Cooling Neutron Hakki Ögelman, Garching (Max-Planck-Institut für Extraterrestrische Physik)

Historically, the first schemes for dis­ covering neutron stars were based on the detection of the thermal radiation from a cooling in the X-ray band. Since neutron stars are the remains of the central cores of massive stars that have consumed all possible internal energy sources, it was natural to as­ sume that they would be cooling from the moment they were created. Follow­ ing the advent of X-ray astronomy in the early 1960s with the discovery of the brightest galactic X-ray source Sco X-1 (Giacconi et al. 1962), detailed calcula­ tions of cooling rates and cooling curves started to appear in the scientific litera­ ture (for a review see Tsuruta 1986). The hope was to find neutron stars several hundred years old, with surface tempe­ ratures around several million degrees. Although the general idea was correct, this method of finding neutron stars turned out to be the difficult way. It is ironic that only recently have we Fig. 1 — Cross-section of a 1.4 MO neutron been able to detect thermal radiation star. Figure taken from Pines and Alpar from cooling neutron stars, after the (1985). development of sensitive focusing X-ray instruments — some 12 years after the ficantly to our understanding of the in­ trons, superfluid neutrons, and a lattice discovery of neutron stars as pulsars ternal structure of the . The of neutron rich nuclei, is reasonably well (Hewish et al. 1968). In retrospect, it is structure is of topical interest not only understood. At deeper layers, going obvious that during the collapse to a for astrophysics, it also provides a uni­ down 10 kilometers to the centre, where neutron star, the original magnetic field que opportunity to study the imperfectly densities are in excess of  0 and nuclei and the rotation rate of the progenitor understood hadron equation of state start dissolving and merging together, star would be amplified by approxima­ at nuclear ( 0  3 x 1014 g/cm3) and the equation of state is not well known. tely the square of the ratio of the initial to higher densities (for reviews see Gor­ It is possible, that charged pions are pro­ final radius ( 1010), and that such ob­ don, Baym and Pethick 1979; Pines duced through n → p +  -, for example, jects should generate all kinds of elec­ 1987; Shapiro and Teukolsky 1983, and having spin 0, then form Bose-Ein- tromagnetic fields and waves at the ex­ Chapter 8). Let us start by examining the stein condensates. At the very extreme pense of their rotational energy. In the salient features of a 1.4 solar (MO densities near the centre, we may even meantime, the strong X-ray sources = 2 x 1033 g) "cold" neutron star with get a relativistic Fermi gas of quarks. discovered five years before the pulsars "stiff" equation of state, shown in Fig. 1 This picture of a "cold" neutron star is have also been identified as neutron (from Pines and Alpar 1985). Going from actually valid for interior temperatures stars, accreting mass from close binary outside to the centre, one encounters up to 1010 K (1 MeV) since, owing to the companions and converting the gravita­ first an atmosphere a few meters thick, high densities involved, the crust mel­ tional energy gained by the gas to X-rays followed by an outer crust, a few hun­ ting temperature is about 1010 K and the emitted from the surface. Although this dred meters in depth and of density Fermi energies of the quantum liquids model was suggested back in 1967 by increasing from 7 x 106 to 4 x 1011 are in the 5 x 1011 K to 5 x 1010 K (5 - Shklovskii to explain Sco X-1, several g/cm3. The outer crust consists of a 50 MeV) range. Considering that follow­ years were to pass before the observa­ solid array of nuclei and degenerate rela­ ing supernovae explosions, neutron tions with the UHURU satellite showed tivistic electrons. The next kilometer or stars are probably born with tempera­ the existence of pulsing X-ray sources so is called the inner crust; it starts with tures of 1011 K, it should take less than a which were unmistakably interpreted as the density 4 x 1011 g/cm3, where the minute to solidify the crust and establish rotating and accreting neutron stars. neutrons find it energetically easier to the superfluid interior. Despite the fact that the radiation exist outside the nuclei and start dripp­ Let us start at this point to examine the emitted from cooling neutron stars has ing out, and extends to O, the