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Simulations of Multigroup Relativistic Transferfor Supernova Shock Breakout

Institute for Theoretical and Experimental PhysicsRussian Federation State scientific center

Alexey Tolstov, Sergey Blinnikov

22nd Rencontres de Blois

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Observations of last years

Supernova remnant of Cassiopeia ASN Type II:SNLS-04D2dc

Interpretation of early light curves and spectra – the explanation of the nature of exploding stars. Theoretical models are needed!

SN 2008D

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Problem statement and aims

Statement There is no reliable simulations of supernova shock breakout where the radiative transfer processes can not be neglected and, in addition, a number of relativistic effects should be taken into account.

SolutionImplementation of numerical method for transfer equation solution in fluids moving with Lorentz factor Г>>1Calculation of supernova light curves and spectra at the epoch of shock breakout

ApplicationsMost reliable predictions for supernova outbursts in experimentsUnknown number of outbursts collapsing SN 1987A type and Ib/c type supernovae (~10-100 s)The detection of type Ib/c explosions – the description of the connection of supernovae with gamma-ray burstsIn the case of nearby supernovae, there can be a correlation with the detection of gravitational waves and neutrinos

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Contents

IntroShocks in supernovae

I. Numerical solution of relativistic transfer equation Development of algorithm for solving a problem of radiation transfer in fluids moving with high values of Lorentz factorExposure of peculiarities in calculation of radiation propagation to the remote observer

II. Supernova shock breakoutShock breakout model for type I b/c and SN 1987A supernovae using multigroup radiation hydrodynamicsThe influence of relativistic and geometric effects of radiationpropagation to the remote observer on light curves and spectraPerspectives of numerical modeling application for data analysis andinterpretation of cosmic experiments

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SN1994D type Ia in NGC4526SNR Tycho in X-rays (Chandra)

For type Ia shocks do not play a role in explanation of the luminescence

The luminescence due to shock interacting with medium can last tens of thousand of years

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Most luminous supernovae

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Supernova factory NGC2770XRT 080109/SN 2008D

In SN2008D shock breakout is detected (Soderberg A. et al., 2008)

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Shock acceleration in outer layers

At star surface velocity grows according analytic solution of Gandelman and Frank-Kamenetsky (1956), Sakurai(1960)

Velocity profiles as a function of optical depth (Blinnikov, 1999). At

photons start running out shock front, accelerating outer layers, but due to radiation losses energy cumulation on small mass is not efficient

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Numerical methods of simulation

STELLA (STatic Eddington-factor Low-velocity Limit Approximation) (Blinnikov, 1998) software package has been successfully used to model the light curves of several supernovae. It is based on solving the hydrodynamic equations consistently with the transfer of non-equilibrium radiation by applying first-order (in velocity) relativistic corrections. This method is well suited to modeling type II supernovae, such as, for example, 1987A and 1993J

RADA (fully Relativistic rADiative transfer Approximation) (Tolstov,Blinnikov, 2003) allows to calculate radiation transfer at in case the shock wave reaches relativistic velocities. It is important for supernova light curves simulations at the epoch of supernova shock breakout.

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I. Relativistic radiation transfer calculationNumerical solution of transfer equation

For moving media transfer equation is convenient in comoving frame of reference (McCrea, Mitra, 1936, Mihalas, 1980). Equation is solved numerically using method of characteristic up to Lorentz factorγ ~ 1000 with accuracy 1% (algorithm RADA).

η – emission coefficient, χ – extinction coefficient, all quantities are in comoving frame of reference

