LATE-TIME OBSERVATIONS OF GRB 080319B: JET BREAK, HOST GALAXY, AND ACCOMPANYING SUPERNOVA

In order to follow the X-ray light curve out to late times, beyond the sensitivity limit of the Swift/XRT, we obtained observations with Chandra/ACIS (S3 chip), roughly 38 and 58 days after the burst. We used the standard processed data (ASCDS version 7.6.11.6) for our analysis, selecting an energy range between 0.3 and 7 keV, which gave an optimal signal to noise. Photometry was performed with a 5 pixel (2.5 arcsec) radius region centered at the source position, and an annular region centered around the source as the background region (inner radius 14 arcsec, outer radius 28 arcsec).

The first epoch consisted of a 9 ks exposure, with 9 counts detected in the source region and a predicted background of 0.4 counts. The second epoch was a 36 ks exposure, resulting in 18 counts in the source region and a 1.48 count background. Data were fitted inside XSpec using appropriate response matrices, with the actual fitted values for photon index and absorption from the Swift/XRT late-time data (Racusin et al. 2008); thus, only the normalization was fitted. The fluxes were then derived using this normalized fit in the 0.3–10 keV range, giving absorption-corrected values of 8.4^+3.2_−2.7 × 10⁻¹⁵ erg cm⁻² s⁻¹ and 3.7^+1.0_−0.8 × 10⁻¹⁵ erg cm⁻² s⁻¹ for epochs 1 and 2, respectively. Here, the 1σ errors were derived using Bayesian confidence limit estimation (Kraft et al. 1991).

Due largely to its brightness, early optical and near-infrared (nIR) observations of GRB 080319B were pursued by several groups, resulting in a very well sampled optical/nIR light curve covering the first few hours after the burst (Racusin et al. 2008; Bloom et al. 2009; Wozniak et al. 2009; Pandey et al. 2009). Despite its initial brightness, the afterglow faded rapidly, and photometric monitoring required large-aperture telescopes after a few days.

A log of all our late-time observations is provided in Table 1. This does not include any correction for dust extinction: the foreground extinction is expected to be small (A_V = 0.037; Schlegel et al. 1998) while the extinction internal to the host, although rather uncertain due to the presence of a break between the optical and X-ray, is also found to be modest (Racusin et al. 2008).

We obtained optical observations with Gemini-North/GMOS, VLT/FORS1, and HST/WFPC2 between ∼3 and ∼460 days post-burst. Processing of ground-based observations was performed using standard iraf routines. In particular, the GMOS reduction made use of the relevant customized software provided by Gemini. Photometric calibrations, both zero-point and color terms, were obtained using Sloan Digital Sky Survey (SDSS) stars in the field (Adelman-McCarthy et al. 2007; Cool et al. 2008). For consistency, the FORS1 B-band imaging was also calibrated to AB magnitudes.

For our HST/WFPC2 observations we placed the target on the WFALL aperture, on the corner of WFC3 closest to the apex, in order to reduce the impact of charge transfer inefficiency (CTE effect), which is significant for the old detectors operating on WFPC2. A four-point dither pattern was used, and subexposures stacked using the drizzle (Fruchter & Hook 2002) software onto a 0.05 arcsec pixel grid (from the native 0.1 arcsec pixels). Photometry of the transient was obtained in a 0.2 arcsec diameter aperture, and aperture corrections to the standard 1 arcsec diameter calculated using brighter point sources on the frame. CTE correction was performed using the method of Dolphin,¹⁴ although we applied only half the correction to the final epoch since the source is clearly extended¹⁵ (extra allowance was made in the error budget for this step). The HST photometry was calibrated to AB magnitudes by reference to the tabulated zero points,¹⁶ and then transformed to SDSS r and i magnitudes for comparison with the ground-based data via the NICMOS Unit Conversion Form.¹⁷

The position of the afterglow was determined, relative to two well-positioned SDSS stars in the field, to be R.A. = 14:31:40.994, decl. = +36:18:08.64 (J2000), with an error of 0.02 arcsec in each coordinate.¹⁸

Figure 2 (top left panel) shows our late-time Chandra observations, as well as early data taken by the Swift/XRT. Our X-ray observations confirm, and increase the confidence in, the break in the X-ray light curve at t_b ≈ 11 days.

