The edge of a gamma-ray burst afterglow

P. Meszaros1 and M. J. Rees2

1Department of Astronomy & Astrophysics, Pennsylvania State University, University Park, PA 16803, USA2Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA

Accepted 1998 July 17. Received 1998 July 17; in original form 1998 June 9

A B S T R A C TWe discuss the formation of spectral features in the decelerating ejecta of gamma-ray bursts,including the possible effect of inhomogeneities. These should lead to blueshifted andbroadened absorption edges and resonant features, especially from H and He. An externalneutral ISM could produce detectable H and He, as well as Fe X-ray absorption edges andlines. Hypernova scenarios may be diagnosed by Fe Ka and H Lya emission lines.

Key words: line: formation – cosmology: miscellaneous – gamma-rays: bursts – X-rays:bursts.

1 I N T RO D U C T I O N

Gamma-ray bursts (GRB) have been localized through spectral linemeasurements of a presumed host galaxy in two cases so far(Metzger et al. 1997; Kulkarni et al. 1998). The GRB environmentand its effect on the detectability and spectral properties of theafterglow are the subject of debate (e.g. Livio et al. 1997; VanParadijs 1998); a dense environment may be more typical of amassive stellar progenitor (Paczynski 1997; Fryer & Woosley 1998)while medium-to-low-density environments could suggest compactmerger progenitors (e.g. Bloom, Sigurdsson & Pols 1998). The lackof an optical afterglow following a detected X-ray afterglow (e.g.GRB 970828) may be a result of a steep temporal fall-off of the flux(Hurley 1997) or may be connected with absorption in a dense gasaround the GRB (Groot et al. 1997). The detection of spectralsignatures which can be associated with the GRB environmentwould be of great interest both for distance measurements and forhelping to answer the above questions, while spectral featuresassociated with the burst ejecta itself would provide informationabout the fireball dynamics and its chemical composition, and cluesabout the triggering mechanism and the progenitor system. In thisLetter we investigate the possibility of detectable spectral featuresarising in the shocked gas and in dense inhomogeneities coexistingwith it, during the decelerating external shock phase of the burstafterglow. We also consider the absorption features arising from gasoutside the region ionized by the energetic photons emitted by theburst, and the reprocessing of X-ray and optical photons by theexternal environment, including possible signatures for a hypernovascenario.

2 A F T E R G L OW C O N T I N U U M R A D I AT I O N

The common model of GRB afterglows considers that their radia-tion arises in the decelerating blast wave of fireball material,produced for example by a compact binary merger or stellarcollapse, impacting on an external medium. The radius at which

deceleration begins is rd ¼ 1016:7ðE52=n0v2j Þ

1=3h¹2=32 cm, at an

observer time td ¼ rd=ð2ch2Þ ¼ 101:9ðE52=n0v2j Þ

1=3h¹8=32 s, where

E0 ¼ 1052E52 ergs¹1 is the initial fireball energy, h ¼ 102h2 is theterminal coasting bulk Lorentz factor, M0 ¼ E=hc2 is the rest massentrained in the initial fireball, and next ¼ 1n0 cm¹3 is the averageexternal density. After the contact discontinuity starts to decelerate,a forward blast wave advances into the external medium and areverse shock moves into the fireball gas. A similar situation arisesalso in the scenario where the mass and energy injection is not adelta function at E0;M0 but rather continues for some time (muchshorter than td), adding more mass and energy as the bulk Lorentzfactor decreases,

Mð> rÞ ~ G¹w; Eð> rÞ ~ G¹wþ1

; ð1Þ

(Rees & Meszaros 1998) in which case the shock is continually re-energized (refreshed shocks) by the new energy and mass arriving atradius r (the reverse and forward shocks being assumed thin relativeto r). The contact discontinuity radial coordinate r and its Lorentzfactor G vary as r ¼ 1017:5þq1 ðE52=n0v

