The Central Engine forGamma-Ray Bursts

S. E. Woosley (UCSC)

Alex Heger (UCSC/Chicago)

Andrew MacFadyen (UCSC/CIT)

Weiqun Zhang (UCSC)

Woods Hole GRB Meeting: Nov. 6, 2001

Requirements on the Central Engineand its Immediate Surroundings

(long-soft bursts)

• Provide adequate energy at high Lorentz factor

• Collimate the emergent beam to approximately 0.1 radians

• In the internal shock model, provide a beam with rapidly variable Lorentz factor

• Allow for the observed diverse GRB light curves

• Last approximately 10 s, but much longer in some cases

• Explain diverse events like GRB 980425

• Produce a (Type Ib/c) supernova in some cases

• Make bursts in star forming regions

Frail et al. ApJL, (2001), astro/ph 0102282 Despite their large inferredbrightness, it is increasingly believed that GRBs are notinherently much more powerfulthan supernovae.

From afterglow analysis, thereis increasing evidence for asmall "beaming angle" and a common total jet energy near3 x 1051 erg (for a conversionefficiency of 20%).

See also: Freedman & Waxman, ApJ, 547, 922 (2001)

Bloom, Frail, & Sari AJ, 121, 2879 (2001)

Piran et al. astro/ph 0108033

Panaitescu & Kumar, ApJL, 560, L49 (2000)

Minimum Lorentz factors for the burst to be opticallythin to pair production and to avoid scattering by pairs.

Lithwick & Sari, ApJ, 555, 540, (2001)

200

Merging neutron star - black hole pairs

Strengths: a) Known event b) Plenty of angular momentum c) Rapid time scale d) High energy e) Well developed numerical models

Weaknesses: a) Outside star forming regions b) Beaming and energy may be inadequate for long bursts c) Uncertain disk physics

Needed: a) Locations of short hard bursts b) Calculations that include jet formation c) Better understanding of disk physics

(Ruffert – this session; Rosswog – poster; Salmonson – poster Lee - poster)

Magnetar Birth

Strengths: a) Star forming regions b) Supernova association c) Magnetars exist d) Sufficient energy if a milliseond pulsar is formed

Weaknesses: a) Requisite dipole field strengths very high b) Model still very qualitative; what holds up the accreting star while the neutron star deposits its energy?

Needed: more work

Wheeler et al, ApJ, 537, 810, (2000)

Black Hole - He-CoreMergers

Strengths: a) Plenty of angular momentum b) Star forming regions c) High energy

Weaknesses: a) Is star's envelope really ejected in the merger? b) Long time scale (>100 s?) c) No calculations of jet formation d) Disk physics uncertain, not neutrino dominated Needed: Calculations to address all of above

Zhang & Fryer, ApJ, 550, 357, (2001)

Collapsars

Strengths: a) Found in star-forming regions b) Large sustained accretion rates c) Form jets naturally d) Detailed numerical models e) GRB makes supernova f) Can be a common occurrence

Weaknesses: a) Is there enough angular momentum? b) Hard to make short bursts c) Uncertain disk physics

Needed: a) Realistic evolution of stars including magnetic torques b) Better simulations of the full event c) Better understanding of disk physics

(MacFadyen – this session)

Collapsar Progenitors

Two requirements:

• Core collapse produces a black hole - either promptly or very shortly thereafter.

• Sufficient angular momentum exists to form a disk outside the black hole (this virtually guarantees that

the hole is a Kerr hole)

Fryer, ApJ, 522, 413, (1999)

With decreasing metallicity, the bindingenergy of the core and the size of the silicon core both increase, making black hole formation more likely atlow metallicity. Woosley, Heger, & Weaver, RMP, 2002 accepted.

Black hole formation may be unavoidable for low Z

Solar metallicity

Low metallicity

The real problem is the angular momentum ...

In the absence of mass lossand magnetic fields, there wouldbe abundant progenitors.

Unfortunately nature has both.

Heger and Woosley - poster paper and in preparation for ApJ.Joss – this session; Wijers – poster paper

15 solar mass helium core born rotating rigidly at f times break up

Ways to improve the situation.

• Use metal deficient stars. These are both more likely to implode to black holes and lose less angular momentum to winds. Max He-core at death for single solar metallicity stars is 11 Msun. For 0.3 solar metallicity stars, it may be 20 Msun. But too small a metallicity can also keep single stars from making GRBs

• Use binary systems - either common envelope mergers after one or both stars are already highly evolved or perhaps tidally induced co-rotation (Joss this session, Heger - poster)

• Find reasons that the magnetic torques may have been overestimated by Spruit, A&A in press, astro/ph-0108207

Some implications ....

