Transcript GRB prompt emission

GRB
Theory and observations
Useful reviews:
Waxman astro-ph/0103186
Ghisellini astro-ph/0111584
Piran astro-ph/0405503
Meszaros astro-ph/0605208
Useful links
http://www-astro.physics.ox.ac.uk/~garret/teaching/
http://www.cv.nrao.edu/course/astr534/
Progenitor Long GRBs: Collapsar model M>30 M
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Leading model for short GRBs Progenitors
NS-NS merging primordial DNS
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Spectrum well described by a broken power law
Band approximation
•Nontermal Spectrum
N(E) 
E
E<E0
E E>E0
BATSE (20 keV-1 MeV)
0.1 MeV < E0< 1 MeV
 -2,  ~ [-1, -0.5]
The compactness problem
•t ~ 1-10 ms
Compact sources R0 c t ~ 3 107 cm
•Cosmological sources (D~3 Gpc)
L~ fD2~1052 erg/s
R of our galaxy ~ 30 kpc: extragalactic objects
1 2≥ (mec2)2  e+e~ p R0nT~TL/4R0c
~1015
 ~ 1 MeV
p fraction of photons above
the thereshold of pair
production
T=6.25x10-25cm2
Optical depth  ( e+e-) >>1
Implications: The fireball
How can the photons escape the source?
Relativistic motion: A plasma of e+ e- , a Fireball, which expands and
accelerate to relativistic velocities, optical depth reduced by relativistic
expansion with Lorentz factor 
The reasons:
1.
In the comoving frame  below the thereshold for
pair production ’=/
’1 ’2≤
(mec2)2
1
 
1 (v /c) 2
2. Number of photons above the threshold reduced by

2(
-1)

(~2 high-energy photon index);
3. Emitting region has a size of 2R0
 reduced by a factor  2+2  6.
 < 1 for  ≥100
Propagation effect
Zhang & Mészàros, IJMPA A19, 2385
(2004)
dtˆ  tˆ2  tˆ1  dr/c
t1  tˆ1  L /c
t 2  tˆ2  (L /c   cosdtˆ )
ˆ  dtˆ /22  dr/(22c)
dt

(1


cos

)d
t

Finally,
•dt’, comoving time of the shell
ˆ /  dt /(1   cos)  Ddt  2dt
dt'

d
t

where D is the Doppler factor.
Fireball evolution
• Fireball expands and cools pairs annihilate and
photons may escape, quasi-thermal emission
against observations!!!
• Therefore a small barion loading (≥10-8M) is
needed and the radiation energy is converted to
kinetic energy.
The Lorentz factor
• As the fireball shell expands, the baryons will
be accelerated by radiation pressure.
• The fireball bulk Lorentz factor increases
linearly with radius.
• 0  E/M0c2, M0 total baryon mass of the
fireball
Fireball Model: Prediction vs.
Postdiction
• Prediction – (from Latin: prae- before + dicere to say):
A foretelling on the basis of observation, experience
or scientific reasoning.
• Postdiction – (from Latin: post- after + dicere to say):
To explain an observation after the fact.
• If your model “predicts” all possible outcomes, it is
not a prediction. This merely states that you can not
constrain the answer with your current model.
Fireball Model
The Fireball model
Assumes a relativistic
Outburst and works
With a variety of
Mechanisms.
We rely heavily on
A review by Tsvi
Piran.
From IXth International
Symposium on Particles,
Strings and Cosmology
Tata Institute of
Fundamental Research,
Mumbai, Inda
Tsvi Piran
http://theory.tifr.res.in/
pascos/Proceedings/Friday/
Piran/index.html
The Fireball
Model
  rays
Relativistic
Particles
>100
or Poynting flux
compact source
~ 107 cm
Goodman; Paczynski;
Narayan, Paczynski & Piran;
Shemi & Piran,
Meszaros & Rees
Shocks
Supernova Remnants
(SNRs) - the Newtonian
Analogue
• ~ 10 solar masses are
ejected at ~10,000 km/sec
during a supernova
explosion.
• The ejecta is slowed down
by the interstellar medium
(ISM) emitting x-ray and
radio for ~10,000 years.
External Shocks
 External shocks are shocks between
the relativistic ejecta and the ISM just like in SNRs. Can be produced
by a single explosion.
Recall, the first
GRB model
(Colgate 1968)
Invoked SN
Shocks to power
GRBs!
External Shock Predictions For
GRBs
• The burst of gammarays should be
accompanied by a burst
of optical photons
(within 1 second of the
explosion).
• Based on these
predictions, fast slewing
optical telescopes were
developed (e.g.
ROTSE, LOTUS).
GRB070228 – Optical Burst Seen! But observed
much later than expected. This spelled the
beginning of the end for the external shock model!
(Although some claimed this as a “prediction”!)
Fireball Theorists then found a lot
Wrong with the external shock model!
A NO GO THEOREM
External shocks cannot
produce a variable light
curve!!!
(Sari & Piran 97)
Time to Revise the Theory
• Gamma-rays and Afterglow arise from
different sources
Birth of the Internal Shock Model
Internal Shocks
Shocks between different
shells of the ejected
relativistic matter
=cT
d=cdT
• dT=R/c2= d/c

