Andrej ČadežColaborators Uroš Kostić

Massimo CalvaniAndreja Gomboc

Tidal energy release before plunging into a black hole

Andrej ČadežUroš KostićMassimo Calvani

What would it look like if a light bulb would be dropped into a black hole?

A far observer, more or less in the orbital plane would see a signal like:

(Note that typical time scales are about 50M = 1000s for GCBH)

Sending a “realistic” object down a black hole

Observations of flares from Galactic center came as an intriguing surprise; they not only look similar, but also

time scales match

• Some sort of a “comet”,15 106km

long with brightness decreasing

exponentially from head to tail and exponentially heating on a plunging orbit

down the black hole, would

produce a light curve that is

strikingly similar to the first IR flare

observed from the Galactic center.

Energetics and time scales:• Typical flare energy ~ 1035erg

• Flare rate ~ 1 /day

Remarkable facts: 1. almost a solar luminosity is turned on in less then

1000s; the turning off is just as fast 2. quasi-periods strongly suggest orbital motion very near

the black hole; accretion into the black hole is almost inevitable

3. mass involved in producing a single flare could not be very large: ~1020 g is consistent with the estimated mass rate and produced energy, but requiering a few percent

mass to energy conversion efficiency.

Dilemma:Disk oscillations – individual accretion events

• If flares are produced by magnetized disk oscillations, the magnetic field must be high enough to essentially influence dynamics, i.e. ½ 0B2~c2. For example, a conservatively high field B=100gauss requires to be lower then 4.5 10-16g/cm3 and has to fill the volume 4/3(13 rg)3 to contain a mass 1021g. Such a high volume could hardly oscillate with a period of ~1000sec.

• If flares are individual accretion events, then quite dense blobs of material must be brought on orbits finally ending in the black hole, the blobs must sustain high tidal stress almost until the last turn down in order not to be smeared much before falling in.

Stars in the Galactic centerDensity of OB supergiants at GCPaumard et all 2006

If a radial distribution would be assumed this surface density would correspond to

n = 0.5 pc-3/(r/pc)3

The distribution extends down to ~0.01 pc (=1’’) The central pc thus contains ~40 OB supergiants and should contain more than 104 solar mass stars if Salpeter function is the same in GC.

The Kuiper belt still contains some 108 asteroids larger than 10 kilometer

Roche radius with respect to GC black hole for stars, planets and asteroids

Note:

0.01pc=5 104 rg

Tidal interaction and its influence on orbital evolution – Hut diagrams

Time scales

=rRoche/rp

Tidal evolution of the orbit in angular momentum energy plane

and periastron-apastron evolution

Tidal evolution of Effective potential as a function of time

Some light curves

Observer almost in the orbital plane

Observer almost perpendicular to orbital plane

Summary

• We favor single individual short duration accretion events (of ~1020g objects) as explanation of Galactic center flares, opposed to disk hot spots. The inner Galactic center contains ~104 stars, and a star like the Sun has ~108 solid satellites with m>1018g.

• In our scenario the maximum emissivity occurs on the way down the black hole beyond the ISCO orbit and, therefore, high angular momentum of the black hole is not required to explain the quasi-periodic substructure of flairs.

• Magnetic fields required to explain the synchrotron nature of emitted radiation and the observed polarization are a natural consequence of magnetic flux conservation during the exponential stretching of the accreting object.