The photometry for the various optical bands, with host contribution subtracted (as described above; see also Section 3.3), is plotted in the other panels of Figure 2. In the B- and g-band observations, the light curve before and after the break is reasonably consistent with the X-ray slope and break time, indicating approximately achromatic behavior, as expected for a jet break. In fact, this is one of the more convincing examples of a jet break identified in the Swift era, when such clear achromatic behavior of X-ray and optical light curves has rarely been seen (e.g., Curran et al. 2008).

Since the jet-break time we find is consistent with that used in earlier studies, notably Racusin et al. (2008) and Bloom et al. (2009), those analyses, and in particular their discussions of deviations from a simple power law at earlier times, are not modified by our findings.

It is instructive to consider the simple case in which the break is interpreted in the context of a single jet (double sided, roughly uniform with reasonably sharp edges). Then a break time, t_b ≈ 11 days, implies a half-opening angle of θ_j ∼ 10°, for a canonical external medium density of n ∼ 1 cm^-3 and (an isotropic equivalent) kinetic energy comparable to the energy observed in gamma rays, $E_{k,\rm iso} \sim E_{\rm \gamma,iso} = 1.4\times 10^{54}\;$erg (Sari et al. 1999). This, in turn, implies a true energy output in gamma rays within the observed energy range of E_γ ∼ 2 × 10⁵² erg, and a comparable kinetic energy in the jet (E_k ∼ E_γ).

Alternatively, the kinetic energy can also be estimated from the X-ray luminosity at 12 hr in the rest frame (Granot et al. 2006; Nousek et al. 2006), from which we find $E_{ k,\rm iso}\approx 7\times 10^{52}\;$erg, for typical microphysical parameters (_e = 0.1, _B = 0.01, and p = 2.2). This corresponds to $\eta \equiv E_{ k,\rm iso}/E_{\gamma,\rm iso} \approx 0.05$ and would in turn imply θ_j ∼ 12° and a true kinetic energy of E_k ∼ 2 × 10⁵¹ erg. The isotropic equivalent kinetic energy at this level would require a very high efficiency of the gamma-ray emission (≳95%) for a single wide jet, unless the microphysical parameters were very different so that $E_{k,\rm iso}$ would be significantly higher. If, on the other hand, the gamma rays were produced by a narrow jet with a considerably higher $E_{k,\rm iso}$, then this can bring down the efficiency requirements to more reasonable values (Peng et al. 2005). In fact, this feature is built into the two-component jet model of Racusin et al. (2008), which postulates a very narrow (θ_j,n ∼ 02), very high Lorentz factor (Γ ∼ 10³) central jet, producing an early break in the light curve, coupled with a wider (θ_j,w ∼ 4°) jet leading to the later time break we see at ∼10⁶ s. This model also mitigates the energy crisis more effectively, with each jet producing E_γ ≈ 2 × 10⁵⁰ erg.

