Supernovae,Gamma-Ray Bursts,

andStellar Rotation

S. E. Woosley (UCSC)A. Heger (Univ. Chicago)

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

2 50 215 10 (5 ms/P) erg

2KE I x

all values between?

The answer depends on following a massive star - including all forms of magnetic and non-magnetictorques – through six major nuclear burning stagesand including mass loss (plus the possible effects ofbinary 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)

Burrows, Hayes,and Fryxell (1995)

Mezzacappa et a l (1998)

The current paradigm forsupernova explosion poweredby neutrino energy depositiongives 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 1970Wheeler et al 2002

Fryer and Heger 2000

~1/day in BATSE

Shortest 6 msGRB 910711 Longest ~2000 s

GRB 971208

Paciesas et al (2002)Briggs et al (2002) Koveliotou (2002)

The majority consensus:

• “Long-soft” bursts are at cosmological distances and are associated with star forming regions

Djorgovski et al (2002)

27 Total

Djorgovski et al (2002)

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

Microquasar GPS 1915in our own Galaxy – time sequence

Artist’s conception of SS433 based on observations

Quasar 3C273 as seen by the Chandra x-ray ObservatoryQuasar 3C 175 as seen in the radio

• GRBs are produced by highly relativistic flows that have been collimated into narrowly focused jets

It is a property of matter moving close to the speedof light that it emits its radiation in a small angle along itsdirection of motion. The angle is inversely proportional to the Lorentz factor

/1

,c/v1

122

This offers a way of measuring the beaming angle. As thebeam runs into interstellar matter it slows down.

c 0.995 v10

c 0.99995 v100.,.

gE

Measurements givean opening angle ofabout 5 degrees.

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%).

• GRBs have total energies not too unlike supernovae

• 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 durationof 10 s can only traverse 3 x 1011 cm. This is longenough to escape a Wolf-Rayet star but not a giant.

Not SN II!

• 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

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 = 56Ni

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 MpcModeled as the 3 x 1052 erg explosion of a massive CO star(Iwamoto et al 1998; Woosley, Eastman, & Schmidt 1999)

GRB 8 x 1047 erg; 23 s

• 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 ~ 1015 – 1016 cm2 s-1) and quite possibly, one way or another, ultra-strong magnetic fields (~1015 gauss). These are exceptional circumstances required, in part, to get relativistic jets.

Prompt models:

Millisecond magnetars

Delayed models (seconds to years):

Supranova Collapsar

The ms Magnetar Model:

49 4 15 2 -1

Assuming the emission of high amplitude ultra-relativistic

MHD waves, one has a radiated power

P ~ 6 x 10 (1 ms/P) (B/10 gauss) erg

and a total rotational kinetic energy

s

52 2 2rotE ~ 10 (1 ms/P) (10 km/R) erg

Wheeler, Yi, Hoeflich, and Wang (2001)Usov (1992, 1994, 1999)

Problems with Alfven radius at -1M 1 M s ?

“Supranovae”Vietri & Stella, 1998, ApJL, 507, L45Vietri & Stella, 1999, ApJL, 527, L43

• First an otherwise normal supernova occurs leaving behind a neutron star whose existence depends on a high rotation rate. M/M 20% 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)

0.1 M

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)

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)

Basics

•Wolf-Rayet Star – no hydrogen envelope – about 1 solar radius.

• Collapse time scale tens of seconds

• Rapid rotation – j ~ 1016 erg s

• Black hole ~ 3 solar masses accretes several solar masses

In the vicinity of the rotationalaxis 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)

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.

Fryer (1998)

The Neutrino-Powered Model (Type I Collapsar Only)

MHD Energy Extraction

22

2 52 2 -115

o

50 -1

From the rotational energy of the black hole:

B M E ~ 0.4 ~ 4 x 10 B erg s

10 M

But only need ~ 4 10 erg s !

Sr c

x

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 ~ 1014 – 1015 gaussfor a 3 solar mass black hole. Well below equipartitionin the disk.

1a

Eventually shuts off when M can no longer sustain

such a large B-field.

