AN EXPLANATION FOR THE DIFFERENT X-RAY TO OPTICAL COLUMN DENSITIES IN THE ENVIRONMENTS OF GAMMA RAY BURSTS: A PROGENITOR EMBEDDED IN A DENSE MEDIUM

The GRB emission is characterized by a light curve that tracks the time evolution of the luminosity and an SED that may also vary with time. The X-ray light curve can be described in general by two different phases (e.g., Willingale et al. 2007). Each phase is frequently modeled and observed to follow a broken power law L∝t^α. The first phase (hereafter referred to as the prompt phase) is strongly related to the prompt γ-ray emission, and consists of a nearly constant emission followed by a steep decay (Tagliaferri et al. 2005; Goad et al. 2006). In the second phase (hereafter the afterglow phase) the light curve flattens and then follows a "normal decay" (the break in this phase is generally interpreted as the shock break-out, i.e., the time when the size of the relativistic beam matches the physical extent of the jet).

In the following, we model the prompt phase considering a constant emission up to t_p = 85 s after the burst followed by a steep decay described by α₁ = −2.0. We consider the transition between the prompt and afterglow phases to occur at t_b = 100 s. From this time on, we model the afterglow light curve by a power law with α₂ = −1.0. We do not model the break in the second phase from flat to "normal" decay. This break usually involves a small change in slope and takes place at later times, when the bulk of the photons has already been emitted. Thus it has little effect on our results. Our choice of α₂ and t_b is based on the average values found by Margutti et al. (2013). The rest of the parameters were constrained to match the average luminosities found for GRBs by these same authors (see below).

Although the GRB emission is believed to be dominated by synchrotron emission, its SED is both predicted and observed to be relatively complex (Sari et al. 1998). One often models it as a series of power laws L_ν∝ν^−β across the electromagnetic spectrum. Our photoionization modeling, however, is only sensitive to the SED at rest-frame energies from 1 Ryd to 100 keV, i.e., the UV to X-ray passbands. Therefore we model the SED as a single power law. We note however, that there can be strong spectral evolution between the prompt and afterglow phases of the light curve and that the early SED has not been studied systematically. However, studies of individual cases show a much harder slope than that in the afterglow (e.g., Butler et al. 2006; Stratta et al. 2009). In the following we assume β = 0.0 in the prompt phase (before t_b = 100 s) and β = 1.0 for the afterglow.

Lastly, we have set the afterglow luminosity. We consider a total X-ray energy E_{X, iso} = 4.1 × 10⁵¹ erg integrated between 0.3–10.0 keV and from t = 0 s to t = 10⁴ s. The amount of X-ray energy released in the prompt phase is E_{X, pt} = 1.4 × 10⁵¹ erg and that in the afterglow is E_{X, ag} = 2.7  ×  10⁵¹ erg. These values are representative of the Swift GRB sample by Margutti et al. (2013). With these considerations, the total amount of ionizing photons emitted by this fiducial GRB is ϕ_o = 2.1 × 10⁶¹ photons up to t = 10⁴ s.

We compare the circumburst models ionized by the above afterglow to a characteristic set of measurements for gas column densities from analysis of X-ray and optical/UV afterglow spectroscopy. Given that the equivalent H column density obtained from the X-rays and the column density of neutral material obtained from the optical spectrum were derived assuming solar abundances (the neutral column density assumes solar abundances as it was measured from metals, not H i), we compare the results of our models not to H, but rather to O. Analysis of those GRBs exhibiting significant X-ray opacity typically yields estimates for the effective hydrogen column densities of N_H ≈ 10²² cm⁻² (Watson et al. 2007; Schady et al. 2011; Campana et al. 2012). These values were derived by assuming solar abundances⁴ and a fully neutral medium. The implied column densities of oxygen therefore scale as 7 × 10⁻⁴, giving $N_{\rm O}^{\rm X}\approx 10^{19} \,{\rm cm^{-2}}$. We adopt this as our fiducial value for a typical GRB showing X-ray absorption.

