Seminar 1. letnik, II stopnja

RELATIVISTIC SHOCK BREAKOUTS

Angela Kocoska

Advisor: doc. dr. Andreja Gomboc

Ljubljana, April 2011

Abstract

This seminar discusses the physics of shock breakouts formed in stellar explo-sions, with an emphasis on the cases where these shocks are accelerated to mildly orultra relativistic velocities. It introduces the dynamical model behind the relativisticradiation mediated shock breakouts and investigates its efficiency in comparison toobserved light curves of long and low-luminosity gamma-ray bursts. The model’sconsistency with the observed parameters shows that a relativistic shock breakoutis a generic process for the production of gamma-ray flares in a variety of stellarexplosions.

Contents

1 Introduction 2

2 Dynamic model of the breakout 52.1 Planar phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Spherical phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Temperature and time scales . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Breakout emission 93.1 Planar phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Spherical phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Application of the model to observed GRBs 104.1 Relativistic jets and shock breakouts in long GRBs . . . . . . . . . . . . . 114.2 Low-luminosity GRBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5 Conclusion 14

1 Introduction

From supernova explosions of massive stars and white dwarfs, to the relatively recentdetections of x-ray and gamma-ray bursts, stellar explosions have contributed a greatamount to our understanding of the dynamics and evolution of the stars and galaxies. Theyare one of the few events which provide us with observational data from distant galaxies,carrying information regarding many branches of modern astronomy, from information onthe progenitor of the explosion and its history, to maybe even information regarding thewhole galaxy it has originated from. They have been the basis for many theories in theprevious century but still, the diversity of the many detected events of this origin leavesmany questions yet to be answered and provides space for a lot of theoretical work yet tobe carried out.

The general idea that has been theoretically deduced so far, explains these observedtypes of stellar explosions in the following way:

1. Supernovae are explosions of massive stars toward the end of their evolution. Whenthe reactions in the stellar core reach Fe as the final stable product in the ther-monuclear burning sequence, the core begins to collapse, releasing a large amount ofgravitational energy which heats and expels the outer layers, producing the observ-able supernova signal. What we see is a star that undergoes a sudden increase inbrightness, most commonly in the optical, infrared and UV part of the spectrum.

2. White dwarf supernovae are a subsample of supernovae produced when an al-ready evolved white dwarf star accretes matter from a companion, enough to triggerthermonuclear reactions in the core which result in a supernova explosion whichundergo the same cycle of theormonuclear reactions up to Fe, and the supernova

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explosion triggered by the gravitational collapse of the unstable core. The featurethat distinguishes the white dwarf supernovae from the massive star supernovae isthe lack of hydrogen lines in their spectra, which implies that the star has expelledits outer layers before the supernova explosion, that is, during its primary evolution.The light curves of all of the supernovae of this type are also very similar, which im-plies that they are all produced by progenitors of very similar mass and size, typicalfor white dwarf stars.

3. X-ray bursts - X-ray bursts are seen coming from globular clusters, which can befound in the halo of our galaxy, and from sources along the plane of our galaxy. Thisdistribution suggests they come from a population of stars that are common in thedisk, named X-ray binaries. X-ray binaries are pairs of stars where one member is acompact object (such as a black hole or neutron star) and the other star is a normalstar. The two stars orbit each other at a separation where the gravitational pull ofthe compact object distorts the normal star and material streams off of it, and ontothe compact object. Hydrogen accreted from the normal star onto the neutron star iscontinuously fused into helium. A layer of helium is then formed near the surface ofthe neutron star. When there is enough helium present, an unstable reaction occurs:virtually all of the helium is fused to carbon at once, which we see as the explosiveburst [1].

