© ESO 2018

1. Introduction

Stellar light in galaxies is absorbed and scattered in the interstellar medium by dust grains. Dust effects are particularly strong in the ultraviolet (UV), where photons are preferentially absorbed and scattered by interstellar dust. Moreover the UV light is emitted by young stars and is a tracer of the recent star formation. It is thus of the utmost importance to well quantify the interaction between the dust and the stellar light in the UV to study the dust properties and to measure accurately the star formation activity inside a galaxy.

Dust attenuation for extended objects should be distinguished from the extinction for point sources. In the case of a point source, the extinction quantifies how many photons are absorbed and scattered out of the line of sight (l.o.s.) and is thus directly linked to dust properties. For extended objects, such as galaxies, dust and stars are mixed and the attenuation does not only quantify how many photons are absorbed and scattered by dust out of the l.o.s. but also how many photons are scattered into the l.o.s. This means that it does not only depend on dust properties but also on the dust-stars geometry in the ISM.

The extinction curve can be directly measured along sightlines where the spectrum of individual stars can be obtained, which due to resolution is only the case in the Local Group so far. Using this technique, extinction curves were obtained in four galaxies where stars can still be resolved: the Milky Way (MW;Witt et al. 1984; Fitzpatrick & Massa 1990, 2007), the Small Magellanic Cloud (SMC; Prevot et al. 1984; Gordon & Clayton 1998; Gordon et al. 2003), the Large Magellanic Cloud (LMC;Clayton & Martin 1985; Fitzpatrick 1985; Misselt et al. 1999), and M 31 (Bianchi et al. 1996; Clayton et al. 2015).

Beyond the Local Group, where individual stars cannot be resolved, several techniques have been developed to derive the dust extinction in extragalactic sources, provided that the intrinsic SEDs of these sources are well characterised (see a more detailed review in Draine 2003). Most of these techniques assume the sources to be point-like which is not the case and therefore geometrical effects are included in the extinction curve. The importance of these effects are discussed by Krügel (2009) and Scicluna & Siebenmorgen (2015). For example, the dust extinction curve can be derived from QSO sightlines by comparing composite spectra of reddened and un-reddened quasars (Richards et al. 2003; Hopkins et al. 2004; Zafar et al. 2015) and it is found that featureless SMC-like extinction curves are the most common along QSO sightlines.

The attenuation curve of a whole galaxy can be derived from observations using UV-optical spectra or multi-band photometric data. For local UV-bright starburst galaxies, Calzetti et al. (1994); Calzetti et al. (2000) derive a mean attenuation curve characterised by a flatter slope than for mean local extinction curves and by a lack of the 2175 Å absorption feature (UV bump). After Calzetti’s work the topic was reinvestigated at low and high redshift (e.g. Buat et al. 2010, 2011, 2012; Wild et al. 2011; Kriek & Conroy 2013; Reddy et al. 2015, 2016; Salmon et al. 2016; Battisti et al. 2016, 2017) leading to a non-universality of the dust attenuation law. Using a similar method as the one of Calzetti et al. (2000; hereafter C00) on a larger sample of about 10 000 local (z  ≲  0.1) star forming galaxies, Battisti et al. (2016, 2017) derive a mean attenuation curve similar to C00 one though a bit shallower in the UV. Reddy et al. (2015) also applied a similar method to the C00 one to estimate the attenuation curve of 224 star forming galaxies at z  ∼  2. They find that the mean attenuation curve shape is again similar to the one of C00 in the UV but with a lower normalisation and similar to the mean SMC extinction curve at larger wavelength. Based on the NOAO Extremely Wide Field Infrared Mosaic (NEWFIRM) Medium-Band Survey, Kriek & Conroy (2013) constrain the dust attenuation of 0.5 <  z <  2 galaxies. They find that a MW and Calzetti law provide poor fits at UV wavelengths, and that steeper laws have stronger UV bumps together with more active galaxies having flatter attenuation curves and weaker UV bumps. Using galaxies from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) at z  ∼  1.5 − 3, Salmon et al. (2016) find a correlation between the colour excess E(B - V) and the slope of the attenuation law: galaxies with high colour excess have shallower attenuation curves and those with low colour excess have steeper attenuation curves.

The attenuation curve of galaxies is also studied using radiative transfer models with various dust physical properties and geometrical distribution of stars and dust. In general, shallower attenuation curves correspond to larger optical depths and mixed star-dust geometries (e.g. Witt & Gordon 2000; Pierini et al. 2004; Tuffs et al. 2004; Panuzzo et al. 2007; Chevallard et al. 2013). Applying radiative transfer models to M 31 and M 51, Viaene et al. (2017) and De Looze et al. (2014) respectively derived very steep attenuation curves with the presence of a UV bump. Most of the numerical simulations using radiative transfer models use the extinction law of local galaxies to characterise the dust properties and compute the attenuation curve one would observe for a given dust-stars geometry (e.g. Witt & Gordon 2000; Pierini et al. 2004; Seon & Draine 2016).

Gamma-ray bursts (GRBs) with their featureless power-law like spectrum shape of their afterglows are excellent probes of dust extinction in their host galaxies (Zafar et al. 2011; Zafar et al. 2018; Schady et al. 2012; Covino et al. 2013; Japelj et al. 2015). Thanks to their extremely high luminosity (up to ∼10⁵³ erg s⁻¹) such studies can be extended to very high redshift. In this work, we take advantage of the fact that both the extinction and attenuation curves can be measured for the same galaxy. The observed difference between attenuation and extinction curves contains information about the GRBH ISM structure. The extinction curves measured along the GRB l.o.s. are taken from the literature. The global dust attenuation in the GRBH galaxies is obtained by deriving the attenuation curve from SED fitting. Assuming GRB extinction curves are representative of the dust properties of their hosts, we compared our results to radiative transfer simulations in order to put some constraint on the dust-stars geometry and local distribution of dust in the ISM. As a by-product of the SED fitting we also derive robust stellar masses and SFR for the GRBHs.

The paper is organised as follows: in Sect. 2, we explain the selection of the GRB extinction curves and later the selection of the GRB host galaxies. In Sect. 3 we will search for correlations between the GRB l.o.s. and the host galaxy properties. In Sect. 4, we derive the attenuation curves of the selected host galaxies using the CIGALE SED fitting algorithm as well as the stellar mass and SFR of the galaxies. In Sect. 5, the extinction curves are compared to the derived attenuation curves and we compare our results with radiative transfer simulations.

2. Selection of the targets

Our strategy was to find reliable GRB extinction curves in the literature and then select the host galaxies for which we were able to derive the attenuation curves. In this section, we briefly explain the methods to measure the extinction curve along GRB afterglow l.o.s. in order and we define selection criteria to select the GRB extinction curves. The last step is the selection of the host galaxies.

2.1. GRB selection

2.1.1. SED of GRB afterglows

GRB afterglows are well described by synchrotron emission from accelerated electrons in a relativistic blast wave interacting with an external medium (Sari et al. 1998; Granot & Sari 2002). The observed synchrotron spectrum is composed of series of power-law segments joined at certain break frequencies (see Sari et al. 1998; Granot & Sari 2002). The NIR-to-X-ray spectrum is then usually modelled as a single power-law or a broken power-law to take into account a possible break in the synchrotron spectrum, most likely the cooling break, located between the X-ray and UV/optical/NIR ranges at the time of observation. Knowing the intrinsic spectral shape, the comparison of the observed spectrum with an expected one gives a direct access to the extinction curve. The non-attenuated intrinsic GRB afterglow SED is modelled by(1)

where F₀ is the flux normalisation, ν the frequency, ν_break the break frequency, β_O and β_X are the spectral slopes of the UV/optical/NIR and X-ray segments respectively. The free parameters are F₀, β_O and β_X. At sufficiently late times the synchrotron emission is expected to radiate in the slow cooling regime, where β_O  =  β_X  +  0.5 (Sari et al. 1998; Zafar et al. 2011). This emitted flux is then attenuated by dust absorption and scattering and photoelectric absorption of soft X-rays in the the host galaxy. The attenuated flux is given by(2)

where A_λ is the wavelength dependent extinction in the host galaxy, N_H, X is the equivalent neutral hydrogen column density derived from the soft X-ray absorption along the GRB l.o.s. in the host galaxy and is a free parameter. σ(ν) is the cross-section for the photoelectric absorption from the gas in the host galaxy.

Fig. 1. Top: mean local extinction curves using data of Table 1 in Pei (1992), normalised to AV. Bottom: difference between the mean local extinction curves, normalised to AV. They start to differ significantly in the FUV. The blue shaded area represents the minimum rest-frame spectral coverage we require, that is, 1600 Å−5500 Å.

2.1.2. Modelling extinction processes

There are two methods to assess A_λ, in other words, the extinction curve. The first method consists in scaling the well defined extinction curves derived for the LMC, SMC, or MW to the data. The mean local extinction curves of Pei (1992), normalised to the amount of extinction in the V band, A_V, are seen on top panel of Fig. 1. These local laws are scaled to the GRB afterglow spectrum using A_V as the scaling factor. This method has the advantage of introducing only one free parameter, A_V, to the SED fitting, but assumes that the wavelength dependence of dust extinction at high redshift is the same as the mean extinction in our local environment. Recently, Zafar et al. (2018) suggested avoiding use of the canonical Pei (1992) SMC curve to fit GRB data and to use the SMC-bar extinction curve from Gordon et al. (2003).

