The Radio-to-Submm Spectral Index as a Redshift Indicator C. L. Carilli and Min Su Yun National Radio Astronomy Observatory, P.O. Box O, Socorro, NM, 87801 9 Received ; accepted 9 9 1 n a December 17, 1998; to appear in Astrophysical Journal (letters) J 2 1 4 v 1 5 2 2 1 8 9 / h p - o r t s a : v i X r a – 2 – ABSTRACT We present models of the 1.4 GHz to 350 GHz spectral index, α350, for 1.4 starburst galaxies as a function of redshift. The models include a semi-analytic formulation, based on the well quantified radio-to-far infrared correlation for low redshift star forming galaxies, and an empirical formulation, based on the observed spectrum of the starburst galaxies M82 and Arp 220. We compare the models to the observed values of α350 for starburst galaxies at 1.4 low and high redshift. We find reasonable agreement between the models and the observations, and in particular, that an observed spectral index of α350 ≥ +0.5 indicates that the target source is likely to be at high redshift, 1.4 z ≥ 1. The evolution of α350 with redshift is mainly due to the very steep 1.4 rise in the Raleigh-Jeans portion of the thermal dust spectrum shifting into the 350 GHz band with increasing redshift. We also discuss situations where this relationship could be violated. We then apply our models to examine the putative identifications of submm sources in the Hubble Deep Field, and conclude that the submm sources reported by Hughes et al. are likely to be at high redshifts, z ≥ 1.5. Subject headings: radio continuum: galaxies — infrared: galaxies — galaxies: redshifts, starburst, evolution – 3 – 1. Introduction Detecting submm continuum emission from objects at z ≥ 2 has revolutionized our understanding of galaxies at high redshift (Hughes et al. 1998, Ivison et al. 1998, Smail, Ivison, and Blain 1997, Eales et al. 1998, Barger et al. 1998). The emission is thought to be thermal emission from warm dust, with implied dust masses ≥ 108 M . A number of these ⊙ submm sources have also been detected in CO emission with implied molecular gas masses ≥ 1010 M (Brown & Vanden Bout 1991, Barvainis et al. 1994, Ohta et al. 1996, Omont ⊙ et al. 1996a, Guilloteau et al. 1997, Frayer et al. 1998). The large reservoirs of warm gas and dust in these systems has led to the hypothesis that these are starburst galaxies, with massive star formation rates ≥ 100 M year−1 (Hughes & Dunlop 1998). In some ⊙ cases, there may be an associated active galactic nucleus (AGN), leading to questions about the dominant dust heating mechanism – star formation, or AGN, or both (cf. Sanders & Mirabel 1996, Downes & Solomon 1998, Smith et al. 1998)? A well studied phenomenon in nearby star forming galaxies is the radio-to-far IR correlation, ie. the tight correlation found between the radio continuum emission and the thermal dust emission (Condon 1992, Helou and Bicay 1993). The radio continuum emission is thought to be synchrotron radiation from relativistic electrons spiraling in interstellar magnetic fields. The standard explanation for the radio-to-far IR correlation involves relativistic electrons accelerated in supernova remnant shocks, and dust heated by the interstellar radiation field. Both quantities are then functions of the massive star formation rate (Condon 1992, Cram et al. 1998, Yun et al. 1998, Gruppioni, Mignal, and Zamorani 1998), although the the detailed physical processes giving rise to the tight correlation remain enigmatic. If the radio-to-far IR correlation is independent of redshift, then the sharp rise in the the Raleigh-Jeans portion of the thermal dust spectrum shifting into the 350 GHz band with increasing redshift implies that the observed spectral index – 4 – between radio and submm frequencies should evolve strongly with redshift (Hughes et al. in preparation). In this paper we explore the possibility of using the radio-to-submm spectral index as a redshift indicator for star forming galaxies. Models of the expected spectral index between 1.4 GHz and 350 GHz (850 µm), α350, are presented based on the standard relationships 1.4 derived for nearby star forming galaxies, and on the observed spectra of two ‘canonical’ starburst galaxies, M82 and Arp 220. We present a simple analytic expression relating redshift to α350, and we compare the models to the observed values of α350 for starburst 1.4 1.4 galaxies at low and high redshift. We find reasonable agreement between the models and the observations, and in particular, that an observed spectral index of α350 ≥ +0.5 indicates 1.4 that the target source is likely to be at high redshift, z ≥ 1. We discuss possible ‘confusing’ mechanisms which could complicate the analysis, such as radio emission driven by an AGN, dust heated solely by a radio quiet AGN, and free-free absorption at low radio frequencies. We then apply our models to examine the putative identifications of submm sources in the Hubble Deep Field (HDF). 