4. Gamma-ray bursts are, unlike the X-ray bursts, distributed isotropically on thesky, and are the most energetic bursts of radiation produced in the universe. Theylast from ten milliseconds to several minutes and the initial gamma-ray burst isusually followed by a longer-lived ”afterglow” emitted at longer wavelengths (X-ray,ultraviolet, optical, infrared, microwave and radio). Their high observed luminosityimplies that they could not be a result of an isotropic spherical explosion, becausethe energy of such an explosion cannot be produced in the observed short duration ofthe burst. Therefore, gamma-ray bursts must be produced by beamed jets emergingfrom the stellar progenitor that coincide with our line of sight.

The distribution of the duration of the bursts implies that there are two differenttypes of gamma-ray bursts: long and short, which suggests different burst progeni-tors. The long gamma-ray bursts are believed to be produced in a core-collapse of amassive star, so they are expected to be related to supernova explosions, a scenariowhich has been observed for a number of events (Figure 1). The short bursts, on theother hand, are believed to be produced during the merging of two compact objectsof stellar origin (neutron stars, black holes).

The most common property of all the explosions of stellar origin is the formation ofa shockwave due to the release of gravitational or rotational energy, which propagatesoutward to produce the observable burst as it breaks out of the surface of the progenitor.Assuming isotropic density distribution of the stellar interior, the shock’s velocity woulddecrease towards the edge of the star, due to the interaction with the surrounding matter.But, in reality, the density in most stars tends to decrease towards the outer shells, whichresults in acceleration of the shockwave as it propagates from shells with higher to shellswith lower density, so the shock breaks out at a velocity higher than the typical velocity

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Figure 1: An artist’s impression of a supernova explosion accompanied by a gamma-ray burst(left)[2] and the light curve of SN1998bw superimposed to the decaying light-curve of GRB041006,which is one of the first observed GRB-SNe related events [3].

of the shock when it is produced. In typical supernova explosions, with total explosionenergy of 1044 J and a progenitor which is not a compact object, the velocity of the shockbreakout is Newtonian, ranging from 5000 � 10000 km/s, while in Wolf-Rayet stars1 thevelocity of the breakout may reach up to 30000� 100000 km/s. The observable propertiesof the breakout depend primarily on the breakout radius and the shock velocity of thebreakout shell. In slow shocks (v   15000 km/s), the radiation in the breakout shell is inthermal equilibrium and produces a spectrum that usually peaks in the UV, while in fastershocks (v � 30000� 100000 km/s) the radiation is away from thermal equilibrium and thetemperature is much higher, producing spectra that peak in X-rays [4]. In cases of moreenergetic explosions or compact progenitors (white dwarfs, neutron stars, black holes) thebreakout can become mildly or ultra relativistic [4].

The shock velocity in many explosions rarely becomes relativistic throughout the wholestar, but only in the presence of steeply declining density gradient, which occurs towardsthe edge of the star. Acceleration of the shock to relativistic velocities would so producea burst which would peak in the high X-ray and gamma-ray frequencies, which has beentheoretically described in detail in the recent model of Nakar and Sari in [4], and is themain topic of discussion of this seminar.

1Wolf - Rayet stars are evolved, massive stars (over 20 solar masses initially), which are losing massrapidly by means of a very strong stellar wind, with speeds up to 2000 km/s. [5]

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2 Dynamic model of the breakout

The process of mass ejection in a supernova explosion begins with the collapse of themassive stellar core, which produces an outward moving blast wave. The blast wavetakes in the matter of the surrounding stellar envelope, so the boundary of the blast waverepresents the shock front, which imprints its velocity on the post shock gas. The shockvelocity is dictated by two opposing processes: deceleration as the shock takes in morematter and acceleration due to the decreasing density as it moves towards the edge of thestar. If the density decline is steep enough, the accelerating prevails. Therefore, in order toobtain an acceleration to relativistic velocities, we must first assume a power-law gradientof the density in the stellar interior of the form:

ρ 9 zn � pR� � rqn (1)

where R� is the radius of the star, r the distance from the stellar center and n is a coefficientwhich varies based on the type of the process that dominates the heat transfer in the stellaratmosphere. For convective atmospheres it is � 3

2, while for radiative atmosphere, which

is the most common case for relativistic breakout progenitors, n � 3.