The second method is to perform a fit to assess directly the wavelength dependence of dust extinction. Usually the fit is performed using the prescriptions of Fitzpatrick & Massa (2007; hereafter FM07) which parametrises the extinction curve as(3)

where R_V  =  A_V/E(B  −  V) is the ratio of absolute-to-selective extinction.

In the UV wavelength range (λ <  2700 Å):(4)

where x  ≡  λ⁻¹ in units of μm⁻¹, c₁ and c₂ represents the UV linear component, c₃ represents the bump strength, c₄ and c₅ the FUV curvature, and the Drude profile modelling the 2175 Å bump is expressed as(5)

where x₀ is the central wavelength number and γ is the width of the bump. In the optical and NIR a spline interpolation is used to estimate the extinction curve. The FM07 parametrisation offers more freedom to fit the actual shape of the extinction curve. However it has nine free parameters which leads to degeneracies between the parameters in the fitting process unless one has a finely-sampled SED. Consequently, this method is mainly used with spectroscopic measurements, as with photometric measurements only one has to fix some of the parameters, such as intrinsic spectral slope. Moreover, photometric observations affected by the IGM absorption are usually not used which further limits the number of data.

2.1.3. Selection criteria for GRB extinction curves

For our study purpose, it is essential to have a well characterised extinction curve. The three local extinction curves (MW, LMC, and SMC) have a very similar shape in the rest-frame NIR and optical and start to differ significantly in the rest-frame FUV (Fig. 1). To be able to distinguish them, observations in the rest-frame UV bluewards of 2000 Å are needed. The lower panel of Fig. 1 shows the difference between the local extinction curves normalised to A_V. We can see that for low to moderate A_V the difference in magnitudes between the local extinction curves may be below a standard photometric accuracy. A typical amount of extinction in the V band of 0.2 mag leads to a difference between the different local extinction curves higher than 0.15 mag only at 1600 Å in the rest-frame. It increases to at least 0.75 mag with A_V  =  1 mag. In the following, the amount of extinction in the V band along the GRB l.o.s. will be denoted . We started by considering only GRB extinction curves derived using the FM07 formula with at least observations between 1600 Å and 5500 Å in the rest-frame. We used the largest sample of GRB extinction curves derived from spectroscopic measurements of the afterglow from Zafar et al. (2011) and the updated results in Zafar et al. (2012). From the 42 GRBs of this sample, we kept the 31 GRBs with evidence of dust extinction along the GRB l.o.s., that is, not consistent with 0 mag within 1σ uncertainty. After applying the minimum wavelength coverage defined above we are left with a sample of eight GRBs: five with an SMC-like extinction curve and three exhibiting a 2175 Å bump (see Table A.1). Initially, GRB 080805 is not part of our sample due to the scarcity of optical data which can not safely constrain the extinction curve slope. However, the spectroscopic confirmation of the presence of a UV bump is an interesting information about the dust inside the galaxy and we decide to include GRB 080805 in our sample. To our knowledge there are only four GRBs with a spectroscopically confirmed UV bump (GRB 070802, GRB 080605, GRB 080607, GRB 080805) and they are all in our sample.

In order to increase our sample we also considered GRB extinction curves derived using the scaling method. We started with the sample of Japelj et al. (2015) based on spectroscopic measurement of the afterglow. It consists of nine GRBs observed within the X-shooter GRB GTO programme between 2009 and 2014. For the scaling method, the slope of the extinction curve is fixed, therefore we apply a relaxed minimum wavelength coverage going from 1600 to 3500 Å in the rest-frame. We kept the eight GRBs with evidence of dust and after applying our wavelength coverage criterion we are left with four GRBs. GRB 120119A is best fitted with an LMC extinction curve, however Japelj et al. (2015) reported that it overpredicts the strength of the UV bump and that none of the mean LMC, SMC and MW is able to accurately match the the binned spectrum of GRB 120119A. Using the afterglow spectrum observed by the X-shooter and with the same data analysis as in Zafar et al. (2011, 2018) find an SMC-like extinction curve using the FM07 formula. In the following we therefore consider the extinction curve to be SMC-like. We are left with 4 GRBs with an SMC-like extinction law. We also considered the sample of Schady et al. (2012) based on broad-band photometry measurement of the afterglow since they required at least one detection at a rest-frame wavelength below 2000 Å. It consists of 49 GRBs. We kept the 36 GRBs with evidence of dust extinction and after applying our relaxed wavelength criterion we were left with 17 GRB extinction curves: eight consistent with an SMC extinction curve, six with an LMC one, and three with an MW one (see Table A.1). At the end we have a sample of 30 GRB extinction curves: 17 with an SMC-like curve, six with an LMC-like, three with an MW-like, and four with a spectroscopically confirmed bump exhibiting various slopes.

2.2. GRB host galaxies selection

Now that we have selected the extinction curves of 30 GRBs, we first compile some properties of their host galaxies, such as the SFR, stellar mass, and amount of attenuation in order to search for a correlation between the dust properties along the GRB l.o.s. and inside the host galaxy. For the second part of our study we selected only the host galaxies for which we can derive the attenuation curves from SED fitting.

2.2.1. GRB host galaxy properties

The SFR derived from the dust corrected H_α luminosity (Kennicutt 1998) is considered as one of the most robust tracers of recent star formation, in the following it will be denoted SFR_Hα. The extinction of emission lines derived from the Balmer decrement is an indicator of the dust extinction towards the HII regions. In the following, the amount of attenuation in the V band in the host derived from the Balmer decrement will be denoted . For homogeneity, these two quantities are exclusively taken from Krühler et al. (2015), with the exception of GRBH 061121 for which the SFR_Hα is taken from Vergani et al. (2017) and is computed from the H_α and H_β fluxes in Vergani et al. (2017) using the same prescriptions as in Krühler et al. (2015). The metallicities were measured using the calibration of Maiolino et al. (2008), and taken from Krühler et al. (2015), Japelj et al. (2016) and Vergani et al. (2017). The stellar masses are taken from Perley et al. (2016).

2.2.2. Golden sample for deriving GRBH attenuation curves

The characterisation of the dust effects is crucial in the UV. From the 30 GRB host galaxies selected with robust GRB extinction curves we select only targets with photometric measurements of the UV rest-frame emission of the host and a UV-to-NIR spectrum reasonably well sampled (with at least six bands) in order to measure physical parameters. After a careful inspection of the photometric and spectroscopic data of the host galaxies of GRBs selected in Sect. 2.2.1, we select seven galaxies with good photometric data on at least six bands, including a detection with the Spitzer Infrared Array Camera at 3.6 μm (IRAC1) and hydrogen recombination lines (except for GRBH 080607 at z  =  3.04) allowing a measure of SFR_Hα and of the Balmer decrement. The photometric data collected for each target are described in Appendix B. The data are corrected for the foreground Galactic extinction using Schlafly & Finkbeiner (2011). The seven hosts are gathered in Table 1.

3. GRB and host properties

Before comparing the extinction curve derived from the GRB l.o.s. with the attenuation curve derived for the host galaxy we are searching for some correlations between properties derived along the GRB l.o.s. and for the whole galaxy to check whether GRB l.o.s. are representative for the dust properties of the hosts.

Fig. 2. Time, since the GRB trigger, at which the SED were evaluated as a function of the extinction along the GRB l.o.s., . The blue, green and red colours represent which local extinction curve (SMC, LMC, MW) scaled the best to the data. The black colour means that the extinction curve was fitted with the FM07 and has a spectroscopically confirmed UV bump. The circles represent the afterglows with spectroscopic measurement and the squares the ones with photometric measurement only. The filled symbols represent SEDs best fitted with a single power law, the empty ones represent SEDs best fitted by a broken power law. Only the names of the GRB in our Golden sample are indicated.

3.1. Importance of a rapid follow-up

As GRB afterglows fade rather rapidly, we first check whether the time at which the GRB SED is extracted has an influence on the study of GRB extinction curves. Figure 2 represents the time, after the GRB trigger, at which the GRB SED is extracted as a function of for different types of extinction curves. We see that at early times, below roughly three hours, GRB afterglows exhibit all type of extinction curves from low to high extinction whereas after three hours only SMC-like extinction curves with low to moderate extinction are found. There are two ways to explain this trend, either as a bias against highly extinguished afterglows or a time dependent dust composition modification. A temporal evolution of the dust properties is expected from theoretical simulations (Waxman & Draine 2000; Fruchter et al. 2001; Perna et al. 2003) where a strong X-ray/UV radiation field can deeply modify the dust properties in the close environment (∼10 − 100 pc) of the source. Dust sublimation is predicted to affect primarily the smaller grains, and the silicates are preferentially destroyed compared to graphite, leading to featureless and shallow extinction curves. A possible early colour variation has been studied in Morgan et al. (2014). However, these processes mainly take place during the first seconds or minutes after the burst and not a few hours after the burst.

