Observing Orbital Motion in Strongly Curved Spacetime
Gabriel Török
Institute of Physics, Silesian University in Opava
CZ.1.07/2.3.00/20.0071 Synergy , GAČR 209/12/P740, 202/09/0772, SGS-11-2013, www.physics.cz
Observing Orbital Motion in Strongly Curved Spacetime
Gabriel Török
Institute of Physics, Silesian University in Opava
CZ.1.07/2.3.00/20.0071 Synergy , GAČR 209/12/P740, 202/09/0772, SGS-11-2013, www.physics.cz
Pavel Bakala, Kateřina Goluchová, Martin Wildner
(see Kateřina today, Martin at INAP conf.)
On marginally stable circular orbits around neutron stars
Gabriel Török
Institute of Physics, Silesian University in Opava
CZ.1.07/2.3.00/20.0071 Synergy , GAČR 209/12/P740, 202/09/0772, SGS-11-2013, www.physics.cz
CO-AUTHORS:
Martin Urbanec, Karel Adámek, Gabriela Urbancová
1. ISCO and NS Compactness
Torok et al. (2010),ApJ
ISCO FREQUENCY:
The influence of NS oblateness on the orbital frequencies has been extensively
studied in the last decade, e.g.,
Morsink, Stella, ApJ (1999); Rosinska et al. A&A (2001); Amsterdamski et al., A&A
(2002), Urbanec et al., MNRAS (2013), Kluzniak & Rosinska (2013)
1. ISCO and NS Compactness
ISCO RADIUS (Hartle-Thorne Spacetime):
q
j
The ISCO radius decreases with spin, but increases with quadrupole.
1. ISCO and NS Compactness
ISCO RADIUS (Hartle-Thorne Spacetime):
q
j
Neutron star radii R evolve with j rather slowly. The non-monotonic behaviour
of r_ISCO thus imply non-monotonic behaviour of the quantity
K= r_ISCO/ R_NS.
1. ISCO and NS Compactness
K= rISCO / RNS
Inverse compactness K= r_ISCO / R_NS (calculated for particular SKI5 EOS).
ISCO above NS surface
ISCO below NS surface
SPIN [Hz]
In the case of high mass, the ISCO is above the NS surface. In the case of low
mass, the ISCO is above the NS surface only for very high spins (when these are
allowed).
1. ISCO and NS Compactness
K= rISCO / RNS
Inverse compactness K= r_ISCO / R_NS (calculated for particular SKI5 EOS).
ISCO above NS surface
ISCO below NS surface
SPIN [Hz]
In the case of intermediate NS mass, the ISCO is above the NS surface for low
and high spins, but not for the intermediate spins. Clearly, there are implications
for the ISCO-NS distribution.
MASS [MSun]
2. NS distribution
Initial Distribution of NS
[K<>1] =>
Distribution of ISCO-NS
SPIN [Hz]
2. NS distribution
MASS [MSun]
Initial Distribution of NS (one concrete EoS)
SPIN [Hz]
2. NS distribution
MASS [MSun]
Initial Distribution of NS (one concrete EoS)
SPIN [Hz]
2. NS distribution
0
MASS [MSun]
1.5
Mass [Msun]
1
ISCO-NS Distribution
2
0 500 1000 1500
Spin [Hz]
SPIN [Hz]
3. Particular application:
0
Several QPO models require ISCO-NS -> the influence on QPO sources distribution
MASS [MSun]
1.5
Mass [Msun]
1
ISCO-NS
Distribution
2
0 500 1000 1500
SPIN [Hz]
Spin [Hz]
HF QPOs due to Paczynski modulation -> fast and slow rotators
4. Conclusions
Number of NS [relative units]
The ISCO-NS distribution has the peaks at the values of the spin which can be
very different from the peak in the distribution of all NS.
• High M -> peak at the original value of spin
• Low M -> peak at the high value of spin
• Inter. M -> two peaks
Distribution of
all NS
SPIN [Hz]
4. Conclusions
Number of ISCO-NS [relative units]
The ISCO-NS distribution has the peaks at the values of the spin which can be
very different from the peak in the distribution of all NS.
• High M -> peak at the original value of spin
• Low M -> peak at the high value of spin
• Inter. M -> two peaks
Distribution of
all NS
SPIN [Hz]
4. Conclusions
Number of ISCO-NS [relative units]
The ISCO-NS distribution has the peaks at the values of the spin which can be
very different from the peak in the distribution of all NS.
• High M -> peak at the original value of spin
• Low M -> peak at the high value of spin
• Inter. M -> two peaks
Distribution of
all NS
SPIN [Hz]
4. Conclusions
Number of ISCO-NS [relative units]
The ISCO-NS distribution has the peaks at the values of the spin which can be
very different from the peak in the distribution of all NS.
• High M -> peak at the original value of spin
• Low M -> peak at the high value of spin
• Inter. M -> two peaks
SPIN [Hz]
4. Conclusions
Number of ISCO-NS [relative units]
The ISCO-NS distribution has the peaks at the values of the spin which can be
very different from the peak in the distribution of all NS.
• High M -> peak at the original value of spin
• Low M -> peak at the high value of spin
• Inter. M -> two peaks
applications
SPIN [Hz]