2. Analysis Condon (1992) presents semi-analytic, linear relationships between the massive star formation rate and the radio and far IR emission from active star forming galaxies. We have used these relationships to derive a simple relationship between redshift and α350, 1.4 by making a simplifying assumption that the source spectrum can be characterized by two power-law spectra, one at low frequencies (observing frequency ≤ 30 GHz) with a spectral index α , and one at high frequencies (observing frequency between 230 GHz radio and 850 GHz), with index α . We define spectral index in terms of frequency, ν, and submm the observed flux density, Sν, as: Sν ∝ να. Equation 21 in Condon (1992) relating radio – 5 – synchrotron luminosity to massive star formation rate can be written in terms of observed flux density as: (1+z)1+αradio ν S = 4×1028[ ][ radio ]αradio ×SFR erg cm−2 s−1 Hz−1 (1) radio 4πD2 1.4 GHz L where S is the observed radio flux density due to synchrotron emission, ν is the radio radio observing frequency, D is the source luminosity distance, and SFR is the star formation L rate for stars with masses ≥ 5 M , in units of M year−1. The equation relating submm ⊙ ⊙ emission from warm dust to massive star formation rate can be derived using the Condon’s Equation 26, assuming a spectrum of the form observed for nearby active star forming galaxies such as M82: (1+z)1+αsubmm ν S = 1×1028[ ][ submm ]αsubmm ×SFR erg cm−2 s−1 Hz−1 (2) submm 4πD2 350 GHz L where S is the submm flux density due to thermal dust emission, and ν is the submm submm observing frequency. We use Ho = 75 km s−1 Mpc−1 and qo = 0.5 where required. Taking the ratio of these two expressions, it is straight forward to show that the spectral index between 1.4 GHz and 350 GHz, α350, behaves as a function of redshift, z, as: 1.4 α350 = −0.24 − [0.42×(α −α )×log(1+z)] (3) 1.4 radio submm This relationship is plotted in Figure 1. For α we adopt the standard value in Condon radio (1992) of −0.8. For α we use values of +3.0 (solid curve) and +3.5 (short dashed submm curve). Note that the observed spectral indices between 270 GHz and 850 GHz for M82 and Arp 220 are +3.4 and +3.0, respectively. We have also derived values of α350 as a function of redshift for two ‘canonical’ starburst 1.4 galaxies, M82 and Arp 220. These two galaxies have well sampled spectra over the entire frequency range from the radio into the optical (Klein et al. 1988, Scoville et al. 1991). The α350 models were derived by fitting accurate polynomials to the observed data from 1.4 1.4 – 6 – GHz to 22 GHz, and from 230 GHz to 20000 GHz. These results are shown in Figure 1 as a dotted curve for M82 and a long dashed curve for Arp 220. The empirical models for M82 and Arp 220 differ from the simplified two power-law models in two important ways. First, the observed spectral indices at zero redshift are typically higher for the empirical models relative to the two power-law model. This difference is most likely due to a low frequency flattening at 1.4 GHz due to free-free absorption in the denser HII regions in the galaxy (Condon 1992). For instance, the observed spectral index for M82 between 1.4 and 5 GHz is −0.58, while the spectral index between 5 GHz and 10.7 GHz is −0.72 (Klein et al. 1988). And second, the two power-law model diverges at large redshift while the empirical models flatten and eventually turn-over at z > 7. This effect is due to the fact that the thermal spectra peak around 3000 GHz (100 µm) for a dust temperature of 30 K. An observed frequency of 350 GHz corresponds to a rest frame frequency of 3000 GHz at z = 7.5, hence at higher redshift the spectrum has gone ‘over-the-top’ of the thermal peak. Plotted on Figure 1 are values of α350 for galaxies detected at 350 GHz and 1.4 GHz. 1.4 The submm data for the low redshift galaxies are from a survey of nearby active star forming galaxies using the JCMT (Hughes et al. 1990, Rigopoulou et al. 1996) while the submm data for the z > 1 sources are from Rowan-Robinson et al. (1993), Isaak et al. (1994), Barvainis et al. (1995), Omont et al. (1996b), Dey et al. (1998), Cimatti et al. (1998), Ivison et al. (1998ab), Lewis et al. (1998), Eales et al. (1998), and Kawabe et al. (1998). All the radio data are from the Very Large Array (VLA) (see also Fomalont et al. 1991). Overall, the models appear to define (within the errors) the range in observed values of α350 as a function of redshift. In particular, the galaxies at z > 1.5 have α350 values ≥ 1.4 1.4 +0.5, while the low redshift galaxies have α350 values ≤ +0.2. 