Regarding the optical/UV spectroscopy, the commonly observed O i transitions are always saturated and one can only estimate $N_{\rm O}^{\rm UV}$ by scaling measurements of non-refractory elements (e.g., S, Si, Zn) assuming solar relative abundances. Values from the literature range from $N_{\rm O}^{\rm UV}= 10^{16\hbox{--}18.5} \,{\rm cm^{-2}}$. As emphasized in the Introduction, a significant fraction of GRBs with X-ray absorption show $N_{\rm O}^{\rm X}\approx 10 N_{\rm O}^{\rm UV}$ (Schady et al. 2011). In the following, we adopt $N_{\rm O}^{\rm UV}= 10^{18} \,{\rm cm^{-2}}$ as our fiducial value.

Given that we will explore the conditions required to measure (much) larger columns in the X-rays than in the optical, and these conditions are likely due to ionization, we will evaluate our models considering that the observed X-ray column density is produced mainly by the ionized gas, while the optical column is produced by the neutral one. As will be clear from the models, this is indeed the case, and any contribution from the neutral material to the X-ray absorption is negligible if larger columns in this spectral region are required. Although we run models with many different conditions, we report here only the most relevant to explain the observations.

We begin by examining the time-dependent results from a series of idealized models with constant gas density extending to a circumburst radius r_CBM = 150 pc. Calculations at larger locations are not required given that the ionization front for all models takes place inside this distance. Within this model framework, we explore a range of gas density (n = 10 and n = 10³ cm⁻³) and metallicity (Z = Z_☉ and Z = 0.01 Z_☉). Figure 2 shows the radius, as a function of time, to two transition regions driven by the afterglow for a series of models. These two transition regions are: (1) r_H i, the radius at which the gas has a 50% hydrogen neutral fraction; and (2) r_O ix, the radius at which the gas has 90% of its oxygen completely stripped of electrons. These define the neutral region ($r > r_{{\rm H\,\scriptsize{I}}}$) within the ambient medium which dominates the UV opacity, and the start of the ionized region ($r=r_{{\rm O\,\scriptsize{IX}}}$) where the X-ray bound–free and bound–bound opacity begins. Both radii have a power-law dependence during the prompt phase emission (t < t_b = 100 s). At t_b the afterglow emission begins and the radiation impinging on the gas becomes much softer (β = 1.0). This produces a rapid rise in r_H i right after t_b, due to the larger number of UV photons. At later times (t > 500 s) both r_O ix and r_H i follow a power law again, but with a different slope.

Zoom In Zoom Out Reset image size

It is evident from the plot that there is relatively weak dependence of the radii with metallicity as these are set by either the density of the gas or the r⁻² dilution of the flux. One also notes that the evolution of r_O ix is weakly dependent on the density. This is because the gas is never optically thick to photons that ionize O⁺⁸ and r_O ix is mainly set by r⁻² geometrical dilution of the afterglow. Each r_O ix curve reaches ≈3 pc at t = 10⁴ s, indicating the gas in the inner few parsecs cannot contribute to the observed X-ray opacity. In contrast, r_H i has a different evolution for the models considered. For models with higher density, the ionization front lies closer to the source owing to the greater opacity of the medium. Due to this larger opacity, in these models r_O ix can even be larger than r_H i for the few tens of seconds after the burst. This unusual ionization structure, where O ix can exist in the neutral H region, is due to the very hard SED of the prompt emission phase.

In Figure 3, we present the cumulative column densities of ionized (solid) and neutral (dotted) oxygen at t = 1000 s for a series of models. It is important to note that the ionized columns include only the contribution from charge states with at least one bound electron, e.g., O ix is not included. Under the assumption that the ionized gas must dominate the X-ray opacity, we require values of $N_{\rm O}^{\rm X}\approx 10^{19} \,{\rm cm^{-2}}$. It is evident from Figure 3 that this requires a very high density (n_H > 10² cm⁻³), even when one adopts a solar metallicity. If the large column densities observed in the X-ray spectra of GRB afterglows are indeed due to ionized material by the burst, then the densities and/or metallicities of the circumburst gas must be very large. Alternatively, one could reproduce the observed $N_{\rm O}^{\rm X}$ values with neutral gas with much lower density extending to circumburst distances r_CBM ≫ 100 pc. This would imply $N_{\rm O}^{\rm UV}\approx N_{\rm O}^{\rm X}$, which is inconsistent with the observations.

