PHYSICAL REVIEW D VOLUME 35, NUMBER 3 1 FEBRUARY 1987

Comments

Comments are short papers which comment on papers of other authors previously published in the Physical Review. Each Comment should state clearly to which paper it refers and must be accompanied by a brief abstract. The same publication schedule as for regular articles is followed, and page proofs are sent to authors.

Comments on "Burning of baryon-rich quark-gluon plasmas"

David Seibert Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 *

and Fermi National Accelerator Laboratory, P.O. Box 500, Batauia, Illinois 60510 (Received 20 May 1986)

We discuss some of the properties of deflagration and detonation solutions for the hadronization process which are mentioned in the article "Burning of baryon-rich quark-gluon plasmas" which was recently published in Physical Review D. These properties include the hadronization velocities and thermodynamic-stability conditions of the two types of solutions and the signals for hadroniza- tion through detonation.

We would like to make some comments on deflagra- tions and detonations as solutions to the problem of a dynamical first-order phase transition. This problem was discussed recently in a paper by Cleymans, Nykanen, and ~uhonen. ' Several of the claims which were made in this paper seem to be incorrect.

First of all, they claim that "deflagration velocities which are comparable to the velocity of light require a drastic supercooling." This is true for deflagration bub- bles, for which they exhibit solutions, but these are hydro- dynamically ~ n s t a b l e . ~ The stable deflagration solutions consist of a deflagration shock without any accompanying structure. These simple deflagrations also differ from de- flagration bubbles by being significantly faster.

Simple deflagration solutions can be constructed which are thermodynamically stable and which eject hadronic matter at velocities arbitrarily close to the velocity of light. The only requirement is that the pressure of the quark matter be sufficiently close to the pressure of the hadronic vacuum. This happens when the quark tempera- ture is near T,, = T,[ 1 - ( g h /gq ) ] 'I4, where gh /gq is the ratio of hadronic to quark degrees of freedom and T, is the transition temperature. For standard hadronization s ~ e n a r i o s , ~ 0.90T, 5 TSp 1 0.98Tt. This shows that there exist fast deflagration solutions which are thermodynami- cally stable without "drastic" supercooling.

Second, they say that "still more supercooling is needed to produce fast detonation bubbles." This is true, as we show in Ref. 2. However, they go on to say that because of this they "have not considered (fast detonation bubbles) here." We take this to mean that they consider systems consisting of detonation shocks without attached similari- ty solutions. However, the thermodynamic stability of these solutions depends only on the thermodynamic stabil-

ity of the detonation shock itself, since continuous hydro- dynamic solutions are isentropic and thus always thermo- dynamically stable.2 This means that all detonation solu- tions are unstable unless the quark matter supercools past the point at which fast deflagrations can occur.

Third, they claim that a single detonation wave "radi- ates off all the available energy in a very short time." We show this to be impossible in heavy-ion collisions, since the apparent velocity of an isotherm is superluminal (greater than the velocity of light).2 We argue from this that one would need multiple waves to completely hadron- ize the plasma, whether one used deflagrations or detona- tions for this purpose.

Finally, they say that hadronization via detonation "would be characterized by a temperature for the outgo- ing hadrons which is much higher than the critical tem- perature, also the transition would take place as a collec- tive effect over the whole length of the rapidity region." The second assertion is shown to be false in Ref. 2 as stat- ed above.

The first is true if by detonations one means bare de- tonation shocks. However, these are shown to be unstable in Ref. 2. To make stable detonations, we attach a rare- faction similarity which cools the hadrons. It is simple to construct examples of stable detonations in which hadrons are ejected at temperatures lower than critical tempera- ture. It is thus clear that this mentioned high temperature and collective hadronization are not necessarily signals for hadronization via detonations, nor is their absence a signal that hadronization does not proceed via detonations.

This work was supported in part by the National Sci- ence Foundation under Grant No. PHY 84- 15064.

'Permanent address. 2585 (1986). 'J. Cleymans, E. Nykanen, and E. Suhonen, Phys. Rev. D 33, 2D. Seibert, Phys. Rev. D 32, 2812 (1985).

35 1078 - 01987 The American Physical Society