Millisecond Magnetars as GRB Central Engines

Todd ThompsonThe Ohio State University

B. Metzger, N. Bucciantini, E. Quataert, P. Chang, J. Arons

Thompson et al. 2004Metzger et al. 2007, 2008a,bBucciantini et al. 2006, 2007, 2008, 2009

Usov 1992Thompson 1994Wheeler et al. 2000

“A nagging question in all these models is what produces the ‘observed’ ultra-relativistic flow? How are 10-5 Msun of baryons accelerated to an ultra-relativistic velocity with ~ 100 or larger? Why is the baryonic load so low? Why isn’t it lower? There is no simple model for that. An ingenious theoretical idea is clearly needed here.”

Piran’s questions circa 1999.

The Basic Character of GRBs

• What is required?– Lorentz Factor: 100 < < 1000 (if internal shocks)

– Timescale: ~ 10 - 100s (+ late-time activity +variability)

– Total Energy: ~ 1051 ergs, highly asymmetric, supernovae

The Basic Character of GRBs

• What is required?– Lorentz Factor: 100 < < 1000 (if internal shocks)

– Timescale: ~ 10 - 100s (+ late-time activity +variability)

– Total Energy: ~ 1051 ergs, highly asymmetric, supernovae

Kinetic luminosity ~ 1051 ergs / 10s ~ 1050 ergs s-1

Mass loss rate ~ 1050 ergs s-1/ / c2

~ 6 10-7 Msun s-1

&E = &Mc2

The Basic Character of GRBs

• What is required?– Lorentz Factor: 100 < < 1000 (if internal shocks)

– Timescale: ~ 10 - 100s (+ late-time activity +variability)

– Total Energy: ~ 1051 ergs, highly asymmetric, supernovae

Kinetic luminosity ~ 1051 ergs / 10s ~ 1050 ergs s-1

Mass loss rate ~ 1050 ergs s-1/ / c2

~ 6 10-7 Msun s-1

Piran:“Why is the baryonic load so low? Why isn’t it lower? There is no simple model for that.”

&E = &Mc2

The Answer The characteristic mass-loss rate in the wind

driven from the surface of a newly-born neutron star is (Duncan et al 1986; Qian & Woosley 1996)

for a timescale of 10 -100 seconds. If a millisecond magnetar, the wind has kinetic luminosity of 1050 ergs/s, with ~ 102 - 103, (or magnetization of > 102 - 103).

&M ~ 3×10−7 Lν, 51

5 /2 Me s−1

The Progenitor

Instability& Collapse

Collapse

Bounce, shock formation

Prompt Shock Stalls (~ ms)R ~ 100 km

Shock Revival & Explosion

~ 0.5 - 1 s

KH cooling epoch, wind.

Bounce

CoolingEpoch

€

e− p →ν en

€

e− p → ν en

€

tKH ~ 10−100s

€

Eν ~ 1053.5ergs

300 km

Burrows et al. (1995)

Collapse Bounce Stall Explosion Wind Cooling

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Wind Emergence: Common to All SN Explosions

Supernova Shockwave

Wind

Required physics:

νen↔ e−p νep↔ e+n+ NSgravitational potential.

Scheck et al. (2006)

&M ~ 3×10−7 Lν , 51

5 /2 Me s−1

Qian & Woosley (1996)

What about rotation and magnetic fields?

Espanek, 1999

Initially, not magnetically-dominated, only ~10s later.

Magnetar-strengthfields dominate dynamics in the cooling/wind epoch!

Rotation?

C. Thompson (1994); T. Thompson (2003), T. Thompson et al. (2004)

During Supernova

t ~ 0 - 0.5 s

Magnetic Field: Sub-Dominant Dominant

t ~ 1 st ~ 10 s

Stage I: Non-relativistic ν-Magneto-Centrifugal WindsRA

Schatzman (1962); Weber & Davis (1967)

- Radial B-field forces wind material to corotate to RA. At large distances, B

dominates.

- Increases both V∞ and J & E & M loss rates.

- Efficient spindown mechanism.

- RA increases as Lν(t) decreases in time.

RL

RA

Stage II: Relativistic ν-Magneto-Centrifugal Winds

- RL = c/ bounds RA.

- As RA approaches RL, V∞ approaches c.

