Do flares in Sagittarius A* reflect the last stage of tidal capture? Andrej Čadež 1, Massimo Calvani 2, Andreja Gomboc 1, Uroš Kostić 1 1 University of.

Do flares in Sagittarius ADo flares in Sagittarius A* reflect * reflect the last stage of tidal capturethe last stage of tidal capture??

Andrej Andrej ČadežČadež11, Massimo Calvani, Massimo Calvani22,,

Andreja GombocAndreja Gomboc11, Uroš Kostić, Uroš Kostić11

11University of Ljubljana, SloveniaUniversity of Ljubljana, Slovenia22Osservatorio Astronomico di Padova, ItalyOsservatorio Astronomico di Padova, Italy

X-ray, XMM Newton, October 2002: X-ray, XMM Newton, October 2002: D. Porquet et al.D. Porquet et al.

IR flare June 2003IR flare June 2003,VLT-NACO,: ,VLT-NACO,: R. Genzel, R. Schodel, T. OttR. Genzel, R. Schodel, T. Ott et al. et al.

Hard X-ray , Chandra,October 2000: Hard X-ray , Chandra,October 2000: F. K. Baganoff et al.F. K. Baganoff et al.

X-ray, XMM Newton, Sept. 2001: X-ray, XMM Newton, Sept. 2001: A. Goldwurm et al.A. Goldwurm et al.

The time scale puzzleThe time scale puzzle

11. The rise and switch off rates of all flares are very similar. The rise and switch off rates of all flares are very similar 22. The rise-switch-off time scale is about . The rise-switch-off time scale is about 900 s900 s 3. The light curve is similar in all wavebands3. The light curve is similar in all wavebands

Radiation diffusion time of a light source (Radiation diffusion time of a light source () : ) :

Let the source be a homogeneous sphere made of the Let the source be a homogeneous sphere made of the most transparent material available – hydrogen at a high most transparent material available – hydrogen at a high enough temperatureenough temperature - -, so that its opacity is due only to , so that its opacity is due only to Thomson scatteringThomson scattering (( = 0.4cm = 0.4cm22/g)/g), and assume that , and assume that photons are loosing no energy when diffusively scattering photons are loosing no energy when diffusively scattering to the surfaceto the surface. . Then: Then: = (1/c) (= (1/c) ( M/R) M/R), or, or

= = 4400 s4400 s (M (M/M/MMoonMoon))2/32/3-1/3-1/3

Infalling point particle: obseved intensity in the Infalling point particle: obseved intensity in the orbital plane as a funtion of time and longitude of orbital plane as a funtion of time and longitude of

observerobserver

IR flare June 2003 IR flare June 2003 modelmodel

Ingredients:Ingredients:a small bodya small body,, like a comet or like a comet or asteroidasteroid,, heated on the way heated on the way

toward complete tidal toward complete tidal disruptiondisruption

on a parabolic orbit with on a parabolic orbit with llorbitalorbital = 4 m.M= 4 m.Mbh.bh.c c

mass of the black hole: mass of the black hole: 4 104 1066 solar mass solar mass

heating time scale heating time scale ss

effective effective length of tidal taillength of tidal tailLLtt = =circumference of last circumference of last

stable orbitstable orbit assumed inclination 90assumed inclination 9000

observer longitude observer longitude ~60~6000

ScenarioScenario

1. stars moving close to the Galactic center 1. stars moving close to the Galactic center black hole are gradually beeing stripped off black hole are gradually beeing stripped off their comets, asteroids, planets. In the their comets, asteroids, planets. In the process the remaining stellar system is process the remaining stellar system is increasing its internal angular momentum at increasing its internal angular momentum at the expence of orbital angular momentum, the expence of orbital angular momentum, making the stellar system orbit more and making the stellar system orbit more and more ellipticalmore elliptical

2. A stripped asteroid is likely to move on a 2. A stripped asteroid is likely to move on a highly eccentric orbit, reaching deep into the highly eccentric orbit, reaching deep into the potential well of the black hole. Each potential well of the black hole. Each periastron passage produces an increasing periastron passage produces an increasing tidal wave and reduces the orbital angular tidal wave and reduces the orbital angular momentum and the orbital energy in such a momentum and the orbital energy in such a way that the orbit is becoming more and way that the orbit is becoming more and more eccentric (parabolic) with the angular more eccentric (parabolic) with the angular momentum slowly approaching the angular momentum slowly approaching the angular momentum of tidal capturemomentum of tidal capture ll==4 m M4 m MBHBH c . c . The last tidal kick, that occurs just before The last tidal kick, that occurs just before capture, releases capture, releases ~~10%10% mc mc22 of tidal energy of tidal energy to the asteroid, which is more than enough to the asteroid, which is more than enough to heat it to X-ray temperatures.to heat it to X-ray temperatures.

3. Time scales and energetics:3. Time scales and energetics:

The radiation diffusion time for an asteroid, The radiation diffusion time for an asteroid, heated to X-ray tempertures is heated to X-ray tempertures is

= = 4400 s4400 s ( (m/Mm/MMoonMoon))2/32/3-1/3-1/3 = 240 s = 240 s

for m=10for m=102121g and g and =1g/cm=1g/cm33

Energy release: up to Energy release: up to ΔΔEE~0.1mc~0.1mc22 = 10 = 104242ergerg

Capture rate: Capture rate: stellar capture rate stellar capture rate × no. of asteroids per star× no. of asteroids per star::

~(10~(10-4-4 y y-1-1) × 10) × 1055 = 10 y= 10 y-1-1

ConclusionConclusion

The light curve of tidal capture of an asteroid size body is The light curve of tidal capture of an asteroid size body is modeled as the light curve of an almost point particle modeled as the light curve of an almost point particle beeing captured and heated by tides on a critical orbit by beeing captured and heated by tides on a critical orbit by the massive black hole. the massive black hole.

The The time scaletime scale fits the known mass of the central galactic fits the known mass of the central galactic black hole, black hole,

the expected the expected energy releaseenergy release is compatible with observation is compatible with observation and and

the observed the observed frequency of eventsfrequency of events is consistent with the is consistent with the expected capture rate.expected capture rate.

This simple model fits the This simple model fits the observed light curveobserved light curve of the IR of the IR flare surprisingly well. flare surprisingly well.