1 Introduction

# GRB 081007 and GRB 090424: the surrounding medium, outflows and supernovae

## Abstract

We discuss the results of the analysis of multi-wavelength data for the afterglows of GRB 081007 and GRB 090424, two bursts detected by Swift. One of them, GRB 081007, also shows a spectroscopically confirmed supernova, SN 2008hw, which resembles SN 1998bw in its absorption features, while the maximum magnitude may be fainter, up to 0.7 mag, than observed in SN 1998bw. Bright optical flashes have been detected in both events, which allows us to derive solid constraints on the circumburst-matter density profile. This is particularly interesting in the case of GRB 081007, whose afterglow is found to be propagating into a constant-density medium, yielding yet another example of a gamma-ray burst (GRB) clearly associated with a massive star progenitor which did not sculpt the surroundings with its stellar wind. There is no supernova component detected in the afterglow of GRB 090424, likely because of the brightness of the host galaxy, comparable to the Milky Way. We show that the afterglow data are consistent with the presence of both forward- and reverse-shock emission powered by relativistic outflows expanding into the interstellar medium. The absence of optical peaks due to the forward shock strongly suggests that the reverse-shock regions should be mildly magnetized. The initial Lorentz factor of outflow of GRB 081007 is estimated to be , while for GRB 090424 a lower limit of is derived. We also discuss the prompt emission of GRB 081007, which consists of just a single pulse. We argue that neither the external forward-shock model nor the shock-breakout model can account for the prompt emission data and suggest that the single-pulse-like prompt emission may be due to magnetic energy dissipation of a Poynting-flux-dominated outflow or to a dissipative photosphere.

gamma-ray burst: individual (GRB 081007, GRB 090424) - supernovae: individual (SN 2008hw) - ISM: jets and outflows

## 1. Introduction

Thanks to the rapid localization of gamma-ray bursts (GRBs) by the Swift satellite (Gehrels et al., 2004), the response of ground-based observations of GRB afterglows has been greatly enhanced and observations of GRB afterglows have become routinely possible within minutes after the explosion. Very early afterglow data are required to estimate the initial bulk Lorentz factor of the ejecta (Molinari et al., 2007), probe the physical composition of the outflow (Fan et al., 2002; Zhang et al., 2003), and constrain the density profile of the medium surrounding the progenitor (Jin & Fan, 2007; Schulze et al., 2011). Late afterglow observations provide us with clues on the medium density profile, which, in turn, may provide hints on the nature of the progenitor star.

The idea that supernova (SN) explosions may also produce energetic gamma-ray emission by some mechanism goes back to Colgate (1968), but the first piece of evidence supporting such a connection was not found until 1998 (Galama et al., 1998). The connection was finally established in 2003 when SN 2003dh and SN 2003lw were unambiguously detected spectroscopically following the nearby GRB 030329 and GRB 031203, respectively (Hjorth et al., 2003; Stanek et al., 2003; Malesani et al., 2004). So far, spectral SN features have been found for only about a dozen GRBs (for recent reviews see Hjorth et al., 2012; Della Valle, 2011). Current data suggest that less than of Type Ib/c SNe are able to produce GRBs following the core collapse of their progenitor star (Guetta & Della Valle, 2007; Soderberg et al., 2010; Ghirlanda et al., 2013).

In this work we present and discuss data of GRB 081007 and GRB 090424. Because of their occurrence at relatively low redshifts, and , respectively, their follow-up in the optical and near-infrared (NIR) bands was particularly effective (see cases of GRBs at similar redshifts reported by Della Valle et al., 2006; Cano et al., 2011; Berger et al., 2011; Filgas et al., 2011; Troja et al., 2012; Sparre et al., 2011). We were able to detect a SN component in the late afterglow of GRB 081007.

GRB 081007 triggered the Burst Alert Telescope (BAT) onboard Swift on 2008 October 7 at 05:23:52 UT. It was a long GRB with a peak  s duration in the 15-350 keV gamma-ray band (Markwardt et al., 2008). This burst also triggered the Gamma-ray Burst Monitor, onboard Fermi, in the 25-900 keV gamma-ray band. The prompt emission consisted of a single pulse with an estimated duration of about 12 s (Bissaldi et al., 2008). The Swift satellite immediately slewed to the field and the X-Ray Telescope (XRT) and the Ultraviolet/Optical Telescope (UVOT) started observations at 99 and 108 s after the trigger, leading to a detection of the X-ray and optical afterglows (Baumgartner et al., 2008). Gemini-South took two 900 s spectra, starting 73 minutes after the burst. Two absorption lines at 6016.7 and 6070.3 Å and an emission line at 5700.9 Å were identified as Ca ii H, K and [O ii] 3727 Å lines respectively at (Berger et al., 2008, see also figure 1).