1.4 The scatter in the data for low redshift galaxies is, again, due in part to variations in – 7 – free-free absorption at 1.4 GHz between sources. In the more extreme cases, the implied (mean) free-free optical depths are ≥ 1 at 1.4 GHz, implying emission measures ≥ 6×106 × (TK)23 for the starburst regions (Taylor et al. 1998). Note that this phenomenon is relevant 104 only for low z galaxies since the low frequency turnover rapidly shifts out of the 1.4 GHz band with increasing redshift. The scatter in the data at high redshift may be due, in part, to contamination of the radio emission by an active nucleus. The frequency of radio AGNs among an IR selected galaxy sample is about 10% for galaxies with LFIR ≥ 1011 L⊙ (Yun et al. 1998). Radio AGN emission will cause the observed value of α350 to fall below the values predicted for 1.4 star forming galaxies. One clear example of this in Figure 1a is the Clover Leaf Quasar, H1413+117 at z = 2.56 (Barvainis et al. 1995), which has a rest frame radio continuum luminosity of 1.3×1032 ergs s−1 Hz−1 at 1.4 GHz, allowing for a magnification factor of 7.6 by gravitational lensing. Even corrected for lensing, the implied star formation rate is unreasonably high (3300 M year−1 using Eq. 21 of Condon 1992), and the expected 350 ⊙ GHz flux density is 230 mJy. The observed 350 GHz flux density is a factor of five lower. It is likely that H1413+117 is a Fanaroff-Riley Class I (‘FRI’ = low luminosity) radio galaxy, with a radio luminosity two times larger than M87. One method for separating AGN-driven radio emission from starburst driven radio emission is sub-arcsecond imaging in the radio and submm, to look for spatial coincidence of the radio and submm emission. Note that we have not included the submm detections of high redshift Fanaroff-Riley Class II (high luminosity) radio galaxies in this study, such as 4C 41.17 at z = 3.8 and 1435+635 at z = 4.25 (Hughes & Dunlop 1998). The extreme radio powers of these objects (1000 × M87) imply α350 ≤ −0.5, which is off the bottom of Figure 1, and they can be unambiguously 1.4 recognized as such. A third possible uncertainty in Figure 1 can arise due to gravitational lensing. A – 8 – number of the high redshift sources are known to be gravitational lenses (cf. Barvainis 1998, Blain 1998). If the radio continuum and submm emission are roughly co-spatial, as would be the case for a starburst galaxy, then gravitational lensing will not affect the α350 1.4 values. However, if the radio emission is distributed differently than the submm emission, as could occur for a radio loud AGN, then differential magnification by a lens could lead to significant variations in the observed α350. 1.4 The general agreement between the models and the data in Figure 1 arises mainly from the very sharply rising submm spectrum of thermal dust emission (α ≥ +3). submm This sharp rise in the submm spectrum, coupled with the large ‘lever-arm’ in frequency between 1.4 GHz and 350 GHz, can mitigate the uncertainties in the radio spectrum, such as free-free absorption, or even low luminosity radio AGN emission (cf. Schmitt et al. 1997). A submm frequency of 350 GHz is a good choice for this study, since it is close to the minimum on the Raleigh-Jeans part of the thermal dust spectrum for low z galaxies (cf. Condon 1992), for which the value of α350 should be close to zero, and it does not reach 1.4 the peak in the dust emission spectrum until z ≈ 7 (see above), where α350 ≥ 1. Since 1.4 the strength of the method lies in the steep rise in the dust spectrum, van der Werf et al. (1999) have recently performed an analogous analysis using the optical-to-far IR spectral index as a redshift indicator. One problem that occurs in the optical is confusion. A typical submm error box of 3′′ has a 50% chance of containing a ‘random’ optical galaxy at the limit of the HDF (I ≤ 29; Williams et al. 1996), while at 1.4 GHz the probability is only 814 1% for finding a ≥ 10 µJy source in the error box (Langston et al. 1990). 