2j Þ

2=hh2ðh¹8Þ=h2 tðh¹6Þ=h

5 cm andG ¼ 100:84þq2 ðE52=n0v

2j Þ

1=hhðh¹8Þ=h2 t¹3=h

5 . Here h ¼ 7 þ A þ w, withh ¼ 8 for the standard adiabatic impulsive model (A ¼ 1;w ¼ 0),and the correction factors q1 ¼ 3:1½ðh ¹ 6Þ=h ¹ 1=4ÿ, q2 ¼

9:3½ð1=h ¹ 1=8ÿ are non-zero with h Þ 8 only for refreshed(w Þ 0) and/or radiative (A ¼ 0) cases. The postshock comovingmagnetic field, whose energy density is a fraction y of the thermalproton energy, is B ¼ 10¹0:5þq2 ðE52=v

2j Þ

1=hnðh¹2Þ=2h0 y1=2

¹2hðh¹8Þ=h2 t¹3=h

5 G,and the observer-frame synchrotron peak frequency is

nm ¼ 1014:32þ4q2 ðE52=v2j Þ

4=hnðh¹8Þ=h0 h4ðh¹8Þ=h

2 y1=2¹2k

23t¹12=h

5 Hz: ð2Þ

The comoving synchrotron cooling time for electrons radiating atthe observed frequency nm is tsy ¼ 105:36¹3q2 ðE52=v

2j Þ

¹3=hnð3¹hÞ=hÞ0

y¹1¹2k

¹13 h¹3ðh¹8Þ=h

2 t9=h5 s, while the comoving expansion time tex ¼

ðr=cGÞ ¼ 105:86þq1¹q2 ðE52=n0v2j Þ

1=hhðh¹8Þ=h2 tðh¹3Þ=h

5 s. The comovinginverse Compton time tic , 0:3y1=2

¹2k1=23 tsy is of the same order as

the synchrotron time, so its effect on the dynamics will beneglected. The synchrotron efficiency is high until t5 , 1 and

Mon. Not. R. Astron. Soc. 299, L10–L14 (1998)

q 1998 RAS

drops afterwards as esy , ðtex=tsyÞ. In the regime where the shortesttime-scale is the expansion time, the comoving intensityI0n0

m, 4n0GðjTcB2k2G2

=8pÞctex, and for a source at luminositydistance D the flux density at observer frequency nm isFnm

. c2t2D¹2G5I0n0

m, or

Fnm¼1030:2þq1þ6q2 D¹2ðE52=v

2j Þ

8=hnð3h¹16Þ=2h0 h8ðh¹8Þ=h

2

× y1=2¹2t3ðh¹8Þ=h

5 erg s¹1 cm¹2 Hz¹1;

ð3Þ

while the source-frame luminosity is Lnm¼ 4pv2

j D2Fnm. The con-

tinuum flux at detector frequency nd for a spectrum of the form ~na

is Fnd, Fnm

ðn=ndÞb ~ td, decreasing as a power law in time after the

peak passes through the detector band nd (where d depends on b aswell as on W ;A and possibly other parameters, e.g. Wijers, Rees &Meszaros 1997; Vietri 1997; Katz & Piran 1997; Sari 1997;Meszaros, Rees & Wijers 1998; Rees & Meszaros 1998).

3 A B S O R P T I O N I N T H E D E C E L E R AT I N GE J E C TA

The baryon density downstream of the forward blast wave and ofthe reverse shock, as long as the expansion remains relativistic, isdominated by the ejecta, rather than by baryons swept up in theexternal shock. Their total number is NpðrÞ ¼ Np0½GðrÞ=G0ÿ