Figure 2: Meridional density profile of a stellar interior with n � 3. The x and z coordinates arenormalized to the stellar radius and density changes 10 times between successive contours [6].

The emission of the breakout is dominated by the shell where the optical depth2 τ �κρz � 1. We refer to this shell as the ”breakout shell”, which should not be confusedwith the outermost shell, where τ ! 1. In a system where (1) holds, the properties of thebreakout are completely defined by the parameters of the breakout shell [4]:

• γ0 - the Lorentz factor of the shock when it crosses the breakout shell

• m0 - mass of the breakout shell

• d0 - the width of the breakout shell in the lab frame time after the shock

2The optical depth in astrophysics is a quantity which is a measure of the extinction coefficient orabsorptivity up to a specific distance in the interior of the star. It is related to the physical distance fromthe outside of the star by a coefficient which depends on the optical properties of the stellar material. [7]

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and the properties of the progenitor:

• R� - the stellar radius

• n - the power law index of the pre-explosion density profile, n � 3 for the purposesof the model

Another important property, assuming (1), is the self- similarity of the shock before andafter the breakout, which means that the profiles of the shock parameters as functions ofposition maintain a constant shape whose time evolution consists of scaling in amplitudeand position [8]. The expanding envelope is best represented as a series of shells, whoseproperties are given by its mass and the properties of the breakout shell [4]:

• γi � γ0

�mm0

� µnn�1

- the Lorentz factor of the shocked shell

• di � zγ2i

- the width of the shocked shell at shock breakout in the lab frame

• d1i � diγi - the width of the shocked shell at shock breakout in the shell rest frame

• Ei � γ2imc2 - the internal energy of the shocked shell at shock breakout in the lab

frame

• ti � dicγ2i - the lab frame time for shell expansion

where ’i’ indicates initial values and µ relates the shock velocity Lorentz factor and thedensity of the pre-shocked medium as γi 9 ρ�µ. It is analytically derived and evaluated atµ � p?3 � 3

2q � 0.23 [8]. If we insert the values for n and µ and take into consideration

the dependency of the different parameters on the shell mass, we may characterize all ofthe shell properties by its mass, m:

γi 9 m�0.17; di 9 m1�2nµn�1 � m0.6; d1i 9 m

1�nµn�1 � m0.42; Ei 9 m

1�np1�2µqn�1 � m0.65;

ti 9 m1

n�1 � m0.25.

After the breakout all the shells expand and accelerate. The distance from the centerof the star, r, can now be expressed as:

r � R� � vt (2)

where v is the velocity of the shell with mass m, and is roughly constant.The self-similarity of the shock propagation implies that the radius and time dependent

parameters change significantly on a timescale on which the radius changes by an amountof order itself. Thereby, we may divide the emission following the breakout into twodynamically different regimes: planar and spherical.

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2.1 Planar phase

During the planar phase, we may approximate r � R�. This implies a constant τ , which,we have already seen is � 1 for the breakout shell before the breakout and remains soduring the planar phase, too. The acceleration of each shell during this phase follows3 [4][8]:

γ � γi

�t

ti

?3�12

(3)

and if the acceleration ends during the planar phase:

t

ti� γ

?3 (4)

Inserting (4) into (3) we obtain the expression for the final value of the Lorentz factor,when the acceleration has ended:

γf � γ1�?3

i 9 m�0.48 (5)

and from (5) the time the acceleration ends:

tf � tiγ3�?3i 9 m�0.57 (6)

Speaking in terms of the shell mass, we can see that more massive shells end their acceler-ation after the breakout at earlier times and lower Lorentz factors, while less massive shellsend their acceleration at higher γf,0, which strongly affects their observed temperature andhence the spectrum of the breakout.

