Thermal evolution and population synthesis of neutron stars Sergei Popov (SAI MSU)

Evolution of neutron stars. I.: rotation + magnetic field Ejector → Propeller → Accretor → Georotator See the book by Lipunov (1987, 1992) astro-ph/ – spin down 2 – passage through a molecular cloud 3 – magnetic field decay

Evolution of NSs. II.: temperature [Yakovlev et al. (1999) Physics Uspekhi] First papers on the thermal evolution appeared already in early 60s, i.e. before the discovery of radio pulsars. Neutrino cooling stage Photon cooling stage

Early evolution of a NS (Prakash et al. astro-ph/ )

NS Cooling NSs are born very hot, T > K At early stages neutrino cooling dominates The core is isothermal Neutrino luminosity Photon luminosity

Core-crust temperature relation Page et al. astro-ph/

Cooling depends on: (see Yakovlev & Pethick 2004) 1. Rate of neutrino emission from NS interiors 2. Heat capacity of internal parts of a star 3. Superfluidity 4. Thermal conductivity in the outer layers 5. Possible heating Depend on the EoS and composition

Main neutrino processes (Yakovlev & Pethick astro-ph/ )

Fast Cooling (URCA cycle) Slow Cooling (modified URCA cycle)  Fast cooling possible only if n p > n n /8  Nucleon Cooper pairing is important  Minimal cooling scenario (Page et al 2004) :  no exotica  no fast processes  pairing included pnpn p pepe p n <p p +p e

Equations (Yakovlev & Pethick 2004) At the surface we have: Neutrino emissivityheating After thermal relaxation we have in the whole star: T i (t)=T(r,t)e Φ(r) 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. ρ D = g/cm 3. The critical mass depends on the EoS. For the examples below M D =1.358 M solar.

Simple cooling model for low-mass NSs. (Yakovlev & Pethick 2004) Too hot Too cold....

Nonsuperfluid nucleon cores (Yakovlev & Pethick 2004) For slow cooling at the neutrino cooling stage t slow ~1 yr/T i9 6 For fast cooling t fast ~ 1 min/T i9 4 Note “population aspects” of the right plot: too many NSs have to be explained by a very narrow range of mass.

Slow cooling for different EoS (Yakovlev & Pethick 2004) For slow cooling there is nearly no dependence on the EoS. The same is true for cooling curves for maximum mass for each EoS.

Envelopes and magnetic field (Yakovlev & Pethick 2004) Envelopes can be related to the fact that we see a subpopulation of hot NS 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. Non-magnetic stars Thick lines – no envelope No accreted envelopes, different magnetic fields. Thick lines – non-magnetic Envelopes + Fields Solid line M=1.3 M solar, Dashed lines M=1.5 M solar

Simplified model: no neutron superfluidity (Yakovlev & Pethick 2004) If proton superfluidity is strong, but neutron superfluidity in the core is weak then it is possible to explain observations. 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.

Neutron superfluidity and observations (Yakovlev & Pethick 2004) Mild neutron pairing in the core contradicts observations.

Page, Geppert & Weber (2006) “Minimal” Cooling Curves Minimal cooling model “minimal” means without additional cooling due to direct URCA and without additional heating Main ingredients of the minimal model EoS Superfluid properties Envelope composition NS mass

Luminosity and age uncertainties Page, Geppert, Weber astro-ph/

Uncertainties in temperature (Pons et al. astro-ph/ ) Atmospheres (composition) Magnetic field Non-thermal contributions to the spectrum Distance Interstellar absorption Temperature distribution

NS Radii A NS with homogeneous surface temperature and local blackbody emission 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 ≈ cm/s 2, H atm ≈ 1-10 cm Spectra depend on g, chemical composition and magnetic field Plane-parallel approximation (locally)

Zavlin & Pavlov (2002 ) Free-free absorption dominates High energy photons decouple deeper in the atmosphere where T is higher

Gravity Effects  Redshift  Ray bending

STEP 1 Specify viewing geometry and B-field topology; compute the surface temperature distribution STEP 2 Compute emission from every surface patch STEP 3 GR ray-tracing to obtain the spectrum at infinity STEP 4 Predict lightcurve and phase-resolved spectrum Compare with observations

CCOs 1. Found in SNRs 2. Have no radio or gamma-ray counterpats 3. No pulsar wind nebula (PWN) 4. Have soft thermal-like spectra

Known objects (Pavlov et al. astro-ph/ ) New candidates appear continuosly.

