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ShVlS NO«iri3N 318V1SV13W GNV
вкай ааааваааваааааааааааааваааяаавэаваиааааямкваакаяаввааааааааававааааваааавааакаааава вааааараааааваааааааваааяваааааастаааиваааакжяяааввмаавааааааааааанпваааааааанаааа! iitim a»ii audit • IIIII авеаэа SDISAHd 1VlN3Wlil3dX3 IIIIII ю 3inniSNi STitANGS, QUAhK, Al.'D МКТАЛТАВЬЕ NEUTRON STAhS: Preprint 1TBP 87-07/M.I.Krivoruchenko - M.: ATOMINFORM, 1987 - 14 p.
Observable consequencea of possible existence of strange, queric. and metastable neutron stars are discussed., Boae conden- sation of dibaryons in dense nuclear matter ia taken into ac- count. The data on glitches from pulsar in Crab Nebula are used to obtain limits on binding energy of stable strange matter and on masses of dibaryon resonances. We suggest a scenario for two atep collapse of supernova SN 1987 a. Masses of diagonal neutrinos are extracted from the data on second neutrino burst observed from supernova SN 1987 a.
Pig. - 2, ref. - 24 Published in Pis«ma т ZhETF, 1987, 46, H 1.
.') ilucTHiyr то1>|*'тмчесио» к »кспорим«нтл ».uo« физики, 1987 •I i \ \ :| Production of strange baryons becomes energetically favor- j able in interiors of massive nsutron stars at high densities and { pressures /1' (see alao '2|3'). tfitten ' ^ has conjectured that i f at range matter in the quark phase may be the true ground state • f. < of baryone for all pressures. Properties of the stable strange /c_q/ matter have been discussed in refs. In thin paper we obtain i limits on binding energy of strange «natter and discuss observable consequences of possible existence of strange stare /4»'~"/ com- /7/ posed of atable strange matter and quark stars the inner part of which consists of weakly unbound strange matter while the outer envelope is made up of normal nuclear matter. The stable strange matter absorbs the nuclear matter. Due to the Coulomb barrier at the surface, V * 20 JleV, atrange etara с can support light envelopes made up of ordinary nuclei. The en- velopes of atrange stars are unable to produce starquakes followed /8/ by noticeable changes in the periods of stellar rotation . The glitchea observed from pulaara PSR O833-45(Vala), О531+21(Crab Sebula), find 1641-4'? are interpreted as results of pulsar crust- quakes (for a review зев ). The neutron and quark a tars are •surrounded by the massive solid crusts, «o pulsars PSR QBJ3-45, O5J1*S*^4 hue recently been observed. f | up of neutrons) requires a very-high-order tweak interaction for I coherent creation of many strange quarks , so the life» i< times of the metestable neutron stars can be very large. ! Two flavor nonetrange quark matter converts to more stable
I strange matter on a weak interaction timeecale, tff ~ Gp m , where m is the nucleon mass, so the critical density for the phase transition to the nonstrange quark matter is to be greater than the central density of an old metestable neutron star. This requirement gives
B> / (,-i*)-p, «71* (1*/*)* } whexe Ц is chemical potential, F is pressure of neutrons in the center of the star, В is QCD vacuum pressure (essentially the ЩТ bag constant), and o£<. is QCD coupling constant. The first term in the right side represents the pressure of the nonstrange quark matter as a function of И The energy per baryon of stable strange matter equals, for zero-таэз strange quarks, E/A » (108 ~Pl B) (1 *• <** /2тг ). Using inequality (1), we obtain
The ratio E/A increases with strange quark mass, so the inequality (2) is correct in general. Strange stars have been discussed first by Itoh '1 . The upper limit on masses of strange stars made up of noninteracting
' This statement has been criticised by M.B.Voloshin. I would like to thank him for prolonged discussion of this point.