2.2 Spherical phase

The expanding sphere transits from planar to spherical phase on a timescale of:

ts � R�c

(7)

For t ¡ ts the radius of the expanding sphere is not constant anymore, as the second termin (2) prevails, so r � vt and the emission is now dominated by photons that are leakingfrom the shell that satisfies τ � c{v. This shell is referred to as the luminosity shell, andthe evolution during the spherical phase depends on its initial temperature and whetherit’s relativistic or not. As long as the Lorentz factor of the luminosity shell is " 1 itsdynamics are well described by the self-similar solutions that held true during the planarphase. For shells with 0.5   γiβi   1 a Newtonian approximation yields more accurateresults.

3The formulae in (3) and (4) are final results of a detailed analytical hydrodynamical derivation, whichcan be found in [8]

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2.3 Temperature and time scales

At relativistic velocities the shock radiation is out of thermal equilibrium and dominated byfree-free emission as the main photon source. When the temperature of the shock T Á 50keV during the propagation through the interior of the star, pairs are generated (and theirnumber exceeds the number of electrons), which significantly increases the rate of photongeneration. The strong dependence of the number of pairs on the temperature sets therest frame temperature in the shock when it hits a shell to be nearly constant Ti � 200keV. During the adiabatic expansion of the shocked shell its rest frame temperature fallsas [4]:

T 9 V �β � V �p1�κq (8)

where κ is the effective adiabatic index, which for a relativistic gas is � 4{3, so it yields avalue for β of 1{3.

The evolution of the volume and temperature during the different phases goes as follows[4]:

• Planar phase: V 9 tγ

– during acceleration (t   tf ) : V 9 tp3�?3q{2 ùñ T � Ti

�tti

� 3�?36

– after acceleration (tf   t   ts) : V 9 t ùñ T � Tiγ�1i

�ttf

� 13

• Spherical phase (ts   t) : V 9 t3 ùñ T � Tiγ�1i

�tstf

� 13 p t

tsq�1

The radiation of the breakout shell is confined to the gas during its expansion until thetemperature drops so low that the pair production becomes negligible. It occurs when thepairs density is lower than the proton (and their accompanied electrons) density, whichbecomes significant once the temperature falls back to � 50 keV. At this temperature thebreakout and all the less massive shells become transparent and their radiation escapes. Wedefine Tth and tth as the temperature and time that the breakout shell becomes opticallythin.

This implies that there are three important dynamical timescales regarding the shockbreakout: the acceleration time of the breakout shell tf,0, its transparency time tth,0 and theplanar to spherical transition time ts. The breakout signal we observe strongly depends onthe values and relative order of these timescales. Although theoretically all arrangementsof the timescales are possible, in practice most of the explosions display parameters thatsatisfy:

tf,0   tth,0 À ts (9)

Therefore, speaking in terms of the dynamics of the expansion, we may state that whenthe breakout shell becomes optically transparent and the radiation escapes, the shell hadalready stopped its acceleration, accelerating from γ0 to γf,0. The transition from planarto spherical phase occurs after or right before the shell has become transparent. Hav-ing determined these conditions, we may proceed to determining the parameters of theobservable breakout signal.

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3 Breakout emission

The main parameters that characterize the breakout emission are [4]:

3.1 Planar phase

• The observed breakout energy, Ebo:

Ebo � E0γf,0γ0

TthT0

� 1

4E0γ

3�?32

f,0 (10)

where E0 � γ0m0c2 is the initial energy of the breakout shell, T0 � 200 keV and

Tth � 50 keV, so the ratio of the temperatures is approximately 1{4. We have alsoexpressed γ0 through γf,0 following eq. (5).

• The observed temperature, Tbo:

Tbo � Tthγf,0 (11)

• The duration of the observable breakout emission (tobsbo ) which is comparable to theobserved time of transition from the planar to the spherical phase:

tobsbo � tobss � R�cγ2f,0

(12)

• The observed breakout luminosity:

Lbo � Ebotobsbo

(13)

Ebo, Tbo and tobsbo are all functions of γf,0 andR�, so their values are sufficient to determinethe values of γf,0 and R�, and are related to each other by the following equation:

tobsbo � 20 s

�Ebo

1039 J

1{2�Tbo

50 keV

� 9�?34

(14)

3.2 Spherical phase

There are two main differences between the planar and spherical phase. First, during thespherical phase we consider the properties of the luminosity shell, which satisfies τ � c{vin contradiction to the dominant breakout shell during the planar phase. The evolution ofthe parameters breakout parameters is also decaying with time, while the planar breakoutemission is roughly constant.

