The Environments of the Most Energetic Gamma-Ray Bursts

The Environments of the Most Energetic Gamma-Ray Bursts

B. P. Gompertz Space Telescope Science Institute, Baltimore, MD 21218, USA Department of Physics, University of Warwick, Coventry, CV4 7AL, UK A. S. Fruchter Space Telescope Science Institute, Baltimore, MD 21218, USA A. Pe’er Physics Department, University College Cork, Cork, Ireland
Abstract

We analyze the properties of a sample of long gamma-ray bursts (LGRBs) detected by the Fermi satellite that have a spectroscopic redshift and good follow-up coverage at both X-ray and optical/nIR wavelengths. The evolution of LGRB afterglows depends on the density profile of the external medium, enabling us to separate wind or ISM-like environments based on the observations. We do this by identifying the environment that provides the best agreement between estimates of , the index of the underlying power-law distribution of electron energies, as determined by the behavior of the afterglow in different spectral/temporal regimes. At 11 rest-frame hours after trigger, we find a roughly even split between ISM-like and wind-like environments. We further find a 2 separation in the prompt emission energy distributions of wind-like and ISM-like bursts. We investigate the underlying physical parameters of the shock, and calculate the (degenerate) product of density and magnetic field energy (). We show that must be to avoid implied densities comparable to the intergalactic medium. Finally, we find that the most precisely constrained observations disagree on by more than would be expected based on observational errors alone. This suggests additional sources of error that are not incorporated in the standard afterglow theory. For the first time, we provide a measurement of this intrinsic error which can be represented as an error in the estimate of of magnitude . When this error is included in the fits, the number of LGRBs with an identified environment drops substantially, but the equal division between the two types remains.

\correspondingauthor

Benjamin Gompertz

1 Introduction

Long gamma-ray bursts (LGRBs) are well established as core-collapse events following the deaths of massive stars, due to their close proximity to very young star forming regions (Fruchter et al., 2006; Levesque et al., 2010) and consistent association with type Ic supernovae (e.g. Hjorth et al., 2003; Cano, 2013). Their emission is best modelled as a collimated jet of relativistic material that is launched from the central star by the initial collapse (cf. Woosley, 1993). The -rays are widely believed to be produced by dissipation of either kinetic (e.g. Paczynski, 1986; Rees & Meszaros, 1992) or magnetic (e.g. Usov, 1994; Drenkhahn & Spruit, 2002; Zhang & Yan, 2011) energy in the expanding jet.

The expanding jet collides with material in the circumstellar environment, causing it to decelerate. As it moves at relativistic speeds, a shock wave is formed (Blandford & McKee, 1976). The shock is believed to accelerate particles to high energies as well as generate a strong magnetic field. The heated particles in turn emit a broad-band radiation (mainly via synchrotron and possibly Compton) known as the ‘afterglow’, with emission ranging from X-rays to radio frequencies.

Broad-band fitting of LGRB afterglows suggests that they can occur in at least two different types of environment (Chevalier & Li, 1999): interstellar medium (ISM)-like environments, in which the density of the circumstellar material does not change with distance from the central object, or wind-like environments, in which the density falls as . The latter case should occur when the progenitor star possessed a strong stellar wind in its final stages of life before collapse (Chevalier & Li, 2000). The former may be the result of a progenitor star with a very weak stellar wind, so that the expanding fireball quickly crosses from the wind-like environment into a homogeneous density region at larger radii (see e.g. Pe’er & Wijers, 2006; van Marle et al., 2006).