3. Discussion Figure 1 can be considered in two ways. The first is as a redshift indicator for star forming galaxies. In this regard, the most important conclusion that can be reached from – 9 – Figure 1 is that a value of α350 ≥ +0.5 indicates that the source is likely to be at high 1.4 redshift, z ≥ 1. One possible mechanism that could lead to larger α350 values for starburst galaxies 1.4 than predicted by the models based on the radio-to-far IR correlation would be to ‘quench’ the radio continuum emission associated with star formation through inverse Compton losses off the microwave background radiation field. However, this mechanism is likely to become important only at very high redshift (z ≥ 6). The energy density in the microwave background increases as (1+z)4, which, at z = 6, corresponds to the energy density in a magnetic field of about 100 µG – comparable to the expected interstellar magnetic fields in starburst nuclei (Condon et al. 1991, Carilli et al. 1998). The lifetime for a relativistic particle radiating at a rest frequency of 10 GHz (= 1.4 GHz observed frequency), is then 0.5 Myr. Contamination of the radio continuum emission by a low luminosity radio AGN could lead to an ambiguity for values of α350 ≤ +0.2, such that the source is either a starburst 1.4 galaxy at low redshift, or a radio loud AGN at higher redshift. The amount of contamination by radio loud AGN in a given galaxy sample will depend on the relative cosmic density of active star forming galaxies versus radio loud AGN, and on the flux density limits of the observations. Assuming sensitive observations can be made of galaxies with star formation rates of order 10 M year−1 out to high redshift (see below), then the expected ⊙ contamination by FRI-class radio galaxies should be ≤ 30%, based on galaxy populations at low redshift (Yun et al. 1998, Osterbrock 1989, Hammer et al. 1995, Richards et al. 1998). Of course, this fraction could change with redshift (Gruppioni et al. 1998). The second use for Figure 1 is as an ‘AGN indicator’. Given a value of α350, and 1.4 an independent estimate of the source spectral redshift, if the source lies well below the curves in Figure 1, then it is likely the source has a radio loud AGN component. Again, – 10 – H1413+117 is a good example of this. Theoretically, a source can appear well above the curves in Figure 1 if the dust heating mechanism is entirely due to a radio quiet AGN. Thus far no examples of this latter type have been found, but current limits on a few sources cannot preclude such a situation. We can apply the analysis in Figure 1 to address the identification of the submm sources detected in the Hubble Deep Field (HDF) by Hughes et al. (1998). Because there are of order 10 optical galaxies within a given SCUBA beam at 350 GHz (FWHM = 15′′), unique identification of the submm sources is difficult from the astrometry alone. Hughes et al. have argued that the submm sources are at z ≥ 1 based on the submm spectral shape. Using the deep radio imaging data from the VLA, Richards (1998) has argued that there is a 6′′ offset between the submm frame with respect to the radio and optical frame, and that the sources HDF850.3 & HDF850.4 could be identified with bright optical galaxies at z ∼ 0.5 instead. As shown in Figure 1b, however, the derived radio-to-submm spectral index for the three proposed identifications by Richards (shown as filled circles) are much too large to be consistent with their redshifts. Reversing the argument, the maximum expected 350 GHz fluxes for the two bright z ∼ 0.5 radio sources are 0.21 and 0.44 mJy, factors of 14 and 5.2 too small compared to the observed values. Conversely, if the SCUBA astrometric accuracy is better than 6′′, only upper limits exist for the 1.4 GHz radio flux (3σ = 23 µJy). The resulting lower limits to α350 for the five 1.4 HDF submm sources are shown in Figure 1b using the redshifts estimated by Hughes et al. The derived α350 is larger than +0.8 in all five cases, and therefore these sources are likely to 1.4 be located at z ≥ 1.5, more in-line with the approximate redshifts estimated for the sources based solely on the submm spectral indices by Hughes et al. (1998). Further, the brightest submm source HDF850.1 has α350 > +1.0, larger than any previously detected submm 1.4 source (see Figure 1a), suggesting z ≥ 3. For comparison, the z=4.7 QSO BR1202-0725 has