Transcript Spectra of Afterglows

Gamma-ray Bursts
& Compact Stars
T Lu (陆 埮)
Purple Mountain Observatory
Chinese Academy of Sciences
Nanjing
2003年度诺贝尔物理奖获得者
俄罗斯元老物理学家
87岁的V L Ginzburg
认为暴是
最重要的10大天体物理问题之一
Contents
 Observational Features
 Toward Standard Model
• Fireball
• Internal - External Shock Model
• Standard Condition
 Origin & Energy Source
 Recent Developments
• Selected Topics
Observations
GRBs
The Discovery of -ray Bursts
Vela5b
•Earliest recorded GRB in
1967
•Vela-US Military Satellite:
discovered 16 -ray bursts
between 1967-1970
•Published in 1973
•http://www.astro.caltech.edu/~jsb/GRB/vela5b_1.gif
Observational Features
Detection Rate: 1 or 2 /day




Temporal Features
Spectral Features
Spatial Features
Afterglows
Temporal Features
 Profiles
• Complicated and irregular
• Multi-peaked or single-peaked
 Durations (T)
• ～ 5 ms to ～ 5×103 s , Typically ～ 10 s
 Variabilities (T)
• ～ 1ms , even ～0.1ms , Typically ～ 10-2 T
Examples of GRBs
 Profiles
• complicated
 Duration
• ～ ms - 1000 s
 Variability
• ～ 1ms
even ～0.2ms
Spectral Features
 Photon Energy Range:
• ～ 10 keV to ～ 10 GeV
• Typically: ～ 0.1 to 1 MeV
 Non-thermal: N(E)dE∝E-αdE, α≈1.8 - 2
 High Energy Tail: no sharp cutoff above 1
MeV
 Fluence:
• Typically ～ (0.1 to 10)×10-6 ergs/cm2
A Typical Spectrum
Schaefer et al 1998
GRB910503
Spectra, Examples
 Photon energy:
10keV – 10GeV
 Non-thermal，
power law
 No cutoff
at high energy
Photon spectra
Energy
Schaefer et al 1998
Spatial distribution of GRBs
since 1992
Isotropic
● Angular:
Dipole and Quadrupole :
(for first 1005 BATSE bursts)
<cosθ>=0.017±0.018
<sin2b-1/3>= - 0.003±0.009
● Sight direction:
Inhomogeneous
 favors:
cosmological distances
of GRBs statistically.
Spatial Distribution
--- BATSE
Highly isotropic
Lack of Weak GRBs
 Slope(strong):~ –3/2
 Slope(weak): ~ – 0.6
For uniform distribution：
slope= –3/2
Where are the difficulties？
 Durations of GRBs are very short, difficult to
arrange detailed observations.
 They occur at random spatially and temporally,
difficult to prepare in advance.
 Except prompt gamma-ray (and maybe weak X-ray),
no counterpart on other wave band was found
before 1997, difficult to be identified
through other wave band with other objects of
known distances.
 Localization is very rough with gamma-rays,
within the error box, too many objects exist,
difficult to find association with object of
known distance.
Observations
Afterglows
BeppoSAX：
leading to the discovery of afterglows
•GRB monitor
40─700 keV
•WFC
2─26 keV
40o×40o
errer box ~3’
WFC covered 5% sky, roughly 1 burst per month.
Distances of GRBs successfully measured
 BeppoSAX:
Leading to the discoveries of the
afterglows of γ-ray bursts (1997)
Measuring the red-shift of host galaxies
of GRBs
Discovery of Afterglow
GRB 970228
 Afterglow in
the overlap
region
Afterglows of GRBs
•General feathers: Mutli-wave bands,
Power law decay, Host galaxies
•Time scales: X-ray: days ;
Optical: months ;
Radio: months
•Decay power law: Fν ∝ t –α
αX = 1.1 to 1.6, αOptical = 1.1 to 2.1
•Host galaxies: Red-shifts: up to 3.4 even 5
 these GRBs are definitely at
Cosmological Distances
Optical Afterglows
 Examples
 Smooth and regular
Radio Afterglows
Examples
 Early fluctuation
 Small space scale
 Late smooth
Great Break-Through
Lower
Energy
Limit
Observable
Time
Precision of
Localization
Before 1997
After 1997
10 keV
10 GHz
100 s
Months or
Year
Milli-seconds
degrees
Orders
improved
8-9
5-6
6-7
Long Burst & Short Burst
 ＜2 s：short burst（～25%）；＞2 s：long burst（～75%）
Toward Standard Model
Stellar Events
δT ～ ms