LGRB afterglows are generally well explained by synchrotron theory(Rees & Meszaros, 1992; Wijers et al., 1997; Sari et al., 1998; Wijers & Galama, 1999; Granot et al., 2002; Gao et al., 2013). It is assumed that electrons at the shock front are accelerated to a power-law distribution of the form , above a minimum Lorentz factor . is the electron’s Lorentz factor. Here the power-law index is . The shape of the distribution means that the minimum Lorentz factor is also the most common, and represents the peak frequency () of the synchrotron spectrum. At sufficiently high frequencies, the radiative cooling time equals the dynamical time, which is the time available to cool. As a result, above the cooling break (), the steady state distribution of the electrons, resulting from both rapid acceleration and cooling, steepens. Finally, at low frequencies the emitted photons are more easily re-absorbed by the emitting material, and this creates a third break in the synchrotron spectrum: the self-absorption frequency .

The positions of these breaks are functions of the physical properties of the plasma flow, such as the energy, magnetic field, density and available time. While there is some knowledge about, e.g., the available energy, the values of parameters like the magnetic field strength and the density are highly uncertain. Nonetheless, these parameters combine to describe a spectrum comprised of four power-law segments smoothly connected by three spectral breaks: , and . At times of around half a day post-burst, is typically found close to X-ray frequencies in LGRBs, with at optical/near infra-red (nIR) frequencies and down at radio wavelengths.

Because the synchrotron spectrum is sensitive to density, its evolution can be used to diagnose the type of environment into which the GRB afterglow is expanding. The theoretical relation between , the spectral index , and the temporal index is given by the synchrotron closure relations, which vary between environment types and in different regions of the synchrotron spectrum. We use the convention when discussing them.

As early as a few years after the detection of the first LGRB optical afterglow (van Paradijs et al., 1997) a split between ISM-like and wind-like environments was observed, with up to 50 per cent of bursts found to be consistent with a homogeneous medium (e.g. Chevalier & Li, 2000; Panaitescu & Kumar, 2001, 2002). In later studies, (e.g. Starling et al., 2008; Curran et al., 2009) ISM-like environments continued to be found in LGRB afterglows. Schulze et al. (2011) studied the environments of a sample of 26 Swift LGRBs (and one SGRB), finding just 6 that showed a wind-like evolution at late times. 18 were classed as ISM-like. Measurements of the spectral and temporal indices for optical (Oates et al., 2012) and X-ray (Oates et al., 2015; Racusin et al., 2016) afterglows of LGRBs all point to a split in environment types between wind and ISM. In the largest previous study to date, Li et al. (2015) investigated the X-ray and optical slopes of a large sample of 87 GRBs (80 with redshift) discovered by the Swift satellite up until 2013, finding that 61 per cent of them were consistent with an ISM-like medium, while just 39 per cent appeared wind-like.

Given the apparent prevalence of ISM-like environments, the signature of the afterglow emission site transitioning across a termination shock from a wind-like to an ISM-like medium (e.g. Dai & Lu, 2002) should in theory be commonly observed within the LGRB afterglow population. However, despite several claims (Dai & Wu, 2003; Jin et al., 2009; Feng & Dai, 2011; Veres et al., 2015), such a signature has never been unambiguously identified. LGRBs therefore warrant further investigations into their environment types, their energies, and the underlying physical parameters of their afterglows. These properties may provide clues as to why a termination shock transition has not been observed. Obtaining a large sample with known redshift allows for well-defined energetics, which provides a previously unexplored attribute when making comparisons between the identified environment types.

In this paper, we investigate the energetics and environments of a sample of 56 Fermi-discovered LGRBs, all of which have an identified redshift and detections in both X-rays and optical/nIR. We include bursts observed by both the Large Area Telescope (LAT; Atwood et al., 2009) and the Gamma-ray Burst Monitor (GBM; Meegan et al., 2009), and those seen by the GBM only. Contrary to previous works, we discriminate between the different environment types based on several independent measures: the observed spectral and temporal indices, and the measured ratio of their optical-to-X-ray fluxes () where appropriate. The increased bandpass of GBM compared to Swift-BAT also allows us to better constrain the isotropic equivalent -ray energy () of each burst and compare it across the sample. This enables us for the first time to make statistical comparisons between environment types based on burst energies.