New population? Gotthelf & Halpern (arXiv: ) recently suggested that 1E and PSR J (in Kes 79) can be prototypes of a different subpopulation of NSs born with low magnetic field (< few 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 (10 3 and 10 6 yrs). However, the former cannot evolve to become the latter ones! Age Temperature CCOs M7 Accreted envelopes (presented in CCOs, absent in the M7) Heating by decaying magnetic field in the case of the M7

Accreted envelopes, B or heating? (Yakovlev & Pethick 2004) It is necessary to make population synthesis studies to test all these possibilities.

The Seven X-ray dim Isolated NSs Soft thermal spectrum (kT  eV) No hard, non-thermal tail Radio-quiet, no association with SNRs Radio-quiet Low column density (N H  cm -2 ) X-ray pulsations in all 7 sources (P  3-10 s) Very faint optical counterparts

SourcekT (eV)P (s)Amplitude/2Optical RX J %V = 25.6 RX J (*) %B = 26.6 RX J %- RX J %B = 26.6 ? RX J (RBS 1223) %m 50CCD = 28.6 RX J (RBS 1556) ???m 50CCD = RXS J (RBS 1774) %- (*) variable source The Magnificent Seven

Featureless ? No Thanks ! RX J is convincingly featureless (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) E line ~ eV; evidence for two lines with E 1 ~ 2E 2 in RBS 1223 (Schwope et al 2006) Proton cyclotron lines ? H/He transitions at high B ? RX J (Haberl et al 2004)

Period Evolution RX J : bounds on derived by Zane et al. (2002) and Kaplan et al (2002) Timing solution by Cropper et al (2004), further improved by Kaplan & Van Kerkwijk (2005): = 7x s/s, B = 2x10 13 G RX J : timing solution by Kaplan & Van Kerkwijk (2005a), = s/s, B = 3x10 13 G Spin-down values of B in agreement with absorption features being proton cyclotron lines B ~ G

SourceEnergy (eV) EW (eV) B line (B sd ) (10 13 G) Notes RX J no ?- RX J (2)Variable line RX J RX J RX J (3)- RX J RXS J

ICoNS: The Perfect Neutron Stars Information on the thermal and magnetic surface distributions Estimate of the star radius (and mass ?) Direct constraints on the EOS ICoNS are key in neutron star astrophysics: these are the only sources for which we have a “clean view” of the star surface

Pulsating ICoNS Quite large pulsed fractions Skewed lightcurves Harder spectrum at pulse minimum Phase-dependent absorption features RX J (Haberl et al 2004)

The Optical Excess In the four sources with a confirmed optical counterpart F opt  5-10 x B (T BB,X ) F opt  2 ? Deviations from a Rayleigh- Jeans continuum in RX J0720 (Kaplan et al 2003) and RX J1605 (Motch et al 2005). A non-thermal power law ? RX J1605 multiwavelength SED (Motch et al 2005)

Blackbody featureless spectrum in the keV band (Chandra 500 ks DDT, Drake et al 2002) ; possible broadband deviations in the XMM 60 ks observation (Burwitz et al 2003) RX J I 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 multiwavelength SED (Braje & Romani 2002)

RX J II A quark star (Drake et al 2002; Xu 2002; 2003) A NS with hotter caps and cooler equatorial region (Pons 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; Perez- Azorin, Miralles & Pons 2005) What spectrum ? The optical excess ? A perfect BB ?

