Abstract

We present high-resolution 345-GHz interferometric observations of two extremely luminous (Lir≳ 1013 L), submillimetre-selected galaxies (SMGs) in the Cosmic Evolution Survey (COSMOS) field with the Submillimeter Array (SMA). Both targets were previously detected as unresolved point sources by the SMA in its compact configuration, also at 345 GHz. These new data, which provide a factor of ≳3 improvement in resolution, allow us to measure the physical scale of the far-infrared in the submillimetre directly. The visibility functions of both targets show significant evidence for structure on ∼0.5–1-arcsec scales, which at z≳ 1.5 translates into a physical scale of ∼5–8 kpc. Our results are consistent with the angular and physical scales of two comparably luminous objects with high-resolution SMA follow-up, as well as radio continuum and CO sizes of other SMGs. These relatively compact sizes (≲5–10 kpc) argue strongly for merger-driven starbursts, rather than extended gas-rich discs, as the preferred channel for forming SMGs.

1 INTRODUCTION

In recent years, it has become increasingly clear that the most infrared (IR)-luminous galaxies play an important role in the star formation history of the Universe. Though they provide only a trivial contribution in the IR-luminosity density in the local Universe, both theory (Hopkins & Hernquist 2010; Hopkins et al. 2010b) and observations (Le Floc'h et al. 2005; Pérez-González et al. 2005; Magnelli et al. 2009; Goto et al. 2010) have shown that by z≳ 1 luminous (1011 < Lir/L < 1012; luminous infrared galaxies) and at higher redshifts by ultraluminous systems [Lir > 1012 L; ultra-luminous infrared galaxies (ULIRGs)] become increasingly cosmologically important. Thus, a detailed study of these populations and the processes driving their tremendous radiative output is critical to a thorough understanding of galaxy formation more generally.

Submillimetre-selected galaxies (SMGs), discovered in the first deep cosmological surveys at 850 μm (Smail, Ivison & Blain 1997; Barger et al. 1998; Hughes et al. 1998) by the Submillimetre Common User Bolometer Array (SCUBA; Holland et al. 1999), represent some of the most extreme objects in the high-redshift Universe (for a review, see Blain et al. 2002). Owing to a strong negative k-correction, the selection function at ≈800–1000 μm is flat from z∼ 1–10 and therefore provides an unbiased view of star formation out to very high redshift (Blain & Longair 1993). Though their bolometric energy output rivals that of luminous quasars, SMGs are several orders of magnitude more numerous at comparable redshifts (z∼ 2.5; Chapman et al. 2005). At the same time, these two extreme populations are thought to be connected via an evolutionary sequence (Narayanan et al. 2009a,b, 2010; Hopkins et al. 2010b) driving the formation of the most massive galaxies (Scott et al. 2002; Blain et al. 2004; Swinbank et al. 2006, 2008; Viero et al. 2009). Thus, in the context of a merger-driven cosmic cycle (e.g. Sanders et al. 1988; Hopkins et al. 2006, 2008a,b), SMGs represent the transition objects potentially powered by a mix of star formation and active galactic nucleus (AGN) activity (Hopkins et al. 2010b) and as such a compelling laboratory for testing models of galaxy formation and evolution in the most extreme environments.

While their bolometric luminosity is thought to be primarily powered by star formation (Alexander et al. 2005a,b, 2008; Menéndez-Delmestre et al. 2007, 2009; Sajina et al. 2007; Valiante et al. 2007; Pope et al. 2008; Murphy et al. 2009; Biggs, Younger & Ivison 2010; Momjian et al. 2010; Serjeant et al. 2010), SMGs could in principle represent one of two very different channels: a steady-state mode wherein large and extended (e.g. Efstathiou & Rowan-Robinson 2003; Kaviani, Haehnelt & Kauffmann 2003) reservoirs of gas in disc galaxies fuelled largely by cosmological gas accretion (e.g. Kereš et al. 2005, 2009a,b; Davé et al. 2009)1 yields a very high steady-state star formation rate (SFR) or interaction-driven events wherein close passages and/or mergers induce strong bars that centrally concentrate the gas supply (Barnes & Hernquist 1996; Hopkins et al. 2009), leading to a brief and intense burst of nuclear star formation (see also Hernquist 1989; Barnes & Hernquist 1991; Mihos & Hernquist 1994, 1996; Cox et al. 2008; Di Matteo et al. 2008). These two modes can be distinguished by the size of the star-forming region, with steady-state discs extending over tens of parsecs [R≈ 28 (Sν/10 mJy)1/2 kpc at z= 2; Kaviani et al. 2003] versus interaction-driven bursts which are much more concentrated. There is no a priori reason to favour either scenario, and indeed both very gas-rich discs (e.g. Erb et al. 2006; Daddi et al. 2009c; Tacconi et al. 2010) and merger-driven, IR-luminous starbursts (e.g. Tacconi et al. 2008; Walter et al. 2009) have been observed in the high-redshift Universe.

To date, observational estimates of the physical scale of star-forming regions in SMGs prefer the interaction-driven scenario. However, the majority of detections are in the radio, where by leveraging the remarkably tight far-IR–radio correlation – in which the total rest-frame 20-cm luminosity provides a proxy for the total SFR among star-forming systems in the local Universe (Helou, Soifer & Rowan-Robinson 1985; Condon 1992; Yun, Reddy & Condon 2001; Thompson et al. 2006; Lacki & Thompson 2009a; Lacki, Thompson & Quataert 2009b) –Chapman et al. (2004), Biggs & Ivison (2008) and Momjian et al. (2010) inferred typical physical sizes of 5–10 kpc for SMGs. At the same time, CO imaging (Neri et al. 2003; Greve et al. 2005; Tacconi et al. 2006; Tacconi et al. 2008; Daddi et al. 2009a,b; Bothwell et al. 2010) tends to yield comparable sizes. However, each of these techniques has its shortcomings: the spatially resolved far-IR–radio correlation is still not well understood (see e.g. Beck & Golla 1988; Hippelein et al. 2003; Hughes et al. 2006; Murphy 2006a; Murphy et al. 2006b; Tabatabaei et al. 2007), and imaging redshifted CO emission in high-j (e.g. J= 4 → 3) rotational lines may substantially underestimate the starburst scale (Narayanan et al. 2008; Ivison et al. 2009b).

Therefore, it is preferable to measure the starburst scale in the far-IR directly. However, the beam sizes characteristic of single-dish instruments are often nearly an order of magnitude too large to probe the relevant spatial scales. And, owing to technical constraints, even interferometric imaging is typically too coarse. In fact, to date virtually all SMGs with interferometric follow-up are compact (COM) relative to the beam [≈2–3-arcsec full width at half-maximum (FWHM); Dannerbauer et al. 2004; Iono et al. 2006; Wang et al. 2007; Younger et al. 2007, 2008a, 2009b; Dannerbauer, Walter & Morrison 2008; Cowie et al. 2009]. Recently, Younger et al. (2008b) imaged two of the brightest SMGs known with the Submillimetre Array (SMA; Ho, Moran & Lo 2004) in its most extended configurations – the highest resolution submillimetre imaging of high-redshift starbursts achieved to date – and found that their far-IR emission was extended on ∼ few × kpc scales. Such extremely bright objects were particularly interesting because at these size scales and luminosities, the implied energetics start to run up against physical limits on the SFR imposed by the dynamical time of the gas (Elmegreen 1999) or the possible effects of radiation (Murray, Quataert & Thompson 2005; Thompson, Quataert & Murray 2005; Murray 2009; Hopkins et al. 2010a) and/or cosmic ray pressure (Socrates, Davis & Ramirez-Ruiz 2008; Sironi & Socrates 2010).

