1. Observing Orbital Motion in Strongly Curved Spacetime Institute of Physics, Silesian University in Opava Gabriel Török CZ.1.07/2.3.00/20.0071 Synergy, GAČR 209/12/P740, 202/09/0772, SGS-11-2013, www.physics.cz

2. Observing Orbital Motion in Strongly Curved Spacetime Institute of Physics, Silesian University in Opava Gabriel Török 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.)

3. Institute of Physics, Silesian University in Opava Gabriel Török CZ.1.07/2.3.00/20.0071 Synergy, GAČR 209/12/P740, 202/09/0772, SGS-11-2013, www.physics.cz On marginally stable circular orbits around neutron stars CO-AUTHORS: Martin Urbanec, Karel Adámek, Gabriela Urbancová

4. KERR 1. ISCO and NS Compactness OBLATENESS 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) Kluzniak et al., ApJ (1990) Torok et al. (2010),ApJ ISCO FREQUENCY:

5. 1. ISCO and NS Compactness ISCO RADIUS (Hartle-Thorne Spacetime): The ISCO radius decreases with spin, but increases with quadrupole. j q

6. 1. ISCO and NS Compactness 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. j q ISCO RADIUS (Hartle-Thorne Spacetime):

7. 1. ISCO and NS Compactness 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). ISCO below NS surface ISCO above NS surface Inverse compactness K= r_ISCO / R_NS (calculated for particular SKI5 EOS). K= rISCO / RNS

8. 1. ISCO and NS Compactness 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. SPIN [Hz] ISCO below NS surface ISCO above NS surface Inverse compactness K= r_ISCO / R_NS (calculated for particular SKI5 EOS). K= rISCO / RNS

9. 2. NS distribution MASS [MSun] SPIN [Hz] Initial Distribution of NS [K<>1] => Distribution of ISCO-NS

10. 2. NS distribution SPIN [Hz] MASS [MSun] Initial Distribution of NS (one concrete EoS)

11. SPIN [Hz] MASS [MSun] 2. NS distribution Initial Distribution of NS (one concrete EoS)

12. 0 500 1000 1500 Spin [Hz] Mass [Msun] 0 1 1.5 2 MASS [MSun] SPIN [Hz] 2. NS distribution ISCO-NS Distribution

13. 0 500 1000 1500 Spin [Hz] Mass [Msun] 0 1 1.5 2 MASS [MSun] SPIN [Hz] 3. Particular application: ISCO-NS Distribution Several QPO models require ISCO-NS -> the influence on QPO sources distribution HF QPOs due to Paczynski modulation -> fast and slow rotators

14. 4. Conclusions SPIN [Hz] Number of NS [relative units] Distribution of all NS 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

15. 4. Conclusions SPIN [Hz] Number of ISCO-NS [relative units] Distribution of all NS 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

16. 4. Conclusions SPIN [Hz] Number of ISCO-NS [relative units] Distribution of all NS 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

17. 4. Conclusions SPIN [Hz] 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

18. 4. Conclusions SPIN [Hz] 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