Jets and shocks in GRB/GW Maxim Lyutikov (Purdue U.)

Transcription

1 Jets and shocks in GRB/GW Maxim Lyutikov (Purdue U.)

2 MHD effects Radiation transfer

3 GRB was unusual Hard prompt ~ 10 kev soft tail Way too hard/dim Pozanenko +, 018

4 GRB was unusual Hard prompt ~ 10 kev soft tail Way too hard/dim Pozanenko +, 018 Close-by sgrb seen off-axis

5 Cocoon - prompt, Jet- to be seen Observer edge of disk wind disk wind optical kilonova emisison BH torus tidal tail - NS-NS merger: hot disk - Time to accumulate B-flux on BH ~ 1 sec - Jet plows through ~ 0.01 MSun - Breakout after ~ 1 sec - Nearly spherical break-out: prompt

6 Cocoon - prompt, Jet- to be seen Observer edge of disk wind disk wind optical kilonova emisison BH torus tidal tail - NS-NS merger: hot disk - Time to accumulate B-flux on BH ~ 1 sec - Jet plows through ~ 0.01 MSun - Breakout after ~ 1 sec - Nearly spherical break-out: prompt

7 Cocoon - prompt, Jet- to be seen Observer edge of disk wind disk wind optical kilonova emisison BH torus tidal tail - NS-NS merger: hot disk - Time to accumulate B-flux on BH ~ 1 sec - Jet plows through ~ 0.01 MSun - Breakout after ~ 1 sec - Nearly spherical break-out: prompt

8 Cocoon - prompt, Jet- to be seen Observer - Second peak from shock-heated wind - Fast spine not yet seen edge of disk wind disk wind optical kilonova emisison BH torus tidal tail - NS-NS merger: hot disk - Time to accumulate B-flux on BH ~ 1 sec - Jet plows through ~ 0.01 MSun - Breakout after ~ 1 sec - Nearly spherical break-out: prompt

9 Cocoon - prompt, Jet- to be seen Observer - Second peak from shock-heated wind - Fast spine not yet seen edge of disk wind disk wind optical kilonova emisison BH torus tidal tail - NS-NS merger: hot disk - Time to accumulate B-flux on BH ~ 1 sec - Jet plows through ~ 0.01 MSun - Breakout after ~ 1 sec - Nearly spherical break-out: prompt Barkov et al, in prep

10 We predict: a second bump in afterglow obs =5 e =0.1 B =10-3 j =5 p= n=10-4, E iso =3x10 53 n=4x10-4, E iso =x10 53 F [mjy] Time [day] - Second peak from shock-heated wind - Fast spine not yet seen

11 Mildly relativistic shock propagating through 10 4 gcm 3 10 M over 10 9 cm Radiation-mediated shocks For µ 1/ (n 3 C) 1/6 10 post-shock radiation pressure > kinetic pressure µ = m p /m e Momentum flux ~ radiation flux v SB T 4 /c Upstream uu Scattered photons Shock transition mediated by Compton scattering Radiation dominated fluid downstream ud pic. from Levinson - Hot post-shock fluid emits photons - photon pressure decelerates the flow - Mildly relativistic flows can be strongly affected by radiation - High optical depth - LTE (?) Highly radiation-dominated: T m e c µ1/4 (n 3 C) 1/4p 1 for 0.3 Pair production (and nuclear reactions) in the wind > radiationdominated n 0.1 1/ p µ n 3 C 1 = gcm 3

12 Resolving radiation and pairmediated shock transitions 1 1 = 1 1 = p tot + tot /=(w tot + tot /) matter flux! momentum flux! energy flux Pressure, enthalpy, density: sums of baryons, pairs and radiation

13 Resolving radiation and pairmediated shock transitions overall jump condition 1 1 = 1 1 = p tot + tot /=(w tot + tot /) matter flux! momentum flux! energy flux Pressure, enthalpy, density: sums of baryons, pairs and radiation

14 Resolving radiation and pairmediated shock transitions overall jump condition 1 1 = 1 1 = p tot + tot /=(w tot + tot /) + F r F r = c ru rad 3n tot T u rad = 4 c SB T 4 matter flux! momentum flux! energy flux Energy redistribution by radiation. Diffusive - approximation! Pressure, enthalpy, density: sums of baryons, pairs and radiation