In this work, we present similar observations of two other exceptionally bright and therefore luminous objects in a 1.1-mm blank-field survey of the COSMOS field (Scott et al. 2008) performed with the AzTEC cameras (Wilson et al. 2008): AzTEC4 and AzTEC8. In both cases, high-resolution follow-up observations provide a measurement (rather than an upper limit) on the scale of the far-IR emission and therefore the starburst itself. This paper is organized as follows: in Section 2 we summarize the observations and data reduction, in Section 3 we present the results, in Section 4 we discuss the implications and in Section 5 we conclude. Throughout this work, we assume the 7-yr Wilkinson Microwave Anisotropy Probe (WMAP) cosmological model of Komatsu et al. (2010), though any set of cosmological parameters within reason will not qualitatively change the interpretation of these results. Finally, we assume a Chabrier (2003) stellar initial mass function (IMF; see below and discussion on applicability to SMGs in Tacconi et al. 2008) and when the redshift of a source is uncertain we consider a range of 2 ≲z≲ 4 (also appropriate for SMGs; see e.g. Chapman et al. 2005; Younger et al. 2007, 2009b).

2 OBSERVATIONS AND DATA REDUCTION

The two targets – AzTEC4 and AzTEC8 – were selected from the SMA/AzTEC interferometric survey (Younger et al. 2007, 2009b) of bright sources in the AzTEC 1.1-mm (270-GHz) survey of the COSMOS field (Scott et al. 2008). They were first identified in the AzTEC map with deboosted flux densities of 5.2+1.3−1.4 and 5.5+1.3−1.3 mJy and were later detected by the SMA in its COM configuration at 870 μm (345 GHz) with flux densities of 14.4 ± 1.9 and 19.7 ± 1.8 mJy (assuming a point-source model). We then targeted both sources with the SMA in its extended (EXT) configuration with a goal of measuring the source size. The observing conditions for and an overview of all available data for the two targets are summarized in Table 1 and the uv coverage presented in Fig. 1.

Table 1

Track details.

Target Configurationa uv Coverage (kλ) Beam size (arcsec) Date (yy.mm.dd) 〈τ225 GHz〉 Obs. timeb (h) Referencec 
AzTEC4 COM 20–75 2.71 × 2.12 07.01.21 0.06 5.9 Y07 
EXT 50–250 0.86 × 0.77 09.02.23 0.05 3.9 This work 
AzTEC8 COM 20–75 2.69 × 2.19 07.12.17 0.05 6.2 Y09 
EXT 50–250 0.86 × 0.55 09.02.16, 09.02.22 0.1, 0.06 3.7, 3.8 This work 
Target Configurationa uv Coverage (kλ) Beam size (arcsec) Date (yy.mm.dd) 〈τ225 GHz〉 Obs. timeb (h) Referencec 
AzTEC4 COM 20–75 2.71 × 2.12 07.01.21 0.06 5.9 Y07 
EXT 50–250 0.86 × 0.77 09.02.23 0.05 3.9 This work 
AzTEC8 COM 20–75 2.69 × 2.19 07.12.17 0.05 6.2 Y09 
EXT 50–250 0.86 × 0.55 09.02.16, 09.02.22 0.1, 0.06 3.7, 3.8 This work 

a For details on SMA configurations, see http://sma1.sma.hawaii.edu/status.html.

b Total on-source integration time in that configuration.

Figure 1

The uv coverage for our high-resolution interferometric imaging of AzTEC4 and AzTEC8 for both the COM (black) and EXT (red, or light grey in the printed edition) configurations. For further details, including weather conditions and on-source integration times, see Table 1.

Figure 1

The uv coverage for our high-resolution interferometric imaging of AzTEC4 and AzTEC8 for both the COM (black) and EXT (red, or light grey in the printed edition) configurations. For further details, including weather conditions and on-source integration times, see Table 1.

A detailed description of the calibration strategy for the COM configuration tracks is provided in Younger et al. (2007, 2009b) for AzTEC4 and AzTEC8, respectively. For the EXT tracks presented in this work, the receiver was tuned to 340 GHz in the lower sideband and averaged with the upper sideband for an effective bandwidth of 4 GHz centred at 345 GHz. Passband calibration was performed using 3C 84 (Bennett 1962), and primary flux calibration was done using either Ceres on 2009 February 16 and 23 or Titan on 2009 February 22. The target was observed on a 10-min cycle with two primary gain calibrators: 1058+015 (∼2 Jy; 15° away) and 0854+201 (∼6 Jy; 24° away). Because Ceres is known to be variable at the ∼ 20–30 per cent level due to rotation (Altenhoff et al. 1994; Redman, Feldman & Matthews 1998; Barrera-Pineda et al. 2005), we confirm this flux scale by checking that the flux density for 0854+201 derived using Ceres as the primary flux calibrator (6.0 ± 0.3 and 5.7 ± 0.3 Jy) was consistent with that using Titan (5.7 ± 0.3 Jy).

In addition to the two primary targets, we observed a nearby test quasar – J1008+063 (∼0.2 Jy) which was 5° away from the targets – once every 60 min throughout the track to empirically verify the phase transfer and inferred source structure and estimate the systematic positional uncertainty. This source is included in both the Jodrell Bank-VLA Astrometric Survey (JVAS) (Patnaik et al. 1992; Browne et al. 1998) and Very Long Baseline Array Calibrator (Ma et al. 1998; Beasley et al. 2002) surveys of COM, flat-spectrum radio sources, has an absolute position known to better than 20 mas and was confirmed to be COM at 345 GHz by Younger et al. (2008b).

We also make use of extensive multiwavelength data in the COSMOS field (see Scoville et al. 2007, for an overview)2 including Subaru ground-based optical and near-IR (Taniguchi et al. 2007), Hubble Space Telescope (HST)/Advanced Camera for Surveys (ACS) i band (Koekemoer et al. 2007), Infrared Array Camera 3.6–8 μm, and Multiband Imaging Photometer for Spitzer 24 μm (Sanders et al. 2007), Very Large Array (VLA) 20 cm (Schinnerer et al. 2007) and Chandra X-ray (Elvis et al. 2009; Puccetti et al. 2009) imaging.

3 RESULTS

Imaging and model fitting for the calibrated visibility data was performed using the miriad software package (Sault, Teuben & Wright 1995). We utilize a natural weighting scheme, yielding dirty maps for the EXT tracks that had rms noise levels of 1.6 and 1.8 mJy beam−1 for AzTEC4 and AzTEC8, respectively. The peak flux density in each map was spatially consistent with detections in earlier COM tracks and highly statistically significant: for AzTEC4 the peak was 8.0 mJy beam−1[signal-to-noise ratio (S/N) ∼ 5] and for AzTEC8 it was 12.8 mJy beam−1 (S/N ∼ 7).

