physics.cz

1. MassandSpin ImplicationsofHigh-Frequency QPO Models across Black Holes and Neutron Stars G. Török, M. A.Abramowicz, P.Bakala, P. Čech, A. Kotrlová, Z. Stuchlík, E. Šrámková &M. Urbanec Institute ofPhysics, Faculty of Philosophy and Science, Silesian University in Opava,Bezručovo n.13, CZ-74601, Opava In collaboration: D. Barret (CESR), M. Bursa & J. Horák (CAS), W. Kluzniak (CAMK), J. Miller (SISSA). We acknowledge the support of Czech grants MSM 4781305903, LC 06014 and GAČR202/09/0772. www.physics.cz

2. 1. Data and their models: the choice of few models High frequency quasiperiodic oscillations appears in X-ray fluxes of several LMXB sources. Commonly to BH and NS they often behave in pairs. There is a large variety of ideas proposed to explain this phenomenon (in some cases applied to both BH and NS sources, in some not). The desire is to relate HF QPOs to strong gravity…. [For instance, Alpar & Shaham (1985); Lamb et al. (1985); Stella et al. (1999); Morsink & Stella (1999); Stella & Vietri (2002); Abramowicz & Kluzniak (2001); Kluzniak & Abramowicz (2001); Abramowicz et al. (2003a,b); Titarchuk & Kent (2002); Titarchuk (2002); Kato (1998, 2001, 2007, 2008, 2009a,b); Meheut & Tagger (2009); Miller at al. (1998a); Psaltis et al. (1999); Lamb & Coleman (2001, 2003); Kluzniak et al. (2004); Abramowicz et al. (2005a,b), Petri (2005a,b,c); Miller (2006); Stuchlík et al. (2007);Kluzniak (2008); Stuchlík et al. (2008);Mukhopadhyay (2009); Aschenbach 2004, Zhang (2005); Zhang et al. (2007a,b); Rezzolla et al. (2003); Rezzolla (2004); Schnittman & Rezzolla (2006); Blaes et al. (2007); Horak (2008); Horak et al. (2009); Cadez et al. (2008); Kostic et al. (2009); Chakrabarti et al. (2009), Bachetti et al. (2010)…]

3. 1. Data and their models: the choice of few models High frequency quasiperiodic oscillations appears in X-ray fluxes of several LMXB sources. Commonly to BH and NS they often behave in pairs. There is a large variety of ideas proposed to explain this phenomenon (in some cases applied to both BH and NS sources, in some not). The desire is to relate HF QPOs to strong gravity…. [For instance, Alpar & Shaham (1985); Lamb et al. (1985); Stella et al. (1999); Morsink & Stella (1999); Stella & Vietri (2002); Abramowicz & Kluzniak (2001); Kluzniak & Abramowicz (2001); Abramowicz et al. (2003a,b); Titarchuk & Kent (2002); Titarchuk (2002); Kato (1998, 2001, 2007, 2008, 2009a,b); Meheut & Tagger (2009); Miller at al. (1998a); Psaltis et al. (1999); Lamb & Coleman (2001, 2003); Kluzniak et al. (2004); Abramowicz et al. (2005a,b), Petri (2005a,b,c); Miller (2006); Stuchlík et al. (2007);Kluzniak (2008); Stuchlík et al. (2008);Mukhopadhyay (2009); Aschenbach 2004, Zhang (2005); Zhang et al. (2007a,b); Rezzolla et al. (2003); Rezzolla (2004); Schnittman & Rezzolla (2006); Blaes et al. (2007); Horak (2008); Horak et al. (2009); Cadez et al. (2008); Kostic et al. (2009); Chakrabarti et al. (2009), Bachetti et al. (2010)…] Here we focus only to few ofhot-spot or disc-oscillation models widely discussed for both classes of sources. (which we properly list and quote slightly later).

4. 1. Data and their models: the choice of three sources

5. 2. Near-extreme rotating black hole GRS 1915+105 (Remillard et al., 2003) (McClintock & Remillard, 2003) a > 0.99 (Remillard et al., 2009)

6. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. Relativistic precession [Stella et al. (1999)]

7. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. Relativistic precession [Stella et al. (1999)]

8. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. -1r, -2v disc-oscillation modes(frequency identification similar to the RP model)

9. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. Tidal disruption of large inhomogenities (mechanism similar to the RP model) Cadez et al. (2008); Kostic et al. (2009);

10. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. Oscillations of warped discs (implying for 3:2 frequencies the same characteristic radii as TD) Kato (1998,…, 2008)

11. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. 3:2 non-linear disc oscillation resonances Abramowicz& Kluzniak (2001), Török et. al (2005) Courtesy of M. Bursa or

12. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. Othernon-linear disc oscillation resonances Abramowicz& Kluzniak (2001), Török et al. (2005),Török & Stuchlík (2005)

13. 2. Near-extreme rotating black hole GRS 1915+105 a > 0.99 Abramowicz et al., (2010) in prep. Breathing modes (here assuming constant angular momentum distribution)

14. 2. Near-extreme rotating black hole GRS 1915+105: summary Abramowicz et al., (2010) in prep. ?

