ILLUMINATING THE DARKEST GAMMA-RAY BURSTS WITH RADIO OBSERVATIONS

Long-duration gamma-ray bursts (GRBs) have been linked to the deaths of massive stars, and hence to star formation activity, through their association with star-forming galaxies (e.g., Djorgovski et al. 1998; Fruchter et al. 2006; Wainwright et al. 2007) and with Type Ic supernova explosions (e.g., Woosley & Bloom 2006). Across a wide range of cosmic history a substantial fraction of the star formation activity (∼70% at the peak of the star formation history, z ∼ 2–4) is obscured by dust, with about 15% of the total star formation rate density occurring in ultra-luminous infrared galaxies (e.g., Bouwens et al. 2009; Reddy & Steidel 2009; Murphy et al. 2011). As a result, we expect some GRBs to occur in dusty environments that will diminish or completely extinguish their optical (and perhaps even near-IR) afterglow emission. Such events can be used as signposts for the locations and relative fraction of obscured star formation across a wide redshift range (e.g., Reichart & Price 2002; Ramirez-Ruiz et al. 2002; Trentham et al. 2002). In addition, they can provide insight into the role of metallicity in GRB progenitors since dusty environments generally require substantial metallicity (see Roseboom et al. 2012).

These so-called optically-dark GRBs are indeed known to exist (e.g., Groot et al. 1998; Djorgovski et al. 2001; Fynbo et al. 2001; Piro et al. 2002), but the lack of an optical detection does not necessarily point to dust obscuration. Most prosaically, the lack of detected optical emission may be due to inefficient follow-up observations, or to intrinsically dim events (e.g., Berger et al. 2002). Another potential origin of dark bursts is a high redshift, with the optical emission suppressed by Lyα absorption at λ_obs ≲ 1216 Å × (1 + z) (Haislip et al. 2006; Salvaterra et al. 2009; Tanvir et al. 2009; Cucchiara et al. 2011). Such events are clearly of great interest since a dropout above ∼1 μm points to z ≳ 7, while events that are also dark in the near-IR can potentially arise at z ≳ 18 (K-band dropout). Naturally, high redshift bursts will also lack host galaxy detections in the optical band. On the other hand, their afterglow emission redward of the Lyα break will follow the expected synchrotron spectrum (F_ν∝ν^−β) with β ≈ 0.5–1 (Sari et al. 1998).

To determine whether a burst is genuinely dark, due to extinction or to a high redshift rather than to an inefficient search, it is a useful diagnostic to compare the observed limits or faint detection with the expected optical/near-IR brightness expected based on the brightness of the X-ray afterglow. This approach relies on the simple power law shape of the afterglow synchrotron emission (see Sari et al. 1998). One definition of dark bursts uses an optical to X-ray spectral index of β_OX ≲ 0.5 (β is the slope of the synchrotron spectrum in log space; see Jakobsson et al. 2004 for details), since this is the shallowest expected slope in the standard afterglow model. A variant of this condition uses knowledge of the X-ray spectral index (β_X), and defines bursts as dark if β_OX − β_X ≲ −0.5 (van der Horst et al. 2009), since this is the shallowest expected relative slope. These definitions can reveal evidence for dust extinction even if an optical afterglow is detected.

This approach of utilizing spectral slopes has been used by several groups to identify and study dark bursts, although different samples and analysis methods yield dramatically different results for the dark burst fraction and the mean extinction relative to the GRB population at large. In the pre-Swift era, Jakobsson et al. (2004) examined 52 bursts with X-ray afterglows and identified five to be dark with β_OX < 0.50. However, they found another five to be potentially dark, strongly cautioning that each burst must be modeled individually and the β_OX cutoff should only be used as a first order diagnostic. The overall fraction of dark bursts in the Jakobsson pre-Swift sample is somewhere between ∼10% and 20%. To avoid selection bias, Fynbo et al. (2009) defined an X-ray-selected sample of 146 Swift bursts and constrained the dark burst fraction to be larger (25%–42%) than the 14% dark burst fraction determined if only GRBs with spectroscopy are considered. Melandri et al. (2012) studied a complete sample of 58 bright Swift bursts, of which 52 have known redshifts and found that the fraction of dark bursts is about 30%, mainly due to extinction (nearly all the dark bursts in their sample have z ≲ 4). Thus, the afterglow emission of ∼1/3–1/2 of all GRBs are affected by dust, although in most cases the required extinction is modest, $A_V^{\rm host}\approx 0.3$ mag (Kann et al. 2006, 2010; Schady et al. 2007; Perley et al. 2009; Greiner et al. 2011).

Several studies have quantified dust extinction in GRBs. Analyzing optical/IR data for 30 GRBs pre-Swift, Kann et al. (2006) found a mean extinction of $A_V^{\rm host}\approx 0.2$ mag, indicating that most events are not dark. Schady et al. (2007) studied several bursts with Swift X-ray and UV/optical detections and found a mean extinction level of $A_V^{\rm host}\approx 0.3$ mag, and that bursts that are dark blueward of V-band are likely to have rest-frame extinction about an order of magnitude larger. Melandri et al. (2008) used rapid optical observations of 63 Swift bursts and found that about 50% showed evidence of mild extinction. A similar conclusion was reached by Cenko et al. (2009) based on rapid optical observations of 29 Swift bursts, with an 80% detection fraction, but with roughly half exhibiting suppression with respect to the X-ray emission. A follow-up study of the latter sample by Perley et al. (2009) aimed at identifying host galaxies in the optical (thereby ruling out a high redshift origin) and found that ≲ 7% of Swift bursts are located at z ≳ 7. The majority of the dark bursts in the Perley et al. (2009) sample instead require $A_V^{\rm host}\gtrsim 1$ mag, with a few cases reaching ∼2–6 mag. There are only a few known cases with large extinction of $A_V^{\rm host}\sim {\rm few}$ mag (see Perley et al. 2013, with 23 Swift galaxies having A_V > 1). A few notable examples of highly extinguished afterglows include GRB 070306 (Jaunsen et al. 2008), GRB 080607 (Prochaska et al. 2009), and GRB 090417B (Holland et al. 2010).

