter (4 p) of 0.4. Using the polynomial Ðts to the radio-to-ir SEDs, we have derived the evolution of a350 with redshift for all 7 sources in Table. The results are shown in Figure 2. The solid curves show the distributions for sources with L [ 2 ] 0 L, while the dashed curves show the distributions FIR for sources _ with L \ 2 ] 0 L. The high-luminosity sources have, on average, FIR lower values _ of a350 than the low-luminosity sources. The mean value of a350 varies from [0.026 at z \ 0to]0.97 at z \ 7 for the high-luminosity sources, while the corresponding values for the low-luminosity sources are [0.06 and ].8, respectively. ConÐrmation of this trend of a350 with FIR luminosity requires signiðcantly larger galaxy samples with well-observed radio-to-ir SEDs. We derive the mean and rms scatter of a350 as a function of redshift using the curves in Figure 2 for all 7 sources. This mean galaxy model is shown by the solid curve in Figure 3, while the dotted curves delineate the ^ p range, as determined from scatter in the distribution of sources. We designate these curves z, z`, and z, respectively. For a normal distribution, the mean ^ p range implies ~ that 67% of the sources in a given sample would fall within the range

4 620 CARILLI & YUN Vol FIG..ÈData points show the radio through infrared spectral energy distributions of four representative galaxies from our sample of 7 listed in Table. The data are obtained from NED (IRAS data points), the NRAO VLA Sky Survey (Condon et al. 998), the Westerbork Northern Sky Survey (Rengelink et al. 997), and from Rigopoulou et al. (996), Benford (999), and Lisenfeld et al. (999). The solid curves show polynimial Ðts to the data. For the M82 spectrum, the straight lines indicate the spectral index that would be derived for the source at z \ 0 and z \ 3 between observing frequencies of and 350 GHz. set by the dotted curves in Figure 3. The rms scatter is roughly constant with redshift, decreasing from 0.4 at z \ 0 to 0.2 at z \ 7. Constant scatter in a350, combined with the Ñattening of a350 with increasing z, implies that the uncertainty in redshift estimates based on measured values of a350 increases with z. Table 2 lists the mean, z (col. [3]), and ^ p error ranges, and z (cols. [2] and mean [4]), for likely redshifts given a measured z` value ~ of a350 (col. []). We Ðnd that the mean galaxy model, z, can be rea- sonably parameterized by a fourth-order mean polynomial, z \ [ 0.308a ] 2.4a2[ 23.0a3] 4.9a4, with a maximum deviation, dz, between the polynomial Ðt and the mean galaxy model of dz \ 0.3. For values of a350 º 0.9, only a likely lower limit to a source redshift can be derived. The dashed curve in Figure 3 shows the a350-z relationship derived for Arp 220, which has been used as a representative template for the a350-z relationship by Barger, Cowie, & Richards (999a). The data points in Figure 3 are for observed submillimeter sources with measured spectroscopic redshifts, as summarized in Carilli & Yun (999). This includes a number of sources with AGN-type spectra, as discussed in detail in Yun et al. (2000). The sources H43]7 and BR 0952[05 are shown to demonstrate how the presence of a radio-loud AGN a ects the position of a source on this diagram. Carilli & Yun (999) point out that, given a source redshift, this diagram can be used to search for evidence of a radio-loud AGN E ects of Dust T emperature Blain (999) has hypothesized that dust temperature may have an important impact on the scatter in the a350-z relationship, leading to a degeneracy between high-redshift, hot-dust sources, and low-redshift, cold-dust sources. He showed that this e ect can be mitigated by considering the quantity ( ] z)/t. In Figure 4 we plot the a350 values against ( ] z)/t, D using dust temperatures from Lisenfeld et al. (999), Gu D sten et al. (992), and Rigopoulou, Lawrence, & Rowan-Robinson (996), with T normalized to D the mean dust temperature of 39 K for the sample. Again,

