Optical Transient from an Explosion Close to the Stellar Surface
Almog Yalinewich
20.11.19
iPTF14hls
Arcavi et al. 2017
Déjà Vu
\mathcal{M}_r @ {\rm 0.1 \,y} = -16 \Rightarrow L \approx 10^{41} \rm erg/s
Arcavi et al. 2017
Theoretical Model
Sequence of Events
What happened in 1954?
80 M_{\odot}
Our Model
Binary Evolution
Progenitor/Relic Mass Relation
NS/BH transition
More massive star -> shorter life
How could a neutron star have formed in the primary's lifetime?
Relic mass
Belczynski et al 2010
Algol Paradox
Less massive but more evolved
Mass transfer
Energy Deposition
Zoom in
accretion
feedback
M82 X-2
Bachetti et al 2014
The Trigger
SAX J1808.4-3658
spontaneous
Pressure build up
energy determined by binding energy
Sanna et al 2017
Giant Flares
Mini EMP from SGR 1806-20
on 21:30:26.5 UT, Dec 27, 2004
10^{46} \, \rm erg
10% of the magnetic energy
Inan et al 2007
The cinematic experience
https://github.com/bolverk/huji-rich
Zoom In
Observational Signature
Energy
adiabatic losses
Temperature
photon production
Strategy
Hydrodynamic evolution
Energy Deposition
Ejecta distribution
Radiative transfer
Atmospheric Structure
\rho \propto x^{\omega}
\omega = \frac{1}{\gamma-1}
adiabatic atmosphere
adiabatic index
x
Shock Trajectory
l
R
l \gg R
R \propto t^{2/5}
l \ll R
R \propto t^{\beta}
\frac{1}{\omega+4} < \beta < \frac{2}{5+\omega}
momentum
conservation
energy
conservation
Fractal Conservation Law
Fractal dimension of the Sierpinski triangle
\log_2 3 \approx 1.585
Crater Growth
radiative
adiabatic
\beta \left(\omega=3.0\right) \approx 0.19
\beta \left(\omega=1.5\right) \approx 0.25
Yalinewich & Matzner 2019
Ejecta Density Profile
radiative
adiabatic
\frac{d \ln \rho}{d \ln r} \approx -4.5
Yalinewich & Matzner 2019
Ejecta Density Profile
R \propto t^{\beta} \Rightarrow \dot{R}\propto R^{1-1/\beta}
v \approx \frac{r}{t} \approx \dot{R} \Rightarrow R \propto \left(\frac{r}{t}\right)^{\frac{\beta}{\beta-1}}
\rho \propto \rho_0 \frac{R^3}{r^3} \propto r^{-\frac{\omega \beta + 3}{1-\beta}}
Radiation Diffusion
\tau \approx \kappa \rho r \approx \frac{c}{v}
Compton Scattering
opacity
cross section
r_e^2
0.1 \, \rm cm^2/g
Thermalisation
Photon production
Thermal Bremsstrahlung
\dot{n}_{bs} \approx \frac{\alpha c}{r_e^4} \left(n r_e^3\right)^2 \sqrt{\frac{m_e c^2}{k T}}
n_{bb} \approx a T^3/k
In blackbody equilibrium
\frac{r}{c} \tau \dot{n}_{bs} \approx n_{bb}
Colour shell
Radiative Transfer
energy deposited
adiabatic loss
luminosity shell
colour shell
photosphere
Progenitor Model
100 R_{\odot}
80 M_{\odot}
10 R_{\odot}
10^{48} \rm erg
Bondi energy
Lightcurve
1954 event
Temperature
1954 event
Early Time Evolution
1954 event
Shock Breakout
\tau \approx \frac{c}{v}
Shock Ascent
1954 event
Distance from edge
Density
Velocity
Stellar surface
Homologous Expansion
v \approx \frac{r}{t}
Planar Expansion
t
x
Same shell
Luminosity
Watching the same shell cool
V \propto t \Rightarrow U \propto t^{-1/3} \Rightarrow L \propto t^{-4/3}
Logarithmic Correction
Spherical Phase
r \gg l
V \propto t^3
Deeper shells are exposed
l
r
Transition to Cratering
Material from depth l is expelled from the crater
l
Photons diffuse from that shell
end of spherical phase and beginning of crater phase
Radiative Crater?
\frac{d \ln R_c}{d \ln t} > \frac{d \ln R_{l}}{d \ln t}
Eventually, the crater radius exceeds the luminosity radius
After that, photons immediately escape from the shock
Snowplough phase
\frac{d \ln R_c}{d \ln t} = \frac{1}{4 + \omega}
Transition time is extremely long
Shock Temperature
k T_m \approx m_p v^2
\rho v^2 \approx a T_r^4
k T_r \approx \rho^{1/4} v^{1/2} c^{3/4} h^{3/4}
k T_p \approx m_e c^2
k T_s \approx m_e c^2 \left(\frac{m_p}{\alpha m_e}\right)^2 \left(\frac{v}{c}\right)^8
Yalinewich et al 2018
Alternative Explanation
Woosley 2018
Alternative Explanation
Moriya et al 2018
Outlook
More events with LSST?
Rare event (1/century)
Aspherical Supernova
Polarisation from Supernova
Aspherical Supernova
G315.78−0.23 a.k.a Frying pan nebula, from Schnitzel et al 2019
Aspherical Supernova
Rapidly spinning Be stars
Application to Fast Blue Optical Transients
Days since explosion
0
30
Apparent magnitude
10
20
Perley et al 2018
Summary
Developed theoretical model for an explosion near stellar surface
Possible explanation for the 1954 Event
Might also explain FBOTs and weird LSST detections
oblique shock breakout
By almog yalinewich