The other explanation is a bias against highly extinguished afterglows due to instrument sensitivity and fast decay of the GRB afterglow brightness. Indeed, if we consider that GRBs in dusty galaxies are not intrinsically brighter than those in galaxies with low dust content, they will be below instrument sensitivities very rapidly, with the exception of extremely bright afterglows. As mentioned in Zafar et al. (2011), where the afterglows in their sample have an average magnitude of 21.1  ±  1.7, a MW-like extinction curve with a rest-frame visual extinction of mag will yield roughly 2–3.5 magnitudes of extinction in the optical at z  =  2. Therefore GRB afterglows with mag are unlikely to be detected with current instrument sensitivity except for the few brightest ones and those with a follow-up within the first minutes after the GRB trigger. The fraction of dark bursts has been estimated between 25 and 42% in Fynbo et al. (2009) and using the complete BAT6 sample, Melandri et al. (2012) derived a 25–35% fraction of genuine optically dark bursts. Using systematic follow-up observations from GROND, Greiner et al. (2011) show that at moderate redshift, the main contribution to dark bursts is a moderate extinction. We conclude that the trend observed in Fig. 2 is very likely driven by the observed GRB brightness and not due to a temporal evolution of dust properties. In Fig. 2, we also see that extinction curves exhibiting a 2175 Å bump are preferentially found in the most extinguished l.o.s. as previously found in (Zafar et al. 2011; Greiner et al. 2011; Krühler et al. 2011). They are therefore more easily detected at early times. It follows that there is an observational bias towards SMC-like extinction curves.

The forthcoming French Ground Follow-up Telescope (F-GFT), a 1.3 m optical/NIR robotic telescope for the Space Variable Object Monitor mission (Wei et al. 2016), with its extremely fast response time of less than 20 s after receiving an alert, should significantly increase the detection of extinguished bursts. It should also be able to observe at early times the rapid afterglow colour change characteristic of a temporal variation of dust properties under the influence of intense X-ray/UV radiation field¹.

Fig. 3. Extinction along the GRB l.o.s. as a function of the host galaxy stellar mass, the latter taken from Perley et al. (2016). Same colours and symbols as in Fig. 2.

3.2. Dust extinction along GRB l.o.s. as a function of GRBH stellar mass

Figure 3 represents as a function of the GRBH stellar mass for different types of extinction curves. It shows that highly extinguished GRB l.o.s. are preferentially found in the most massive host galaxies. Previous studies (e.g. Zahid et al. 2013; Heinis et al. 2014) showed that the amount of dust attenuation in a galaxy is correlated with the stellar mass of the galaxy. Vijh et al. (2003) found a similar relation between the UV attenuation and UV luminosity of Lyman break galaxies. This relation holds if the GRB afterglow probes not only the dust capable to survive the intense radiation of the afterglow in the surrounding environment of the GRB progenitor but also the dust located at sufficiently large distances to be representative of the whole galaxy. Interestingly, this figure also shows that GRB extinction curves exhibiting a UV bump are preferentially found in the most massive host galaxies as already noticed in Krühler et al. (2011). Noll et al. (2009b) find that galaxies with evidence of a UV bump have a more evolved stellar population than galaxies lacking this feature.

4. Fitting the SED of the hosts

For the seven GRBHs in our Golden sample defined in Table 1 we perform SED fitting to derive the attenuation curve. The method and the models are first described, then we discuss the SED fitting analysis of each GRB host galaxy. In the last part of this section we discuss the star formation activity of these seven GRBHs.

4.1. SED fitting method

The SED fitting is performed with the version v0.11 of the CIGALE code (Code Investigating GALaxy Emission)². CIGALE combines a UV-optical stellar SED with a dust component emitting in the IR and fully conserves the energy balance between dust absorbed emission and its re-emission in the IR. Star formation histories as well as dust attenuation characteristics, including the attenuation law, are input parameters that can be either taken free or fixed according to the available data or the specific aims. The main characteristics of the code are described in Noll et al. (2009a). We refer to Boquien et al. 2017 (in prep.) for a detailed description of the new version of the code and to the online information to use the code. Here we only describe the assumptions and choices specific to the current study. The main parameters and range of input values are reported in Table 2. The output values of the parameters are estimated by building the probability distribution function (PDF) and by taking its mean and standard deviation. To assess the quality of the fit we compare the results to the SFR derived from the dust corrected H_α luminosity and the amount of dust attenuation derived from the Balmer decrement.

Different scenarios of star formation history are implemented in CIGALE. In this work, we have adopted a delayed star formation rate (SFR  ∝  t ⋅ e^−t/τ ) on which we add a young burst of constant star formation with a free age and amplitude. This scenario aims at reproducing both the general star formation history of distant galaxies (i.e. Lee et al. 2010; Maraston et al. 2010; Pforr et al. 2012) and a possible recent burst of star formation. The hosts of GRBs are known to be active in star formation (Savaglio et al. 2009; Perley et al. 2013; Hunt et al. 2014; Japelj et al. 2016). As rest-frame UV photometric data can probe down to the last 20 Myr of star formation history (Boquien et al. 2014), the age of the burst is allowed to vary from 20 Myr–100 Myr. The fraction of stellar mass in the recent burst is allowed to vary from 0 to 50% of the main stellar population.

The initial mass function of Chabrier (2003) is adopted with the stellar synthesis models of Bruzual & Charlot (2003). The nebular emission is included with standard parameters. The metallicity is fixed and chosen to be the closest value to the measurements between Z  =  0.008 and 0.02 (solar value).

To model the attenuation by dust, we used a modified version of the attenuation law of C00, which offers the possibility of varying the steepness of this law and adding a bump centred at 2175 Å. We refer to Noll et al. (2009a) for a complete description of the dust attenuation prescription, which still holds in the new version of the code. In brief, the dust attenuation is described as(6)

where λ_V  =  5500 Å, k′(λ) comes from C00. D_{λ0, γ, Eb}(λ), the Lorentzian-like Drude profile commonly used to describe the UV bump (Fitzpatrick & Massa 1990), is defined as(7)

with λ₀  =  2175 Å. An extinction curve as steep as the SMC corresponds to δ  ≃   − 0.5 and the bump amplitude found in the average extinction curve of the MW corresponds to E_b  =  3.5. For a sample of UV selected galaxies at intermediate redshift Buat et al. (2012) find E_b  =  1.6 and δ  =   − 0.27, which is close to the shape of the LMC2 extinction curve with a UV bump of moderate amplitude.

The photometric data partially overlap the bump for GRBHs 061121, 070802, 080605, 080805, 100814A and 120119A. For these six sources the bump will be fixed at λ₀  =  2175 Å with a width γ  =  350 Å and the amplitude is taken free. Because of the lack of wavelength coverage the other fits are performed without adding any bump in the attenuation curve and only varying its slope (δ).

The stellar emission absorbed by dust is re-emitted in the IR. The IR templates used in this work are from (Dale et al. 2014; without the AGN component) which are parametrised with a single parameter α corresponding to the exponent of the distribution of heating intensity over dust mass. A single template (α  =  2) is used except for the only galaxy detected in IR, GRBH 080607, for which different α of between 1 and 2 are tested to cover the range of values found from quiescent to active star-forming galaxies (Dale & Helou 2002).

The attenuation of the continuum obtained from the SED fitting will be denoted .

4.2. Analysis of the sources

4.2.1. GRBH 061121

From H_α measurements, Vergani et al. (2017) derived a SFR _Hα of . Using the Balmer lines measurements by Vergani et al. (2017), we computed mag corresponding to mag (using R_V = 3.08 as in Krühler et al. 2015). From IRAC1 measurement Perley et al. (2016) derived a stellar mass of 2  ×  10¹⁰ M_⊙.

The radio component is added to the fit with standard parameters (a FIR/radio correlation coefficient of 2.58 and a slope of 0.8 for the power-law synchrotron emission). The best model is obtained for Z  =  0.008 and shown in Fig. 4. No evidence of a UV bump is found. The SFR is found equal to 62  ±  26 M_⊙ yr⁻¹ consistent with SFR _Hα. A strong burst involving 29  ±  14% of the total mass with an intermediate age of 58  ±  31 Myr is needed to reproduce the SED. The stellar mass is M_⋆  =  6.9  ±  2.4  ×  10⁹ M_⊙ a factor 3 lower than the one measured by Perley et al. (2016). The resulting specific SFR, defined as sSFR  =  SFR/M_⋆ is equal to 9 Gyr⁻¹. The dust attenuation is found moderate with E(B  −  V)_s  =  0.15  ±  0.04 mag, with a flat attenuation law (δ  =  0.22  ±  0.2) marginally consistent with the starburst law of C00. The resulting amount of visual extinction is mag. A metallicity of Z  =  0.02 returned a slightly higher χ² with similar values for the SFR, the stellar mass, δ and .

Fig. 4. Best-fitted SED for GRBH 061121. Red points are the observed fluxes with their uncertainties. The black line represents the best fitted spectrum composed of attenuated stellar emission, dust emission, non-thermal radio emission and nebular lines. The dashed blue line represents the unattenuated stellar emission and the blue shaded area indicates the amount dust attenuation. The lower panel shows the relative residual. The upper right panel is an enlargement of the UV/optical/NIR domain.