|; * * * * constituent quarks with equal masses m = m. = m = m car/, be /1 2/ obtained by simple rescaling of OV limit for neutron stars . The maximum mass for strange stars can be written as M • -1/9 * 9 OV OV /19/
(Hcllf) ' ^ (m/m ) M where M " = 0.7 MQ ' ' , Nc = 3 is the number of colors, and И_ = 3 is the number of flavors of the quarks. In ref. the numerical results are given for too large constituent quark masses. For m = m/3 we get M = 3 M = 2.1a-0 The similar result has been obtained by Witten within the
framework of MIT bag model. For zero-mass current quarke m = m, = m =0 the upper limit takes the form M =2.0 MQ where B^ = 58 MeV Fm iB the KIT bag model value for QCD vacuum pressure. Using inequality (1), we obtain •/ir . . . p (3) ! The attempts of quantitative description of glitchea for Vela pulsar give no conclusive results . Only one glitch has been observed from pulsar PSR 1641-45. Within the framework of two component model of neutron stars (neutron liquid plus charged component including the crust), a reasonable agreement is obtained with the data on Crab pulsar glitches. The ratio between the moment of inertia for the neutron liquid and the total moment
B f of inertia is found to be large, In/I 0.95 . The charged component is therefore small. Strange matter consists of quarks, charged particles. We thus conclude that pulsar in Crab Nebula can not be a quark star, only the neutron star. If strange matter is stable, pulsar in Crab Nebula is really the metastable neutron •tar. The lifetimes of ordinary nuclei with respect to decay to •table strange caunJcs are greater by a factor M/^/m(^ Fe) than 4 the lifetimes of metastable neutron stars • The age of pulsar in Crab Nebula is T = 930 years. The nuclei lifetimes are there- fore T £, 10 years. The Earth's detectors with sensitivity of about. 103 years can not be used for search for the nuclei decays (the neutron stars are certainly the best detectors). The time interval between glitches from Crab pulsar is At » 5 years. In tensor interaction model (TI) of nuclear matter
and in Reid model (R) Д t = 5 years, respectively, for U TI = 3 1088 MeV, PTJ = 21 MeV Fm~ , M^ = 1.3 MQ , and MR = 1014 MeV,
3 3 13 ?K = 13 MeV Fm"* , Mg = 0.3 MQ^ ' ^, where A*- is chemical potential, P is pressure of neutrons in center of the star, and
II is the stellar mass. The inequality (1) gives BTI > (85 - 67<=tt) 3 3 MeV Pm" t BR> (67-51 <*c) MeV Pm~ . The binding energy of a
nucleon in strange matter, £ s E/A - m, becomes £ TI >
-(26 + 36 o(c) MeV, £ ? > -' (79 + 27 otc) MeV. The use is made of inequality (2). The inequality (3) gives M^j < (1.65 + 0.65.^ ) M 6 1 M yor m O » "R < d'8 + °«7 <*c) Q • 8 * ° *be inequality (2)
can be improved. For mo » 150 MeV the corresponding limits take
the form £ f- > (+ 18 - 59 •*„) MeV, £ E > - (33 + 48 <*c ) /6/ MeV. Prom existence of nuclei it follows that £ ы > - 91
MeV for ms - 0, £ B > - (64 + 7 otc ) MeV for mg « 150 MeV. We get E^j >£ g111^ £j[ П* In R model, the mass of pulsar in Crab Hebula is underestimated (see '13'), so TI model gives more realistic constraints. TI model prefers unbound strange matter for low o(e and weakly bound etrange matter for large «*c . A reasonable «atiaatt for to» binding energy of stable strange mat» tar la t£\^ (30 -40) MaT. Whtn cbaodoal pottntial of neutrons io increased beyond a critical ralua, it beoonaa energetically favorable for neutrone