GRB 090424 triggered BAT on 2009 April 24 at 14:12:09 UT. It was a multi-pulse long GRB with total duration of about 60 s in the 15-350 keV gamma-ray band (Cannizzo et al., 2009). XRT and UVOT started observations 85 and 91 s after the trigger and detected the X-ray and optical afterglow (Cannizzo et al., 2009). Gemini-South took two 1200 s spectra, starting 11.7 hr after the burst, and found that GRB 090424 is at , similar to GRB 081007 (Chornock et al., 2009, see also figure 2).

The main properties of the two GRBs are summarized in Table 1. This work is structured as follows: in Section 2 we present the data. The discussion and interpretation of the observations are reported in Section 3. We summarize our results in Section 4.

## 2. Observations and Results

### 2.1. The GRB 081007 and GRB 090424 afterglows

Many robotic telescopes reacted to the trigger from GRB 081007. RAPTOR started observations detecting the optical counterpart after about 24 s in the band (Wren et al., 2008). Four of the 40 cm PROMPT telescopes at CTIO in Chile began observing after 41 s (West et al., 2008). The 60 cm Rapid Eye Mount (REM) on La Silla, Chile, started multi-band observations of GRB 081007 after 46 s in the , and bands (Covino et al., 2008). The 2 m Faulkes Telescope North (FTN; Haleakala, Hawaii) started to observe GRB 081007 about 17 minutes after the Swift trigger in the , , , and bands (Smith et al., 2008). The 2 m Faulkes Telescope South (FTS; Siding Spring, Australia) observed the field of GRB 081007 from to days after the burst in the and bands. Between 2008 October 24 and 2009 January 3, FORS2 at the Very Large Telescope (VLT) was used to search for the SN associated with GRB 081007.

The 2 m Liverpool Telescope (LT; La Palma, Canary Islands, Spain) began observing the field of GRB 090424 at 21:29:47 UT (Guidorzi et al., 2009), hr after the burst. The optical counterpart was clearly detected in the and filters. Later observations were made by the FTN at 17.66 and 333.89 days after the trigger in the filter only. Between 2009 May 1 and July 5, FORS2 at the VLT was also used to observe the GRB 090424 field for nine runs. Three years later, this field was observed again between 2012 May 1 to 3 with the 3.5m telescope at the Calar Alto Observatory.

Our dataset also includes Swift/UVOT data47 and we have retrieved and analyzed public Gemini archival data 48 of GRB 081007 and GRB 090424, confirming results reported by Berger et al. (2008) and Chornock et al. (2009).

In this paper we analyzed all available photometric and spectroscopic data, following standard procedures: bias or dark removal, flat-field correction, astrometry for imaging frames and wavelength calibration for spectroscopy. Aperture photometry was calibrated by means of secondary standard stars in the field from the APASS catalog49 or the Sloan Digital Sky Survey (SDSS) catalog50 in the optical and the Two Micron All Sky Survey (2MASS) catalog51 in the near-infrared (NIR). R and I band observations were calibrated by means of and secondary standard stars. Late-time photometric observations, since all secondary standard stars in the field were heavily saturated, were calibrated by means of standard star fields observed under photometric conditions. Spectroscopic observations were also calibrated by observations of suitable spectro-photometric standard stars.

We also collected data available from these GCN circulars: 8339 (Cobb, 2008) for GRB 081007; 9224 (Yuan, 2009), 9236 (Gorosabel et al., 2009), 9239 (Oksanen, 2009), 9240 (Urata et al., 2009), 9245 (Olivares et al., 2009), 9246 (Nissinen & Hentunen, 2009), 9248 (Im et al., 2009a), 9253 (Im et al., 2009b), 9278 (Roy et al., 2009), 9305 (Mao et al., 2009), 9313 (Cobb, 2009), 9320 (Rumyantsev et al., 2009) for GRB 090424.

The photometric data are shown in Figures 3 and 4 and they are reported in the Appendix of the online journal (Tables 3 - 5). The (small) Galactic extinction, , of 0.016 and 0.025 mag (Schlegel et al., 1998) for GRB 081007 and GRB 090424, respectively, was taken properly into account in the analysis.