/c=T
• The observed light curve
reflects the activity of the
“inner engine”. Need
TWO time scales.
• To produce internal shocks
the source must be active
and highly variable over a
“long” period.
d
T
T
Internal
Shocks
Afterglow
=cT
d=cdT
• Internal shocks can convert only a fraction of
the kinetic energy to radiation
(Sari and Piran 1997; Mochkovich et. al., 1997;
Kobayashi, Piran & Sari 1997).
It should be followed by additional
emission.
“It ain't over till it's over” (Yogi Berra)
Gamma-Ray Burst: 4
Stages
1) Compact Source, E>1051erg
2) Relativistic Kinetic Energy
3) Radiation due to Internal shocks = GRBs
Plus burst of optical emission!
4) Afterglow by external shocks
The Central Compact Source is Hidden
The Internal-External Fireball Model
-rays
Inner
Engine
Relativistic
Wind
Internal
Shocks
Afterglow
External
Shock
There are no direct observations of the inner engine.
The -rays light curve contains the best evidence on the
inner engine’s activity.
THE FIREBALL MODEL
Postdicted PREDICTED GRB
AFTERGLOW (late emission
in lower wavelength that will
follow the GRB)
Rhodes & Paczynksi, Katz,
Meszaros & Rees, Waxman,
Vietri, Sari & Piran
Fireball Model History
• External Shock model: relativistic ejecta from
very energetic explosion shocks with the
interstellar medium. Synchrotron radiation in
shock produces gamma-rays and optical
burst.
• Optical burst appeared late – theorists move
to internal shocks to explain gamma-rays.
How the energy is dissipated
• In order to have some emission from the
firebal the energy must be dissipated
somehow.
• Observed GRB produced by dissipation of the
kinetic energy of this relativistic expanding
fireball regardless the nature of the
underlying source.
• Possible dissipation mechanism Internal
shocks: collisions between different parts
of the plasma
The internal/external shock scenario
[Rees & Meszaros 1992, ’94]
ISM
 10 cm
13
 ray phase
Efficient! [Guetta Spada & Waxman 2001]
 1016cm
X-ray, Opt.-IR,
Radio
The radiation mechanisms
The efficiency of internal shocks
Shells collide and merge in a single shell with
 M11  M22 
  

M
/

M
/
 1 1
2
2 
E in  M11  M22  M1  M2 c 2
The conversion efficiency of kinetic energy into internal energy

M1  M2  
 1 


M11  M22 
To get high efficiency 1>> 2 and M1=M2 only a fraction e
radiated max 20% can be radiated (Guetta et al. 2001) But the total
afterglow energy
~ burst energy! (Freedman and Waxman 2001)

Problem 1: Low efficiency of internal shocks
Internal shock radius
Let’s assume that a faster shell (2) impacts on a
slower the leading shell (1);
If t=tv is the average interval between two
pulses (interval between shells ejection)
d  ctv
2  1  0
ris  cd /(v 2  v1 )  2 d  2 ctv
2
1
2
1
 
ris  1013 cm(0 /100) 2 (t v /0.1s)

Emission properties determined
by ris
1
1 (v /c) 2
Light curves from internal shocks
Rapid variability and complexity of GRB lightcurves result of
emission from multiple shocks in a relativistic wind
t (interval between ejected shells) determines the
pulse duration and sepration:
IS reproduce the observed correlation between the duration of
the pulse (tp) and the subsequent interval (tp)
Numerical simulations reproduce the observed light curves
(Spada et al. 2000)
Spectrum of the prompt emission
Prompt emission observed has most of energy in 0.1-2 MeV
Generic phenomenological photon spectrum a broken power law
• Internal shocks are mildly relativistic, sh~a few,
particle acceleration in subrelativistic shocks. Electrons
are accelerated to a power law with energy distribution
dne
p
 e
d e
with p~2 and e> m
Electrons accelerated in magnetic field: synchrotron emission?
i.e. emission from relativistic electrons gyrating in
random magnetic fields

