Gamma-Ray Burst

XIANG DanFeng

2017.12.29

Summary• What is a GRB(Gamma-Ray Burst)?

• Short and intense pulses of soft gamma rays with non-thermal spectra

• The bursts last from a fraction of a second to several hundred seconds.

• Narrowly beamed

• Long lasting afterglow(in X-ray, optical, radio wavelengths)

• The physical pictures• High energy physical processes

• Relativistic effects

• Synchrotron emission, inverse Compton scattering

• Internal and external shocks

• Stellar collapse & neutron star merger

Observation featuresof GRB

GRB: observation

• Spatial distribution

• Prompt Emission

• Afterglow

• Association with supernovae

Spatial Distribution

• BATSE (Burst and Transient Source Explorer)

Cosmic origin!Isotropic

For a constant peak luminosity: 𝑉/𝑉𝑚𝑖𝑛 = 0.5

But the observed value: 𝑉/𝑉𝑚𝑖𝑛 = 0.348

NOT homogeneous!

GRB: observation

• Spatial distribution: isotropic but not homogeneous, cosmic origin

• Prompt Emission• Fast γ-ray emission, together with X-ray flash(XRF) and

possible optical and radio emission(very rare)

• Afterglow

• Association with supernovae

Prompt emission

Spectrum• Non-thermal spectrum peaks at a few hundred

keV, and many events have a long high-energy tail extending up to GeV.

• An empirical fit for the spectrum: broken power-law

• Peak Energy:

• Break Energy:

• Paucity of soft or harder events• Intrinsic or observational artifact? –Not clear

Hardness vs. duration

• NHE(no high energy) bursts:• no emission above 300keV(very negative β)

• Fainter than regular ones

• Many bursts have NHE pulses along with regular pulses

• High energy tail• GRB941017(González et al. 2003)

• Remains roughly constant

• The “tail”(10Mev-200MeV) contains more than 50 times energy than the main γ-ray(30keV-2MeV) energy

• Low Energy tail• Some bursts have steeper low-energy

power spectrum(α>1/3)

Prompt emission: spectrum

-18 to 14 s

14 to 17 s

47 to 80 s

80 to 113 s

113 to 211 s

Spectra of GRB 941017

Prompt emission: Temporal structure

• GRB duration: T90(T50)• the time in which 90% (50%) of

the counts of the GRB arrive

• Hardness: N(100–300 keV) / N(50–100 keV)

• Hardness – duration correlation• Long & short • Ultra-long

• Variable• Variability time scale(δt) much

shorter than the burst duration• ~80% GRBs show variability

structures• The rest have rather smooth light

curves with a fast-rise exponential decay(FRED)

• Variability luminosity correlation

Prompt emission: Temporal structure

GRB920627

• Pulses

• The bursts are composed of series of individual pulses• Light curve of an individual pulse is a FRED with an average rise-to-

decay ratio of 1:3

• The low-energy emission is delayed compared to the high-energy emission

• The pulses’ low-energy light curves are wider compared to the high-energy light curves(width ~ E-0.4)

• Width-symmetry-intensity correlation: High intensity pulses are (statistically) more symmetric (lower decay-to-rise ratio) and with shorter spectral lags

• Hardness-intensity correlation: The instantaneous spectral hardness of a pulse is correlated to the instantaneous intensity

Prompt emission: Temporal structure

GRB: observation

• Spatial distribution: isotropic but not homogeneous, cosmic origin

• Prompt Emission• Fast γ-ray emission, together with X-ray flash(XRF) and

possible optical and radio emission(very rare)

• Afterglow• slowly fading emission at longer wavelength

• Association with supernovae

Afterglow

• X-ray

• Optical and IR

• Radio

Venn diagram(till 2001)

• X-ray• 𝑓𝜈(𝑡) ∝ 𝜈−𝛽𝑡−𝛼(α~1.4, β~0.9)

• Normal distribution of the flux in 1-10keV, 11h after burst

• Constant luminosity

• Beam effect

• Optical and IR afterglow• Power-law decay (~t-α), or

broken power law• Fν(t)=f*(t / t*)−α1{1−exp[−(t

/ t*)(α1−α2)](t / t*)(α1−α2)}.

• Power-law spectrum(~ν-β)• Absorption lines• Providing information of

the host galaxy: distance and redshift

• Dark GRBs• ~50% GRBs do not have

optical afterglow• Observational artifact?

Absorption, higher z, or intrinsically fainter?