Zoom In Zoom Out Reset image size

An additional interesting point is obvious when comparing the model with Z = 0.01 Z_☉ and n = 10³ cm⁻³ with that having Z = Z_☉ and n = 10 cm⁻³. Although the ionization front takes place at different distances (Figure 2), the column densities inferred for ionized O have similar values within a factor of a few. This is expected, as the total column density of O depends almost linearly on both metallicity and density. However, without an a priori knowledge of where the ionization front takes place (as is the case with spectroscopic observations of GRBs), there is a degeneracy between the metallicity and the density of the material. Because of this, we will discuss models for solar metallicity in the rest of the paper, and will present those with different metallicities when appropriate.

A uniform prediction of these constant density models is that the column density of neutral material matches or even exceeds the ionized phase within the first 100 pc from the burst. This follows from the fact that $r_{{\rm H\,\scriptsize{I}}}\lesssim 20$ pc (Figure 2) such that the medium is dominated by neutral gas along any given sightline.

Integrating to r = 100 pc, all the models predict larger columns of neutral than ionized O (by at least a factor of a few). As such, one predicts column densities probed by X-rays that exceed the optical/UV by only as much as 50% ($N_{\rm O}^{\rm X}< 1.5 N_{\rm O}^{\rm UV}$). We note that it is likely that the ISM of the host galaxy extends further beyond the first 100 pc from the burst, making the X-ray and optical/UV columns even more similar. This violates the constraints of our fiducial afterglow model where $N_{\rm O}^{\rm X}\sim 10N_{\rm O}^{\rm UV}$. Thus, unless the circumburst medium has size r_CBM ≪ 100 pc, this model contradicts what is frequently observed. In this case, the bulk of the opacity (in both wavelength ranges) would be dominated by neutral material. We conclude that if the large columns found in the X-rays are indeed due to material ionized by the GRB afterglow, then the density and metallicity should be large, and the distribution of material cannot be homogeneous.

Given that the progenitors of long GRBs might be massive stars with stellar winds (Woosley 1993), possibly embedded in intense star-forming regions, we must consider the possibility that the material within a few tens of parsecs from the progenitor was ionized prior to the onset of the burst. Indeed, simple treatments of likely progenitors for GRBs predict such "pre-ionization" (Perna & Lazzati 2002; Whalen et al. 2008). Then, it is important to test how these conditions may affect the results presented above. We have produced a series of models varying r_preion, the radius to which the gas has been pre-ionized prior to the GRB event. We assume an initial ionization distribution consistent with gas ionized by radiation following the SED of a massive star (M ∼ 30 M_☉) giving a H neutral fraction of $f({\rm H\,\scriptsize{I}})\sim 10^{-5}$. For r_CBM ≈ 100 pc, values of r_preion < 50 pc yield very similar results to those models without pre-ionization, as can be seen in Figure 3 (magenta line). This is because, although the ionization front and the ionized columns of material are larger due to the effects of the pre-ionization, at distances r ∼ 2r_preion from the burst the neutral column becomes comparable to that of ionized material. We note that r_preion might actually be much larger, satisfying the condition r_preion ≈ r_CBM = 100 pc. In this case, the contribution to the total column density from the neutral material up to r_CBM would be negligible (given that this gas was already ionized by the progenitor). However, as before, at a distance ∼2r_preion the neutral material from the ISM of the host galaxy would contribute as much as the ionized material to the total column density, so that again $N_{\rm O}^{\rm X}\sim N_{\rm O}^{\rm UV}$. Then, in order to have $N_{\rm O}^{\rm X}\sim 10N_{\rm O}^{\rm UV}$, the total optical path length from the burst location to the ending radius of the galaxy would have to be ∼r_CBM. While this might be indeed the case for a few GRBs, we consider this possibility unlikely, because it requires that most GRBs are located near the edge of their host galaxies contrary to observations (Bloom et al. 2002; Fruchter et al. 2006).

Homogeneous models predict similar column densities in the X-ray and the optical/UV domains, with the bulk of the opacity due to neutral material at distances larger than a few tens of parsecs from the GRB. Furthermore, high column densities of ionized material require a circumburst medium with large density (or metallicity). Motivated by these results, we have explored simple models with gradients of density as a possible explanation for the larger X-ray column densities. The models presented here assume larger densities close to the burst, decreasing outward. We explore models with a step in the density: n = n₁ at r ⩽ r_step and n = n₂ at r > r_step, with n₁ > n₂. In all models we assume n₂ = 1 cm⁻³. Although this model is overly simplistic, models with radial gradients in density give similar results.