nuclear cooling of the neutron star. For the pur­ not been the best way to discover them, density regime. The properties of this poses of a first order calculation, let us this information should contribute signi­ region which contains degenerate elec­ assume a two component thermodyna- 98 mic model of a one solar mass neutron star: 1) an isothermal interior starting around the density   1010 g/cm3, within which almost all of the thermal energy resides; 2) an outer envelope starting with the surface and extending to the isothermal interior along which the temperature in­ creases from TsS of the surface to TcC of the interior (see Shapiro and Teukolsky 1983, Chapter 11 for a review of neutron star cooling). The Board of the Eindhoven University of Technology, With such a simple model, the cooling Eindhoven, the Netherlands, curve of a neutron star would have been announces the vacancy for a similar to that of a soft boiled egg if it were not for the fact that the neutron star interior is at very high temperatures where the dominant cooling is through FULL PROFESSOR OF PHYSICS neutrino emission. As will be estimated below, it takes about 105 years for the (m/f) neutron star to cool down to Tc  108 K (Ts  106 K) with neutrino emission, The appointee will work in the group of Applied Nuclear Techniques, part of a division of the after which the photon emission from Department of Technical Physics that also includes the Plasma, Atomic and Molecular the surface becomes the dominant cool­ Physics group. ing process; i.e., the neutron star starts to cool like the egg. Coming back to the The professor appointed neutrino cooling, it is fortunate that we - will be expected to carry out and initiate application-oriented research using nuclear do not need to worry about the interac­ physics techniques in interaction with atomic physics, in co-operation with members of tions of the neutrinos subsequent to the staff and with the second professor in the group, whose main interest is accelerator their production; below temperatures of physics and techniques: 1010 K the mean free path of the emitted - will have several particle beams (energy up to 40 MeV) and dye laser beams (an explora­ neutrinos is greater than the entire thick­ tory study of an electron storage ring is in progress) at his disposal; the use of other radiation facilities in and outside the Netherlands through national and international ness of the neutron star. Hence, we can co-operation could be a natural extension of the research programme of the group; write down the cooling equation simply - should have acknowledged qualifications in experimental physics, flexibility and a as: profound knowledge of the field of research; dU/dt = Cv dTc/dt = -(Lv + L) - will be expected to be open to interdisciplinary research and to give guidance to the where the rate of change of thermal research group with youthful enthusiasm; energy dU/dt, which also equals the - will be expected to obtain financial support from public and industrial funds; - has to participate in the Department's teaching programme by giving lectures on heat capacity Cv = dU/dTc times the general physics and by supervising the research work of undergraduate students and of rate of temperature change, has been graduate students working on a Ph.D.-thesis; equated to the total energy loss rate, Lv - should be willing to participate in the administrative activities of the group and of the due to neutrinos, plus L due to photons Department; from the surface. The heat capacity of - should have an adequate knowledge of the Dutch language within two years after the the degenerate fermions (predominantly appointment. neutrons) for a one solar mass neutron star, in the absence of superfluidity, can Letters of applications be simply estimated as: - are awaited within six weeks after the date of appearance of this announcement; Cv  1048 (Tc/109) erg K-1 - should be accompanied by a detailed curriculum vitae and list of publications as well as The heat capacity is expected to de­ the names and addresses of at least two qualified persons who are prepared to give references about the applicant; crease exponentially as the temperature - should be addressed, with the Indication V7247, to the drops below the transition temperature Dean of the Department of Technical Physics, to the superfluid regime; we ignore the Prof. dr. H.M. Gijsman, superfluidity effects in our simple esti­ Eindhoven University of Technology, Postbus 