5 No. 2, 2000 SCATTER IN REDSHIFTÈSPECTRAL INDEX RELATIONSHIP FIG. 2.Èa350-z relation for the 7 galaxies in Table, derived from the polynomial Ðts to the centimeter through IR SEDs. The solid curves show the distributions for sources with L [ 2 ] 0 L, while the dashed curves show the distributions for sources FIR with L \ _ 2 ] 0 L. Note that the spectral index is related to the log Ñux density FIR ratio by the _ scale factor log (350/) \ 2.4. the solid lines show high-luminosity sources, while the dashed lines show low-luminosity sources. If we consider all the sources, the rms is dominated by two sources, NGC 448 and Mrk 23, and the rms scatter of a350 at a given value of ( ] z)/t has not decreased signið- D FIG. 3.ÈMean a350-z relation for the 7 galaxies in Table, derived from the curves in this Ðgure, shown by a solid line. The ^ p curves are shown as dotted lines. In the text, we designate these curves z (solid line), (dotted line), and z (dotted line), respectively. The long-dashed mean line shows z` Arp 220. Filled circles ~ and squares respectively represent galaxies with and without an AGN signature in the optical spectrum. A possible systematic vertical o set between the galaxies with and without an AGN suggests excess radio emission associated with the AGN. The data points are for sources taken from Yun et al. (2000) and references therein. FIG. 4.Èa350-( ] z)/t relation for the 7 galaxies in Table, derived from the polynomial Ðts shown D in Fig. 2, and normalized to the sample mean T \ 39 K. The solid curves show the distributions for sources with L [ 2 D ] 0 L, while the dashed curves show the distributions for sources FIR with L \ _ 2 ] 0 L. FIR _ cantly from that in Figure 2 (pb0.3). However, if we remove the two outliers, we Ðnd a signiðcant decrease in the rms values, from 0. for the distribution in Figure 2 to for the distribution in Figure 4, and the rms is roughly constant with ( ] z)/t. D 2.3. V ariations in Radio Properties The radio spectral indices from 330 MHz through 5 GHz for the sources listed in Table show a large scatter, from [0.2 to [0.9. The canonical value for synchrotron emission from star-forming galaxies is [0.8 (Condon 992). Possible causes for Ñatter spectra include () free-free absorption at low frequencies, (2) free-free emission at high frequencies, or (3) a synchrotron self-absorbed AGN component. Here we examine the possible contribution of freefree absorption to the observed values of a350. We compare the observed spectral indices between and 5 GHz to those between 0.33 and GHz (cols. [2] and [3] in Table ). No evidence for systematic Ñattening of the spectra with increasing star-forming activity is found for the majority of the galaxies, as would occur due to free-free absorption. However, the presence of a patchy absorbing medium could lead to complicated spectral shapes, and this alone is not a sufficient reason to rule out the importance of free-free absorption. One method used by Condon et al. (99) to investigate the possibility of free-free absorption at GHz was to correct the radio spectra by assuming a constant radio spectral index of [0.8 and normalizing to the observed Ñux densities at 5 GHz. This analysis will mitigate free-free absorption e ects at least out to z \ 2.6 ( ] z \ 5/). We have investigated this possibility for the galaxies in our sample with 5 GHz detections. We Ðnd that the rms scatter at low redshift decreases only marginally, from 0.4 to 0.2. Given these results, and the fact that free-free opacity decreases quadratically with increasing frequency, we con-

6 622 CARILLI & YUN Vol. 530 clude that free-free absorption for rest frequencies above GHz is not likely to be a dominant cause of scatter in the a350-z relationship. Multifrequency, high-resolution radio imaging of a large sample of star-forming galaxies is required to properly address this issue T he Redshift Distribution of Faint Submillimeter Sources Smail et al. (999a) have discussed using a statistical distribution for source redshifts to provide constraints on models of the star formation history of the universe using submillimeter source counts. Based on the original Carilli & Yun (999) and Blain (999) models for the a350-z relation- ship, they concluded that the median redshift for their faint submillimeter sources is likely to be between 2.5 and 3, with a conservative lower limit of about 2. We have repeated the cumulative redshift distribution analysis of Smail et al. (999a) using the values of a350 for the 4 Ðeld galaxies in their Table, plus our new a350-z model. The results are shown in Figure 5. Note that for seven of these galaxies only lower limits to a350 are avail- able, which leads to lower limits to the possible redshifts. We have performed the analysis using both and z z` mean curves, as shown in Figure 3. The model leads to a z` conservative lower limit to the median redshift of the sources of 2.05, while the z model leads to a median mean redshift of These results strengthen the primary conclusions of Smail et al. (999a) that the majority of the faint submillimeter sources are likely to be at z º 2, and that there is no prominent low-z tail in the distribution FIG. 5.