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Strange Stars, Strange Dwarfs, and Planetary-like Strange-Matter Objects” t

F. Weber, Ch. Schaab, M. K. Weigel

Institute for Theoretical Physics Ludwig-Maximilians University

Theresienstrasse 37/11I, D-80333 Munich, Germany

and

N. K. Glendenning

Nuclear Science Division Lawrence Berkeley Laboratory, MS: 70A-3307

University of California Berkeley, California 94720, U.S.A.

May 18, 1995

Presented at the Ringberg Workshop March 6-10, 1995

Tegernsee, Germany Organized by the Max-Planck-Institute for Astrophysics, Garching, Germany

*This manuscript is based on the authors’ contribution to the proceedings of the International Symposium on Strangeness and Quark Matter, September 1-5, 1994, Crete, Greece, to be published by World Scientific.

+This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of Nuclear Physics, of the U.S. Department of Energy under Contract

t”? DE-AC03-76SF00098. $ 2

fa

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Strange Stars, Strange Dwarfs, and Planetary-like S trange-Mat ter Objects

F. Weber, Ch. Schaab, M. K. Weigel Institute for Theoretical Physics, Ludwig-Maximilians University,

The resie nst rass e 37/III, D- 80333 Munich, Germany

and

N. K. Glendenning Nuclear Science Division, Lawrence Berkeley Laboratory, MS: 7OA-3307

University of California, Berkeley, California 94720, U.S. A.

Abstract

This paper gives an overview of the properties of all possible equilibrium sequences of compact strange-matter stars with nuclear crusts, which range from strange stars to strange dwarfs. In contrast to their non-strange coun- terparts, -neutron stars and white dwarfs-, their properties are determined by two (rather than one) parameters, the central star density and the density at

*the base of the nuclear crust. This leads to stellar strange-matter configura- tions whose properties are much more complex than those of the conventional sequence. As an example, two generically different categories of stable strange dwarfs are found, which could be the observed white dwarfs. Furthermore we find very-low-mass strange stellar objects, with masses as small as those of Jupiter or even lighter planets. Such objects, if abundant enough, should be seen by the presently performed gravitational microlensing searches.

1 Introduction The theoretical possibility that strange quark matter may be absolutely stable with respect to iron, that is, the energy per baryon is below 930 MeV, has been pointed out independently by Bodmer [l], Terazawa [2], and Witten [3]. This so-called strange matter hypothesis constitutes one of the most startling possibilities of the behavior of superdense nuclear matter, which, if true, would have implications of fundamental importance for cosmology, the early universe, its evolution to the present day, astro- physical compact objects, and laboratory physics (for an overview, see Ref. [5] and Table 1). Even to the present day there is no sound scientific basis on which one can either confirm or reject the hypothesis, so that it remains a serious possibility of fundamental significance for various phenomena.

On theoretical scale arguments, strange quark matter is as plausible a ground state its the confined state of hadrons [3, 23, 461. Unfortunately it seems unlikely that QCD calculations will be accurate enough in the foreseeable future to give a definitive

1

Figure 1: Relative densities of quarks and leptons, n;/n, where n denotes the total quark density, in cold, beta-stable, electrically charge neutral quark-star matter as a function of energy density (B1i4 = 145 MeV) 141.

prediction on the stability of strange matter, and one is left with experiment, Table 2, and astrophysical tests, as performed here, to either confirm or reject the hypothesis.

One striking implication of the hypothesis would be that pulsars, which are con- ventionally interpreted as rotating neutron stars, almost certainly would be rotating strange stars (strange pulsars) [3, 16, 17, 231. Part of this paper deals with an investi- gation of the properties of such objects. In addition to this, we develop the complete sequence of strange stars with nuclear crusts, which ranges from the compact mem- bers, with properties similar to those of neutron stars, to white dwarf-like objects (strange dwarfs) and discuss their stability against acoustical vibrations [28, 541. The properties with respect to which strange-matter stars differ from their non-strange counterparts are discussed, and observable signatures of strange stars are pointed out.