Concurrent studies of the neutral hydrogen column density distribution, inferred from the X-ray afterglow spectra, suggest that dark bursts exhibit systematically larger values of N_{H, int} ≳ 10²² cm⁻² compared with bursts with little or no extinction, which have a median of N_{H, int} ≈ 4 × 10²¹ cm⁻² (Campana et al. 2012; Margutti et al. 2013). On the other hand, the measured extinction for GRBs is generally lower than expected based on the values of N_{H, int} and the Galactic A_V–N_H relation, previously attributed to dust destruction by the bright X-ray/UV emission (e.g., Galama & Wijers 2001; Schady et al. 2007; Perley et al. 2009). Furthermore, Watson & Jakobsson (2012) point out that the tendency for bursts with very high X-ray column to have dusty sight lines may introduce a bias that at least partially explains the observed trend of increasing N_{H, X} with redshift. Above z ∼ 4 there is typically less dust extinction, and so the high-N_{H, X} bursts in this regime appear to require another explanation.

Finally, the host galaxies of at least some dark bursts appear to be redder, more luminous, more massive, and more metal rich than the hosts of optically-bright GRBs (Berger et al. 2007; Levesque et al. 2010; Perley et al. 2009, 2011a; Krühler et al. 2011), potentially indicating that the extinction is interstellar in origin rather than directly associated with the burst environment. One specific example is GRB 030115, not only one of the first examples of a heavily extinguished GRB afterglow, but residing in a host classified as an extremely red object (ERO; see Levan et al. 2006). More recently, Rossi et al. (2012) report seven additional potential ERO hosts. Some host galaxies of optically-bright bursts have been detected in the radio and (sub)millimeter ranges (e.g., Tanvir et al. 2004, indicating obscured star formation rates of ∼10²–10³ M_☉ yr⁻¹ (Berger et al. 2003a). This suggests that the dust distribution within the host galaxies is patchy and that not all GRBs in dusty host galaxies are necessarily dust-obscured (Berger et al. 2003a; Perley et al. 2009). Further work by Svensson et al. (2012) indicates that dark GRB host galaxies may be systematically redder and more massive than optically bright GRB host galaxies and have lower metallicity than submillimeter galaxies, leading to prior biases in GRB host galaxy population studies.

Here we present multi-wavelength observations that reveal two of the darkest known bursts to date, GRBs 110709B and 111215A. These events have such large rest-frame extinction that they lack any afterglow detection in the optical and near-IR bands (to λ_obs ≈ 2.2 μm) despite rapid follow-up. However, both events are detected in the radio, providing sub-arcsecond positions and secure associations with host galaxies detected in the optical. This allows us to rule out a high redshift origin, while the combination of radio and X-ray data place robust lower limits on the rest-frame extinction, with $A_V^{\rm host}\gtrsim 5.3$ and ≳ 8.5 mag (for z = 2), respectively. The radio and X-ray data also allow us to determine the explosion properties and the circumburst densities. This study demonstrates that radio detections with the JVLA, and soon with the Atacama Large Millimeter/submillimeter Array (ALMA), provide a promising path to accurate localization of dark GRBs, robust estimates of the extinction in the absence of any optical/near-IR detections, and a comparative study of their explosion properties and parsec-scale environments.

The plan of the paper is as follows. We describe the multi-wavelength observations of GRBs 110709B and 111215A and their host galaxies in Section 2. These observations establish that both events are dark due to extinction. We model the radio and X-ray data to extract the minimum required extinction, as well as the explosion and circumburst properties in Section 3. In Section 4 we place the large inferred extinction values and the inferred burst properties within the framework of existing samples of optically-bright and dark bursts. We summarize the results and note key future directions in Section 5. Throughout the paper we report magnitudes in the AB system (unless otherwise noted) and use Galactic extinction values of E(B − V) ≈ 0.044 mag for GRB 110709B and E(B − V) ≈ 0.057 mag for GRB 111215A (Schlafly & Finkbeiner 2011). We use the standard cosmological parameters: H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.73, and Ω_M = 0.27.

2.1. Discovery and Burst Properties

2.2. X-Ray Observations

2.2.1. GRB 110709B

We analyzed the XRT data using the HEASOFT package (v6.11) and corresponding calibration files. We utilized standard filtering and screening criteria, and generated a count-rate light curve following the prescriptions by Margutti et al. (2010). The data were re-binned with the requirement of a minimum signal-to-noise ratio (S/N) of 4 in each temporal bin.

The XRT data exhibit significant spectral evolution during the early bright phase (δt ≲ 1 ks), with spectral hardening when the burst re-brightened at ∼11 minutes. Due to this variation, we performed a time-resolved spectral analysis, accumulating signal over time intervals defined to contain a minimum of about 1000 photons. Spectral fitting was done with Xspec (v12.6; Arnaud 1996), assuming a photoelectrically absorbed power law model and a Galactic neutral hydrogen column density of N_{H, MW} = 5.6 × 10²⁰ cm⁻² (Kalberla et al. 2005). We extracted a spectrum in a time interval when no spectral evolution was apparent (15–150 ks) and used this to estimate the contribution of additional absorption. We find that the data are best modeled by an absorbed power-law¹⁷ model with a spectral photon index of Γ = 2.3 ± 0.1 and excess absorption of N_{H, int} = (1.4 ± 0.2) × 10²¹ cm⁻² at z = 0 (90% c.l., C-stat = 559 for 604 degrees of freedom). The excess absorption was used as a fixed parameter in the time-resolved spectral analysis, allowing us to derive a count-to-flux conversion factor for each spectrum. The resulting unabsorbed 0.3–10 keV flux light curve properly accounts for spectral evolution of the source. We note that for the purpose of display in Figure 1 we binned the XRT data by orbit at δt ≲ 2 days and by multiple orbits thereafter.

