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Quark star RX J1856.5Quark star RX J1856.5--3754 and its mass3754 and its mass

Kazunori Kohri（郡 和範）

RESCEU, Univ. of Tokyo

K. Kohri, K. Iida and Katsuhiko Sato,

Prog. Thor. Phys. 105 (2002) in press

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ContentsContents

・ Introduction

・ Observations of RX J1856.5-3754

・ Two-temperature model?

・ Quark matter in bag model

・ Quark star

・ Systematic study of mass of the star

in bag model

・ Other constraint on mass of the star

・ Other theoretical model of quark matter

・ Conclusion

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IntroductionIntroduction

Recent deep Chandra LETG+HRC-S observations of RX J1856.5-3754reports,

Black body of Black body of

XX--ray luminosity,ray luminosity,

Drake et al., ApJ. 572 (2002) 996-1001

Radiation radiusRadiation radius

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Distance toward RX Distance toward RX J1856.5J1856.5--37543754

Drake et al., ApJ. 572 (2002) 996-1001

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Spectra of RX J1856.6Spectra of RX J1856.6--37543754

Drake et al., ApJ. 572 (2002) 996-1001

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The 3The 3σσequivalent width equivalent width upper limit to line featuresupper limit to line features

Drake et al., ApJ. 572 (2002) 996-1001

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XMMXMM--Newton observationNewton observationV. Burwitz et al, astro-ph/0211536

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RX J1856.5RX J1856.5--3754 is 3754 is quark quark star?star?

i) No pulsation

ii) No spectral features

iii) Small radiation radius

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MassMass--radius relation of radius relation of compact starcompact star

(Quark star)

(Neutron star)(White dwarf)

M

Courtesy of K. Iida

R

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with heavy-element atmosphere

F.Walter and J.Lattimer, ApJ (2002)

T.M. Braje and R.W. Romani, ApJ (2002)

Two temperature modelTwo temperature model

Hot

Hot

Cold

X-ray

X-ray

UV/Optical

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Broad band spectral fit Broad band spectral fit in twoin two--temperature temperature

blackbodyblackbody

T. Braje and R.W. Romani, ApJ (2002)

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Thermodynamic potentialThermodynamic potential

Energy densityEnergy density

Quark matterQuark matter(zero-temperature uds quark matter)

where

QCD coupling constant

Strange quark mass

Bag constant

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Quark matterQuark matter--22Number densityNumber density

PressurePressure

Baryon numberBaryon number

ConditionsConditionsIn equilibrium through weak interactions

Charge neutrality

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Bag model parameters Bag model parameters fitted to fitted to hadronhadron mass mass

spectraspectra

Kohri, Iida and Sato, arXiv:astro-ph/0210259

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Energy per baryonEnergy per baryon

((ααｃｃ＝＝00））

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Energy per baryonEnergy per baryon((ααｃｃ＝＝0.60.6））

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Equation of stateEquation of state

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Quark starQuark starEquation of hydrostatic equilibrium

(Tolman-Oppenheimer-Volkoff (TOV) equation)

Equation of mass conservation

Then, the radius is determined by

The mass is

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Mass of quark starMass of quark star

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Radius of quark starRadius of quark star

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MassMass--radius relationradius relation

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MassMass--radius relationradius relation

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Observed XObserved X--ray ray luminosityluminosity

Bondi accretion rate

where,

Then,

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Contours of upper Contours of upper limit of masslimit of mass

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Effects of the Effects of the pressurepressure--dependentdependent bag constantbag constant

Generally, we can parameterize the EOS as

Then, we transform it into

where

Namely, inside the star the bag Namely, inside the star the bag constant effectively becomes large!constant effectively becomes large!

A ~ 3 -- 4, for Lattice data , Peshier,Kampfer,Soff (2001).

A ~ 2, for Relativistic Mean Field, Dey et al. (1998) etc.

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Contour of the effective Contour of the effective bag constant bag constant

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Contours of the upper Contours of the upper limintlimint of the massof the mass

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ConclusionConclusion

・ We have systematically computed mass-radius relation of quark star within the bag model.

・ Assuming that RX J1856.5--3754 is a pure quark star, we have derived an upper limit on its mass.

・ We find the upper limit can amount to 1 M around

B ~ (200MeV).4