4.2.2. GRBH 070802

The Balmer lines are measured by Krühler et al. (2015), corresponding to a moderate attenuation with mag corresponding to mag and .

The best model is obtained for Z  =  0.008 and shown in Fig. 5. The SFR is found equal to 32.2  ±  17.8 M_⊙ yr⁻¹ consistent with SFR _Hα. A strong burst involving 26  ±  15% of the total mass with an intermediate age of 55  ±  32 Myr is needed to reproduce the SED. The stellar mass is M_⋆  =  3.7  ±  1.6  ×  10⁹ M_⊙.

The dust attenuation is found moderate with E(B  −  V)_s  =  0.21  ±  0.05 mag, with a relatively steep attenuation law (δ  =   − 0.12  ±  0.30) consistent within 1σ uncertainty with the starburst law of C00. The resulting amount of visual extinction is mag.nd 6, as observed in MW sighlines, a significant bump is found with E_b  =  3.6  ±  1.7. This detection is due to the flux drop observed in the i′ band, the large uncertainty does not allow to tightly constrain the bump amplitude (i′  =  25.5  ±  0.3 mag). As the PDF of the bump amplitude is cut close to the peak of the PDF, we have performed the fit again by letting the bump amplitude to vary between 0 and 10 and it results in E_b  =  5.3  ±  2.6 with a better defined PDF, while the χ² and estimations for the other output parameters remain unchanged. We also performed the fit without bump and the estimation of the SFR, M_⋆ and E(B - V)_s remain unchanged while the slope of the attenuation curve becomes steeper with δ  =   − 0.31  ±  0.26. with a higher χ². A metallicity of Z  =  0.02 returned a slightly higher χ² with similar values for the SFR, the stellar mass, δ and .

Fig. 5. Best-fitted SED for GRBH 070802. Colour and symbols convention as in Fig. 4.

4.2.3. GRBH 080605

The Balmer lines are measured by Krühler et al. (2015), corresponding to a moderate attenuation with mag and mag with an intense star formation: SFR . From IRAC1 measurement, Perley et al. (2016) derive a stellar mass of 3.4 × 10¹⁰ M_⊙

The best model is obtained for Z  =  0.02 and shown in Fig. 6.

The SFR found equal to 44.9  ±  22.9 M_⊙ yr⁻¹ is in very good agreement with the one measured with the H_α flux. A recent burst of star formation is found with an amplitude of 15  ±  14% of the total mass and an age of 75  ±  31 Myr. The stellar mass is M_⋆  =  12.3  ±  4.2  ×  10⁹ M_⊙ a factor 2.8 lower than the one measured by Perley et al. (2016). We estimate a sSFR for this starbursting galaxy of 3.6 Gyr⁻¹.

Dust attenuation is characterised by a colour excess E(B  −  V)_s  =  0.09  ±  0.05 mag and a shallow attenuation curve consistent with C00 (δ  =   − 0.08  ±  0.38). This results in a modest amount of visual extinction of mag. No evidence for a UV bump is found. A metallicity of Z  =  0.008 returned a higher χ² with similar values for the SFR, the stellar mass, δ and .

Fig. 6. Best-fitted SED for GRBH 080605. Colour and symbols convention as in Fig. 4.

4.2.4. GRBH 080607

The stellar mass is measured with IRAC1 data by Perley et al. (2016): M_⋆  =  2.8  ×  10¹⁰ M_⊙. No measure of the Balmer lines is available.

We adopted a solar metallicity (Z  =  0.02) as measured for the host ISM from afterglow absorption-line observations (Prochaska et al. 2009). With only one measurement for the dust emission, we cannot run CIGALE with a free dust component. Instead we performed several runs varying the α parameter (α  =  1, 1.5 and 2), the quality of the fits are similar. Varying α changes the dust temperature and the position of the peak of the dust component. The IR luminosity, SFR, stellar mass and attenuation vary accordingly: L_IR, SFR, M_⋆ and decrease from ∼7.2  ×  10¹¹ L_⊙, ∼70 M_⊙ yr⁻¹, ∼3.4  ×  10¹⁰ M_⊙ and ∼2 mag to ∼1.9  ×  10¹¹ L_⊙, ∼20 M_⊙ yr⁻¹, ∼2.1  ×  10¹⁰ M_⊙ and ∼1 mag when α increases from 1 to 2. As expected the stellar mass remains similar. Taking in mind this uncertainty we fix α  =  1.5, describing a galaxy extremely active in star formation. The best fit is shown in Fig. 7.

The stellar mass fraction due to the recent burst is 8  ±  11%, consistent with no burst, consequently we decide to report the results without any recent burst. The total IR luminosity of the galaxy is L_IR  =  3.6  ±  1.4  ×  10¹¹ L_⊙ with a SFR equal to 35.2  ±  13.9 M_⊙ yr⁻¹. The stellar mass, M_⋆  =  2.75  ±  0.8  ×  10¹⁰ M_⊙ is in very good agreement with the one measured by Perley et al. (2016). The sSFR is equal to 1.3 Gyr⁻¹. The dust attenuation is characterised by a colour excess of E(B  −  V)_s  =  0.31  ±  0.04 mag and a flat attenuation curve (δ  =  0.05  ±  0.10) consistent with C00. The resulting amount of visual extinction is   =  1.39  ±  0.29 mag.

The fit with a recent burst gives a slightly higher SFR of 49.7  ±  14 M_⊙ yr⁻¹, a slightly lower stellar mass, M_⋆  =  2.3  ±  1  ×  10¹⁰ M_⊙, and similar colour excess and slope for the dust attenuation.

Fig. 7. Best-fitted SED for GRBH 080607. Colour and symbols convention as in Fig. 4.

4.2.5. GRBH 080805

The Balmer lines are measured by Krühler et al. (2015). They derive a high colour excess although with a large uncertainty, mag corresponding to an attenuation of mag, and a highly uncertain star formation rate, . The stellar mass derived from IRAC1 measurement by Perley et al. (2016) is M_⋆  =  7.2  ×  10⁹ M_⊙.

The best model is obtained for Z  =  0.02 and shown in Fig. 8. The SFR is found equal to 20.6  ±  12 M_⊙ yr⁻¹ is in agreement with the one measured with the H_α flux within errorbars. A burst of star formation is found with an amplitude of 22  ±  16% of the total mass and an age of 60  ±  33 Myr. The stellar mass is M_⋆  =  3.4  ±  1.7  ×  10⁹ M_⊙. We estimate a sSFR for this galaxy of 6 Gyr⁻¹. The dust attenuation is characterised by a colour excess E(B  −  V)_s  =  0.37  ±  0.07 mag and a steep attenuation curve, similar to that of the SMC (δ  =   − 0.45  ±  0.24). This results in an amount of visual extinction of mag. No evidence for a UV bump is found. A metallicity of Z  =  0.008 returns a worse χ² with similar values for the SFR and stellar mass but different values for the dust attenuation: δ (−0.19  ±  0.23) and (1.38  ±  0.47 mag).

In order to improve the agreement between the SFR found from the SED and from H_α measurements, we checked whether the presence of a very young starburst could enhance the current star formation rate. We ran again CIGALE with a recent burst taking place within the last 10–20 Myr. The SFR increases to 48.2  ±  29.9 M_⊙ yr⁻¹, in very good agreement with the H_α measurements. The burst of star formation is found with an amplitude of 22  ±  16% of the total mass and an age of 15  ±  4 Myr. As expected, the stellar mass is reduced to M_⋆  =  2.9  ±  1.6  ×  10⁹ M_⊙. The attenuation curve becomes shallower, but still steeper than the one of C00, with δ  =   − 0.25  ±  0.24 and the amount of attenuation in the optical increases to mag. This indirect use of the H_α emission line indicates that a very recent episode of star formation can explain the measured SFR_Hα. In a future work, taking into account the emission lines in the fit would allow to probe star formation at timescales lower than 20 Myr. We retain the result with a burst age older than 20 Myr as the reference.

Fig. 8. Best-fitted SED for GRBH 080805. Colour and symbols convention as in Fig. 4.

Fig. 9. Best-fitted SED for GRBH 100814A. Colour and symbols convention as in Fig. 4.

4.2.6. GRBH 100814A

The Balmer lines are measured by Krühler et al. (2015), they derive a colour excess of mag corresponding to an attenuation of mag, and the lowest SFR of our sample with . The stellar mass measured from the IRAC1 measurement in Perley et al. (2016) is M_⋆  =  3.3  ×  10⁹ M_⊙.

The best model is obtained for Z  =  0.008 and shown in Fig. 9. No recent burst of star formation is added to the SFH. The SFR is equal to 4  ±  2.3 M_⊙ yr⁻¹ which is in good agreement with the one measured with the H_α flux. The stellar mass is M_⋆  =  2.9  ±  0.8  ×  10⁹ M_⊙ in agreement with the one measured by Perley et al. (2016). We estimate a sSFR of 1.4 Gyr⁻¹.