513, mation of the cooling curve. We can also NL - 5600 MB Eindhoven, the Netherlands. write down the photon luminosity term, assuming that the emitted radiation is Additional information may be obtained from the Chairman of the Appointment Commit­ blackbody-like: tee, Ly = 4 R2σT4s Prof. dr. ir. D.C. Schram, (telephone: (40) 47 25 50) or where R is the radius of the neutron star the Dean of the Department, Prof. dr. H.M. Gijsman (telephone: (40) 47 25 28), and σ is the Stefan-Boltzmann constant. Eindhoven University of Technology, Postbus 513, Let us proceed to examine the neu­ NL - 5600 MB Eindhoven, the Netherlands. trino luminosity. In the interior, the inter­ Those wishing to draw the committee's attention to potential candidates are kindly acting constituents are p, n, e- . At the requested to contact the Chairman of the Appointment Committee. temperatures and densities involved, the most important neutrino production pro- 99 cess of these particles is the modified URCA process (the name was coined back in 1941 by Gamov and Schönberg after the losers coming in and out of the gambling house of the Casino de Urca in Rio de Janeiro): n + n → n + p + e + v e; and n + p + e- → n + n+ve This process is in principle just the neu­ tron decay process: n → p + e_ + v e , with rearrangement and addition of a bystander neutron in order to conserve momentum in the degenerate environ­ ment. The neutrino luminosity from the modified URCA process is estimated to be: LvURCA = 5 X 1039 (Tc /109)8 erg/s Fig. 2 — Cooling curves for a one solar mass neutron star. The shaded region represents the range of standard cooling calculations with and without superconductivity and finite relaxa­ Notice the very strong dependence on tion time effects; soft and hard equations of state have also been included. The lower curve the temperature which is primarily due represents the case of pion condensate cooling. The measured EINSTEIN data points are to the phase-space factors of the inter­ taken from the summary of Tsuruta (1986), PSR 1929+10 from Alpar et al. (1987), PSR acting species. Additional processes, 1055-52 from Brinkmann and Ögelman (1987). such as the nucleon-nucleon brems- strahlung: The most dramatic difference to the through lunar occultation experiments, n + n (or p) → n + n (orp) + v + v cooling curve is introduced by the pos­ no experimental information on neutron in the interior and electron-nuclei brems- sible existence of pion condensates star cooling existed prior to the EIN­ strahlung: which increase the neutrino luminosity STEIN - EXOSAT era (for a review of EIN­ e- + (Z,A) → e- + (Z,A) + v + v to: STEIN observatory results see Helfand in the crust, are also expected to con­ Lv   1045 (Tc/109)6 erg/s 1983, and Helfand and Becker 1984; for tribute to a lesser extent to the neutrino As shown in Fig. 2, in this case the neu­ EXOSAT results see Alpar et al. 1987, luminosity. tron star cools very much faster; typical­ and Brinkmann and Ögelman 1987). A So far, we have estimated the heat ly the interior temperatures should be a major part of the problem stems from capacity Cv and neutrino luminosity Lv factor of 50, and surface temperatures a the difficulty of finding neutron stars as a function of the internal core tempe­ factor of eight lower than the standard that radiate only their cooling luminosity. rature T , but the surface photon lumi­ cooling case. For young neutron stars such as the nosity L as a function of the surface Let us now confront the experiments. Crab pulsar (born 1054 AD), where we temperature Ts. In order to solve the How does one go about measuring the expect hot conveniently detectable sur­ cooling equation we need to calculate cooling curves of neutron stars? By far, face conditions, the dynamo action of one more relationship, namely that of Tc the largest fraction of the cooling lumi­ the fast rotating (30 Hz) strong magne­ to Ts. Basically, the conductive opacity nosity comes out as neutrinos. How­ tic field (1012 gauss on the surface) (thermal insulation) of the envelope de­ ever, the same weak interacting proper­ creates such large accelerating voltages termines this relationship, which can be ty that lets them come out of the neu­ in the magnetosphere that the ensuing approximated by Tc  1.6 x 10-3T9/5. tron star so easily, makes it very difficult non-thermal high energy radiation, in­ Plugging this relationship, the estimated to observe them. So until neutrino de­ cluding X-rays, swamps