2 Quark-lepton Composition of Strange Matter The relative quark/lepton composition of quark-star matter at zero temperature is shown in Fig. 1. All quark flavor states that become populated at the densities shown are taken into account. (Strange and charm quark masses of respectively 0.15 GeV and 1.2 GeV are assumed.) Since stars in their lowest energy state are electrically charge neutral to very high precision [55], any net positive quark charge must be balanced by leptons. In general, as can be seen in Fig. 1, there is only little need for leptons, since charge neutrality can be achieved essentially among the quarks themselves. The concentration of electrons is largest at the lower densities of Fig. 1

4

2

1000.0

800.0

- E

600.0

200.0

0.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

crust potential [MeV]

Figure 2: Gap width, R,, versus electrostatic crust potential, eKrust. The labels refer to temperature (in MeV).

due to the finite s-quark mass which leads to a deficit of net negative quark charge, and at densities beyond which the c-quark state becomes populated which increases the net positive quark charge.

3 Nuclear Crusts on Strange Stars The presence of electrons in strange quark matter is crucial for the possible existence of a nuclear crust on such objects. As shown in Refs. [17, 41, the electrons,. because they are bound to strange matter by the Coulomb force rather than the strong force, extend several hundred fermi beyond the surface of the strange star. Associated with this electron displacement is a electric dipole layer which can support, out of contact with the surface of the strange star, a crust of nuclear material, which it polarizes [17]. The maximal possible density at the base of the crust (inner crust density) is determined by neutron drip, which occurs at about 4.3 x 10’l g/cm .

The determination of the electrostatic electron potential at the surface of a strange star performed in Ref. [17] has been extended to finite temperatures only recently [4]. The results obtained there for the gap between the surface of the star’s strange core and the base of the inner crust are shown in Fig. 2. A minimum value of Rgap N 200 fm was established in Ref. [17] as the lower bound on Rgap necessary to guarantee the crust’s security against strong interactions with the strange-matter core. For this value one finds from Fig. 2 that a hot strange pulsar with T - 30 MeV can only carry nuclear crusts whose electrostatic potential at the base is rather smaller, e&rust 5 0.1 MeV. Crust potentials in the range of 8-12 MeV, which are expected for a crust

3

3

Table 1: Strange Matter Phenomenology (not complete).

Phenomenon References

High-energy gamma ray sources Cyg X-3 and Her X-3 Centaur0 cosmic ray events [37 6, 71

[8, 91 Strange matter hitting the earth:

strange meteors nuclearite-induced earthquakes strange nuggets in cosmic rays 1117 121

Strange matter in supernovae Strange star (pulsar) phenomenology

Strange dwarfs Strange planets Burning of neutron stars to strange stars

Cosmological aspects of strange matter

Strangelets in nuclear collisions

[13, 14, 151 [4, 16, 17, 18, 19, 20, 21, 221 123, 24, 25, 26, 27, 281 [28, 29, 30, 31, 321 [28, 31, 32, 331 [34, 35, 361

[3, 18, 38, 39, 40, 411

[43, 44, 451

Gamma-ray bursts [I77 371

Strange matter as compact energy source ~421

at neutron drip density [17], are only possible for core temperatures of T 5 5 MeV. Therefore we conclude that only strange stars with rather low temperatures can carry the densest possible crusts.

4 Equation of State of Strange Stars with Crust The somewhat complicated situation of the structure of a strange star with crust described above can be represented by a proper choice of equation of state [27], which consists of two parts. At densities below neutron drip it is represented by the low- density equation of state of charge-neutral nuclear matter, for which we use the Baym- Pethick-Sutherland equation of state. The star’s strange-matter core is described by the bag model (for details, we refer to Refs. [4, 27,46, 561). The graphical illustration of such an equation of state is shown in Fig. 3. Notice that there is a discontinuity in energy density between strange quark matter and hadronic matter across the electron surface (dipole gap) inside the star where the pressure of the hadronic crust at its base equals the pressure of the strange core at its surface [27].

st- 4 10-4 10-6

10-8 PI

10-10 IO

E [MeV/fm3]

Figure 3: Equation of state of a strange star surrounded by a nuclear crust. &ip( hip) denotes the pressure at the maximum possible inner crust density determined by neutron drip, emst = 0.24 MeV/fm3 (4.3 x 10" g/cm3). Any inner crust value smaller than that is possible. As an example, we show the equation of state for ecmt = MeV/fm3 (10' g/cm3).

