Using Observables in LMXBs to Constrain the Nature of Pulsar

1. Using Observables in LMXBs to Constrain the Nature of Pulsar Dong, Zhe & Xu, Ren-Xin Peking University Sep. 16th 2006

2. Outline • Motivation • Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar • Discussion upon Accretion Phenomenon • Conclusion and Prospect

3. Outline • Motivation • Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar • Discussion upon Accretion Phenomenon • Conclusion and Prospect

4. Motivation • Low-Mass Ultra-Compact X-Ray Binaries (LMXBs) are ideal laboratories for Study of: • Gravitational Wave • Space Plasma • QPOs • Accretion • Property of Pulsars • …… • LMXBs’ Periods spread from 5.4-min to 80-min • LMXBs; IMXBs; HMXBs

5. Motivation -- MSPs GC MSPs: A Rapidly Growing Population

6. Some Sources and Observables • J 0806.3+1527: 5.4 min no evidence of accretion disk • J 1914+24: 569 sec 1kpc 3*10^35 ergs/s • 4U 1850-087: 20.6 min NGC 6712 X-ray Burst Source flux=3.4*10^-10erg/cm^2/s^-1 • 4U 1543-624: 18 min • 4U 1820-30: 569 sec • …… • Typical Scalar Chosen in This Discussion • Distance: 2~10 Kpc • Flux

7. Phenomena Predicting after Releasing the Mass-Constraint upon Pulsars • Observables  Spectrum • Period (Detected) • Periodic Modulation (Expected) • Flux (Expected) • Theoretical Works • Release the Constraint upon the Mass of Pulsars • Fit the Observables and Get the Dominating Factors • Interesting Conclusion • When we release the constraint upon the mass, a pulsar, which is a quark star with mass approximate 0.2 mass of sun, is appropriate and reasonable in the LMXB • When we release the constraint, unstable mass transfer may be inevitable

8. Get Masses of Donor Star and Accreting Star • Since we only have the parameter of period, and we want to theoretically predict the systems’ phenomena, we should get: • Mass of Donor Star • Mass of Accreting Star • Radius of both • Separation between them • Assumption: • Let the Mass Donor Star Fully or Partially Imbue the Roche-Lobe

9. M-M Relation toward LMXBs M-M Relation Mass Ratio

10. Using Observable Phenomena Constrains • Input  Period • Output  Observables • Periodic Modulation • Luminosity

11. Periodic Modulation Constrain • What affects it? • Gravitational Radiation • Mass Transfer • Gravitational Inducing Mass Transfer • Other Angular Momentum Inducing Mass Transfer • Tidal Effect • Synchronizing Torque • Focusing On RX J 1914-24 • 569 Sec • Approximately 10^-11s/s periodic modulation

12. Gravitational Radiation • Thoroughly Considered by Paczyński, B. 1967 Acta. Astronomica17, 287 Not Sufficient! Not a single factor modulate it!

13. Mass Transfer • With brief calculation and general consideration: mass transfer mainly leaded by Gravitational Radiation • If the systems are conservative towards total mass, (strong assumption)

14. Assumption in the Mass Transfer Calculation • There should be some force to trigger the mass transfer • The variation of Roche-Lobe Radius and White Dwarf Radius should be synchronous, approximately.

15. Function Deducing Dangerous! Leading to Instability

16. Mass Transfer

17. When will be unstable? • Depends on Mass Ratio! • If choose The unstable happens when mass ratio exceeds 0.6338

18. Using the Chakrabarty’s Formula This formula is totally deduced from stable mass transfer

19. Take all factors into account <0.1 Appropriate

20. Luminosity Constrain With the Constraint from the luminosity: Gravitational Energy (Upwards) & Baryon Phase Transition (Rightwards), we can conclude that a quark star with 0.2 Mass of Sun is proper.

21. Outline • Motivation • Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar • Discussion upon Accretion Phenomenon • Conclusion and Prospect

22. Conclusion • When we release the constraint upon the mass of pulsars, from the constraints by periodic modulation and luminosity, we can conclude: • If the pulsar is a 0.15(Mass of sun) quark star, it will be appropriate! • If the pulsar mass is not pre-assumed to be 1.4(Mass of sun), the unstable mass-transfer should be inevitable, when the mass ratio is larger than 0.7.

23. What will happen towards a NS This blue region is excluded due to rotation Adapted from Fig. 2 of Lattimer and Prakash 2004, Science

24. Open Questions and Dilemma • In LMXBs, with the heating process from Neutron Stars, the surface of white dwarfs may not be totally degenerate. And the radius of white dwarf will be distorted. • How to model the surface temperature distribution of white dwarf? • What is WD shaped? Since the WD is partially non-degenerate. • If introduce an uncertainty-constant into the M-R relation of WD, what is the proper range toward the constant? • Within the discussion, we concluded that the unstable mass transfer may be inevitable. So, could the unstable mass transfer leading to an X-ray burst? If not, what are the observables? • Can neutron star survive, after the mass-constraint released

25. Acknowledgement • Sponsored by Undergraduate Research Program of Peking University • Thanks for Supervisor Prof. Xu, Ren-Xin (PKU) • Thanks for Communication with Prof. Chakrabarty, Deepto (MIT) • Thanks for Prof. Chu, Ming-Chung & Lin, Hai-Qing (CUHK) for Summer Research