EARLY SUPERNOVA EMISSION - LOGARITHMIC CORRECTIONS TO THE PLANAR PHASE
Almog Yalinewich
Norm's Group Meeting
5.9.19
Hunt for the Progenitor
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Forensics
Prompt
Breakout
Stellar Swan Song
Enter LSST
Physical Model
Explosion Mechanism
Shock Ascent
Distance from edge
Density
Velocity
Radiation Leak
x \approx D/v, \, D\approx \lambda c\Rightarrow \tau \approx c/v
Radiative Processes
Why photons come
Why they stay
\sigma \approx r_e^2
\dot{n}_{bs} \approx \frac{\alpha c}{r_e^4} \left(n_b r_e^3\right)^2 \sqrt{\frac{m_e c^2}{k T}}
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
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}
Energy Problem
Energy would run out after one diffusion time
We have to go deeper!
Today's Paper
Diffusion in an Expanding Medium
\frac{\partial u}{\partial t} = \frac{\partial}{\partial x} \left(D \frac{\partial u}{\partial x}\right)
D \approx \lambda c \approx \frac{1}{\kappa \rho}
dm = \rho dx \propto d \tau
\frac{d x}{d t} = \frac{x}{t} \Rightarrow \rho \approx m^{\zeta} t^{-1}
\frac{\partial u}{\partial t} \approx \rho \frac{\partial^2u}{\partial m^2} \approx \frac{m^{\zeta}}{t} \frac{\partial^2 u}{\partial m^2}
\tau \propto m \propto \left(\ln t\right)^{\frac{1}{2-\zeta}}
Effect on Luminosity
Effect on Temperature
Progenitor Models
Red Supergiant
Red Supergiant
Red Supergiant,
stronger explosion
Blue Supergiant
Blue Supergiant
Wolf Rayet
