High Energy Gamma-Raysin Magnetar Powered Supernovae:

Heating Efficiency and Observational Signatures

Dmitry A. Badjin1,2

with Maxim V. Barkov and Sergei I. Blinnikov

1 N.L. Dukhov Research Institute of Automatics (VNIIA), Moscow, Russia2 Institute for Theoretical and Experimental Physics, Moscow, Russia

18th Workshop on Nuclear AstrophysicsRingberg Castle

March 14 – 19, 2016

Magnetar Powered Supernova

Sources of additional power:• Rotation energy potentially available:

Erot = 12 IΩ

2 ∼ 1052 erg

• Spin-down losses: Lrot = L0(1 + t

τ

)−α ,L0 ∼ 1045 erg

s , τ ∼ 105 s, α ≈ 2

• Inner Shock heating

• HEGR heating

! Simple deposition of Lrot at the shell baseseems promising for fitting observed SLSNlight curvesD. Kasen, L. Bildsten, ApJ, 2010, 717, p.245

C. Inserra et al. ApJ, 2013, 770:128

M. Nicholl et al. Nature, 2013, 502, p.346

2

Magnetar Powered Supernova

Magnetar Driven Shock: 1D-simulations

D.Kasen, B.Metzger, L.Bildsten, arXiv:1507.03645, accepted to ApJ

3

Magnetar Powered Supernova

Questions:• Whether the magnetar powering is pronounced against the initial (strong) SLSN explosionand Ni-Co-Fe decays??∃t: LM(t) & Lburst(t), LNi(t)

It seems better:• the magnetar to be strong (but this means a short time-scale of losses)• or the explosion – weak (but how could it provide a strong M?)

• or t – long (but heating power is also weak)

• HEGRs may be locked inside the wind cavern by high opacity for pair-production on thethermal background of ejecta, until the latter cools enough.

Tests are required.

4

Tested ScenarioMRI-driven Hypernova with Magnetar Powering

Eburst = 1− 10 foe, LM = 3× 1045 ergs , Ni-free but with HEGRs

according to Barkov M.V. & Komissarov S.S., Mon.Not.Roy.Astron.Soc., 2011, 415, pp.944-958

5

Magnetar Cavern

• Initial burst – a ‘Thermal Bomb’

• SN ejecta (IV) expands into ISM (V)⇒ Forward Shock (FS)

• Magnetar e±-wind (I) (γe = 103 − 109!) is terminated byIV⇒

• 3 discontinuities: Termination shock (TS), leptons-plasmaContact (CD), Inner shock (IS)

• 2 regions: shocked wind (II), shocked plasma (III).

• Plasma is hot (104 − 105 K)⇒ thermal emission (TE)inwards (∼ free escape) and outwards (diffusion→ freeescape)

• Relativistic e± + B and TE⇒ HEGRs: synchrotron (10 MeV– 10 GeV) and IC (up to 100 TeV)

• HEGRs + plasma (direct Compton) and TE (pair production)⇒ heating and pressure.

6

Methods of Testing

Radiative Hydrodynamics with STELLA (Blinnikov et al., 1998) for TE:• Spherical symmetric lagrangean hydrodynamics

• Coupled (unsplit) + multigroup time dependent radiation transport of energy and flux (0thand 1st moments of the Boltzmann equation, variable Eddington factor closure, O(v/c) inmoving media)

• High order accurate implicit solver(2-nd in space, up to 6-th in time)

• Scattering and expansion opacity

• Artificial mixing acceleration

Improvements for high-energy effects:• + Source of HEGR accounts for spin-down luminosity (e± injection), coupling of wind andplasma via pressure and energy balance.

• + Spectral transport of HEGRs. Energy deposition. Outcoming emission ectimation.

• + Optimization of moment equations closure

HEGRStella (Badjin)

7

Wind-Plasma Coupling Scheme

at TS:pe + pB = E

3V + B28π = Lw

4πcR2TSEe = Le + (η − 1)Lγ − peVEB = LB − pBVLγ = LSyn(B, TTE) + LIC(J(ν), B)

at CD: pe + pB ↔ nkT

everywhere above TS:γ + e− → γ′ + heatγ + hν → e± → heatheat = Ee or 32nkT

8

HEGR Source Calculation

• Input: B, Le(t),dN0e (t,γe)

dγe∼ Le(t)γ−2e , Trad or Jν(ν) from native

STELLA

• Quasi-stationary fast e-cooling:dNe(γe,t)

dt = N0(t)γαe− Ne(γe,t)

tcool(Trad,B,γe)+

γe,max∫γe

Ne(γ′e ,t)tcool(Trad,B,γ′e→γe)

dγ′e = 0

• dNe(γe,t)dγe

⇒ dNγ(ε,t)dε |Syn, dNγ(ε,t)

dε |IC ⇒ Lγ(t)

• HEGR spectral density over 100 MeV – 100 TeV logarithmic grid• special thanks to Dmitry V. Khangulyan

9

HEGRs & Compton Scattering

• HEGRs are emitted by ultrarelativistic leptons⇒ strong radialcollimation⇒ sharp angular dependence, low-order momentapproximations do not work.

• Direct CS (off cold e−): HEGRs either are weakly deflected, or(otherwise) lose most of energy

• Strongly downscattered photons do not contribute photon densityat final energy significantly⇒

• Simplification: HEGRs are discretized intoa set of expanding spherical shellsof photons collimated within θc < 1− 3:small-angle scattering – gradual softening,large-angle scattering – photon destruction,immediate energy thermalization.

