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Astronomy meets QCD

Astronomy meets QCD. Sergei Popov (SAI MSU). Phase diagram. The first four are related to the NS structure!. Astrophysical point of view. Astrophysical appearence of NSs is mainly determined by: Spin Magnetic field Temperature Velocity Environment.

hermione-woodard
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Astronomy meets QCD

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  1. Astronomy meets QCD Sergei Popov (SAI MSU)

  2. Phase diagram

  3. The first four are related to the NS structure! Astrophysical point of view • Astrophysical appearence of NSsis mainly determined by: • Spin • Magnetic field • Temperature • Velocity • Environment See a recent review on astrophysical contraints on the EoS in 0808.1279.

  4. Structure and layers Plus an envelope and an atmosphere...

  5. Neutron stars Radius: 10 km Mass: 1-2 solar Density: about the nuclear Strong magnetic fields

  6. NS interiors: resume (Weber et al. ArXiv: 0705.2708)

  7. R=2GM/c2 P=ρ R~3GM/c2 R∞=R(1-2GM/Rc2)-1/2 ω=ωK Lattimer & Prakash (2004)

  8. Quark stars • Quark stars can be purely quark (with and without a tiny crust) or hybrid • Proposed already in 60-s (Ivanenko and Kurdgelaidze 1965). Then the idea was developed in 70-s. Popular since the paper by Witten (1984) • Renessance in recent 10 years or so.See a recent astrophysical review in 0809.4228.

  9. How to recognize a quark star? • Mass-radius relation. Smaller for smaller masses. • Cooling. Probably can cool faster due to additional channels. • Surface properties. If “bare” strange star – then there is no Eddington limit.

  10. TOV equation Tolman (1939) Oppenheimer- Volkoff (1939) EoS

  11. EoS (Weber et al. ArXiv: 0705.2708 )

  12. Particle fractions Effective chiral model of Hanauske et al. (2000) Relativistic mean-field model TM1 of Sugahara & Toki (1971)

  13. Au-Au collisions

  14. Experimental results and comparison 1 Mev/fm3 = 1.6 1032 Pa (Danielewicz et al. nucl-th/0208016)

  15. Astrophysical measurement In binaries, especially in binaries with PSRs.In future – lensing. • Mass • Radius • Red shift (M/R) • Temperature • Moment of inertia • Gravitational vs. Baryonic mass • Extreme rotation In isolated cooling NS, in bursters in binaries,in binaries with QPO Via spectral line observations In isolated cooling NSs and in sometransient binaries (deep crustal heating) In PSRs (in future) In double NS binaries, if good contraintson the progenitor are available Millisecond pulsars (both single and binary)

  16. NS Masses • Stellar masses are directly measured only in binary systems • Accurate NS mass determination for PSRs in relativistic systems by measuring PK corrections

  17. Maximum -mass neutron star Brown dwarfs, Giant planets Neutronstars White dwarfs Maximum-mass white dwarf c Minimum-mass neutron star Neutron stars and white dwarfs

  18. Minimal mass In reality, minimal mass is determined by properties of protoNSs. Being hot, lepton rich they have much higher limit: about 0.7 solar mass. Stellar evolution does not produce NSs with barion mass less thanabout 1.4 solar mass (may be 1.3 for so-called electron-capture SN). Fragmentation of a core due to rapid rotation potentially can lead to smallermasses, but not as small as the limit for cold NSs

  19. BHs ? Page & Reddy (2006) However, now somecorrections are necessary

  20. Compact objects and progenitors.Solar metallicity. There can be a range of progenitormasses in which NSs are formed,however, for smaller and larger progenitors masses BHs appear. (Woosley et al. 2002)

  21. Mass spectrum of compact objects Results of calculations (depend on the assumed modelof explosion) (Timmes et al. 1996, astro-ph/9510136)

  22. A NS from a massive progenitor Anomalous X-ray pulsar in the associationWesterlund1 most probably has a very massive progenitor, >40 MO. So, the situation with massive progenitorsis not that clear. (astro-ph/0611589)