### 2.2. Discovery of a supernova accompanying GRB081007

A 2 hr spectrum of GRB 081007 was obtained with VLT equipped with FORS2 and the 300I grism on 2008 November 2 (Della Valle et al., 2008), about 26 days after the GRB trigger, and reduced following standard methods. After subtracting a starburst galaxy template (Sb1 template from Kinney et al., 1996), three broad bumps at about 4600, 5400, and 6400 Å emerge. These features are very similar to those exhibited by SN 1998bw (Patat et al., 2001) around maximum (see Figure 5), but the luminosity of the SN at maximum light is significantly lower than that of SN 1998bw at the same time, only about half as large as that of SN 1998bw (see Figure 6). This SN was designated SN 2008hw (Della Valle et al., 2008). Some similarities with other two broad-lined type Ic SNe, namely SN 1997ef (Mazzali et al., 2000) and SN 2004aw (Taubenberger et al., 2006) were also identified.

### 2.3. Host galaxy of GRB 090424

The optical counterpart of GRB 090424 shows no apparent variation from 18 days onwards, according to our FTN and VLT observations, no significant variation is found in Kann et al. (2010) either. This means the afterglow had faded below the host-galaxy brightness before this epoch. The VLT observed and band magnitudes of the host are and , corresponding to a luminosity four times brighter than SN 1998bw at maximum light. An underlying SN akin to SN 1998bw would only have produced little additional brightening, at a level below the uncertainty in the galaxy luminosity. Additionally to the bright host galaxy, the afterglow suffers from significant host-frame extinction according to Kann et al. (2010); Schady et al. (2012) and Covino et al. (2013), which will further dim any SN component. This fact may explain the lack of detection of the SN component in the afterglow of GRB 090424 (see Figure 7).

The GRB 090424 host-galaxy spectrum was obtained with VLT-FORS2 and grism 300I on 2009 May 22, and with the Gran Telescopio Canarias (GTC) on 2013 April 8, about a month and 4 years after the high energy event respectively. These spectra were reduced following standard methods. The signal-to-noise ratio (S/N) of our VLT-FORS2 spectrum is in the blue part and goes down to  5-10 in the red part, the strong residual around 9400Å is due to telluric water vapor. Two absorption lines at 6077 and 6133 Å and emission lines at 6704, 7508, 7733, and 10135 Å are clearly detected, which are identified as Ca ii K and H, H, H, [O iii] and H at (see Figure 8). The S/N of our GTC spectrum is , it extends the VLT-FORS2 spectrum to the blue-ward, and an extra strong emission line at 5758 Å is detected, it is identified as [O ii] at (see Figure 8). We derived the fluxes for these lines first by removing the background with a polynomial fit and then by modeling the lines with Gaussians. The resolution of our spectra does not justify a more sophisticated modeling. The results are summarized in Table 2.

## 3. Interpretation and implication of the data

### 3.1. Interpreting the GRB 081007 afterglow

The most interesting feature of the early REM light curve of GRB 081007 is a bright peak in the band data (see Figure 6). The light curve first rises as and peaks at approximately 130 s, then it decays very rapidly as until about 300 s. Finally, there is a slower decay . The RAPTOR, REM, and PROMPT data (see Figure 6), and PROMPT and data (see Figure 3) also show a similar behavior, the three -band points also follow an analogous decay but they are affected by large uncertainties and therefore we disregard them in our subsequent analysis of the afterglow.

The temporal behavior of the early-time optical afterglow is a powerful diagnostic of the circumburst medium density profile (Piran, 1999), usually modeled as a power-law, , where is the particle number density and the distance from the burst progenitor. A homogeneous medium has , while represents an environment shaped by a stellar wind from the GRB progenitor. In this scenario, the early optical afterglow rise could be due to the onset of either the forward shock from the outflow getting decelerated in the interstellar medium (ISM) or of the reverse shock emission if it is sub-relativistic (Rees & Mészáros, 1992; Sari, 1998; Sari & Piran, 1999; Jin & Fan, 2007). In both cases, however, a wind-shaped environment can be ruled out, since the optical afterglow rise cannot be faster than (Mészáros & Rees, 1997; Mészáros et al., 1998; Chevalier & Li, 2000; Jin & Fan, 2007), because of the rapidly decreasing circumburst density seen by the outflow.

The rapid optical decline () after the peak can only be interpreted in the context of reverse shock emission, such as the one observed in GRB 990123 (Akerlof et al., 1999; Sari & Piran, 1999; Kobayashi, 2000). Forward shock emission can decay so steeply only after a jet-break, which is unlikely the case at such early time. Therefore, the early rise is also due to the onset of the reverse shock emission from an outflow propagating in a constant density circumburst medium.

