# Presentation: 760006

## GRB Engines:  Past and Current Models

- Lecture 4:  Using fireball constraints to determine true engine – C. Fryer (UA/LANL)

## Sedov Solution Useful – Relativistic version needs some tuning

- [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)

## 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
- Question on m: m determined simply by assuming a constant fraction of the shock energy goes into electrons.

## Particles in a B-field radiate

- 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

## 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?

## Occam’s Razor

*“**Pluralitas non est ponenda sine neccesitate*m”
-     “Plurality should not be posited without necessity”
-                  - William of Ockham

- “We are to admit no more
- causes of natural things than
- such as are both true and sufficient to explain their appearances."
-                              - Isaac Newton

- All Saints Church, Ockham

- Corollary:  Don’t invent new physics unless you need it!

## Energy Source:  Gravitational Potential Energy

- Hydroelectric Power

- Energy from Falling Water
-       Drives Turbines!

- Hoover Dam - Arizona/Nevada

- 1-2000 MegaWatts

## Chemical Energy

- Ames, Iowa ~500MW
- Refuse Derived
- Fuel and Coal
- Fired Power
- Plant

- Reforming Bonds in Molecules
- Tighter Configurations give off Energy

## Nuclear Energy

- Breaking Bonds
- Within the Atom
- 1) Fission

- Diablo Canyon, CA

- 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

- Nuclear Energy
- Released in the Sun
- Must Make Its Way
- Out of the Sun Via
- The Transport of
- Light or Neutrinos.

- Photons (Light) or Neutrinos
- Can Transport Energy

## Radiation

- Solar Power Plant – Mojave Desert

- Photo-Cells

- Light from the sun travels to the Earth where we convert it
- To Electricity.

## 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!

- Garcia-Senz et al. 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!

- Helium Detonation on NS

- 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

- E = G M2/r
- 1-10 solar masses
- 3-10 km
-      E=1053-1054 erg
- Allowing a 1-10%
- Efficiency!

- 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

## Gamma-Ray Burst Durations

- Two Populations:
-   Short – 0.03-3s
-   Long – 3-1000s
- Possible third Population
- 1-10s

## Burst Variability

- Burst Variability on
- the <10-100
- Millisecond level

- Not only must any model
- Or set of models predict
- A range of durations,
- But the bursts must also
- Be rapidly variable!

## Durations and Variabilities

**NS,**
**BH**

- 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

## Durations and Variabilities

**NS,**
**BH**

- 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

## Black Hole Accretion

- Disk Models:
- Material accreting
- Onto black hole
- Through disk
- Releases potential
- Energy.  If this
- Energy can be
- Harnessed to
- Drive a relativistic
- Jet, a GRB is
- formed.

## Harnessing the Accretion Energy

- Accretion
- Disk

- 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.

- Details Lecture 5

## Black-hole – neutron-star merger (NS-NS Mergers):

- _Black-hole – neutron-star merger (NS-NS Mergers):_

- Black hole and neutron star (or 2 neutron stars) orbiting each other in a binary system

- Neutron star will be destroyed by tidal effects; neutron star matter accretes onto black hole

- Accretion disk

## NS/BH (NS/NS) Mergers

- Advantages
- Progenitors known (e.g. Hulse-Taylor Pulsar system)
- Energetics and rate roughly correct

-   Disadvantages
- Size of disk 10-30km – Duration <1s: not a working model for long-duration bursts
- Many predictions don’t match afterglow era science.

## 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)

## Magnetic NSs in Collapse

- With the SN/GRB association, Wheeler and collaborators sought a new GRB mechanism arguing that all supernovae produce GRBs
- During Collapse, magnetic fields grow in proto-neutron star.

## Magnetic NSs in Collapse – Cont.

- Using a pulsar-like mechanism (magical/magnetic fields strike again), Wheeler argued that this fast-spinning, newly born, neutron star will produce jets in most stellar collapses.

## Advantages of Magnetic NSs in Collapse 

- Supernovae do not appear symmetric!

## Advantages of Magnetic NS models – Polarization

- Supernovae are polarized.
- Polarization Increases with time (implying that we are uncovering a central engine that is asymmetric).
- Wheeler and collaborators argue that all supernovae (or maybe just all Ib/Ic supernovae) have jets – only a fraction are observed as GRBs!

