2014/07/08 RIKEN-IPMU-RESCEU seminar

Theoretical expectation ofsupernova shock breakout in therelativistic limit
Yukari Ohtani (RESCEU), Akihiro Suzuki (U. Kyoto) andToshikazu Shigeyama (RESCEU)

SN shock breakout
Luminous X-ray/UVtransient results from theshock passing through thestellar surface• ∆𝑡~ 𝑅 𝑐 ≲ 104 s• 𝐿peak ≳ 1043 erg s −1

XRO 080109/SN 2008D
detected by Swift/XRT• ∆𝑡 = 600 s• 𝐿𝑋 = 6 × 1043 erg s −1
• 𝐸𝑋 = 2 × 1046 erg∝ 𝐸 −2.3±0.3• non-thermal component(Soderberg et al. 2008)

Li, L.-X. (2008)

bulk Compton effect
Repeated scattering by
high velocity electrons
moving in the radial
direction boost the photonenergy.

𝑁 𝐸 ∝ 𝐸 −2.4

shock front

photonbulk motion

Suzuki and Shigeyama (2010)
When 𝑉𝑠 ≥ 0.3 𝑐, the non-thermal
component of XRO 080109 can bereproduced.

SB in the relativistic jet• Wolf-Rayet star
• shock Lorentz factor ~ 100• 𝛾-ray photons• correlation with GRBs

SB at stellar surfaceΓsb = 10thermal• integration of Doppler shiftedblackbody radiation

non-thermal• comparable to the electron
rest energy in the comovingframe(Ohtani et al. 2013)

SB at stellar surface
Consistent with GRBs
• cut-off energy• the logarithmic slope of thehigher energy side of theBand FC

Γsb = 10𝐸𝛼𝐸𝛽Inconsistent with GRBs
• the lower energy side of theBand FC• duration (≪ 2 s)
• total energy (< 1049 erg s −1 )(Ohtani et al. 2013)

𝐸peak

𝛼 = −1.0+0.9
𝛽 = −2.5−2.2
𝐸peak = 250 keV 120 keV

SB in the CSM• thermal radiation at lower temperatures than that of thestellar surface- lower energy component of the Band FC ?

• larger size of the region- extended duration ?

ModelBlandford and McKee (1976)
Initial• 𝑛 ∝ 𝑟 −𝑘 , 𝑘 = 2shock• Γ ∝ 𝑡 −𝑚 2 , 𝑚 = 0

ejecta104 𝑏𝑋𝑠−2

post- preshock shock
𝜏=1

𝑏𝑋𝑠−2
𝑋𝑐

𝑋𝑠log 𝑟Γ = 100, 𝑅sb = 1012 cm

MC code
inverse Compton scattering + free-free absorption
contact surface shock front
𝑋𝑐
𝑋𝑠
photonbulk motion

photosphere: the position atwhich 50% of generated
photons can be escaped, andother photons are absorbed

Most of photons are generated
behind the contact surface.

Generation of photons stops when the shocked matter become thin.

Overview of photon traveling“straight on” photons (= radial)• enhanced upto 𝐸max = Γ𝑚𝑐 2• scattering dominant“deviated” photons (≠ radial)• degrated• absorption dominant
𝛼𝑠 = 𝜎KL 𝑛 ∝ 𝑛
𝛼ff ∝ 1 − 𝑒 −𝐸 𝑘𝑏𝑇 𝑛2

in the observer’s frame
shocked matter shock front

photonin the comoving frame
𝜃<𝜋 2“Deviated” photons are tend tobe generated at later time than“straight on” photons.

𝜃>𝜋 2

Spectrainitial photon = integration of the Doppler shifted blackbody emission
Γ = 10Γ = 100∝ 𝐸 −0.4

deviated∝ 𝐸 −3.5

straight on

exponential

inaccuracy ofdetermination of thetime when the shocked
matter become thin ?

Γ𝑚𝑐 2

breakout needs to occur in accelerating phase ?

Light curve< 0.3 keV: removed
Γ = 10Γ = 100
𝑇99 = 900 s

𝑇99 = 40 s

• The timescale is determined by diffusion. (∝ 1 Γ)
• Low-energy photons are tends to delay.

Spectral evolution
Γ = 10Γ = 100“Deviated” photons are tend to delay by several seconds in their arrival time.

Summary
radiation from the shocked matter in CSM (constant Γ)• duration ≳ 10 s
• early: high energy bulk component• later: lower energy• not power-law, but exponential

our next calculation: breakout at the accelerating phase