out the radia­ internal temperature dependence of the tectors improve vastly, we have to rely tion due to surface cooling. For the case heat capacity, and luminosities back into on the photons from the surface. The of a very young neutron star, such as one the cooling equation gives the following surface temperatures of interest lie in that may at this moment be lurking in­ general features: the range 3 x 105/K to 3 x 106K; con­ side the 1987A in the Large For about t  105 years following its for­ sidering that the neutron star is a small Magellanic Cloud, there is the additional mation, the neutron star cools predomi­ object about 10 km in size, the total problem of the ejected outer parts of the nantly by neutrino emission with Tc ~ luminosity L for an object of Ts ~ 106 K progenitor star blocking the emitted f1/2 (TS ~ t-1/11). After this time, the pho­ is of the order of 1033 erg/s, about the radiation. In the case of accreting neu­ ton luminosity becomes the dominant total luminosity of the . The typical tron stars in close binary stellar systems, cooling process where Tc ~ t-5 (Ts ~ energy of these photons would be in the the surface is reheated to temperatures t-11/4). At the break point the internal soft X-ray region, a region which is only way above the cooling temperature by temperature is about 2 x 108K, and the accessible for observations above the the infalling material. surface temperature is about 106 K. atmosphere. In this band of the electro­ For older pulsars, with ages larger A number of authors have added more magnetic spectrum, the contemporary than 104 years, compact nebulae of rela­ thought and physics to the first order astronomical instruments employ graz­ tivistic electrons emitting X-rays via syn­ calculations discussed above and come ing angle telescopes with imaging ins­ chrotron radiation in the surrounding up with various alternatives and correc­ truments at the focus. fields appear to be common (Helfand tions to the cooling curve (see Tsuruta The first such satellite payload was 1983). Nevertheless, with better angu­ 1986; and Nomoto and Tsuruta 1987); the EINSTEIN observatory (1978-1981), lar and spectral resolution of future ins­ the range of these differences is summa­ followed by the European X-Ray Astro­ truments, we should be able to identify rized in Fig. 2 together with the recent nomy Satellite EXOSAT (1983-1986). the diffuse shape and the non-thermal experimental results from EINSTEIN and With the exception of an upper limit of spectrum of these compact nebulae. At EXOSAT satellites. 7S ≤ 3 x 106 K for the Crab pulsar the present, these measurements are at 100 the borderline of instrumental resolution In addition to the surface emission, and can easily be mistaken for neutron there has been another indirect method SPIE'S INSTITUTES star cooling. proposed to measure the internal tempe­ FOR ADVANCED OPTICAL TECHNOLOGIES For pulsars older than 106 years, the ratures. Alpar et al. (1985) have develo­ additional process of reheating, such as ped a theory of vortex creep (movement that due to internal friction, may also of the quantized rotation of superfluid affect the cooling curve. As we have neutrons through the inner crust lattice) SPIE Volume 634 already mentioned, the interior of the and interpreted the glitches in the rota­ neutron star consists of solid and super­ tion rates of Crab and Vela pulsars. The OPTICAL fluid components. As the pulsar radiates internal temperature of the neutron star AND dipole radiation and slows down, the dif­ is one parameter in this model which, ferential rotation rate between the solid after theoretical estimates of the other HYBRID and superfluid parts introduces internal parameters, can be fitted to the data. friction which eventually is dissipated as These measurements give again an in­ COMPUTING heat from the surface. It is estimated ternal temperature for Crab that is con­ that in pulsars with a slow-down rate sistent with standard cooling. However, of 10-13 radian/s2, the internal heating for the Vela pulsar this method also Second in the Series gives temperatures lower than that ex­ 38 papers, 485 pages should lead to a surface temperature ISBN 0-89252-669-6 around 2 x 105 K. From another re­ pected from standard cooling. Copyright 1987 heating process, energetic particles re­ Summarizing the neutron star cooling Editor: H. H. Szu, impacting on the surface, similar tempe- story, we can say that at present the Naval Research Laboratory