Figure 4 presents our results. The most important difference with the homogeneous cases is that, in general, in the step function model the neutral column density can be, by design, much lower than that for the constant density models. This is clearly observed when comparing the models with n₁ = 10³ cm⁻³ (blue and cyan lines in Figure 4 and blue line in Figure 3).

Zoom In Zoom Out Reset image size

Indeed, some step function models do predict $N_{\rm O}^{\rm X}\sim 10N_{\rm O}^{\rm UV}$. For instance, a model with n₁ = 10³ cm⁻³ and r_step = 5 pc produces X-ray and UV column densities similar to the fiducial afterglow values (blue line in Figure 4). However, if the same model is considered, but with r_step = 10 pc (cyan line), then $N_{\rm O}^{\rm X}\sim N_{\rm O}^{\rm UV}$ and this condition is no longer satisfied. This is because in the second model $r_{\rm step}> r_{{\rm H\,\scriptsize{I}}}$, and the dense region can contribute significantly to the neutral absorption. In general, these models are only capable of producing larger columns in the X-rays than in the UV if $r_{\rm step}\sim r_{{\rm H\,\scriptsize{I}}}$. Since there is no physical reason to assume a relation between the size of the ionization radius (which depends on the GRB properties) and the size of the dense region, we conclude that these models cannot naturally explain the ensemble of observations. This motivates a further addition to the model.

Finally, we explore models with gradients of density, considering that the medium surrounding the GRB was already ionized before the burst explosion. As discussed before, there are strong arguments to assume a pre-ionized medium (Perna & Lazzati 2002; Whalen et al. 2008). We explore the same density distribution as in Section 4.2 (n = n₁ at r ⩽ r_step and n = n₂ at r > r_step, with n₁ > n₂ and n₂ = 1 cm⁻³). To avoid cases where $r_{\rm step}> r_{{\rm H\,\scriptsize{I}}}$, which produce $N_{\rm O}^{\rm X}\sim N_{\rm O}^{\rm UV}$ (Section 4.2), we consider only models where the region of pre-ionized gas contains the dense cloud of material (that is r_preion > r_step). As before, we assume a H neutral fraction $f({\rm H\,\scriptsize{I}})\sim 10^{-5}$. Figure 5 presents our results. There are two notable benefits in these models.

• 1.  
  Given the pre-ionization condition, the column density of the ionized material is dominated by gas at r < r_step. Therefore, the value of $N_{\rm O}^{\rm X}$ measured is determined by the density and size of the denser region.
• 2.  
  The neutral column density is produced, by design, outside the denser region. Therefore, $N_{\rm O}^{\rm UV}$ is systematically lower than the column of ionized gas, i.e., $N_{\rm O}^{\rm X}\gg N_{\rm O}^{\rm UV}$.

Zoom In Zoom Out Reset image size

We find that a model with n₁ = 10³ cm⁻³ and r_step = 10 pc presents X-ray and UV column densities similar to the fiducial afterglow values. The cyan line in Figure 5 presents this model. This is not a unique solution, of course; many solutions are possible, with lower n₁ requiring larger r_step. However, the solutions must satisfy two important conditions: (1) $r_{\rm step}\lesssim r_{\rm preion}< r_{{\rm H\,\scriptsize{I}}}$, so that there is no contribution from the dense region to the neutral column density, and (2) we require $r_{\rm step}> r_{{\rm O\,\scriptsize{IX}}}$ so that the GRB does not entirely ionize the dense medium that provides the X-ray opacity.