GRB 990510

Days after the burstO

bse

rved

mag

• Radio afterglow• ~50% GRBs have radio

afterglow, among which ~80% have optical counterparts

GRB 970508

Afterglow of short GRB

GRB 130603B GRB 050724

GRB: observation

• Spatial distribution: isotropic but not homogeneous, cosmic origin

• Prompt Emission• Fast γ-ray emission, together with X-ray flash(XRF) and

possible optical and radio emission(very rare)

• Afterglow• slowly fading emission at longer wavelengths

• Only Long bursts

• Association with supernovae• Related to stellar death

• Association with

supernovae(SNe)

• A SN bump in the

afterglow

• Only the long bursts

• The GRB SNe are very

different from normal type

Ib/c supernovae

GRB 090618

Physical Processesin GRB

Physical Process: Relativistic Motion

• For gamma photons to produce e+e- pairs:

• We get a optically thick source!

• Considering relativistic motion, the source is optically thin!

• Relativistic time effect

• 𝛿𝑡 =𝑅2−𝑅1

𝑣−

𝑅2−𝑅1

𝑐≈ (𝑅2 − 𝑅1)/2𝑐Γ

2

• 𝑅 = 2𝛿𝑡𝑐Γ2

• Hugoniot shock jump conditions(when the upstream matter is cold):

Physical Process: Relativistic shocks

• How the electrons been accelerated?

• diffuse shock acceleration model

• The role of magnetic filed

• The acceleration resulted in a power law spectrum in form of : 𝑁 𝐸 d𝐸 ∝ 𝐸−𝑝d𝐸

• With:

Physical Process: Particle acceleration

• Energy source for the prompt emission and afterglow

• To study the synchrotron emission, you need to consider the motion of the electron and the source

• In observer’s frame:

• Power( in local frame):

• Cooling time(in observer’s frame):

Physical Process: Synchrotron

• Synchrotron spectrum(optical thin)

• Sum of power law: 𝐹𝜈 ∝ 𝜈1/3

• Peak power at 𝜈𝑠𝑦𝑛(𝛾𝑒):

• The overall spectrum: sum of emission of all electrons

• Self absorption: 𝜈𝑎

• For intermediate frequency: Cooling of electrons• Fast cooling(𝛾𝑒,𝑚𝑖𝑛 > 𝛾𝑒,𝑐)

• Slow cooling(𝛾𝑒,𝑚𝑖𝑛 < 𝛾𝑒,𝑐)

Physical Process: Synchrotron

Synchrotron spectrum• Slow cooling(𝛾𝑒,𝑚𝑖𝑛 < 𝛾𝑒,𝑐)

• Fast cooling(𝛾𝑒,𝑚𝑖𝑛 > 𝛾𝑒,𝑐)

• Jets

Considering a spherical shell with constant velocity

• Time delay for light from angle θ: 𝑅(1 − cos 𝜃)/𝑐 ≈ 𝑅𝜃2/2𝑐

• Relativistic beaming: 𝜃~1/Γ

• Jet angle: 𝜃𝑗~1/Γ

• For an instantaneous flash of power law spectrum 𝑓𝜈 ∝ 𝜈−𝛼, the observed flux

will decay as power law with 𝑡−(2−𝛼) at late times

• The photons earn energy through interaction with electrons

• Comptonization parameter

• 𝑌 =𝜖𝑒

𝑈𝐵𝑖𝑓 𝑈𝑒 ≪ 𝑈𝐵

• 𝑌 = 𝑈𝑒/𝑈𝐵 𝑖𝑓 𝑈𝑒 ≫ 𝑈𝐵

• Add ultrahigh energy component to the spectrum(𝛾𝑒2)

• Speed up cooling, shorten cooling time tsyn(by a factor of Y)

Physical Process: Inverse Compton scattering

Physical Mechanicsand

Progenitors

Core-Collapse of massive stars

• Association with supernovae

SN1998bw SN2002dh etc.

Core-collapse > central engine >

Merger of compact stars : kilonova

sGRB prompt emission & afterglow

Kilonova

Gravitational wave & sGRBGW170817/GRB170817A/AT2017gfo

Multi-Messenger Astronomy!!

Tidal disruption eventsGRB 110328A(Swift J2058.4+0516)

Unanswered questions

• what is the composition of jet/ejecta (baryonic, e± or magnetic outflow)?

• how are γ-rays, particularly of energy less than ∼10 MeV, produced?

• is a black hole or a rapidly rotating, highly magnetized, neutron star (magnetar) produced in GRBs?

• what is the mechanism by which relativistic jets are launched?

• what are the properties of long and short duration GRB progenitor stars?

References

• Kumara, P., Zhang B. The physics of gamma-ray bursts & relativistic jets. PhR, 561, 1-109(2015)

• Piran T. The physics of gamma-ray bursts. RvMP, 76, 1143-1210(2004)

Thanks

GRB energetics• Isotropic luminosity

function(dlnL)• Related to star formation rate

• NOT isotropic but beamed

• 𝐸𝛾 =𝜃2

2𝐸𝛾,𝑖𝑠𝑜

Afterglow

• Central engine

• Shocks

• Jet

X-ray afterglow

Associated with prompt emission

External shock

forward shock

Jet break

late central engine activities