The Collapsar Model for Gamma-Ray Bursts * S. E. Woosley (UCSC) Weiqun Zhang (UCSC) Alex Heger (Univ. Chicago)

Topics To Be Addressed: Brief Review of Basic Collapsar Model Fe/Ni Production and Neutronization in the Disk Jet and Cocoon Break Out and Spreading and the Production of X-Ray Flashes Short Hard Bursts from Collapsars! Post Burst Behavior of Collapsars (Supernova and Delayed Energy Input)

Collapsars Type Mass/sun(He) BH Time Scale Distance Comment I He prompt 20 s all z neutrino-dominated disk II He delayed 20 s – 1 hr all z black hole by fall back III >130 He prompt ~20 s z>10? time dilated, redshifted *(1+z) very energetic, pair instability, low Z A rotating massive star whose core collapses to a black hole and produces an accretion disk. Type I is what we are usually talking about. The 40 solar mass limit comes from assuming that all stars above 100 solar masses on the main sequence are unstable (except Pop III). Bodenheimer and Woosley (1982) Woosley (1993) MacFadyen and Woosley (1999)

Collapsar Type I Basics Wolf-Rayet Star – no hydrogen envelope – about 1 solar radius. Collapse time scale tens of seconds Rapid rotation – j ~ erg s Black hole ~ 3 solar masses accretes several solar masses favored by low metallicity surrounded by medium (clumpy)

I n the vicinity of the rotational axis of the black hole, by a variety of possible processes, energy is deposited. Must wait ~5 sec for polar axis to clear. It is good to have an energy deposition mechanism that proceeds independently of the density and gives the jet some initial momentum along the axis 7.6 s after core collapse; high viscosity case. The star collapses and forms a disk (log j > 16.5)

Initial opening angle 20 degrees; erg/s Initial opening angle 5 degrees; erg/s Independent of initial opening angle, the emergent beam is collimated into a narrow beam with opening less than 5 degrees (see also Aloy et al. 2000)

Lorentz factor Density

The jet explodes the star (sort of)

The Production of 56 Ni Needed to provide the visible light of the supernova (if there is to be one). M( 56 Ni) = 0.1 to 0.5 solar masses. A bigger problem than most realize. The jet doesn’t do it (density is too low and too little mass) The explosion doesn’t do it (heavy elements fell in BH)

The disk wind: MacFadyen & Woosley (2001) Neglecting electron capture in the disk

Electron capture in the Disk Pruet, Woosley, & Hoffman (2002) Popham, Woosley, & Fryer (1999) * *

Implications The jets of merging neutron stars and supranovae will be composed mostly of free neutrons The disk winds of collapsars will be chiefly iron-group elements – 56 Ni if the accretion rate is low (late times or Type II), otherwise non-radioactive species. The Ni is made farther out in the disk. Only get visible supernovae in the collapsar model if  > 0.1 and for accretion rate < about 0.05 solar masses per second. Small variations can make big differences. Neutron excess in jet sensitive to the Kerr parameter see also Belobodorov

Jet Break Out and Spreading

zoning: cylindrical grid 1500 x 2275 zones r = 0 to 6 x cm z = 1.0 x to 2.0 x cm Model AModel B PARTICULARS Fine zoned 15 solar mass helium star. R = 8 x cm. Jet introduced at cm = R/8 Model C Total KE 2 jets – 20 s 12 x x x per jet per second 3 x x x  f o

The jet approaches the surface: Maximum Lorentz factors are mild -  ~ 10, but the internal energy loading is high, also ~ 10

Model A - 11 seconds at break out note the mildly relativistic cocoon

Density structure at break out Note plug!