measurements are just on the borderline 24-27 March 1986 ratures are estimated. So the conclusion Leesburg, Virginia USA is that there may always exist some of being accurate enough to restrict or challenge the existing theories and emission processes in the vicinity of the In 1986 a small group of about 40 neutron star which can mask the effect hence models of neutron star interiors. experts came together in a synergistic of cooling of the initial heat content. At Future satellite programs of the next manner for four days and three nights in a best, the present measurements should decade may indeed accomplish this retreat environment and devoted task. Along with experimental improve­ themselves to assessing and projecting the be considered as upper limits. future of optical computing. This peer- When we examine the data points in ments, we can expect better theories in­ reviewed volume is the result of that cluding the effects of the magnetic interaction. Fig. 2, we can see that most of them lie fields and other exotic particles. To be within the range of standard cooling able to study hadron physics through Part One scenarios. Out of the four objects that observations of neutron star cooling is a Algorithms for Linear fall below this range, only the Vela pulsar fine example of the progress of scientific and Nonlinear Systems is a bona fide neutron star. That is to say, 13 papers the other three, Cas A, Tycho and understanding through solidarity in very Part Three SN1006 are historically recorded super­ diverse fields. Neural Networks for Computing novae, but it is possible that these super­ 8 papers REFERENCES novae have left no neutron star behind. Part Two Indeed, Type I supernovae are believed Alpar M.A., Nandkumar R. and Pines D., Architectures Based on to occur when a accretes Astrophys. J. 288 (1985) 191. Bistable and Molecular Devices mass over the Chandrasekhar limit (1.4 Alpar A.M., Brinkmann W., Kiziloglu Ü, 7 papers MO), and undergoes a thermonuclear ex­ Ogelman H. and Pines D., 1987, Astron. Part Four Astrophys. 177 (1981) 101. Application Driven Devices plosion. In theoretical studies of these Brinkmann W. and Ogelman H., Astron. and System Developments type of explosions, the white dwarf is Astrophys. (1987) to be published. IO papers totally disrupted and no neutron star re­ Giacconi R., Gursky H., Paolini F.R. and mains. In the case of the Vela pulsar, Rossi B.B., Phys. Rev. Lett. 9 (1962) 439. Th e concept of the SPIE Institutes for Advanced Optical Technologies however, we not only see a supernova Helfand D.J., in Supernova Remnants and developed out of SPIE’s desire to foster remnant, but we also find a pulsar rota­ their X-ray Emission, IAU Symposium No. increased interaction and collaboration ting with a period of 89 milliseconds. 101, eds. J. Danziger and P. Gorenstein among researchers working in emerging (Reidel, Dordrecht) 1983, p. 471. optical technologies. Using the size of the supernova remnant Helfand D.J. and Becker R.H., Nature 307 or the period and period-derivates of the (1984) 215. pulsar, one can extrapolate back and ar­ Hewish A., Bell S.J., Pilkington J.D.H., SPIE Member $65 rive at a consistent age of 11 000 years. Scott P.F. and Collins R.A., Nature 217 Nonmember North America $ 79 Being fairly close-by, only 500 parsec (1968) 709. Nonmember All Other Countries $91 (1.6 x 1021 cm) away, both EINSTEIN Nomoto K. and Tsuruta S., Astrophys. J. and EXOSAT observatories have been 312 (1987) 711. able to resolve the compact nebula from Pines D„ in Proc. of NATO ASI on High the central point source that must be the Energy Phenomena Around Collapsed SPIE—The International Society pulsar. One possible way of explaining Stars, ed. F. Pacini (Reidel, Dordrecht) 1987, for Optical Engineering p. 193. the low surface temperature of the Vela Pines D. and Alpar M.A., Nature 316 pulsar, below the standard cooling (1985) 27. curves, is to postulate that this neutron Shapiro S.L. and Teukolsky S.A., in Black To order: contact SPIE, Avenue de la Tanche 2, B-1160 star is sufficiently massive ( 1.4 MO) holes, white dwarfs, and neutron stars (John Brussels, Belgium; Telephone 2/660.45.11; Telex and hence of sufficiently high central Wiley and Sons) 1983. 25387 AvvAL B. In North America, contact SPIE, P.O. Box 10, Bellingham, WA 98227-0010 USA; Telephone density that some pion condensate Tsuruta S., Comments on Astrophysics XI 206/676-3290; Telex 46-7053. cooling is effective. (1986) 151. 101