Almog Yalinewich
Norm's group meeting 24.10.19
Eddington Luminosity
{\color{cyan} \frac{G M \mu}{r^2} } \approx {\color{yellow} \frac{L \sigma}{c r^2}} \Rightarrow L \approx \frac{G M \mu c}{\sigma}
\mu
L \approx 10^{38} \frac{M}{M_{\odot}} {\rm \frac{erg}{s}}
The Fault in our Stars
Eddington lifetime
t_e \approx \frac{\eta M c^2}{L} \approx
\approx 3 \cdot 10^6 \, \rm yr
Stellar Mass Limit
Hydrostatic equilibrium
\frac{G M^2}{R^4} \approx S R^{-3 \gamma}
Instability when
\gamma\le \frac{4}3{}
Massive stars are radiative
\gamma - \frac{4}{3} \approx \beta \ll 1
At high masses, GR effects become important
Stellar Mass Limit
Helium burning temperature
T_c \approx 10^8 \, K
Eddington luminosity
L \approx \frac{G M^2}{R} \frac{c}{R \tau} \approx \frac{\sigma_{SB} T_c^4 R^2} {\tau}
R \approx \sqrt[4]{\frac{G M^2 c}{\sigma_{SB} T_c^4}} \approx 0.5 \left(\frac{M}{M_{\odot}}\right)^{1/2} R_{\odot}
\beta \approx \frac{\frac{M}{m_p} k T_c}{a T_c^4 R^3} \approx\frac{c^{3/4} h^{3/4}}{G^{3/4} \sqrt{M} m_p} \approx 5.4 \left(\frac{M}{M_{\odot}}\right)^{-1/2}
\chi \approx \frac{G M}{c^2 R} \approx \frac{G^{3/4} \sqrt{M} k T_c}{c^{11/4} h^{3/4}} \approx 10^{-6} \left(\frac{M}{M_{\odot}}\right)^{1/2}
Stellar Mass Limit
Stars cannot support themselves if
M > 10^{6} M_{\odot}
In the range
10^6 M_{\odot} > M > 10^2 M_{\odot}
>
\chi \approx \beta
X Ray Binaries
Clues to the Progenitor
Circinus X-1
L_x \approx 10^{36} \rm \frac{erg}{s}
SS 433
L_x \approx 10^{36} \rm \frac{erg}{s}
Luminosity Function
M82 X-1
L \approx 5 \cdot 10^{40} \rm \frac{erg}{s}
M82 X-2
>
L \approx 2 \cdot 10^{40} \rm \frac{erg}{s}
What about the Eddington Luminosity?
Ultra - luminous X - Ray Binaries with a Neutron star
Are there enough neutron stars for all ultra luminous X ray binaries?
Synthetic population
Stellar structure
Semi empirical relations
BSE
Formation Channels
Results
Neutron stars can explain all ULX
No need for intermediate mass black holes
A sizeable fraction of the companions are He stars