The spherical phase can be divided into a relativistic and Newtonian phase. Thetransition time between the two takes place at:

tNW � R�cγ1.05f,0 � tobss γ3.05f,0 (15)

The time dependences of the luminosity and temperature for times ts   tobs   tNW follow:L 9 t�1.12

obs , T 9 t�0.68obs , while for tNW   tobs   10tNW the light curve decay is steeper and

goes as: L 9 t�0.35obs , T 9 t�0.6

obs . For t ¡ 10tNW there is a sharp break in the temperatureevolution as it drops quickly until thermal equilibrium is obtained.

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3.3 Spectrum

During breakout emission, the observer receives photons from shells that are outer of thebreakout shell, which have higher observed temperature, as they have reached higher γf,i.These photons generate a high frequency power-law spectrum at frequencies hν ¡ kTbo.Thus, the integrated spectrum of the breakout flare exhibits a power-law, which covers alarge range of high frequencies, while the low frequency power-law is limited only to theemission by the breakout shell. Therefore, the breakout emission spectrum is dominatedprimarily by the high frequency photons from the outer shells.

4 Application of the model to observed GRBs

According to the analytical model developed in the previous sections, the evolution of alight-curve of a shock breakout will go through the following phases [9]:

1. A gamma-ray flare is generated by the breakout shell when it becomes transparent.

2. The breakout flare contains photons from faster and lighter shells, producing a highfrequency power-law spectrum. It also contains photons emitted by the breakoutshell after it becomes transparent and cools adiabatically.

3. The flare ends with a sharp decay at a time that coincides with the transition to thespherical phase.

4. After the flare ends, spherical evolution dictates a steady decay of the luminosity.

5. The post flare temperature decays at first at a steady rate, generated during thespherical phase. A sharp drop in the temperature is observed when shells which werenot loaded by pairs during the shock crossing dominate the emission. The drop istypically from the X-ray range to the UV.

6. The energy emitted before the steep temperature drop is often comparable to thatemitted during the breakout flare. Thus, a signature of relativistic breakout in manyscenarios is a bright and short gamma-ray flare and a delayed X-ray emission withcomparable energy.

A typical parameter that may be measured from the observation of a supernova explo-sion in the optical part of the spectrum is the kinetic energy (Ek) that is carried by theejected mass (Mej). In order to determine the quantities in (10) to (13), we may expressthem as functions of Ek, Mej and the radius of the stellar progenitor R�. The initialLorentz factor of the breakout shell in terms of Ek, Mej and R� is [?] [4]:

γ0 � 2.6

�Ek

1045J

0.62�Mej

5Md

�0.45�R�

5Rd

�0.35

(16)

Inserting (16) into (5) we obtain:

γf,0 � 14

�Ek

1045J

1.7�Mej

5Md

�1.2�R�

5Rd

�0.95

(17)

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and substituting (17) in equations (10) to (13), we obtain the final form of the breakoutparameters:

Ebo � 6 � 1039 J

�Ek

1045J

2.3�Mej

5Md

�1.65�R�

5Rd

0.7

Tbo � 700 keV

�Ek

1045J

1.7�Mej

5Md

�1.2�R�

5Rd

�0.95

tobsbo � 0.06 s

�Ek

1045J

�3.4�Mej

5Md

2.5�R�

5Rd

2.9

Lbo � 4 � 1040 J{s�

Ek1045J

5.1�Mej

5Md

�3.65�R�

5Rd

�1.85

This last set of equations, together with (14), satisfy a wide range of energetic ex-plosions, from white dwarf supernova explosions and extremely energetic supernovae tolow-luminosity and long gamma ray bursts.