¹w,where Np0 ¼ ðE0=hmpc2Þ is the value for an impulsive fireball andE0 and G0 ¼ h are the initial energy and Lorentz factor. Thecorresponding baryon column density Sp ¼ Np=ð4pv2

j r2Þ is

Sp ¼1016:8þq3¹2q1 Eðh¹w¹4Þ=h52 vðwþ4¹2hÞ=h

j nðwþ4Þ=h0 hð8w¹5hþ32Þ=h

2

× tð3w¹2hþ12Þ=h5 cm¹2

;

ð4Þ

where q3 ¼ 9:3w=h. The refreshed case (w Þ 0) is interestingbecause Sp can be larger than in the impulsive case. The meancomoving baryon density downstream of the reverse shock isnp ¼ Sp=ctex or

np ¼100:44¹3q1þq2þq3 Eðh¹w¹5Þ=h52 vðwþ5¹2hÞ=h

j nðwþ5Þ=h0 hð8w¹6hþ40Þ=h

2

× t3ðw¹hþ5Þ=h5 cm¹3

:

ð5Þ

For t5 & 1 the cooling time tcool < tex, and the comoving electroninverse Compton temperature is

Tic ¼ hnm=hG ¼ 103:1þ3q2 ðE52=v2j Þ

3=hnðh¹6Þ=h0 h3ðh¹8Þ=h

2 y1=2¹2k

23t¹9=h

5 K;

ð6Þ

while the black-body temperature is of order Tbb , 102:5¹q1=4þ2q2 K.At the (adiabatic postshock) density (5) the recombination timetrec , 3 × 1011T1=2

3 Z¹2n¹1p s exceeds the comoving expansion time.

However, if tcool < tex and there is good coupling between protonsand electrons, then Compton cooling behind the shock affects theprotons as well. The shock would then be radiative (A ¼ 0) and thegas adjusts in pressure equilibrium to a density

neq , n0mpc2G=kTic , 1010:6¹2q2 ðE52=v2j Þ

¹2=hnðhþ4Þ=2h0

× h¹2ðh¹8Þ=h2 t6=h

5 cm¹3:

ð7Þ

At this density (7) the recombination time is much shorter than theexpansion time, the ionization parameter in the comoving frameY ¼ Lnm

nm=nbr2G2 & 1, and the hydrogen as well as heavier ele-ments in the shocked ejecta will be in their neutral state (Kallman &McCray 1982).

The outflow may also include denser blobs or filaments ofthermal material, entrained from the surrounding debris torus orcondensed through instabilities in the later stages of the outflow.Previously (Meszaros & Rees 1998) we considered the effect of

such blobs in internal shocks at r , 1013 cm leading to g-rayemission. Here we consider the effects of blobs that catch up withexternal shocks from the initial part of the ejecta around r , 1016 –1017 cm. One cannot predict how much material would be present insuch blobs, but possible instabilities affecting them would beminimized when their Lorentz factor Gb is close to that of thesurrounding flow. For an equipartition magnetic field B in the flowframe G, the pressure equilibrium blob density at the inverseCompton temperature in its comoving frame is

nb , ðB2=8pkTicÞðGb=GÞ ¼ 1012:1ðGb=GÞn1=2

0 k¹23 cm¹3

: ð8Þ

If the smoothed-out blob density seen in the flow frame is taken tobe a fraction a of the mean flow density, nb ¼ anpðG=GbÞ, thesmoothed-out baryon column density in blobs is

Sb ¼ aSpðG=GbÞ2; ð9Þ

cf. equation (4). The filling factor of such blobs, fv ¼ ðnb=nbÞ is verysmall, of order 10¹11:7¹3q1þq2þq3 , while the surface covering factorfs ¼ Sb=ðnbrbÞ can be larger than unity for blob radii smaller thanrb ¼ aSpn¹1

b ðG=GbÞ2, which is of order ,105¹2q2þq3 cm, for nomi-

nal parameters taken at t5 , 1. At these blob densities and tem-peratures the recombination time is very short compared toexpansion times, and also the ionization parameter in the blobcomoving frame Yb ¼ Lnm