The Swift/XRT light curve of GRB 081007 can be divided into three power-law decay stages with indices , , and (UK Swift Science Data Centre, Evans et al., 2009). The last two stages are similar to the simultaneous optical ones, which can be fitted by a and a decay, except for the last several observations, when the SN is already dominating the flux. The SN-dominated phase can be interpreted by the sum of a power-law afterglow, a SN template and an underlying host galaxy (see Figure 6). The initial sharp decay in X-rays suggests that this emission is the tail of the prompt emission (e.g., Zhang & Mészáros, 2004).

The X-ray and optical data between 500 and s exhibit pretty much the same decay slope (see Figure 6). The early shallow decline in both the X-ray and optical/NIR bands, roughly can be interpreted as forward shock emission for a flat electron spectral index , while the late, roughly , decay may be due to the jet effect as long as the sideways expansion of the decelerating ejecta can be ignored (for which the light curve slope before and after the break would steepen by 0.75, close to what we observed). This interpretation is however inconsistent with the X-ray spectrum. The time-averaged photon spectral index of second X-ray epoch (between ks) Swift/XRT data is (UK Swift Science Data Centre, Evans et al., 2009), which suggests a normal electron spectral index . We thus interpret the decay, too shallow compared to model predictions, as the emission of the forward shock with continued energy injection as from the central engine, and the decay as the end of injection. Following Zhang et al. (2006), it is straightforward to show that the afterglow decay index is , so the temporal index for an energy injection index can reproduce the data, assuming that the optical band is above both the cooling frequency and the typical synchrotron radiation frequency of the forward shock. When both the cooling and synchrotron radiation frequency lie redward of the optical, a similar intrinsic spectral index of about -1.1 is expected in X-ray and optical bands (Zhang & Mészáros, 2004), and is consistent with the spectral energy distribution (SED) fit by Covino et al. (2013). For the energy injection from a spinning-down pulsar the early energy injection rate should have (Dai & Lu, 1998a), which is not consistent with what we observe. Therefore, a magnetized pulsar as a central engine cannot explain the observations.

### 3.2. Interpreting the GRB 090424 afterglow

GRB 090424 was also bright at early times (see Figure 4) as shown by UVOT observations, as well as -band observations by TAOS and ROTSE-III (see Figure 7). The optical light curve was already decaying at the time of the first observations and the decay index was , consistent with the prediction for the reverse shock emission. The optical and X-ray light curves can be well-fitted with a simple broken power-law. The indices of three optical slopes are , , and 0, respectively. Assuming that the first phase is dominated by the reverse-shock component, the second phase is likely dominated by the forward shock emission that gradually overshone the fading reverse shock emission. At late times, the emission is dominated by the host galaxy, as shown by the constant luminosity. The best fit to the X-ray emission is four phases with decay indices , , , and , respectively (UK Swift Science Data Centre, Evans et al., 2009).

According to standard predictions of the fireball model in a wind-shaped environment, the X-ray light curve should be shallower than the optical light curve (e.g., Piran, 1999; Jin et al., 2009), which is not the case for our data. The X-ray emission is likely due to the forward shock since, in most cases, the reverse-shock emission in the X-ray band is very weak and can be ignored (Fan & Wei, 2005; Xue et al., 2009). We thus interpret the X-ray emission as being due to the forward shock. Between 3000 and 3s, its decay index is steeper than the optical by a factor about 0.25, a spectral break between X-ray and optical is then required. This is also confirmed by the SED fits to the X-ray and optical observations by Schady et al. (2012) and Covino et al. (2013), a spectral break of 0.5 is required from X-ray to optical bands. With an ISM-like constant density medium the forward shock is expected to be in the slow cooling phase, i.e., the typical syncrotron frequency is below the cooling frequency (). We find that , here and represent the optical and X-ray bands of the observations. We also notice that around 3 ks, the decay of the X-ray light curve steepens by about 0.25 (the X-ray light curve before 3 ks can also be fitted with a single power law with decay index , see UK Swift Science Data Centre, Evans et al., 2009), which is expected when the cooling frequency crosses the observational band ( Hz, or about 0.3 keV). Applying standard relations (e.g., Zhang & Mészáros, 2004), this change can be interpreted as () to (), with the electron power-law distribution index being . Given the time evolution of the cooling frequency, , it will have crossed the band ( Hz) at about  s. Finally, the last steepening from to is likely due to a jet break. Fixing the final stage of X-ray decay to , the break is occurring at  s.

From the break time, the jet opening angle can be estimated as explained e.g., by (Sari et al., 1999):

where is the isotropic-equivalent energy of the prompt gamma-ray emission, is the number density of the medium in cm and is the GRB efficiency, which we take to be and respectively. Here and throughout this text, the convention has been adopted in cgs units except for some special notations. Therefore for GRB 090424, with , we have ; while for GRB 081007, with we have .