5 Properties of Strange-Matter Stars

5.1 Strange and Charm Stars Figure 4 shows the impact of the bag constant on the masses of sequences of dense quark-matter stars. Stars with central densities smaller than a few times 1015 g/cm3 are composed of quark matter made up of up, down and strange quarks and are thus referred to as strange stars. Charm quarks are present at central densities larger than - lOI7 g/cm . Stars with densities larger than that are denoted charm stars. Recall that only those sequences constructed for B1/4 = 145 MeV consist of matter that is absolutely stable at zero external pressure with respect to iron. The other two sequences correspond to strange matter whose energy per baryon number is about - 960 MeV = 167 MeV) and - 1030 MeV (B1j4 = 180 MeV). For the absolutely bound sequence, the dispersed mass of the equivalent number of nucleons, defined by MA m~ X J dvpropnA ( m ~ and nA denote the mass of the hydrogen atom and baryon number density, respectively), is clearly larger at all densities than the gravitational mass. Consequently the strange and charm stars of this sequence are stable against evaporation of baryons, which is different for the other two sequences where MA 5 M at higher densities [57]. Charm stars however turn out to be unstable against radial oscillations [54] and thus cannot exist stably in the universe. So the only type of

3

5

Table 2: Overview of search experiments for strange matter.

Experiment References Cosmic ray searches for strange nuggets:

balloon-borne experiments I477 483 MACRO I493

P O , 511

[53] 1531

IMB ~501

1521 tracks in ancient mica

Rutherford backscattering of 238U and 208Pb Heavy-ion experiments at BNL: E864, E878, E882-B, E896-A Heavy-ion experiments at CERN: NA52

Table 3: Features of strange quark-matter stars.

Features of strange quark-matter stars observable definite signal?

0 Strange Stars: Small rotational periods, P < 1 msec yes + possibly 0 Light, planetary-like objects Yes no

0 Cooling behavior Yes being studied not known *

0 Post-glitch behavior Yes not known* t Until recently rotational periods of P - 1 millisecond were the

* Presently under investigation.

0 Strange Dwarfs (white-dwarf-like) Yes ? *

0 Glitches Yes

borderline of detectability.

quark stars that could possess physical significance are strange-matter stars.

5.2 Complete Sequences of Strange-Matter Stars Since the nuclear crusts surrounding the cores of strange stars are bound by the gravitational force rather than confinement, the mass-radius relationship of strange- matter stars with crusts is qualitatively similar to the one of purely gravitationally bound stars, -neutron stars and white dwarfs-, as illustrated in Fig. 5. The strange- star sequence is computed for the maximal possible inner crust density, ccmst = chip.

Of course there are other possible sequences of strange stars with any smaller value of inner crust density. These will be discussed below [28]. From the maximum- mass star (dot), the central density decreases monotonically through the sequence in each case. The neutron-star sequence is computed for a representative model for the equation of state of neutron star matter, the relativistic Hartree-Fock equation of state (HFV of Ref. [58]), which has been combined at subnuclear densities with the

6

2.5

2.0

1.5

1 .o

0.5

0.0 10

Figure 4: Gravitational mass (solid curves) of strange and charm stars compared to mass at infinity, MA (dashed), of the equivalent number of neutrons as corresponding to quark number. The bag constants are B1j4 = 145 MeV, 167, and 180.

Baym-Pethick-Sutherland equation of state. Hence the white dwarfs shown in Fig. 5 are computed for the latter. (For an overview of the bulk properties of neutron stars, constructed for a representative collection of modern nuclear equations of state, we refer to Refs. [25,26,59, 601.) Those gravitationally bound stars with radii 5 200 km and 2 3000 km represent stable neutron stars and white dwarfs, respectively. The fact that strange stars with crust possess smaller radii than neutron stars leads to smaller rotational mass shedding (Kepler) periods PK, as indicated by the classical expression PK = 27r J='. Of course the general relativistic expression, which is to be appIied to neutron and strange stars, is considerably more complicated. However the qualitative dependence of PK on mass and radius remains valid [61]. So one finds that, due to the smaller radii of strange stars, the complete sequence of such objects (and not just those close to the mass peak, as is the case for neutron stars) can sustain extremely rapid rotation [28]. In particular, a strange star with a typical pulsar mass of - 1.45M0 can rotate at (general relativistic) Kepler periods as small as 0.55 5 PK/msec 5 0.8, depending on crust thickness and bag constant 127, 281. This range is to be compared with PK - 1 msec obtained for neutron stars of the same mass [25, 261.