  23. NS+NS binaries Secondary companion in double NS binaries can give a good estimateof the initial mass (at least, in this evolutionary channel). Pulsar Pulsar mass Companion mass B1913+16 1.44 1.39 B2127+11C 1.35 1.36 B1534+12 1.33 1.35 J0737-3039 1.34 1.25 J1756-2251 1.40 1.18 J1518+4904 <1.17 >1.55 J1906+0746 1.25 1.35 (PSR+companion)/2 J1811-1736 1.30 J1829+2456 1.25 GC 0808.2292 Non-recycled Also there arecandidates, for examplePSR J1753-2240 arXiv:0811.2027 In NS-NS systems we can neglect all tidal effects etc.

  24. PSR J1518+4904 Surprising results !!! Mass of the recycled pulsar is <1.17 solar masses Mass of its component is >1.55 solar masses Central values are even more shocking: 0.72+0.51-0.58 and 2.00+0.58-0.51 V~25 km/s, e~0.25 The second SN was e--capture? [Janssen et al. arXiv: 0808.2292]

  25. NS+WD binaries Some examples • PSR J0437-4715. WD companion [0801.2589, 0808.1594]. The closest millisecond PSR.MNS=1.76+/-0.2solar.Hopefully, this value will not be reconsidered. • The case of PSR J0751+1807. • Initially, it was announced that it has a mass ~2.1 solar [astro-ph/0508050]. • However, then in 2007 at a conference the authors announced that the resultwas incorrect. Actually, the initial value was 2.1+/-0.2 (1 sigma error).New result: 1.24 +/- 0.14 solar[Nice et al. 2008, Proc. of the conf. “40 Years of pulsars”] • 3. PSR B1516+02B in a globular cluster. M~2 solar (M>1.72 (95%)). A very light companion. Eccentric orbit. [Freire et al. arXiv: 0712.3826] Joint usage of data on several pulsars can give stronger constraints on thelower limit for NS masses. • It is expected that most massive NSs get their additional “kilos” due toaccretion from WD companions [astro-ph/0412327].

  26. Pulsar masses With WD companions With NS companions [Nice et al. 2008]

  27. PSR 0751+1807 Massive NS: 2.1+/-0.3 solar masses – Now shown to be wrong (!) [see Nice et al. 2008] (Trumper)

  28. Binary pulsars

  29. Relativistic corrections and measurable parameters For details seeTaylor, Weisberg 1989ApJ 345, 434

  30. Mass measurements PSR 1913+16 (Taylor)

  31. Double pulsar J0737-3039 (Lyne et al. astro-ph/0401086)

  32. Masses for PSR J0737-3039 The most precise values. (Kramer et al. astro-ph/0609417)

  33. Neutron stars in X-ray binaries Study of close binary systems gives an opportunity to obtain mass estimate forprogenitors of NSs (see for example, Ergma, van den Heuvel 1998 A&A 331, L29). For example, an interesting estimate was obtained for GX 301-2.The progenitor mass is >50solar masses. On the other hand, for several other systems with both NSs and BHsprogenitor masses a smaller: from 20 up to 50. Finally, for the BH binary LMC X-3 the progenitor mass is estimated as >60 solar. So, the situation is tricky. Most probably, in some range of masses, at least in binary systems, stars canproduce both types of compact objects: NSs and BHs.

  34. Mass determination in binaries:mass function mx, mv - masses of a compact object and of a normal star (in solar units), Kv – observed semi-amplitude of line of sight velocity of the normal star (in km/s), P – orbital period (in days), e – orbital eccentricity, i – orbital inclination (the angle between the prbital plane and line of sight). One can see that the mass function is the lower limit for the mass of a compact star. The mass of a compact object can be calculated as: So, to derive the mass it is necessary to know (besides the line of sight velocity)independently two more parameters: mass ration q=mx/mv, and orbital inclination i.