Within these restrictions, the values that can reproduce our observations are constrained to be in the ranges 30 pc >r_step > 5 pc and 10⁴ cm⁻³ > n₁ > 5 × 10² cm⁻³. Different solutions produce X-ray and optical/UV column densities much different than the ratio of 10 from our fiducial value. For instance, a model with r_step = 20 pc and n₁ = 10³ cm⁻³ (blue line in Figure 5) would easily produce two orders of magnitude larger column in the X-rays than in the optical/UV, as found in several objects (Campana et al. 2010). These restrictions also impose a minimum pre-ionization radius around the GRB progenitor (condition (1) above); regions with r_preion ∼ 20–30 pc are enough to explain the observations (see Figure 5). We consider these values to be very conservative, since detailed modeling shows that the progenitor can pre-ionize the surrounding material at distances ≳ 100 pc (Whalen et al. 2008). We note that our results do not place much restriction on the value of n₂ (the only condition being to keep the neutral column density small). Assuming again that the neutral gas in the ISM extends for at least ∼100 pc beyond the circumburst region implies that n₂ ≲ 10 cm⁻³.

Given that step function models are very simplistic, we have also computed models assuming a constant density up to a distance r_step from the burst, and a density law parameterized by a power law (n = n_o(r/r_step)^−α) at larger distances. We find qualitatively similar results to the step models provided α ≳ 2. These models also yield $N_{\rm O}^{\rm X}> N_{\rm O}^{\rm UV}$ for r_step < 30 pc.

We conclude that the different column densities found in the X-ray and optical/UV regimes of GRB afterglow spectra can be well explained by the presence of ionized material within a few tens of parsecs of the burst location. This requires that the GRBs are produced in dense clouds of material within the host galaxy, with column densities characteristic of molecular clouds, and that this material is ionized prior to the explosion (Whalen et al. 2008). Our results even permit ionized versus neutral column density ratios up to 2–3 orders of magnitude or more, as reported by Campana et al. (2010). We note that some evidence of evolution with cosmic time in the X-ray absorbing column has been reported in previous works (Campana et al. 2010; Behar et al. 2011). We plan to test different scenarios to explain this evolution in a forthcoming paper.⁵

An independent constraint on the metallicity of the medium surrounding the GRB may come from stellar evolutionary theory. In this theory, late-type massive stars, such as Wolf–Rayet stars, are considered the most likely progenitor candidates for GRBs (Woosley & Heger 2006). Furthermore, low metallicities (Z ≲ 0.1–0.3 Z_☉) are preferred by the models to avoid the spindown of the stellar core (Izzard et al. 2004; Yoon & Langer 2005; Woosley & Heger 2006). We note however, that it is possible that the circumburst medium of the GRB has been contaminated with metals by the progenitor (at least to some extent). Thus, an extremely low metallicity is not strictly required to reconcile stellar evolutionary results with those presented here. However, somewhat low metallicities may still be expected in the circumburst region, and thus they are definitely desirable in the models. We note that it is possible to get large columns of ionized material with arbitrarily low metallicities, provided that the density of the clouds where the progenitors are embedded is large enough.

Nevertheless, large densities may imply unphysically large masses for the progenitor's cloud. For the more massive model presented in Figure 5 (blue line), the implied mass for r_step = 20 pc is ≈10⁶ M_☉. This mass is characteristic of molecular clouds within the Galaxy (Murray 2011). Even a circumburst medium with Z = 0.1 Z_☉ may match our fiducial value for $N_{\rm O}^{\rm X}$ (red line in Figure 3). Only if Z ≪ 0.1 Z_☉ (e.g., GRB 050730; Chen et al. 2005) would one require significantly larger density (n₁ > 10⁴ cm⁻³; magenta line) and a correspondingly larger mass of the circumburst medium. To the best of the authors' knowledge, no GRB has been detected with such a low metallicity medium that also shows significant X-ray opacity.

We conclude that the cloud's radius, density, and mass required to explain the differences between the X-ray and optical/UV column densities may be large (particularly if low metallicities are also required), but are fully comparable with those found in giant molecular clouds. Thus, our results support a scenario where GRBs explode in giant molecular clouds within their host galaxies (Campana et al. 2006; Prochaska et al. 2008; Campana et al. 2010). A statistical study with observations of a large number of GRBs, spanning a wide range of luminosities, as well as X-ray and optical column densities, is required to further explore the properties of these clouds.