The minimum-mass configuration of the strange-star sequence (labeled 'a' in Fig. 5) has a mass of about Mmin - O.O17M, (about 17 Jupiter masses). More than that, we find stable strange-matter stars that can be even by orders of magnitude lighter than this star, depending on the chosen value of inner crust density [28]. If abundant enough in our Galaxy, such low-mass strange stars could be seen by the gravitational

7

1.5

100 101 102

Figure 5: Mass versus radius of strange-star configurations with nuclear crusts (solid curve) and gravitationally bound stars (dotted). (NS=neutron star, SS=strange star, wd=white dwarf, sd=strange dwarf.) The cross denotes the termination point of the strange-dwarf sequence (ecrust = €drip). The dots and vertical arrows refer to the maximum- and minimum-mass star of each sequence.

microlensing searches that are being performed presently. Strange stars located to the right of 'a' consist of small strange cores (R,,, 5 3 km) surrounded by a thick nuclear crust (made up of white dwarf material) which follows from Figs. 5 and 6. We thus call such objects strange dwarfs. Their cores have shrunk to zero at 'd'. What is left is a ordinary white dwarf with a central density equal to the inner crust density of the former strange dwarf [28, 291. A detailed stability analysis of strange stars against radial oscillations [28, 541 shows that the strange dwarfs between 'b' and 'd' in Figs. 5 and 6 are unstable against the fundamental eigenmode. Hence such objects cannot exist stably in nature. However all other stars of this sequence ( E , , ~ = €drip)

are stable against oscillations. 430, in contrast to neutron stars and white dwarfs, the branches of strange stars and strange dwarfs are stably connected with each other [28, 331.

So far our discussion was restricted to inner crust densities equal to neutron drip. The impact of emst < c a p on strange dwarfs is shown in Fig. 7. One sees that for decreasing inner crust densities the termination point (open circle) of the strange- dwarf sequence with = €drip ('1') moves from left to right, since this is the direction in which the central density along the white-dwarf sequence decreases. We divide the strange dwarfs into two distinct categories. The first one consists of a core

2.0 I ' ' """I ' """'I ' """'I

1.5 - -

2 ............................ ~-.-.-.-.-.-.-.-.-._. 3 1.0 ;

\ si +. - - -- ' :

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0.5 - 4 ' . 1 : 1 -

0.0 - - I , , I .,... I . , , I * . . . I , , . ,,... I

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R,, b l Figure 6: Gravitational mass versus strange-core radius of sequences of strange stars with inner crust densities of: (1) 4.3 x lo1' g/cm3, (2) 5 x lo9, (3) lo8, and (4) lo7. The mass-radius relationship of sequence '1' is shown in Fig. 5. Only sequences with Emt 2 lo9 g/cm3 possess a maximum-mass strange dwarf (labeled 'b7), where the sequence in the direction of decreasing &ore changes from stability to instability against radial oscillations. Conversely all stars along sequences with Emst 5 lo9 g/cm (sequences '3' and '4,) are stable.

3

of strange matter enveloped within ordinary white dwarf matter ('3' to '57, the second forms a entire new class of stars that contain nuclear material up to - 4 x lo4 times denser (sequence '1 ') than in ordinary white dwarfs of average mass [283, M - 0.6 Ma , whose central density is - lo7 g/cm3. The entire family of such strange stars owes its stability to the strange core. Without the core they would be placed into the unstable region between ordinary white dwarfs and neutron stars [33].

6 Cooling Behavior In Fig. 8 we exhibit the time dependence of the redshifted surface temperature of a strange star with crust (B'i4 = 145 MeV) [62]. The star's mass amounts 1.4Ma. The quarks are treated as both superfluid particles [63, 641 as well as normal ones [65, 66, 671. From detailed cooling calculations [62, 68, 691, it is know that surface emission from the star quickly brings the temperature down to a few times lo6 K, so that we plot our results only after the temperature has dropped down to such a value. The cooling curves are compared with the upper limits on temperature

9

F 1 . . . . I I I . . . . I 500 1000 2000 5000 10000 20000

R C h l Figure 7: Mass-radius relationship of sample strange dwarfs with inner crust densities (1) 4.3 x 10" g/cm3, (2) lo1', (3) lo9, (4) lo8, and (5) lo7. The dotted curve corresponds to white dwarfs, the open circles denote the termination points of strange- matter sequences. Only stars beyond the mass peak (in the direction of increasing radii) are hydrostatically stable.

established from the Einstein Observatory, and absolute temperature ranges derived from ROSAT data.

