Using Observables in LMXBs to Constrain the Nature of Pulsar

Dong, Zhe & Xu, Ren-Xin

Peking University

Sep. 16th 2006

Outline

1. Motivation

2. Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar

3. Discussion upon Accretion Phenomenon

4. Conclusion and Prospect

Outline

1. Motivation

2. Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar

3. Discussion upon Accretion Phenomenon

4. Conclusion and Prospect

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

Motivation -- MSPsGC MSPs: A Rapidly Growing Population

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 352*10 ( /1 ) /d kpc erg s

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

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-1/3

White-Dwarf

2

Roche-Lobe 2 4/3 1/3

White-Dwarf Roche-Lobe

R =0.013m

0.49qR = a

0.6q +q log 1+q

R =R

0 0.2 0.4 0.6 0.8 1 1.2 1.4Mass Of Donor StarMsun0

0.02

0.04

0.06

0.08

suideRR nus

M-M Relation toward LMXBs

•M-M Relation

•Mass Ratio

0 0.2 0.4 0.6 0.8 1 1.2 1.4Mass Of PulsarMsun0.12

0.13

0.14

0.15

0.16

0.17

ssaMfo

ronoDratSM nus

0 0.2 0.4 0.6 0.8 1 1.2 1.4Mass Of PulsarMsun0

5

10

15

20

ssaMoitaRM

ronoDM rasluP

Using Observable Phenomena Constrains

• Input Period

• Output Observables

1. Periodic Modulation

2. Luminosity

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

Gravitational Radiation

• Thoroughly Considered by Paczyński, B. 1967 Acta. Astronomica 17, 287

3

5 4

32

5

3

D P D P

GR

GR GR

M M M MJ G

J c a

P J

P J

0 0.1 0.2 0.3 0.4 0.5 0.6Mass Of Donor StarMsun

-1.2 10-10

-110-10

-810-11

-610-11

-410-11

-210-11

0cidoireP

noitaludoMs nus

•Not Sufficient!

•Not a single factor modulate it!

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)

D D P

D P

M M -MP J=3 +3

P J M M

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.

Roche-Lobe Roche-LobeR R a,q

RL RL RL

RL RL

3P D P D

5 4D

1/3 1/3 1/3-1

2/3 2/3 1/3

D

P

RL DRL D

2/3RL

2/3 1/3

D

dR lnR R1 1 da 1 dq= +

R dt lna a dt R q dt

M M (M +M )32GdM 5c a=-dt 2 1+q ln 1+q -qβn 3

+1-q+ 1+q q2α 0.6q +ln 1+q 1+q q

Mq=

M

dR dR=β ,R =αR

dt dt

R 0.49q=

a 0.6q +ln 1+q

R

-1/3

5/3 D

sun sun

M=0.0128 1+X

R M

Function Deducing

•Dangerous! Leading to Instability

Mass Transfer

0 0.2 0.4 0.6 0.8 1 1.2 1.4Mass Of PulsarMsun

-510-10

-2.5 10-10

0

2.5 10-10

510-10

7.5 10-10

110-9

cidoirePnoitaludoMs nus

When will be unstable?

• Depends on Mass Ratio!

• If choose

The unstable happens when mass ratio exceeds 0.6338

3P D P D

5 4D

1/3 1/3 1/3-1

2/3 2/3 1/3

M M (M +M )32GdM 5c a=-dt 2 1+q ln 1+q -qβn 3

+1-q+ 1+q q2α 0.6q +ln 1+q 1+q q

1

0.2 0.4 0.6 0.8 1 1.2 1.4

2

4

6

8

10

12

Using the Chakrabarty’s Formula8/3

105.5*10 /1.4 0.03 18.2min

P D

GR sun sun

M M pM grams yr

M M

•This formula is totally deduced from stable mass transfer

0 0.2 0.4 0.6 0.8 1 1.2 1.4Mass Of PulsarMsun

-210-11

0

210-11

410-11

cidoirePnoitaludoMs nus

Take all factors into account

•<0.1 Appropriate

0 0.2 0.4 0.6 0.8 1 1.2 1.4Mass Of PulsarMsun-7.5 10-10

-510-10

-2.5 10-10

0

2.5 10-10

510-10

7.5 10-10

cidoirePnoitaludoMs nus

0 0.2 0.4 0.6 0.8 1 1.2 1.4Mass Of PulsarMsun-2.5 10

-10

-210-10

-1.5 10-10

-110-10

-510-11

0

510-11

cidoirePnoitaludoMs nus

Luminosity Constrain

0 0.2 0.4 0.6 0.8 1Mass Of PulsarMsun

-210-11

-1.5 10-11

-110-11

-510-12

0

cidoirePnoitaludoMss

0 0.2 0.4 0.6 0.8 1Mass Of PulsarMsun-0.000035

-0.00003

-0.000025

-0.00002

-0.000015

-0.00001

-510-6

0

cidoirePnoitaludoMss

3

3

10 ~100

44

3

56 /

donorprimaryMassTransfer

primary

donor

QuarkStarBaryonBaryon

quarkstar

MITBagConst

GM ML

R

ML MeV

m

M B R

B MeV fm

•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.

Outline

• Motivation

• Phenomena Predicting after Releasing the Mass-Constraint upon Pulsar

• Discussion upon Accretion Phenomenon

• Conclusion and Prospect

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.

What will happen towards a NS

This blue region is excluded due to rotation

Adapted from Fig. 2 of Lattimer and Prakash 2004, Science

Open Questions and Dilemma1. In LMXBs, with the heating process from Neutron Stars, th

e 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

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