Ri ≤ cδT = 300 km
(Ri: scale of initial region)
Even for black hole, combined with R = 2GM/c2,

M ≤ 100 M⊙

-ray bursts: Stellar Objests
(Compact)
Initial Fireball
 F ~10－6 erg/cm2, D ~3 Gpc  E0~1051 erg
(1 Gpc = 31027 cm)
 T ~1 ms  Ri ~cT ~3 107 cm:
take Ri ~107 cm
 For pure radiation fireball, we have：
E0＝(4/3)Ri3 aT 4  Ti  6.5 MeV
a=(4/c)=7.5610-15 erg/cm3K4
=5.6710-5 erg/cm2K4s is Stefan-Boltzmann constant
Estimate of optical depth of fireball
 Estimate：

   nR  T2

4
3
E0
T
R

i
3
3
Ri me c 2
4
3
E0
2 1018

2
2
3
Ri me c
 is the photon energy in units of mec2. Thus,
the optical depth is very large. （≫1）
 The initial fireball should have black body
spectrum, in disagreement with observations.
Expanding Fireball
(Original fireball, under such high pressure, should expand to ultrarelativistic speed, and become optically thin, leading to nonthermal gamma-ray radiation.)
Non-thermal
Ri ≤ cδT
optically thick  Solution  optically thin

Ultra-relativistic Expansion with
Lorentz factor:  ≫ 1
Compactness Problem
Expanding with Lorentz factor γ
Ri ≤ cδT

Re ≤ γ2 cδT
fp/γ2α

fp
2  1 2  2
ˆ
   (emax / mec ) 
   1 (optically thin)

 >10 2
 M E/ < 10-5(E / 2×1051 ergs)M⊙
Baryon
Contamination Problem
Expanding
Fireball
A sketch showing
the fireball
( C. Kouveliotou, Science, 1997)
Cosmological
distance
Steps toward the
Standard Model
Large
energy
obs
Optically thick
Small
volume
Variabilities
obs
Compactness
Problem
obs
Observed spectra
Non-thermal
Optically thin
Shock
Internal
shock
Prompt
GRB
Relativistic
expansion
obs
External
shock
obs
Baryon
Contamination
problem
Afterglo
w
Regions of External Shocks
R.Sari, T.Piran, ApJ, 455(1995), L143
Shock condition：
e2 /  2   2  1   2
n2 / n1  4 2  3  4 2
e3 /  3   3  1
Velocity, Lorentz factor, distance, time use observer’s
frame；thermal quantities use fluids’ rest frame.
p2=p3, 2= 3, e2=e3=e, 2= 3
 (=nmpc 2)
1、4 cold；2、3 very hot：
e1=e4=0, p2=p3=e /3
n3 / n4  4 3  3
Only assume： 4≫1
(thus 2≫1)。
3
Reverse shock
 3 is Lorentz factor of region
3 relative to region 4. Equality
of preasures and velocities
along CD yields: e2＝e3 and
 3   4 /  2   2 /  4  / 2
The time for reverse shock
across the shell width ：
  n4 

