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/m 2 and l = Φ/m.)

Centre–of–Mass energy The CM energy of two colliding particles having 4-momenta p 1 μ and p 2 μ, rest masses m 1 and m 2 is given by where total 4-momentum

Centre–of–Mass energy Limits on colliding particles 2 > l > -7 Extremal efficiency for l 1 = l 2 = -7 The simplest case: m 1 =m 2, q 1 =q 2 =0,l 1 =l 2 =0

Centre–of–Mass energy 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

Centre–of–Mass energy

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.

Escape cones of collision products 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 of collision products Escape cones LNRF. The LNRF source at r = M. Superspinar spin a=1 + 8× θ = 5ºθ = 45ºθ = 85º

Escape cones of collision products Escape cones LNRF. The LNRF source at r = M. Superspinar spin a=1 + 5× θ = 5ºθ = 45ºθ = 85º

Escape cones of collision products Escape cones LNRF. The LNRF source at r = M. Superspinar spin a= θ = 5ºθ = 45ºθ = 85º

Escape cones of collision products Escape cones LNRF. The LNRF source at r = M. Superspinar spin a= θ = 5ºθ = 45ºθ = 85º

Escape cones of collision products Escape cones LNRF. The LNRF source at r = M. Superspinar spin a= θ = 5ºθ = 45ºθ = 85º

Escape cone statistics θ o =85 deg, r e =M

Escape cone statistics θ o =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 r in = r ms to r out = 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

Profiled spectral line Emitter is expected to be locally isotropic and monochromatic The frequency shift is The specific flux is

Profiled spectral lines: Keplerian ring

Comparison of bh and susp profiled lines SuSp spin is a = 1.1, and black hole spin is a = 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 = 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 θ o = 85° and the source radial coordinate is r = 1.2 r ms.

Influence of radius of superspinar surface SuSp spin is a = 2.0, the observer inclination is θ o = 85° 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 θ o = 30° and the source radial coordinate is r = 1.2 r ms.

Influence of radius of superspinar surface SuSp spin is a = 2.0, the observer inclination is θ o = 30° and the radial source coordinate is r = 1.2 r ms

Influence of radius of superspinar surface SuSp spin is a = 1.1, the observer inclination is θ o = 85° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 2.0, the observer inclination is θ o = 85° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 1.1, the observer inclination is θ o = 30° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 2.0, the observer inclination is θ o = 30° and the radiation comes from the region between r = r 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= The observer inclination is θ o = 85° and the radiation comes from the region between r = r ms and r = 10M.

Comparison of bh and susp disk profiled lines SuSp spin is a = 1.1, bh spin is a= The observer inclination is θ o = 30° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 1.1, the observer inclination is θ o = 85° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 2.0, the observer inclination is θ o = 85° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 6.0, the observer inclination is θ o = 85° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 1.1, the observer inclination is θ o = 30° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 2.0, the observer inclination is θ o = 30° and the radiation comes from the region between r = r ms and r = 10M.

Influence of radius of superspinar surface SuSp spin is a = 6.0, the observer inclination is θ o = 30° and the radiation comes from the region between r = r ms 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.