Fermi acceleration at shock
• Suppose to have a shock wave propagating in a medium where
energetic particles are already present.
• Shock is a wave propagating with v>vsound
• Density after (downstrem) and before (upstream) the shock is
2/1=+1/-1 where  is the politropic index of the gas. For a gas
completely ionized =5/3 and 2/1=4, v1/v2=4
Shocks
Shocks
Fermi acceleration at shocks
U=vu
Hot shocked
gas vu
eUnshocked gas vd=1/4vu
Consider the case of a shock propagating into cold gas at speed vu. In the shock
frame we see the unshocked gas ahead of us approaching at speed vu and the hot
shocked gas streaming behind us at speed vd=1/4 vu.
Consider now electrons initially at rest in the unshocked gas frame. They see the
shock approaching at vu but they also see the hot shocked gas approaching at 3/4
vu. As they cross the shock they are accelerated to a mean speed of 3/4 vu, as
viewed from the frame of the unshocked gas, and are also thermalized to a high
temperature. The clever part is next: consider what would happen if, as a result of
its thermal motion, an electron is carried back over the shock front. With respect to
the frame it has just come from the shocked gas frame it is once again accelerated
by 3/4 vu. The particle gain energy from the gas behind the shock.
Let us say the fractional change in kinetic energy at each crossing is β. After n
crossings, a particle with initial energy E0 will have energy E = E0βn. The particles
will not continue crossing the shock indefinitely: the net momentum flux of the
shocked gas downstream will carry them away in due course. So let us call the
probability of remaining in the shock-crossing region after each crossing P . Then
after n crossings there will be N = N0Pn of the original N0 electrons left.
Fermi acceleration at shocks
Fermi acceleration at shocks
Now we want to find k=-1+logP/log

E
= Energy gain aft er one collision
E0
E
u
T he average energy gain in one cycle is
2
where u is the discontinuity in the gas flux
E
c
velocity before and aft er the shock. T he average is on all incidence angles between particle and
E
4 u
4 u
4 3U
U

and   1
 1
 1
E
3 c
3 c
34 c
c
Now we need to find P:
number of particles that cross the shock
- number of part icles that go out from the shock
P=
number of particles that cross the shock
1/4N1c  u2 N 2
P
where N1 and N 2 are t he part icle densit ies before and aft er t he shock uand
2 is the
1/4N1C
velocity after the shock. Now,
the part icles are assumed to be relat ivistics and therefore they do
4u
U
not "see" the shock,i.e. N1  N 2 and P  1 2  1 . T hen:
c
c
log P
log 1 U /c
U /c


 1  k = -2
log 
log 1 U /c
U /c
shock:
Synchrotron emission
Both prompt emission and afterglow emission are clearly
non-thermal, and most natural process is synchrotron
emission, i.e. emission from relativistic electrons
gyrating in random magnetic fields.
For an electron with comoving energy emec2 and bulk
Lorentz factor  the observed emission frequency is:
=e2(eB/2 mec)
Motion of a particle in a magnetic field
• Gyro radiation is produced by electrons whose velocities are much
smaller than the speed of light: v<<c.
• Mildly relativistic electrons(kinetic energies comparable with rest
massXc2) emit cyclotron radiation.
• Ultrarelativistic electrons (kinetic energies >> rest massXc2) produce
synchrotron radiation.
Gyro radiation:
F  e(  B)
Force is perpendicular to particle velocity,
F  v  0. Separating
the v components along the field
v|| and in a plane perpendicular to the field
v :
a v|| v
v-
dv||
dv e
 0;

(v  B) i.e. v|| = constant. But since the total
v is constant,
dt
dt m c
then alsov = constant. T he solution of this equation is a uniform circular motion
of the projected motion on the normal plan,
since the acceleration in this plane is
normal to v and of constant magnitude. T he combination of this motion and of the
uniform motion along the field is a helical motion.
Motion of a particle in a magnetic field
In the inertial frame moving with velocit|| ,ythe
v particle
orbits in a circle perpendicular to t he magnet ic field wit h
the angular velocity needed to balance t he cent ripetal and
magnetic forces:
e
e
eB
m vÝ m 2 R  v  B  RB   L 
c
c
mc
 B 
L
4.8 1010  B
L 