1 

t 
c(  4   2 )   3n3 
4
shocked
shell
2
shocked
ISM
Forward shock
Unshocked
shell
CD
1
ISM
r
Contact Discontinuity
Importance
of
Non-relativistic Case
Generic Model
Generic Model
for GRB Ejecta
 Newtonian Phase of Afterglows
 Conventional Dynamic Model
• Model
• Wrong Limit of Conventional Model
 Generic Dynamic Model
• Model
• Sedov Limit of Generic Model
Newtonian Phase of Afterglows
Y.F. Huang, Z.G. Dai, T. Lu, A&A, 336(1998), L69-72.
Usually only a few days or tens of days after
the burst, a fireball will enter into the adiabatic
& non-relativistic phase. A useful model for
accounting afterglows should thus be able to
describe the overall processes from ultrarelativistic and highly radiative phase to nonrelativistic and adiabatic phase. Especially, it
should lead to the well known Sedov limit:
β∝ R-3/2,
as the expansion getting into the nonrelativistic and adiabatic phase.
Conventional Dynamic Model
based on:
d
 2 1

dm
M
(Blandford-McKee 1976; Chiang-Dermer 1998)
m --- rest mass of swept-up medium,  --- bulk Lorentz factor,
M --- total mass in co-moving frame, including internal energy U
It gives a non-relativistic and adiabatic limit:
β ∝ R-3
which is wrong, non-consistent with Sedov limit.
Generic Dynamic Model
(Y.F. Huang, Z.G. Dai, T. Lu, 1999)
van Paradijs, Kouveliotou, Wijers, ARA&A, 2000, has a detailed discussion
d
 2 1

dm
M
d
 2 1

dm
M ej  m  2(1   )m
It gives the overall description from ultra-relativistic and highly
radiative phase to non-relativistic and adiabatic phase, especially
leads to the correct Sedov limit:
β∝ R-3/2,
as the fireball getting into the non-relativistic and adiabatic phase.
Review Article
ARA&A-2000
(van Paradijs, Kouveliotou, Wijers)
Generic Model: v-R
Dynamical Evolution
 Solid:
generic model
 Dash-dotted:
ultra-relativistic
 Dashed:
Newtonian
Generic Model: v-t
Dynamical Evolution
 Solid:
generic model
 Dash-dotted:
ultra-relativistic
 Dashed:
Newtonian
Radiation
 In the shocked region, electrons accelerated by
the shock, state can be known there.
 Two important parameters are energy density in
relativistic electrons and in magnetic fields which
are expressed as fractions e and B of the total
internal energy density. They could at present time
only be determined by observations.
Spectra of Afterglows
R. Sari et al, ApJ, 1998, 497, L17
 Define 3 characteristic parameters:
 a is self absorption frequency ((sa)=1)
 νm is synchrotron radiation frequency of typical energy
electron;
 νc is cooling frequency, synchrotron radiation
frequency of the electron cooling within the local
hydrodynamic time scale.
 The frequencies of νm, νc, νa decrease with time as
indicated in figure; the scalings above the arrows
correspond to an adiabatic evolution, and the scalings
below, in square brackets, to a fully radiative evolution.
F   
R. Sari et al, ApJ, 1998, 497, L17
 Fast cooling: νc < νm
=2 (ν < νa) Wien’s law
=+1/3 (νa < ν < νc) synchrotron low energy tail
=–1/2 (νc < ν < νm)
=–p/2 (νm < ν)
Emitting electrons:
 Slow cooling: νm < νc
–p
N(e)

e
=2 (ν<νa)
=+1/3 (νa < ν < νm)
=–(p–1)/2 (νm < ν < νc)
=–p/2 (νc < ν)
Spectra of Afterglows
Spectra of Afterglows
Slow Cooling
Synchrotron Light Curve
R. Sari et al, ApJ, 1998, 497, L17




Consider spherical shock into constant density medium
Extreme limits: fully radiative & fully adiabatic
Ignoring self-absorption
There are 3 criticle times: t0, tc, tm. Note: c and m are
dependent on time t. At t0, c=m. At tc(tm), c(m) cross the
observed .
 Scalings within square brackets are for radiative evolution,
other scalings are adiabatic evolution.
 Flux are calculated according to synchrotron radiation.
Light Curve: Power Law
 High Frequency
Light Curve: Power Law
 Low Frequency
Afterglows: Power Law Fading
R
lg (days since triggering)
Spectrum of Afterglow Observed
T.J.Galama et al, ApJL, 1998
GRB970508
X-ray to radio
Origin
Non-uniform Environment
n ~ r-k
GRB970616