Postage stamps of these maps, along with contours overlaid on optical, near-IR and radio data, are shown in Fig. 2. Neither source has a statistically significant detection in the optical or near-IR, though there is a marginal ≈23.3-mag K-band detection associated with AzTEC4. In the radio, as expected there is no emission coincident with AzTEC4 (as in Younger et al. 2007) and the centroid of AzTEC8 is consistent with that of an 89 ± 11 - μJy source – as in the COM data (which has a comparable noise level; Younger et al. 2009b), the nearby secondary radio counterpart of AzTEC8 is not detected in the EXT image.

Figure 2

Postage stamps for AzTEC4 (top) and AzTEC8 (bottom) including (left to right): 870-μm SMA (natural weighting), Subaru B band, HST/ACS i band, CFHT Ks band and VLA 20-cm imaging. For both sources, we only include SMA data from the EXT tracks. The red contours indicate 3, 5, 7, …× the rms noise level, the grey hashed ellipse the beam size and the grey solid line 1 arcsec for scale.

Figure 2

Postage stamps for AzTEC4 (top) and AzTEC8 (bottom) including (left to right): 870-μm SMA (natural weighting), Subaru B band, HST/ACS i band, CFHT Ks band and VLA 20-cm imaging. For both sources, we only include SMA data from the EXT tracks. The red contours indicate 3, 5, 7, …× the rms noise level, the grey hashed ellipse the beam size and the grey solid line 1 arcsec for scale.

We then combined the new EXT with existing COM data and inspected the visibility function for each target (see the top panels of Fig. 3). When binned by uv distance and vector- averaged, both AzTEC4 and AzTEC8 show significant evidence for structure at ≳100 kλ, which corresponds to angular scales of ≲0.6 arcsec. This is consistent with the images, which exhibits lower peaks in the higher resolution maps: for AzTEC4 the peak flux density in COM is 13.2 ± 1.7 mJy beam−1 versus 8.0 ± 1.8 mJy beam−1 in EXT, and for AzTEC8 the peaks are 19.7 ± 1.8 mJy beam−1 in COM and 12.8 ± 1.8 mJy beam−1 in EXT. In both cases, the test quasar empirically confirms that this structure is real and not the result of decorrelation on the longest baselines (see the bottom panels of Fig. 3).

Figure 3

Binned and vector-averaged real visibility amplitudes as a function of uv distance for the target (top row) and test quasar (bottom row). The targets – AzTEC4 (left) and AzTEC8 (right) – and the calibration strategy are discussed in Section 2. For the targets we include all available data, including both COM and EXT tracks, details of which are provided in Table 1 and the uv coverage presented in Fig. 1; for the test quasars, we only include the EXT data. For comparison, we provide a series of symmetric Gaussian source models with FWHM sizes of (left to right) 10, 5, 2, 1, 0.5 arcsec. The flat solid and dotted lines indicate a point-source fit (including only the COM data for the targets and only the EXT data for the test quasars) and the associated statistical uncertainty. We find that both AzTEC4 and AzTEC8 show clear evidence of structure on ≈ 0.5–1-arcsec scales and the test quasars confirm the phase transfer.

Figure 3

Binned and vector-averaged real visibility amplitudes as a function of uv distance for the target (top row) and test quasar (bottom row). The targets – AzTEC4 (left) and AzTEC8 (right) – and the calibration strategy are discussed in Section 2. For the targets we include all available data, including both COM and EXT tracks, details of which are provided in Table 1 and the uv coverage presented in Fig. 1; for the test quasars, we only include the EXT data. For comparison, we provide a series of symmetric Gaussian source models with FWHM sizes of (left to right) 10, 5, 2, 1, 0.5 arcsec. The flat solid and dotted lines indicate a point-source fit (including only the COM data for the targets and only the EXT data for the test quasars) and the associated statistical uncertainty. We find that both AzTEC4 and AzTEC8 show clear evidence of structure on ≈ 0.5–1-arcsec scales and the test quasars confirm the phase transfer.

The combined calibrated visibility data were fitted to one of two simple source models – an elliptical Gaussian profile or a uniform elliptical disc – the results of which are presented in Table 2. The best-fitting parameters for both sources show structure on ≈ 0.5–1-arcsec scales at >rsim 2σ confidence. We also confirm that this size measurement is not artificially imposed by differing flux scales between the COM and EXT data by fitting the same source model to each set of calibrated visibilities independently: when we assume e.g. the Gaussian model we find total flux densities (for the COM and EXT data, respectively, and including an estimate of the systematic uncertainty in the flux scale3) of 14.1 ± 2.5stat± 0.8sys and 9.2 ± 3.1stat± 0.5sys mJy for AzTEC4 and 17.9 ± 3.7stat± 0.9sys and 21.0 ± 4.8stat± 1.0sys mJy for AzTEC8; the fact that these are consistent between configurations to within the statistical and systematic uncertainties indicates that the size measurements listed in Table 2 are robust.

Table 2

Positions and source structure.

Name Config.a Model α[J2000] δ[J2000] Δαb (arcsec) Δδb (arcsec) F890μm (mJy) θcmaj (arcsec) θcmin (arcsec) ϕd (deg) 
AzTEC4 Point 09:59:31.72 +02:30:44.0 0.15 0.24 14.4 ± 1.9 – – – 
C+E Gaussian 09:59:31.709 +02:30:44.06 0.11 0.08 13.1 ± 1.8 0.6 ± 0.2 0.4 ± 0.2 
C+E Disc 09:59:31.709 +02:30:44.06 0.09 0.07 13.1 ± 1.7 1.0 ± 0.4 0.7 ± 0.6 30 
AzTEC8 Point 09:59:59.34 +02:34:41.0 0.10 0.10 21.6 ± 2.3 – – – 
C+E Gaussian 09:59:59.334 +02:34:41.12 0.064 0.058 17.7 ± 2.3 0.6 ± 0.2 0.5 ± 0.3 40 
C+E Disc 09:59:59.334 +02:34:41.09 0.054 0.056 17.2 ± 2.1 1.0 ± 0.5 0.4 ± 0.8 20 
Name Config.a Model α[J2000] δ[J2000] Δαb (arcsec) Δδb (arcsec) F890μm (mJy) θcmaj (arcsec) θcmin (arcsec) ϕd (deg) 
AzTEC4 Point 09:59:31.72 +02:30:44.0 0.15 0.24 14.4 ± 1.9 – – – 
C+E Gaussian 09:59:31.709 +02:30:44.06 0.11 0.08 13.1 ± 1.8 0.6 ± 0.2 0.4 ± 0.2 
C+E Disc 09:59:31.709 +02:30:44.06 0.09 0.07 13.1 ± 1.7 1.0 ± 0.4 0.7 ± 0.6 30 
AzTEC8 Point 09:59:59.34 +02:34:41.0 0.10 0.10 21.6 ± 2.3 – – – 
C+E Gaussian 09:59:59.334 +02:34:41.12 0.064 0.058 17.7 ± 2.3 0.6 ± 0.2 0.5 ± 0.3 40 
C+E Disc 09:59:59.334 +02:34:41.09 0.054 0.056 17.2 ± 2.1 1.0 ± 0.5 0.4 ± 0.8 20 

a See Table 1 and Fig. 1 for details.

b Combined statistical and systematic uncertainty, where the systematic uncertainty is estimated from the position of the test quasar.

c θmaj and θmin represent the FWHM or diameter of the major and minor axes for the Gaussian and elliptical disc models, respectively.

d Position angle.