2.8

MHz
28
10
Gauss
2 9.110  3 10  6.28
T he frequency of the emission is simply t he gyration
frequency. T herefore,Gyro radiation is observable only
in very st rong magnetic fields. An extreme astrophysical
example is the magnetic field of a neutron stBar, 1012
Gauss. For example,the binary X- ray source Hercules X-1
exhibits an X- ray absorption line at phot on energy~E34 keV.
Synchrotron emission
We can use Larmor's formula to calculate the synchrotron power and
synchrotron spectrum of a single electron in an inertial frame in which the
electron is instantaneously at rest, but we need the Lorentz transform of
special relativity to transform these results to the observer frame.
Power irradiated per unit solid angle
:
dP
e2 2 2

vÝ sin  where  is the angle between the emitted radiation ad the acceleration
3
d 4c
dP
2e 2 2
P 
d  3 vÝ
d
3c
T he Larmour formula must be generalized to relativistic motions. We must find an expressi
which is Lorentz invariant and that reduce to the classic expression above

for0
In this way,it is possible to calculate the total power radiated by an ultrarelativistic electron
magnetic field. We use primed coordinates to describe an inertial frame in which the electro
(temporarily) nearly at rest.
Synchrotron emission
During the helical motion let's consider the point when B is parallel to the x axis.
2e 2
2e 2
2e 2 Ý 2
Ý
2
2
P  3 (a )
P'  3 (a'  ) =
(
v
'
)
what
is
a'
or
v
' ?


3
3c
3c
3c
v' y
dy dy dt'
dy' dt'
dt'
vy 

but y'  y then vy 
 v' y

dt dt' dt
dt' dt
dt

dv
dv dt'
a'
a'
1 dv' y dt'
ay  y  y

 2 y and similarlyaz  2 z so
dt dt' dt  dt'
dt


B
2e 2
2e 2 2
2e 2 4
2
2
2
a  2  P'  3 (a'  ) 
(a
)
finally,
P'

P
then
P

(a
)



3c
3c 3
3c 3
[Demonst rat ion: Imagine t wo ident ical electrons of rest mass one
m, at rest in t he unprimed frame
and t he ot her at rest in t he primed frame. If one electron is slightly displaced from the other along
the y- axis, t hey will int eract as they pass each other and be accelerated in the y direction. Observe
at rest in each frame seetheir"
"
electron move wit h some small
v y << c , but the "ot her" electron will
a'

appear to move in the opposite y direction by a fact
 more
or slowly because of time dilation
—recall the result
v y = v' y / above. Invoking moment um conservation,
observers in each frame
conclude t hat theot
" her" electron has inert ial mass and hence its energy is greater by the same
me 
factor . T hus:
dE dE dt'
dE dE' dt'
1
P


 P'
P
i.e. the power is t he same in all frames.]
dt dt' dt
dE' dt' dt

Synchrotron emission
2e 2
2e 2 4
dv
dv
2
2
P' 3 (a' )  P 
(a
)
a

;
v


s





3c
3c 3
dt
dt
ds
    v  v sin 
where is the angle between v and
B
dt
eB

L 
  L Electrons st ill move on spiral paths along magnetic
mec

field lines, but the angular frequencies of their orbits are lower because the
inertial masses of t he electrons are higher by a factor
. T
ofhen:
2e 2 2 e 2 B 2 2 2
P
v sin   2 T  2 2cUB sin 2 
3
2 2
3c me c
2
8  e 2 
using:  T 


3 me c 2 
B2
and U B 
8
T he average synchrotron power per electron in an ensemble of electrons with t he same Lorent
factor but random pitch angles is t herefore
:
4
P  2 T  2 2cUB sin 2    T  2 2cUB
3
2
sin
d 1

1 2 
1
4 2
2
2
2
sin  

sin

d

sin

sin

d

d


2



   0
4

4

4

3
3
d

 0
Synchrotron spectrum
Our next problem is to explain how the synchrotron mechanism can yield radiation at
frequencies much higher than =L/. To solve it, we first calculate the angular
distribution of the radiation in the observer's frame.
In the non relativistic case P goes like sin2, where  is the angle between the
direction of the acceleration and the direction of the photons.
In the relativistic case, relativistic aberration causes the Larmor dipole pattern in the
electron frame to become beamed sharply in the direction of motion as v
approaches c. This beaming follows directly from the relativistic velocity
equations implied by the differential form of the Lorentz transform. For an
electron moving in the x direction:
In the y direction perpendicular to
the electron velocity, the velocity
formula gives:
Synchrotron spectrum
Consider the synchrotron photons emitt ed with speed c at an angle
' from the x'axis. Let v'x and v'y
be the projections of the phot on speed onto the
andx'y' axes. T hen:
v'
v'
cos ' x ; sin  ' y
c
c
In the observer frame for t he same photons we have
:
v
vx
; sin   y
and using the above eq. for the velocities we :get
c
c
 v'x v 1  c cos 'v 1 cos '
cos  
  
 
1

v'
/c
c
1

c
cos

'
/c

c 1  cos '


x
cos 
sin  
v'y
c (1 v'x /c)

sin  '
 (1  cos ')
In the frame moving with the electron,
the Larmor equation implies a power pattern proport ional
to cos2, with nulls at  /2. In the observer'
s frame, these nulls appear at much smaller angles
:
sin  
sin  '
1
 
 (1  cos ') 
Synchrotron spectrum
Relativistic beaming transforms the dipole pattern of Larmor radiation in the
electron frame (dotted curve) into a narrow searchlight beam in the
observer's frame. The solid curve is the observed power pattern for =5. The
observed angle between the nulls of the forward beam ~2/ , and the peak
power gain ~2 .
For example, a 10 Gev electron has ~20000 so 2/~ 20 arcsec! The
observer sees a short pulse of radiation emitted during only the tiny fraction:
2
2

1

of the electron orbit, when the electron is moving directly toward the
observer.