Lorentz factor Density

To summarize:

All currently favored massive star models forGRBs require a collapsing iron core to have sufficientangular momentum to make a millisecond pulsar(j ~ 6 x 1015 cm2 s-1). The collapsar model may need even more (~2 x 1016 cm2 s-1).

Do current views regarding the evolution ofmassive stars with helium cores over 10 solar massesallow this to happen? (need not be a common phenomena)

note models “b” (withB-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

.

Heger and Woosley (2002) using prescription for magnetictorques from Spruit (2001)

15 M Helium Star(probably in a binary)

In the absence of mass lossand magnetic fields, there wouldbe 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. Thisis a problem shared by all current GRB models that invokemassive stars...

with mass loss with mass loss and B-fields

no mass loss orB-field

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

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 sincetheir last interaction is at the edge of the neutron star.

Thomas Janka estimates that the total angular momentumof the collapsing iron core is reduced by about 30%.

So for example, 7 ms in the earlier table becomes 9 ms.

r-Mode Instability (Gravity Waves)

1 113 e

spin down

e

330 Hz 2 x 10 yr

0.1

= saturation amplitude

could be 0.1

<<

Arras et al (astroph 0202345) submitted to ApJfind that the r-mode waves saturate at amplitudesfall lower than obtained in (erroneous) previousnumerical calculations that assumed an unrealisticallylarge driving force. Much less gravitational radiation.

The Neutrino Powered WindDuncan, Shapiro, and Wasserman (1986)Qian and Woosley (1996)

e

4 5/3 -151,M 9.2 10 (L ) M s

R = 10 km M= 1.4 M

x

A magnetic stellar wind?: (Mestel and Spruit (1987)

Wind magnetically confined until at rcrit

2 2 2 2( ( )) / 4wv r B

-5 -1

5 -3 8 -1

-4 -1

8 -3 8 -1

)100 km; M = 10 M s ; R = 10 km

10 g cm , v 1 - 2 10 cm s

)100 km; M = 10 M s ; R = 30 km

10 gm cm ; v 10 cm s

a

x

b

2crit

Angular momentum lost is

r m

Results:

Depend on and how magnetic field strength scaleswith radius (r-2 or r-3 ?)

Case b) (high mass loss rate- early on) requires extremely large fields (> 1016 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 > 1014 gauss and B scales as r-2.

MacFadyen, Woosley, and Heger, (2001)

25 solar masssupernova explosionswith various final energies

-7 -5/3 -15

55

M 10 t M

Typically, after 1

s

t

000

=

s,

t(se 10

c)/

Fall back and the propeller mechanism

Propeller MechanismIllarionov and Sunyaev (1975)Alpar (2001)

coupled to fallback:

Chevalier (1989)Lin, Woosley and Bodenheimer (1991)MacFadyen Woosley, and Heger (2001)

Fallback accretion rate:

-5/326 5

2626

M 2 t gm/sec

M accretion rate/10 gm/s

Alfven Radius:

4/ 7 2/ 7 330 26 30 12 66.8 M km = B RAr

So long as the calculated Alfven radius is smallerthan the neutron star radius (10 km), the magnetic field will be pushed to the surface of the star and no brakingcan occur. For B ~ 1012 gauss it takes of order one day until the accretion rate subsides to the point that rA > 10 km. 26That is M 1

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 casethe matter will accrete rather than be ejected andmagnetic braking will be inefficient until.

-4 7 /3 226 3 30

3

M 5.7 x 10

Rotation rate (rad sec) =

1000

<

This turns out to be very restrictive and will onlyallow appreciable braking (of if that is B ~ 1014 gauss.

When the necessary restrictions on the accretion rateand magnetic field apply, the torque is given by

2 3/ AI r

Putting it all together, a neutron star can be braked toa much slower rotational rate provided 30 > 78, 43, 25for initial periods of 6, 21, and 60 ms respectively.

If the field is much weaker than 5 x 1013 gauss, brakingby 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.

To summarize:

It is very difficult to brake the rotation of neutronstars born with periods less than about 5 msbut slower rotaters can be braked to almost arbitrarily slow rates by fallback - if the surfacedipole field is 1014 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 downto an arbitrarily low value.

But what about the much faster values neededfor GRBs?

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, whilepulsars (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?

6

?rr