n ~ r-2
(wind environment)
(Dai, Lu, MNRAS, 1998)
Support the view of massive star origin for GRBs.
(Chevaliar, Li, ApJ, 2000)
Example: GRB970616
 Generally, we assume an inhomogeneous medium
with density: n  R-k.
 In this case, the X-ray afterglow light curve index:
 = (6-k)/(4-k) - [(3-k)/(8-2k)][(3-p)/2]
(Dai & Lu 1998, MNRAS, 298, 87)
 GRB970616:
━ About 4h after the burst, RXTE detected
its X-ray afterglow (2-10 keV).
━ On June 20.35 UT, ASCA detected an X-ray
flux.
From these data, we have  = 1.86
 Spectrum requires p=2.5, so we found k = 2
implying a wind environment of GRB970616.
 We further pointed out: “a massive star as a
GRB progenitor may be able to produce such a
stellar wind”.
 Therefore, we suggested, for the first time, that
GRB970616 is a possible wind interactor, that is,
its environment is a pre-burst stellar wind.
Dense Environment
·Break in optical light curve of GRB990123:
n～106 cm-3
(Relativistic to non-relativistic transition  break)
Dai-Lu, ApJL, 1999
·Rapidly declining optical to X-ray afterglows of GRB980519
can be explained well by dense medium, and its radio
afterglow can also be excellently explained.
Wang-Dai-Lu, MNRAS, 2000
Meaning of Environmental Effects
•Stellar Wind Effects
Stellar wind provides environment for progenitor of GRB
•Density Effects
Dense environment might be molecular cloud
Association of GRB with star forming region
Both environmental effects support the view:
“GRB originated from the collapse of massive star”
Energy Source
GRB971214: NASA news
 Z=3.4 (Keck II, Caltech team): 1.2  1010 light years.
 -ray energy in the duration of 50 s is as large as the total
radiation energy of the Milky Way in 200 years. Perhaps, there
may be much larger energies carried by gravitational radiations
and neutrinos.
 Within 1 or 2 seconds, this burster is as luminous as all the
Universe except the burster.
 Within 100 miles round the burster, the situation can be similar
to that of the early universe 1 ms after the Big Bang.
 The energy of the -ray burst is several hundreds bigger than
SN.
GRB990123: 10GRB971214
 Z=1.6
 11.982 Gpc
(H0=65 km/s, Ω0=0.2, Λ=0)
 Peak absolute V-band magnitude: MV ～36.5
 Intrinsic luminosity:
LV ～21016 L⊙ ～Type I SN
 Eiso = 3-4.5 1054 erg = 1.9 M⊙c2
 Optical peak:
8.95 m
 Initial optical flash contains most of optical fluence:
～ergs/cm2, about of the γ-ray
fluence.
Energy Source Models
Merger of NS-NS, NS-BH (Eichler et al., 1989; Paczynski, 1991)
► ~ 108 yr
(Gravitational radiation timescale)
 Massive star collapse
(Woosley, 1993; Paczynski, 1998)
►Association with Star Forming Regions
►Association with supernovae
 Phase Transition of NS⇨SS
(Cheng-Dai, PRL, 1996; Dai-Lu, PRL, 1998)

Natural ways to avoid baryon contamination:
►A strange star
Mcrust 10-5 M
►A rapidly rotating
Black Hole +

Maximum available energy
(through Blandford-Znajek mechanism)
29% MBHc2
spin energy
Disk

42% Mdiskc2
binding energy
Strange Star
Physically
Astronomically
• a huge nucleon, also
a strange huge atom
• bound by strong interaction:
confinement
• tightly bound even without
gravitation
• one possible final stage of
stellar evolution
• produced through phase
transition from NS
• composed of nearly equal
number of u, d, s quarks
A Story
Damping of Radial Vibration
Wang-Lu, PLB, 1984
 Damping and dissipation occurs only in 3rd case,
the domonative process is u+d u+s.
1
• dw
,
v
is
the
volume
per
unit
mass.