Synchrotron spectrum
T he beamed radiation for a relat ivist ic elect ron is visible
only while the electron velocity points within
 1/  of the
line of sight. T he particle will be visible only for a t ime
t 

,
v
where  is the radius of the orbit. Suppose that
 is large and
that the curvature is negligible,
then, the radiat ion emitted at
t1
t2

during the timet. During

t1
will travel a distance D= ct =
1/
the same time the distance travelled by t he electron is

. T herefore,the radiat ion emitted at
t 2 will travel a

   1
 1 
distance: D - x 
  ( 1)  (
)
   
 
x = vt 
t p  (D - x) /c 

1

2 3c 2 2
=
c

Synchrotron spectrum
T he duration of the pulse
t p 
1
is much shorted that the t ime needed by the electron t o mo
2 2
 1
the distancex : t  x /v  
v 
T he observed synchrot ron power spectrum
is the Fourier transform of this series of
pulses. A signal lastingt p has in general
harmonics up to a critical frequency
:
1
2 2  3c
c 


2t p
2


For    c the radiation will be emitt ed at angles
 1/  , thent p will no more be  t and
thereforet p will no more be a funct ion of
 . T he only residual t race of the dynamic of t he part ic
is the gyration radius. T he spectral distribution will be a function
e,c,of
 L . Because

c
is
e2
adimensional and has t he dimention of erg/s/hz
 L energy per unit time and frequency
:

L 
e2

f(

c
).
Synchrotron spectrum
 c
3
At  c L 
f(
) =
f( )

c
 2
e2
e2
c
but L c  L / c and L = 4/3 T c 2 2e 2 B 2 t herefore:
3
e 2  
f ( )   and L      2 / 3 1/ 3
2
  c 
1/ 3
i.e. quite a flat spectrum.
T his is the spect rum of one particle in relativist ic motion.
s now
Let' consider a volume V big in comparison
with the gyration radius and with the disomogeneit ies of the magnet ic field. In this case the emissio is
isotropic.
P 
 N
L d where N  k  p
V
P  V 1/ 3   2 / 3  p d
P  V 1/ 3 inf
now,  c 
if p  1/3 the integral is dominat ed by the lower extreme.
 p 1/ 3
c
2
 3   G  2 where  G 
c
2
  c inf   G  inf
2
  
  
 G 
1/ 2
for a    c inf follows t hat inf
P  V 1/ 3 inf
 p 1/ 3
and therefore:
( p 1/ 3)/ 2
p 1
p1


 


1/ 3
2 2
 V  
 Vv
 V 2
 G 
Extrapolating the power law at low frequency
the energy density would will increase until a
thermodinamic equilibrium will set, I.e. energy
equipartition: 3/2KT~mc2 . The electron
temperature will be proportional to  and
~(c/L)1/2 and therefore at each frequency
there will be a temperature T~ (c/L)1/2 .
Lets define the brightness temperature:
Tb=Fc2/ 2, the temperature for which if F is
given by the RJ formula (F~KT2) T=Tb. But we
are in this situation and therefore the spectrum
at low frequency is the RJ spectrum. The
difference with the BB is that in the BB T=const,
while in this case T~ (c/L)1/2 and therefore F~
 5/2.
Log l
Spectrum: Power Law + Self
Absorption
5/2
-(p-1)/2
Log 
Spectrum of the prompt emission
 E 3 / 2 E  E b
N(E)   1 p / 2
E  Eb
E
Characteristic frequency of synchrotron emission is determined
by m and B, Eb=hm=hm2eB/mec
The strength of the magnetic field is unknown, but its
energy density B2/8 is a fraction B of the internal energy.
B
2
2 2
B~1016-17 G more
U B  4R c B /8  B Lin  L
e
than a magnetar
1/ 2
L
E b 11/B 2e3 / 2 2  ,52 MeV
2.5t v,2