4 DISCUSSION

4.1 The physical scale of the far-infrared

The angular scales are qualitatively consistent with size measurements of similar objects derived from previous high-resolution far-IR imaging (Younger et al. 2008b), as well as other wavelengths including radio continuum (Chapman et al. 2004; Biggs & Ivison 2008; Momjian et al. 2010) and CO (Neri et al. 2003; Tacconi et al. 2006, 2008) imaging. In our view, imaging in the far-IR directly is the most robust method for measuring the spatial extent of a starburst because it directly probes the obscured starburst; though the galaxy-wide far-IR–radio correlation is thought to apply – at least in a qualitative sense – at redshifts typical of SMGs (Garrett 2002; Gruppioni et al. 2003; Appleton et al. 2004; Boyle et al. 2007; Murphy 2009; Younger et al. 2009a; Ivison et al. 2009a), the spatially resolved correlation is not particularly well understood (Beck & Golla 1988; Hippelein et al. 2003; Hughes et al. 2006; Murphy 2006a; Murphy et al. 2006b, 2008; Tabatabaei et al. 2007) with the potential for substantial overestimates of the starburst region (e.g. large radio haloes like those seen in NGC 4631 that extend several kpc beyond the far-IR disc; Ekers & Sancisi 1977), while CO imaging is largely restricted to excited states with higher critical densities than the bulk of the star-forming gas and therefore may be biased towards smaller sizes (Narayanan et al. 2008; Ivison et al. 2009b). However, given the agreement between these three methods – now including twice as many objects with sizes measured in the far-IR directly – we have newfound confidence that the general conclusion that the most luminous SMGs (Lir≳ 1013 L) have typical angular scales of ≈0.5–1 arcsec is robust.

To translate this into a physical size requires knowledge of the angular diameter distance. Fortunately, at 2 ≲z≲ 4 and assuming the 7-yr WMAPΛ cold dark matter cosmological model (Komatsu et al. 2010), this quantity has a very weak scaling with redshift. In general, the physical size (ℓ) is approximately  

1
formula
Therefore, existing size measurements for SMGs suggest a typical physical scale of ≈4–8 kpc at 2 ≲z≲ 4. While there is clear evidence for ≳20-kpc sizes among some SMGs (Ivison et al. 2009b), the data presented in this work strongly argue against pure steady-state star formation fed by cosmological gas accretion (Kereš et al. 2005, 2009a, 2009b; Davé et al. 2009) as the primary mechanism for producing SMGs and rather favour the merger-driven scenario (Narayanan et al. 2009a, 2010) in which interaction-driven starbursts give rise to these extreme objects. For hyperluminous SMGs (Lir≳ 1013 L and SFR ≳ 2000 M yr-1), this is also consistent with physical limitations; their extremely high specific SFRs (SSFRs) –M/SFR ≳ 2–5 Gyr-1 and up to ≈15 Gyr-1 for e.g. GN20 (Borys et al. 2005; Tacconi et al. 2006; Carilli et al. 2010) – combined with the long duty cycles implied by cosmological accretion (see the above references) would lead to unphysically massive galaxies. It furthermore fits into a more general evolutionary picture in which SMGs are transition objects (Hopkins et al. 2010b) between isolated, gas-rich spirals and luminous quasars, and the progenitors of passive, elliptical galaxies (e.g. Sanders et al. 1988; Hopkins et al. 2006, 2008a,b).

4.2 Are the most luminous submillimetre galaxies Eddington-limited starbursts?

Size measurements are particularly interesting for the most luminous SMGs because their star formation is sufficiently rapid to run up against fundamental physical limitations. This requires converting the observed submillimetre flux into a total IR luminosity, which unfortunately is a somewhat complex function of both the redshift and dust properties of the source (Blain et al. 2002; Blain, Barnard & Chapman 2003). However, by assuming a greybody model (e.g. Hildebrand 1983) with fixed emissivity β= 1.35 and critical frequency νc= 2000 GHz (calibrated to local IR-luminous systems; see Yun & Carilli 2002, and references therein),4 and assuming a Chabrier (2003) IMF,5 we can approximate the bolometric correction for 2 ≲z≲ 4 and Td≳ 20 K with a simple analytic fitting form:  

2
formula
where log γ(Td) = 1.0–1.3(Td/35 K). Samples of SMGs with 350-μm photometry have Td= 35 ± 10 K (Kovács et al. 2006, 2010; Dye et al. 2007; Coppin et al. 2008); over this range in Td and again 2 ≲z≲ 4, we get a median conversion and associated uncertainty of  
3
formula
At the same time, Eddington-type arguments (Murray et al. 2005) – under a series of simplifying assumptions such as a spherically symmetric geometry, an isothermal sphere density structure, a small volume filling factor for molecular gas and again a Chabrier (2003) IMF – yield a maximum SFR of  
4
formula
where σ is the line-of-sight gas velocity dispersion in units of 400 km s-1, κ100 is the opacity in units of cm2 g-1 (usually taken to be ≈1; Murray et al. 2005; Thompson et al. 2005) and Dkpc is the characteristic physical scale of the starburst – either the Gaussian FWHM or the elliptical disc diameter.

Younger et al. (2008b) found that GN20 and AzTEC1 – two of the most luminous SMGs known – were potentially at or close to this Eddington limit. In this work, we measured sizes for two comparably luminous objects: taking the total flux densities inferred from the EXT+COM data, we arrive at SFRs of ≈ 4000+3800−1100 and ≈ 5500+5000−1400 M yr−1 for AzTEC4 and AzTEC8, respectively. Both have characteristic sizes of ℓ≈ 5–8 kpc– where the range represents uncertainty arising from a Gaussian versus disc source structure – yielding a maximal SFR: SFRmax≈ 1900–3800 M yr−1. While the inferred SFR is clearly rather imprecise owing to large systematic uncertainties in the bolometric correction, given the sizes of these two objects – as with GN20 and AzTEC1 – they are consistent with their forming stars at or near the Eddington limit for a starburst.

There are, however, a number of important caveats to consider as follows.

  1. Uncertainties in estimating the SFR. There are few observational constraints on the stellar IMF at high redshift and in extreme environments (e.g. Baugh et al. 2005; Fardal et al. 2007; Davé 2008; Swinbank et al. 2008; Tacconi et al. 2008; van Dokkum 2008) and the shape of the far-IR spectral energy distribution (SED) as a function of luminosity (e.g. Chary & Elbaz 2001; Lagache, Dole & Puget 2003).

  2. The volume filling factor of molecular gas. In the optically thick limit – in which the molecular gas has a volume filling factor near unity – the Eddington limit is an order of magnitude higher. A number of recent studies have found that this limit describes even local ULIRGs (Scoville et al. 1991; Downes, Solomon & Radford 1993; Solomon et al. 1997; Downes & Solomon 1998) and therefore we might expect it to apply well to the much more extreme environments in SMGs. This does, however, require a rather low effective dust temperature; in the optically thick limit, the brightness temperature at 345 GHz (TB) is equal to the physical temperature (Td). While the sizes and flux densities of AzTEC4 and AzTEC8 require Td≈ 5 (1 +z) K (see fig. 5 and discussion in section 4 of Younger et al. 2008b), which at 2 ≲z≲ 4 is rather low compared to other SMGs for which Td has been measured independently via far-IR SED fitting (〈Td〉∼ 35 K for typical SMGs, and the most luminous objects may be preferentially hotter; Kovács et al. 2006, 2010; Dye et al. 2007; Coppin et al. 2008), it is certainly not out of the question.