nm=nbr2G2b # 1, so hydrogen, and also

heavier elements inside the blobs, will be in their neutral state.For hydrogenic atoms the absorption cross section at threshold is

ja ¼ 7:9 × 10¹18Z¹2 where Z is the effective ionic charge. If thefraction of ions with charge Z is xz, the opacity at the ionization edgeis

tZ , 0:8xzZ¹2S17 ~ tð¹2hþ12þ3wÞ=h

5 ; ð10Þ

where the baryon column density S17 ¼ ðS=1017 cm¹2Þ may beowing either to the neutral diffuse gas, if e–p coupling is effectivebefore the adiabatic stage (equation 4), or to blobs and filaments(equation 9) [absorption from blobs would occur for blob velocitiesGb $ GðtÞ]. Note that for t5 < 1 or for continued input (w Þ 0, h > 8)S could be larger than 1017 cm¹2. For H, the observed frequency ofthe edge would be at 13:6G eV, with G given below equation (1), oraround 0:1ð1 þ zÞ¹1 keVat t5 , 1. For He II, whose ionization edgeis 54.4 eV at rest, the observed edge is around 0:4ð1 þ zÞ¹1 keV inthe observer frame. If the blobs are made up predominantly ofheavy metals, e.g. Fe, the rest-frame edge is near 9.2 keV, or

hnZ , 64ðZ=26Þ2ð1 þ zÞ¹110q2 ðE52=n0v2j Þ

1=hhðh¹8Þ=h2 t¹3=h

5 keV ð11Þ

in the observer frame, for ions of charge Z in a GRB at redshift z.The edges will generally not be sharp, since they will be observedfrom a ring-like region around the edges of the front hemisphere ofthe remnant (Panaitescu & Meszaros 1998), over which the simul-taneously observed radiation samples a bulk Lorentz factor range ofat least DG=G , Dn=n , 0:3. The time dependences of equations(10, 11) refer to the diffuse gas and also to blobs, provided thedensity (or a parameter) of the latter is appreciable over the range ofvalues Gb $ GðtÞ. Resonant lines from Lya lines of H and He havecross-sections comparable to those for ionization, and would beexpected at energies redwards of the absorption edges. They absorbover a narrow energy range and will therefore produce only ashallow and wide trough owing to the above Lorentz factor smear-ing. On the other hand, H and He emission lines from recombinationin the dense cooled ejecta or in blobs should be more prominent,even when broadened by Dn=n , 0:3, since they correspond to amuch larger amount of energy taken out from the continuumbluewards of the absorption edges. Such broad emission features

Edge of a GRB afterglow L11

q 1998 RAS, MNRAS 299, L10–L14

would enhance the detectability of the drop seen just bluewards of itfrom the continuum absorption.

4 A B S O R P T I O N I N A N E X T E R N A L N E U T R A LM E D I U M

The X-ray and UV photons from GRB will ionize the surroundingmedium out to a radius that can be estimated from the total numberof ionizing photons produced. For simplicity, we assume in thissection a canonical adiabatic impulsive afterglow (h ¼ 8;A ¼ 1;w ¼ 0). From (3) the synchrotron peak luminosity isLnm

¼ 4pD2Fnm, 1031E52n1=2

0 y1=2¹2 erg s¹1 Hz¹1, and the time

when nm reaches 13.6 eV is (equation 2) t13:6 , 1:6 ×104ðE52=v

2j Þ

1=3y3=4¹2k

33 s. The total number of ionizing photons pro-

duced is Ni , Lnmt13:6=h , 2:4 × 1061E4=3

52 v¹2=3j n1=2

0 y5=4¹2k

23. Loeb &

Perna (1998) have calculated the time dependence of the equivalentwidths of atomic lines for an afterglow flux time dependence ~t¹3=4,for which the largest (integrated) contribution to the ionizationhappens at late times, and show that for finite cloud sizes of columndensity Sp , 3 × 1020cm¹2 the equivalent widths would vary con-siderably over time-scales of days to weeks. Recent afterglowsindicate that the more commonly observed continuum flux timedependences are steeper than t¹1, so that most of the ionizingphotons are created at early times, within the first few hours. In thiscase, after an initial transient similar to that described by Loeb &Perna (1998), one expects the edges and equivalent widths tostabilize; we consider their behavior after this time, but beforerecombination occurs (e.g. few hours & t & year).