If the emissivities of quark matter used here constitute reliable estimates, which at present is an unresolved issue, Geminga, Monogem, and PSR 1055-52 could be ruled as strange pulsar candidates of mass M = 1.4MO. It remains to be studied in detail how sensitive the cooling behavior of strange stars is against variations in neutrino emissivities, the value of the strong coupling constant, the assumed mass of strange quarks, and other QCD related uncertainties. At the present level of development, it appears that only superfluid strange quark matter may lead to pulsar temperatures that are compatible with the temperatures of some of the observed pulsars.

Should a more detailed analysis in fact confirm a considerably faster cooling of strange stars with and without nuclear crusts, relative to neutron stars, this would provide a definitive signature (together with rapid rotation) for the identification of a strange star. Specifically, the prompt drop in temperature at the early stages of a pulsar, say within the first 50 years after its formation, could offer a good signature of strange stars (701. This feature,. provided it withstands a more rigorous analysis of the microscopic properties of quark matter, could become particularly interesting if continued observation of SN 1987A would reveal the temperature of the possibly existing pulsar at its center.

10

1 os

Figure 8: Cooling behavior of a strange star with nuclear crust. The star's mass is M = 1.4MO.

7 Summary This work deals with an investigation of the properties of the complete sequences of strange-matter stars that carry nuclear crusts. The facets of these sequences have not been studied before. We arrive at the following important findings,

0 The complete sequence of compact strange stars can sustain extremely rapid rotation and not just those close to the mass peak, as is the case for neutron stars!

0 If the strange matter hypothesis is correct, observed white dwarfs should contain strange-matter cores in their centers. Their maxima1 possible baryon number compatible with hydrostatic stability is smaller than A,,, 5 2 x

0 The masses and radii of stable strange stars Iie in the ranges 5 Mss/Ma 5 2 and 2 5 Rss/km 5 lo3. Those of the strange dwarfs are given by lo-* 5

11

Md/M, 5 1 and lo3 5 &/km 5 lo4. Thus, if their abundance in our Galaxy is sufficiently large enough, the presently performed gravitational microlensing experiments should see them all!

0 Strange stars can possess nuclear crusts of thickness - (1 - lo4) km! This will be of great importance for their cooling behavior (presently under investigation [711).

0 Contrary to claims in the literature [72], we find that the moment of inertia of the crust on a strange star can account for both the observed relative frequency changes of pulsars (glitches) as well as the relative change in spin-down rate!

As becomes clear from Table 3, there remain many interesting aspects of strange pulsars, strange dwarfs, and possibly strange planets, that need to be worked out in detail. From their analysis one may hope to arrive at definitive conclusion about the behavior of dense nuclear matter and the true ground state of the strong interaction.

Acknowledgement: This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of Nuclear Physics, of the U.S. Department of Energy under Contract DE-AC03-76SF00098.

References [l] A. R. Bodmer, Phys. Rev. D 4 (1971) 1601.

[2] H. Terazawa, INS-Report-338 (INS, Univ. of Tokyo, 1979); J. Phys. SOC. Japan, 58 (1989) 3555; 58 (1989) 4388; 59 (1990) 1199.

[3] E. Witten, Phys. Rev. D 30 (1984) 272.

[4] Ch. Kettner, F. Weber, M. K. Weigel, and N. K. Glendenning, Phys. Rev. D 51 (1995) 1440.

[5] Strange Quark Matter in Physics and Astrophysics, Proceedings of the Interna- tional Workshop, Aarhus, Denmark, 1991, ed. by J. Madsen and P. Haensel, Nucl. Phys. B (Proc. Suppl.) 24B (1991).

[6] J. D. Bjorken and L. ‘McLerran, Phys. Rev. D 20 (1979) 2353.

171 S. A. Chin and A. K. Kerman, Phys. Rev. Lett. 43 (1979) 1292.

[8] R. L. Jaf€e, Phys. Lett. 38 (1977) 195.

[9] G. Baym, E. W. Kolb, L. McLerran, T. P. Walker, and R. L. Jaffe, Phys. Lett. 160B (1985) 181.

[lo] A. De Riijula and S. L. Glashow, Nature 312 (1984) 734.

12

[ll] H. Terazawa, J. Phys. SOC. Japan, 60 (1991) 1848.

[12] H. Terazawa, J. Phys. SOC. Japan, 62 (1993) 1415.

