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Thermal evolution and population synthesis of neutron stars Sergei Popov (SAI MSU) Evolution of neutron stars. I.: rotation + magnetic field Ejector → Propeller → Accretor → Georotator 1 – spin down 2 – passage through a molecular cloud 3 – magnetic field decay astro-ph/0101031 See the book by Lipunov (1987, 1992) Evolution of NSs. II.: temperature Neutrino cooling stage Photon cooling stage First papers on the thermal evolution appeared already in early 60s, i.e. before the discovery of radio pulsars. [Yakovlev et al. (1999) Physics Uspekhi] Early evolution of a NS (Prakash et al. astro-ph/0112136) NS Cooling NSs are born very hot, T > 1010 K At early stages neutrino cooling dominates The core is isothermal dEth dT CV L L dt dt Photon luminosity Neutrino luminosity L 4 R 2 Ts4 , Ts T 1/ 2 ( 1) Core-crust temperature relation Page et al. astro-ph/0508056 Cooling depends on: 1. 2. 3. 4. 5. Rate of neutrino emission from NS interiors Heat capacity of internal parts of a star Superfluidity Thermal conductivity in the outer layers Possible heating (see Yakovlev & Pethick 2004) Depend on the EoS and composition Main neutrino processes (Yakovlev & Pethick astro-ph/0402143) Fast Cooling (URCA cycle) n p e e p e n e Slow Cooling (modified URCA cycle) n n n p e e n p e n n e p n p p e e p p e p n e Fast cooling possible only if np > nn/8 Nucleon Cooper pairing is important Minimal cooling scenario (Page et al 2004): no exotica no fast processes pairing included pp pn pe pn<pp+pe Equations Neutrino emissivity heating After thermal relaxation we have in the whole star: Ti(t)=T(r,t)eΦ(r) At the surface we have: (Yakovlev & Pethick 2004) Total stellar heat capacity Simplified model of a cooling NS No superfluidity, no envelopes and magnetic fields, only hadrons. The most critical moment is the onset of direct URCA cooling. ρD= 7.851 1014 g/cm3. The critical mass depends on the EoS. For the examples below MD=1.358 Msolar. Simple cooling model for low-mass NSs. Too hot ...... Too cold .... (Yakovlev & Pethick 2004) Nonsuperfluid nucleon cores Note “population aspects” of the right plot: too many NSs have to be explained by a very narrow range of mass. For slow cooling at the neutrino cooling stage tslow~1 yr/Ti96 For fast cooling tfast~ 1 min/Ti94 (Yakovlev & Pethick 2004) Slow cooling for different EoS For slow cooling there is nearly no dependence on the EoS. The same is true for cooling curves for maximum mass for each EoS. (Yakovlev & Pethick 2004) Envelopes and magnetic field Non-magnetic stars No accreted envelopes, Envelopes + Fields Thick lines – no envelope different magnetic fields. Envelopes can be related to the fact that we see a subpopulation of hot NS Thick lines – non-magnetic in CCOs with relatively long initial spin periods and low magnetic field, but do not observed representatives of this population around us, i.e. in the Solar vicinity. Solid line M=1.3 Msolar, Dashed lines M=1.5 Msolar (Yakovlev & Pethick 2004) Simplified model: no neutron superfluidity Superfluidity is an important ingredient of cooling models. It is important to consider different types of proton and neutron superfluidity. There is no complete microphysical theory whiich can describe superfluidity in neutron stars. If proton superfluidity is strong, but neutron superfluidity in the core is weak then it is possible to explain observations. (Yakovlev & Pethick 2004) Neutron superfluidity and observations Mild neutron pairing in the core contradicts observations. (Yakovlev & Pethick 2004) Minimal cooling model “Minimal” Cooling Curves “minimal” means without additional cooling due to direct URCA and without additional heating Main ingredients of the minimal model • • • • Page, Geppert & Weber (2006) EoS Superfluid properties Envelope composition NS mass Luminosity and age uncertainties Page, Geppert, Weber astro-ph/0508056 Uncertainties in temperature • Atmospheres (composition) • Magnetic field • Non-thermal contributions to the spectrum • Distance • Interstellar absorption • Temperature distribution (Pons et al. astro-ph/0107404) NS Radii A NS with homogeneous surface temperature and local blackbody emission L 4 R T L 2 4 F R / D T 2 4 D 2 4 From X-ray spectroscopy From dispersion measure NS Radii - II Real life is a trifle more complicated… Strong B field Photon propagation different Surface temperature is not homogeneous Local emission may be not exactly planckian Gravity effects are important Atmospheres Local Surface Emission Much like normal stars NSs are covered by an atmosphere Because of enormous surface gravity, g ≈ 1014 cm/s2, Hatm ≈ 1-10 cm Spectra depend on g, chemical composition and magnetic field Plane-parallel approximation (locally) Free-free absorption dominates 3 , h kT High energy photons decouple deeper in the atmosphere where T is higher Zavlin & Pavlov (2002) Gravity Effects Redshift Ray bending L 4 R T 2 4 2 2 1 0 0 0 4 T d d du 4 2 E , 2 E ,1 dE I ( E, B, cos , Ts , ) STEP 1 Specify viewing geometry and B-field topology; compute the surface temperature distribution STEP 2 Compute emission from every surface patch STEP 4 Predict lightcurve and phase-resolved spectrum Compare with observations STEP 3 GR ray-tracing to obtain the spectrum at infinity CCOs 1. 2. 3. 4. Found in SNRs Have no radio or gamma-ray counterpats No pulsar wind nebula (PWN) Have soft thermal-like spectra Known objects New candidates appear continuosly. (Pavlov et al. astro-ph/0311526) New population? Gotthelf & Halpern (arXiv:0704.2255) recently suggested that 1E 1207.4-5209 and PSR J1852+0040 (in Kes 79) can be prototypes of a different subpopulation of NSs born with low magnetic field (< few 1011 G) and relatively long spin periods (few tenths of a second). These NSs are relatively hot, and probably not very rare. Surprisingly, we do not see objects of this type in our vicinity. In the solar neighbourhood we meet a different class of object. This can be related to accreted envelopes (see, for example, Kaminker et al. 2006). Sources in CCOs have them, so they look hotter, but when these envelopes disappear, they are colder than NSs which have no envelopes from the very beginning. So, we do not see such sources among close-by NSs. M 7 and CCOs Both CCOs and M7 seem to be the hottest at their ages (103 and 106 yrs). However, the former cannot evolve to become the latter ones! Temperature CCOs M7 Age • Accreted envelopes (presented in CCOs, absent in the M7) • Heating by decaying magnetic field in the case of the M7 (Yakovlev & Pethick 2004) Accreted envelopes, B or heating? It is necessary to make population synthesis studies to test all these possibilities. The Seven X-ray dim Isolated NSs Soft thermal spectrum (kT 50-100 eV) No hard, non-thermal tail Radio-quiet, no association with SNRs Low column density (NH 1020 cm-2) X-ray pulsations in all 7 sources (P 3-10 s) Very faint optical counterparts The Magnificent Seven Source kT (eV) P (s) Amplitude/2 Optical RX J1856.5-3754 60 7.06 1.5% V = 25.6 RX J0720.4-3125 (*) 85 8.39 11% B = 26.6 RX J0806.4-4123 96 11.37 6% - RX J0420.0-5022 45 3.45 13% B = 26.6 ? RX J1308.6+2127 (RBS 1223) 86 10.31 18% m50CCD = 28.6 RX J1605.3+3249 (RBS 1556) 96 6.88? ?? m50CCD = 26.8 104 9.43 4% - 1RXS J214303.7+065419 (RBS 1774) (*) variable source Featureless ? No Thanks ! RX J1856.5-3754 is convincingly featureless RX J0720.4-3125 (Haberl et al 2004) (Chandra 500 ks DDT; Drake et al 2002; Burwitz et al 2003) A broad absorption feature detected in all other ICoNS (Haberl et al 2003, 2004, 2004a; Van Kerkwijk et al 2004; Zane et al 2005) Eline ~ 300-700 eV; evidence for two lines with E1 ~ 2E2 in RBS 1223 (Schwope et al 2006) Proton cyclotron lines ? H/He transitions at high B ? Period Evolution . RX J0720.4-3125: bounds on Pderived by Zane et al. (2002) and Kaplan et al (2002) Timing solution by Cropper et al (2004), further improved