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We also observed GRB 110709B for 15 ks with the Advanced CCD Imaging Spectrometer (ACIS-S) on-board the Chandra X-ray Observatory on 2011 July 23.60 UT (δt ≈ 13.7 days). The afterglow is detected with a count rate of (4.1 ± 0.5) × 10⁻³ s⁻¹ (0.5–8 keV), corresponding to an unabsorbed 0.3–10 keV flux of (6.0 ± 0.7) × 10⁻¹⁴ erg s⁻¹ cm⁻² using the XRT spectral parameters. Relative astrometry with the Chandra position will be discussed in Section 2.6. A second, 9 ks Chandra/ACIS-S observation was performed on 2011 October 31.83 UT (δt ≈ 113.4 days). The X-ray afterglow is not detected to a 3σ limit of ≲ 9 × 10⁻¹⁵ erg s⁻¹ cm⁻², well above the extrapolation of the early light curve to this epoch (Figure 1).

At δt ≳ 12 days the XRT light curve flattens to a level of about 10⁻¹³ erg s⁻¹ cm⁻². The Chandra observations reveal that this is due to a contaminating source located about 38 from the GRB position, well within the point spread function (PSF) of XRT. We subtract the flux of this source, (6.0 ± 0.7) × 10⁻¹⁴ erg s⁻¹ cm⁻², from the XRT light curve of GRB 110709B in Figure 1.¹⁸

2.2.2. GRB 111215A

We analyzed the XRT data for GRB 111215A in the same manner described above. At δt ≲ 2 ks the light curve exhibits flares with a hard-to-soft spectral evolution. To obtain a reliable estimate of the intrinsic neutral hydrogen absorption in addition to the Galactic value (N_{H, MW} = 5.5 × 10²⁰ cm⁻²; Kalberla et al. 2005), we extracted a spectrum collecting the photon count data in the time interval 5–2000 ks, when no spectral evolution is apparent. The data are best modeled by an absorbed power-law with Γ = 2.2 ± 0.1 and N_{H, int} = (3.1 ± 0.4) × 10²¹ cm⁻² at z = 0 (90% c.l., C-stat = 499.13 for 512 degrees of freedom). The resulting unabsorbed 0.3–10 keV flux light curve is shown in Figure 2.

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2.3. Optical/Near-IR Afterglow Limits

2.4. JVLA Centimeter Observations

2.4.1. GRB 110709B

We observed GRB 110709B with the NRAO Karl G. Jansky Array (JVLA) beginning on 2011 July 11.97 UT (δt ≈ 2.1 days) at a mean frequency of 5.8 GHz and detected a single, unresolved radio source within the XRT error circle. This detection provided the first accurate position for the burst. Follow-up observations demonstrated that the source initially brightened and subsequently faded away, establishing it as the radio afterglow of GRB 110709B.

All observations utilized the WIDAR correlator (Perley et al. 2011b) with ∼2 GHz bandwidth. We calibrated and analyzed the data using standard procedures in the Astronomical Image Processing System (AIPS; Greisen 2003). We excised edge channels and channels affected by radio frequency interference, reducing the effective bandwidth by ∼25% at 5.8 GHz. Due to the low declination of the source, we also excised data when >2 m of a given antenna was shadowed by another antenna. For the observation at 21.8 GHz, we performed reference pointing at 8.4 GHz and applied the pointing solutions, per standard high frequency observing procedures. We observed 3C286 for band-pass and flux calibration and interleaved observations of J1048−1909 for gain calibration every 3 m at 21.8 GHz and J1112−2158 every 4 m at 5.8 GHz. The resulting flux densities at 5.8 and 21.8 GHz are listed in Table 2. The uncertainties are 1σ statistical errors, and we note an additional uncertainty in the absolute flux scaling of ∼5%. The 5.8 GHz light curve is shown in Figure 1.

Table 2. JVLA Observations of GRB 110709B

UT Date	δt	ν	Fν
	(days)	(GHz)	(μJy)
2011 Jul 11.97	2.07	5.8	190 ± 14
2011 Jul 12.92	3.02	5.8	250 ± 27
2011 Jul 16.88	6.98	5.8	310 ± 18
2011 Jul 21.97	12.07	5.8	210 ± 14
2011 Jul 29.96	20.06	5.8	98 ± 17
2011 Aug 19.85	40.59	5.8	98 ± 6
2011 Sep 17.70	69.72	5.8	<38a
2011 Jul 22.01	12.11	21.8	<135

Notes. Dates specify the mid-time of the observations. ^aUpper limits are 3σ.

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Finally, to determine the position of the radio afterglow we fit the source in each image with a Gaussian profile (AIPS task JMFIT), and calculated the mean radio position weighted by the resulting statistical uncertainties. We find a weighted mean position of R.A. = 10^h58^m37113 (±0.001), decl. = −23°27'1676 (±0.02).

2.4.2. GRB 111215A

We observed GRB 111215A with the JVLA beginning on 2011 December 17.00 UT (δt ≈ 1.4 days), and subsequently detected the radio afterglow starting at δt ≈ 3.35 days. Observations between 1.4 and 140 days were obtained at mean frequencies of 5.8, 8.4, and 21.8 GHz. We used 3C48 for band-pass and flux calibration and interleaved observations of J2311+3425 every ∼4 m for gain calibration at 21.8 GHz and J2340+2641 every ∼5.5 m for gain calibration at 5.8 and 8.4 GHz. The data were analyzed in the same manner described above, and the resulting flux densities are listed in Table 3. The light curves are shown in Figures 2 and 3.