Pdv

dt
average

period
Calculation of Vibrational Damping
Wang-Lu, PLB, 1984
To calculate
Considering
dw
dt

average
1


,
Pdv
,
v  v0  v cos(2t /  )
expanding p(t) to
p(t )  p0  (p / v) 0 v
period
 (p / nd ) 0 nd  (p / ns ) 0 ns
and using thermodynamic relations
and Weinberg-Salam-Glashow
theory, we can obtain the damping
of NS with strange core or of SS in
sub-second time scale.
Sketch of Calculation
p(t )  p0  (p / v)0 v  (p / nd )0 nd  (p / ns )0 ns




dw
dt

average
1

 Pdv 
t period





dn
t
,
here

(



)
dn

nd  ns   dt
s
d 
P(t )  
  dt
dt
0

v
dt

0 0
(dn/dt denotes net rate of us ud)

 (  s   d ) 
5 1 1/ 4 2
3

  3.23 10 v 15 ms ,150erg.g.cm 
v

0
dn / dt  2.45 1039 vT93 155 / 4 [ I ( )  I ( )] g 1s 1
where

3
( x   )2   2
I ( ) 
dx,   (  s   d ) / kT
2 
x
 x 
(2 )  (1  e )(1  e
)
Bulk Viscosity
 Wang-Lu(1984):
dw
dt

average
1

 Pdv
period
Radial vibration damping
• Sawyer(1989):
dw
1
 2   v 
  v0 
  
dt average
2


  v0 
Bulk viscosity coefficient ζ
2
2

R

1
)( 6 ) 2 ( 25
)
 nuc 10 cm 10 gcm -1s -1
Time scale for damping of vibrations τD
 D  1s(
Viscosity influenced by αc
Dai-Lu, Z. Phys. A, 1996
 Approximation:
States --- αc considered; matrix --- not
• Strong interaction effects:
the non-leptonic weak rate is strongly
suppressed by αc
 At low temperatures, viscosity is strongly
suppressed; at high temperatures, it is slightly
enhanced.
A Wrong Discovery
Nature:
16 March 1989

Kristian et al.
claimed their
discovery of an
optical pulsar with
period as short as
only 0.5ms at
SN1987A early 1989
Keplerian Spin Limit
 Upper limit of rotation of neutron stars is set by Keplerian
speed:
1/ 2
3  M max
 K  7.7 10 
 M sun
  Rmax 
 

  10km 
3 / 2
s -1
 Upper limit for strange stars: (B0=57MeVfm-3)
1/ 2
 B  1
 K  9.4  10   s
 B0 
3
Neutron Stars, Strange Stars
& Spin Limit
 Upper: dashed, dotted,
solid---K=300, 240, 210
MeV
 Lower: dotted, dashed,
dash-dotted---B1/4=145,
170, 200 MeV
 Pulsar Spin: 1.6ms, 0.5ms
 M-R relations are quite
different for NS than for SS
Importance of Viscosity
 Gravitational radiation reaction instabilities set spin
limit for NSs far lower than Kepler limit.
 High viscosities can damp away the gravitational
radiation reaction instabilities.
 Due to very high viscosities in SSs, spin rate can
be much closer to Kepler limit.
 This gives an important way to discover SSs from NSs
based on period measurement.
Declaring a
Discovery
Wrong
Published in
Nature two years
later by the same
group of authors
1989• two years apart •1991

by the same group

A Way to Soften the
Problem of Energy Crisis
---Beaming & Jets
Why beamed?
 Variability time scale in GRB light curves:
as short as: 0.1ms
R < c Δt  GRBs are due to stellar objects
 However, the energy is huge in some GRBs!
GRB 971214: E,iso ~ 0.1 M⊙c2
GRB 991216: E,iso ~ 0.2 M⊙c2
GRB 990123: E,iso ~ 1.9 M⊙c2
 Beaming can safely relax the crisis
Evolution of jetted GRB ejecta
Huang-Dai-Lu, MNRAS 2000
●Evolution of jetted GRB ejecta, a set of equations:
dR
 c (   2  1) ;
dt
2
d cs (    1 )

dt
R
cs2  ˆ (ˆ  1)(  1)
;
dm
 2R 2 (1  cos )nmp
dR
;
d
 2 1

dm
M ej  m  2(1   )m
;
1
c2
1  ˆ (  1)
,
here ˆ  (4  1) /(3 ) is the adiabatic index.
●A set of "standard" parameters:
E0/Ω0=1054ergs/4π; γ0=300; n=1 cm-3; ξB2=0.01; p=2.5;
ξe=0.1; θ0=0.2; θobs0; DL=106 kpc (luminosity distance)
A Standard Picture
Meszaros 2001

