# Presentation: 115236

## From Observations to the Central Engine

- Lecture 3:  The Fireball Model – C.Fryer (UA/LANL)

## What have we learned from Afterglows?

- GRBs are in Star Forming Galaxies

## What have we learned from Afterglows?

- GRBs are in Star Forming Galaxies
- GRBs occur in dusty (star-forming?) regions

## What have we learned from Afterglows?

- GRBs are in Star Forming Galaxies
- GRBs occur in dusty (star-forming?) regions
- GRBs trace the stellar distribution

## What have we learned from Afterglows?

- GRBs are in Star Forming Galaxies
- GRBs occur in dusty (star-forming?) regions
- GRBs trace the stellar distribution
- Burst move through wind-swept media

## What have we learned from Afterglows?

- GRBs are in Star Forming Galaxies
- GRBs occur in dusty (star-forming?) regions
- GRBs trace the stellar distribution
- Burst move through wind-swept media
- Bursts include SN-like outbursts

## What have we learned from Afterglows?

- GRBs are in Star Forming Galaxies
- GRBs occur in dusty (star-forming?) regions
- GRBs trace the stellar distribution
- Burst move through wind-swept media
- Bursts include SN-like outbursts
- Bursts have few foe

- Explosion energies and are beamed to a few percent

- 15 events with z and t_jet

## Most SNe are not GRBs (but GRBs may all produce SNe)

- VLA/ATCA survey of 34 Type Ib/c SNe to detect off-axis GRBs via radio emission

- Berger PhD

- Most nearby SNe Ib/c do not have relativistic ejecta
- Two distinct populations
- Ek(GRB)<<1 foe (hydo collapse)
- <10% are 1998bw-like

## GRBs as Cosmology Probes

- Binary Mergers

- Collapsars

## From Observations to the Central Engine

- History of the Fireball Model :  prediction vs. postdiction, external shock vs. internal shock Fireball model
- Fireball Shock Basics:  relativistic flows, synchrotron radiation, comparing to GRB spectra
- Optical Bursts
- Jets

## 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

- 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
- Assumes a relativistic
- Outburst and works
- With a variety of
- Mechanisms.
- We rely heavily on
- A review by Tsvi
- Piran.

##    The Fireball Model

-  compact source

- Relativistic Particles
- >100
- or Poynting flux

- ~ 107 cm

- Goodman; Paczynski;                                      Shemi  & Piran,
- Narayan, Paczynski & Piran;                           Meszaros & Rees

## 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 gamma-rays 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”!)

## A NO GO THEOREM

- External shocks cannot produce a variable light curve!!!
- (Sari & Piran 97)

- Fireball Theorists then found a lot
- Wrong with the external shock model!

## Time to Revise the Theory

- Gamma-rays and Afterglow arise from  different sources
- Birth of the Internal Shock Model

## Internal Shocks

**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.**_ _

**Internal Shocks**
**Shocks between different shells of the ejected relativistic matter**

**T**

****

## Internal Shocks Afterglow

-      **(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)**

**Internal ****Shocks ********Afterglow**

## 1) Compact Source,  E>1051erg
2) Relativistic Kinetic Energy
3) Radiation due to Internal shocks = GRBs

4) Afterglow by external shocks

     The Central Compact Source is Hidden

**2) Relativistic Kinetic Energy**
- 3) **Radiation due to Internal shocks = GRBs**
**4) Afterglow by external shocks**
-      **The Central Compact Source is Hidden**

- Gamma-Ray Burst:  **4** Stages

- Plus burst of optical emission!

## The Internal-External Fireball Model

**The Internal-External Fireball Model**

## THE FIREBALL MODEL PREDICTED GRB AFTERGLOW (late emission in lower wavelength that will follow the GRB)

- Rhodes & Paczynksi, Katz, Meszaros & Rees, Waxman, Vietri, Sari & Piran

- Postdicted

## 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.

## Physics of GRB Observations under the Internal Shock Model

- Basic Model (relativistic shock with synchrotron emission)
- Relativistic flows and Sedov analysis
- Synchrotron Radiation and GRB spectra

## Afterglow Theory

- Hydrodynamics: **deceleration of the**
**relativistic shell by collision with the surrounding medium** **(Blandford & McKee 1976)**** **
**(Meszaros & Rees 1997, Waxman 1997, Sari 1997, Cohen, Piran & Sari 1998)**** **
- Radiation: synchrotron + IC (?)
**(Sari, Piran & Narayan 98)**
- Clean, well defined problem.
- Few (?) parameters:E, n, p, e, B