• The production of GRBs may be favored in metal- deficient regions, either at high red shift or in small galaxies (like the SMC). The metallicity- dependence of mass loss rates for RSGs is an important source of uncertainty. (Kudritzsky (2000); Vink, de Koters, & Lamers A&A, 369, 574, (2001))

• But below some metallicity Z about, 0.1, single massive stars will not make GRBs because they do not lose their hydrogen envelope.

• GRBs may therefore not track the total star formation rate, but of some special set of stars with an appreciable evolutionary correction.

• Similarly, the GRBs happening today (e.g., GRB 980425) may have different properties - probably weaker, than GRBs at high redshift because the collapsing core is smaller.

Progenitor Winds

Massive Wolf-Rayet stars are known to have largemass loss rates, approximately 10-5 solar masses/yror more. This wind may be clumpy and anisotropic, but it isunavoidable and its metallicity dependence is uncertain. The density dependence of matter around a single star in vacuum is thus approximately 1000 (1016 cm/R)2 cm-3 composed of carbon, oxygen, and helium. The wind theburst interacts with was ejected during carbon burning.

At some radius this wind will terminate due to interaction with the ISM at 1018 /n 1/2 cm(Ramirez Ruiz et al. MNRAS, 2001).

The GRB jet will start to be decelerated by thiswind at about 3 x 1015 cm.

The Star Collapses (log j > 16.5)

alpha = 0.1 alpha = 0.001

MacFadyen & Woosley ApJ, 524, 262, (1999)

7.6 s 7.5 s

Neutrino flux high Neutrino flux low

In the vicinity of the rotationalaxis of the black hole, by a variety of possible processes, energy is deposited.(Van Putten – this session; Ruffini – this session; Vlahakis - poster)

The exact mechanism forextracting this energy, either from the disk or the rotationof the black hole, is fascinatingphysics, but is not crucialto the outcome, so long as the energy is not contaminated bytoo much matter.

It is good to have an energy deposition mechanism that proceeds independently of the density.

7.6 s after core collapse; high viscosity case.

a=0.5

a=0.5

a=0

Optimisticnu-deposition

Neutrino annihilation energydeposition rate (erg cm –3 s-1)

MacFadyen & Woosley (1999)

Given the rather modest energy needs of current central engines (3 x 1051 erg?)the neutrino-powered model is still quite viable and has the advantageof being calculable.

A definitive calculation of the neutrinotransport coupled to a realistic multi-dimensional hydrodynamical model is still lacking.

Fryer (1998)

The Neutrino-Powered Model

Gamma-Ray Bursts are Inefficient

Typical masses accreted are several solar masses.

The energy of the last stable orbit is approximately 10% Mc2

or about 5 x 1053 erg. The GRB jet uses less than a percentof this.

Such inefficiency is more reminiscent of supernovaethan of active galactic nuclei.

Part of the energy goes into blowing up the star, but most islost to neutrinos or swept into the hole.

Jet Initiation - 1

The jet is initially collimated by the density gradient leftby the accretion.

It will not start until the ram pressure has declined below a critical value.

MacFadyen, Woosley, & Heger, ApJ, 550, 410, (2001)

High disk viscosity (7.6 s + 0.6 s)

Low disk viscosity (9.4 s + 0.6 s)

(Energy deposition of 1.8 x 1051 erg/s commenced for 0.6 s; opening angle 10 degrees) log rho = 5 - 11.5

Jet Initiation -2

Why is the jet energy nearly constant?

• The black hole mass and the total mass accreted do not vary greatly from event to event.

• The explosion is self-limiting in the sense that the jet that makes the GRB also blows up the star that

makes the jet.

• A minimum threshold energy is required for the jet to propagate out of the central regions of the star and not be swept into the hole by accretion.

Relativistic Jet Propagation Through the StarZhang, Woosley, & MacFadyen (poster); Aloy – this session

Ramirez-Ruiz – this session

Initiate a jet of specified Lorentz factor (here 50), energy flux (here 1051 erg/s),and internal energy (here internal E is about equal to kinetic energy), at a givenradius (2000 km) in a given post-collapse (7 s) phase of 15 solar mass helium coreevolved without mass loss assuming an initial rotation rate of 10% Keplerian. Thestars radius is 8 x 1010 cm. The initial opening angle of the jet is 20 degrees.

480 radial zones120 angular zones 0 to 30 degrees80 angular zones 30 to 90 degrees

15’ near axis

Note instabilities:

Pressure in the same model

The jet can be divided into three regions: 1) the unshocked jet, 2) the shocked jet, and 3) the jet head.