### 3.3. Estimating the Lorentz factor of the outflows

For both GRB 081007 and GRB 090424 the prompt emission duration is shorter than the outflow deceleration time . In this case the reverse shock crossing time is comparable to the forward-shock deceleration time (for a review see Mészáros, 2006), that is:

 t×=tdec=10(Ek,53n0)1/3Γ−8/32.5 s, (2)

where . The outflow Lorentz factor in turn can be estimated as (e.g., Molinari et al., 2007):

 Γ∼160[Eγ,iso,53(1+z)3η0.2n0t3dec,2]1/8. (3)

For GRB 081007, ,  erg, and  s, yielding . For GRB 090424, , erg, and  s, yielding .

In both cases the initial GRB outflows are relativistic, consistent with what has been found in previous works (e.g., Molinari et al., 2007; Sari & Piran, 1999; Xue et al., 2009).

### 3.4. Constraining the magnetization of the outflows

Based on the relative strength of forward- and reverse-shock emission, early GRB afterglows can be classified into three categories (Jin & Fan, 2007; Zhang et al., 2003): Type I, showing both peaks of the forward- and reverse-shock emission; Type II, where the strong reverse-shock emission outshines the peak emission of the forward shock; Type III, where the reverse-shock emission is absent. The difference between these three types is attributed to the very different magnetization degrees of the outflow (see Jin & Fan, 2007, for more detail). Note that the classification in types I, II and III has here a different meaning than in Zhang et al. (2007). For GRB 081007 and GRB 090424, bright optical peaks from the reverse-shock emission have been identified, and no forward-shock optical peak emission can be detected, therefore, they are both Type II afterglows, for which the reverse-shock region is expected to be mildly magnetized, as shown in previous works (e.g., Fan et al., 2002; Zhang et al., 2003; Fan et al., 2005b). In case the observer frequency lies above but below , the ratio between the reverse-shock optical emission at its crossing time () and the forward-shock optical peak emission can be estimated by (as in Jin & Fan, 2007):

 Frobs(t×)Fobs(tp)=0.08Rp−1eR(p+1)/2B(tpt×)3(p−1)/4, (4)

where , () is the fraction of the reverse (forward) shock energy given to the magnetic field, , and () is the fraction of the reverse (forward) shock energy given to the electrons.

For GRB 081007, we have  Jy and  s. The underlying forward-shock emission peaks () between and  s (when it outshines the reverse-shock emission), and the peak flux is  Jy. For we have .

For GRB 090424, if we consider the first TAOS -band observation (Urata et al., 2009) as the reverse-shock peak, then the flux is 0.02 Jy at 90 s. The forward-shock emission dominates the afterglow at 400 s, when the corresponding flux is 0.002 Jy. Taking and  s, we have . It is possible that the reverse-shock peak is earlier and the flux is higher or the forward-shock emission peak is earlier: so the derived is only a lower limit.

The numerical fit to the multi-wavelength afterglow data of GRBs usually gives (e.g., Panaitescu & Kumar, 2001). Since , we have a few and then a few. In other words the reverse-shock regions are mildly magnetized. One straightforward speculation from this is that the optical flash photons should have a moderate linear polarization degree, as has been detected in GRB 090102 (Steele et al., 2009).

### 3.5. Linking SN 2008hw with homogenous circumburst medium

GRB 081007 is an event showing an optical onset and a clearly identified SN associated with it. As discussed in Sect. 3.1, afterglow data allow us to constrain the density profile of the circumburst medium, while the occurrence of a SN confirms that the progenitor is a massive star. The afterglow analysis suggests, as it is indeed fairly common for GRBs (e.g., Schulze et al., 2011), that the outflow powering GRB 081007 was propagating in a constant density medium. On the other hand, a massive stellar progenitor is expected, during its final stages of evolution, to eject a dense wind shaping the surrounding density profile, in possible contradiction with results based on afterglow analysis. In the past, GRBs with bright optical flashes and an associated SNe were GRB 021211/SN2002lt (Fox et al., 2003; Li et al., 2003; Della Valle et al., 2003), GRB 050525A/SN 2005nc (Shao & Dai, 2005; Della Valle et al., 2006; Blustin et al., 2006) and GRB 080319B (Racusin et al., 2008; Bloom et al., 2009; Tanvir et al., 2010).