by Kaplan & Van Kerkwijk (2005): . -14 s/s, B = 2x1013 G = 7x10 P 13 -1014 G B ~ 10 RX J1308.6+2127: .timing solution by Kaplan & Van Kerkwijk (2005a), P = 10-13 s/s, B = 3x1013 G Spin-down values of B in agreement with absorption features being proton cyclotron lines Source Energy (eV) EW (eV) Bline (Bsd) (1013 G) Notes RX J1856.5-3754 no no ? - RX J0720.4-3125 270 40 5 (2) Variable line RX J0806.4-4123 460 33 9 - RX J0420.0-5022 330 43 7 - RX J1308.6+2127 300 150 6 (3) - RX J1605.3+3249 450 36 9 - 700 50 14 - 1RXS J214303.7+065419 ICoNS: The Perfect Neutron Stars ICoNS are key in neutron star astrophysics: these are the only sources for which we have a “clean view” of the star surface Information on the thermal and magnetic surface distributions Estimate of the star radius (and mass ?) Direct constraints on the EOS Pulsating ICoNS RX J0420.0-5022 (Haberl et al 2004) Quite large pulsed fractions Skewed lightcurves Harder spectrum at pulse minimum Phase-dependent absorption features The Optical Excess RX J1605 multiwavelength SED (Motch et al 2005) In the four sources with a confirmed optical counterpart Fopt 5-10 x B(TBB,X) Fopt 2 ? Deviations from a RayleighJeans continuum in RX J0720 (Kaplan et al 2003) and RX J1605 (Motch et al 2005). A non-thermal power law ? RX J1856.5-3754 - I Blackbody featureless spectrum in the 0.1-2 keV band (Chandra 500 ks DDT, Drake et al 2002); possible broadband deviations in the XMM 60 ks observation (Burwitz et al 2003) RX J1856 multiwavelength SED (Braje & Romani 2002) Thermal emission from NSs is not expected to be a featureless BB ! H, He spectra are featureless but only blackbody-like (harder). Heavy elements spectra are closer to BB but with a variety of features RX J1856.5-3754 - II A quark star (Drake et al 2002; Xu 2002; 2003) A NS with caps and cooler Whathotter spectrum ? equatorial region (Pons The optical excess ? et al 2002; Braje & Romani 2002; Trűmper et al 2005) A bare NS (Burwitz et al 2003; Turolla, Zane & Drake 2004; Van Adelsberg et al 2005; PerezA perfect BB ? 2005) Azorin, Miralles & Pons Bare Neutron Stars At B >> B0 ~ 2.35 x 109 G atoms attain a cylindrical shape Turolla, Zane & Drake 2004 Formation of molecular chains by covalent bonding along the field direction RX J0720.4-3125 Interactions between molecular chains can lead to the formation of a RX J1856.5-3754 3D condensate Critical condensation temperature Fe H depends on B and chemical composition (Lai & Salpeter 1997; Lai 2001) Spectra from Bare NSs - I The cold electron gas approximation. Reduced emissivity expected below p (Lenzen & Trümper 1978; Brinkmann 1980) Spectra are very close to BB in shape in the 0.1 - 2 keV range, but depressed wrt the BB at Teff. Reduction factor ~ 2 - 3. Turolla, Zane & Drake (2004) Spectra from Bare NS - II Proper account for damping of free electrons by lattice interactions (e-phonon scattering; Yakovlev & Urpin 1980; Potekhin 1999) Spectra deviate more from BB. Fit in the 0.1 – 2 keV band still acceptable. Features may be present. Reduction factors higher. Turolla, Zane & Drake (2004) Is RX J1856.5-3754 Bare ? Fit of X-ray data in the 0.15-2 keV band acceptable Radiation radius problem eased Optical excess may be produced by reprocessing of surface radiation in a very rarefied atmosphere (Motch, Zavlin & Haberl 2003; Zane, Turolla & Drake 2004; Ho et al. 2006) Details of spectral shape (features, low-energy behaviour) still uncertain Long Term Variations in RX J0720.4-3125 A gradual, long term change in the shape of the X-ray spectrum AND the pulse profile (De Vries et al 2004; Vink et al 2004) Steady increase of TBB and of the absorption feature EW (faster during 2003) Evidence for a reversal of the evolution in 2005 (Vink et al 2005) De Vries et al. 2004 A Precessing Neutron Star ? Evidence for a periodic modulation in the spectral parameters (Tbb, Rbb) but no complete cycle yet Phase residuals (coherent timing solution by Kaplan & Van Kerkwijk 