15 Resolving radiation and pairmediated shock transitions overall jump condition 1 1 = 1 1 = p tot + tot /=(w tot + tot /) + F r F r = c ru rad 3n tot T u rad = 4 c SB T 4 matter flux! momentum flux! energy flux Energy redistribution by radiation. Diffusive - approximation! Pressure, enthalpy, density: sums of baryons, pairs and radiation Even though the radiation pressure is small, it can fly far-far Higher order diff. equation - very different structure of solutions

16 Very simple case Radiation energy density is negligible, but efficient redistribution 1 1 = 1 1 = T + m p /=( 1 m p T + /) + F r

17 Very simple case Radiation energy density is negligible, but efficient redistribution 1 1 = 1 1 = T + m p /=( 1 m p T + /) + F r

18 Very simple case Radiation energy density is negligible, but efficient redistribution 1 1 = 1 1 = m p T + = 1 = v v 1 p = nt /=( 1 m p T + /) + F r

19 Very simple case Radiation energy density is negligible, but efficient redistribution 1 1 = 1 1 = m p T + = 1 = v v 1 p = nt /=( 1 m p T + /) + F r T = (1 )m p v

20 T = (1 )m p v Zeldovich & Raiser =/( + 1) = 3/4 Two branches - initially on upper, final state on lower, no way to pass throughout Final T reached before final compression 0.4 f =( 1)/( + 1) = 1/4 isothermal jump 0. final state T / T,max T,f / T,max =8 ( 1) (1 + ) =3/4

21 Fluid subshock 1.0 precursor compression & heating - Precursor: on scales >> photon mean free path: slow down and heat-up =/( + 1) = 3/4 M>1 - On scales << photon mean free path: fluid subshock, radiation continuous 0.6 M=1 = /(1 + )=5/8 M=1 fluid sub-shock M s = s ( 1) = p isothermal jump IJ = 1 = 1 3 Continue on momentum conservation curve 0. f =( 1)/( + 1) = 1/4 M<1 post sub-shock compression & cooling T / T,max T,f / T,max =8 ( 1) (1 + ) =3/4

22 Fluid subshock 1.0 precursor compression & heating - Precursor: on scales >> photon mean free path: slow down and heat-up =/( + 1) = 3/4 M>1 - On scales << photon mean free path: fluid subshock, radiation continuous 0.6 M=1 = /(1 + )=5/8 M=1 fluid sub-shock M s = s ( 1) = p IJ = f =( 1)/( + 1) = 1/4 isothermal jump M< T / T,max 1 = 1 3 post sub-shock compression & cooling T,f / T,max =8 ( 1) (1 + ) =3/4 Continue on momentum conservation curve We did not say anything about how energy is redistributed!

23 Resolving the isothermal jump 1.0 (x) fluid sub-shock M s = s ( 1) = 3 p 5 0.8, / max precursor (x)/ max isothermal transition overall x

24 Resolving the isothermal jump 1.0 (x) fluid sub-shock M s = s ( 1) = p , / max precursor (x)/ max Itoh isothermal transition overall x

25 Resolving the isothermal jump 1.0 (x) fluid sub-shock M s = s ( 1) = p , / max precursor (x)/ max Itoh isothermal transition overall x

26 Add pairs and radiation limit of large density Standing shocks in core collapse, high density limit: isothermal jump - post-shock T is 5% higher, but density 30% lower For highly radiatively dominated shocks (low density) isothermal jump disappears - no shock, continuos transition (can also be shown analytically) - This turns out to be the regime in post NS-NS merger winds.

27 From this workshop Shock-induced nuclear reactions in the polar section of the wind (?) Mild Lj~10 50 erg/sec, gcc T ~ me c can modify nuclear composition, blue bump? fairly low density, high tau Not LTE: low rate of photon production on tau=1 length (hot photons, but not enough by numbers)

28 Conclusion Shocks in NS-NS mergers evolve in new, poorly explored regime of mildly relativistic velocities, relativistic temperatures, photon and pair loading, perhaps induced nuclear reactions

29

30 Finite upstream Mach: bifurcation of solutions

31