4.1 Relativistic jets and shock breakouts in long GRBs

Figure 3: An artist’s impression of the formation and propagation of jets inside a collapsingmassive star.

Gamma-ray bursts with duration grater than two seconds are classified as long gamma-ray bursts. They are the most common observed events of this type, and therefore, the beststudied of all. The most widely accepted model of the long gamma-ray bursts progenitor isthe collapsar model. According to this model, when an iron core of a massive star collapses,a system consisting of a black hole or a proto-neutron star and an accretion disk is formed

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at the center of the progenitor, which is expected to spin rapidly4. The gas along therotational axis can fall freely into the center while the gas along the equatorial plane onlygradually falls because of stronger centrifugal force. Thus, regions with lower density arecreated along the rotational axis, and these regions are where by some means of extractionof the gravitational or rotational energy of the system, the jets are formed and acceleratedto relativistic velocities.

Inside the jet, shocks between fast moving shells of particles encountering slower movingshells result in particle acceleration and emission of gamma-rays. Also, during the prop-agation through the stellar envelope the jets induce mildly relativistic shocks and inflatea cocoon that may collimate the jets to an even narrower angle than their initial openingangle. After the core collapse, the outer envelopes begin to fall freely, but the free falltimescale of the envelopes is longer than the dynamical time scale for the jet to propagatewithin the progenitor and to hit its surface, so it eventually breaks out of the surface ofthe progenitor into the interstellar medium [10] [11]. The interaction of the jet with theinterstellar medium produces the observable light curve in X-ray, UV and the optical partof the spectrum. A distinguishable feature of these light curves are the X- ray promptemissions during the plateau phase, which are believed to be produced by a reverse shockas the jet hits the interstellar medium; and the steep decline of luminosity towards theend, referred to as jet break, which is believed to occur at the time the jet slows down andcan no longer beam its radiation effectively.

Figure 4: A sketch of a typical long GRB light curve.

In this scenario, the term ”shock breakout” refers to the emission of the breakoutshell after the shock (which is now driven by the jet head and the cocoon) breaks out.Considering some typical values for a long gamma-ray burst:

4The rotation of the progenitor along with the beaming of jets is crucial for the explanation of theobserved luminosity of long gamma-ray bursts, as a spherical breakout would imply energies that areimpossible to be produced by a stellar- mass progenitor in such a short time.

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θ0 � 0.1 rad the half-opening angle of the jetL � 1043J{s the total luminosity of the gamma-ray burstM� � 5Md the mass of the progenitorR� � 5Md the radius of the progenitor

we obtain an initial value of the breakout shell energy of the order � 1041 J, whichis released by a short (� ms) pulse of high energy photons. So, a shock breakout wouldmanifest itself in the gamma-ray burst light curve as a pulse with a higher-energy spectrumand lower flux compared to the total burst emission. The total luminosity depends on theprogenitor size, making it possible to detect the pulse generated by large (R� ¡ 5Rd)progenitors. Otherwise, it is undetectable, or may be undistinguishable from the gamma-ray burst produced by the jet emission. In favor of the model, there indeed have beendetections of gamma-ray bursts which show an initial pulse of short high-energy spikes,shown in Figure 5.

Figure 5: A set of gamma-ray burst light curves which show initial spikes followed by a another,longer gamma-ray burst [12].

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4.2 Low-luminosity GRBs

The most significant of the applications of the relativistic breakout model is the one tolow-luminosity gamma-ray bursts, which could not be explained by theoretical models sofar. As we have seen in the previous chapter, according to the collapsar model, relativisticjets are produced during the collapse of a massive star, and they pierce through the stellarenvelope. It has been shown though, that in some cases of low-luminosity gamma-raybursts, the jets are probably not energetic enough to break through the surface of theprogenitor, and remain contained within the opaque stellar envelope. Still, the observedgamma-ray radiation must be contributed to some process, which is most likely the jet-driven shock breakout.