X
O
Recent Developments
Only Selected Topics
Large polarization discovered
in the prompt gamma-ray
emission in GRB021206
Large Polarization Detected in Prompt
Gamma-ray Emission in GRB021206
Coburn, Boggs, Nature, 2003, 423, 415
Degree: 80% ±20%
Use RHESSI
Angular distance close brom the sun,
no afterglow observation
Debate
14 October
Debate-17 October
Paper: astro-ph/0310515
From: Steven E. Boggs <[email protected]>
Date: Fri, 17 Oct 2003 20:17:17 GMT (4kb)
Title: Statistical Uncertainty in the Re-Analysis of Polarization in GRB021206
Authors: Steven E. Boggs, Wayne Coburn
Comments: Submitted to MNRAS
\\
We recently reported the first detection of an astrophysical gamma-ray
polarization from GRB021206 using the Reuven Ramaty High Energy Solar
Spectroscopic Imager (RHESSI) spacecraft. Our analysis suggested gammaRay polarization at an astoundingly high level, 80+/-20%. A recent manuscript
re-analyzes this event in the RHESSI data, and sets an upper limit on potential
polarization of 4.1% -- clearly inconsistent with our initial analysis. This
manuscript raises a number of important concerns about the analysis, which
are already being addressed in a separate methods paper under preparation.
We note here, however, that the limit set on the potential polarization by this
re-analysis is significantly underestimated using their novel statistical methods.
\\ ( http://arXiv.org/abs/astro-ph/0310515 , 4kb)
Associations
GRB with SN
Comparison between GRBs & SNs
Burst
Energy (up to)
Time Scale
Profile
Wave band
GRBs
SNs
1054 ergs
10 sec
irregular
γ-ray
Afterglow
1051 ergs
month
smooth
Optical
Remnant
Relic
Time Scale
Month
103 yr
Wave band
Multi-band
Multi-band
Understanding
Fireball expansion Ultra-relativistic
Non-relativistic
Mechanism
Stellar core collapse
？？？
Key process
 process
？？？
SN/GRB Associations
▲GRB980425/SN1998bw
GRB 980425:Red-shift: 0.0085; Energy: E = 5×1047 ergs
(Galama et al, Nature, 1998)
SN 1998bw: Ic type
▲GRB980326
3 weeks after the burst it was brightened to 60 times than
extrapolated from early time
(Bloom et al., astro-ph/9905301)
▲GRB970228
Red-shift: 0.695; Energy: E=5×1051 ergs
Late afterglow does not be consistent with fireball model; extreme
reddening with time, V-I increased by ≈1.6 mag (Reichart, astro-ph/9906079)
▲GRB030329/SN2003dh
Red-shift: 0.169; Energy: E = 1.3×1052 ergs
SN 2003dh: Ic type
(Hjorth, et al, Nature, 2003)
GRB030329/SN2003dh
P. Meszaros, Nature, 2003, 423, 809
GRB030329 was detected by HETE-II
P A Price et al, Nature, 423, 844
Very bright event!
GRB030329: 1.5 hours since burst,
it reached R=12.6 mag. In comparison,
GRB021004: at the same time, 16 mag;
GRB990123: 17 mag.
This source was also detected by RIKEN
automated telescope independently.
GRB030329: Light Curve of Optical Afterglow
P A Price et al, Nature, 423, 844
A good broken
power law
Errors smaller than
the plotted points
Spectral Evolution of the
Combined Spectra of Afterglow,
SN and Host Galaxy
J.Hjorth, Nature, Vol.423, 847
Comparison of the spectral
evolution of SN2003dh and
SN1998bw
J.Hjorth, Nature, Vol.423, 847
Thank you