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

2. Outline 1.Motivation 2.Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar 3.Discussion upon Accretion Phenomenon 4.Conclusion and Prospect

3. Outline 1.Motivation 2.Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar 3.Discussion upon Accretion Phenomenon 4.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 1.Periodic Modulation 2.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 Paczy ń ski, B. 1967 Acta. Astronomica 17, 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 1.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. 1.How to model the surface temperature distribution of white dwarf? 2.What is WD shaped? Since the WD is partially non- degenerate. 3.If introduce an uncertainty-constant into the M-R relation of WD, what is the proper range toward the constant? 2.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? 3.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