Finally, we draw attention to the sharpness of the late-time jet break as seen in the X-rays, which is also consistent with the optical observations, notably in the g band. Such a sharp break is not expected for a wind-like external medium (Kumar & Panaitescu 2000), as considered by Kumar & Panaitescu (2008), and so would require some modification to that simple model, which otherwise nicely fits the afterglow data between ∼10³ and ∼10⁶ s. One possibility would be the coincidental presence of a wind-termination shock in the ambient medium surrounding the progenitor, at approximately the same radius at which the jet break occurs.¹⁹ If we again consider a simple wide jet, this radius is given by $R_j = 1.2\times 10^{19}(E_{k}/10^{51})(A_*/0.03)^{-1}\rm \, cm$, where $A_*=(\dot{M}/10^{-5}\,{M_{\odot }\,\rm yr^{-1}})/(v/10^8\,{\rm cm\,s^{-1}})$ is the conventional mass-loss scaling (cf. Panaitescu & Kumar 2000). Using the relations $E_k = \eta E_{\gamma,\rm iso}\theta _j^2/2$ and $\theta _j^2 = [16\pi Ac^3 t_b/(1+z)E_{\gamma,\rm iso}\eta ]^{1/2}$ together with the observed values of z, $E_{\gamma,\rm iso}$, and t_b gives $R_j = 3.1\times 10^{19}\eta ^{1/2}(A_*/0.03)^{-1/2}\rm \, cm$. Racusin et al. (2008) argued for a tenuous wind with an upper limit on A_* < 0.03 and η ∼ 0.07.

Now, we obtain the wind-termination shock radius using Equation (3) of Pe'er & Wijers (2006): $R_0 = 9.0\times 10^{17}(A_*/0.03)^{3/10}(v_{w,8}\,t_{*,6})^{2/5}n_{0,3}^{-3/10}\rm \, cm$, where v_w,8 is the wind velocity in units of $10^8\,\rm cm\,s^{-1}$, t_*,6 is the lifetime in units of $10^6\,\rm yr$ of the Wolf–Rayet phase presumed to have driven the wind, and n_0,3 is the surrounding interstellar matter (ISM) particle density in units of $10^3\,\rm cm^{-3}$. Hence, the two radii are comparable (around R ∼ 10¹⁹ cm) if, for example, η ∼ 0.07, A_* = 0.03, and n_0,3 has a rather low value ∼0.0014. If the prompt gamma rays were also produced by this jet then the total energy would be given by E_tot ≈ E_γ = E_k/η = 9.8 × 10⁵¹(A_*/0.03)^1/2(η/0.07)^−1/2 erg, comparable to, but somewhat less than, the values found above for a single jet with a uniform external medium of density n ∼ 1 cm⁻³. If, on the other hand, the gamma rays come from a narrow jet, then E_γ can be much lower, and E_tot could be dominated by kinetic energy, E_k = 6.9 × 10⁵⁰(A_*/0.03)^1/2(η/0.07)^1/2 erg.

The r-, i-, and z-band observations (Figure 2, right-hand panels) do not show a break at the same time as the bluer bands, but rather exhibit at first a flattening optical decay, and marked reddening, followed by a steepening again after about 40 days. This is illustrated by the change in color of the optical transient from g − i = 0.60 ± 0.12 at 14 days post-burst to g − i = 1.88 ± 0.19 at 26 days. We interpret this as being due to the contribution to the optical light of an underlying SN that begins to dominate the afterglow in the redder bands. Such SN "red humps" have been seen in the light curves of several long-duration GRBs which have been monitored sufficiently deeply at late times (e.g., Galama et al. 2000; Zeh et al. 2004).

As stated above, we follow the conventional procedure of assuming a light curve for the SN component based on that of SN1998bw, which accompanied the low-redshift GRB 980425 (Galama et al. 1998; McKenzie et al. 1999). We redshifted and k-corrected these light curves to produce templates in our observed wave bands appropriate to z = 0.937, and faded these by 0.3 mag, consistent with the typical GRB-SN "humps" found by Zeh et al. (2004).

When added to the broken power-law afterglow, this produces quite a reasonable match to the photometry of the transient. Thus, we find that GRB 080319B was accompanied by an SN a little fainter than the prototype SN1998bw: an even better match to the photometry would have been achieved with an SN model having a peak time a little earlier (a stretch factor <1 in the language of Zeh et al. 2004). This is in slight disagreement with Bloom et al. (2009) who, using a more preliminary and less complete set of late-time photometry, concluded that an SN component rather brighter than SN1998bw was required.

