Figure 5. Observed spectral energy distribution of GRB 160625B (points) at late times, interpolated as necessary to the indicated dates, and the best fits given by boxfit (lines) at indicated participation fraction \( \xi \), using an constant CBM density profile. Data denoted by grey points are ignored in the fitting (see text).

with spectra produced by boxfit at these epochs. The power-law slope of the SED, \( \beta \), between the optical (r) and X-ray (5 keV) bands, steepens slightly over time, from −0.79 ± 0.02 between 3 and 10 d to −0.86 ± 0.04 at 141 d. This is steeper than −0.65, expected from \( p \approx \) 2.3 implied by the early optical and X-ray light curves (see Section 4.2.1) for \( \nu < \nu _ { c } \), but shallower than−1.15, which is expected for \( \nu > \nu _ { c } \). Alexander et al. (2017) obtain an early X-ray spectral slope similar to this, \( \beta _ { X } = - 0 . 8 6 _ { - 0 . 1 0 } ^ { + 0 . 0 9 } \), and explain this as \( \nu _ { c } \) being lo-catedj ust below the X-ray band. However, according to the UKSSDC Swift Burst Analyser11 the X-ray pho-ton index \( \Gamma _ { X } \) (and thus the spectral slope in X-ray) does not significantly evolve over the first 30 d but stays around ∼ 1.8, after which the spectrum seems to flatten to \( \Gamma _ { X } \sim \)\( 1 . 1 \). This feature may not be real, though, as the Burst Analyzer light curve deviates much more from a clean power law when this is used in flux calculation– thus we assume a constant \( \Gamma _ { X } \) 12. If \( \nu _ { c } \) was initially just below X-ray and changed as \( \nu _ { c } \propto t ^ { - 1 / 2 } \), one would expect the spectrum to instead steepen over time to its \( \nu \gg \nu _ { c } \) value. We discuss this evolution further in Sec-tion 4.2.1.

Figure 6. Observed F160W (extinction-corrected), X-ray and interpolated 6 and 9 GHz light curves of the afterglow of GRB 160509A (points) and our power law fits including the broken power laws described by Eq. 1 (lines). The red triangle is the upper limit of the F160W flux at 24.8 d. X-ray flux densities from Swift/XRT (solid triangles) and Chan-dra/ACIS-S (open triangles) are reported at 5 keV. Both choices of \( \omega \) fit the late light curve equally well. The early light curve exhibits a shallower decay and another break, and thus points before \( 4 \times 1 0 ^ { 4 } \) s (grey) are ignored.

# 3.2. GRB 160509A

It was noted in Laskar et al. (2016) that the host galaxy of GRB 160509A contributes substantially to the

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11 http://www.swift.ac.uk/burst analyser/00020667/12 The post-break X-ray slope would not change by changing \( \Gamma _ { x } \) at the latest Swift points, as Chandra points would be affected equally – but \( t _ { j , \mathrm { X } } \) could be delayed.

optical and infrared photometry, and that the event oc-curred behind a significant amount of extinction in the host galaxy. In order to estimate the host galaxy extinc-tion along the line of sight to the GRB, we removed the foreground Galactic reddening of \( E ( B - V ) \) = 0.2519 mag (Schlafly & Finkbeiner 2011) using the Cardelli et al. (1989) law, and assumed a \( f _ { \nu } \propto \nu ^ { \beta } \) SED, where \( \beta = - \) 0.6 (consistent with \( \nu < \nu _ { c } \) and \( p \approx \) 2.2, deter-mined based on the X-ray spectrum and light curve by Laskar et al. 2016). For the host, we assume the Pei (1992) extinction law for the Small Magellanic Cloud (SMC), as both Kann et al. (2006) and Schady et al. (2012) found the extinction curve in the SMC consis-tent with their samples. We fitted the observed optical-infrared SED simultaneously at two epochs, corrected using this extinction curve, to find the required extinc-tion correction to match \( \beta = - \) 0.6. The GRB flux in the \( g ^ { \prime } \) band at 1 d was estimated by subtracting the observed flux at 28 d (\( g ^ { \prime } = 2 5 . 3 9 \pm \) 0.12; Laskar et al. 2016) from the flux at 1.0 d \( ( g ^ { \prime } = 2 5 . 0 3 \pm \) 0.15; Cenko et al. 2016). The host is assumed to dominate at 28 d due to the flatness of the light curve even after the X-ray break. In the J band, we subtracted the flux of the host galaxy measured in the HST F110W filter (using a 1 arcsec aperture) from the flux at 1.2 d (\( J \approx \) 19.7;Tanvir et al. 2016). The \( r ^ { \prime } \) band was not included in the SED, as the late and early fluxes are consistent within 1 \( \sigma \) (Cenko et al. 2016; Laskar et al. 2016). Our F110W and F160W observations at 35.3 d made up the other epoch to be fitted simultaneously. The resulting host extinction is \( A _ { V } = 2 . 8 \pm 0 . 1 \) mag in the rest-frame (this is somewhat lower than the result obtained by Laskar et al. 2016, using an afterglow model fit where the host flux was a free parameter). Using the Pei (1992) law, the extinction correction in F160W (approximately i-band in the rest frame) is thus 1.5 mag. In the Milky Way, the adopted \( N _ { \mathrm { H , i n t } } = 1 . 5 2 \times 1 0 ^ { 2 2 } \) \( \mathrm { c m ^ { - 2 } } \) would cor-¨respond to \( A _ { V } \approx 6 . 9 \) mag (G¨uver & Ozel2009), sug-gesting a low \( A _ { V } / N _ { H } \) ratio for Milky Way standards but higher than that of most GRB hosts. This ratio is consistent with the \( A _ { V } \) vs. \( N _ { H } / A _ { V } \) relation in Kr¨uhler et al. (2011). As in the case of GRB 160625B, we com-bined our Chandra data of GRB 160509A with the data from the Swift/XRT light curve repository converted to 5 keV flux densities.