11 s 12 s Note large internal energy loading in the cocoon as well as in the jet

Model A

0.1 radian

Expansion to about 20 stellar radii

Model A Total energy  > 5

Model B Total energy  > 5

Some Implications for X-Ray Flashes Equivalent isotropic energy off axis is small but viewing angle – 1/  – is large. Similar energy observed in both:  ~ 200, E iso ~ erg/4  ster  ~ 10, E iso ~ – erg/4  ster but solid angle visible goes as 1/  2 Softer spectrum because lower  Longer time scale because lower 

Some Implications for X-Ray Flashes Suppose have the equivalent (per solid angle) of erg in matter with Lorentz factor 10. This implies gm. This will decelerate when it runs into M/  = gm, which for a wind with mass loss rate solar masses per year at 1000 km/s occurs at cm. The duration will be ~ R/2   c ~ 250 s, but a factor of 10 variation is easy. This model is a little bit like a “dirty fireball” and a little like a jet viewed off axis, but in fact is neither (or both).

Some Implications for X-Ray Flashes XRFs will occur in the same objects that make GRBs and will thus share their properties. The absence of an optical afterglow – so far - is mysterious. XRFs will be accompanied by supernovae XRFs are inherently much more numerous than GRBs, but may be harder to detect. XRFs should underlie all GRBs and may even be the cause of soft precursor activity seen in some cases.

GRB GRB Hard x-ray bursts Unusual supernova (polarization, radio source) A Unified Model for Cosmological Transients    5 o, internal shocks ~20 o, external shocks? (analogous to AGNs)

Short-Hard Bursts The equivalent isotropic energy contained in the “plug” and in other dense material near the axis is about erg. This is the energy of a “short hard burst”. The Lorentz factor of this material is about 20 at the last calculation (70 s, cm). Might this make a short-hard burst (by external shock interaction)? Predictions: Short hard bursts in association with massive stars Short hard bursts and long soft bursts mixed together (but not always)

Model AModel B THE PLUG Model C Jet E – 70 s 5.2 x erg 1.4 x erg 3.9 x erg Plug E – 70 s 1.8 x x x Jet M – 70 s 5 x gm 1.2 x gm 4.1 x gm Plug M – 70 s 1 x x x Plug thin 1 x cm 2 x cm 1 x cm (if  = 20) Jet Thin 4 x x x Jet will run into plug if plug stays at  = 20 at about cm, but of course plug will accelerate and not stay at  = 20 Conclusion – the jet may or may not give up a lot of its energy to the plug before it begins to radiate. The plug is about 1 light second thick and gets compressed. RT unstable?

GRB BATSE Trigger 1997 BATSE Channels 1 – 4 (> 20 keV) BATSE Channel 4 (> 300 keV) See also GRB – Lamb et al astroph – submitted to ApJ

The Jet Explodes the Star Continue the spherical calculation for a long time, at least several hundred seconds. See how the star explodes, the geometry of the supernova, and what is left behind.

Density and radial velocity at 80 s (big picture)

Zoom in by 5... The shock has wrapped around and most of the star is exploding. Outer layers and material along the axis moves very fast. Most of the rest has more typical supernova like speeds ~ 3000 – 10,000 km s seconds

t = 80 seconds But shown on a magnified scale, there is still a lot of dense low velocity material near the black hole (Zoom in *100)

at 240 seconds The shock has wrapped around and the whole star is exploding (initial radius was less than one tick mark here). A lot of matter in the equatorial plane has not achieved escape velocity though and will fall back. Continuing polar outflow keeps a channel open along the rotational axis. radial velocity/c

By this time the star has expanded to over ten times its initial radius the expansion has become (very approximately) homologous. Provided outflow continues along the axis as assumed, an observer along the axis (i.e., one who saw a GRB) will look deeper into the explosion and perhaps see a bluer supernova with broader lines (e.g., SN2001ke; Garnavich et al. 2002). Continued accretion is occurring in the equatorial plane. 240 seconds Caution: Effect of disk wind not included here Observer

Some Implications: The “opening angle” will increase with time as the jet blows the outer part of the star away. There may not be a single  jet, but one that evolves.  jet may be bigger for afterglows than for GRBs. The energy input by continuing accretion during the first day may still be very appreciable, perhaps even exceeding that in the active GRB producing phase. This may be output as mildly relativistic matter. The energy measured from afterglows may exceed appreciably what the GRB actually required. There will be a continuing energy source for powering lines at late times as assumed by e.g., Meszaros and Rees. Bursts may have long “tails” of continuing activity