The dust attenuation is characterised by a colour excess E(B  −  V)_s  =  0.05  ±  0.04 mag and a flat attenuation curve (δ  =  0.09  ±  0.51). This results in an amount of visual extinction of mag. No evidence for a UV bump is found. A metallicity of Z  =  0.02 returned an equivalently good fit with very similar values for the SFR, the stellar mass, δ and . A recent burst in the SFH leads to an SFR estimation of 17.2  ±  14.2 M_⊙ yr⁻¹ and a colour excess of 0.16  ±  0.07 mag which are not in agreement with the SFR_Hα and the colour excess derived from the Balmer lines Krühler et al. (2015). For this reason, we keep the results without any recent burst in the SFH as the reference.

4.2.7. GRBH 120119A

The Balmer lines are measured by Krühler et al. (2015), they derive a colour excess for the emission lines of mag corresponding to a visual attenuation of mag, and a SFR_Hα of . The stellar mass measured from the IRAC1 measurement in Perley et al. (2016) is 8  ×  10⁹ M_⊙.

The best model is obtained for Z  =  0.008 and shown in Fig. 10. The SFR is found equal to 25.5  ±  14.1 M_⊙yr⁻¹ marginally consistent with the one measured with the H_α flux. A burst of star formation is found with an amplitude of 23  ±  15% of the total mass and an age of 64  ±  33 Myr. The stellar mass is M_⋆  =  3.8  ±  1.2  ×  10⁹ M_⊙ a factor of 2.1 lower than the one measured by Perley et al. (2016). We estimate a sSFR for this starbursting galaxy of 6.7 Gyr⁻¹. The dust attenuation is characterised by a colour excess E(B  −  V)_s  =  0.24  ±  0.06 mag and a attenuation curve steeper than the one of C00 (δ  =   − 0.39  ±  0.22). This results in an amount of visual extinction of mag. No evidence for a UV bump is found. A metallicity of 0.02 returned a slightly worse χ² with similar values for the SFR, stellar mass, δ and .

As for GRBH 080805, in order to improve the agreement between the SFR found from the SED and from H_α measurements, we checked whether the presence of a very young starburst could enhance the current star formation rate. We ran again CIGALE with a recent burst taking place within the last 10–20 Myr. The resulting fit is slightly better with a lower χ². The SFR increases to 44.4  ±  26.6 M_⊙ yr⁻¹, in very good agreement with the H_α measurements. The burst of star formation is found with an amplitude of 16  ±  15% of the total mass and an age of 15  ±  4 Myr. The stellar mass is only reduced to M_⋆  =  3.6  ±  1.4  ×  10⁹ M_⊙. The attenuation curve becomes shallower with δ  =   − 0.29  ±  0.24. The amount of attenuation is mag. We keep the result with a burst age older than 20 Myr as the reference.

Fig. 10. Best-fitted SED for GRBH 120119A. Colour and symbols convention as in Fig. 4.

4.3. Star formation activity and SFR-M_⋆ comparison

The results of the SED fitting are reported in Table 3. The scenario with a recent burst on top of a delayed star formation history is favoured over a delayed only SFH for five of our seven GRB host galaxies. Generally, our stellar mass estimates are lower than in Perley et al. (2016) where stellar masses are derived from the IRAC 3.6 μm luminosities using a continuous SFH. In order to check whether this difference is due to the SED fitting algorithm or to the adopted SFH we perform our fits with a constant SFR over 1–3.5 Gyr similarly to the method in Perley et al. (2016). However, we are using all the photometry data and not only the IRAC1 detection, and the stellar population age was fixed according to the stellar mass in Perley et al. (2016) which is not the case in our method. In the right panel of Fig. 11 we compare the SFR derived with a continuous SFH and our results to the SFR_Hα derived in Krühler et al. (2015). The continuous SFH leads to lower SFR estimates that are not consistent with the SFR_Hα except for GRBHs 080607 and 100814A where a recent burst is not required. On the contrary, the SFRs we derive with the delayed or delayed  +  burst SFH are always found in agreement with the SFR_Hα. As shown in the left panel of Fig. 11, the assumption of a constant SFR also impacts the mass measurements and our stellar mass estimates are lower (up to a factor three) than the ones in Perley et al. (2016) except for GRBHs 080607 and 100814A. The fact that we include all observations instead of just the IRAC1 measurement might partly explain the observed difference in some cases. In all cases the fits return a worse χ² with a continuous SFH compared to delayed or delayed  +  burst SFH. We conclude that the discrepancy on the stellar mass estimation is mainly explained by the introduction of a strong and recent burst.

Figure 12 represents the main sequence of all GRBHs having a stellar mass estimation in Perley et al. (2016) and a SFR _Hα in Krühler et al. (2015). The main sequence of star-forming galaxies for z  =  0.5, 1.5 and 3, covering the GRBH redshifts, are represented using the relation from Schreiber et al. (2015). For the four GRBHs (061121, 080605, 080805, 120119A) with a delayed  +  burst SFH, our lower stellar mass estimates shift the galaxies to the starbursts domain we define as four times the main sequence. These objects are dusty starbursting hosts and we do not expect such a strong effect for all GRB host galaxies, as illustrated by GRBH 100814A. Comparing our results with Krühler et al. (2011), we find that our SFR estimations are consistent within errorbars for the 4 galaxies we have in common. We derive higher stellar mass for GRBH 080605 and GRBH 080607. They were limited to optical/NIR data up to the Ks band, which explained the difference with our stellar mass estimation as we have a better NIR coverage. The old stellar population contributes significantly to the total stellar mass and dominates the NIR stellar emission, so the use of IRAC1 (and IRAC2 for GRBH 080607) detections allows a more reliable stellar mass estimation.

Given the importance of the stellar mass estimation in the evidence of a mild metallicity threshold (Vergani et al. 2015; Vergani et al. 2017; Japelj et al. 2016) necessary to form long GRB (LGRB), it would be of interest to revisit GRBH stellar masses estimation on a larger sample. LGRB hosts also offer the opportunity to identify and study distant low mass (∼10⁸ − 10¹⁰ M_⊙) starbursting galaxies generally absent or badly represented in blind surveys.

Fig. 11. Left: stellar masses estimated from: IRAC1 measurement in Perley et al. (2016, red), this work with either a delayed or delayed  +  burst SFH (green), CIGALE using same configuration as in Table 2 but with a continuous SFH with a main stellar population age between 1 and 3.5 Gyr (blue). Right: SFR estimated from: Hα measurement from Krühler et al. (2015) and Vergani et al. (2017, red) this work using either a delayed or delayed  +  burst SFH (green), CIGALE using same configuration as in Table 2 but with a continuous SFH with a main stellar population age between 1 and 3.5 Gyr (blue).

Fig. 12. SFR-stellar mass relation. Blue points represent stellar masses from Perley et al. (2016) and SFR from Krühler et al. (2015) where we highlighted the GRBHs in our sample using a star symbol and the corresponding name. The colour map encodes the redshift. The black circles with blue interiors correspond to the GRBHs of our sample with SFR and stellar masses derived from the SED fitting. The grey lines represent the main sequence relation from Schreiber et al. (2015), the dashed line is four times the main sequence at z  =  1.5 representative of starbursting galaxies (most of our our GRBHs are at z  ∼  1.5).

5. Dust attenuation in GRBHs

In this section, we first characterise the attenuation curves we derived for the seven GRBHs of the Golden sample. Then we study the characteristics of the dust attenuation as a function of GRBH properties (the stellar mass, SFR, sSFR, and ). We compare the attenuation curves derived from the SED fitting with the extinction curves along the GRB l.o.s. and finally compare these results to radiative transfer simulations to constrain dust-stars geometry in the ISM of these GRBHs.

5.1. Measure of the attenuation curve slopes

The dust attenuation is described using Eq. (6) where the colour excess, E(B  −  V)_s, and the attenuation slope, δ, are free parameters. The probability density functions obtained with CIGALE for the attenuation slope of each GRBH are shown in Fig. 13. They are well defined with the exception of GRBH 100814A whose PDF is too flat due to the low amount of dust within the host galaxy characterised by a colour excess of mag for the emission lines (Krühler et al., 2015) and mag for the stellar continuum. Therefore we will not consider this galaxy in the following.

There are a great variety of slopes with GRBH 070802, GRBH 080605 and GRBH 080607 similar to the Calzetti attenuation law defined by δ  =  0. The attenuation curve of GRBH 061121 is flatter than C00. GRBH 080805 and GRBH 120119A have an attenuation curve slope as steep as the mean SMC extinction curve, corresponding to δ  ∼   − 0.5.

Fig. 13. Probability density functions of the attenuation slope for the GRBHs.

5.2. Variation of the slope with GRB host properties

Figure 14 represents the variation of the attenuation curve slope, δ, with some physical properties of the GRBH. We only have seven GRBHs in the sample so the conclusions are statistically limited. In the first panel representing the evolution of δ with , although no obvious trend is seen with a visual inspection of the plot, the orthogonal distance regression shows a trend with highly attenuated galaxies having flatter attenuation curves. This trend has already been observed for galaxies at z  =  1.5 − 3 (Salmon et al. 2016) and for galaxies at 0.5 <  z <  2 (Kriek & Conroy 2013). Radiative transfer simulations (i.e. Witt & Gordon 2000; Chevallard et al. 2013) also predict a steeper dust attenuation curves at small attenuation optical depths, and shallow attenuation curve at larger optical depths. In the second panel, representing the variation of δ with the stellar mass, a clear trend is seen with lower (higher) stellar masses correlating with steeper (shallower) attenuation curves. This is also in agreement with the work of Salmon et al. (2016) where the more massive galaxies in their spectroscopic redshift sample tend to prefer “starbust” (i.e. shallow) dust attenuation curves and less massive galaxies the SMC92 (i.e. steep) dust attenuation curves.

