Population synthesis of isolated NSs and tests of cooling curves Sergei Popov (Sternberg Astronomical Institute) Co-authors: D. Blaschke, H.Grigorian, B. Posselt, R. Turolla JINR, Dubna, September 01, 2006

2 Plan of the talk Intro. Close-by NSs Population synthesis Solar vicinity. Stars Spatial distribution Mass spectrum Two tests of cooling Brightness constraint Sensitivity of two tests Mass constraint Application to hybrid stars Future plans Age-Distance diagram Final conclusions

3 Isolated neutron stars population: in the Galaxy and at the backyard  INSs appear in many flavours Radio pulsars AXPs SGRs CCOs RINSs RRATs  Local population of young NSs is different (selection) Radio pulsars Geminga+ RINSs

4 Close-by radioquiet NSs Discovery: Walter et al. (1996) Proper motion and distance: Kaplan et al. No pulsations Thermal spectrum Later on: six brothers RX J

5 Magnificent Seven NamePeriod, s RX RX RBS RBS RX RX RBS Radioquiet (?) Close-by Thermal emission Long periods

6 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. It is useful to study these stars using the population synthesis technique

7 Population synthesis: ingredients Birth rate of NSs Initial spatial distribution Spatial velocity (kick) Mass spectrum Thermal evolution Interstellar absorption Detector properties A brief review on population synthesis in astrophysics can be found in astro-ph/ To build an artificial model of a population of some astrophysical sources and to compare the results of calculations with observations. Task:

8 Gould Belt : 20 NS Myr -1 Gal. Disk (3kpc) : 250 NS Myr -1 Arzoumanian et al ROSAT Cooling curves by Blaschke et al. Mass spectrum 18° Gould Belt Population synthesis – I. © Bettina Posselt

9 Solar vicinity Solar neighborhood is not a typical region of our Galaxy Gould Belt R= pc Age: Myrs SN per Myr (Grenier 2000) The Local Bubble Up to six SN in a few Myrs

10 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

11 Distribution of open clusters (Piskunov et al. astro-ph/ )

12 Surface density of open clusters (Piskunov et al.)

13 Spatial distribution of close-by open clusters in 3D (Piskunov et al.) Grey contours show projected density distribution of young (log T<7.9) clusters.

14 Clusters and absorption (Piskunov et al.) Triangles – Gould Belt clusters.

15 Initial spatial distribution A very simple model for PS-I: The Gould Belt as a flat inclined disc plus contribution from the galactic disc up to 3 kpc.

16 Some results of PS-I.: 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

17 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/ (masses of secondary objects in NS+NS)

18 Woosley et al Progenitor mass vs. NS mass

19 Woosley et al Core mass vs. initial mass

20 Two tests Age – Temperature & Log N – Log S

21 Standard test: temperature vs. age Kaminker et al. (2001)

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

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

24 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

25 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/

26 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

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

28 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

29 Model III Pions Gaps from Yakovlev et al. (2004), 3 P 2 neutron gap suppressed by 0.1 T s -T in from Blaschke, Grigorian, Voskresenky (2004) Cannot reproduce observed Log N – Log S

30 Model IV No Pions Gaps from Yakovlev et al. (2004), 3 P 2 neutron gap suppressed by 0.1 T s -T in from Blaschke, Grigorian, Voskresenky (2004) Cannot reproduce observed Log N – Log S

31 Model V 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

32 Model VI No Pions Gaps from Yakovlev et al. (2004), 3 P 2 neutron gap suppressed by 0.1 T s -T in from Yakovlev et al. (2004) Cannot reproduce observed Log N – Log S

33 Model VII Pions Gaps from Yakovlev et al. (2004), 3 P 2 neutron gap suppressed by P 0 proton gap suppressed by 0.5 T s -T in from Blaschke, Grigorian, Voskresenky (2004) Cannot reproduce observed Log N – Log S

34 Model VIII Pions Gaps from Yakovlev et al. (2004), 3 P 2 neutron gap suppressed by P 0 proton gap suppressed by 0.2 and 1 P 0 neutron gap suppressed by 0.5. T s -T in from Blaschke, Grigorian, Voskresenky (2004) Can reproduce observed Log N – Log S

35 Model IX No Pions Gaps from Takatsuka & Tamagaki (2004) T s -T in from Blaschke, Grigorian, Voskresenky (2004) Can reproduce observed Log N – Log S

36 HOORAY!!!! Log N – Log S can select models!!!!! Only three (or even one!) passed the second test! …….still………… is it possible just to update the temperature-age test??? May be Log N – Log S is not necessary? Let’s try!!!!