ris
As observed!
GRBs – 2 additional
Constraints with n(e)
=e2qeB/(2mec):
Below some frequency,
we are below the
minimum electron Lorentz
factor:
m=e(p-2)/(p-1) mp/me
Above a critical
frequency, the electron
loses a significant fraction
of its energy to radiation:
c=6mec/(TB2t)
Sari, Piran, & Narayan 1998
GRBs – 2 phases
mc:
All the electrons cool
down to c: fast
cooling.
Sari, Piran, & Narayan 1998
c>m:
Only electrons with
e>c can cool: slow
cooling.
Time Evolution
(4ct/L)1/7L
(4ct/L)-3/7
adiabatic radiative
• (t)=
(17E)1/8/
(1024mp
nc5t3)1/8
adiabatic radiative
• R(t)=
(17Et)1/4/
(4mpnc)1/4
Sari, Piran, & Narayan 1998
Time Evolution
c=2.7x1012B-3/2E52-1/2n1-1td-1/2Hz
m=5.7x1014B1/2e2E521/2td-3/2Hz
F,max=1.1x105B1/2E52n11/2
D28-2mJy
Sari, Piran, & Narayan 1998
c=1.3x1013B-3/2E52-4/724/7
n1-13/14td-2/7Hz
m=1.2x1014B1/2e2E524/72-4/7
n1-1/14td-12/7Hz
F,max=4.5x103B1/2E528/7n15/14
2-8/7D28-2td-3/7mJy
The Early Afterglow and
the Optical Flash
 The late afterglow observations confirmed relativistic
motion.
 But what is the value of  during the GRB phase?
 100 < 0 = E0/M0 < 105
 “dirty”
“clean”
 This could be tested
-rays
 by early afterglow
 observations (Sari &
 Piran: Rome, Oct 1998;
x-rays
 Astro-ph/11/1/1999):
optical
A very
strong
optical
flash
coinciding
with
the GRB
The Internal-External Fireball Model
-rays
Inner
Engine
Relativistic
Wind
Internal
Shocks
Afterglow
External
Shock
OPTICAL FLASH
Optical Flash Revisited
• Do internal shocks also predict prompt
bursts?
Predictions of
the Optical
Flash
Depending upon the
Exact details of the
Explosion (width of
Shock, structure of
Internal shocks in
Addition to all of the
Many Fireball free
Parameters)
Sari & Piran 1999
The Parameter space allowed for
Optical Flashes
Sari & Piran 1999
The amount of energy
In the optical flash
Varies over many
Orders of magnitude.
Prediction – depending
Upon the model, you
will/will not see the flash.
GRB 990123 - The
Prompt Optical Flash
ROTSE’s detection of a 9th magnitude prompt
optical flash.
Summary of GRB models
Fireball Model - Summary
• Thusfar, the fireball model has made very few
true predictions
• Current Favorite form of the Fireball model uses
internal and external shocks.
-rays
Inner
Engine
Relativistic
Wind
Internal
Shocks
Afterglow
External
Shock
Particles in a B-field radiate
Relativistic Particles
Psynchrotron = 2q2/3c3 4
q2B2/(2m2c2)vperp2
= 2/3 r02cperp22B2
where r0=e2/mc2
Isotropic velocities
B
perp2 =22/3
<
>
Psynch=4/3Tc22B2/(8)
where T=8r02/3 is the
Thompson Cross-Section
vpar
vperp
Fireball Model - Summary
• Basic Fireball model
simple – Relativistic
shocks with synchrotron
+ inverse Compton
emission
• Internal Shocks
produce optical burst
and gamma-rays,
External Shocks
produce afterglow
• Jets alter the spectra in
an observable way.
Jets Make a Sharp
Break in the light curve
* synch emission does not include the effects of cooling.
Observations place several
constraints on the Engine!
• Few times 1051 erg explosions (few foe)
• Most of energy in gamma-rays (fireball model
works if explosion relativistic)
• Rapid time variability
• Duration ranging from 0.01-100s
• Accompanied by SN-like bursts
• Occur in Star Forming Regions
• Explosion Beamed (1-10 degrees)
• …
With the fireball model, these
constraints are strengthened!
• Relativistic factors above 100!
• Some explosions must occur in windswept
media
• Some (all?) explosions are jets
GRB Engines
• Energy sources and conversion on earth and in
astrophysics
• Variability constraints – Compact object models
• With observational constraints, models now fall into
two categories:
I) Black hole accretion disk models (compact binary
merger, collapsar)
II) Neutron Star Models (magnetar, supranova)
Energy Sources: What Powers
These Explosions?
Energy Source: Gravitational
Potential Energy
Hydroelectric Power
Energy from Falling Water
Drives Turbines!
1-2000 MegaWatts
Hoover Dam - Arizona/Nevada
Diablo Canyon, CA
Nuclear
Energy
Breaking Bonds
Within the Atom
1) Fission
1,000 MWatts
Large Atom (e.g. Uranium)