The ISM may generally extend beyond the finite ionized regionconsidered by Loeb & Perna (1998), in which case the ionizationstructure would be photon-bounded, rather than density-bounded,i.e. there is neutral matter beyond the ionization zone. The ioniza-tion radius is

Ri , ðNi=4n0v2j Þ

1=3 . 2 × 1020E4=952 n¹1=6

0 y5=12¹2 k3 cm: ð12Þ

The n¹1=60 weak dependence is model-specific (equation 3), and

could be n¹1=30 in a more generic source. For a typical (neutral)

column density Sn ¼ 1020Sn20 cm¹2 (beyond Ri, but within thegalaxy, e.g. the neutral component of a galactic disc) one gets a K-edge optical depth

tZ , 0:8 × 103xzZ¹2Sn20; ð13Þ

where xz is the fraction of the species with effective nuclear chargeZ. This is large for H and He, while if Sn , 2 × 1021 (for which thelocal visual absorption Av ¼ 5 × 10¹22Sn would reach one magni-tude) the optical depth of Fe at solar abundances (xFe;( ¼ 3 × 10¹4)would be tFe , 0:1, and similarly for other metals. Unlike the blue-shifted ejecta edges of equation (11), the ISM K-edge observedenergy is

hnZ , 13:6Z2ð1 þ zÞ¹1eV , 9:2ðZ=26Þ2ð1 þ zÞ¹1 keV; ð14Þ

bluewards of which the flux is blanketed up ton=nz , 10Z¹2=3ðxzSn20Þ

1=3.Resonant Lya absorption from hydrogen in the neutral ISM will

be conspicuous for high enough column densities. The Doppler-broadened Lya would have a large optical depth at line centre, theequivalent widths being dominated by the damping wings, inthe square-root regime of the curve of growth, ðWn=nÞ ¼

ðrel2luc¹1fluAulSÞ1=2. For analogous hydrogen-like Ka resonant

transitions in other species,

ðWn=nÞ ¼ 8:3 × 10¹13ðxzSnÞ1=2 . 10¹2x1=2

z Sn201=2: ð15Þ

For Sn20 * 1 one gets H equivalent widths of order tens ofangstroms. Similar features in He, and in other elements like C,would be blocked out by H I continuum absorption at the samefrequencies. However, this absorption would not affect Fe, and the6.7-keV X-ray Fe Ka widths at solar abundances are of order tens ofeV. Other possibly detectable features include the Fe edge at 9.1 keVand the O VIII edge at 0.871 keV. Some Si lines at 1.66 keVand 2.28keV may also be detectable. For continuum fluxes ~t¹1:2 or steeper,these should remain constant after the first few hours.

X-ray photons can also be re-emitted by Fe fluorescent inner-shell scattering in the external ISM, and much interest has beenraised by the possibility of X-ray and UV/O emission lines fromthis. The source X-ray continuum can be approximated as a pulse ofradial width cdt , 1013dt3 cm (for X-ray light curves decayingfaster than t¹1). This X-ray pulse occupies the volume between thetwo paraboloids given by the equal-arrival time surfacesrð1 ¹ cos vÞ ¼ ct and the same for cðt þ dtÞ, where t is observertime, r is distance from source centre and v is the polar anglevariable (we ignore here effects from a possible jet opening anglevj). The base of the paraboloid towards the observer is the ionizationradius Ri (equation 12), and the medium outside the outer para-boloid and/or Ri is neutral. The total number of X-ray continuumphotons emitted over 4p is Nx , Lnm

h¹1dt , 1060E3=252 n1=2

0 y2k23

photons. The fraction incident on the paraboloid is roughlyNxv

2 , 1053t3R¹1i20 ph (v p 1, thin paraboloids). The optical depth

of the paraboloid wall is tf , n0xFejfdr , n0xFejfRidt=t ,6 × 10¹4x¹3:5n0Ri20dt3t¹1