∂ ∂∂ ∂

⎧ ⎫⎡ ⎤∂ ∂ ∂⎪ ⎪⎨ ⎬⎢ ⎥∂ ∂ ∂⎪ ⎪⎣ ⎦⎩ ⎭

⎧ ⎫⎡ ⎤∂ ∂ ∂⎪ ⎪⎨ ⎬⎢ ⎥∂ ∂ ∂⎪ ⎪⎣ ⎦⎩ ⎭

0 0 0 0 0 00 0

22 200 0 0 0 0 0

0

2 220

0 0 0 0 0 0 0 00

0

I (μ ,ν ) I (μ ,ν )γ (1+βμ ) +γ(μ +β) +c t r

(1+βμ ) β γ β+ γ(1-μ ) -γ (μ +β) - (1+βμ ) I (μ ,ν ) -μ r r c t

β(1-μ ) β γ β- γν +γ μ (μ +β) + μ (1+βμ ) I (μ ,ν ) +ν r r c t

2μ +β(+γ⎧ ∂

+⎨ ∂⎩⎫∂⎬∂ ⎭

22 2 0

0 0

2 20 0 0 0 0 0 0 0 0 0 0 0

3-μ ) β+γ (1+μ +2βμ )r r

γ β+ [2μ +β(1+μ )] I (μ ,ν )=η (ν )-χ (ν )I (μ ,ν )c t

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STELLA RADA integration

− −⎛ ⎞= − + − = +⎜ ⎟

⎝ ⎠∫

s ( s') 20 0

I ( s ) I e e e ds' , 0.5 s sτ τ τη η ηη χ τ χ χχ χ χ% % %

%% % %

Algorithm RADA turns on before shock breakout startsSTELLA uses Lagrangian grid over mass coordinate, RADA – short characteristics with physical quantities interpolation

dI ( s ) s I ( s ) sI ( s )s

= η + η − χ − χ% % = +b Jν ν ν νη α σ

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Radiation fluxfor the remote observer

⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

∫min

31 2 0

obs 0 00

F ( t ) 2 p I ( R( ), ,cos (cos )) dν μ

ν νπ μ μ ν δ δ μν ν

Allowance of time delay, Doppler effect and aberrationFlux F in the point of observation – integral of intensity over the surface:

0I

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Effects of Lorentz covariance

Transfer equation Lorentz covariance, Doppler effect and aberration:

lead to the following visible effects in moving to radiation sources:

1. Radiation flux increases2. Spectrum becomes harder3. The space is towards the direction of motion

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Star sky viewin acceleration of the observer

Parameters of the model: 1000 stars of spectral class M-A (2000-10000 K), magnitude m=0-10.Visible camera angle Ω ~ 1 sr, Lorentz factor Г=1…1000.

Parameters: 1000 stars,

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Radiation flux calculation at relativistic velocities for the remote observer

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Radiation flux decreaseat relativistic expansion

Radiation flux at a remote point of observation from an envelope of radius R = 1 lsScenario 1 – at t = 0 an outburst occurs with intensity 100I and duration dt=0.1R/c sfollowed by envelope expansion Сценарий 2 –expansionСценарий 3 – an outburst without any subsequent expansion

- flux at t=00FFor arbitrary envelope dynamics radiation flux at a remote point can be calculated only numerically

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II. Supernova shock breakout Evolutionary type Ib/c presupernova model

Evolutionary calculation of KEPLER program for a main sequence star(Woosley et al., 1995)

STELLA provides a shock velocity at breakout up to 0.6с (Blinnikov, 1998)

M = 3.199 MR = 1.41 1011 сmE = 1.24 1051 erg

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SN Ib/c model s1b7a

Qualitative comparison of early monochromatic light curves

Gray line – STELLA in comoving frame of reference taking into account observer time correction:

Black line – STELLA in observer’s frame of reference with accurate allowance of time delay effect

→ −t t R( t ) / c

Decrease in radiation flux at maximum andbroadening of the light curve peak

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Light curvesin observer’s frame of reference

Comparison of the monochromatic light curves at the epoch of shock breakout. The thin and thick lines represent, respectively, the STELLA calculation with the delay effect and the RADA calculation.

Time delay allowance leads to steep decline of light curve (≈ 82 s)

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Spectrain observer’s frame of reference

Comparison of the instantaneous spectra for various times at the epoch of shock breakout. The thin and thick lines represent, respectively, the STELLA calculation with the delay effect and the RADA calculation.