  3. The depth of the potential well. The maximal SFR has a strong dependence on the gravitational potential, which enters as σ2400. Dynamical masses measured via CO spectroscopy have found that in the mean σ400≈ 1 for SMGs (Greve et al. 2005; Tacconi et al. 2006). However, merger-driven models for SMGs suggest that the brightest 850-μm sources are also the most massive (Narayanan et al. 2010) and therefore would likely have σ400≳ 1.5 (for GN20, σ400≈ 1.4; Carilli et al. 2010) or so which could lead to significantly higher Eddington limits, even in the optically thin limit.

4.3 Obscured AGN versus star formation

Though in general SMGs are thought to be star formation dominated (Alexander et al. 2005a,b, 2008; Menéndez-Delmestre et al. 2007, 2009; Sajina et al. 2007; Valiante et al. 2007; Pope et al. 2008; Murphy et al. 2009; Biggs et al. 2010; Momjian et al. 2010; Serjeant et al. 2010), in principle they could contain a significant contribution from an obscured AGN. In fact, a preliminary analysis of recent very long baseline interferometry observations provides strong evidence that the radio continuum in at least some SMGs is powered primarily by an ultracompact AGN core (Biggs et al. 2010). Clearly, if this was the case for either AzTEC4 or AzTEC8 it would severely compromise their interpretation as extreme starbursts at or near their Eddington limit – the Eddington limit for an ∼ 109 - M supermassive black hole is well in excess of forumla.

Recent X-ray imaging of the COSMOS field (the C-COSMOS Survey; Elvis et al. 2009) provides some constraints on the AGN content of these objects; though starbursts also produce significant X-ray emission, a detection in the hard band (2–8 keV) would be strong evidence for the presence of a buried AGN – particularly at high redshift. Therefore, we have examined the C-COSMOS X-ray imaging data for AzTEC4 and AzTEC8. While AzTEC8 shows no evidence for a detection, AzTEC4 exhibits a tentative hard X-ray source. A formal source extraction (as in Puccetti et al. 2009) yields net counts in the hard band of 5.5 ± 2.7 counts, which translates into a flux of FHX= 8.0 ± 3.9 erg cm−2 s−1– an ∼ 2σ detection. If we assume the bolometric corrections of Hopkins, Richards & Hernquist (2007), this implies an AGN with bolometric luminosity Lbol/1011 L= 1.2 ± 0.5, 3.4 ± 1.4 and 7 ± 2.4 at z= 2, 3 and 4, respectively, which translates into MBHηedd/107 M= 0.4 ± 0.2, 1.0 ± 0.4 and 2.1 ± 0.8, where ηedd is the Eddington ratio of the AGN (typically near unity during the peak of the starburst; Hopkins et al. 2005a,b). While we cannot rule out significant X-ray absorption (Compton-thick in the case of non-detections), at these redshifts and energies the optical depths are unlikely to be extreme owing to the falling X-ray absorption cross-section (in the high-energy limit E≳ 5 keV, the photoelectric cross-section scales as ∼E−7/2 where E is the rest-frame photon energy; Tanaka & Bleeker 1977). Therefore, the X-ray data suggest that AGN do not contribute significantly to the IR luminosity of AzTEC4 or AzTEC8.

4.4 A multicomponent source structure?

The visibility functions for AzTEC4 and AzTEC8 show clear evidence for structure on ≈ 0.5–1-arcsec scales (see Fig. 3), and fitting a model to the visibility data yields a statistically significant size measurement (see Table 2). However, these observations are not of sufficiently high resolution, nor do they have sufficient S/N to distinguish an extended source structure from multiple COM components separated by less than the beam size. When we fit a dual point-source model to the visibility data, both sources – especially AzTEC8 – yield statistically significant (>rsim 2σ) measurements for the implied sub-component flux densities and separations (see Table 3). Therefore, while the visibility functions are consistent with an extended source structure, the data could also indicate a multicomponent source structure produced by either more COM starbursts or Compton-thick AGN. However, provided we are not resolving out significant extended emission – plausible considering the recovered flux densities in the EXT versus COM configurations (see discussion in Section 3) – the sizes listed in Table 2 can be thought of as upper limits on the physical scale of the starburst in these objects and therefore still argue against an extended star-forming disc.

Table 3

Positions and source structure.

Name Fa1,890 μm (mJy) Fb2,890 μm (mJy) Δθc (arcsec) 
AzTEC4 5.8 ± 2.5 6.8 ± 2.6 0.48 ± 0.12 
AzTEC8 13.0 ± 1.6 5.4 ± 1.6 0.75 ± 0.19 
Name Fa1,890 μm (mJy) Fb2,890 μm (mJy) Δθc (arcsec) 
AzTEC4 5.8 ± 2.5 6.8 ± 2.6 0.48 ± 0.12 
AzTEC8 13.0 ± 1.6 5.4 ± 1.6 0.75 ± 0.19 

a The flux of the first component derived from fitting a two-component point-source model to the calibration visibilities.

b The flux of the second component derived from fitting a two-component point-source model to the calibration visibilities.

c The separation of the two fitted components.

It is tempting to interpret such a multicomponent source structure – particularly if it appears circularly supported with significant extra-nuclear star formation – as inconsistent with a major merger (see e.g. Carilli et al. 2010), arguing instead for an alternative scenario in which local instabilities in turbulent, high-redshift discs lead to clumpy star formation (Elmegreen et al. 2008). This is, however, not the case. First, both hydrodynamical simulations (Ceverino et al. 2010) and analytic arguments (Dekel et al. 2009) indicate that this mode of star formation is steady-state, while the SSFR of GN20, for example, is ≈ 10–30 Gyr−1 (Carilli et al. 2010); a long duty cycle at this high SSFR is unphysical and furthermore is inconsistent with cold-mode accretion rates from cosmological simulations (Kereš et al. 2009a,b). Secondly, significant non-nuclear CO emission is not inconsistent with the merger scenario, particularly one involving more than two participating galaxies (though admittedly a more extreme case; see e.g. Narayanan et al. 2006). Finally, should the clumps appear to exhibit discy kinematics, this would also be consistent with such a gas-rich merger; hydrodynamical simulations have shown that discy gas kinematics are generically conserved when the progenitors are extremely gas-rich (Robertson et al. 2004; Hopkins et al. 2009).