3 , where jf , 10¹20cm2. The numberof fluorescent X-rays is Nf , Nxv

2tf , 3 × 1049x¹3:5n0dt3 andthe luminosity Lf , 3 × 1038x¹3:5n0 erg s¹1 gives a fluxFf , 3 × 10¹19E3=2

52 n3=20 x¹3:5y¹2k

23D¹2

28 erg cm¹2 s¹1, constant. Asimilar estimate is obtained using the photons scattered by the‘back’ (near) half of the paraboloid. The light pulse volume betweenthe paraboloids is dV ¼ ðp=3Þc3t3½ð1 þ dt=tÞ3 ¹ 1ÿ½ðRi=ctÞ2 ¹

1ÿ , pR2i cdt, constant for t q dt. An upper limit on the fluorescent

photons that can be produced is Nf;m & dVn0ZxFe , 3 ×1052n0x¹3:5R2

i;20ðZ=26Þdt3 photon, each Fe scattering 26 photonsbefore being fully ionized (recombinations take too long at ISMdensities; this is also why H and He emission lines from the ISMoutside Ri are negligible). With a time-scale 103dt3 s the luminosityis Lf;m , 3 × 1041 erg s¹1, and the flux upper limit isFf;m , 3 × 10¹16E4=9

52 n5=60 x¹3:5y

5=12¹2 k3D¹2

28 erg cm¹2 s¹1. The con-tinuum is Fx , 10¹10E52n1=2

0 y1=2¹2D¹2

28 erg cm¹2 keV¹1 s¹1, and theequivalent width is Wn=n & 10¹6E¹5=9

52 n1=30 x¹3:5y

¹1=122 k3. Fluorescent

emission lines from the ISM would thus be hard to detect, unless thehost galaxy ISM environment is exceptionally dense (leading tohigh optical extinction), or metal rich. If detected, they would offeruseful information on the nature of (and location within) the hostgalaxy.

5 P O S S I B L E H Y P E R N OVA S I G N AT U R E S

In contrast to the previous discussion, where ISM conditions wereassumed, the lines and edges may be more prominent in a hyper-nova scenario, because the circumburst environment could be muchdenser. Whereas NS–NS or NS–BH mergers can lead to a BH +torus system producing magnetic fireballs of 1053 –1054 erg (e.g.Meszaros & Rees 1997; Narayan, Paczynski & Piran 1992), in thehypernova scenario a similar system and energy is derived from thecollapse of a single or binary fast rotating star, or a He–BH merger(Paczynski 1997, 1998; Fryer & Woosley 1998), i.e. it involves aclose stellar companion and/or a massive envelope. The extent ofthe dispersed medium should depend on whether there has been a

L12 P. Meszaros and M. J. Rees

q 1998 RAS, MNRAS 299, L10–L14

radiation-driven (slow) outflow before the burst, such as expected ifthe event were preceded by inward spiralling of a white dwarf or BHthrough the atmosphere of a companion. Consider, as an example, adispersed envelope of 1 M( or Na , 1057 nucleons spread over aradius 3 × 1015r15:5 cm. Its density is n , 1010 M0r¹3

15:5 cm¹3, with aThompson depth tT , few. The fireball propagates in a less densefunnel along the rotational axis, and for n0 , 102nf 2, h2 * 1 thedeceleration radius and X/O afterglow radius are inside the envel-ope. At observer times t , 105t5 s most of the afterglow photons areoptical, and the envelope electron inverse Compton temperature isT , 104 K. The ionization parameter Y , L=nr2 , 106 so Fe ismostly Fe XXVI. The recombination time is trec , 5 ×102T1=2