Our second-epoch HST observations revealed that the afterglow, while still detected, was clearly superimposed upon faint, extended host galaxy emission, with the transient slightly offset north by about 0.2 arcsec from the center of this emission (Levan et al. 2008). By the third epoch the galaxy clearly dominates and is revealed to be a very faint, low surface brightness source extending over roughly 0.5 arcsec. This corresponds to a physical size of about 4 kpc (assuming conventional cosmological parameters) which is quite typical for GRB hosts (Fruchter et al. 2006). The host is not well detected in the WFPC2 images, so the photometry carries a large uncertainty. Our best estimates of the host photometry come from the latest-epoch ground-based imaging, with the g-band measurement being corrected to remove the residual transient light by subtracting the flux predicted by our simple model, as described above. Hence, we find (foreground extinction-corrected) host magnitudes of i(AB) = 26.17 ± 0.15, r(AB) = 26.96 ± 0.13, and g(AB) = 26.81 ± 0.14.

This final photometry, while limited, does allow for a crude fit to the galaxy SED. In particular, the relatively blue g−r color (−0.15 ± 0.19), coupled with the red r−i (0.79 ± 0.20), is suggestive of a moderately strong Balmer break, implying the presence of an older stellar population, in addition to the young population which produces the blue rest-frame UV color, and presumably seeded the GRB.

In Figure 3, we show these photometric points fitted with a star-forming galaxy template with the following properties: M_V = −17.49 ± 0.15 and M_B = −17.23 ± 0.15 (quoted errors are statistical). The best fit has an internal extinction A_V = 0, which, although poorly constrained by our limited photometry, is consistent with the low extinction seen to the afterglow. These numbers imply a star formation rate (SFR) ≈0.13 M_☉ yr⁻¹ and stellar mass M ≈ 1.2 × 10⁸ M_☉, although observational and modeling uncertainties make such determinations only accurate to factors of a few. As shown in Figure 4, this indicates that GRB 080319B has one of the smaller hosts found to date, although note that a small number of the faintest GRB hosts, which only have photometric detections in one band, are not included in this figure. The best-fit specific SFR is therefore Φ = 1.1 Gyr⁻¹ (but with an even greater error bar), which is close to the average for the sample of z < 1.2 GRB hosts studied by Svensson et al. (2010).

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This luminosity corresponds to about $\frac{1}{40}L_*$ at the observed redshift (cf. Willmer et al. 2006). Such a small galaxy is likely to have low metallicity, although quantifying this is hard, not least because of the small number of data points available for the fit and their large photometric uncertainties. Based on the z ∼ 0.7 mass–metallicity relationship of Savaglio et al. (2005), the implied metallicity is $12+{\rm log}(\rm O/H)=7.9$ or about 20% of Solar. However, this numerical value should be treated with caution for various reasons: first, the absolute calibration of the mass–metallicity relation is difficult, and we note that Savaglio et al. (2009), using a revised calibration based on Kewley & Ellison (2008), found metallicities to decrease by ∼0.5 dex; and second, in the same paper Savaglio et al. (2009) show that GRB hosts with spectroscopically estimated metallicities scatter quite widely around this relation in any case.

These properties are within the range of other GRB host galaxies (e.g., Fruchter et al. 2006; Savaglio et al. 2009), but place the GRB 080319B host at the faint end of the available sample. The location of the galaxy in the redshift–magnitude plane is shown in Figure 5, which shows that it is the faintest yet observed by HST at comparable redshift. Similarly, the model fit would imply an SFR and stellar mass at the low end, compared to a sample of other GRB hosts (Figure 4). We caution that a proportion of these redshifts were obtained from host rather than afterglow spectroscopy, and hence there is some bias against very faint hosts. For illustration, hosts without redshift are shown in a separate panel on the right side of Figure 5. A particular case in point is that of GRB 980326, which also exhibited an "SN hump" in its light curve suggestive of a redshift z ∼ 1, but had a host galaxy with R>27 (Bloom et al. 1999).

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