Two key ingredients in testing any model of the circumburst medium around GRBs is to study (1) the column densities of individual charge states, and (2) the possible variability (or lack of it) in the overall absorption properties of the material. In the following, we only discuss step function models including a pre-ionized medium, as these are the only ones consistent with the different X-ray and optical/UV column densities. We note that models with gradients of density are more likely to produce variability than models with constant density, because a charge state that was produced within the dense medium surrounding the GRB at short times after the burst might be produced outside this region at later times. This would result in strong changes in column density for that particular ion.

To exemplify this, in Figures 6–8 we present the time evolution of the fraction of Si iv, C iv, and N v for two different models with n₁ = 10³ cm⁻³ and Z = 0.1 Z_☉. In the left upper panel of the plots (where a model with r_step = 15 pc is presented) one observes that 100 s after the burst, the vast majority of these ions are produced in the dense medium. However, when the observed time is ∼1000 s, they are fully produced at >15 pc in the low density regions. Between these two times, the column density of these charge states decreases rapidly, as the peak in their fractional distributions moves out from the dense region into the diffuse medium (see solid lines in the bottom panel of Figures 6–8).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

An important additional constraint on the structure of the dense clouds of gas is set by the measured column densities of N v, which traces more highly ionized gas. The UV transitions from this ion have thus far been observed to be unsaturated, with column densities N(N⁺⁴) ∼ 10¹⁴ cm⁻³ (e.g., Prochaska et al. 2008; Fox et al. 2008). This implies that N v must be produced outside of the dense regions during these observations. In the case of our fiducial model, this means that the maximum allowed dense region size is r_step = 15–20 pc, because for larger sizes N v would be produced inside r_step even thousands of seconds after the burst, and the predicted column densities would be ∼100–1000 times larger (see Figure 8). However, we note that the GRBs where N v and other high ionization UV charge states can be observed are distant (z ≳ 2) and >10 times brighter than our fiducial GRB luminosity (which is based on the average luminosity distribution by Margutti et al. 2013 and includes objects at all redshifts). Indeed, a model with five times more ionizing photons than our fiducial GRB produces N v at distances larger than 40 pc only 1000 s after the burst (see the upper right panel and dotted line in the bottom panel of Figure 8). This makes possible much larger sizes for the dense region. In these bright GRBs, absorption from different charge states can be produced at large distances from the burst (hundreds of parsecs or more depending on the GRB luminosity), consistent with the observations (e.g., Fox et al. 2008). This is because of the much smaller opacity in a pre-ionized medium, with respect to a neutral one. Thus, pre-ionization is not only required to explain the large X-ray to optical/UV column density ratios, but also to explain absorption by photoionized elements at large distances from the GRB.

We remark that our models predict no variability in the total column densities of optical/UV observed charge states at times >500 s, when the earliest spectroscopic observations in these wavebands are possible (e.g., Fox et al. 2008; D'Elia et al. 2009a). Our models, however, are not in contradiction with possible variations in individual charge states, as these can be produced by additional inhomogeneities in the diffuse medium, beyond r_step. These models are also consistent with the observations of variability in excited lines (e.g., Vreeswijk et al. 2007; D'Elia et al. 2009a), as these lines arise from material at large distances from the GRB region in the ISM of the host galaxy. The spectral variations are produced by UV pumping from the GRB afterglow radiation into the excited levels of a single ion (e.g., Prochaska et al. 2006; D'Elia et al. 2009a) and not by variations in the total column density of that particular ion.

Finally, it is interesting to study how the total column density would vary with time. In Figure 9 we present the time evolution of the X-ray column density for the same models presented in Figure 5. The plot shows the expected variability for ionized O (excluding again O ix that does not contribute to the opacity). Only mild variations in the column density of ionized O should result in small variations in the measured column density in multi-time X-ray spectra of the afterglows. As can be observed, the different step models predict variations by a factor ≲ 2, according to their r_step. Variations by these factors cannot be measured in actual X-ray data (given the limited signal-to-noise ratio in the data and the uncertainties in the modeling). Nevertheless, a trend is expected with smaller columns found at larger times. Larger column density variations may be expected for GRBs embedded in smaller radii clouds (with $r_{\rm step}\sim r_{{\rm O\,\scriptsize{IX}}}=5$ pc), as most of the gas cloud would be fully ionized at later times. However, this would also imply much smaller X-ray to optical/UV column ratios at later times.

Zoom In Zoom Out Reset image size