RL

RA

Stage II: Relativistic ν-Magneto-Centrifugal Winds

- RL = c/ bounds RA.

- As RA approaches RL, V∞ approaches c.

- = B2/(4c2) (~ ∞ ) if efficient conversion field dissipation.(Drenkhahn & Spruit 02; Arons 07)

RL

RA

Stage II: Relativistic ν-Magneto-Centrifugal Winds

- RL = c/ bounds RA.

- As RA approaches RL, V∞ approaches c.

- = B2/(4c2) (~ ∞ ) if efficient conversion field dissipation.(Drenkhahn & Spruit 02; Arons 07)

- Lν(t) dictates evolution!

(t) ∝ &M (t)−1

Neutron Star Birth in Real Time

Theoreticalcalculations ofproto-neutron star cooling provide expectations for the time evolution of luminosity.

Also, SN 1987A!

Pons et al. (1999)

Lν (t) ~t−1

&M (t) ∝ Lν5 /2 (t)

(t) ∝ &M (t)−1

Evolutionary Calculations

Lν (texp)

€

log10(t)

€

1s

€

10s

€

100s

Sup

erno

va E

xplo

sion

Pha

se

texp

Evolutionary Calculations

€

Lν ∝ t−1

€

log10(t)

€

1s

€

10s

€

100s

Sup

erno

va E

xplo

sion

Pha

se

Lν ∝ exp[−t / tKH ]

Evolutionary Calculations

&M ∝ Lν

5 /2

€

Lν ∝ t−1

€

log10(t)

€

1s

€

10s

€

100s

Sup

erno

va E

xplo

sion

Pha

se

Evolutionary Calculations

€

Lν ∝ t−1

€

log10(t)

€

1s

€

10s

€

100s

€

(RL ) =B2

4πρc 2

~ γ∞

€

˙ E

Sup

erno

va E

xplo

sion

Pha

se

&M ∝ Lν

5 /2

Evolutionary Calculations

€

Lν ∝ t−1

€

log10(t)

€

1s

~1

€

100s

€

(RL ) =B2

4πρc 2

~ γ∞

€

˙ E

Non-Relativistic Relativistic Ultra-Relativistic Force-Free

Sup

erno

va E

xplo

sion

Pha

se

10s

~103

~102

&M ∝ Lν

5 /2

What we’ve done• We solve the free 1-D equatorial non-relativistic neutrino-heated

magneto-centrifugal wind problem for a ms-proto-magnetar.

– Derive wind structure (T, , V, X ), the spindown rate, the mass loss rate -- given a monopole field geometry.

(Thompson et al. 2001, 2004; Metzger et al. 2007, 2008a,b)

• Solve the free 1-D and 2-D axisymmetric relativistic MHD wind problem in the regimes < 1 (non-relativistic) and > 1 (relativistic, magnetically dominated).

– Assess 1-D assumptions!

– Calculate spindown explicitly when >> 1, but with significant mass-loss (spindown is not “force-free,” not “vacuum” dipole, is not infinity, not Usov 1992!).

– Calculate interaction of wind with the overlying progenitor.

(Bucciantini et al. 2006, 2007, 2008, 2009)

Evolutionary Calculations (Metzger et al. 2007)

€

1015G€

1016G

€

˙ E

€

1015G

€

1016G

=B2

4πρc2

RL

→ γ ∞

Evolutionary Calculations (Metzger et al. 2007)

€

1015G€

1016G

€

˙ E

€

1015G

€

1016G

=B2

4πρc2

RL

→ γ ∞

Conclusion:Millisecond proto-magnetars drive winds with

Exactly in the range needed for GRBs.

What about asymmetry?

,σ > 100 and &E ~ 1050 ergs s-1

on 10 -100s timescales.

Jet Production

• Wind hits spherical SN shockwave in ~ few seconds.

• Creates reverse shock, contact discontinuity.

• Residual Bphi squeezes (pinch force) flow.

• Net polar acceleration.

• Analogous to models of pulsar wind nebulae by Li & Begelman ‘92; Chevalier & Luo ‘93. See also Konigl & Granot ‘02; Komissarov & Lyubarsky 03,04; Uzdensky & MacFadyen ‘07; Nagataki ‘09).