## Sedov Explosion (non-relativistic dimensional analysis)

- [r]=cm where r is the shock radius
- [t]=s where t is the time
- [E]=g cm2 s-2 where E is the explosion energy
- []=g cm-3 where  is the density:  = 0r

- Primary Units:

## Sedov Continued

- [r]=[E/]1/5[t]2/5=[E/0]1/5r/5t2/5
- r (1-/5) ~ (E0/0)1/5t2/5
- r ~ (E0/0)1/(5-)t2/(5-)
- v = dr/dt = (E0/0)1/(5-) 2/(5-) t(-3)/(5-)
-    = v0(t/t0)(-3)/(-5)

## Sedov for Relativistic Flows

-   = C [1(r)rN+1]-a, where N=0,1,2 for plane, cylindrical, and spherical shocks, respectively.  For decelerating shocks [m(r)=-dln1(r)/dlnr<N+1], a=1/2, for accelerating shocks [m(r)>N+1],a=1/5
-  =2/(3+N)[E/1(r)c2]1/2r-(N+1)/2, for accelerating shocks (m(r)<N+1), where a=a(N,,) is the similarity constant: (2,4/3,   ) =0.237 for an ultra-relativistic shock, while (2,5/3,1)=0.603 for a non-relativistic shock.
-  =minmin[1(r1)/1(r) (r1/r)N+1]1/5 for m(r)>N+1 (e.g. constant density)

- 8

- Gnatyk 1985

## What do Fireball Theorists use?

-  =const r-g = const t-g/(1+2g)
- r = const t1/(1+2g)
- Where g is (3,3/2) for the radiative, adiabatic regime (assuming constant density).  This is different than what we would expect for a constant density solution from Gnatyk but agrees with Gnatyk’s accelerating solution.  Fireball Theorists are making the assumption that they are in the ultra-relativistic limit.

## Comparison with Observations(Sari, Piran & Narayan 98; Wijers & Galama 98; Granot, Piran & Sari 98; Panaitescu & Kumar 02)          

**Radio observations**

**Radio to X-ray**

## Synchrotron Radiation – Basics (see, for example, Rybicki & Lightman)

- Synchroton radiation – relativistic particles accelerated in a magnetic field
- d/dt(m**v**)=q/c **v**x**B**
- d/dt(mc2)=q**v****.****E**=0           =constant
- d**v**par/dt =0, d**v**perp/dt=q/(mc) **v**perpx**B**
**           ****|v**par**| **= constant**          |v**perp**|**=constant

## Power from Accelerated Particles – Synchrotron Cont.

- Relativistic Particles
- P = 2q2/3c3(a’perp2+a’par2)
-     (convert to observer’s frame and set apar=0)
-    = 2q2/3c3 4 (aperp2)
- Psynchrotron = 2q2/3c3 4 q2B2/(2m2c2)vperp2

**B**

**v**perp

**v**par

## Power from Accelerated Particles – Synchrotron Cont.

- Relativistic Particles
- Psynchrotron = 2q2/3c3 4 q2B2/(2m2c2)vperp2
-     = 2/3 r02cperp22B2
-    where r0=e2/mc2
- Psynch=4/3Tc22B2/(8)
-   where T=8r02/3 is the Thompson Cross-Section

**B**

**v**perp

**v**par

- Isotropic velocities

- <perp2>=22/3

## Synchrotron Spectra

- P()=(3/2)1/2q3Bsin/(mc2) F(/c)
- Where c=32qBsin/(2mc)

******-1**

- Radiation is beamed with
- an opening angle = -1

- Spectral shape depends only on
- the frequency of gyration.

## Spectrum from Power-Law Electron Distribution

- Assume N(E)dE=CE-pdE, E1<E<E2
- Ptot() is the proportional to the integral of F(c)-pd
- xc, =c1x1/2, d=c2x-1/2dx
- Ptot() = C-(p-1)/2

- Log 

- Log l

- -(p-1)/2

## Spectrum:  Power Law + Self Absorption

- Self Absorption occurs when a photon interacts with a charge in magnetic field.  This process is related to stimulated emission through Einstein coefficients.
- A21=2h3/c2 B21
- Assumes thermodynamic equilibrium.

- Kirchhoff’s law related emission to absorbtion in a thermal emiiter:  j=B
- A21=transition probability per unit time for spontaneous emission
- B12**J**=transition probability per unit time for absorption where J is the integral of the flux times the line profile.
- B21**J**=transition probablity per unit time for stimulated emission.