2005) show periodic behavior over a much longer timescale Haberl et al. 2006 (> 10 yrs) Periods consistent within the errors, Pprec ~ 7.1-7.7 yr (Haberl et al. 2006) M7 and RRATs Similar periods and Pdots In one case similar thermal properties Similar birth rate? (arXiv: 0710.2056) M7 and RRATs: pro et contra Based on similarities between M7 and RRATs it was proposed that they can be different manifestations of the same type of INSs (astro-ph/0603258). To verify it a very deep search for radio emission (including RRAT-like bursts) was peformed on GBT (Kondratiev et al.). In addition, objects have been observed with GMRT (B.C.Joshi, M. Burgay et al.). In both studies only upper limits were derived. Still, the zero result can be just due to unfavorable orientations (at long periods NSs have very narrow beams). It is necessary to increase statistics. (Kondratiev et al, in press, see also arXiv: 0710.1648) M7 and high-B PSRs Strong limits on radio emission from the M7 are established (Kondratiev et al. 2008: 0710.1648 ). However, observationally it is still possible that the M7 are just misaligned high-B PSRs. Are there any other considerations to verify a link between these two popualtions of NSs? In most of population synthesis studies of PSRs the magnetic field distribution is described as a gaussian, so that high-B PSRs appear to be not very numerous. On the other hand, population synthesis of the local population of young NSs demonstrate that the M7 are as numerous as normal-B PSRs. So, for standard assumptions it is much more probable, that high-B PSRs and the M7 are not related. INSs and local surrounding Massive star population in the Solar vicinity (up to 2 kpc) is dominated by OB associations. Inside 300-400 pc the Gould Belt is mostly important. De Zeeuw et al. 1999 Motch et al. 2006 Population of close-by young NSs Magnificent seven Geminga and 3EG J1853+5918 Four radio pulsars with thermal emission (B0833-45; B0656+14; B1055-52; B1929+10) Seven older radio pulsars, without detected thermal emission. To understand the origin of these populations and predict future detections it is necessary to use population synthesis. Population synthesis: ingredients Birth rate of NSs Initial spatial distribution Spatial velocity (kick) Mass spectrum Thermal evolution Interstellar absorption Detector properties Task: To build an artificial model of a population of some astrophysical sources and to compare the results of calculations with observations. The Gould Belt Poppel (1997) R=300 – 500 pc Age 30-50 Myrs Center at 150 pc from the Sun Inclined respect to the galactic plane at 20 degrees 2/3 massive stars in 600 pc belong to the Belt Mass spectrum of NSs Mass spectrum of local young NSs can be different from the general one (in the Galaxy) Hipparcos data on near-by massive stars Progenitor vs NS mass: Timmes et al. (1996); Woosley et al. (2002) astro-ph/0305599 Progenitor mass vs. NS mass Woosley et al. 2002 Log of the number of sources brighter than the given flux Log N – Log S calculations -3/2 sphere: number ~ r3 flux ~ r-2 -1 disc: number ~ r2 flux ~ r-2 Log of flux (or number counts) Cooling of NSs Direct URCA Modified URCA Neutrino bremstrahlung Superfluidity Exotic matter (pions, quarks, hyperons, etc.) (see a recent review in astro-ph/0508056) In our study for illustrative purposes we use a set of cooling curves calculated by Blaschke, Grigorian and Voskresenski (2004) in the frame of the Nuclear medium cooling model Some results of PS-I: Log N – Log S and spatial distribution Log N – Log S for closeby ROSAT NSs can be explained by standard cooling curves taking into account the Gould Belt. Log N – Log S can be used as an additional test of cooling curves More than ½ are in +/- 12 degrees from the galactic plane. 