37 Brightness constraint Effects of the crust (envelope) Fitting the crust it is possible to fulfill the T-t test … …but not the second test: Log N – Log S !!! (H. Grigorian astro-ph/ )

38 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

39 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.

40 Another attempt to test a set of models: hybrid stars We studied several models for hybrid stars applying all possible tests: - T-t - Log N – Log S - Brightness constraint - Mass constraint nucl-th/ We also tried to present examples when a model successfully passes the Log N – Log S test, but fails to pass the standard T-t test or fails to fulfill the mass constraint.

41 Model I Brightness - OK T-t - OK Log N – Log S - poor Mass - NO

42 Model II Brightness - OK T-t - No Log N – Log S - OK Mass - NO

43 Model III Brightness - OK T-t - poor Log N – Log S - OK Mass - NO

44 Model IV Brightness - OK T-t - OK Log N – Log S - OK Mass - OK

45 Resume for HySs One model among four was able to pass all tests.

46 1. Spatial distribution of progenitor stars a) Hipparcos stars up to 400 pc [Age: spectral type & cluster age (OB ass)] b) Star associations: birth rate ~ N star c) Field stars in the disc up to 3 kpc Population sythesis – II. recent improvements

47 3. Further improvements: Mass spectrum fainter XMM EPIC PN count rates cooling curves (Grigorian et al. 2005, Popov et al. 2006) 2. Spatial distribution of ISM (N H ) instead of :now : + new cross sections & abundances 1kpc Population synthesis – II. recent improvements (by Bettina Posselt)

48 b= +90° b= -90° First results The new initial distribution of progenitor stars: For comparison: ROSAT, old ISM distribution, masses etc. as before GB 500 pc GB 300 pc New Popov et al Outlook Different log N - log S curve for distinct sky regions Population synthesis for fainter (XMM) sources Count rate > 0.05 cts/s

49 Age-distance diagram (astro-ph/ ) Detectability of close-by young NSs strongly Depends on their ages and distance from the Sun. A toy-model: a local sphere (R=300 pc) and a flat disk. Rate of NS formation in the sphere is 235 Myr -1 kpc -3 (26-27 NS in Myr in the whole sphere). Rate in the disc is 10 Myr -1 kpc -2 (280 NS in Myr up to 3 kpc). visibility 13 sources 1 source

50 More realistic age-dist. diagram Initial distribution from Popov et al Spatial evolution is not followed. For the line of “visibility” (solid line in the middle) I assume the limiting flux erg s -1 cm -2 and masses are <1.35 (Yakovlev et al. curves). In 4.3 Myr in 1 kpc around the Sun 200 NSs are expected to be born. (astro-ph/ )

51 Realistic age-distance diagram Realistic initial distribution. Spatial evolution is taken into account. The line of “visibility” is drawn as the dotted line. Five curves correspond to 1, 4, 13, 20 and 100 NSs. At the moment in 1 kpc only about 10% of NSs with ages <4-5 Myrs are observed. (astro-ph/ ) visibility

52 Resume We live in a very interesting region of the Milky Way! Log N – Log S test can include NSs with unknown ages, so additional sources (like the Magnificent Seven) can be used to test cooling curves. Two tests (LogN–LogS and Age-Temperature) are perfect together. Additional considerations (brightness and mass constraints) have to be taken into account. More detailed PS models are welcomed. Age-distance diagram can be used as an additional tool.

53 THAT’S ALL. THANK YOU!

54 Radio detection Malofeev et al. (2005) reported detection of 1RXS J (RBS 1223) in the low-frequency band ( MHz) with the radio telescope in Pushchino. In 2006 Malofeev et al. reported radio detection of another one. (back)

55 NS+NS binaries Pulsar Pulsar mass Companion mass B B C B J J (PSR+companion)/2 J J J (David Nice, talk at Vancouver 2005) (Back)Back