' K.0»SeliTanoT» Private eonoastaatloii» 1967. • f, 5 _ \; to merge to 6q-bags. The dibaryons are Bose particles, so Воее condensate of 6q-bage is to occur in dense nuclear matter. The critical density for tlae dibaryon condensation is determined by mass of the lightest dibaryon resonance with suitable quantum • numbers. | We simplify the problea assuming that dibaryons are weakly ) interacting particles. The chemical potential of neutrons in the cold nuclear matter with the dibaryon condensate component is frozen at a critical value M-° = m(6q)/2 where m(6q) is the lightest dibaryon mass. The dibaryons do not contribute to the pressure» since they are re3t particles, so the pressure does not increase with the density. The nuclear matter loses elasticity* The neutron stars whose interiors contain the dibaryon condensate component are not gravitationally stable. They convert to strange stars, quark stars, or black holes. The sufficiently light dibaryon resonance determines the upper limit on masses of gravi- tationally stable neutron stars. The best established lightest dibaryon resonance is Л N(2130) I,JP • 1/2,1+ ^14/. The corresponding critical value for the chemical potential of neutrons M-c = 1065 MeV. The chemical potential of neutrons in center of pulsar in Crab Nebula does not exceed Л*-с (substantially - for TI model), 00 the suppo- eition that pulsar in Grab Nebula is a neutron star does not dis- t agree witn the criterion of stability u. She critical value is noticeably smaller than U- TI « 1088 Me? *nd №rim ЮН KeV, ao pulsar in Crab Hebula can not be the neutron star (light dibaryona destabilise massive neutron star*). б i It can not be also a strange star (the glitches can apparently be associated «dth neutron and quark stars). We argued above that Crab pulsar can not be a quark star as well ( the low value of №• c implies existence of massive strange matter core for the quark star, whereas the charged component of Crab pulsar la actu- • ally small). We arrive at a contradiction. The astrophysical data \ bring status of HN(196O) dibaryon resonance into the challenge. Assuming the validity of conventional models of pulsar in Crab Nebula, we obtain a lower limit on masses of dibaryon reson- ances. Within the framework of TI and E models, we get, respect- ively, m(6q)TI > 2M,TI = 2176 MeV, m(6q)R > 2iOR =» 2028 MeV. The dibaryon condensate does not exist in ordinary nuclei, so the masses of dibaryon resonances are to be greater than 2 ( m + £.p), where £„ * 40 MeV is Fermi energy of nucleons in nuclei. The corresponding limit takes the form m(6q)K >2(m+ £, p) » 1960 MeV. We get m(6q)£*n> m(6q)jfn > mCSqJjf11. Light dibaryon resonances play very important role for the dynamics of pulaars. Further experimental study of light dibaryons would certainly be desirable. The above discussions rely decisively on the validity of suggestion that glitches occur as a result of pulsar crustquakes. This model of glitches is elaborated in details. It describes well the data on pulsar in Crab Nebula. The model ^'5/ anjonggt other alternative models is of special interest for 3trange stars since it does not require the existence of massive pulsar crusts. This model provides геазопа for glitches via instabilities in pulsar magnetoapheres. We do not consider here the alternative models. The conversion epeed of strange matter in nuclear matter 7 with temperature T » 10 MeV тГ * (10 - 6 103) cm/вес ^'. The lower values of iT correspond to greater values of E/A. The con- version time of the metestable neutron stars can be estimated as t - 10 km/гг » (0.05 - 30) hours. This time is many orders of magnitude greater than the typical time of collapse of a neutron star due to formation of pion condensate ' ' . The conversion of a gravitatioaally stable neutron star whose mass exceeds Itoh- Witt en upper limit on masses of strange stars, M a 2 UQ , pro- duces at the final stage of the slow conversion a fast gravita- tional collapse of the strange matter core. As a result of collapse of an ordinary star there can appear a gravitationally stable neu- tron star of mass M > M with an admixture of strange matter. In