4 Z¹2n¹110 s, which is , 1 s for Fe. Each Fe ion can reprocess

t=trec , 105t5 continuum X-ray photons into lines, and the totalnumber of Fe recombinations is Nrec;Fe , NaxFeðt=trecÞ ,1059M0x¹3T¹1=2

4 n10. The number of continuum X-ray photonsat t , 105 s is Nx , 1061E52n1=2

f 2 photon. A fraction,10¹2E¹1

52 n¹1=2f 2 M0x¹3n10 of the X-ray continuum can thus be

reprocessed into Fe lines, which is significant. For H, the recombi-nation time is ,5 × 102 s, and the number of H recombinations attime t is Nrec;H , Naðt=trecÞ , 2 × 1060M0T¹1=2

4 n10, while thenumber of optical continuum photons is ,1063E52n1=2

f 2 , so Hrecombinations can also produce a Lya flux significant comparedto the continuum flux. The equivalent widths are Wn=n , 10¹2 forFe Ka and Wn=n , 10¹3 for H Lya. Besides these emission lines,absorption edges may also be seen if the observer line of sight goesthrough the envelope.

A variant of this scenario occurs when the envelope is moremassive and is Thompson optically thick, e.g. there is a funnelcreated by a puffed up companion or a common envelope, with theGRB at the centre. In this case, when the beaming angle G¹1 iswider than the funnel, a substantial fraction of the emitted X-ray andoptical continuum would be reflected from the funnel walls. Byanalogy with AGN reflection models (e.g. Ross & Fabian 1993) onewould expect detectable Fe edges and Ka features (at 9.1 and 6.7keV respectively), as well as a Ly edge and Lya features imprintedin the reflected optical component.

6 D I S C U S S I O N

We have shown that the decelerating external shock of a fireballafterglow may produce a significant absorption edge in the cooledshocked ejecta, as long as cooling is faster than adiabatic losses andprotons are well coupled to electrons. Absorption edges can alsoarise from cool, dense blobs or filaments in pressure equilibriumwith the shocked smooth ejecta. These edges can reach opticaldepths of order unity and will be blueshifted by a mean bulkLorentz factor of typically G , 5–7 around t , 1 day, withlarger optical depths and blueshifts at earlier times. The edgeswill be broadened by the spread Dn=n , DG=G , 0:3 in the ringof observed material. The H, He and Fe edges would be atenergies ,ð0:1; 0:4; 9:2Þ ð1 þ zÞ¹1t¹3=8

5 keV for a standardadiabatic remnant around t , 105t5 s or 1 day (equation 11).Strong blueshifted Fe edges would only be expected in thepresence of metal-rich blobs, whereas H and He edges could arisein the diffuse cooled ejecta. The latter would be a diagnostic for theA ¼ 0 radiative dynamical regime (which, e.g., for a w ¼ 0 no-injection case in a homogeneous external medium evolves asG ~ r¹3).

Information on the dynamics of the explosion may be obtainedfrom the time dependence of the edge characteristics. For instance,it may be possible to distinguish between an impulsive adiabatic

case (A ¼ 1, w ¼ 0, h ¼ 8), an impulsive radiative case (A ¼ 0,w ¼ 0, h ¼ 7) and a refreshed shock case (say A ¼ 1, w ¼ 2,h ¼ 10 as an example) because the edge depth (equation 10)would vary as t¹1=2, t¹2=7 or t¹2=10, while the edge energies (equation11) would vary as t¹3=8

