High Energy Gamma-Rays in 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, Russia 2 Institute for Theoretical and Experimental Physics, Moscow, Russia

18th Workshop on Nuclear Astrophysics Ringberg Castle March 14 – 19, 2016 Magnetar Powered Supernova

Sources of additional power: • Rotation energy potentially available: E = 1 IΩ2 ∼ 1052 erg rot 2 t −α • Spin-down losses: Lrot = L0 1 + τ , L 1045 erg , 105 s, 2 0 ∼ s τ ∼ α ≈ • Inner Shock heating • HEGR heating

! Simple deposition of Lrot at the shell base seems promising for ﬁtting observed SLSN light curves D. 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 explosion and 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 the thermal background of ejecta, until the latter cools enough. Tests are required.

4 Tested Scenario MRI-driven Hypernova with Magnetar Powering E 1 10 foe, L 3 1045 erg , Ni-free but with HEGRs burst = − M = × s

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) ± 3 9 • Magnetar e -wind (I) (γe = 10 − 10 !) is terminated by IV ⇒ • 3 discontinuities: Termination shock (TS), leptons-plasma Contact (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 → free escape) • 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 (0th and 1st moments of the Boltzmann equation, variable Eddington factor closure, O(v/c) in moving 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 and plasma 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: 2 E B Lw pe + pB = 3V + 8π = 2 4πcRTS E˙e = Le + (η − 1)Lγ − peV˙ E˙B = LB − pBV˙ Lγ = LSyn(B, TTE) + LIC(J(ν), B)

at CD: pe + pB ↔ nkT

everywhere above TS: γ + e− → γ0 + heat γ + hν → e± → heat 3 heat = Ee or 2 nkT

8 HEGR Source Calculation

0 dNe (t,γe) −2 • Input: B, Le(t), ∼ Le(t)γ , Trad or Jν(ν) from native dγe e STELLA • Quasi-stationary fast e-cooling: γ e,max 0 dNe(γe,t) N0(t) Ne(γe,t) R Ne(γe ,t) 0 = α − + 0 dγe = 0 dt γe tcool(Trad,B,γe) tcool(Trad,B,γe →γe) γe

dNe(γe,t) dNγ (ε,t) dNγ (ε,t) • ⇒ |Syn, |IC ⇒ Lγ(t) dγe dε dε • 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 radial collimation ⇒ sharp angular dependence, low-order moment approximations 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 density at final energy significantly ⇒ • Simplification: HEGRs are discretized into a set of expanding spherical shells ◦ of 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 on every elementary path r0 → r1 = r0 + c∆t. • Transfer equation formal solution:

−∆τ(ε) 3 Nε(r1, ε) = Nε(r0, ε)e + σT SC(ε) 4

0 ε r r r1 max 1 R 00 R 00 Z Z − χ¯(ε0)dr − χ¯(ε)dr Nε(r0, ε0)F(ε, ε0) 0 r 0 0 SC(ε) = ne(r )e 0 r dr d ln ε0 ε0 ε1 r0

r Z 1 ∆τ(ε) = χ¯(ε, r0, t0(r0))dr0

11 Kinetics and Opacity

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

1 1 2 1 1 2 F(ε, ε0) = (1 + (1 + − ) + εε0( − ) ) ε0 6 εmax(ε, θ) ε0 ε ε0 ε • opacity χ¯ accounts for CS:

2 3 σT 2 2ε (1 + ε) χKN (ε) = ne 4 + (ε − 2 − ) ln(1 + 2ε) + , 8 ε2 ε (1 + 2ε)2

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

 1  2 3 Z 2r0 Θ 2 −νs χpp(ε, ν) = 3 ν sσ(s) ln(1 − e ) ds , πΛe ∞

2 4 2 ν(ε, Teff ) = m c /(εkTeff ), Θ = kTeff /mec , 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 −2.1 erg • L = 3 · 1045 1 + t , B ∼ 1015 w 105s s • Magnetization parameter σ = 0.1 − 10 → 0.1:

σLB + Le = (σ + 1)Lw −2 3 9 • Lepton spectrum: ∼ γe , γe = 10 − 10 • Output: light curves and spectra of outcoming HEGRs and observable TE during the ﬁrst several years

13 Conditions in the Cavern

104 104 Rsrc R 3 3 cd 10 10 B T rad 102 102 101 K

1 5 10 0 10 , 10 cm rad 14 100 10-1 -2 R, 10 -1 10 10

10-3 B, kGs; T 10-2 10-4 -3 10 -5 10

10-4 10-6 10-2 10-1 100 101 102 103 t, days

14 HEGR Outcome

Source Outcome

46 44 Bol 43 0.1-1 GeV 44 1-10 GeV 42 10-100 GeV 0.1-1 TeV

42 -1 41

, erg s 40 γ 40 log L 39

38 38 37

36 36 0.1 1 10 100 1000 10 100 1000

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

15 HEGR Blocking

Key effect: • Plasma is hot ⇒ a lot of thermal hν, to “kill” the most of HEGRs before they pass the CD • HEGRs (almost) do not enter the plasma ⇒ no re-heating of the shell • Cold shell ⇒ does not intercept HEGRs ⇒ no re-heating, weak TE. • Negative feedback hν − γ. Magnetar energy turns into work.

16 Magnetar Driven Shock

The MDS is radiative ⇒ Dense Shell.

HEGRStella Optically and geometrically thin dense shell ⇒ Blondin, Chevalier & Frierson, ApJ, 2001, 563, p.806 Extremely hard for numerical differential transfer Long-characteristic integral scheme for TE

17 Magnetar Driven Shock

The MDS is radiative ⇒ Dense Shell.

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

HEGRStella Optically and geometrically thin dense shell ⇒ Credit: S. Glazyrin ⇒ Extremely hard for numerical differential transfer Time to smear Long-characteristic integral scheme for TE Artiﬁcial RT-viscosity boost 102 − 103

17 Thermal Emission: Bolometric

The work is actually in progress

45 NoHEGR NoNi 3 foe + HEGR 1.2 foe + HEGR 44 NoHEGR + 0.1 MNi

-1 43 , erg s 42 TE,bol

log L 41

39 1 10 100 t, days

18 ... and new questions. • Why the MDS does not shine brightly? Non-Eq emission into the central cavity or an artifact of mixing? • If there are other ways of the shocked wind energy dissipation and heat conduction? • The radiative thin dense shell around CD requires special TE transfer methods or properly enhanced mixing (based on multi-D analysis).

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 2 (t > TNi→Co→Fe ∼ 10 d.) • Unless the shell is too cold, its thermal background blocks the HEGRs within the cavern, otherwise – it is transparent. HEGRs heat not the ejecta but the shocked wind

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 2 (t > TNi→Co→Fe ∼ 10 d.) • Unless the shell is too cold, its thermal background blocks the HEGRs 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 the central cavity or an artifact of mixing? • If there are other ways of the shocked wind energy dissipation and heat conduction? • The radiative thin dense shell around CD requires special TE transfer methods or properly enhanced mixing (based on multi-D analysis). 19 Thank you!