such a case t -~ 10 km/ * (0.05 - 30) hours later the second collapse is to occur. The formation of 3trange matter in the neu- tron star can result, for instance, via an intermediate phase transition to the nonstrange quark matter. Two neutrino bursts detected with the interval of few hours during the supernova Slf /17/ 1987 e explosion can be associated successively with collapse of an ordinary star and collapse of strange matter core of the neutron star. The timescale of the second collapse is t ~ 10 кш/с ш 30 microseconds, while duration of the second neutrino burst at the Earth is about ^0 seconds. The blowup of the burst can be related to finite neutrino masses. The diagonal neutrinos ^ with Dirac masses m- are auperpoui tions of v*tf , Л- * ... We can treat all the neutrinos as if they have been emitted on thu instant. The lightest neutrinos *i arrive first, then more maaaive neutrinos «^ arrive, etc. We have eee chains of reactions V. t> -> e* n» with more energetic electrons detected before less energetic ones. The total number of events »-' p~?t*w is proportional to \^ >? \ J^ > \ 8 The events 1-6 from Kamiokande II detector can be related to neutrinos /4 of mass m1 - 4 eV, whereas events 7-16 from Kamiokande II and 1-8 from 1MB detectors can be related to neu- trinos V^ of mass m2 • 22 eV. If we assume equal flux and energy for all neutrinos, we l Z obtain |<;,|0e> ) cr 4/(4 • Ю) - 2/7, | where g. - 1.25, ^ " sin Q» " 1^4 » °ei s •lectrOn •*••» and О is mean energy of the neutrinos. ?or <-*^ & 20 McV, B1 •* 2/4, and R2 ^ 1/10 we get | /4-9/t Tne yadii Of neutron and quark stars are greater than R a 10 ton (see Pig.2). The lower limit on periods of rotation w c of neutron and quark stars can be estimated as *min' 2* %ir/ ' 0.2 me. For strange stare we have Р^п « 0. There exist radio pulsars with periods P ~ (1 - 10*) me. The finding of a pulsar with period P < Р^д will be the direct and unambiguous proof of existence of strange stars. A careful search for pulsars with ultrashort periods would certainly be welcome. Quark stars have been discussed first by Ivanenko and Kurdgelaidze '^'. We consider a model for quark stars which re- presents a simplest generalisation of Witten's model for strange stars. We describe the nuclear phase of matter by ideal degenerate Fermi gas of neutrons, protons, and electrons, and the phase of strange matter by ideal { otc • 0} degenerate Fermi gas of up, down, strange quarks, and electrons. The model of such a type is consistent for not very large critical densities of the phase transition /20»21'. чы.в is Just the case for weakly un- bound strange matter. We have two paenomenological parameters: QCD vacuum pressure В and strange quark mass a . At the boundary с ш с + 2 of the phases, following relations take placet / п / и Ал chemical potentials of the particles. The electron nuaber density in nuclear matter differs from the one in etrange matter, so a Jump of electrostatic potential is to occur at the boundary of the phases, k*r * T/e. The equations of states of the cold nuclear 3 and strange aatter for В • 98 lie? Fa" , ae - 150 MeV, and critical density for the phase transition n - 0.17 Гя~Э. are plotted in I то Pig.1. The massee of the quark and neutron stare versus the stellar radii are shown in Fig.2. The maximum and minimum masses of the quark stars are MA = 1.44 MQ , 4Г = 0.35 UQ , and of the metastable neutron stars 1Г =0.61 MQ , VT = 0.45 UQ . The upper limit on masses of the neutron stars, и , is determined by the lightest dibaryon Л N(2130) I,JP = 1/2, 0+. Botice that 1^ < M0V, so the neutron stars become unstable before reaching the OV limit. The spontaneous conversion of a metastable neutron star to the quark or strange star changes the characteristic pulsar age «-£ , = P/2P