## Spectrum:  Power Law + Self Absorption

- =h/(4)[n(E1)B12-n(E2)B21]21()
- P(,E2)=hA2121() = (2h3/c2)hB2121()
- =c2/(8h3)[n(E2-h)-n(E2)]P(,E2)
- With some work, we get:
- Source Function =P()/4=C5/2

- Log 

- Log l

- -(p-1)/2

- 5/2

## Spectrum:  Power Law + Self Abs. + Bound Free Absorption

- At even lower energies, bound-free absorption can change the slope yet again.
- Thermal Emission in an optically thick region.
- bf=D-3

- Log 

- Log l

- -(p-1)/2

- 5/2

- 2

## GRBs – 2 additional 

- 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.
- c>m:
- Only electrons with e>c can cool:  slow cooling.

- Sari, Piran, & Narayan 1998

## 
R(t)=

 (t)=

- R(t)=
-  (t)=

- Time Evolution

- (17Et)1/4/
- (4mpnc)1/4

- (4ct/L)1/7L

- adiabatic

- radiative

- (17E)1/8/
- (1024mp
- nc5t3)1/8

- (4ct/L)-3/7

- adiabatic

- radiative

- 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
-           D28-2Jy

- 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-3/7Jy

- Sari, Piran, & Narayan 1998

## 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 ****= E****0****/M****0**** < 10****5**
**“****dirty”                 “clean”**
**This could be tested **
**by early afterglow **
**observations**** ****(Sari & **
** ****Piran: Rome, Oct 1998; **
**Astro-ph/11/1/1999):**

## The Internal-External Fireball Model

**The Internal-External Fireball Model**

- Internal
- Shocks

- -rays

## 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

- 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.

- Sari & Piran 1999

## GRB 990123 - ThePrompt Optical Flash

- ROTSE’s detection of a 9th magnitude prompt optical flash.

## Moving away from Spherical Symmetry

- GRB engines predict jets, not spherical explosions
- What are the consequences on the fireball model
- Do these consequences affect the observations

## GRB Energies

- Etot - The total energy
- E-Observer  ray energy

##  The  Resolution of the Energy Crisis

- Etot - The total energy
- Eiso-Observed (iostropic) ray energy

## JETS and BEAMING

- Jets with an opening angle ****** **expand forwards until ************ and then expand sideways rapidly lowering quickly the observed flux **(Piran, 1995; Rhoads, 1997; Wijers et al, 1997; Panaitescu & Meszaros 1998).**

********

- Particles remain
- within initial cone

- Radiation is
- “beamed” into
- a narrow cone

## Jets – Predicted by 

- Jets – Predicted by
- the Collapsar Model

- m=C

- t-2, jet

- t-3/2, spherical

- c=C

- const, jet

- t-1/2, spherical

- Fmax=C

- t-1, jet

- const, spherical

- a=C

- t-1/5, jet

- const, spherical

- Sari, Piran, & Halpern 1999

## Jets – Predicted by 

- Fa=C

- const, jet

- t1/2, spherical

- Jets – Predicted by
- the Collapsar Model

- Fa<<m=C

- t-1/3, jet

- t1/2, spherical

- Fm<<c=C

- t-p, jet

- t-3(p-1)/4, spherical

- Fa<<m=C

- t-p, jet

- t-3p/4+1/2, spherical

- Sari, Piran, & Halpern 1999

## A Sharp (Not Achromatic) Break!

*** ****synch emission does not include the effects of cooling.**

## 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.

## Fireball Model - Summary

- Basic Fireball model simple – Relativistic shocks with synchrotron + inverse Compton emission

## 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.

## References

- Blast Wave Overview:  P. Meszaros, Annual Review of Astronomy and Astrophysics, 2002, 40, 137
- Relativistic Blast Waves for GRBs:  Tan, Matzner & McKee 2001, ApJ, 551, 946
- GRB Spectra and Light Curves:  Sari, Piran, & Narayan 1999, ApJ, 497, L17
- GRB Spectra and Light Curves:  E. Waxman 197, ApJ, 485, L5
- GRB Jet Spectra and Light Curves: Sari, Piran & Halpern 1999, ApJ, 519, L17

## Tomorrow – Past and Current Models of the Central Engine

- Energy Sources in Astrophysics
- Arguments for compact objects
- Black hole models (Collapsar and compact binary mergers) versus magnetar (highly magnetized neutron star) models.