It is widely speculated that strong episodes of mass loss occur before the death of massive stars (e.g., Pastorello et al., 2007), which is why GRBs are expected to explode in wind-shaped media (Dai & Lu, 1998b; Chevalier & Li, 2000; Ofek et al., 2013). However, this does not seem to be the case for GRB 081007/SN 2008hw, as we have shown in this work. A similar situation was encountered with other nearby GRB/XRF associated with energetic and luminous SNe: GRB 030329/SN 2003dh, XRF 060218/SN 2006aj (e.g., Fan, 2008), although both the gamma-ray signatures and SNe were quite different (Stanek et al., 2003; Hjorth et al., 2006; Mazzali et al., 2003; Campana et al., 2006; Pian et al., 2006; Mazzali et al., 2006). Also for GRB 090618, at a similar redshift , observations seem to favor a homogeneous ISM environment over a wind environment (Page et al., 2011; Cano et al., 2011).

The GRB 081007 data suggest that the expansion and interaction of SN shells is occurring in a medium with density profile more typical of a homogenous () ISM rather than a stellar wind () medium. One possible explanation for this inconsistency is that mass loss occurring during the final stages of the life of the massive progenitor proceeds “discretely” through sudden ejection of blobs of matter (e.g., Pastorello et al., 2007) rather than “smoothly” with a continuous, constant rate. If the time between blob-ejection is long enough, then there is time to redistribute matter inside the circumstellar medium and to make it sufficiently homogeneous. Afterglow data, extending up to 10 days after the trigger in the observer frame, can be used to set a lower limit on the time interval that separates pulses. Since the external shock propagates with almost luminal velocity, the distance covered by the plasma is , where is the Doppler factor. If we assume an average value during this time, it will take years for a wind moving at 1000 km s to cover this distance. This first order computation roughly estimates the time needed for the medium surrounding the progenitor to change the trend of the density profile from to . This time can be used to constrain models of mass ejection in the late phases of massive-star evolution, which is still poorly understood.

### 3.6. Origin of the “single-pulse” prompt emission of GRB 081007

The prompt emission of GRB 081007 can be modeled as a single pulse (Markwardt et al., 2008; Bissaldi et al., 2008). In some nearby under-luminous bursts such as GRB 980425 (Pian et al., 2000), XRF 060218 (Campana et al., 2006) and XRF 100316D (Starling et al., 2011), the prompt emission was also characterized by a single pulse. The physical origin of the prompt emission is still widely debated, with theories also including the shock breakout of the SN explosion and the external forward-shock emission. For GRB 081007, these two models are actually disfavored. The inferred is so high that the “shock breakout” radius would be as large as  cm, which is too large. In the case of the external-shock model, a single-pulse-like prompt emission is in principle possible and the duration of the prompt emission would trace the deceleration of the outflow. However, the well-delineated peak of the optical afterglow, likely marking the deceleration of the outflow at a time  s, renders the interpretation of the short-lived prompt emission as the external shock(s) unlikely.

Below we discuss the possibility that GRB 081007 was powered by the magnetic energy dissipation of a Poynting-flux dominated outflow. Such a model is partly motivated by the mild magnetization inferred from the optical afterglow data.

Following Usov (1994), the radius at which the MHD condition breaks down can be estimated following Fan et al. (2005a)

 rMHD∼2×1016L1/250σ−11tv,m,−3Γ−12 cm, (5)

where is the ratio of the magnetic energy flux to the particle energy flux, is the total luminosity of the outflow, and is the minimum variability timescale of the central engine. Beyond this radius, significant magnetic dissipation processes are expected to happen which convert energy into radiation. The radiation timescale is (Gao & Fan, 2006)

 τ∼(1+z)rMHD2Γ2c=33 s (1+z)L1/250σ−11tv,m,−3Γ−32, (6)

and the corresponding synchrotron radiation frequency can be estimated as (Fan et al., 2005a; Gao & Fan, 2006)

 νm,MHD∼6×1016σ31C2pΓ2tv,m,−3(1+z)−1 Hz, (7)

where , and is the fraction of the dissipated comoving magnetic-field energy converted to the comoving kinetic energy of the electrons. Adopting erg s, and , the prompt emission data of GRB 081007 (including the duration as well as the peak energy) can be well reproduced.