where P is the period of stellar rotation. If we assume magnetodipoTe character of pulsar energy emission, we get x cb/ "£ ch8 " 2n ^.e^q.s8» where I is moment of inertia and R is radius of the stars. In our model t ?./ t ?u = Ю for 3 И = l/P. Young pulsar PSR 1509-58 (Tch = 1.7 Ю years )is situ- ated in old supernova remnant MSH 15-52 (trem = 2 10 years * or a 10 "c ctl« ^ discussion see ). The age of pulsar can be adjusted to the age of the nebula if we suppose that after the supernova explosion a metastable neutron star has appeared, which then comparatively recently, .£10 years ago, converted sponta- neously to the quark or strange star. , After completing this work we have gotten to know about /24/ important papers where Bose condensation of dibaryons (out of the estrophysical context) has been discussed. I We would like to thank S.I.Blinnikov, I.Yu.Kobzarev, L.A.Kondratyuk, V.A.Lubimov, I.M.Sarodetakii, L.B.Okun, M A.Shifman, V.I.ZaJcharov for uaeful diacuseiona and Ya.B.Zeldovich for valuable remarks. 11 P{MeT Fm"3) 100 ~. В ш 98 MeV Pm.-3 ms« 150 MeV n • 0.1? Pm"3 С 10 г —, , , 1 i x— 320/ 340 360 380 400 420 440 46 0 480 500 nuclear matter 0.1 fig.1. The pressures of strange natter (ABD) with subtracted QCD-vacuum pressure B=98 MeV ft»"*-* and of nuclear natter (CDS) as functions of the chemical potential of d-quarlca for n»1501l»V and critical density for the phase transition n «0.17 fa J. Sue to asymptotic freedom ot QCD, the ideal Term! gets model tor strange matter is exact in the limit ftd^0® » The nuclear pha- se of natter is metastaole at pd > f^at »338 MeV. The conden- sate of Д N(2130) dibaryon resonances occurs at ^обг/^ЗбОВеУ. The points A and В characterise the state of strange natter in [centers of the quark stars with maximum and minima» masses (see (fig.2). In the interval BD there are no gravitationally stable qu« .ark star» (for general theorems see /24/) • Ш 1.5 в = 98 MeV йп*3 150 MeV Л 0.17 Fm"3 1.0 0.5- v R(km) i 8 10 12 14 16 18 20 *fa* Bfteeee of quark and neutron stars versus the total radii. The notations are the sane as in Fig. 1. The ourree |S and CUB represent the grayitationally stable quark and neutron jtter*» Vbe curve CD is due to the itetastable neutron stars. 13 HBPBBSHCBS 1. Ambartsumyan V.A., Saakyan G.3. - Sov.Aatron.,1960, £, 187; 1961, £, 601. 2. Zeldovlch Та.В., Hovikov I.D. Theory of Gravity and Evolution of Stars. K.t Haute, 1971* 3* Shapiro S.L., Seukoleky A. Black Holes, White Dwarf8 and Heut- t ron Stars. Wiley-Interecience, Hew Tork, 1983» 4. Witten S. - Phys.Bev., 1984, D30. 272. 5. De Bujula A., Glashow 3. - nature, 1984, 3,12» 734. 6. ?arhi B.t Jaffe H.L. - Phye.Hev., 1984, 1Ц0, 2379. 7. 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Работа поступила в ОНГЛ 8.05.87 Подписано к печати 27.05.87 TI3362 Формат 60x90 I/I6 О&сетн.печ. Усл.-пет. д.0,75. Уч.-изд.л.О,5. Тираж 250 экз. Заказ 87 . Индекс 3624 Цена 7 код. Отпечатано в ИГЭ5, II7259, Москва, Б.Черемутпкинская,25 * •Л,. ИНДЕКС 3624 •'•••'«••'•'••I | • • » • » « #aaaieaa*aKet*aafaa««t*««eaB*s*sk*iiits • a a a » a *4* tuxftatiXt fi . ;• s к :- • '< » fi' • t > • i • ; i • a a • a a > I a a 111 •••••••• *Ч1Л ni ч 9«eii;iBi>i9aitiM аавамаваа в I «aaa аввввздРаа ааанаакасаяаааааасааевсяе зве E;«!iiisiiiiiLiiiaa м • a » в * ••«»»••»» 4Jf"&4 aiaaai«titi>fiaiatiaa«a>eiat • в >г3 *flMjLf|t' » • * inautaaaatla aaa a • aaiiat«nii«(aaitaiiiaHcai>aiiiet>ii<« ates Д M "'Wwnn • '. P^t «jlaiataaaa aaiaaKiia 1#* '•>•>>•• aa iaitiiaiaaaaati sei>>»>«>i>aaa»giii>iaaa>iiaianaiaiiiiaa aaaaiaaaiiamataaiiiiaaiaaa s-i>ii:iii|!i«iitiiisin «Д aaa «a «№3N at naialiiiaaifii «aaafiu «*<*«•» et*«f>«tTTfait e а э а б| * z «iti sin aw шташ И ан aaa cjf a jp a a a a • iiiliaaKiaaaHi aiflee w >*aaw ?аяа esn)9>s М..ПРЕПРИНТ ИТЭФ, 1987, № 87, c.1-12