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Table 3. Radio Observations of GRB 111215A

Telescope	UT Date	δt	ν	Fν
		(days)	(GHz)	(μJy)
JVLA	2011 Dec 17.00	1.41	4.9	<115a
			6.7	<93
	2011 Dec 23.05	7.46	4.9	470 ± 28
			6.7	460 ± 34
	2011 Dec 29.03	13.44	4.9	300 ± 21
			6.7	540 ± 19
	2011 Dec 31.00	15.41	4.9	820 ± 30
			6.7	1180 ± 30
	2012 Jan 10.99	26.40	4.9	590 ± 33
			6.7	820 ± 36
	2012 Jan 29.84	45.25	4.9	420 ± 52
			6.7	400 ± 55
	2012 Mar 12.82	88.23	4.9	330 ± 39
			6.7	300 ± 34
	2011 Dec 31.00	15.41	8.4	1340 ± 63
	2012 Jan 10.99	26.40	8.4	880 ± 120
	2012 Jan 29.84	45.25	8.4	470 ± 81
	2012 Mar 12.82	88.23	8.4	240 ± 95
	2011 Dec 18.93	3.35	19.1	1520 ± 74
			24.4	1990 ± 47
	2011 Dec 27.08	11.49	19.1	1670 ± 47
			24.4	1650 ± 74
	2011 Dec 31.00	15.41	19.1	1530 ± 49
			24.4	1370 ± 62
	2012 Jan 10.99	26.40	19.1	840 ± 65
			24.4	730 ± 78
	2012 Jan 29.84	45.25	19.1	500 ± 66
			24.4	460 ± 69
	2012 Mar 12.82	88.23	19.1	214 ± 66
			24.4	180 ± 72
CARMA	2011 Dec 17.05	1.46	93	2300 ± 200
	2011 Dec 20.02	4.43	93	1900 ± 220
	2011 Dec 22.04	6.45	93	1900 ± 220
	2011 Dec 24.10	8.51	93	1400 ± 180
	2011 Dec 26.01	10.42	93	1400 ± 270
	2012 Jan 1.14	16.55	93	940 ± 200
PdBI	2011 Dec 26.67	11.08	94.5	1378 ± 65
	2011 Dec 27.56	11.99	86.7	1356 ± 69
	2012 Jan 1.78	17.19	104.7	799 ± 70
	2012 Jan 9.68	24.09	86.7	644 ± 94
	2012 Jan 12.65	27.06	86.7	478 ± 58
	2012 Jan 26.49	40.91	86.7	<264b1
	2012 Feb 27.76	73.17	93.7	<294b2
	2012 Feb 28.53	73.94	93.7	<189b3
SMA	2011 Dec 18.30	2.71	230	<2600

Notes. Dates specify the mid-time of the observations. 1σ errors are statistical and do not incorporate uncertainty in overall flux scaling. ^aUpper limits are 3σ. Formal measurements are 197 ± 88 μJy (b1), 9 ± 98 μJy (b2), and 161 ± 63 μJy (b3).

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We obtain a weighted mean position from all 21.8 GHz detections of R.A. = 23^h18^m13314 (±0.004), decl. = +32°29'3907 (±0.06). The JVLA data (along with CARMA observations: Section 2.5) provide the only sub-arcsecond position for GRB 111215A.

2.5. Millimeter Observations

2.6. Host Galaxy Observations and Redshift Constraints

2.6.1. GRB 110709B

We obtained Hubble Space Telescope (HST) observations of GRB 110709B with the Wide Field Camera 3 (WFC3; Kimble et al. 2008) on 2011 November 8.94 UT (δt ≈ 122 days) using the ultraviolet imaging spectrograph (UVIS) with the F606W filter, and on 2011 November 12.94 UT (δt ≈ 126 days) using the infrared (IR) channel with the F160W filter (PI: Levan). One orbit of observations was obtained in each filter, with exposure times of 2610 s (F606W) and 2480 s (F160W). The data were processed using multidrizzle (Fruchter & Hook 2002; Koekemoer et al. 2002) with output pixel scales set at 002 and 007, respectively.

To locate the absolute radio and X-ray afterglow positions on the HST images we tie the F606W and F160W images to the 2MASS reference frame using a wider field Gemini-South GMOS r-band image as an intermediary. Using 20 common sources with 2MASS, the absolute astrometry of the Gemini image has an rms scatter of σ_GMOS-2MASS = 015 in each coordinate. The HST images are tied to the GMOS image using 30 common sources with a resulting rms scatter of σ_HST-GMOS = 003 in each coordinate. We further refine the Chandra afterglow position relative to the HST astrometric frame using a single common source. This leads to a shift in the X-ray position of δR.A. = −010 (−007) and δdecl. = +020 (+018) relative to the F606W (F160W) reference frame. There are no common sources between the HST and JVLA images.

The resulting uncertainty in the radio afterglow position in the HST reference frame is dominated by the absolute astrometry, and corresponds to a radius of 022 (1σ; the centroid uncertainty of the radio position is only 002 in each coordinate). The uncertainty in the X-ray afterglow position is reduced by the relative tie of the Chandra and HST reference frames, leading to a radius of 010 (1σ; the centroid uncertainty of the Chandra position is about 008 in each coordinate). Within the uncertainty regions we find a single galaxy in both HST images (Figure 4), which we identify as the host of GRB 110709B. Photometry of this source using the tabulated WFC3 zero points gives m_F606W = 26.78 ± 0.17 AB mag and m_F160W = 25.13 ± 0.10 mag, corrected for Galactic extinction.