The third panel represents the variation of δ with the SFR and a clear trend is seen: GRBH with low (high) SFR have steeper (shallower) attenuation curves.

The bottom panel represents the evolution of δ with the sSFR and again although no trend can be seen with a visual inspection, the orthogonal distance regression shows that steep (shallow) attenuation curves are found in the more (less) active GRBHs. However the large uncertainties make this trend very uncertain. This result contradicts the results in Kriek & Conroy (2013) which show that high H_α equivalent widths (i.e. high sSFRs) correlate with flat attenuation curves.

Fig. 14. Top: attenuation curve slope as a function of the SED continuum amount of attenuation. Middle top: attenuation curve slope versus the stellar mass. Middle bottom: attenuation curve slope versus the SFR. Bottom: attenuation curve slope versus the specific SFR. The blue points correspond to the quantities derived with CIGALE. The black dashed line represents the slope of the mean SMC extinction curve and the yellow dashed line the slope of the Calzetti law. The grey dash-dotted line illustrates the best fit using an orthogonal distance regression (using SciPy’s scipy.odr). The χ2, number of degrees of freedom and Null Hypothesis Probability (NHP) of these fits are indicated.

Fig. 15. Top: amount of global attenuation in the GRBH in the V band as a function of the amount of extinction in the V band along the GRB l.o.s. Middle: colour excess for the stellar continuum as a function of the colour excess for the Balmer lines. The grey line represents the C00 relation. Bottom: amount of attenuation of the Balmer lines in the V band as a function as the amount of extinction in the V band along the GRB l.o.s. For all panels the grey dash-dotted line represents the best fit using an orthogonal distance regression (using SciPy’s scipy.odr) and the grey shaded area its 1σ uncertainty. The χ2, number of degrees of freedom and Null Hypothesis Probability (NHP) of these fist are indicated.

5.3. Global dust attenuation and dust extinction along GRB l.o.s.

Top panel of Fig. 15 represents the evolution of the amount of dust extinction along the GRB l.o.s. as a function of the amount of dust attenuation averaged over the whole GRBH. We see that they are correlated and GRB l.o.s. are dustier than the average attenuation of the host galaxy. The orthogonal distance regression returns the relation for our sample. The LGRB progenitors are expected to be a result of the collapse of young massive stars and thus they should suffer more attenuation than the more evolved stellar population which had enough time to migrate outside their birth clouds (e.g. C00, Charlot & Fall 2000; Granato et al. 2000). On a larger sample of 23 GRBHs selected with the criteria of having an obscured GRB l.o.s. mag), Perley et al. (2013) find a similar trend: . However for mag, corresponding to less massive galaxies they find the opposite trend although dispersion is large. The middle panel of Fig. 15 represents the evolution of the colour excess for the stellar continuum as a function of the colour excess for the Balmer lines. For our sample, we have E(B  −  V)_s  =  (0.51  ±  0.08)  ×  E(B  −  V)_g, which is in agreement with C00. The bottom panel of Fig. 15 represents the amount of attenuation for nebular lines in the V band as a function of the amount of extinction along the GRB l.o.s. The orthogonal distance regression returns: which is consistent with the 1:1 relation within 1σ uncertainty, meaning that the GRB and HII regions suffer a similar attenuation.

5.4. Comparison of extinction and attenuation curves

The attenuation curves derived by the SED fitting are compared to the extinction curves along GRB l.o.s. on Fig. 16. There is a great variety of cases that can be sorted into three categories. Category A, in which the attenuation curve is shallower than the extinction curve (061121 and 080605), category B, in which both attenuation and extinction curves are similar (080607, 070802, 120119A), and category C, in which the attenuation curve is steeper than the extinction curve (080805). The attenuation curves of 061121, 080605, and 080607 are consistent with the Calzetti law, those of 070802, 080805, and 120119A are not. We note than the better constrained attenuation curves are those with radio (GRBH 061121) and sub-millimeter (GRBH 080607) detections.

Fig. 16. Top: GRBH 061121, GRBH 070802 and GRBH 080805, bottom: GRBH 080605, GRBH 080607 and GRBH 120119. The solid black line is the extinction curve normalised to , the blue one is the attenuation curve normalised to and the green one is the normalised Calzetti law. The blue shaded area represents the 1σ uncertainty on the attenuation curve.

5.4.1. General shape

Category A corresponds to the case with a flat attenuation curve and a steeper extinction curve. A far-UV rise in the extinction curve indicates the presence of small silicate grains and the UV bump the presence of PAHs or small carbonaceous grains. A shallow attenuation curve is usually obtained for high optical depth (Witt & Gordon 2000; Seon & Draine 2016), highly inclined galaxies (Pierini et al. 2004; Inoue 2005), a high density environment (Inoue 2005) or a clumpy ISM (Witt & Gordon 2000; Seon & Draine 2016).

Category B corresponds to similar attenuation and extinction curves. At low optical depth an ISM in which dust and stars are uniformly mixed or stars surrounded by dust (shell geometry) with homogeneous and clumpy local dust distribution can reproduce an attenuation curve with a similar slope as the extinction curve, even as steep as the SMC extinction curve (Witt & Gordon 2000). At higher optical depth only the shell geometry with an homogeneous dust distribution is able to produce such a steep attenuation curve from SMC dust type (Witt & Gordon 2000).

The case of GRB/GRBH 080607 is interesting because it has the highest redshift in our sample and the extinction curve is unusually flat. This may be due either to variations of dust properties and/or geometry in the ISM. The geometrical effect is supported by the detection of a molecular cloud in the afterglow spectrum at > 100 pc from the GRB, probably arising in a neighboring star-forming region (Prochaska et al. 2009). Another possible explanation of the flat extinction curve is due to the dust composition: in the earliest evolutionary stage of dust evolution the dust content is dominated by large grains originated from stellar sources which results in a flat extinction curve (≲1 Gyr). Later on, the abundance of small grains increases through shattering and accretion processes which results in the progressive apparition of a 2175 Å bump and a steeper extinction curve (Asano et al. 2013, 2014). This explanation can be supported by the redshift of GRBH 08607 of z  =  3.04 which corresponds to an age of the Universe of about 2.1 Gyr adopting the ΛCDM cosmology of Planck Collaboration (2016). The rather high value of R_V  ∼  4 measured from the extinction curve is also indicative of a large grain size distribution though the uncertainty is quite large (Prochaska et al. 2009; Zafar et al. 2011). The forthcoming SVOM mission might potentially bring more data to constrain the dust evolution processes at high redshift.

Category C corresponds to an attenuation curve steeper than the extinction curve. A steep attenuation curve can be the result of a low optical depth (Witt & Gordon 2000; Seon & Draine 2016) for example in a face-on galaxy. It may also result from an age-dependent attenuation where the young stellar population is embedded in dense clouds and more attenuated than the old stellar population which had time to migrate to the more diffuse ISM (e.g., Inoue 2005).

5.4.2. Presence of the UV bump in the attenuation curves

For many years, there has been a debate whether a Calzetti-like attenuation curve can ever arise if the underlying extinction curve exhibits a UV bump. While the works of Gordon et al. (1997); Witt & Gordon (2000) and Pierini et al. (2004) suggested that a Calzetti-like attenuation law implies a bump-free extinction curve, for example, a SMC-like law, Silva et al. (1998) and Granato et al. (2000) could reproduce a Calzetti-like attenuation law with an underlying MW extinction curve. In our sample of GRB extinction curves, five out of six exhibit a UV bump with four spectroscopically confirmed detections. The presence or lack of a UV bump in the attenuation curves should provide valuable information.

The UV bump is best constrained using spectroscopic measurements of galaxies (e.g., Noll et al. 2007) but intermediate filter bands also allow to constrain the bump amplitude (e.g., Buat et al. 2011; Kriek & Conroy 2013. However, this is very difficult using broad filter bands only as it relies only on one filter band overlapping the UV bump with a passband width higher than the bump width. In our sample, GRBHs 061121, 070802, 080605, 080805 and 120119A have a filter band which overlaps the UV bump. The rest-frame spectral coverage of each GRBH observation can be seen in Appendix C. For GRBH 070802, we already reported a bump amplitude of E_b  =  5.3  ±  2.6 in Sect. 4.2.2. For the other GRBHs, we already ran CIGALE with the same configuration as described in Sect. 4.1 with a varying UV bump amplitude (E_b >  0) and did not find clear evidence of its presence. The PDFs of the UV bump amplitude exhibit a simple power law shape with the highest probability associated to an amplitude of zero and a decreasing probability as the amplitude increases. Given the rather weak UV bump amplitudes measured in the extinction curves, we run CIGALE again letting the UV bump amplitude vary from −2 to 2 this time, similarly as in Buat et al. (2012), in order to obtain better defined PDFs for a more reliable Bayesian estimation of the UV bump amplitude if PDFs are centred around zero. The results are reported in Table 5, all UV bump amplitudes are compatible with zero within 1σ uncertainty. The estimation of the other parameters remain unchanged. We conclude that we do not find evidence of a UV bump with the possible exception of GRBH 070802, but we can not exclude the presence of a weak UV bump in the attenuation curves. Further observations using spectroscopy or intermediate filter bands are required in order to have a better constraint.