After the identification of a distinct thermal radiation component in GRB 090902B (e.g., Ryde et al., 2010; Zhang et al., 2011), the photospheric radiation model has attracted wide attention. In such a scenario, the prompt gamma-rays are produced by the significantly modified quasi-thermal radiation from the photosphere of the outflow or from sites with an optical depth of (Beloborodov, 2013, and references therein). For GRB 081007, such an origin can not be ruled out. With future ray polarimetry data (see Götz et al., 2009; Yonetoku et al., 2011, for preliminary results) we may be able to distinguish between the global-magnetic-energy-dissipation model and the photospheric-radiation model, since the former usually predicts a moderate or high linear polarization while the latter usually does not. One exception is that in a specific photosphere model moderate linear polarization is possible if our line of sight happens to be at the edge of the ejecta (Fan, 2009).

### 3.7. Host galaxy parameters

The apparent magnitudes of host galaxy of GRB 090424 are and , so the absolute magnitudes are approximately and , considering the Galactic extinction . These figures are close to the values for our Galaxy, and are brighter than for most GRB hosts (see e.g., Hjorth et al. 2012).

The metallicity of a galaxy can be derived from the ratio of different emission lines in its spectrum. Several methods have been studied and adopted (for a recent review, see Kewley & Ellison, 2008). In our case, we used the N2 and O3N2 indices, as recalibrated by Pettini & Pagel (2004). We find a metallicity of about 8.39 and 8.43 using the N2 and O3N2 methods, respectively. These two methods are also weakly affected by intrinsic or Galactic extinction.

The observed fluxes of the H and H emission lines are and erg s cm. To estimate the SFR from the H or H line, we followed the relations used in Savaglio et al. (2009): SFR and SFR. Correcting for Galactic extinction, the lower limit (since the host galaxy extinction is not corrected) of SFR is SFR or SFR.

## 4. Summary

In this paper we have presented and interpreted multi-wavelength observations of GRB 081007 and GRB 090424, and we summarize here the results.

i) The early stages of both afterglows are characterized by a bright optical/NIR component, which we interpret as the reverse-shock emission.

ii) The late-time afterglow of GRB 081007 is dominated by a SN component (SN 2008hw) similar to SN 1998bw near maximum light. The presence of a SN associated with the GRB clearly suggests that this burst originated from a massive star that should have shaped its circumburst environment with wind. On the other hand, the afterglow data can only be interpreted assuming a surrounding ISM-like medium, characterized by a constant density profile. A process to make the circumburst medium around the progenitor star homogeneous has likely been effective.

iii) The entire set of the afterglow data of GRB 081007 can be interpreted within the forward- and reverse-shock model, consider a long-lasting energy injection following the law .

iv) The initial Lorentz factor of GRB 081007 outflow is estimated by the afterglow data to be , which makes the interpretation of its single-pulse prompt emission in terms of both external forward shock and shock breakout unlikely. The identification of a reverse-shock emission component peaking at  s after trigger rules out the possibility that the short-lived prompt emission was due to external-shock emission. The absence of the peak of forward-shock optical emission strongly suggests that the reverse-shock regions should be mildly magnetized. We therefore suggest that the prompt emission, characterized by a single pulse, may be due to the magnetic energy dissipation of a Poynting-flux dominated outflow or to a dissipative photosphere.

v) For GRB 090424, we set a lower limit on the initial Lorentz factor of the outflow of . Unlike GRB 081007, we did not detect the SN component in the afterglow, likely due to the considerably bright host galaxy, roughly comparable to the Milky Way. The bright initial optical/NIR afterglow has also been attributed to emission from a mildly-magnetized reverse shock. The late time X-ray and optical data are consistent with the forward-shock model and the surrounding medium is also found to be ISM-like.

All these results demonstrate that multi-band afterglow data, in particular with very early observations, are a necessary and valuable tool to better understand GRB physics. Significant progress is expected in the near future as more data will be collected.

## Acknowledgments

We acknowledge the support from the ASI grants I/011/07/0 and I/088/06/0, the INAF PRIN 2009 and 2011, and the MIUR PRIN 2009ERC3HT. We thank the Paranal Science Operations staff, and in particular T. Rivinius, P. Lynam, S. Brillant, F.J. Selman, T. Szeifert, L. Schmidtobreick, A. Smette, A. Ahumada, K. O’Brien, C. Ledoux for effectively carrying out our service-mode observations. We wish to acknowledge the anonymous referee who has significantly improved the presentation and the discussion of the data. The Dark Cosmology Centre is funded by the DNRF. J.P.U.F. acknowledges support from the ERC-StG grant EGGS-278202. The RAPTOR project is supported by the DOE sponsored LDRD program at LANL. The Liverpool Telescope is operated by Liverpool John Moores University at the Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. The Faulkes Telescopes are owned by Las Cumbres Observatory. CGM acknowledges support from the Royal Society. Data collected with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, on the island of La Palma. Based on observations collected with the 3.5m telescope of the German-Spanish Astronomical Centre, Calar Alto, Spain, operated jointly by the Max-Plank-Institut für Astronomie (MPIA), Heidelberg, and the Spanish National Commission for Astronomy. This study was carried out in the framework of the Unidad Asociada IAA-CSIC at the group of planetary science of ETSI-UPV/EHU and supported by the Ikerbasque Foundation for Science. The research of J.G., A.J.C.T and R.S.R. is supported by the Spanish programmes AYA2008-03467/ESP, AYA2012-39727-C03-01 and AYA2009-14000-C03-01. Z.P.J. thanks Dr. Yi-Zhong Fan for stimulating discussion. Z.P.J. was supported by the National Natural Science Foundation of China under the grants 11073057 and 11103084.