ÈPlot of the cumulative redshift distribution for the 4 Ðeld galaxies from the Smail et al. (999a) sample. The dashed line shows the distribution predicted using the model, while the solid line shows the distribution predicted using the z z` model. Note that seven of the sources in the Smail et al. (999a) sample mean have only lower limits to the values of a350, so these curves should be considered strictly lower limits to the true distributions. In addition, for three of the galaxies reliable spectroscopic redshifts are available. The dotted line shows the expected fraction of uncollapsed 02 M structures derived using the standard cold dark matter Press-Schechter _ formalism with a bias factor of 2 (Peebles 993). There are three Ðeld galaxies in Table of Smail et al. (999a) with reliable spectroscopic redshifts. For two of the sources, SMM J40]0252 at z \ 2.55 and SMM J02399[034 at z \.06, the redshifts spec predicted by the mean galaxy model spec in Figure 3 are remarkably close to the spectroscopic values, z \ 2.53 and.0, respectively. For the source SMM model J02399[036, the mean galaxy model predicts a redshift of.65, which is well below the spectroscopic redshift of This may indicate the presence of a radio-loud AGN in this source, and the source has been shown to contain an optical AGN, and possibly an extended radio jet source (Ivison et al. 998). On the other hand, the source is not far beyond the limit of z \ 2.45 predicted by the z model in Figure 3. For comparative ~ illustration, the dotted line in Figure 5 shows the expected fraction of uncollapsed 02 M structures derived using the standard cold dark matter _ Press- Schechter formalism with a bias factor of 2 (Peebles 993). There is an interesting, perhaps fortuitous, similarity between the observed redshift distribution for the formation of structures of this mass, comparable to elliptical galaxies, and the redshift distribution of the faint submillimeter sources. In particular, structures of this mass Ðrst separate from the general expansion of the universe and collapse under their own self-gravity at z B 5, and are mostly in place by z B (Kaiser & Cole 989). 3. DISCUSSION We have derived the mean and rms scatter for redshift estimates based on the a350-z relationship from a sample of 7 low-z star-forming galaxies with well-sampled centimeter to infrared SEDs. We emphasize that this analysis should be treated as strictly statistical. Given the rms scatter in a350, and the shallow slope of the a350-z relationship at high redshift, the uncertainty in the redshift for any individual source is large. However, for a large sample of sources, and assuming a normal error distribution, one can say that 67% of the sources are within the ^ p curves in Figure 3, and that 84% of the sources are at redshifts higher than the ] p curve in Figure 3. We have repeated the analysis using the median values plus inner quartile ranges, and reach essentially the same conclusions, although the outliers tend to increase the error range when considering rms deviations. Applying the mean galaxy model to the sample of Smail et al. (999a), we Ðnd that 80% of the sources are likely to be between z \.5 and 4. Blain et al. (999a) have derived a cumulative source surface density of 2.2 sources arcmin~2 for sources with Ñux densities º mjy at 350 GHz, after correcting for magniðcation by gravitational lensing. The implied comoving number density is then 9.5 ] 0~4 Mpc~3. These sources correspond to star-forming galaxies with FIR luminosities comparable to, or larger than, that of Arp 220. The comoving space density of these high-z sources is a factor of 03 larger than that of low-z ultraluminous infrared galaxies (Sanders & Mirabel 996), and is comparable to that of low-z elliptical galaxies (Lilly et al. 999; Cowie & Barger 999). Hence, the normalization and shape of the redshift distribution (see Fig. 5) for the faint submillimeter sources are consistent with those expected for forming elliptical galaxies (Tan et al. 999). The uppermost curve in Figures 2 and 4 shows the dis-