The CIRCE H-band fluxes were converted to the nar-rower F160W filter assuming \( \beta \, = \, - \) 0.6. The F160W and X-ray data and our power-law fits are presented in Figure 6, and the parameters of the fits are listed in Table 7. For our power law fits we ignore the data points before \( \sim | \)\( \mathbf { i } \cdot \mathbf { j } \) 5 d \( ( 4 \times 1 0 ^ { 4 } \) s), as the early X-ray light curve may contain a plateau and/or a flare; see Figure Table 7. Parameters of the best smooth broken power law fits to the GRB 160509A X-ray light curve.

<table><tr><td>Parameter</td><td>\( \omega \) = 3</td><td>\( \omega \) = 10</td></tr><tr><td>\( t _ { j , \mathrm { X } } \)</td><td>3.2 \( \pm \) 0.9 d</td><td> 3.7 \( \pm \) 0.8 d</td></tr><tr><td>\( _ { \alpha 1 , \mathrm { x } } \)</td><td>−1.06 ± 0.10</td><td>−1.20 ± 0.06</td></tr><tr><td>\( \alpha _ { 2 , \mathrm { X } } \)</td><td>−1.98 ± 0.10</td><td>−1.96 ± 0.09</td></tr><tr><td>Reduced \( \chi ^ { 2 } \)</td><td>0.84</td><td>0.85</td></tr></table>

6. In this case the smooth- and sharp-break scenarios give similar results: the best fit for the post-break de-cline for \( \omega \) = 3 is \( \alpha _ { 2 , \mathrm { X } } = - 1 . 9 8 \pm 0 . 1 0 \) and for \( \omega \) = 10,\( \alpha _ { 2 , \mathrm { X } } \, = \, - 1 . 9 6 \pm 0 . 0 9 \). Thej et-break times, 3.2 \( \pm \) 0.9 d and 3.7 \( \pm \) 0.8 d, respectively, are consistent with each other as well.

In the radio, we obtained the fluxes at 6 and 9 GHz at the epochs earlier than 79.9 d by power-law interpolation between observed fluxes – our measurements at 36.9 d and those published in Laskar et al. (2016) at earlier times. We then fitted a single power law to the points where the reverse shock should no longer dominate the radio flux (i.e. \( \geq \) 10 days; Laskar et al. 2016). The resulting decline slopes are \( \alpha _ { \mathrm { 6 G H z } } \, = \, - 0 . 9 1 \pm 0 . 1 1 \) and \( \alpha _ { 9 \mathrm { G H z } } = - 0 . 9 2 \pm 0 . 1 3 \). Since the reverse shock may still be contributing a non-negligible fraction of the flux at 10 d, we also performed the fit without this epoch. The results are consistent but less constraining: \( \alpha _ { \mathrm { 6 G H z } } = \)−1.07 ± 0.18 and \( \alpha _ { 9 \mathrm { { G H z } } } \; = \; - 0 . 9 2 \pm 0 . 2 1 \). The slopes at other frequencies between 5 and 16 GHz, fitted from 10 to 20 d, are all consistent with these, ranging from−0.80 ± 0.10 (7.4 GHz) to −1.02 ± 0.04 (8.5 GHz). In F160W and/or H, we only have two points and an upper limit; therefore we simply measure the decline assuming a single power law. As the first point at 5.8 d is after thej et break time we obtained from the X-ray fit, there should be no significant deviation from a single power law. The measured decline is \( \alpha _ { 2 , \mathrm { F 1 6 0 W } } = - 2 . 0 9 \pm 0 . 1 0 \), consistent within 1 \( \sigma \) with the X-ray decline.

Using boxfit, we again fitted the light curve at three different values of \( \xi \): 1, 0.1 and 0.01. As with the power-law fits, the X-ray points before 0.6 d were ignored, since boxfit cannot accommodate continuous energy injec-tion. Radio points with a significant reverse shock con-tribution were also ignored (i.e. \( < \) 10 d; at frequencies \( < \) 5 GHz also 10.03 d; see Laskar et al. 2016). We ran boxfit with the boosted-frame wind-like CBM model (with both strong and medium boost) and a lab-frame model with ISM-like CBM, as the lack of optical data makes it difficult to distinguish between different CBM profiles (although the ISM scenario is tentatively favored by Laskar et al. 2016). However, as shown in Figure 7, our fits in a wind CBM do not reproduce thej et break