NUCLEAR PHYSICS A
ELSEVIER Nuclear Physics A621 (1997) 385e-388c
Neutron Stars, Strange Pulsars and Strange Dwarfs
Fridolin Weber a, M. K. Weigel b and N. K. Glendenning c
aLudwig Maximilians University, Munich, Germany
bLudwig Maximilians University, Munich, Germany
CLawrence Berkeley National Laboratory, Berkeley, California, U.S.A.
This paper deals with an investigation of the properties of hypothetical strange-matter stars, which are composed of u, d, s quark matter whose energy per baryon number lies below the one of ~6Fe. Observable quantities which allow to distinguish such objects from their "conventional" counterparts, i.e., neutron stars and white dwarfs, are pointed out.
1. In t roduct ion
The hypothesis that strange quark matter may be the absolute ground state of the strong interaction (not 56Fe) has been pointed out by Boder , Witten , and Terazawa . If the hypothesis is true, then a separate class of compact stars could exist, which are called strange stars [2,4,5]. They form a distinct and disconnected branch of compact stars and are not part of the continuum of equilibrium configurations that include white dwarfs and neutron stars. The properties of sequences of strange stars as well as the properties with respect to which such stars differ from their non-strange counterparts are discussed in this paper.
2. Const ruct ion of Models of Rapid ly Rotat ing Strange Stars in General Relativity
I) Einstein equation:
1 ~. G u~ ~ Ru '~-~9 R=8~Tu' (c ,P (e ) ) (1)
ds 2 = e2V(r,;~)dt2 _ e2:~dr 2 _ e2(d - wdt) 2 - e2UdO 2
II) Rotation at Kepler (mass shedding) frequency:
~U = [eU-V ($l, ffJ) ~- o3(ll, ~J)]at star, s equato r ,
0375-9474/97/$17.00 1997 - Elsevier Science B.V. All rights reserved. PIE S0375-9474(97)00276-5
386c E Weber et aL /Nuclear Physics A621 (1997) 385c-388c
Ow l Or ,h-, I Ov/O r ( Ow l Or )2 v - 2 + o--67X +
III) Moment of inertia :
f0 f0 e~+~+~+~[e + P(e)] fl - w ~/2dO R dr (4)
Equations (1) to (3) are solved selfconsistently using the equation of state of a strange star with nuclear crust  as an input.
3. Resu l ts
The main features of strange-matter stars with nuclear crusts can be stated as follows:
Our model calculations  show that strange stars with typical pulsar masses, 1.45 ./14o, can rotate at Kepler periods, PK - - 2~'/~g, as small as half a millisecond. The situation may be different for neutron stars of the same mass, for which a limiting rotational Kepler period of about ~ 1 msec has been established [7,8]. Moreover, a certain part of the sequence of the low-mass strange stars can have rotational periods that rival even the minimal possible periods of heavy neutron stars!
From  it follows that the crustal moment of inertia relative to the star's total moment of inertia, Icrust/Itotal, varies between 10 -3 and ~ 10 -8. If the angular momentum of the pulsar is conserved in a star quake, then the relative frequency change and moment of inertia change are equal and one arrives at 
A~ A I A I A I /crust - - Io > ~r - - /crust I = f X (10 -5 - 10-3), (5)
where I0 (< Itot~) denotes the moment of inertia of that part of the star whose frequency is changed in the quake, and f is the fractional change of the crust's moment of inertia necessary to account for the glitch. Since observed glitches have A~/~ _~ 10 -9 - 10 -8 ~ f~ (10 -1 -- 10) X f . (6)
Since A~/~t = 10 -3 to 10 -2 from observation (Crab and Vela) :=> f < 10 -4 - 10 -1 which is consistent with f~
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Strange stars can possess nuclear crusts of thickness ~ 1 km to ~ 103 km, depending on central star density [9-11], which is of importance for their cooling behavior !
Strange stars possess masses in the range ~ 2 M o to 10 -4 M@ and radii from several kilometers to ~ 103 km [9-11]. Because masses and radii of ~ 10-4MG and ~ 10 3 km are completely excluded for both neutron stars as well as white dwarfs, such star properties may serve as additional signatures for hypothetical strange stars!
If the light, planetary-like strange stars exist and if they are abundant enough in our Galaxy, then the gravitational microlensing experiments should see them!
We find white-dwarf-like strange stars that owe their stability solely to the strange cores at their centers (strange dwarfs) [9,13]. They carry nuclear crusts whose density at the base is up to about 400 times higher than the central density in the most massive white dwarf. Hence such strange dwarfs constitute a possible new class of dense stars, if the strange matter hypothesis is correct!
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(1989) 3555; 58 (1989) 4388; 59 (1990) 1199. 4. C. Alcock, E. Farhi, and A. V. Olinto, Astrophys. J. 310 (1986) 261. 5. C. Aleock and A. V. Olinto, Ann. Rev. Nucl. Part. Sei. 38 (1988) 161. 6. N. K. Glendenning and F. Weber, Astrophys. J. 400 (1992) 647. 7. 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.
8. F. Weber and N. K. Glendenning, Hadronic Matter and Rotating Relativistic Neu- tron 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. Z. He, and X. Q. Li, World Scientific, Singapore, 1993.
9. N.K. Glendenning, Ch. Kettner, and F. Weber, Astrophys. J. 450 (1995) 253. 10. F. Weber, Ch. Kettner, M. K. Weigel, and N. K. Glendenning, Strange-Matter Stars,
Proceedings of the International Symposium on Strangeness and Quark Matter, Crete, Greece, eds. G. Vassiliadis, A. D. Panagiotou, S. Kumar, and J. Madsen, World Scientific, 1995, p. 308.
11. N. K. Glendenning, Ch. Kettner, and F. Weber, Possible New Class of Dense White Dwarfs, Proceedings of the International Conference Strangeness '95, January 4-7, 1995, Tucson, Arizona, U.S.A., ed. by J. Rafelski, American Institute of Physics, New York, 1995, p. 46.
12. Ch. Schaab, F. Weber, M. K. Weigel, and N. K. Glendenning, "Thermal Evolution of Compact Stars", to appear in Nuclear Physics A, (astro-ph/9603142).
13. N. K. Glendenning, Ch. Kettner, and F. Weber, Phys. Rev. Lett. 74 (1995) 3519.