1. Supernovae, Gamma-Ray Bursts, and Stellar Rotation S. E. Woosley (UCSC) A. Heger (Univ. Chicago)

2. When a massive star (M > 8 solar masses) dies, what is the angular momentum of its iron core? In terms of the resulting pulsar period – or its equivalent. Is it < 1 ms needed for current GRB models < 5 ms will necessarily influence the supernova kinematics > 20 ms with considerable variability - as is implied by observed pulsars all values between?

3. The answer depends on following a massive star - including all forms of magnetic and non-magnetic torques – through six major nuclear burning stages and including mass loss (plus the possible effects of binary membership) The answer is critically important to understanding: How supernovae explode How gamma-ray bursts work The strength of potential sources of gravitational radiation The nature of pulsars and supernova remnants Nucleosynthesis.... Baade & Zwicky (1939) Hoyle (1946)

4. Burrows, Hayes, and Fryxell (1995) Mezzacappa et a l (1998) The current paradigm for supernova explosion powered by neutrino energy deposition gives ambiguous results. Rotation could alter this by Providing extra energy input Creating ultrastrong B fields and jets Changing the convective flow pattern Ostriker and Gunn 1971 LeBlanc and Wilson 1970 Wheeler et al 2002 Fryer and Heger 2000

5. ~1/day in BATSE

6. Shortest 6 ms GRB 910711 Longest ~2000 s GRB 971208 Paciesas et al (2002) Briggs et al (2002) Koveliotou (2002)

7. The majority consensus: “Long-soft” bursts are at cosmological distances and are associated with star forming regions Djorgovski et al (2002) 27 Total

8. Djorgovski et al (2002)

9. Minimum Lorentz factors for the burst to be optically thin to pair production and to avoid scattering by pairs. Lithwick & Sari, ApJ, 555, 540, (2001)

10. Microquasar GPS 1915 in our own Galaxy – time sequence Artist’s conception of SS433 based on observations Quasar 3C273 as seen by the Chandra x-ray Observatory Quasar 3C 175 as seen in the radio GRBs are produced by highly relativistic flows that have been collimated into narrowly focused jets

11. It is a property of matter moving close to the speed of light that it emits its radiation in a small angle along its direction of motion. The angle is inversely proportional to the Lorentz factor This offers a way of measuring the beaming angle. As the beam runs into interstellar matter it slows down. Measurements give an opening angle of about 5 degrees.

12. Frail et al. ApJL, (2001), astro/ph 0102282 Despite their large inferred brightness, it is increasingly believed that GRBs are not inherently much more powerful than supernovae. From afterglow analysis, there is increasing evidence for a small "beaming angle" and a common total jet energy near 3 x 10 51 erg (for a conversion efficiency of 20%). GRBs have total energies not too unlike supernovae

13. If typical GRBs are produced by massive stars, the star must have lost its hydrogen envelope before it died. A jet that loses its power source after the mean duration of 10 s can only traverse 3 x 10 11 cm. This is long enough to escape a Wolf-Rayet star but not a giant. There may be several hundred unusual explosions for every gamma-ray burst we see Very approximately 1% of all supernovae make GRBs but we only see about 0.5% of all the bursts that are made – a rare phenomenon

14. There may even be an observational connection between supernovae and GRBs “Bumps” seen in the optical afterglows of at least three GRBs - 970228, 980326, and 011121 – at the time and with a brightness like that of a Type I supernova Bloom et al (2002) A spectrum please!! note SN = 56 Ni

15. 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)] Type Ic supernova, d = 40 Mpc Modeled as the 3 x 10 52 erg explosion of a massive CO star (Iwamoto et al 1998; Woosley, Eastman, & Schmidt 1999) GRB 8 x 10 47 erg; 23 s

16. It is the consensus that the root cause of these energetic phenomena is star death that involves an unusually large amount of angular momentum (j ~ 10 15 – 10 16 cm 2 s -1 ) and quite possibly, one way or another, ultra-strong magnetic fields (~10 15 gauss). These are exceptional circumstances required, in part, to get relativistic jets. Prompt models: Millisecond magnetars Delayed models (seconds to years): Supranova Collapsar

17. The ms Magnetar Model: Wheeler, Yi, Hoeflich, and Wang (2001) Usov (1992, 1994, 1999) Problems with Alfven radius at

18. “Supranovae” Vietri & Stella, 1998, ApJL, 507, L45 Vietri & Stella, 1999, ApJL, 527, L43 First an otherwise normal supernova occurs leaving behind a neutron star whose existence depends on a high rotation rate. Shapiro (2000); Salgado et al (1994) The high rotation rate (~ 1 ms) is braked by pulsar- like radiation until a critical angular momentum is reached The neutron star then collapses on a dynamic time scale to a black hole leaving behind a disk (this may be sensitive to the EOS) Accretion of this disk produces a delayed GRB (time scales of order a year after the supernova)

19. Collapsars A rotating massive star whose core collapses to a black hole and produces an accretion disk. Bodenheimer and Woosley (1982) Woosley (1993) MacFadyen and Woosley (1999)

20. 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)

21. Basics Wolf-Rayet Star – no hydrogen envelope – about 1 solar radius. Collapse time scale tens of seconds Rapid rotation – j ~ 10 16 erg s Black hole ~ 3 solar masses accretes several solar masses

22. I n the vicinity of the rotational axis of the black hole, by a variety of possible processes, energy is deposited. 7.6 s after core collapse; high viscosity case. The star collapses and forms a disk (log j > 16.5)

23. a=0.5 a=0 Optimistic nu-deposition Neutrino annihilation energy deposition rate (erg cm –3 s -1 ) MacFadyen & Woosley (1999) Given the rather modest energy needs of current central engines (3 x 10 51 erg?) the neutrino-powered model is still quite viable and has the advantage of being calculable. Fryer (1998) The Neutrino-Powered Model (Type I Collapsar Only)

24. MHD Energy Extraction Blandford & Znajek (1977) Koide et al. (2001) van Putten (2001) Lee et al (2001) etc. The efficiencies for converting accreted matter to energy need not be large. B ~ 10 14 – 10 15 gauss for a 3 solar mass black hole. Well below equipartition in the disk.