There are several common features observed in all low-luminosity gamma-ray bursts,which strongly suggest shock breakouts as their origin [4]:

1. All low-luminosity gamma-ray bursts show 1041 - 1043 J of gamma-rays or higher-frequency X-rays that are emitted in a single pulsed light curves, showing spectrathat move towards lower frequencies with time.

2. They show radiowave afterglows which indicate energies of mildly relativistic ejecta.

3. The observed energy is only a small fraction of the total energy observed in theassociated supernova.

A quantitative analysis of the observed parameters of four well studied low luminositygamma-ray bursts, with application of equations (10) to (14) confirms this theory:

GRB 060218 and 100316D GRB 980425 and 031203 GRB 101225ATbo � 40 keV � 150 keV � 40 keVEbo � 1042 J � 1041 J � 1044 Jtbo (calculated) � 1500 s � 10 s � 104 stbo (observed) � 2000 s � 30 s Á 1 h

We can see that, considering only equation (14), the calculated duration is of the orderof the actual observed duration of the gamma- ray burst. Calculations of the final Lorentzfactor γf,0 and the radius of the progenitor R� are also consistent with the observationsof the associated supernovae and other models of the bursts. The differences between theobserved and calculated properties are mainly a consequence of the fixed n � 3 in themodel, which may, of course, not be the actual value of n in the observed progenitor’sinterior.

5 Conclusion

Relativistic shock breakouts may be produced in various stellar progenitors with suitableproperties, such as high explosion energy and steeply declining density profile, which accel-erate the shock to relativistic velocities. The dynamical description of the propagation and

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breakout of the shock provides quantitative description of the observed breakout parame-ters. A most significant accomplishment of this model is the equivalence of the calculatedwith the observed parameters of the previously unexplained low-luminosity gamma-raybursts. It also provides a possible explanation of a set of short bursts followed by long burstof different spectral ranges, which according to the model are shock breakouts followed bygamma-ray radiation from the jets during the core-collapse of a massive star. In conclu-sion, a relativistic shock breakout is a generic process for the production of gamma-rayflares, which unifies a variety of stellar explosions, ranging from white dwarf supernovae,extremely energetic supernovae and various types of gamma-ray bursts, thus opening anew window for their study and detection.

References

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html, 09.04.2012

[2] Supernovae linked to gamma ray bursts http://www.abc.net.au/science/articles/

2010/01/28/2803839.htm, 05.04.2012

[3] Supernova - gamma-ray burst connection http://astronomy.swin.edu.au/cosmos/S/

Supernova-Gamma+Ray+Burst+Connection, 05.04.2012

[4] Ehud Nakar and Re’em Sari, Relativistic shock breakouts. The Astrophysical Journal,Volume 747, Issue 2, article id. 88, 2012.

[5] Wolf-Rayet star http://en.wikipedia.org/wiki/Wolf%E2%80%93Rayet_star,30.03.2012

[6] G. P. Horedt, Polytropes: applications in astrophysics and related fields. Springer, 1edition, 2004.

[7] Optical depth (astrophysics) http://en.wikipedia.org/wiki/Optical_depth_

(astrophysics), 30.03.2012.

[8] Maragaret Pan and Re’em Sari, Self-similar solutions for relativistic shocks emergingfrom stars with polytropic envelopes. The Astrophysical Journal, Volume 643, pp.416422, 2006.

[9] Review: Relativistic shock breakouts http://astrojournalclub.wordpress.com/2011/

07/09/review-relativistic-shock-breakouts/, 04.04.2012.

[10] Omer Bromberg, Ehud Nakar, Tsvi Piran, Reem Sari. The propagation of relativisticjets in external media. The Astrophysical Journal, Volume 740, Number 2, 2011.

[11] Weiqun Zhang and S. E. Woosley. Relativistic Jets from Collapsars: Gamma-RayBursts. The Astrophysical Journal, Volume 586, Number 1, 2003.

[12] J. P. Norris and J. T. Bonnell. Short gamma-ray bursts with extended emission. TheAstrophysical Journal, Volume 643, pp. 266-275, 2006.

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