For some time, perhaps all of the burst, the jet that emerges has been shocked and has most of its energyin the form of internal energy. Information regardingthe central engine is lost.

Zhang, Woosley, & MacFadyen ApJ, in preparation.

jet head at 4.0 s

Initial opening angle 20 degrees; 1051 erg/s Initial opening angle 5 degrees; 1051 erg/s

Independent of initial opening angle, the emergent beamis collimated into a narrow beam with opening less than 5 degrees

In terms of energy at least, the jet can be "hollow",at least for the calculation initiated with large angle (20 deg)

The opening angle gradually increases, but not monotonically.

Zhang, Woosley, & MacFadyen (2002)

The jet emerges with a small opening angle:(see also Aloy et al ApJL, 510, 119, (2000))

Energy flux at 9 x 1010 cm (just outside star)

0

28

20

0

10

14

The termination of the unshocked jet remains inside the star for a long time. Note the variability of Lorentz factor is correlated with angle. Smaller angle means more instability.

Narrower opening angles should be correlated with higher luminosityalong the axis and with greater variability.

(20 degrees) (5 degrees)

Once the jet has broken out, the energy input at the bottom emerges at the top as relativistic ejecta with almost 100% efficiency.

Terminal Lorenz factor

Lorentz factor at break out

Dark solid lines indicate the Lorentz factor shortly after break outin two models.

The lighter lines indicate the Lorentzfactor that will exist at infinitywhen all the internal energy has converted

10+10 = 200

2121 2

SN 1998bw/GRB 980425

NTT image (May 1, 1998) of SN 1998bw in the barred spiral galaxy ESO 184-G82[Galama et al, A&A S, 138, 465, (1999)]

WFC error box (8') for GRB 980425and two NFI x-ray sources. The IPNerror arc is also shown. 1) Were the two events the same thing?

2) Was GRB 980425 an "ordinary" GRB seen off-axis?

SN 1998bw/GRB 980425

The supernova - a Type Ic - was very unusual.

Large mass of 56Ni 0.3 - 0.9 solar masses; (note: jets acting alone do not make 56Ni) Sollerman et al, ApJL, 537, 127 (2000) McKinzie & Schaefer, PASP, 111, 964, (1999)

Extreme energy and mass > 1052 erg > 10 Msun Iwamoto et al., Nature, 395, 672 (1998) Woosley, Eastman, & Schmidt, ApJ, 516, 788 (1999) Mazzali et al, ApJ, 559, 1047 (2001)

Exceptionally strong radio source Li & Chevalier, ApJ, 526, 716, (1999) Relativistic matter was ejected 1050 - 1051 erg Wieringa, Kulkarni, & Frail, A&AS, 138, 467 (1999) Frail et al, ApJL (2001), astroph-0102282

Probability favors the GRB-SN association Pian et al ApJ, 536, 778 (2000)

We conclude that SN 1998bw and GRB were the same event,but was it an ordinary GRB seen off-axis or an inherentlyweak GRB?

Spreading at late times in an ordinary GRB Zhang, Woosley, & MacFadyen (2001)

Weak or truncated jet - only mildlyrelativistic at break out. MacFadyen, Woosley, & Heger (2001)

1051 erg/s Gamma = 10, 5o

high internal energy1051 erg/s Gamma = 50, 5o

low internal energy35 s

For the models on the previous page, the energy fluxes at 6.0, 7.5, and 9.0 x 1011 cm at a time of 35 s after jet break out. At large angles one will see a weak burst characterized by a moderate (about 10) Lorentz factor.

At 30 degrees in Model A2, the equivalent isotropic energy is about 1049 erg/s. This result is very dependent upon the artificial wayin which the jet was turned down, but is suggestive.

Lorentz factor and total energy flux as a function of angle

After Break-Out .....

Some Conclusions:

• The collapsar model is able to explain many of the observed attributes of GRBs. It naturally provides a reasonable energy and collimation to the jet - provided the necessary angular momentum and prompt black hole formation are achieved.

• The light curves of (long-soft) GRBs may reflect more the interaction of the jet with the star than the time variability of the engine itself.

• SN 1998bw and GRB 980425 were the same event. It remains unclear at this point if the burst was weak because of a deficiency, at all angles, of highly relativistic ejecta, or if it was an ordinary GRB viewed off axis. The latter hypothesis is favored. Every ordinary GRB may make an event like this beamed to a much larger fraction of the sky.

• The emergent jet in the collapsar model may still contain a large fraction of its energy as internal energy. Expansion after break out of material with Lorentz factor of order 10 can still give final Lorentz factors over 100.

• 3D calculations of jet propagation are needed.