5.5. Comparison with radiative transfer simulations

To investigate the ISM geometry, we compared the derived attenuation curves with CIGALE with the results of the recent radiative transfer code developed by Seon & Draine (2016). This model offers the possibility to choose between three theoretical dust models adopted from Weingartner & Draine (2001) and Draine (2003) for the MW, LMC, and SMC-bar, and two empirical models for the MW and SMC from Witt & Gordon (2000). The former dust models are noted WD-MW, WD-LMC and WD-SMC and the later WG-LMC and WG-SMC.

We selected the dust model according to the GRB extinction curves (cf. Table 4). Following Schady et al. (2012) GRB 061121 is best fitted with a LMC-like extinction curve³. The extinction curve of GRB 070802 is very similar to the mean LMC2 super shell extinction curve (Gordon et al. 2003) so we choose a LMC dust model. The far-UV rise of the extinction curve of GRB 080605 is similar to an SMC extinction curve, however due to the spectroscopically confirmed detection of a UV bump, we chose an LMC dust model. For GRB 080607 and GRB 080805 due to the flat FUV part and the presence of a UV bump, we select a MW dust model. For GRB 120119A, we choose an SMC-like dust model according to Zafar et al. (2018). For SMC and MW like extinction curves both theoretical and empirical dust models are tested and we kept the one reproducing the best the attenuation curve derived with CIGALE.

The attenuation curves computed with the radiative transfer model of Seon & Draine (2016) are defined with three parameters: τ_V, R_s/R_d and M_s. τ_V is the optical depth in V band and take discrete values between 0.1 and 20. R_s/R_d corresponds to the ratio of the distribution radius of stars and dust respectively, it takes discrete values between 0 and 1. R_s/R_d  =  0 corresponds to a compact OB association surrounded by a cloud and R_s/R_d  =  1 corresponds to the uniform distribution of photon sources over the spherical dusty medium (similar to the “DUSTY” configuration of Witt & Gordon 2000). To qualitatively assess our results we followed a formalism similar to the one of Witt & Gordon (2000) by referring to a Dusty ISM for R_s/R_d  ≥  0.8 when stars are approximately uniformly distributed with dust and to a Shell ISM for R_s/R_d  ≤  0.5 with the stars surrounded by a dust cloud. M_s is the Mach number governing the variance of the ISM density field , in other words, quantifying the clumpiness of the ISM. It takes discrete values between 0 and 20. M_s  =  0 corresponds to a homogeneous ISM and M_s  =  20 to a very clumpy ISM. In the following, we will refer to a homogeneous ISM for M_s  ≤  3, to a Clumpy ISM for 4  ≤  M_s  ≤  15 and to a Very Clumpy ISM for M_s  ≥  15.

We compared the attenuation curves derived with CIGALE to the attenuation curves computed with the radiative transfer model for the different values of τ_V, R_s/R_d, M_s. For each attenuation curve derived with CIGALE, a χ² grid is then built using(8)

with the amount of attenuation from the radiative transfer model of Seon & Draine (2016), and the amount of attenuation and its 1σ uncertainty derived with CIGALE. These quantities are evaluated at the N_data wavelengths used by Seon & Draine (2016) and covering the GRB hosts observations.

From the χ² grid, we compute the PDF of each parameter by marginalising the PDF over the two other parameters. The PDFs are shown in Fig. 17 and the results are summarised in Table 4. The cases of GRBH 061121, 070802, 080605 are similar with a low optical depth and high values for R_s/R_d and M_s indicating that a Dusty and Very clumpy ISM best reproduces the attenuation curves derived with CIGALE. Simulations with R_s/R_d >  1 are not provided in the publicly available simulations of Seon & Draine (2016)⁴. It would be interesting to perform radiation transfer simulations with values of R_s/R_d higher than 1 as in the work of Witt & Gordon (2000) where the CLOUDY configuration has R_s/R_d  ∼  1.45. For GRBH 080607, the R_s/R_d PDF peaks at ∼0.5 and the M_s PDF disfavours a homogeneous ISM comparing to a Clumpy or even Very clumpy ISM. For GRBH 080805 and 120119A, both having steep attenuation curves, a bimodal solution is found with either a Dusty-homogeneous ISM or a Shell-Clumpy ISM. The attenuation curves computed with the radiative transfer model best fitting the attenuation curves derived with CIGALE are represented in Fig. C.1. All attenuation curves computed with the radiative transfer model with a LMC or MW dust grain type that best fit the CIGALE attenuation curves exhibit a UV bump but the uncertainty associated to the CIGALE attenuation curves does not allow to constrain them.

Fig. 17. Probability density functions of τV, Rs/Rd and Ms for each GRBH with the chosen dust model.

6. Conclusion

We have selected 30 GRBs with a rest-frame coverage from UV to optical and find that the type of GRB extinction curves and the amount of extinction along the GRB l.o.s. correlate with the host galaxies properties with the more extinguished GRBs preferentially found in the more massive hosts. The UV bump is also preferentially found in the most extinguished GRB l.o.s. It follows that without a rapid follow-up there is an observational bias towards SMC-like extinction curves for GRBs. This correlation presumably indicates that the GRB afterglow probes along its l.o.s. not only the dust in the vicinity of the burst but also the dust located at large distances to be representative enough of the host galaxy.

From these 30 GRBs we have selected seven host galaxies whose SEDs have photometric measurements of the UV rest-frame emission and a UV-to-NIR spectrum reasonably well sampled (with at least six bands). The results of our SED fitting show that a recent burst of star formation is required for five out of seven GRBHs to recover the SFR measured from H_α flux. This leads to a lower estimate of the stellar masses than the ones derived in Perley et al. (2016) using a mass-to-light relation with the IRAC 3.6 μm luminosities. Consequently these GRBHs are shifted to the starburst domain, defined as four times the star-forming main sequence. For these relatively dusty GRBHs, we find that GRB and HII regions suffer a similar attenuation. Our estimates of the amount of attenuation for the whole galaxy, derived from the SED fitting, correlate with the amount of extinction along the GRB l.o.s., with the galaxy attenuation amounting to about 70% of the GRB l.o.s. extinction. The ratio of colour excess between the stellar continuum and the Balmer lines is consistent with the one of C00.

The attenuation curves derived from the SED fitting show a great variety of cases: the attenuation curves have flatter, similar or steeper slopes than the extinction curves. Half of the sample is consistent with the C00 law and there is evidence of a UV bump in only one attenuation curve. We find that steeper (shallower) attenuation curve slopes are found preferentially in the less (more) massive galaxies and with higher (lower) SFR and . These trends encourage us to further study these possible correlations on a larger sample of GRBHs.

Comparing our results with the radiative transfer simulations in Seon & Draine (2016), we find a variety of dust-stars geometries. For half of the sample, a uniform distribution of stars and dust with a very clumpy local dust distribution reproduces the derived attenuation curves the best. In one case, the ISM structure is best represented with stars surrounded by a dust cloud with a clumpy local dust distribution. For the two steepest attenuation curves, two configurations are found almost as likely, either a uniform distribution of stars and dust with a homogeneous local dust distribution or stars surrounded by a dust cloud with a clumpy local dust distribution.

This method is promising and a dedicated radiative transfer simulation on each of these objects would allow to understand more precisely the dust-stars distribution in these GRBHs.

Acknowledgments

DC acknowledges H. Hirashita, A.K. Inoue, T.T. Takeuchi and D. Donevski for helpful and stimulating discussions. DC acknowledges support by the Centre National d’Etudes Spatiales and support by the Région Provence-Alpes-Côte d’Azur for the funding of his PhD. JJ acknowledges support from NOVA and NWO-FAPESP grant for advanced instrumentation in astronomy. This work was supported by the Programme National de Cosmologie et Galaxies (PNCG). SDV, SBo, RS, JP, acknowledges the support of the French National Research Agency (ANR) under contract ANR-16-CE31-0003 BEaPro (PI: SDV).

References

Appendix A

GRB samples

Appendix B

SED data for the golden sample

B.1. GRBH 061121

Multi-wavelength data of the host galaxy are available from Perley et al. (2015). It was one of the four galaxies detected in radio from their VLA survey at 3 GHz. The galaxy was also observed in the optical (uBgiz with the Keck-I/LRIS, R with the VLT/FORS2) and near-IR (J with the P200/WIRC, K with the VLT/ISAAC and 3.6 μm with Spitzer/IRAC).