7 No. 2, 2000 SCATTER IN REDSHIFTÈSPECTRAL INDEX RELATIONSHIP 623 tribution for NGC 448, while the lowest curve is for Mrk 23. Mrk 23 is well known to contain a radio-loud AGN, although there is also evidence for radio emission from a starburst disk (Downes & Solomon 998; Carilli, Wrobel, & Ulvestad 999b; Taylor et al. 999). Below GHz the spectrum appears to be dominated by a possible starforming disk seen on subkiloparsec scales, while above GHz the parsec-scale AGN component raises the total Ñux density by about a factor of 2 (Taylor et al. 999). In fairness to high-z samples, for which such detailed imaging information is not available, we have made no attempt to remove the AGN emission for Mrk 23 in the mean galaxy model shown in Figure 3. The relatively Ñat radio spectrum of NGC 448 (a4.9 \ [0.26) may indicate that the source is partially free-free 0.33 absorbed, thereby leading to the source appearing radio-quiet with respect to most low-z starforming galaxies. In addition, Lisenfeld et al. (999) have pointed out that the dust spectrum of NGC 448 is anomalous relative to the rest of their sample, with a low value of b and a high dust temperature, leading to the unusual distribution for the source in the temperature-corrected curves shown in Figure 4. Lisenfeld et al. suggest that such an anomalous dust spectrum may be due to signiðcant dust opacity at submillimeter wavelengths. Whether such optical depth e ects (free-free absorption at centimeter wavelengths and dust opacity at submillimeter wavelengths) are important for a signiðcant fraction of high-redshift sources remains to be determined. We have found that the scatter in a350 decreases by about 30% when the dust temperature is also included in the analysis, as predicted by Blain (999), with the exception of the two anomalous sources discussed above. Unfortunately, even after correcting for dust temperature, the allowed range in redshift for a given value of a350 is large, e.g., for a350 \ 0.8 and T \ 39 K, the ^ p redshift range is D.9 \ z \ 2.9, further emphasizing that the a350-z relation- ship should be used statistically, and not be considered an accurate measure of an individual sourceïs redshift. A further complication is that accurate determination of T D requires sensitive observations to be made at a number of millimeter and submillimeter wavelengths. Implicit in the analysis given in 2 is the assumption that there is no systematic change in the intrinsic SEDs for starforming galaxies with redshift, as might occur through cooling of the synchrotron-emitting relativistic electrons by inverse Compton scattering o the microwave background radiation at high z, or by a systematic change in the interstellar matter (ISM) magnetic Ðelds in high-z galaxies. Such a variation can only be tested with extensive observations at centimeter through submillimeter wavelengths of a large sample of high-z star-forming galaxies with known redshiftsèa task that remains problematic at present. The sparse data that currently exist appear to be consistent with the derived models based on low-z galaxies. A massive star-forming galaxy with a star formation rate of a few hundred M year~ at z \ 3 has a submillimeter Ñux density of a few _ mjy at 350 GHz and a radio Ñux density of º20kJy at GHz (Carilli & Yun 999; Cowie & Barger 999). Such Ñux levels are currently accessible with long integrations using existing bolometer arrays on millimeter and submillimeter telescopes, and using the Very Large Array (VLA). In some studies, magniðcation by cluster gravitational lensing has been used to improve the e ective senstivities by a factor of 2 or so (Smail et al. 997). Future instrumentation, such as the Atacama Large Millimeter Array and the upgraded VLA, should be able to detect high-z galaxies with star formation rates of the order of 0 M yr~. Moreover, the very wide bandwidths (º8 _ GHz) available on these future instruments will allow for searches for CO emission over large redshift ranges in reasonable integration times, thereby bypassing the requirement of optical spectroscopy for accurate redshift determinations. We would like to thank the referee, I. Smail, and R. Ivison, A. Blain, F. Owen, F. Bertoldi, and K. Menten for useful comments and discussions. C. C. acknowledges support from the Alexander von Humboldt Society. The National Radio Astronomy Observatory is operated by Associated Universities, Inc., under a cooperative agreement with the National Science Foundation. This research made use of the NASA/IPAC Extragalactic Data Base (NED), which is operated by the Jet propulsion Lab, Caltech, under contract to NASA. REFERENCES Barger, A. 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