Turning on RADA makes the spectrum harder and the flux more powerful

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Supernova shock breakout

Calculated dynamics of outburst as if it would be seen by observer – the result of radiation time delay allowance

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Early light curves of SN 1987A

Comparison of the bolometric light curves at the epoch of shock breakout in the observer’s frame of reference for an SN1987A-type presupernova model. The solid and dashed lines represent, respectively, the STELLA and RADA calculations.

RADA leads to a decrease in radiation flux at maximum and to a broadening of the light curve peak.

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Observational data interpretation

Outburst spectrum of one second maximums in assumption that the distance to the source is 50 Mpc

Type Ib/c supernova outbursts can be used for estimations of observations in LOBSTER experiment. Mainly for outbursts ofRSG, BSG. Estimation for I b/c – several outbursts in a year at = 50 MpcMAXI (Monitor of All-sky X-ray Image) (Matsuoka et al. 1997) is launchedEXIST (Energetic X-ray Imaging Survey Telescope) satellite (Grindlay et al. 2003; Band et al. 2008) is planned

maxD

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Perspectives

Purposes for LOBSTER and theory (Calzavara, Matzner, 2004):

Unknown number of supernova SN 1987A type (~ 100 s) – very important for star evolution theory verification. Estimations for LOBSTER – 50 - 600 SNe type II for 3 years of experiments at = 250 MpcType Ib/c supernova explosions are also difficult to observe due to their short duration ( 10 s), but, in this case, the radiation has the hardest spectrum and the X-ray radiation from the shock propagating within the presupernova wind can be detectedTo improve existing estimations the theoretical modeling methods we developed can be used

maxD

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Conclusions

Numerical algorithm RADA (Relativistic rADiation transfer Approximation) is developed for solving radiation transfer equation in fluids, moving with relativistic velocities

Algorithm of radiation flux calculation from comoving frame of reference of spherically symmetric source to observer’s frame of reference is developed taking into account Doppler effect, aberration and time delay effect

Numerical models of radiation transfer at the epoch of shock breakout for supernova type Ib/c and SN 1987A are build. Light curves and spectra are calculated. A comparison with previous simulation is performed

Estimations of outburst detections for type Ib/c supernovae in future cosmic experiments is performed

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Future theoretical models improvements

Developing of fast algorithm for radiation transfer calculationsMore accurate allowance for the hydrodynamic effectsMore correct description of the scattering processesMore complete description of the radiation mechanismsDeveloping multidimensional algorithms to allow for the observed asymmetry effects

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References

Blinnikov S.I. et al., Astrophys.J., 496, 454 (1998)Band, D. L et al., ApJ, 673, 1225Blinnikov S.I., AstL, 25, 359 (1999)Blinnikov S.I., Chugai N.N., Lundqvist P., et al., Proc. of ESO/MPA/MPE Workshop on Observable Effects of Shocks in Compact and Extended Presupernovae. From Twilight to Highlight: The Physics of Supernovae (2003), p. 23; arXiv:astroph/0212569.Gandelman G.M., Frank-Kamenetsky D.A., Doklady Akad. Nauk SSSR, 107, 811 (1956)Calzavara A.J., Matzner C.D. MNRAS, 351, 694 (2004)Grindlay, J. E. et al., (SPIE) Conference Series, ed. J. E. Truemper & H. D. Tananbaum, 331–344Matsuoka et al, SPIE Conference Series, ed. O. H. Siegmund & M. A. Gummin, 414–421Matzner, C. D. & McKee, C. F. 1999a, apj, 51McCrea W.H., Mitra, K.K., Zeitschrift für Astrophysik, 11, 359 (1936)Mihalas, D., Astrophys.J., 237, 574 (1980)Sakurai A., Commun. Pure Appl. Math., 13, 353 (1960)Soderberg A.M., et al., Nature, 453, 469 (2008)Tolstov A.G., Blinnikov S.I., AstL, 29, 403 (2003)Tolstov A.G., AstL, 36, 2, 109, (2010)Woosley S.E., Langer N., Weaver T.A., Astrophys. J. 448, 315 (1995)

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Thank you!

Institute for Theoretical and Experimental PhysicsRussian Federation State scientific center