26. Lorentz factor Density

27. To summarize: All currently favored massive star models for GRBs require a collapsing iron core to have sufficient angular momentum to make a millisecond pulsar (j ~ 6 x 10 15 cm 2 s -1 ). The collapsar model may need even more (~2 x 10 16 cm 2 s -1 ). Do current views regarding the evolution of massive stars with helium cores over 10 solar masses allow this to happen? (need not be a common phenomena)

28. note models “b” (with B-fields) and “e” (without) Heger, Woosley, & Spruit, in prep. for ApJ Spruit, (2001), A&A, 381, 923 - red supergiants at death. Pulsar periods 3 to 15 ms

29. . Heger and Woosley (2002) using prescription for magnetic torques from Spruit (2001) (probably in a binary)

30. In the absence of mass loss and magnetic fields, there would be abundant progenitors. Unfortunately nature has both. 15 solar mass helium core born rotating rigidly at f times break up The difficult problem is the angular momentum. This is a problem shared by all current GRB models that invoke massive stars... with mass loss with mass loss and B-fields no mass loss or B-field

31. Suppose all neutron stars are born rotating very rapidly. What processes can brake them?

32. Neutrino Braking: (an invisible sink for E and j) Upon birth, a neutron star radiates about 20 – 30% of its rest mass as neutrinos. These carry away angular momentum as well as energy, especially since their last interaction is at the edge of the neutron star. Thomas Janka estimates that the total angular momentum of the collapsing iron core is reduced by about 30%. So for example, 7 ms in the earlier table becomes 9 ms.

33. r-Mode Instability (Gravity Waves) Arras et al (astroph 0202345) submitted to ApJ find that the r-mode waves saturate at amplitudes fall lower than obtained in (erroneous) previous numerical calculations that assumed an unrealistically large driving force. Much less gravitational radiation.

34. The Neutrino Powered Wind Duncan, Shapiro, and Wasserman (1986) Qian and Woosley (1996) A magnetic stellar wind?: (Mestel and Spruit (1987) Wind magnetically confined until at r crit

35. Results: Depend on  and how magnetic field strength scales with radius (r -2 or r -3 ?) Case b) (high mass loss rate- early on) requires extremely large fields (> 10 16 gauss) if P  ~ 5 ms. Case a) (low mass loss rate- later) can brake the rotation of neutron stars in about 10 s but only if the rotation rate is already pretty slow (P > 50 ms) and the surface field is > 10 14 gauss and B scales as r -2.

36. MacFadyen, Woosley, and Heger, (2001) 25 solar mass supernova explosions with various final energies Fall back and the propeller mechanism

37. Propeller Mechanism Illarionov and Sunyaev (1975) Alpar (2001) coupled to fallback: Chevalier (1989) Lin, Woosley and Bodenheimer (1991) MacFadyen Woosley, and Heger (2001) Fallback accretion rate:

38. Alfven Radius: So long as the calculated Alfven radius is smaller than the neutron star radius (10 km), the magnetic field will be pushed to the surface of the star and no braking can occur. For B ~ 10 12 gauss it takes of order one day until the accretion rate subsides to the point that r A > 10 km.

39. Additionally there is a critical accretion rate, for a given field strength and rotation rate, above which the corotation speed at the Alfven radius will be slower than the Keplerian orbit speed. In this case the matter will accrete rather than be ejected and magnetic braking will be inefficient until. This turns out to be very restrictive and will only allow appreciable braking (of    if    that is B ~ 10 14 gauss.

40. When the necessary restrictions on the accretion rate and magnetic field apply, the torque is given by Putting it all together, a neutron star can be braked to a much slower rotational rate provided  30 > 78, 43, 25 for initial periods of 6, 21, and 60 ms respectively. If the field is much weaker than 5 x 10 13 gauss, braking by the propeller mechanism will be negligible in most interesting situations. The ejection of material by the propeller also shuts off the accretion, so the process is self limiting.

41. To summarize: It is very difficult to brake the rotation of neutron stars born with periods less than about 5 ms but slower rotaters can be braked to almost arbitrarily slow rates by fallback - if the surface dipole field is 10 14 gauss or more. So, if the rotation period at birth is 10 ms (Heger et al) then there may be other ways to slow it down to an arbitrarily low value. But what about the much faster values needed for GRBs?

42. Question to the Community: How can we have it both ways? Can a few massive Wolf-Rayet stars die with cores rotating at nearly the break up speed, while pulsars (in red supergiants) are still born rotating slowly? Anisotropic mass loss? Accretion in a binary? Mergers? It helps to have the WR star itself rotate rapidly, but this is not the only problem. WR mass loss rates too high? Heger, Woosley, and Spruit off by ~5? Fall back? Large B-fields in the explosion?