5 CONCLUSION

We present high-resolution interferometric observations of two SMGs in the COSMOS field – AzTEC4 and AzTEC8 – performed with the SMA at 345 GHz. The targets, two of the most luminous SMGs known, were previously detected as COM sources with the SMA at the same frequency in its COM configuration (beam size of ≈ 2.7 × 2.2 arcsec2; Younger et al. 2007, 2009b). These new observations, which offer a factor of ≳3 improvement in resolution, allow us to measure the angular size of the two targets. The visibility functions show significant evidence of structure on angular scales of ≈ 0.5–1 arcsec, in agreement with the sizes of two comparable objects measured by the SMA (Younger et al. 2008b), as well as radio continuum (Chapman et al. 2004; Biggs & Ivison 2008; Momjian et al. 2010) and CO (Neri et al. 2003; Tacconi et al. 2006, 2008; Bothwell et al. 2010) imaging. Owing to the weak scaling of angular diameter distance with redshift for z≳ 1.5, we can convert this angular scale to physical units and find that the far-IR in these SMGs is extended over ∼ few × kpc; both AzTEC4 and AzTEC8 have characteristic physical sizes of ℓ≈ 5–8 kpc, depending on the choice of source model. The COM nature of these sources provides evidence in favour of a merger-driven scenario for forming SMGs (Narayanan et al. 2009a, 2010) rather than extended gas-rich discs and cosmological accretion (Davé et al. 2009).

1
Here disc refers to a stable, gas-rich disc rather than one that is clump unstable and highly turbulent (Elmegreen, Bournaud & Elmegreen 2008; Dekel, Sari & Ceverino 2009; Ceverino, Dekel & Bournaud 2010). This scenario is discussed in Section 4.3 in the context of a potentially multicomponent far-IR morphology.
2
More current information is available at http://cosmos.astro.caltech.edu/
3
Estimated from measurements of the flux density of 0854+201 which are available online as part of the SMA Calibrator List at http://sma1.sma.hawaii.edu/callist/callist.html.
4
While there is some uncertainty in β (see e.g. Yang & Phillips 2007) and νc (see e.g. Scoville et al. 1991; Solomon et al. 1997; Downes & Solomon 1998), the uncertainty in the bolometric correction is dominated by Td.
5
Tacconi et al. (2008) find that this form of the stellar IMF provides a good match to the mass-to-light ratios observed in some SMGs. Using a Salpeter (1955) IMF will tend to raise the inferred SFR by a factor of ≈2 (Kennicutt 1998; Bell 2003; Bell et al. 2005; Hopkins et al. 2010b).

We are thankful to the referee for his helpful comments. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. This research has made use of data obtained from the Chandra Data Archive and software provided by the Chandra X-ray Center (CXC) in the application packages ciao and sherpa. This research was based in part on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan, as well as observations obtained with WIRCam, a joint project of Canada–France–Hawaii Telescope (CFHT), Taiwan, Korea, Canada, France and the CFHT which is operated by the National Research Council (NRC) of Canada, the Institute National des Sciences de l'Univers of the Centre National de la Recherche Scientifique of France and the University of Hawaii. We furthermore utilize observations made with the NASA/ESA HST. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc., and the James Clerk Maxwell Telescope is operated by The Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the United Kingdom, the Netherlands Organisation for Scientific Research and the National Research Council of Canada. JDY acknowledges support from NASA through Hubble Fellowship grant HF-51266.01 awarded by the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. STScI is operated by the association of Universities for Research in Astronomy, Inc., under the NASA contract NAS 5-26555. The HST COSMOS Treasury programme was supported through NASA grant HST-GO-09822. Work with the AzTEC data is supported, in part, by NSF grants AST 0828222 and AST 0907952.

