Download Do flares in Saggitarius A* reflect the last stage of tidal capture

Do flares in Sagittarius A* reflect
the last stage of tidal capture?
Andrej Čadež1, Massimo Calvani2,
1
1
Andreja Gomboc , Uroš Kostić
1University
of Ljubljana, Slovenia
2Osservatorio Astronomico di Padova, Italy
X-ray, XMM Newton, October 2002:
D. Porquet et al.
IR flare June 2003,VLT-NACO,:
Genzel, R. Schodel, T. Ott et al.
R.
Hard X-ray , Chandra,October 2000:
K. Baganoff et al.
F.
X-ray, XMM Newton, Sept. 2001:
Goldwurm et al.
A.
The time scale puzzle
 1. The rise and switch off rates of all flares are very similar
 2. The rise-switch-off time scale is about 900
 3. The light curve is similar in all wavebands
s
 Radiation diffusion time of a light source (tg) :
Let the source be a homogeneous sphere made of the
most transparent material available – hydrogen at a high
enough temperature -, so that its opacity is due only to
Thomson scattering (k = 0.4cm2/g), and assume that
photons are loosing no energy when diffusively scattering
to the surface. Then: tg = (1/c) (k M/R), or
= 4400 s (M/MMoon)2/3r-1/3
tg
Infalling point particle: obseved intensity in the
orbital plane as a funtion of time and longitude of
observer
IR flare June 2003
model
Ingredients:
a small body, like a comet or
asteroid, heated on the way
toward complete tidal
disruption
on a parabolic orbit with
lorbital = 4 m.Mbh.c
mass of the black hole:
4 106 solar mass
heating time scale t
2300s
=
effective length of tidal tail
Lt =circumference of last
stable orbit
assumed inclination 900
observer longitude ~600
Scenario
 1. stars moving close to the Galactic center
black hole are gradually beeing stripped off
their comets, asteroids, planets. In the
process the remaining stellar system is
increasing its internal angular momentum at
the expence of orbital angular momentum,
making the stellar system orbit more and
more elliptical
 2. A stripped asteroid is likely to move on a
highly eccentric orbit, reaching deep into the
potential well of the black hole. Each
periastron passage produces an increasing
tidal wave and reduces the orbital angular
momentum and the orbital energy in such a
way that the orbit is becoming more and
more eccentric (parabolic) with the angular
momentum slowly approaching the angular
momentum of tidal capture l=4 m MBH c .
The last tidal kick, that occurs just before
capture, releases ~10% mc2 of tidal energy
to the asteroid, which is more than enough
to heat it to X-ray temperatures.
3. Time scales and energetics:
 The radiation diffusion time for an asteroid,
heated to X-ray tempertures is
tg = 4400 s (m/MMoon)2/3r-1/3 = 240
s
for m=1021g and r=1g/cm3
 Energy release: up to ΔE~0.1mc2 = 1042erg
 Capture rate:
stellar capture rate × no. of asteroids per star:
~(10-4 y-1) × 105 = 10 y-1
Conclusion
 The light curve of tidal capture of an asteroid size body is
modeled as the light curve of an almost point particle
beeing captured and heated by tides on a critical orbit by
the massive black hole.
 The time scale fits the known mass of the central galactic
black hole,
 the expected energy release is compatible with observation
and
 the observed frequency of events is consistent with the
expected capture rate.
 This simple model fits the observed light curve of the IR
flare surprisingly well.