B.2. GRBH 070802

The galaxy was observed by Elíasdóttir et al. (2009) with the VLT and detected in the R band of the VLT/FORS2 and K band of the VLT/ISAAC. Krühler et al. (2011) reported detections with the i band of the NTT/EFOSC and J band of the VLT/HAWK-I. Further detections in the NIR are reported by Perley et al. (2013) with the HST/WFC3 in F105W and F160W and with Spitzer/IRAC. We decided to keep only the IRAC2 measurement as the IRAC1 measurement is affected by a bright star (Perley et al. 2013).

B.3. GRBH 080605

The host galaxy is observed by Krühler et al. (2011) with GROND and detected in the griz bands. The HST observations (WFC3/F160W) and LIRIS observation (J, Ks) are reported by Krühler et al. (2012) and IRAC1 magnitude by Perley et al. (2016).

B.4. GRBH 080607

We used the photometric data published in Perley et al. (2013) from the observations first reported by Chen et al. (2010): the gVIK data from the Keck-I observations (LRIS and NIRC), a deep r-band measurement from the Magellan/IMACS, and near-IR measurements with HST/WFC3 (F160W) and Spitzer/IRAC (IRAC1 and IRAC2). ALMA flux at 345 GHz is reported by Wang et al. (2012).

B.5. GRBH 080805

Krühler et al. (2011) reported photometric observations of the host with the NTT/EFOSC (VRi bands) and the VLT/HAWK-I (JK bands). The HST observations (WFC3/F160W) are reported by Blanchard et al. (2016) and IRAC1 magnitude by Perley et al. (2016). We discarded the i measurement whose error is twice larger than in the V, R bands.

B.6. GRBH 100814A

The photometry for the host galaxy is taken from Nardini et al. (2014): we consider the last available griz GROND observations where the host dominates the afterglow, 63 days after the burst for iz and 145 days after the burst for gr. De Pasquale et al. (2015) reported a J detection with the Calar Alto 3.5 m telescope three years after the burst. We do not consider UVOT data as they are available for only six days after the burst and likely to be contaminated by the GRB afterglow. The Spitzer/IRAC observations were carried out and reported by Perley et al. (2016) and the target was detected in the IRAC1 channel.

B.7. GRBH 120119A

Some of the Morgan et al. (2014) observations were conducted at a late epoch after the burst. The host galaxy was clearly detected and its emission measured with the Keck/LRIS in the B, R, and RG850 bands 0.85 year after the burst, and with the HST/WFC3 in the F125W and F160W bands 0.77 year after the burst. The Spitzer/IRAC observations were carried out and reported by Perley et al. (2016) and the target was detected in the IRAC1 channel.

Appendix C

Best fits with radiative transfer simulations

In this appendix, we compare the attenuation curves computed with radiative transfer simulations of Seon & Draine (2016) best fitting attenuation curves derived with CIGALE in Sect. 4.1 using the method explained in Sect. 5.5. Attenuation curves are compared only at wavelengths used in the radiative transfer simulations and covered by the broad-band filter observations. Only the best fit is reported in Fig. C.1 with the corresponding values of τ_V, R_s/R_d and M_s. In this Figure we also report the rest-frame spectral coverage of each host galaxy observation⁵.

Fig. C.1. Best fits of the attenuation curve derived with CIGALE with the ones from radiative transfer simulations of Seon & Draine (2016). The blue errors bars correspond to the attenuation curve and associated uncertainty derived with CIGALE estimated at wavelengths used in the radiative transfer simulations and covered by observations. The red line corresponds to the attenuation curve from radiative transfer simulations which best fits the CIGALE attenuation curve. The black lines represent the spectral coverage of the host galaxy observations.

All Tables

All Figures

	Fig. 1. Top: mean local extinction curves using data of Table 1 in Pei (1992), normalised to AV. Bottom: difference between the mean local extinction curves, normalised to AV. They start to differ significantly in the FUV. The blue shaded area represents the minimum rest-frame spectral coverage we require, that is, 1600 Å−5500 Å.
In the text

Fig. 2. Time, since the GRB trigger, at which the SED were evaluated as a function of the extinction along the GRB l.o.s., . The blue, green and red colours represent which local extinction curve (SMC, LMC, MW) scaled the best to the data. The black colour means that the extinction curve was fitted with the FM07 and has a spectroscopically confirmed UV bump. The circles represent the afterglows with spectroscopic measurement and the squares the ones with photometric measurement only. The filled symbols represent SEDs best fitted with a single power law, the empty ones represent SEDs best fitted by a broken power law. Only the names of the GRB in our Golden sample are indicated.

In the text

	Fig. 3. Extinction along the GRB l.o.s. as a function of the host galaxy stellar mass, the latter taken from Perley et al. (2016). Same colours and symbols as in Fig. 2.
In the text

Fig. 4. Best-fitted SED for GRBH 061121. Red points are the observed fluxes with their uncertainties. The black line represents the best fitted spectrum composed of attenuated stellar emission, dust emission, non-thermal radio emission and nebular lines. The dashed blue line represents the unattenuated stellar emission and the blue shaded area indicates the amount dust attenuation. The lower panel shows the relative residual. The upper right panel is an enlargement of the UV/optical/NIR domain.

In the text

	Fig. 5. Best-fitted SED for GRBH 070802. Colour and symbols convention as in Fig. 4.
In the text

	Fig. 6. Best-fitted SED for GRBH 080605. Colour and symbols convention as in Fig. 4.
In the text

	Fig. 7. Best-fitted SED for GRBH 080607. Colour and symbols convention as in Fig. 4.
In the text

	Fig. 8. Best-fitted SED for GRBH 080805. Colour and symbols convention as in Fig. 4.
In the text

	Fig. 9. Best-fitted SED for GRBH 100814A. Colour and symbols convention as in Fig. 4.
In the text

	Fig. 10. Best-fitted SED for GRBH 120119A. Colour and symbols convention as in Fig. 4.
In the text

Fig. 11. Left: stellar masses estimated from: IRAC1 measurement in Perley et al. (2016, red), this work with either a delayed or delayed  +  burst SFH (green), CIGALE using same configuration as in Table 2 but with a continuous SFH with a main stellar population age between 1 and 3.5 Gyr (blue). Right: SFR estimated from: Hα measurement from Krühler et al. (2015) and Vergani et al. (2017, red) this work using either a delayed or delayed  +  burst SFH (green), CIGALE using same configuration as in Table 2 but with a continuous SFH with a main stellar population age between 1 and 3.5 Gyr (blue).

In the text

Fig. 12. SFR-stellar mass relation. Blue points represent stellar masses from Perley et al. (2016) and SFR from Krühler et al. (2015) where we highlighted the GRBHs in our sample using a star symbol and the corresponding name. The colour map encodes the redshift. The black circles with blue interiors correspond to the GRBHs of our sample with SFR and stellar masses derived from the SED fitting. The grey lines represent the main sequence relation from Schreiber et al. (2015), the dashed line is four times the main sequence at z  =  1.5 representative of starbursting galaxies (most of our our GRBHs are at z  ∼  1.5).

In the text

	Fig. 13. Probability density functions of the attenuation slope for the GRBHs.
In the text

Fig. 14. Top: attenuation curve slope as a function of the SED continuum amount of attenuation. Middle top: attenuation curve slope versus the stellar mass. Middle bottom: attenuation curve slope versus the SFR. Bottom: attenuation curve slope versus the specific SFR. The blue points correspond to the quantities derived with CIGALE. The black dashed line represents the slope of the mean SMC extinction curve and the yellow dashed line the slope of the Calzetti law. The grey dash-dotted line illustrates the best fit using an orthogonal distance regression (using SciPy’s scipy.odr). The χ2, number of degrees of freedom and Null Hypothesis Probability (NHP) of these fits are indicated.

In the text

Fig. 15. Top: amount of global attenuation in the GRBH in the V band as a function of the amount of extinction in the V band along the GRB l.o.s. Middle: colour excess for the stellar continuum as a function of the colour excess for the Balmer lines. The grey line represents the C00 relation. Bottom: amount of attenuation of the Balmer lines in the V band as a function as the amount of extinction in the V band along the GRB l.o.s. For all panels the grey dash-dotted line represents the best fit using an orthogonal distance regression (using SciPy’s scipy.odr) and the grey shaded area its 1σ uncertainty. The χ2, number of degrees of freedom and Null Hypothesis Probability (NHP) of these fist are indicated.

In the text

	Fig. 16. Top: GRBH 061121, GRBH 070802 and GRBH 080805, bottom: GRBH 080605, GRBH 080607 and GRBH 120119. The solid black line is the extinction curve normalised to , the blue one is the attenuation curve normalised to and the green one is the normalised Calzetti law. The blue shaded area represents the 1σ uncertainty on the attenuation curve.
In the text

	Fig. 17. Probability density functions of τV, Rs/Rd and Ms for each GRBH with the chosen dust model.
In the text

Fig. C.1. Best fits of the attenuation curve derived with CIGALE with the ones from radiative transfer simulations of Seon & Draine (2016). The blue errors bars correspond to the attenuation curve and associated uncertainty derived with CIGALE estimated at wavelengths used in the radiative transfer simulations and covered by observations. The red line corresponds to the attenuation curve from radiative transfer simulations which best fits the CIGALE attenuation curve. The black lines represent the spectral coverage of the host galaxy observations.

In the text