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To determine the probability of chance coincidence, P_cc(< δR) = 1 − exp[ − π(δR)²σ(⩽ m)], we use the galaxy number counts, σ(⩽ m) = 10^{0.33(m − 24) − 2.32} arcsec⁻² (Hogg et al. 1997; Beckwith et al. 2006). For the XRT error circle we infer P_cc ≈ 0.1, while for the more precise JVLA and Chandra positions we find P_cc ≈ 0.006 and ≈0.001, respectively. Thus, the sub-arcsecond radio and X-ray positions enable a robust association with the galaxy, while the XRT position alone would have led to marginal confidence. This is essential since the detection of the host galaxy in the F606W filter limits the redshift to z ≲ 4, indicating that GRB 110709B is dark due to extinction and not a z ≳ 18 origin.

For a redshift from z ∼ 1, the F606W band samples the rest-frame UV emission from the host galaxy. Based on the observed flux density calculated from the apparent magnitude (m_F606W = 26.78  ±  0.17 AB mag) assuming the standard cosmological parameters noted in Section 1 to calculate the luminosity distance (Wright 2006), we utilize Equation (1) in Kennicutt (1998)

$$\begin{equation} {\rm SFR}\, (M_{\odot }\ {\rm yr}^{-1}) = 1.4 \times 10^{-28} {L}_\nu\; {\rm (erg\ s^{-1}\ Hz^{-1})} \end{equation} \tag{ 1 }$$

to infer SFR ≈ 0.3–3.2 M_☉ yr⁻¹ for z = 1–4, not corrected for possible galactic-scale extinction.

2.6.2. GRB 111215A

We obtained i-band observations of GRB 111215A with GMOS on the Gemini-North 8 m telescope on 2011 December 23.21 UT (δt ≈ 7.6 days), with a total exposure time of 2160 s in 09 seeing. Astrometric matching to the 2MASS catalog using 30 common sources reveals a galaxy within the enhanced XRT error circle at R.A. = 23^h18^m13317, decl. = +32°29'3877, with an uncertainty of about 016 in each coordinate (absolute) and an uncertainty of about 006 in the galaxy centroid; see Figure 5. We obtained imaging observations with the Low-Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on the Keck I 10 m telescope on 2012 July 15.20 UT (δt = 212.6 days) in the g- and I-band filters. Finally, we also obtained observations of the GRB 111215A host galaxy with the OSIRIS instrument (Sánchez et al. 2012) on the 10.4 m Gran Telescopio Canarias (GTC) on 2012 August 23.02 UT in the griz bands with an average seeing of 09.

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Taking into account the uncertainty in the JVLA radio afterglow position (006 in each coordinate), the resulting overall uncertainty in the location of the afterglow on the Gemini image is 026 radius (1σ). Similarly, the uncertainty in the CARMA mm afterglow position (008 in each coordinate) leads to an overall uncertainty of 027 radius (1σ). The resulting offset between the host centroid and radio positions is 030 ± 026.

Photometry of the galaxy relative to the Sloan Digital Sky Survey catalog results in a brightness of m_g = 24.40 ± 0.18, m_r = 24.24 ± 0.15, m_i = 23.87 ± 0.18, and m_z = 23.90 ± 0.36 (GTC), and m_g = 24.50 ± 0.15 mag and m_i = 23.64 ± 0.05 mag corrected for Galactic extinction (Gemini). The probability of chance coincidence for this galaxy within the XRT error circle is P_cc ≈ 0.01, with a slightly lower probability of ≈7 × 10⁻³ using the radio position, dominated by the physical extent of the galaxy of about 1''. Given the low chance coincidence probability we consider this galaxy to be the host of GRB 111215A.

To determine the redshift of the host we obtained an 1800 s spectrum with the Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995; Rockosi et al. 2010) on Keck I using a 07 slit with the 400/3400 grism in the blue arm and the 400/8500 grating in the red arm, providing effectively continuous wavelength coverage from the atmospheric cutoff to 10280 Å (with a total throughput within 50% of peak to about 10030 Å). The slit was oriented to cover the host galaxy, as well as the fainter extended source to the northeast. The spectrum was reduced using standard techniques implemented in a custom pipeline.

We detect continuum emission from both galaxies on the blue side, and from the host galaxy on the red side. We identify only one emission feature from the nearby galaxy, a marginally resolved line centered at 8019 Å. Interpreted as the [O ii]λ3727 doublet, this indicates a redshift²⁰ of z = 1.152. We do not identify any emission lines from the host galaxy. Given that the galaxy is reasonably bright in g- and i-band and is expected to be actively star-forming, the lack of emission lines indicates that z ≳ 1.8 (from the non-detection of [O ii]λ3727 to 10030 Å) and z ≲ 2.9 (from the absence of a break due to the Lyman limit to 3860 Å).²¹

At z ∼ 1.8–2.9, the observed i- and g-band fluxes trace the host galaxy rest-frame UV emission. The observed color of g − i ≈ 0.85 ± 0.20 mag is indicative of extinction; for example, it is well-matched to the observed color of Arp 220, a local ULIRG. Using the observed i-band flux density, which is less susceptible to extinction corrections, we infer SFR ≈ 15–30 M_☉ yr⁻¹ (z = 1.8–2.9), which should be considered as a minimum value due to the uncertain extinction.

GRBs 110709B and 111215A are dark in both the optical and near-IR bands due to rest-frame dust extinction; a high-redshift origin is ruled out by the association with optically-detected host galaxies. It is also of note that for extreme redshifts (z  >  18), the N_{H, int} implied by the observed excess in the X-ray spectra would be very high (e.g., >10²⁴ cm⁻²), further supporting the rejection of an extreme redshift for either event. In addition to providing accurate localizations and hence secure host associations, the radio data also allow us to determine the properties of the bursts and their local environments. This not only provides a more robust measure of the required rest-frame extinction than using β_OX alone (which requires an assumption about the location of the synchrotron cooling frequency), but it also allows us to compare the explosion properties of dark and optically-bright bursts.

