Transcript Relativistic cross sections of tidal disruption events

Relativistic cross sections of
tidal disruption events
Pavel Ivanov
Lebedev Physical Institute
A simple formulation of the problem
In a very crude approach, one may say that the star is tidally disrupted
when its periastron, rp, is smaller than the tidal radius:
When the tidal radius is smaller than the gravitational radius
the star is swallowed by the black hole without disruption. This happens
when M > 108 M☼ . The strength of tidal interaction is characterized
by either a parameter η=(r p/rT)3/2 or by penetration factor β=r T/rp .
Orbit’s parameterization in GR
The orbital parameters of a highly
elongated orbit can be characterized
by three numbers since the orbital
energy (per unit of mass, in the
natural units) is approximately 1. One
can specify e.g. the inclination with
respect to the rotational axis, θ∞, at
the periastron, and components of
specific angular momentum in θ and
φ directions: j θ and j φ .
Alternatively, one can use
projection of the angular momentum
onto the rotational axis:
Lz = jθsin θ∞ and the Carter integral
Q= j φ2+ j θ2 cos θ∞.
Since Q > 0 for nearly parabolic
orbits, we use q=√Q below.
A computationally efficient model of a tidally
disrupted star.
• It has been developed in papers Ivanov &
Novikov 2001, Ivanov, Novikov &
Chernyakova 2003, Ivanov & Chernyakova
2006.
• 1) The model is a generalization of the
affine model of Carter and Luminet. The
star is assumed to consist of elliptical
shells. Unlike the affine model the shell are
not
• self-similar, their parameters are functions
of time and a Lagrangian coordinate (say,
mass enclosed in a shell)
• 2) Dynamical equations are derived for socalled virial
• relations written for every shell.
• 3) It is a one-dimensional model.
Therefore, it is numerically much faster
than the 3D schemes.
Testing the model: in general our simple model demonstrates
rather good agreement with more numerically expensive three
dimensional hydrodynamical schemes. For example, below
it is shown the amount of mass lost in our model (black circles)
and in the recent model of Guillochon and Ramirez-Ruiz 2012
against the penetration parameter β, for stars with polytropic
indices n=1.5 and 3.
a=0.75. The angle θ∞ =π/2.
a=0.75. The angle θ∞ =π/2.
The case of angle θ∞ not equal to π/2.
When cross
sections are
plotted on the
plane (Lz, q)
this dependence
is practically
absent!
Other degeneracies
• Our results suggest that the levels of equal mass
loss on the plane (Lz, q) are very close to
segments of circles. Therefore, for
• a given value of mass loss, M, a, the cross
• section may be characterized by only one
• number!, the shift of the circle with respect to the
coordinate origin. The length of the circle may
be determined by its intersection with the know
cross section of direct capture. In my opinion,
• It’s important to check this statement with help of
• more advanced numerical schemes.
Conclusions/Discussion
• 1) The anisotropy of the tidal disruption cross sections can, in
principal, manifest itself in an induced anisotropy of distribution of
stars around SMBH. This could test the spin of SMBH.
• 2) It would be very interesting to check whether these degeneracies
of the cross sections are present in more realistic models of tidally
disrupted star/more realistic
• stellar models.
• 3) The reported results deal with ‘the first passage problem’. But,
assuming that the orbit of the star is approximately unchanged after
a partial mass loss, it could be easier to destroy the remnant during
next periastron passages. Thus, the whole business should be
generalized on the multipassage case.
• 5) In general, the problem should be considered together with orbital
evolution, due to tides and due to star-star scatterings. The results
could be different in the regimes of ‘empty and full loss cones’. This
could have some implications on the regimes of disc formation
(whether the disc is formed after a partial mass stripping or full
disruption). Also, there is a possibility of survival of the remnants,
especially in the case of full loss cone. A possible discovery of such
remnants could test the whole paradigm.
• 6) Details are in Ivanov & Chernyakova, A&A, 448, 843, 2006.