[13] F. Curtis Michel, Phys. Rev. Lett. 60 (1988) 677.

[14] 0. G. Benvenuto and J. E. Horvath, Phys. Rev. Lett. 63 (1989) 716.

[15] J. E. Horvath, 0. G. Benvenuto, and H. Vucetich, Phys. Rev. D 45 (1992) 3865.

[16] P. Haensel, J. L. Zdunik, and R. Schaeffer, Astron. Astrophys. 160 (1986) 121.

[17] C. Alcock, E. Farhi, and A. V. Olinto, Astrophys. J. 310 (1986) 261.

[18] C. Alcock and A. V. Olinto, Ann. Rev. Nucl. Part. Sci. 38 (1988) 161.

[19] P. Haensel and J. L. Zdunik, Nature 340 (1989) 617.

[20] N. K. Glendenning, Phys. Rev. Lett. 63 (1989) 2629.

[21] N. K. Glendenning, Supernovae, Compact Stars and Nuclear Physics, invited paper in Proc. of 1989 Int. Nucl. Phys. Conf., Sa0 Paulo, Brasil, Vol. 2, ed. by M. S. Hussein et al., World Scientific, Singapore, 1990.

f22J R. F. Sawyer, Phys. Lett. 233 (1989) 412.

[23] N. K. Glendenning, Mod. Phys. Lett. A5 (1990) 2197.

[24] R. R. Caldwell and J. L. Friedman, Phys. Lett. 264B (1991) 143.

[25] F. Weber and N. K. Glendenning, Hadronic Matter and Rotating Relativistic Neutron Stars, Proceedings of the Nankai Summer School, “Astrophysics and Neutrino Physics”, p. 64-183, Tianjin, China, 17-27 June 1991, ed. by D. H. Feng, G. 2. He, and X. Q. Li, World Scientific, Singapore, 1993.

[26] F. Weber and N. K. Glendenning, Neutron Stars, Strange Stars, and the Nuclear Equation of State, Proceedings of the First Symposium on Nuclear Physics in the Universe, ed. by M. W. Guidry and M. R. Strayer, IOP Publishing Ltd, Bristol, UK, 1993, p. 127.

[27] N. K. Glendenning and F. Weber, Astrophys. J. 400 (1992) 647.

[28] N. K. Glendenning, Ch. Kettner, and F. Weber, From Strange Stars to Strange Dwarfs, (LBL-34869), November 1994, to appear in The Astrophys. Journal.

[29] P. F. C . Romanelli, Strange Star Crusts, B.S. Thesis, MIT (1986).

[30] Ch. Kettner, F. Weber, M. K. Weigel, and N. K. Glendenning, Stability ofstrange Quark Stars with Nuclear Crust against Radial Oscillations, International Sym- posium on Strangeness and Quark Matter, September 1-5, 1994, Crete, Greece, to be published by World Scienkific, (LBL-36209).

13

[31] F. Weber, Ch. Kettner, M. K. Weigel, and N. K. Glendenning, Strange-Matter Stars, International Symposium on Strangeness and Quark Matter, September 1-5, 1994, Crete, Greece, to be published by World Scientific, (LBL-36210).

[32] N. K. Glendenning, Ch. Kettner, and F. Weber, Possible New Class of Dense White Dwarfs, Proceedings of the International Conference Strangeness '95, Jan- uary 4-7, 1995, Tucson, Arizona, U.S.A., World Scientific, (LBL-36964).

[33] N. K. Glendenning, Ch. Kettner, and F. Weber, Phys. Rev. Lett. 74 (1995) 3519.

1341 A. V. Olinto, Phys. Lett. 192B (1987) 71.

[35] J. A. Frieman and A. V. Olinto, Nature 341 (1989) 633.

[36] J. E. Horvath and 0. G. Benvenuto, Phys. Lett. 213B (1988) 516.

[37] J. E. Horvath, H. Vucetich, and 0. G. Benvenuto, Mon. Not. R. Astr. SOC. 262 (1993) 506.

[38] J. Madsen, H. Heiselberg, and K. Riisager, Phys. Rev. D 34 (1986) 2947.

[39] J. Madsen, Phys. Rev. Lett. 61 (1988) 2909.

E401 J. Madsen and M. L. Olesen, Phys. Rev. D 43 (1991) 1069, ibid., 44, 566 (erra- tum).