We model the radio and X-ray data for GRBs 110709B and 111215A using the standard afterglow synchrotron model (Granot & Sari 2002; Sari et al. 1999) to (1) determine the expected optical and near-IR brightness, and hence the required level of rest-frame extinction given the observed limits; and (2) determine the properties of the bursts and their circumburst environments. We follow the standard assumptions of synchrotron emission from a power-law distribution of electrons (N(γ)∝γ^−p for γ ⩾ γ_m) with constant fractions of the post-shock energy density imparted to the electrons (_e) and magnetic fields (_B). The additional free parameters of the model are the isotropic-equivalent blast-wave kinetic energy (E_{K, iso}), the circumburst density (parameterized as n for a constant density medium: ISM; or as A for a wind medium with ρ(r) = Ar⁻²), and a jet break time (t_j). To determine the opening angle (θ_j), we use the conversions from t_j given by Sari et al. (1999) and Chevalier & Li (2000), with the appropriate dependence on E_{K, iso} and the circumburst density (n or A, respectively).

Using the time evolution of the synchrotron spectrum for both the interstellar medium (ISM) and wind density profiles in the pre- and post-jet break phases (Chevalier & Li 2000; Granot & Sari 2002) we simultaneously fit all X-ray and radio observations for each burst. The resulting best-fit parameters are summarized in Tables 4 and 5 using redshifts of z = 1, 2, 3, 4 for GRB 110709B and z = 2 for GRB 111215A. In both cases we find that the most stringent constraint on the rest-frame extinction are provided by the observed K-band limits. We use the Small Magellanic Cloud (SMC) extinction curve to determine the rest-frame extinction, although the Milky Way extinction curve gives similar results.

Table 4. Results of Broadband Afterglow Modeling for GRB 110709B

Parameter	z = 1	z = 2	z = 3	z = 4
EK, iso, 52 (erg)	0.5	2.8	7.1	13.2
A* (5 × 1011 g cm−1)	4.0	5.7	7.2	8.5
$\bar{\epsilon }_e$	0.18	0.11	0.08	0.07
B	0.002	0.002	0.002	0.002
p	2.07	2.06	2.05	2.05
tj (days)	3.65	3.45	3.27	3.11
θj (rad)	0.40	0.25	0.19	0.16
EK, 51 (erg)	0.4	0.9	1.3	1.7
Eγ, iso, 52a (erg)	7.0	26	52	83
Eγ, 51 (erg)	5.4	8.0	9.4	10.6
AVb (mag)	≳ 10.5	≳ 5.3	≳ 4.4	≳ 3.4

Notes. See Section 3 for description of model parameters. ^aUsing the Konus-WIND 20–5000 keV fluence. ^bUsing the SMC extinction curve.

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Table 5. Results of Broadband Afterglow Modeling for GRB 111215A

Parameter	z = 2	z = 3
EK, iso, 52 (erg)	7.7	13.3
A* (5 × 1011 g cm−1)	17	19
$\bar{\epsilon }_e$	0.16	0.14
B	9.0 × 10−5	1.0 × 10−4
p	2.30	2.30
tj (days)	12	13
θj (rad)	0.35	0.30
EK, 51 (erg)	4.6	5.8
Eγ, iso, 52a (erg)	4.5	9.0
Eγ, 51 (erg)	2.7	3.9
AVb (mag)	≳ 8.5	≳ 6.8

Notes. See Section 3 for description of model parameters. ^aUsing the fluence in the Swift/BAT 15–150 keV band. ^bUsing the SMC extinction curve.

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For GRB 110709B we find that the data favor a wind environment, with a jet break at t_j ≈ 3.1–3.6 days, corresponding to an opening angle, θ_j, ≈9°–23°; the jet break occurs earlier and the resulting opening angle is narrower as the redshift increases from z = 1 to z = 4. The resulting beaming-corrected energies are E_K ≈ (0.4–1.7) × 10⁵¹ erg and E_γ ≈ (5.4–10.6) × 10⁵¹ erg (in the observed 20–5000 keV fluence of the initial event). The circumburst density is characterized by a mass-loss rate of $\dot{M}\approx (4\hbox{--}8)\times 10^{-5}$ M_☉ yr⁻¹ for a wind velocity of v_w = 10³ km s⁻¹ (i.e., A* ≈ 4–8). Finally, using the near-IR K_s-band limit we find that the required extinction ranges from $A_V^{\rm host}\gtrsim 10.5$ mag at z = 1 to ≳ 3.5 mag at z = 4. We note that the best-fit ISM model also requires a high density of ∼10–100 cm⁻³ at z ∼ 1–4.

For GRB 111215A we again find that a wind environment provides a better fit, with a jet break at t_j ≈ 12 days, corresponding to an opening angle of θ_j ≈ 24°. The resulting beaming-corrected energies are E_K ≈ 3.7 × 10⁵¹ erg and E_γ ≈ 3.9 × 10⁵¹ erg (in the observed 15–150 keV band). The circumburst density is characterized by a substantial mass-loss rate of $\dot{M}\approx 2\times 10^{-4}$ M_☉ yr⁻¹ (for a wind velocity of v_w = 10³ km s⁻¹). Finally, using the near-IR K_s-band limit we find a required extinction of $A_V^{\rm host}\gtrsim 8.5$ mag (for z = 2). We note that the best-fit ISM model also requires a density of ∼100–300 cm⁻³. Dust extinction this large is indicative of dust associated with the local environment of the GRB (e.g., Reichart & Price 2002; Campana et al. 2006).