In Section 2 we introduce the data collected for the sample. Section 3 describes how we ascertain the environment type for each burst. Our results are presented in Section 4, and are discussed in Section 5. We outline our conclusions in Section 6. We use a cosmology of  km s Mpc, and (Planck Collaboration et al., 2016) throughout this paper.

2 Data

We collected all LGRBs that were detected by the Fermi satellite, had been observed by both Swift-XRT and ground-based optical/nIR telescopes, and had an identified redshift. Our sample is the largest and most comprehensive collection of Fermi-discovered GRBs with redshift and multi-wavelength observations, comprising events.

2.1 Prompt Data

To calculate the isotropic -ray energy release, , we take the GBM fluence measured in the -  keV bandpass from the Fermi-GBM catalogue (Gruber et al., 2014; von Kienlin et al., 2014; Narayana Bhat et al., 2016). Comparing energies between bursts of different redshifts requires a cosmological k-correction (Bloom et al., 2001) in order to account for the shift in the observer frame bandpass, and this requires knowledge of the spectral shape of the prompt emission. GRB prompt emission spectra are usually fitted with the Band function (Band et al., 1993), comprised of a low-energy spectral index , a peak energy , and a high energy spectral index . Taking the Band function spectral parameters from the Fermi-GBM catalogue (Gruber et al., 2014; von Kienlin et al., 2014; Narayana Bhat et al., 2016), we convert the observer frame -  keV fluence into between -  keV in the rest frame for each burst. This is one area in which our work has a significant advantage over studies done with Swift-BAT, since the BAT bandpass of -  keV often does not capture , making the true prompt emission energy uncertain. Our prompt emission parameters, including k-corrected energies, are displayed in Table LABEL:tab:prompt.

GRB Fluence T E E
(erg cm) (s) (keV) (erg)
LAT
080916C
090323
090328A
090902B
090926A
091003
091208B
100414A
100728A
110731A
120711A
130427A
130518A
130907A -
131108A
131231A
141028A
150314A
150403A
150514A
160509A
160623A
160625B
GBM
080916A
081007
081121
090423
090424
090618
091020
091127
100906A
101219B
110213A
111228A
120119A
120729A
120811C
121211A
130420A
140213A
140423A
140506A
140512A
140606B
140620A
140703A
140801A
140907A
141004A
150301B
150821A
151027A
160804A
161017A
170113A
Table 1: The prompt emission properties of the sample. Fluence is  keV in the observer frame unless marked. values have been k-corrected (Bloom et al., 2001) to  keV in the rest frame. Fluence, T, E, and come from the Fermi-GBM catalogue (Gruber et al., 2014; von Kienlin et al., 2014; Narayana Bhat et al., 2016) unless otherwise marked.

2.2 X-ray Data

The X-ray data (Table 2) come almost exclusively from the UK Swift Science Data Centre (UKSSDC; Evans et al., 2007, 2009)111www.swift.ac.uk. For each GRB, the data point closest to  h in the rest frame is identified. The Swift-XRT GRB catalog automatically fits the X-ray light curves with a broken power law model, and we take the temporal and spectral222The UKSSDC actually gives the photon index, , where the spectral index indices for the power law segment local to the selected data point. Absorption is accounted for by taking the ratio of the unabsorbed counts-to-flux over the observed counts-to-flux from the spectrum of the local power law, and applying it as a multiplication factor to the flux. We then convert to flux density via (cf. Gehrels et al., 2008):

(1)

where and are the lower and upper bounds of the bandpass in keV, is the target energy for the flux density in keV, is the measured flux in erg cm s, and is the estimated unabsorbed X-ray photon index. A k-correction (cf. Bloom et al., 2001) is applied to the flux density to account for the disparate redshifts of the rest frame bandpass between bursts, which keeps the results comparable between GRBs at different cosmological distances. Note that these may not be the same values for k as in the calculations in Table LABEL:tab:prompt due to the spectral break in the Band function. The flux densities are then extrapolated to hours rest-frame using the identified temporal index , and to  keV in the rest frame ( keV) using . We use 5 keV because at this energy the error in the flux density, caused by the uncertainty in the estimate of intrinsic absorption, is relatively small.