  35. Recent mass estimates ArXiv: 0707.2802

  36. Massive NSs We know several candidates to NS with high masses (M>1.8 Msun) in X-ray binaries: • Vela X-1, M=1.88±0.13 or 2.27±0.17 Msun(Quaintrell et al., 2003) • 4U 1700-37, M=2.4±0.3 Msun (Clark et al., 2002) • 2S 0921-630/V395 Car, M=2.0-4.3 Msun [1] (Shahbaz et al., 2004) We will discuss formation of very massive NS due to accretion processes in binary systems.

  37. What is «Very Massive NS» ? • 1.8 Msun < Very Massive NS < 3.5 Msun • 1.8Msun: (or ~2Msun) Upper limit of Fe-core/young NS according to modeling of Supernova explosions (Woosley et al. 2002). • ~3.5Msun: Upper limit of rapidly rotating NS with Skyrme EOS (Ouyed 2004).

  38. Evolution For our calculations we use the “Scenario Machine’’ code developed at the SAI. Description of most of parameters of the code can be found in (Lipunov,Postnov,Prokhorov 1996)

  39. Results 1 000 000 binaries was calculated in every Population Synthesis set 104 very massive NS in the Galaxy (formation rate ~6.7 10-7 1/yr) in the model with kick [6 104 stars and the corresponding formation rate ~4 10-6 1/yr for the zero kick]. astro-ph/0412327

  40. Results II Mass distribution of very massive NS Luminosity distribution of accreting very massive NS Dashed line: Zero natal kick of NS ( just for illustration). Solid line: Bimodal kick similar to (Arzoumanianet al. 2002).

  41. Outside of the star redshift Bounding energy Apparent radius

  42. Baryonic vs. Gravitational mass Podsiadlowski et al. [astro-ph/0506566] proposed that in the double pulsarJ0737-3039 it is possible to have a very good estimate of the initial massof one of the NSs (Pulsar B). The idea was that for e--capture SN baryonic massof a newborn NS can be well fixed. However, in reality it is necessaryto know the baryonic mass with1% precision. Which is not easy. [Bisnovatyi-Kogan et al. In press]

  43. r0 l=∫eλdr≠r0 0 Equator and radius ds2=c2dt2e2Φ-e2λdr2-r2[dθ2+sin2θdφ2] In flat space Φ(r) and λ(r) are equal to zero. • t=const, r= const, θ=π/2, 0<Φ<2π l=2πr • t=const, θ=const, φ=const, 0<r<r0 dl=eλdr

  44. Gravitational redshift Frequency emitted at r Frequency detected byan observer at infinity This function determinesgravitational redshift It is useful to use m(r) – gravitational mass inside r –instead of λ(r)

  45. NS Radii A NS with homogeneous surface temperature and local blackbody emission From dispersion measure From X-ray spectroscopy

  46. Limits from RX J1856 (Trumper)

  47. Radius determination in bursters Explosion with a ~ Eddington liminosity.Modeling of the burst spectrumand its evolution. See, for example, Joss, Rappaport 1984, Haberl, Titarchuk 1995

  48. Burst oscillations Fitting light curves of X-ray bursts. Rc2/GM > 4.2 for the neutron star in XTE J1814-338 [Bhattacharyya et al. astro-ph/0402534]

  49. Fe K lines from accretion discs Measurements of the inner disc radius provide upper limits on the NS radius. Ser X-1 <15.9+/-1 4U 1820-30 <13.8+2.9-1.4 GX 349+2 <16.5+/-0.8 (all estimates for 1.4 solar mass NS) [Cackett et al. arXiv: 0708.3615] Suzaku observations

  50. Mass-radius diagram and constraints Rotation! Unfortunately, there are nogood data on independentmeasurements of massesand radii of NSs. Still, it is possible to putimportant constraints. Most of recent observationsfavour stiff EoS. (astro-ph/0608345, 0608360)

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