4.1. Extinction and Neutral Hydrogen Column Density

The large rest-frame extinction that is required to explain the lack of optical and near-IR emission from GRBs 110709B and 111215A is uncommon amongst known GRBs. In Figure 6 we plot the minimum values of $A_V^{\rm host}$ for the two bursts as a function of redshift, along with several comparison samples from the literature of optically-bright bursts and previous dark bursts. In general, optically-bright GRBs have inferred extinction values of ≲ 1 mag, with a mean of ∼0.2–0.3 mag (Kann et al. 2006, 2010; Schady et al. 2007; Perley et al. 2009; Krühler et al. 2011). Dark GRBs span $A_V^{\rm host}\approx 1\hbox{--}6$ mag (Perley et al. 2009; Krühler et al. 2011; Prochaska et al. 2009; Castro-Tirado et al. 2007; Rol et al. 2007), with the largest extinction values of ∼5–6 mag inferred for GRBs 061222, 070306, and 070521 (Perley et al. 2009; Krühler et al. 2011; Jaunsen et al. 2008). In this context, the extinction values measured here are at the top of the distribution, $A_V^{\rm host}\gtrsim 5.3$ mag (110709B) and ≳ 8.5 mag (111215A) at z = 2.

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In Figure 7 we plot the intrinsic neutral hydrogen column densities, N_{H, int}, from our X-ray analysis as a function of redshift, in comparison with the population of all Swift long GRBs with known redshifts (up to 2010 December; Margutti et al. 2013; see also Jakobsson et al. 2006 and Fynbo et al. 2009). We find that GRBs 110709B and 111215A lie at the upper end of the distribution for long GRBs. In particular, at a fiducial redshift of z = 2 they have log(N_{H, int}) ≈ 22.1 and ≈22.5, respectively, in comparison with the median value of all detections and upper limits of 〈log(N_{H, int})〉 ≈ 21.7. This result confirms recent suggestions that dark GRBs have systematically larger neutral hydrogen columns, generally with log(N_{H, int}) ≳ 22 (Perley et al. 2009; Campana et al. 2012); see Figure 7. In their spectroscopic sample of GRBs, Fynbo et al. (2009) also find dark bursts to have higher excess absorption in general, and more specifically, the three bursts with highest column densities are dark. Indeed, only a handful of events in the Swift sample have values of N_{H, int} comparable to that of GRB 111215A (if z ≳ 2). The same conclusion is true for GRB 110709B if it resides at the upper end of the allowed redshift distribution (z ∼ 3–4), although at z ∼ 1 its neutral hydrogen column is typical of the overall long GRB population.

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A correlation between extinction and N_H is known to exist in the Milky Way and the Magellanic Clouds, with N_H ≈ 2 × 10²¹ A_V cm⁻² (Predehl & Schmitt 1995; Güver & Özel 2009; Watson 2011). As shown in Figure 8, optically-bright GRBs generally have lower values of $A_V^{\rm host}$ than would be inferred from this relation (e.g., Galama & Wijers 2001; Stratta et al. 2004; Zafar et al. 2011), with mean values of N_{H, int} ≈ 5 × 10²¹ cm⁻² and $A_V^{\rm host}\approx 0.2\hbox{--}0.3$ mag; the expected extinction based on the Galactic relation is $A_V^{\rm host}\approx 2.5$ mag. Dark GRBs also generally have lower extinction than expected, with N_{H, int} ≈ (5–50) × 10²¹ cm⁻² and $A_V^{\rm host} \approx 1\hbox{--}5$ mag, whereas extinctions of $A_V^{\rm host}\approx 5\hbox{--}25$ mag would be expected.

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For the bursts presented here we find potentially different results. GRB 111215A agrees with the Galactic relation if it resides at the lower redshift bound (z ≈ 1.8), in which case N_{H, int} ≈ 2.5 × 10²² cm⁻² and $A_V^{\rm host}\gtrsim 11$ mag. At the higher redshift bound (z ≈ 2.7) we find N_{H, int} ≈ 5 × 10²² cm⁻² and $A_V^{\rm host}\gtrsim 6$ mag (with an expected $A_V^{\rm host}\approx 23$ mag). This is still consistent with the Galactic relation since we only place a lower bound on $A_V^{\rm host}$. Similarly, GRB 110709B crosses the Galactic relation at z ≈ 2, with N_{H, int} ≈ 1.2 × 10²² cm⁻² and $A_V^{\rm host}\gtrsim 5.3$ mag. However, at z ≲ 2 it has larger extinction than expected; for example, at z = 1 we measure $A_V^{\rm host}\gtrsim 10.5$ mag compared with the expected value of ≈2.5 mag. At z ≳ 2 the situation is similar to GRB 111215A, namely the minimum value of $A_V^{\rm host}$ is below the expected Galactic relation, but this is only a lower limit. We therefore conclude that the dark bursts with the largest known extinction values are potentially in line with the Galactic N_H–A_V relation, although they may also reside below the expected correlation in line with the bulk of the GRB population.

4.2. Explosion and Circumburst Properties of Dark Bursts

4.3. Burst Durations

Using X-ray, optical/near-IR, and radio observations we have demonstrated that: (1) GRBs 110709B and 111215A are dark bursts; (2) they are robustly associated with galaxies at z ≲ 4 (110709B) and z ≈ 1.8–2.9 (111215A); (3) they require unusually large rest-frame extinction (among the highest values to date) of $A_V^{\rm host}\gtrsim 5.3$ mag (110709B) and ≳ 8.5 mag (111215A) at z = 2; (4) they exhibit commensurately large neutral hydrogen column densities in their X-ray spectra, N_{H, int} ≈ (1–3) × 10²² cm⁻², which at z ∼ 2 are consistent with the Galactic N_H–A_V relation, unlike the overall long GRB population; and (5) their circumburst environments on a sub-parsec scale are shaped by large progenitor mass-loss rates of ≈(6–20) × 10⁻⁵ M_☉ yr⁻¹.