Captures an Electron Causing
It to Become Unstable and
Break Apart.
Some Mass is Converted to Energy
E=Mc2
Nuclear Energy
II) Fusion
Combining Atoms To Form A Larger
Atom Can Also Release Energy!
Atomic Bomb –
Can Be Fusion
or Fission
Energy Conversion
Energy released through gravitational potential, chemical, or
nuclear sources must be converted into useful energy.
Useful = Electricity on Earth (to Most of Us)
Explosion Energy (to the Astronomy Observer)
This usually requires a mediator – something to transport
the energy:
Magnetic Fields – e.g. a Dynamo
Radiation – e.g. Photons (light), Neutrinos
Magnetic
Dynamo
Water (Accelerated by
Gravity Or Thermal
Pressure) Spins
Large Magnets.
The Motion Of the
Magnets Drives an
Electric Current
-- Electricity!
Radiation
Photons (Light) or Neutrinos
Can Transport Energy
Nuclear Energy
Released in the Sun
Must Make Its Way
Out of the Sun Via
The Transport of
Light or Neutrinos.
Energy Sources
• Chemical – rarely important
in astrophysics
• Nuclear Physics – Stars,
Type Ia Supernovae, X-ray
Bursts
• Gravitational Potential
Energy – All other
supernovae, X-ray Binaries,
Pulsars (neutron star spin
arises from potential energy)
and, for most theories,
GRBs!
Garcia-Senz et al. 1999
Energy Sources
Helium Detonation on NS
• Chemical – rarely important
in astrophysics
• Nuclear Physics – Stars,
Type Ia Supernovae, X-ray
Bursts
• Gravitational Potential
Energy – All other
supernovae, X-ray Binaries,
Pulsars (neutron star spin
arises from potential energy)
and, for most theories,
GRBs!
Zingale et al. 2001
Energy Sources
• Chemical – rarely important
in astrophysics
• Nuclear Physics – Stars,
Type Ia Supernovae, X-ray
Bursts
• Gravitational Potential
Energy – All other
supernovae, X-ray Binaries,
Pulsars (neutron star spin
arises from potential energy)
and, for most theories,
GRBs!
Fryer & Heger 1999
Energy Sources
• Chemical – rarely important
in astrophysics
• Nuclear Physics – Stars,
Type Ia Supernovae, X-ray
Bursts
• Gravitational Potential
Energy – All other
supernovae, X-ray Binaries,
Pulsars (neutron star spin
arises from potential energy)
and, for most theories,
GRBs!
Energy Sources
• Chemical – rarely important
in astrophysics
• Nuclear Physics – Stars,
Type Ia Supernovae, X-ray
Bursts
• Gravitational Potential
Energy – All other
supernovae, X-ray Binaries,
Pulsars (neutron star spin
arises from potential energy)
and, for most theories,
GRBs!
Energy Sources
• Chemical – rarely important
in astrophysics
• Nuclear Physics – Stars,
Type Ia Supernovae, X-ray
Bursts
• Gravitational Potential
Energy – All other
supernovae, X-ray Binaries,
Pulsars (neutron star spin
arises from potential energy)
and, for most theories,
GRBs!
GRB Energy Sources
Energy Needed: ~1052 erg
Of useful energy (not leaked
Out in neutrinos or
Gravitational waves or
Lost into a black hole)!
Most GRB Models invoke
Gravitational potential energy
As the energy source.
Collapse to a NS or stellar
Massed BH most likely source
E = G M2/r
1-10 solar masses
3-10 km
E=1053-1054 erg
Allowing a 1-10%
Efficiency!
Gamma-Ray Burst Durations
Two Populations:
Short – 0.03-3s
Long – 3-1000s
Possible third
Population
1-10s
Burst Variability
Not only must any model
Or set of models predict
A range of durations,
But the bursts must also
Be rapidly variable!
Burst Variability on
the <10-100
Millisecond level
Durations and Variabilities
Variability =
size scale/speed of light
Again, Neutron Stars and
Black Holes likely
Candidates (either in an
Accretion disk or on the
NS surface).
2  10km/cs = .6 ms
cs = 1010cm/s
NS,
BH
Durations and Variabilities
Duration = Rotation
Period / Disk Viscosity
( = 0.1-10-3)
Period = 2 r3/2/G1/2MBH1/2
= .3 ms near
BH surface
Duration for small disks –
3-300ms
NS,
BH
Harnessing the Accretion Energy
Mechanism I:
Neutrinos from hot
disk annihilate
Above the disk –
Producing a
Baryon-poor,
High-energy jet
Mechanism II:
Magnetic fields are
Produced by
Differential rotation
In the disk. This
Magnetic field
produces a jet.
Accretion
Disk
Details Lecture 5