Bare Neutron Stars At B >> B 0 ~ 2.35 x 10 9 G atoms attain a cylindrical shape Formation of molecular chains by covalent bonding along the field direction Interactions between molecular chains can lead to the formation of a 3D condensate Critical condensation temperature depends on B and chemical composition (Lai & Salpeter 1997; Lai 2001) RX J RX J Turolla, Zane & Drake 2004 HFe

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 keV range, but depressed wrt the BB at T eff. Reduction factor ~ 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 J Bare ? Fit of X-ray data in the 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 J 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 T BB 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 (T bb, R bb ) but no complete cycle yet Phase residuals (coherent timing solution by Kaplan & Van Kerkwijk 2005) show periodic behavior over a much longer timescale (> 10 yrs) Periods consistent within the errors, P prec ~ yr (Haberl et al. 2006) Haberl et al. 2006

M7 and RRATs Similar periods and Pdots In one case similar thermal properties Similar birth rate? (arXiv: )

M7 and RRATs: pro et contra (Kondratiev et al, in press, see also arXiv: ) Based on similarities between M7 and RRATs it was proposed that they can be different manifestations of the same type of INSs (astro-ph/ ). 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.

M7 and high-B PSRs Strong limits on radio emission from the M7 are established (Kondratiev et al. 2008: ) 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 De Zeeuw et al Motch et al Massive star population in the Solar vicinity (up to 2 kpc) is dominated by OB associations. Inside pc the Gould Belt is mostly important.

Population of close-by young NSs Magnificent seven Geminga and 3EG J Four radio pulsars with thermal emission (B ; B ; B ; B ) 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 To build an artificial model of a population of some astrophysical sources and to compare the results of calculations with observations. Task:

The Gould Belt Poppel (1997) R=300 – 500 pc Age 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/

Woosley et al Progenitor mass vs. NS mass

Log N – Log S Log of flux (or number counts) Log of the number of sources brighter than the given flux -3/2 sphere: number ~ r 3 flux ~ r disc: number ~ r 2 flux ~ r -2 calculations

Cooling of NSs Direct URCA Modified URCA Neutrino bremstrahlung Superfluidity Exotic matter (pions, quarks, hyperons, etc.) 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 (see a recent review in astro-ph/ )

Some results of PS-I: Log N – Log S and spatial distribution (Popov et al Ap&SS 299, 117) More than ½ are in +/- 12 degrees from the galactic plane. 19% outside +/- 30 o 12% outside +/- 40 o Log N – Log S for close- by 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

Spatial distribution of progenitor stars a) Hipparcos stars up to 500 pc [Age: spectral type & cluster age (OB ass)] b) 49 OB associations: birth rate ~ N star c) Field stars in the disc up to 3 kpc Population synthesis – II. recent improvements We use the same normalization for NS formation rate inside 3 kpc: 270 per Myr. Most of NSs are born in OB associations. For stars <500 pc we even try to take into account if they belong to OB assoc. with known age.

Spatial distribution of ISM (N H ) instead of : now : Population synthesis – II. recent improvements Hakkila (see astro-ph/ for details) Modification of the old one N H inside 1 kpc

tracks, new ISM model Agueros Chieregato Candidates: radiopulsars Magn. 7 Predictions for future searches

Age and distance distributions Age 1 < cts/s < < cts/s < < cts/s < 0.1 Distance New cands.

Different models: age distributions Bars with vertical lines: old model for R belt =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+ Dist., pc Cyg OB Cep OB Cep OB Cam OB L= (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  Sensitive to ages <10 5 years  Uncertain age and temperature  Non-uniform sample Log N – Log S  Sensitive to ages >10 5 years (when applied to close-by NSs)  Definite N (number) and S (flux)  Uniform sample Two test are perfect together!!! astro-ph/

List of models (Blaschke et al. 2004) Model I. Yes C A Model II. No D B Model III. Yes C B Model IV. No C B Model V. Yes D B Model VI. No E B Model VII. Yes C B’ Model VIII.Yes C B’’ Model IX. No C A 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 T s -T in Pions Crust Gaps

Model I Pions. Gaps from Takatsuka & Tamagaki (2004) T s -T in from Blaschke, Grigorian, Voskresenky (2004) Can reproduce observed Log N – Log S (astro-ph/ )

Model II No Pions Gaps from Yakovlev et al. (2004), 3 P 2 neutron gap suppressed by 0.1 T s -T in 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 (> 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/ (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