REFERENCES

Alexander
D. M.
Smail
I.
Bauer
F. E.
Chapman
S. C.
Blain
A. W.
Brandt
W. N.
Ivison
R. J.
,
2005a
,
Nat
 ,
434
,
738
Alexander
D. M.
et al.,
2005b
,
ApJ
 ,
632
,
736
Alexander
D. M.
et al.,
2008
,
AJ
 ,
135
,
1968
Altenhoff
W. J.
Johnston
K. J.
Stumpff
P.
Webster
W. J.
,
1994
,
A&A
 ,
287
,
641
Appleton
P. N.
et al.,
2004
,
ApJS
 ,
154
,
147
Barger
A. J.
et al.,
1998
,
Nat
 ,
394
,
248
Barnes
J. E.
Hernquist
L. E.
,
1991
,
ApJ
 ,
370
,
L65
Barnes
J. E.
Hernquist
L.
,
1996
,
ApJ
 ,
471
,
115
Barrera-Pineda
P. S.
Lovell
A. J.
Schloerb
F. P.
Carrasco
L.
,
2005
,
Rev. Mex. Astron. Astrofis.
 ,
24
,
188
Baugh
C. M.
Lacey
C. G.
Frenk
C. S.
Granato
G. L.
Silva
L.
Bressan
A.
Benson
A. J.
Cole
S.
,
2005
,
MNRAS
 ,
356
,
1191
Beasley
A. J.
Gordon
D.
Peck
A. B.
Petrov
L.
MacMillan
D. S.
Fomalont
E. B.
Ma
C.
,
2002
,
ApJS
 ,
141
,
13
Beck
R.
Golla
G.
,
1988
,
A&A
 ,
191
,
L9
Bell
E. F.
,
2003
,
ApJ
 ,
586
,
794
Bell
E. F.
et al.,
2005
,
ApJ
 ,
625
,
23
Bennett
A. S.
,
1962
,
Mem. R. Astron. Soc.
 ,
68
,
163
Biggs
A. D.
Ivison
R. J.
,
2008
,
MNRAS
 ,
385
,
893
Biggs
A. D.
Younger
J. D.
Ivison
R. J.
,
2010
,
MNRAS
 , submitted (1004.0009)
Blain
A. W.
Longair
M. S.
,
1993
,
MNRAS
 ,
264
,
509
Blain
A. W.
Smail
I.
Ivison
R. J.
Kneib
J.-P.
Frayer
D. T.
,
2002
,
Phys. Rep.
 ,
369
,
111
Blain
A. W.
Barnard
V. E.
Chapman
S. C.
,
2003
,
MNRAS
 ,
338
,
733
Blain
A. W.
Chapman
S. C.
Smail
I.
Ivison
R.
,
2004
,
ApJ
 ,
611
,
725
Borys
C.
Smail
I.
Chapman
S. C.
Blain
A. W.
Alexander
D. M.
Ivison
R. J.
,
2005
,
ApJ
 ,
635
,
853
Bothwell
M. S.
et al.,
2010
,
MNRAS
 , submitted (0912.1598)
Boyle
B. J.
et al.,
2007
,
MNRAS
 ,
376
,
1182
Browne
I. W. A.
Wilkinson
P. N.
Patnaik
A. R.
Wrobel
J. M.
,
1998
,
MNRAS
 ,
293
,
257
Carilli
C. L.
et al.,
2010
,
ApJ
 , submitted (1002.3838)
Ceverino
D.
Dekel
A.
Bournaud
F.
,
2010
,
MNRAS
 , in press (0907.3271)
Chabrier
G.
,
2003
,
PASP
 ,
115
,
763
Chapman
S. C.
Smail
I.
Windhorst
R.
Muxlow
T.
Ivison
R. J.
,
2004
,
ApJ
 ,
611
,
732
Chapman
S. C.
Blain
A. W.
Smail
I.
Ivison
R. J.
,
2005
,
ApJ
 ,
622
,
772
Chary
R.
Elbaz
D.
,
2001
,
ApJ
 ,
556
,
562
Condon
J. J.
,
1992
,
ARA&A
 ,
30
,
575
Coppin
K.
et al.,
2008
,
MNRAS
 ,
384
,
1597
Cowie
L. L.
Barger
A. J.
Wang
W.-H.
Williams
J. P.
,
2009
,
ApJ
 ,
697
,
L122
Cox
T. J.
Jonsson
P.
Somerville
R. S.
Primack
J. R.
Dekel
A.
,
2008
,
MNRAS
 ,
384
,
386
Daddi
E.
et al.,
2009a
,
ApJ
 ,
694
,
1517
Daddi
E.
et al.,
2009b
,
ApJ
 ,
695
,
L176
Daddi
E.
et al.,
2009c
,
ApJ
 , submitted (0911.2776)
Dannerbauer
H.
et al.,
2004
,
ApJ
 ,
606
,
664
Dannerbauer
H.
Walter
F.
Morrison
G.
,
2008
,
ApJ
 ,
673
,
L127
Davé
R.
,
2008
,
MNRAS
 ,
385
,
147
Davé
R.
Finlator
K.
Oppenheimer
B. D.
Fardal
M.
Katz
N.
Kereš
D.
Weinberg
D. H.
,
2009
,
MNRAS
 , submitted (0909.4078)
Dekel
A.
Sari
R.
Ceverino
D.
,
2009
,
ApJ
 ,
703
,
785
Di Matteo
P.
Bournaud
F.
Martig
M.
Combes
F.
Melchior
A.
Semelin
B.
,
2008
,
A&A
 ,
492
,
31
Downes
D.
Solomon
P. M.
,
1998
,
ApJ
 ,
507
,
615
Downes
D.
Solomon
P. M.
Radford
S. J. E.
,
1993
,
ApJ
 ,
414
,
L13
Dye
S.
et al.,
2007
,
MNRAS
 ,
375
,
725
Efstathiou
A.
Rowan-Robinson
M.
,
2003
,
MNRAS
 ,
343
,
322
Ekers
R. D.
Sancisi
R.
,
1977
,
A&A
 ,
54
,
973
Elmegreen
B. G.
,
1999
,
ApJ
 ,
517
,
103
Elmegreen
B. G.
Bournaud
F.
Elmegreen
D. M.
,
2008
,
ApJ
 ,
688
,
67
Elvis
M.
et al.,
2009
,
ApJS
 ,
184
,
158
Erb
D. K.
Steidel
C. C.
Shapley
A. E.
Pettini
M.
Reddy
N. A.
Adelberger
K. L.
,
2006
,
ApJ
 ,
646
,
107
Fardal
M. A.
Katz
N.
Weinberg
D. H.
Davé
R.
,
2007
,
MNRAS
 ,
379
,
985
Garrett
M. A.
,
2002
,
A&A
 ,
384
,
L19
Goto
T.
et al.,
2010
,
A&A
 , in press (1001.0013)
Greve
T. R.
et al.,
2005
,
MNRAS
 ,
359
,
1165
Gruppioni
C.
et al.,
2003
,
MNRAS
 ,
341
,
L1
Helou
G.
Soifer
B. T.
Rowan-Robinson
M.
,
1985
,
ApJ
 ,
298
,
L7
Hernquist
L.
,
1989
,
Nat
 ,
340
,
687
Hildebrand
R. H.
,
1983
,
QJRAS
 ,
24
,
267
Hippelein
H.
et al.,
2003
,
A&A
 ,
407
,
137
Ho
P. T. P.
Moran
J. M.
Lo
K. Y.
,
2004
,
ApJ
 ,
616
,
L1
Holland
W. S.
et al.,
1999
,
MNRAS
 ,
303
,
659
Hopkins
P. F.
Hernquist
L.
,
2010
,
MNRAS
 ,
402
,
985
Hopkins
P. F.
Hernquist
L.
Martini
P.
Cox
T. J.
Robertson
B.
Di Matteo
T.
Springel
V.
,
2005a
,
ApJ
 ,
625
,
L71
Hopkins
P. F.
Hernquist
L.
Cox
T. J.
Di Matteo
T.
Martini
P.
Robertson
B.
Springel
V.
,
2005b
,
ApJ
 ,
630
,
705
Hopkins
P. F.
et al.,
2006
,
ApJS
 ,
163
,
1
Hopkins
P. F.
Richards
G. T.
Hernquist
L.
,
2007
,
ApJ
 ,
654
,
731
Hopkins
P. F.
Hernquist
L.
Cox
T. J.
Kereš
D.
,
2008a
,
ApJS
 ,
175
,
356
Hopkins
P. F.
Cox
T. J.
Kereš
D.
Hernquist
L.
,
2008b
,
ApJS
 ,
175
,
390
Hopkins
P. F.
Cox
T. J.
Younger
J. D.
Hernquist
L.
,
2009
,
ApJ
 ,
691
,
1168
Hopkins
P. F.
Murray
N.
Quataert
E.
Thompson
T. A.
,
2010a
,
MNRAS
 ,
401
,
L19
Hopkins
P. F.
Younger
J. D.
Hayward
C. C.
Narayanan
D.
Hernquist
L.
,
2010b
,
MNRAS
 ,
17
Hughes
D. H.
et al.,
1998
,
Nat
 ,
394
,
241
Hughes
A.
Wong
T.
Ekers
R.
Staveley-Smith
L.
Filipovic
M.
Maddison
S.
Fukui
Y.
Mizuno
N.
,
2006
,
MNRAS
 ,
370
,
363