[41] S. J. Cho, K. S. Lee, and U. Heinz, Phys. Rev. D 50 (1994) 4771.

[42] G . L. Shaw, M. Shin, R. H. Dalitz, and M. Desai, Nature 337 (1989) 436.

[43] H.-C. Liu and G. L. Shaw, Phys. Rev. D 30 (1984) 1137.

[44] C. Greiner, P. Koch, and H. Stijcker, Phys. Rev. Lett. 58 (1987) 1825.

[45] C. Greiner, D.-H. Rischke, H. StEicker, and P. Koch, Phys. Rev. D 38 (1988) 2797.

[46] E. Farhi and R. L. Jaffe, Phys. Rev. D 30 (1984) 2379.

[47] T. Saito, Y. Hatano, Y . Fukuda, and H. Oda, Phys. Rev. Lett. 65 (1990) 2094.

[48] T. Saito, Search for Strange Quark Nuggets in Galactic Cosmic Rays, Inter- national Symposium on Strangeness and Quark Matter, September 1-5, 1994, Crete, Greece, to be published by World Scientific.

[49] MACRO collaboration, Phys. Rev. Lett. 69 (1992) 1860.

[50] A. De RGjula, S. L. Glashow, R. R. Wilson, and G. Charpak, Phys. Rep. 99 (1983) 341.

[51] P. B. Price, Phys. Rev. Lett. 52 (1984) 1265.

14

[52] M. Briigger, K. Liitzenkirchen, S. Polikanov, G. Herrmann, M. Overbeck, N. Trautmann, A. Breskin, R. Chechik, 2. Fraenkel, and U. Smilansky, Nature 337 (1989) 434.

[53] J. Thomas and P. Jacobs, A Guide .to the High Energy Heavy Ion Experiments, UCRL-ID- 1 191 81.

[54] Ch. Kettner, F. Weber, M. K. Weigel, and N. K. Glendenning, Stability of Strange Quark Stars with Nuclear Crust against Radial Oscillations, elsewhere in this volume, (LBL-36209).

1551 N. K. Glendenning, Phys. Lett. 114B (1982) 392; N. K. Glendenning, Astrophys. J. 293 (1985) 470; N. K. Glendenning, Z. Phys. A 326 (1987) 57; N. K. Glendenning, Z. Phys. A 327 (1987) 295.

[56] B. A. Freedman and L. D. McLerran, Phys. Rev. D 16 (1977) 1130; 16 (1977) 1147; 16 (1977) 1169.

[57] N. K. Glendenning, Nuclear and Particle Astrophysics, Proc. Int. Summer School on the Structure of Hadrons and Hadronic Matter, Dronten, Netherlands, August 5-18, 1990, ed. by 0. Scholten and J. H. Koch, World Scientific, Singapore, 1991, p. 275.

[58] F. Weber and M. K. Weigel, Nucl. Phys. A505 (1989) 779.

[59J N. K. Glendenning, Astrophys. J. 293 (1985) 470.

[60] F. Weber and N. K. Glendenning, Astrophys. J. 390 (1992) 541.

[61] N. K. Glendenning and F. Weber, Phys. Rev. D 50 (1994) 3836.

[62] Ch. Schaab, Diploma thesis, University of Munich, 1995 (unpublished).

[63] D. Bailin and A. Love, Phys. Rep. 107 (1984) 325.

[64] J. E. Horvath, 0. G. Benvenuto, and H. Vucetich, Phys. Rev. D 44 (1991) 3797.

[65] N. Iwamoto, Phys. Rev. Lett. 44 (1980) 1637; Ann. Phys. 141 (1982) 1.

[66] R. C. Duncan. S. L. Shapiro, and I. Wasserman, Astrophys. J. 267 (1983) 358.

[67] A. Goyal and J. D. Anand, Phys. Rev. D 42 (1990) 992.

[68] M. B. Richardson, H. M. Van Horn, K. F. Ratcliff, and R. C. Malone, Astrophys. J. 255 (1982) 624.

[69] K. A. Van Riper, Astrophys. J. Suppl. 75 (1991) 449.

I701 P. Pizzochero, Phys. Rev. Lett. 66 (1991) 2425.

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[71] Ch. Schaab, N. K. Glendenning, and F. Weber, “Cooling of Strange-Matter Stars”, (in preparation).

[72] M. A. Alpar, Phys. Rev. Lett. 58 (1987) 2152.

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