Probing Galactic Centres with Tidal Disruption Events
Almog Yalinewich
21.5.19
Journey to the Galactic Centre
A glimpse to the Supermassive Black Hole in M87
Galactic Centre Mysteries
Star formation in extreme environments
Star - Central Black Hole interactions
Gas Accretion
The Twist
Types of Galactic Centres
Active
Very bright
Quiescent
very close
Tidal Disruption Events
Evidence
r \left(\tau=1\right) \propto t^0
L \propto \frac{E}{t} \propto \frac{1}{t} \frac{1}{a} \propto \frac{1}{t} \frac{1}{t^{2/3}} \propto t^{-5/3}
Schematic
Tidal Radius
Apoapse Distance
Tidal Radius
R_t
To black hole
2 R_s
\frac{G M_s}{R_s^2} \approx \frac{G M_h}{R_t^3} R_s \Rightarrow R_t = R_s \left(\frac{M_h}{M_s}\right)^{1/3}
Black Hole Mass Limit
R_s \left( \frac{M_h}{M_s}\right)^{1/3} > \frac{G M_h}{c^2}
Tidal radius
gravitational radius
M_h < M_s \left(\frac{R_s c^2}{G M_s}\right)^{3/2} \approx M_{\odot} \left(\frac{R_{\odot} c^2}{G M_{\odot}}\right)^{3/2} \approx 10^8 M_{\odot}
Apoapse Distance
a
To black hole
2 R_s
\frac{G M_h R_s}{R_t^2} \approx \frac{G M_h}{a} \Rightarrow a = R_s \left(\frac{M_h}{M_s}\right)^{2/3}
Forensics
?
Optical and X - Ray Signals
Outflow Driven Radio
black hole & accretion disc
cold outflow
cold ambient medium
hot outflow
hot ambient medium
Non Thermal Radio
Radio supernova
Synchrotron
Fermi Acceleration
Diffuse Shock Acceleration
\frac{\partial f}{\partial t} + u \frac{\partial f}{\partial x} = \frac{\partial}{\partial x} \left(D \frac{\partial f}{\partial x}\right) + \frac{1}{3} \frac{d u}{d x} p \frac{\partial f}{\partial p}
think about adiabatic compression
u = \left\{\begin{matrix}
u_1 & x>0\\ u_2 & x<0
\end{matrix}\right.
u_1
u_2
\frac{\partial f}{\partial t} = 0
f \propto p^{-\alpha}
\alpha = \frac{3}{1-u_2/u_1}
Self Absorption
L_{\nu,o} \approx \frac{m_e c^2}{r_e^2} \sqrt[4]{\frac{m_e c^2}{r_e^3 B^2}} \left(\frac{\nu r_e}{c}\right)^{5/2} A
L_{\nu,t} \approx \sqrt{B^2 r_e^3 m_e c^2} \left[\frac{1}{\gamma_{\min} }\sqrt{\frac{\nu r_e}{c}} \sqrt[4]{\frac{m_e c^2}{r_e^3 B^2}} \right]^{-p}N
\frac{d n_e}{d \gamma} \propto \gamma^{-p}
\gamma>\gamma_{\min}
Synchrotron Spectra for ASASSN-14li
Degeneracy
Origin of the Outflow
Accretion disc Jet
Accretion disc Jet
Unbound debris
Unbound Debris
q = \frac{M_h}{M_s}
\alpha_{xy} \approx q^{-1/6}
\alpha_{xz} \approx q^{-1/3}
The Precursor
M_d \approx 10^{-4} M_{\odot}
Energetics
f_{\nu} \approx 1 {\rm mJy}
Radio signal from ASASSN-14li
\nu \approx 10 \, \rm GHz
d \approx 90 \, \rm Mpc
t \approx 1 \, \rm y
u \approx 4 \pi\nu f_{\nu} d^2 t \approx 10^{45} \, \rm erg
v \approx 10^4 \rm km/s
m \approx \frac{u}{\varepsilon v^2} \approx 10^{-4} M_{\oplus}
\varepsilon_e \approx 10^{-2}
Simulations
High impact parameter
Simulations
Low impact parameter
Mass Velocity Distribution
high impact parameter
low impact parameter
Bow Shock
Shocked region = 3 x obstacle size
Density Profile for ASASSN 14li
Event Rate
R_p
R_t
Full loss cone
\dot{N} \propto \frac{R_p}{R_t}
Empty loss cone
\dot{N} \propto \log \frac{R_p}{R_t}
That's gas density.
What about the stellar density?
Generalised Bondi Problem
Governing Equations
\frac{\partial \rho}{\partial t} + \frac{1}{r^2} \frac{\partial}{\partial r} \left(\rho u r^2\right) = q
\rho \frac{\partial u}{\partial t} + \rho u\frac{\partial
u}{\partial r}=-\frac{\partial p}{\partial r}-\rho
\frac{{\rm d} \Phi}{{\rm d} r} -q u
\frac{\partial \epsilon}{\partial t}+ \frac{1}{r^2}
\frac{\partial}{\partial r} \left[\rho r^2 u \left(\epsilon
+\frac{p}{\rho}\right)\right]=\frac{1}{2} q v_w^2+q\Phi
\Phi = - \frac{G M_h}{r}
\epsilon \equiv \frac{1}{2} v^2 + \Phi + \frac{p}{\rho (\gamma-1)}
q = D r^{-\eta}
Mach Number Profile
to the black hole
outside
Density Profile
Asymptotic Expansion
r \ll R_b
\rho \propto r^{-3/2}
r \gg R_b
\rho \propto r^{1-\eta}
Total number of stars
Stellar density slope
Implications for ASASSN 14li
\eta \approx 5/2
If there is no break
Governing equations can be solved analytically
\tilde{\rho} = \frac{\rho}{\rho_b} = \frac{4 \sqrt{6}}{3 \tilde{r}^{3/2}}
\rho_b = \frac{D R_b^{1-\eta}}{v_w^2}
\tilde{r} = \frac{r}{R_b}
R_b = \frac{G M_h}{v_w^2}
Summary
Radio Loud TDE -> density profile in a GC
Density profile -> Density of wind emitting stars
Wind emitting -> main sequence stars?
questions?
Probing Galactic Centres with Tidal Disruption Events
By almog yalinewich