## Appendix: Table for observations52

### Footnotes

1. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
2. affiliation: Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China
3. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
4. affiliation: INAF-Osservatorio Astronomico di Capodimonte, Salita Moiariello 16, I-80131 Napoli, Italy
5. affiliation: International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, I-65122 Pescara, Italy
6. affiliation: Instituto de Astrofísica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain
7. affiliation: Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38205 La Laguna, Tenerife, Spain
8. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
9. affiliation: Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen Ø, Denmark
10. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
11. affiliation: Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
12. affiliation: INAF-Istituto di Astrofisica Spaziale e Fisica Cosmica, via P. Gobetti 101, I-40129 Bologna, Italy
13. affiliation: INAF-IASF Milano, via E. Bassini 15, I-20133 Milano, Italy
14. affiliation: Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
15. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
16. affiliation: Centre for Astrophysics and Cosmology, Science Institute, University of Iceland, Reykjavik, Iceland
17. affiliation: Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía s/n, E-18008, Granada, Spain
18. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
19. affiliation: Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen Ø, Denmark
20. affiliation: Mathematics & Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia
21. affiliation: Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía s/n, E-18008, Granada, Spain
22. affiliation: Unidad Asociada Grupo Ciencia Planetarias UPV/EHU-IAA/CSIC, Departamento de Física Aplicada I, E.T.S. Ingeniería, Universidad del País Vasco UPV/EHU, Alameda de Urquijo s/n, E-48013 Bilbao, Spain
23. affiliation: Ikerbasque, Basque Foundation for Science, Alameda de Urquijo 36-5, E-48008 Bilbao, Spain
24. affiliation: Department of Physics, University of Ferrara, via Saragat 1, I-44122 Ferrara, Italy
25. affiliation: Department of Physics and Astronomy, University of North Carolina, Chapel Hill NC 27599, USA
26. affiliation: Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen Ø, Denmark
27. affiliation: Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
28. affiliation: Department of Physics and Astronomy, University of North Carolina, Chapel Hill NC 27599, USA
29. affiliation: European Southern Observatory, Casilla 19001, Santiago, Chile
30. affiliation: Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
31. affiliation: Max-Planck-Institut für Astrophysik, Karl-Schwarzschildstr. 1, D-85748 Garching, Germany
32. affiliation: INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
33. affiliation: Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
34. affiliation: INAF-Osservatorio Astronomico di Roma, via Frascati 33, I-00040 Monte Porzio Catone, Roma, Italy
35. affiliation: Department of Physics and Astronomy, University of North Carolina, Chapel Hill NC 27599, USA
36. affiliation: Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía s/n, E-18008, Granada, Spain
37. affiliation: Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
38. affiliation: Astrophysics Research Institute, Liverpool John Moores University, Liverpool Science Park, 146 Brownlow Hill, Liverpool L3 5RF, UK
39. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
40. affiliation: Department of Physics and Astronomy, University of Leicester, Leicester LE1 7RH, UK
41. affiliation: INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy
42. affiliation: INAF-Osservatorio Astronomico di Brera, via Emilio Bianchi 46, I-23807 Merate (LC), Italy
43. affiliation: Space and Remote Sensing, Los Alamos National Laboratory, MS-B244, Los Alamos, NM 87545, USA
44. affiliation: Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, I-56126 Pisa, Italy
45. affiliation: Yale University, Department of Physics, 217 Prospect Street, New Haven, CT 06511, USA
46. affiliation: Space and Remote Sensing, Los Alamos National Laboratory, MS-B244, Los Alamos, NM 87545, USA
47. The Swift/UVOT data are provided by the High Energy Astrophysics Science Archive Research Center (HEASARC).
48. Gemini data are obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy.
49. http://www.aavso.org/apass
50. http://www.sdss.org
51. http://www.ipac.caltech.edu/2mass
52. The following material only appears online

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