international workshop on astronomical x-ray optics fingerprints of superspinars in astrophysical...

International Workshop on Astronomical X-Ray Optics

Fingerprints of Superspinars in Astrophysical Phenomena

Zdeněk Stuchlík and Jan Schee

Institute of Physics, Faculty of Philosophy and Science, Silesian university in Opava,

Czech Republic

Superspinar

String Theory suggests existence of Kerr superspinars violating the general relativistic bound on the spin of compact objects (a >1)

They could be primordial remnants of the high-energy phase of very early period of the evolution of the Universe when the effects of the String Theory were relevant

[Gimon&Hořava PhLB 672(3) 2009].

Superspinars and Naked Singularities

It is assumed that spacetime outside the superspinar of radius R, where the stringy effects are irrelevant, is described by the standard Kerr naked singularity geometry

The exact solution describing the interior of the superspinar is not known in the 3+1 theory, but it is expected that its extension is limited to the radius satisfying the condition 0 < R < M .

Minimal radius R=0 – keeping in consideration the whole causally well behaved region of the Kerr geometry.

Near-extreme Kerr superspinar

Classical instability related to Keplerian discs because of decrease of angular momentum for both corotating and retrograde accretion

Conversion to a black hole in the era of high redshift quasars, z ≈ 2

It is then possible to observe ultra high energy particle collisions and profiled spectral lines in the vicinity of near-extreme Kerr superspinars with extremal properties

[Stuchlík et al. CQG 28(15) 2011, Stuchlík&Schee CQG 29(6) 2012]

Ultra-high energy particle collisions

Collisions

Consider freely falling particle with covariant energy E=m being fixed and the other constants of motion Φ and Q to be free parameters.

The equation of latitudinal motion

implies

(We define specific quantities: q = Q/m2 and l = Φ/m .)

Centre–of–Mass energy

The CM energy of two colliding particles having 4-momenta p

1μ and p

2μ, rest masses m

1 and m

2 is

given by

where total 4-momentum


Limits on colliding particles

2 > l > -7

Extremal efficiency for l1 = l2 = -7

The simplest case: m1=m2, q1=q2=0,l1=l2=0


In the case of head-on collisions of particles freely falling from infinity along radial trajectories with fixed θ =const with particles inverted their motion near r = 0 we have

Escape cones of collision products

Due to enormous energy occurring in the CM local system during collisions at r = M we expect that generated particles are highly ultrarelativistic or we can directly expect generation of high-frequency photons

The created particles (photons) can be distributed isotropically in the CM system.


Determining relative velocity of CM system in LNRF we find

We conclude that in such a case the CM system is identical with the LNRF.

The construction of light escape cones is described in details in [Stuchlík&Schee CQG 27(21) 2010]


Escape cones LNRF. The LNRF source at r = M.Superspinar spin a=1 + 8×10-2.

θ = 5º θ = 45º θ = 85º


Escape cones LNRF. The LNRF source at r = M.Superspinar spin a=1 + 5×10-2.

θ = 5º θ = 45º θ = 85º


Escape cones LNRF. The LNRF source at r = M.Superspinar spin a=1 + 10-2.

θ = 5º θ = 45º θ = 85º



θ = 5º θ = 45º θ = 85º

Escape cone statistics

θo=85 deg, r

e=M

Escape cone statistics

θo=45 deg, r

e=M

Appearance of Keplerian disc

a=0.998

a=1.1

Keplerian discs in the vicinity of bh (top) and susp (bottom). The observer inclination is 85º and the disc spans from rin= rms to rout= 20 M.

Profiled spectral lines

Profiled spectral line

Emitter is expected to be locally isotropic and monochromatic

The frequency shift is

The specific flux is

F g=∑ g 3 I νe dΠ

Profiled spectral line

Emitter is expected to be locally isotropic and monochromatic

The frequency shift is

The specific flux is

F g=∑( i )

N g

g ( i )3 I νe ( i ) dΠ ( i )

I νe ( i ) =ε0 r ( i )− p

Profiled spectral lines:

Keplerian ring

Comparison of bh and susp profiled lines

SuSp spin is a = 1.1, and black hole spin is a = 0.9999. The observer inclination is θ

o = 85° and the source radial coordinate is r = 1.2 r

ms.

Comparison of bh and susp profiled lines

SuSp spin is a = 1.1, and black hole spin is a = 0.9999. The observer inclination is θ

o = 30° and the source radial coordinate is r = 1.2 r

ms.

Influence of radius of superspinar surface

SuSp spin is a = 1.1, the observer inclination is θo = 85° and

the source radial coordinate is r = 1.2 rms

.




.


SuSp spin is a = 2.0, the observer inclination is θo = 30°

and the radial source coordinate is r = 1.2 rms


SuSp spin is a = 1.1, the observer inclination is θo =

85° and the radiation comes from the region between r = r

ms and r = 10M.




ms and r = 10M.

Profiled spectral line:

Keplerian disc

Comparison of bh and susp disk profiled lines

SuSp spin is a = 1.1, bh spin is a=0.9999. The observer inclination is θ

o = 85° and the radiation comes from the

region between r = rms

and r = 10M.

Comparison of bh and susp disk profiled lines

SuSp spin is a = 1.1, bh spin is a=0.9999. The observer inclination is θ



and r = 10M.


SuSp spin is a = 1.1, the observer inclination is θ



and r = 10M.





and r = 10M.

Summary

Near extreme KNS naturally enable observable ultrahigh energy processes.

Energy of observable particles created in the collisions is mainly given by energy of colliding particles.

Summary

In the case of Keplerian ring, the profiled lines “split” into two parts, where the “blue” one is strongly influenced by the superspinar surface radius.

In the case of Keplerian disc, the superspinar “fingerprints” are in the shape of the profiled line and in its frequency range.

Of course, the inclination of observer plays important role too and should be known prior the analysis.

There is strong qualitative difference between profiled lines created in the field of Kerr superspinars and Kerr black holes.

Thank you for your attention.

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