Due to the mis-identification of flares, for some bursts the UKSSDC automatic fitting routine gives obviously erroneous results. For these cases, we manually fit the X-ray light curves to obtain the local temporal index, then run the UKSSDC time slice spectrum routine for the identified power law segment to ascertain the local spectral index and counts-to-flux ratio. The affected bursts are GRB 100728A and GRB 120119A. For four bursts in the sample, we have additional X-ray observations from Chandra (Fruchter et al. in prep). In these cases, we again fit the light curves manually to find the temporal indices, and use the UKSSDC time slice spectrum tool to find the spectral index for the local power law segment. The four bursts are GRBs 110731A, 120711A, 130427A and 150314A.

GRB F Absorption k F
(h) (erg cm s) Correction (Jy)
LAT
080916C
090323
090328A
090902B
090926A
091003
091208B
100414A
100728A
110731A
120711A
130427A
130518A
130907A
131108A
131231A
141028A
150314A
150403A
150514A
160509A
160623A
160625B
GBM
080916A
081007
081121
090423
090424
090618
091020
091127
100906A
101219B
110213A
111228A
120119A
120729A
120811C
121211A
130420A
140213A
140423A
140506A
140512A
140606B
140620A
140703A
140801A
140907A
141004A
150301B
150821A
151027A
160804A
161017A
170113A
Table 2: X-ray properties of the sample. is in the range  keV in the observer frame. The absorption correction is the ratio of the counts-to-flux unabsorbed over the counts-to-flux observed from the spectrum on the UKSSDC. has been extrapolated to hours and  keV in the rest frame, and has had a k-factor applied to account for the redshift of the observed bandpass. k is the ratio of the observer frame fluence to rest frame fluence, as in Bloom et al. (2001). All tabulated values are from the UKSSDC unless marked otherwise. Manual fit. (1) - Cano et al. (2011)

2.3 Optical Data

Our optical data (Table LABEL:tab:optical) are collected from the literature, as well as GCN circulars. We select data that is as close to the rest-frame R-band as possible, which usually means the J, H or K nIR bands in the observer frame where available. We also aim to collect data as close to  hours in the rest frame as possible. Because optical/nIR coverage is never as comprehensive as it is for the X-ray, it is rarer to find values for the temporal, and in particular the spectral, indices in the literature. Where no published value exists, we fit light curves and SEDs from GCN circulars to provide our own values where possible. Light curves are fitted with both a single power law and a broken power law, which is assessed for an improvement in the fit using an f-test, and a break is accepted at the 3 level. It is the index local to the observed data point that is reported in Table LABEL:tab:optical. SEDs are fitted with a power law multiplied by the parameterised extinction curves of Cardelli et al. (1989). If the model does not converge when both the spectral index and rest frame V-band extinction are free parameters (usually due to a lack of nIR detections in the fitted SED), we fit the data with to account for the case where the synchrotron cooling break () does not lie between the two bands, then fix to account for the case where it does. We then report the extinction for the best fit, but do not report the spectral index, since this would effectively double-count in our analysis.

We correct the magnitudes reported in the literature for galactic extinction using the maps from Schlafly & Finkbeiner (2011), and for intrinsic extinction where it can be identified. Magnitudes are then converted to flux densities and extrapolated from their observed wavelength to the rest frame R-band wavelength (Å) using , and to  h in the rest frame using . In the absence of an SED or sufficient data for a light curve, we take the mean spectral and temporal indices from the sample of known values when extrapolating to the desired time/frequency, and introduce the associated standard deviation into the uncertainty of the flux density. This is indicated by the bracketed values in Table LABEL:tab:optical.

GRB m Filter F
(h) (Gal) (Int) (Jy)
LAT
080916C K (AB)
090323 R
090328A J (AB)
090902B J