Radio observations played a critical role in this study for three reasons. First, they provided sub-arcsecond positions, which led to a secure identification of the host galaxies. This allowed us to distinguish the extinction scenario from a high-redshift origin. Second, the combination of radio and X-ray data allowed us to robustly determine the required extinction, instead of simply assuming an optical to X-ray spectral index. Indeed, in cases with only X-ray data the unknown location of the synchrotron cooling frequency prevents a unique determination of the extinction. Finally, the radio and X-ray data allowed us to determine the burst parameters, including the geometry, beaming-corrected energy, and the circumburst density. We find that the energy scale for GRBs 110709B and 111215A is similar to the overall population of optically-bright GRBs. However, the inferred mass-loss rates are larger by about an order magnitude compared with optically-bright bursts, potentially indicating that GRB progenitors in dusty environments have stronger metal line driven winds.

The increased sensitivity of the JVLA played an important role in the study and utilization of the radio afterglow. ALMA will provide similar capabilities, with an expected spatial resolution of about 004–5'' at 100 GHz (depending on configuration), and hence an assured sub-arcsecond centroiding accuracy for S/Ns of ≳ 10 even in the most compact configuration. As demonstrated here, Chandra observations can also provide sub-arcsecond positions, but such observations may not be available for all dark GRB candidates (e.g., GRB 111215A). In addition, Chandra data will not enhance the ability to determine the required extinction through broadband modeling.

The JVLA and ALMA will also allow us to study the host galaxies of GRBs 110709B and 111215A (as well as those of past and future dark bursts) in greater detail than optical/near-IR studies alone. In particular, they will address the question of highly-obscured star formation in these galaxies, and may even lead to redshift determinations through the detection of molecular lines. Existing observations with the Very Large Array and the MAMBO and SCUBA bolometers (in the small samples published to-date) have led to only a few detections of GRB hosts (Berger et al. 2003a), with no obvious preference for dark burst hosts (Barnard et al. 2003). However, the enhanced sensitivity of ALMA will allow for detections even with star formation rates of tens of M_☉ yr⁻¹ at z ∼ 2. The combination of detailed host galaxy properties from rest-frame radio to UV, coupled with measurements of the local environments of dark bursts through broadband afterglow modeling will shed light on the location of the obscuring dust (interstellar versus circumstellar) and the impact of metallicity on GRB progenitor formation.

We thank R. Chary for helpful discussions regarding obscured star formation in distant galaxies and Y. Cao for his assistance in attaining the optical spectrum of GRB 111215A while observing at Keck. The Berger GRB group at Harvard is supported by the National Science Foundation under grant AST-1107973, and by NASA/Swift AO7 grant NNX12AD69G. B.A.Z., E.B., R.M., W.F., and A.S. acknowledge partial support of this research while in residence at the Kavli Institute for Theoretical Physics under National Science Foundation Grant PHY11-25915. E.N. acknowledges partial support by an ERC starting grant. F.O.E. acknowledges funding of his PhD through the Deutscher Akademischer Austausch-Dienst (DAAD). A.J.C.T. acknowledges support from the MINECO Spanish Ministry projects AYA 2009-14000-C01 and AYA 2012-39737-C03-01. We thank the referee for useful comments and suggestions.

Funding for GROND was generously granted from the Leibniz Prize to G. Hasinger (DFG grant HA 1850/28-1). D.P. is supported by grant HST-HF-51296.01-A, provided by NASA through a Hubble Fellowship grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. Support for this work was provided by the National Aeronautics and Space Administration (NASA) through Chandra Award Number 09900712 issued by the Chandra X-ray Observatory Center, which is operated by the SAO for and on behalf of NASA under contract NAS8-03060. The JVLA is operated by the National Radio Astronomy Observatory, a facility of the NSF operated under cooperative agreement by Associated Universities, Inc. JVLA observations were undertaken as part of project numbers 10C-145 and 11B-242. Support for CARMA construction was derived from the Gordon and Betty Moore Foundation, the Kenneth T. and Eileen L. Norris Foundation, the James S. McDonnell Foundation, the Associates of the California Institute of Technology, the University of Chicago, the states of California, Illinois, and Maryland, and the NSF. Ongoing CARMA development and operations are supported by the NSF under a cooperative agreement, and by the CARMA partner universities. CARMA observations were undertaken as part of projects c0773 and cx334. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory (SAO) and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. SMA observations were undertaken as part of project 2011B-S003. The IRAM Plateau de Bure Interferometer is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). Some observations were obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the NSF (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). Gemini observations were undertaken as part of programs GS-2011A-Q-25 and GN-2011B-Q-10. Some observations were made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. HST observations were undertaken as part of program 12378. This work utilized observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofsica de Canarias, in the island of La Palma. This research has made use of Swift data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center. This research has made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASI Science Data Center (ASDC), Italy.

Facilities: Swift (XRT) - Swift Gamma-Ray Burst Mission, CXO (ACIS-S) - Chandra X-ray Observatory satellite, Gemini:South (GMOS) - Gemini South Telescope, Keck:I (LRIS) - KECK I Telescope, HST (ACS, WFC3) - Hubble Space Telescope satellite, GTC - Gran Telescopio CANARIAS 10.4m telescope (GRANTECAN), OSN - , CARMA - Combined Array for Research in Millimeter-Wave Astronomy, SMA - SubMillimeter Array, VLA - Very Large Array, IRAM:Interferometer - Institute de Radioastronomie Millimetrique Interferometer, ESO 2.2m/GROND