## Problems with the Magnetic NS model 

- Magnetic Field Model requires very strong magnetic fields!  Only shown to work with hand-wavy approximation.
- SN spectra are different than the SN-like spectra in GRBs and hypernovae.

- Hungerford et al. 2003

- Nickel distribution from
- asymmetric explosion

## Problems with the Magnetic NS model:  SNe vs. SN-like outbursts – spectra different!

- Ia

- Ic

- Ib

- 94I

- 97ef

- 98bw

- He

- Ca

- O

- SiII

- Hyper  -novae

**Hypernovae**:
-   _broad features_
- _  _
-   blended lines
-   “_Large mass_ at _high velocities_”

**Ic**: no H,
-      no strong He,
-      no strong Si

## Problems with the Magnetic NS model 

- Magnetic Field Model requires very strong magnetic fields!  Only shown to work with hand-wavy approximation.
- SN spectra are different than the SN-like spectra in GRBs and hypernovae.
- Why do we get 3 branches of supernova energies?

- Hungerford et al. 2003

- Nickel distribution from
- asymmetric explosion

## Supernovae/Hypernovae

**Supernovae/Hypernovae**

- Nomoto et al. (2003)

- Failed SN?

- 13M~15M

*E*K

## But Most Supernovae are not GRBs!!!!!  Death

- Of the Pulsar Model for GRBs

- Radio shows
- A definite
- Break between
- GRBs and
- Normal type
- Ib/Ic SNe!
- At Most, 5%
- Of supernovae
- Are GRBs
- (Berger et al.
- 2003).
- Must be right,
- Done by
- GRB observers!

## 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

## Advantages of the Supranova Model

- GRB occurs after supernova explosion
- Iron produced in supernova can then be lit up by gamma-ray burst – producing iron lines!
- Iron lines observed!

- X-ray spectrum of GRB010220
- From XMM-Newton.
- The solid line shows a power
- Law fit, the residuals to this
- Fit indicate, to some, the
- Presence of an emission line.

## Iron Lines hard to Explain with Collapsar Model

- Bottcher et al. (1999,2001) tried to explain these lines using the excretion disk of a binary merger in the collapsar model.

## Iron Lines hard to Explain with Collapsar Model

- Although they could produce iron lines, they could not produce iron lines that survived long enough to explain all observations – Supranova model can easily explain all iron lines.

## But are these iron lines real?  If not, the supranova has no real advantage over the collapsar model.

- Analysis
- by  Bob
- Rutledge
- (McGill)
- suggests
- This line
- Can be
- Explained
- Away as Noise!

## Disadvantages of the Supranova Model

**NS,**
**BH**

- Mass thing...
- Duration can’t be
- Longer than 3-3000ms

## Disadvantages of the Supranova Model

**NS,**
**BH**

- 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!

## The straw that broke the camel’s back – observations (not physics)!

- In the supranova model, the supernova explosion should occur months before the GRB
- Observations (again limited to long-duration bursts) find that the supernova-like explosion occurs alongside the GRB.

- http://www-cfa.harvard.edu/~jbloom/valencia

## Summary of Burst Models

- NS/NS, BH/NS Mergers – Durations too short for long-duration GRBs
- Pulsar-like, Magnetar models – although favored for Soft gamma-ray repeaters (SGRs), predicts that most SNe are GRBs – a prediction proved false by observations
- Supranovae predict that the SN outburst occurs BEFORE GRB – also disproved by observations (hard to explain long-duration bursts in any event).
- Collapsar – Still the Favored Model

## Energy Sources

- Two Main Energy Sources
- In Astrophysics
- Gravitational Potential
- Energy
- II)    Nuclear Energy

## Energy Transport

- Radiation (photons, neutrinos)

## Energy Transport

- Radiation (photons, neutrinos)
- Magnetic Fields

## Variabilities of GRBs limits models to compact objects (NS, BH)

**NS,**
**BH**

- 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

## Black Hole Accretion 

- Black Hole Accretion
- Disk Models:
- Compact Mergers
- And collapse of
- Stars.

## Neutron Star Models

- Magnetar Models – ruled out because most supernovae do NOT produce GRBs.
- Supranova models – ruled out for long-duration bursts by duration times

## Tomorrow- Black Hole Accretion Disks

- Structure of a Relativistic Disk
- Neutrino Driven Explosions from a Black Hole Accretion Disk
- Magnetic Field Driven Explosions from a Black Hole Accretion Disk