VOLUME 81, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 7 SEPTEMBER1998

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Comment on “Kaon Production in Heavy-IonCollisions and Maximum Mass of Neutron Stars”

In their Letter, Li, Lee, and Brown [1] overlook a num-ber of relevant physical effects that can be found in thliterature and that would mitigate against their conclusion—that kaon condensation is the likely mechanism freducing the limiting neutron star mass from a value oabout2MØ or more, obtained with simple models baseonly on neutrons or on neutrons, protons, and electronto a value of about1.5MØ. We make the following dis-tinct points.

(I) As early as 1985 [2] it was shown that hyperonvery likely prevent kaon condensation because (1) thhave a conserved quantum number, the baryon numb(2) the Pauli principle distributes the baryon numbein dense matter over many baryon species; (3) charneutrality can be achieved among the conserved baryoat densities above saturation without having to pay thprice of either electron Fermi energy or kaon masThe electron chemical potential becomes saturated2–3 nuclear density and thereafter decreases, as showFig. 2 of Ref. [2] (saturation was also found in Ref. [3])The authors ignore the likely saturation that rests mainon the Pauli principle and baryon conservation. Insteathey assume a monotonically increasing electron chemicpotential that rises to meet their decreasing Kaon massa function of increasing density.

One may question coupling constants in the hyperochannels, just as one can question them for the kaoWith respect to hyperons, the couplings are constrainin Ref. [4] by (1) the lambda binding in nuclear mat-ter, (2) hypernuclear levels, and (3) neutron star massThere is still some latitude, but in all cases the saturtion of the electron chemical potential and reduction othe limiting mass occurs [4–6].

(II) Not all mechanisms that can soften the equatioof state are on an equal footing. Hyperonization iprotected by the two principles—baryon conservatioand the Pauli principle. Kaons, being bosons, are nas protected. Kaons cannot prevent hyperonization bhyperons can prevent kaon condensation. The reason wfully explained in Ref. [2].

(III) The reduction in stellar mass of0.4MØ, attributedto kaon condensation, depends for its magnitude on tunderlying theory of matter that the authors employebut did not specify. More seriously, the value to whichthe limiting mass is reduced depends on unmeasurproperties of superdense matter and can be shiftedor down by representing matter as stiff or soft at higdensity.

(IV) There is a flaw in the paper which is subtleFigure 3 shows a flat plateau in the sequence of sta

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with a kaon condensed phase. The plateau betraysregion of densities in the equation of states for whicthe pressure is a constant and for which the stellmass cannot change for central densities in the constpressure region. Constant pressure is characteristic ofirst order phase transition in a substance havingonlya single component. However, the pressure increasmonotonically as the density for substances with mothan one component such as beta stable neutron smatter [7]. Their treatment of the phase transition itherefore incorrect.

I do not wish to detract from the nice work theauthors have done in connection with their mediumcalculations of the kaon mass. The main point of mComment is to emphasize that several high densphenomena decrease the limiting neutron star mass athat even if the limit were actually known, one couldnot point to a particular mechanism as being responsibwithout having independent observations that discriminabetween them. It is well established in the literature thnegative Bose condensation ranks last in the hierarchyphase transitions that can soften the equation of staand hence lower the limiting neutron star mass; thhierarchy in order of precedence is quark deconfinemehyperonization, and Bose condensation.

This work was supported by the Director, Officeof Energy Research, Office of High Energy and Nuclear Physics, Division of Nuclear Physics, of the U.SDepartment of Energy under Contract No. DE-AC0376SF00098.

Norman K. GlendenningNuclear Science Division & Institute for Nuclear andParticle Astrophysics,Lawrence Berkeley National LaboratoryUniversity of CaliforniaBerkeley, California 94720

Received 9 June 1998 [S0031-9007(98)06995-6PACS numbers: 25.75.Dw, 24.10.Lx, 26.60.+c, 97.60.Jd

[1] G. Q. Li, C. H. Lee, and G. E. Brown, Phys. Rev. Lett.79,5214 (1997).

[2] N. K. Glendenning, Astrophys. J.293, 470 (1985).[3] J. Schaffner and I. N. Mishustin, Phys. Rev. C53, 1416

(1996).[4] N. K. Glendenning and S. A. Moszkowski, Phys. Rev. Lett

67, 2414 (1991).[5] J. I. Kapusta and K. A. Olive, Phys. Rev. Lett.64, 13

(1990).[6] J. Ellis, J. I. Kapusta, and K. A. Olive, Nucl. Phys.B348,

345 (1991).[7] N. K. Glendenning, Phys. Rev. D46, 1274 (1992).

© 1998 The American Physical Society