Neutrino Driven Jets
Neutrinos from accretion disk deposit their energy above
the disk. This deposition can drive an explosion.
Disk Cools via Neutrino
Emission
Densities above 1010-1011 g cm-3
Temperatures above a few MeV
Neutrino Driven Jets
e+,e- pair plasma
Neutrino
Annihilation
Disk Cools via Neutrino
Emission
Densities above 1010-1011 g cm-3
Temperatures above a few MeV
Neutrino Summary
• Critical Densities for most-likely accretion
disks: 104-108 g/cm3
• For Collapsars type I, this corresponds to
black hole masses of 10-25 Msun and delays
between collapse and jet of 30-300s. Does
the neutrino-driven Collapsar type I model
work?
• Alternatives – magnetic fields, Collapsar type
II (MacFadyen & Woosley 1999)
Magnetic Field Driven Jets
“And then the theorist raises his magic…. I mean
magnetic wand… and viola, there are jets” Shri Kulkarni
Lots of Mechanisms proposed, but most boil down
to a reference to the still unsolved mechanism
behind the jet mechanism for Active Galactic
Nuclei (Generally the Blandford-Znajek
Mechanism).
We are extrapolating from a non-working model –
dangerous at best.
Magnetic Field Mechanism –
Sources of Energy
• Source of
Magnetic Field –
Dynamo in
accretion disk.
• Source of Jet
Energy I) Accretion Disk
II) Black Hole
Spin
Magnetic Dynamos
• Duncan & Thompson (1993): High
Rossby Number Dynamo (convection
driven) – Bsat~(4vconvective2)1/2
• Akiyama et al. (2003): Shear-driven
Dynamo – Bsat2~(4r22(dln/dlnr)2
• Popham et al. (1999): Disk Dynamo –
Bsat2~(4vtot2)
Schematic Cross-Section of a black hole and magnetosphere
The poloidal field is shown in solid lines, typical particle velocities
are shown with arrows. In the magnetosphere, spark gaps (SG) form
that create
electron/
positron
pairs.
Blandford & Znajek 1977
Electromagnetic structure
of force-free magnetosphere
with (a) radial and (b) paraboloidal magnetic fields.
For paraboloidal fields, the
Energy appears to be
Focused alonge the rotation
Axis.
“The overall efficiency of
Electromagnetic energy
Extraction from a disk
Around a black hole is
Difficult to calculate with
Any precision”
Blandford & Znajek (1977)
Magnetic Jet Power
• Blandford-Znajek: L~3x1052 a2 dM/dt erg/s
with B~2x1015(L/1051 erg/s)1/2 (MBHa)-1
• Popham et al. 1999 (Based on BZ):
L~1050a2(B/1015G)2 erg/s, B~v2 where
~1%
• Katz 1997 (Parker Instability):
L~1051(B/1013G)(/104s-1)5(h/106cm) (r/1013g
cm-3)-1/2(r/106cm)6 erg/s
Magnetic Field Summary
• Magnetically driven jets could possibly
produce much more energy than neutrino
annihilation (easily enough for GRBs). If it
works for AGN, it must work for GRBs.
• Most estimates extrapolate from an already
faulty AGN jet model. No “physics”
calculation or derivation has yet to be made.
Black Hole Accretion Disk Models
Collapsar (aka
hypernova:
Supernova explosion of a
very massive (> 25 Msun)
star
Iron core collapse
forming a black hole;
Material from the outer
shells accreting onto
the black hole
Accretion disk =>
Jets => GRB!
Collapsars
Observations
Explained
• Energetics
explained
• Duration and
variability explained
Observations
Predicted
• SN-like explosions
along with GRB
outburst
• Bursts occurring in
star forming regions
• GRB Beaming
Massive Star Models
With the observations pushing toward
massive stars, a number of other
massive star models appeared –
pushing for neutron star mechanisms!
• Explosions from Magnetars
• Supranova (neutron star which later
collapses to a black hole)
Supernovae/Hypernovae
Nomoto et al. (2003)
EK
Failed SN?
13M~15M
Supranova Model For
GRBs:
If a neutron star is rotating
extremely rapidly, it could escape
collapse (for a few months) due to
centrifugal forces.
Neutron star will gradually slow
down, then collapse into a black
hole => collapse triggers the GRB
Disadvantages of the Supranova
Model
Mass thing…
Duration can’t be
Longer than 3-3000ms
NS,
BH
Disadvantages of the Supranova
Model
Duration = Rotation
Period / Disk Viscosity
( = 0.1-10-4)
Duration can’t be
Longer than 3-3000ms
Current bursts with
Iron lines are all
Long-duration!
NS,
BH