19% outside +/- 30o 12% outside +/- 40o (Popov et al. 2005 Ap&SS 299, 117) Population synthesis – II. recent improvements Spatial distribution of progenitor stars We use the same normalization for NS formation rate inside 3 kpc: 270 per Myr. Most of NSs are born in OB associations. a) Hipparcos stars up to 500 pc [Age: spectral type & cluster age (OB ass)] b) 49 OB associations: birth rate ~ Nstar c) Field stars in the disc up to 3 kpc For stars <500 pc we even try to take into account if they belong to OB assoc. with known age. Population synthesis – II. recent improvements Spatial distribution of ISM (NH) instead of : now : Modification of the old one NH inside 1 kpc (see astro-ph/0609275 for details) Hakkila 50 000 tracks, new ISM model Predictions for future searches Candidates: Agueros Chieregato radiopulsars Magn. 7 Age and distance distributions 0.01 < cts/s < 0.1 Age New cands. Distance 0.1 < cts/s < 1 1 < cts/s < 10 Different models: age distributions Bars with vertical lines: old model for Rbelt=500 pc White bars: new initial dist Black bars: new ISM (analyt.) and new initial distribution Diagonal lines: new ISM (Hakkila) and new initial distribution Different models: distance distr. Where to search for more cowboys? We do not expect to find much more candidates at fluxes >0.1 cts/s. Most of new candidates should be at fluxes 0.01< f < 0.1 cts/s. So, they are expected to be young NSs (<few 100 Mys) just outside the Belt. I.e., they should be in nearby OB associations and clusters. Most probable candidates are Cyg OB7, Cam OB1, Cep OB2 and Cep OB3. Orion region can also be promising. Name l- l+ b- b+ Cyg OB7 84 96 -5 9 Cep OB2 96 108 -1 12 700 Cep OB3 108 113 1 700-900 7 Dist., pc 130 L=110 90 10 600-700 0 -10 Cam OB1 130 153 -3 8 800-900 (ads.gsfc.nasa.gov/mw/) Standard test: temperature vs. age Kaminker et al. (2001) Log N – Log S as an additional test Standard test: Age – Temperature Log N – Log S Sensitive to ages <105 years Uncertain age and temperature Non-uniform sample Sensitive to ages >105 years (when applied to close-by NSs) Definite N (number) and S (flux) Uniform sample Two test are perfect together!!! astro-ph/0411618 List of models (Blaschke et al. 2004) Pions Crust Blaschke et al. used 16 sets of cooling curves. They were different in three main respects: 1. Absence or presence of pion condensate 2. Different gaps for superfluid protons and neutrons 3. Different Ts-Tin Model I. Yes Model II. No Model III. Yes Model IV. No Model V. Yes Model VI. No Model VII. Yes Model VIII.Yes Model IX. No C D C C D E C C C Gaps A B B B B B B’ B’’ A Model I Pions. Gaps from Takatsuka & Tamagaki (2004) Ts-Tin from Blaschke, Grigorian, Voskresenky (2004) Can reproduce observed Log N – Log S (astro-ph/0411618) Model II No Pions Gaps from Yakovlev et al. (2004), 3P2 neutron gap suppressed by 0.1 Ts-Tin from Tsuruta (1979) Cannot reproduce observed Log N – Log S Sensitivity of Log N – Log S Log N – Log S is very sensitive to gaps Log N – Log S is not sensitive to the crust if it is applied to relatively old objects (>104-5 yrs) Log N – Log S is not very sensitive to presence or absence of pions We conclude that the two test complement each other Mass constraint • Mass spectrum has to be taken into account when discussing data on cooling • Rare masses should not be used to explain the cooling data • Most of data points on T-t plot should be explained by masses <1.4 Msun In particular: • Vela and Geminga should not be very massive Phys. Rev .C (2006) nucl-th/0512098 (published as a JINR preprint) Cooling curves from Kaminker et al. Conclusions • Studies of cooling NSs is a unique opprtunity to learn something about very high density matter physics • Different populations of cooling NSs are observed: CCOs, normal radio pulsars, Magnificent seven, one of the RRATs, .... • Population synthesis studies of cooling NSs can be a useful test for models of their thermal evolution • Population synthesis can be useful in planning how to search for more INSs • Joint studies of different populations can help to understand reasons for their diversity and evolutionary links between them