Iono
D.
et al.,
2006
,
ApJ
 ,
640
,
L1
Ivison
R. J.
et al.,
2009a
,
MNRAS
 ,
1794
Ivison
R.
Smail
I.
Papadopoulos
P. P.
Wold
I.
Richard
J.
Swinbank
A. M.
Kneib
J.
Owen
F. N.
,
2009b
,
MNRAS
 , in press (0912.1591)
Kaviani
A.
Haehnelt
M. G.
Kauffmann
G.
,
2003
,
MNRAS
 ,
340
,
739
Kennicutt
R. C.
Jr
,
1998
,
ApJ
 ,
498
,
541
Kereš
D.
Katz
N.
Weinberg
D. H.
Davé
R.
,
2005
,
MNRAS
 ,
363
,
2
Kereš
D.
Katz
N.
Fardal
M.
Davé
R.
Weinberg
D. H.
,
2009a
,
MNRAS
 ,
395
,
160
Kereš
D.
Katz
N.
Davé
R.
Fardal
M.
Weinberg
D. H.
,
2009b
,
MNRAS
 ,
396
,
2332
Koekemoer
A. M.
et al.,
2007
,
ApJS
 ,
172
,
196
Komatsu
E.
et al.,
2010
,
ApJ
 , in press (1001.4538)
Kovács
A.
et al.,
2006
,
ApJ
 ,
650
,
592
Kovács
A.
et al.,
2010
,
ApJ
 , in press (1004.0819)
Lacki
B. C.
Thompson
T. A.
,
2009a
,
ApJ
 , submitted (0910.0478)
Lacki
B. C.
Thompson
T. A.
Quataert
E.
,
2009b
,
ApJ
 , submitted (0907.4161)
Lagache
G.
Dole
H.
Puget
J.
,
2003
,
MNRAS
 ,
338
,
555
Le Floc'h
E.
et al.,
2005
,
ApJ
 ,
632
,
169
Ma
C.
et al.,
1998
,
AJ
 ,
116
,
516
Magnelli
B.
Elbaz
D.
Chary
R. R.
Dickinson
M.
Le Borgne
D.
Frayer
D. T.
Willmer
C. N. A.
,
2009
,
A&A
 ,
496
,
57
Menéndez-Delmestre
K.
et al.,
2007
,
ApJ
 ,
655
,
L65
Menéndez-Delmestre
K.
et al.,
2009
,
ApJ
 ,
699
,
667
Mihos
J. C.
Hernquist
L.
,
1994
,
ApJ
 ,
431
,
L9
Mihos
J. C.
Hernquist
L.
,
1996
,
ApJ
 ,
464
,
641
Momjian
E.
Wang
W.
Knudsen
K. K.
Carilli
C. L.
Cowie
L. L.
Barger
A. J.
,
2010
,
AJ
 , in press (1002.3324)
Murphy
E. J.
,
2009
,
ApJ
 ,
706
,
482
Murphy
E. J.
et al.,
2006a
,
ApJ
 ,
638
,
157
Murphy
E. J.
et al.,
2006b
,
ApJ
 ,
651
,
L111
Murphy
E. J.
Helou
G.
Kenney
J. D. P.
Armus
L.
Braun
R.
,
2008
,
ApJ
 ,
678
,
828
Murphy
E. J.
et al.,
2009
,
ApJ
 ,
698
,
1380
Murray
N.
,
2009
,
ApJ
 ,
691
,
946
Murray
N.
Quataert
E.
Thompson
T. A.
,
2005
,
ApJ
 ,
618
,
569
Narayanan
D.
et al.,
2006
,
ApJ
 ,
642
,
L107
Narayanan
D.
et al.,
2008
,
ApJ
 ,
684
,
996
Narayanan
D.
Cox
T. J.
Hayward
C. C.
Younger
J. D.
Hernquist
L.
,
2009a
,
MNRAS
 ,
400
,
1919
Narayanan
D.
et al.,
2009b
,
MNRAS
 , submitted (0910.2234)
Narayanan
D.
Hayward
C. C.
Cox
T. J.
Hernquist
L.
Jonsson
P.
Younger
J. D.
Groves
B.
,
2010
,
MNRAS
 ,
401
,
1613
Neri
R.
et al.,
2003
,
ApJ
 ,
597
,
L113
Patnaik
A. R.
Browne
I. W. A.
Wilkinson
P. N.
Wrobel
J. M.
,
1992
,
MNRAS
 ,
254
,
655
Pérez-González
P. G.
et al.,
2005
,
ApJ
 ,
630
,
82
Pope
A.
et al.,
2008
,
ApJ
 ,
675
,
1171
Puccetti
S.
et al.,
2009
,
ApJS
 ,
185
,
586
Redman
R. O.
Feldman
P. A.
Matthews
H. E.
,
1998
,
AJ
 ,
116
,
1478
Robertson
B.
Yoshida
N.
Springel
V.
Hernquist
L.
,
2004
,
ApJ
 ,
606
,
32
Sajina
A.
Yan
L.
Armus
L.
Choi
P.
Fadda
D.
Helou
G.
Spoon
H.
,
2007
,
ApJ
 ,
664
,
713
Salpeter
E. E.
,
1955
,
ApJ
 ,
121
,
161
Sanders
D. B.
Soifer
B. T.
Elias
J. H.
Madore
B. F.
Matthews
K.
Neugebauer
G.
Scoville
N. Z.
,
1988
,
ApJ
 ,
325
,
74
Sanders
D. B.
et al.,
2007
,
ApJS
 ,
172
,
86
Sault
R. J.
Teuben
P. J.
Wright
M. C. H.
,
1995
, in
Shaw
R. A.
Payne
H. E.
Hayes
J. J. E.
, eds, ASP Conf. Ser. Vol. 77,
Astronomical Data Analysis Software and Systems IV
 .
Astron. Soc. Pac.
, San Francisco, p.
433
Schinnerer
E.
et al.,
2007
,
ApJS
 ,
172
,
46
Scott
S. E.
et al.,
2002
,
MNRAS
 ,
331
,
817
Scott
K. S.
et al.,
2008
,
MNRAS
 ,
385
,
2225
Scoville
N. Z.
Sargent
A. I.
Sanders
D. B.
Soifer
B. T.
,
1991
,
ApJ
 ,
366
,
L5
Scoville
N.
et al.,
2007
,
ApJS
 ,
172
,
1
Serjeant
S.
et al.,
2010
,
A&A
 , in press (arXiv:1002.3618)
Sironi
L.
Socrates
A.
,
2010
,
ApJ
 ,
710
,
891
Smail
I.
Ivison
R. J.
Blain
A. W.
,
1997
,
ApJ
 ,
490
,
L5
Socrates
A.
Davis
S. W.
Ramirez-Ruiz
E.
,
2008
,
ApJ
 ,
687
,
202
Solomon
P. M.
Downes
D.
Radford
S. J. E.
Barrett
J. W.
,
1997
,
ApJ
 ,
478
,
144
Swinbank
A. M.
et al.,
2006
,
MNRAS
 ,
371
,
465
Swinbank
A. M.
et al.,
2008
,
MNRAS
 ,
391
,
420
Tabatabaei
F. S.
et al.,
2007
,
A&A
 ,
466
,
509
Tacconi
L. J.
et al.,
2006
,
ApJ
 ,
640
,
228
Tacconi
L. J.
et al.,
2008
,
ApJ
 ,
680
,
246
Tacconi
L. J.
et al.,
2010
,
Nat
 ,
463
,
781
Tanaka
Y.
Bleeker
J. A. M.
,
1977
,
Space Sci. Rev.
 ,
20
,
815
Taniguchi
Y.
et al.,
2007
,
ApJS
 ,
172
,
9
Thompson
T. A.
Quataert
E.
Murray
N.
,
2005
,
ApJ
 ,
630
,
167
Thompson
T. A.
Quataert
E.
Waxman
E.
Murray
N.
Martin
C. L.
,
2006
,
ApJ
 ,
645
,
186
Valiante
E.
et al.,
2007
,
ApJ
 ,
660
,
1060
van Dokkum
P. G.
,
2008
,
ApJ
 ,
674
,
29
Viero
M. P.
et al.,
2009
,
ApJ
 ,
707
,
1766
Walter
F.
Riechers
D.
Cox
P.
Neri
R.
Carilli
C.
Bertoldi
F.
Weiss
A.
Maiolino
R.
,
2009
,
Nat
 ,
457
,
699
Wang
W.-H.
et al.,
2007
,
ApJ
 ,
670
,
L89
Wilson
G. W.
et al.,
2008
,
MNRAS
 ,
386
,
807
Yang
M.
Phillips
T.
,
2007
,
ApJ
 ,
662
,
284
Younger
J. D.
et al.,
2007
,
ApJ
 ,
671
,
1531
Younger
J. D.
et al.,
2008a
,
MNRAS
 ,
387
,
707
Younger
J. D.
et al.,
2008b
,
ApJ
 ,
688
,
59
Younger
J. D.
et al.,
2009a
,
MNRAS
 ,
394
,
1685
Younger
J. D.
et al.,
2009b
,
ApJ
 ,
704
,
803
Yun
M. S.
Carilli
C. L.
,
2002
,
ApJ
 ,
568
,
88
Yun
M. S.
Reddy
N. A.
Condon
J. J.
,
2001
,
ApJ
 ,
554
,
803