10

HEGR Transport Equation

• Superposition of ‘direct’ and ‘scattered’ (only within θc) emission onevery elementary path r0 → r1 = r0 + c∆t.

• Transfer equation formal solution:

Nε(r1, ε) = Nε(r0, ε)e−∆τ(ε) +34σTSC(ε)

SC(ε) =

εmax∫ε1

Nε(r0, ε0)F(ε, ε0)

ε0

r1∫r0

ne(r′)e−

r′∫r0χ(ε0)dr′′−

r1∫r′χ(ε)dr′′

dr′d ln ε0

∆τ(ε) =

r1∫r0

χ(ε, r′, t′(r′))dr′

11

Kinetics and Opacity

• Downscattering rate ε0 → ε (if allowed by the angular selectionrule):

F(ε, ε0) = (1 + (1 +1ε0

− 1ε

)2 + εε0(1ε0

− 1ε

)2) ε0 6 εmax(ε, θ)

• opacity χ accounts for CS:

χKN(ε) = ne38σTε2

(4 + (ε− 2− 2

ε) ln(1 + 2ε) +

2ε2(1 + ε)

(1 + 2ε)2

),

• and pair production of photons of local effective temperature Teff :

χpp(ε, ν) =2r20Θ

3

πΛ3e

ν2 1∫∞

sσ(s) ln(1− e−νs) ds

,

ν(ε, Teff ) = m2c4/(εkTeff ), Θ = kTeff/mec2, Λe = ~/mec

(derived from Gould & Schreder, 1967)

12

Calculation Setup

• RSG Mass: 15− 25M→ 15

• Scale factor for CE: 1–10→ 10

• MRI-SN burst energy 1-10×1051 erg, duration – 30-100 s→ 3, 30

• Lw = 3 · 1045(1 + t

105s

)−2.1 ergs , B ∼ 1015

• Magnetization parameter σ = 0.1− 10→ 0.1:σLB + Le = (σ + 1)Lw

• Lepton spectrum: ∼ γ−2e , γe = 103 − 109

• Output: light curves and spectra of outcoming HEGRs andobservable TE during the first several years

13

Conditions in the Cavern

10-4

10-3

10-2

10-1

100

101

102

103

104

10-2 10-1 100 101 102 10310-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104R

, 1014

cm

B, k

Gs;

Tra

d, 1

05K

t, days

RsrcRcd

BTrad

14

HEGR Outcome

Source Outcome

36

38

40

42

44

46

0.1 1 10 100 1000

36

37

38

39

40

41

42

43

44

10 100 1000lo

g Lγ,

erg

s-1

Bol0.1-1 GeV1-10 GeV

10-100 GeV0.1-1 TeV

• Strong absorption in the shell⇒ the signal is rather weak and late

15

HEGR Blocking

Key effect:

• Plasma is hot⇒ a lot of thermalhν , to “kill” the most of HEGRsbefore they pass the CD

• HEGRs (almost) do not enter theplasma⇒ no re-heating of theshell

• Cold shell⇒ does not interceptHEGRs⇒ no re-heating, weak TE.

• Negative feedback hν − γ.Magnetar energy turns into work.

16

Magnetar Driven Shock

The MDS is radiative⇒ Dense Shell.

HEGRStellaOptically and geometrically thin dense shell⇒Extremely hard for numerical differential transfer

Long-characteristic integral scheme for TE

Blondin, Chevalier & Frierson, ApJ, 2001, 563, p.806

17

Magnetar Driven Shock

The MDS is radiative⇒ Dense Shell.

HEGRStellaOptically and geometrically thin dense shell⇒Extremely hard for numerical differential transfer

Long-characteristic integral scheme for TE

But! It is known to be RT-unstable(Bernstein & Book 1978)

Credit: S. Glazyrin⇒Time to smear

Artificial RT-viscosity boost 102 − 103

17

Thermal Emission: Bolometric

The work is actually in progress

39

40

41

42

43

44

45

1 10 100

log

LT

E,b

ol, e

rg s

-1

t, days

NoHEGR NoNi3 foe + HEGR

1.2 foe + HEGRNoHEGR + 0.1 MNi

18

STELLA: 15M, 1-3 foe: Conclusions ...• Magnetars seem not so ‘almighty’. At least in extended envelopes.SLSN - ?

• Distinctive ‘magnetar tail’ – only at the latest stages(t > TNi→Co→Fe ∼ 102 d.)

• Unless the shell is too cold, its thermal background blocks theHEGRs within the cavern, otherwise – it is transparent.HEGRs heat not the ejecta but the shocked wind

... and new questions.

• Why the MDS does not shine brightly? Non-Eq emission into thecentral cavity or an artifact of mixing?

• If there are other ways of the shocked wind energy dissipation andheat conduction?

• The radiative thin dense shell around CD requires special TEtransfer methods or properly enhanced mixing (based on multi-Danalysis).

19

STELLA: 15M, 1-3 foe: Conclusions ...• Magnetars seem not so ‘almighty’. At least in extended envelopes.SLSN - ?

• Distinctive ‘magnetar tail’ – only at the latest stages(t > TNi→Co→Fe ∼ 102 d.)

• Unless the shell is too cold, its thermal background blocks theHEGRs within the cavern, otherwise – it is transparent.HEGRs heat not the ejecta but the shocked wind

... and new questions.

• Why the MDS does not shine brightly? Non-Eq emission into thecentral cavity or an artifact of mixing?

• If there are other ways of the shocked wind energy dissipation andheat conduction?

• The radiative thin dense shell around CD requires special TEtransfer methods or properly enhanced mixing (based on multi-Danalysis).

19

Thank you!

20