; t¹3=7; t¹3=10, the third set of numbers being

for this particular w.The energetic photons will ionize the surrounding matter out to a

radius Ri , 60E4=952 n¹1=6

0 pc (equation 12), and after a brief initialtransient lasting less than a few hours, reprocessing would benegligible except in the external environment. The neutral gasoutside this ionized region will produce the absorption edges andresonant absorption lines typical of the ISM in the host galaxy.These would be non-blueshifted absorption features, unaffectedby any broadening from bulk Lorentz factor smearing in theafterglow. They should be affected only by a cosmological redshift,and would thus provide valuable distance information. The HLyman continuum optical depths can be very substantial formodest galactic disc column densities, as are the Ly¹a absorptionequivalent widths (equations 13 and 15), which would be in theoptical range for z * 3. Reprocessed emission lines from the ISMwould be hard to detect, unless the event occurs in an exceptionallydense or metal-rich environment. If detected, they would offeruseful information on the nature of, and location within, the hostgalaxy.

A hypernova scenario could be distinguished by the presence of asignificant flux of Fe Ka and H Lya emission lines, reprocessed by amoderately Thompson optically thick companion or envelope. For amore massive, Thompson optically thick envelope, a significantreflected component would be expected, in which Fe absorptionedges and Ka features, as well as hydrogen Lyman edge and Lya

features would be imprinted.

AC K N OW L E D G M E N T S

This research has been supported by NASA NAG5-2857 and theRoyal Society. We are grateful to B. Paczynski, G. Garmire andmembers of the Swift team for stimulating comments.

REFERENCES

Bloom J., Sigurdsson S., Pols O., 1998, MNRAS, submitted (astro-ph/9805222)

Fryer C., Woosley S., 1998, ApJL, submitted (astro-ph/9804167)Groot P. et al., 1997, in Meegan C., Preece R., Koshut T., eds, AIP Conf.

Proc. 428, Gamma-Ray Bursts. Am. Inst. Phys., New York, p. 557Hurley K., 1997, in Meegan C., Preece R., Koshut T., eds, AIP Conf. Proc.

428, Gamma-Ray Bursts. Am. Inst. Phys., New York, p. 387Kallman T., McCray R., 1982, ApJS, 50, 263Katz J., Piran T., 1997, ApJ, 490, 772Kulkarni S. et al., 1998, Nat, 393, 35Livio M. et al., 1997, in Meegan C., Preece R., Koshut T., eds, AIP Conf.

Proc. 428, Gamma-Ray Bursts. Am. Inst. Phys., New York, p. 483Loeb A., Perna R., 1998, ApJL, in press (astro-ph/9712051)Meszaros P., Rees M. J., 1997, ApJ, 482, L29Meszaros P., Rees M. J., 1998, ApJL, 502, L105Meszaros P., Rees M. J., Wijers R. A. M. J., 1998, ApJ, 499, 301 (astro-ph/

9709273)Metzger M. et al., 1997, Nat, 387, 878Narayan R., Paczynski B., Piran T., 1992, ApJ, 395, L83Panactescu A., Meszaros P., 1998, ApJ, 492, 638Paczynski B., 1997, in Meegan C., Preece R., Koshsut T., eds, AIP Conf.

Proc. 428, Gamma-Ray Bursts. Am. Inst. Phys., New York, p. 783

Edge of a GRB afterglow L13

q 1998 RAS, MNRAS 299, L10–L14

Paczynski B., 1998, ApJ, 494, L45Rees M. J., Meszaros P., 1998, ApJL, in press (astro-ph/9712252)Ross R., Fabian A. C., 1993 MNRAS, 261, 74Sari R., 1997, ApJ, 489, L37Van Paradijs J., 1998, review talk at Columbus APS meeting

Vietri M., 1997, ApJ, 488, L105Wijers R. A. M. J., Rees M. J., Meszaros P., 1997, MNRAS, 288, L51

This paper has been typeset from a TEX=LATEX file prepared by the author.

L14 P. Meszaros and M. J. Rees

q 1998 RAS, MNRAS 299, L10–L14