Jet Production (Bucciantini et al. 07, 08, 09)

Wind shocks on the outward-going SN shockwave at ~104 km, toroidal B exerts a pinch force that drives jet. Models are Poynting

flux-dominated at breakout from progenitor.

jet 20

wind ~ 20

jet

supernova

Jet Production (Bucciantini et al. 09)

• Magnetic dissipation in outflow is uncertain: consider both high & low magnetization limits.

– Low- : wind(~RL) ~ jet(~ Rstar)

– High- : If (~RL) ~ 60, then jet(~ Rstar) ~ 10 -15 (but, accelerating), magnetic field ~5 times equipartition.

– Jet production robust in either case.

• All of the spindown energy goes to the jet, virtually none goes to the spherical “supernova.”

• For weaker winds, the reverse shock propagates back into the outflow, coupling the wind & bubble dynamics: not a “free” wind (see also Uzdensky & MacFadyen; Komissarov & Barkov).

• Worries: 3D stability, entrainment, etc. (e.g., McKinney & Blandford)

Nucleosynthesis (Bucciantini et al. 09)

• For most cases, not hot enough for significant excess 56Ni production. However, exact prediction is sensitive to timing of wind-bubble interaction.

• However, we expect 10-2

Msun of Ne & O & C with v ~ 0.1 - 0.2c along the poles.

• The power of the wind (B, P) is directly connected with abundance of nucleosynthetic products, their velocity distribution.

Compare w/ Nagataki et al; Maeda et al; Mazzali et al

• For magnetar B & ms P, everything works for GRBs. How?– Weak physics sets baryon loading of the wind.– B & P set Lorentz factor, magnetization, & kinetic luminosity.– Neutrino diffusion time sets characteristic timescale.– Interaction of wind with progenitor leads to collimation.

• Robust to most uncertainties (e.g, magnetic dissipation)• Nucleosynthesis connected to timing, wind power, etc.

– Association with supernovae is free. – Non-Association with supernovae? Maybe AIC of WD.

• This model predicts well-defined (testable) correlations between these quantities in an average sense. They are not independent.

• The model appeals to the idea that neutron stars are probably born with a range of B & P, implying a connection with normal supernovae (e.g., Soderberg). Diversity: B(P).

• If you believe in the “Collapsar” mechanism, you (should) believe the ms-magnetar mechanism: angular momentum requirements.

Summary

• Wind & Spindown:

– Couple physics more realistically to the supernova explosion, feedback effects on wind and magnetar torque in weak-wind limit

– Does time dependence of outflow at magnetar surface imprint itself on the outflow dynamics of the jet at the progenitor surface?

• Jets: Stability in 3D? Entrainment?

• Lightcurves:

– Use Lorentz factor, magnetization, opening angle, kinetic luminosity to predict prompt lightcurves (model-dependent). Try to make contact with observations. See Metzger et al. 2008: SGRBEEs!)

• Late-time activity: power-source for plateau? Flares? (Dall’Osso et al. today; talk by Margutti)

• LIMITATIONS: Energetics (e.g., Cenko et al. today): Maximum energy ~ few x 1052 ergs (e.g., 090926A)

The Present & Future

The observation of a long-duration GRB does not imply black hole birth

(necessarily).

EnergyLorentz FactorTimescale

Collimation

Lightcurves?

• Picture: WD/WD merger or AIC of a WD to a rapidly rotating magnetar.

• SGRB: ~ 0.1Msun disk accretes on ~ 0.1-1s. Polar GRB as in NS-NS merger calculations. (e.g., Dessart et al. 07)

• EE: Remaining magnetar spins down, drives wind.

A Model for Short-Duration GRBs with “Extended Emission”

Gehrels et al. 2006Gal-Yam et al. 2006

GRB 060614

Proto-magnetar winds can account for EE:s

Short GRBs with Extended Emission

Metzger et al. (2008a)

• Characteristics of the model:– As time increases, degree of relativity increases.– As time increases, energy loss rate decreases.– A magnetar is left behind. Late-time activity? Flares?– Maximum total GRB energy: ~ 5 1052 ergs. Gravity waves.

(e.g., Cenko et al. 2009)

• Some questions:– Magnetic dissipation? – What is the nature of SN-less long-duration GRBs? AIC?– What is the nature of the short-duration GRBs with extended

emission? AIC?– Can we predict prompt lightcurves? (model-dependence)– With energy & Lorentz factor & jet opening angle, can we calculate

character of afterglow? Yes.

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