XR/NIR flares from the Galactic center
We consider whether the flare activity observed at the GC is due to the capture of a small body, of comparable mass to that of a comet or an asteroid. The only important physical constraints on the source are the requirement that: 1) the source can provide sufficient energy, and 2) it is sufficiently small to produce observable modulation of the light curve. The timescales in our simulations agree with the timescales of flares, if we assume that the source of the flares moves on an unstable, circular orbit at 4 rg around a Schwarzschild black hole of mass 3.6 ◊ 106 M⊙.
We assume that the energy released during this process originates in the gravitational potential energy of the object and is thus proportional to its mass. Since potential energy differences in an orbit at 4 rg are of the order of a few percent of mc2, it follows that objects producing them probably have masses of the order of 1020 g. If the sources of flares were gaseous blobs of such a large mass, they would find themselves below the Roche radius far away from the black hole, and would therefore be completely disrupted before producing any modulation of the light curve. We conclude that the source of the flares is a small, solid object that orbits the black hole above the effective Roche radius.
Figure 1: Flare observed in Sgr A* and our fit (line) to the observed light
curve obtained with a very rudimentary model, assuming that asteroidís
luminosity is increasing exponentially withtime and the luminosity of its
tidal tail is decreasing exponentially with the distance from the asteroidís
Using ray-tracing techniques, the appearance and the luminosity of such an event as seen by observers was calculated at different inclinations and position angles with respect to the orbit of the infalling asteroid. In this simple toy-model, we introduced five parameters: mass of the black hole Mbh, tidal heating timescale τh, length of the tidal tail ltail, inclination of the orbit i, and the longitude of the line of nodes Ω. A robust description of the June 16th 2003 IR flare was found for the following parameter values: Mbh = 4 ◊ 106 M⊙, τh = 2300 s, ltail = 108 km, i ≈ 90◦. Despite the model simplicity, the value of Mbh that we find is in good agreement with the measured value. The fit is in Figure 1.
Figure 2: The XMM-Newton/EPIC light curve of the flare
of April 4, 2007 (Porquet et al. 2008), fitted with the
simple intensity distribution shown in the inset at top
right. Residuals are shown as crosses at the bottom.
We were also able to describe the XMM-Newton/EPIC light curve of the flare of April 4, 2007 (Porquet et al. 2008) with the following scenario: after the tidal deformation develops, the deformed object can be imagined as a long string of freely falling beads threading the same orbit. The light curve S(t) of such a string can thus be described by a convolution of a Greenís function G(t,t′) belonging to the orbit (the signal, as a function of time t, of a single bead, crossing a fixed reference point at time t′), and K(t′) (the distribution of luminosity among the beads). The Greenís function depends on the orbital angular momentum l and energy E of the orbit. We are interested in plunging orbits with ζ∼ 1, since tidal evolution produces these orbits, and only in such orbits can the length of the tidal tail grow exponentially and produce a flare. For such an orbit, the Greenís function is dominated by a series of sharp spikes produced during the last few turns before plunging behind the horizon.
We use the observed signal S(t) to obtain the luminosity distribution K(t′). Depending on the Greenís function used, different solutions are obtained, most of which are physically unrealistic highly variable functions. Only for l/mrgc = 4.3 and E = 1.04 mc2 does the distribution become a simple positive function K(t′), which can be well approximated with a steep, exponential rise, followed by a slower, exponential decay. Both, K(t′) and its smooth approximation K(t′) are shown in the inset of Figure 2.
Finally, we emphasize that our scenario differs from other models in the following respects: 1) Flares originate in marginally-bound and not marginally-stable orbits. This allows them to travel closer to the black hole and provides a mechanism for the rapid extraction of energy. It also agrees with measurements of the size of the flaring region in the Galactic centre, which imply that it is not larger than 6 rg (Reid 2008), and relaxes constraints on the angular momentum of the black hole. 2) Our model does not require a fairly rapidly rotating black hole as needed by Genzel et al. (2003), Aschenbach et al. (2004) and Trippe et al. (2007). 3) An accretion disk at the Galactic centre is not required. Yusef-Zadeh et al. (2008) highlited that ďthere is no definitive evidence that Sgr A∗ has a diskĒ. 4) Elongated structures invoked in other models to fit flare data (e.g. Falanga et al. (2007); Zamaninasab et al. (2008) and Hamaus et al. (2008)) develop naturally in the proposed model as a result of the tidal evolution of a melted body. 5) The evolving elongated structures also provide a natural explanation of rapid changes in magnetic-field density inferred from observations, increasing first as the body is squeezed by tides and finally decreasing as the body crosses the horizon of the black hole.