15. 3. Neutron stars: high mass approximation through Kerr metric NS require three parametric description (M,j,Q), e.g., Hartle&Thorne (1968). However, high mass (i.e. compact) NS can be well approximated via simple and elegant terms associated to Kerr metric assumed on previous slides. This fact is well manifested on ISCO frequencies: Torok et al., (2010) submitted Several QPO models predicts rather high NS masses when the non-rotating approximation is applied. For these models Kerr metric has a potential to provide rather precise spin-corrections which we utilize in next. A good example to start is the RELATIVISTIC PRECESSION MODEL.

16. 3. Neutron stars: relativistic precession model One can solve the RP model definition equations Obtaining the relation between the expected lower and upper QPO frequency which can be compared to the observation in order to estimate mass M and “spin” j … The two frequencies scale with 1/M and they are also sensitive to j.For matching of the data it is an important question whether there exist identical or similar curves for different combinations of M and j.

17. 3. Neutron stars: frequency relations implied by RP model One can find combinations M, j giving the same ISCO frequency and plot related curves. Resulting curves differ proving thus the uniqueness of frequency relations. On the other hand they are very similar: M = 2.5….4 MSUN Torok et al., (2010) submitted For a mass M0of the non-rotating neutron star there is always a set of similar curves implying a certain mass-spin relation M (M0, j) here implicitly given by the above plot. The best fits of data of given source should be therefore reached for combinations of M and j which can be predicted just from a one parametric fit assuming j = 0.

18. 3. Neutron stars: RP model vs. the data of 4U 1636-53 The best fits of data of given source should be therefore reached for combinations of M and j which can be predicted just from a one parametric fit assuming j = 0. The best fit of 4U 1636-53 data (21 datasegments) for j = 0 is reached for Ms = 1.78M_sun, which implies M= Ms[1+0.75(j+j^2)], Ms = 1.78M_sun

19. 3. Neutron stars: RP model vs. the data of 4U 1636-53 Color-coded map of chi^2 [M,j,10^6 points] well agrees with rough estimate given by simple one-parameter fit. M= Ms[1+0.75(j+j^2)], Ms = 1.78M_sun Best chi^2 chi^2 ~ 300/20dof chi^2 ~ 400/20dof Torok et al., (2010) in prep.

20. 3. Neutron stars: other models vs. the data of 4U 1636-53 For several models there are M-j relations having origin analogic to the case of RP model. chi^2 maps [M,j, each 10^6 points]: 4U 1636-53data

21. 3. Neutron stars: models vs. the data of Circinus X-1 For several models there are M-j relations having origin analogic to the case of RP model. chi^2 maps [M,j, each 10^6 points]: Circinus X-1data

22. 3. Neutron stars: nearly concluding table

23. 3. Neutron stars: nearly concluding table

24. 3. Neutron stars: nearly concluding table

25. 3. Neutron stars: nearly concluding table

26. 3. Neutron stars: nearly concluding table

27. 3. Neutron stars: nearly concluding table

28. 3. Neutron stars: nearly concluding table

29. 3. Neutron stars:M and j based on 3:2 epicyclic resonance model which FAILS a) b) (Abramowicz et al., 2005) giving for j=0 Mass-spin inferred from epicyclic model assuming Hartle-Thorne metric and 600:900Hz Mass-spin after including several EOS and lower-eigenfrequency 580-680Hz q/j2 j j Urbanec et al., (2010) in prep.

30. 3. Neutron stars:epicyclic resonance model and Paczynski modulation After Abr. et al., (2007), Horák (2005) Urbanec et al., (2010) in prep. The condition for modulation is fullfilled only for rapidly rotating strange stars, which most likely falsifies the postulation of 3:2 resonant resonant mode eigenfrequencies being equal to the geodesic radial and vertical epicyclic frequency…. (this postulation on the other hand seems to work for GRS 1915 + 105)

31. E N D