Five and a half roads to from a millisecond pulsar. Thomas Tauris AIfA, University of Bonn Max-Planck-Institut für Radioastronomie, Bonn

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1 Five and a half roads to from a millisecond pulsar Thomas Tauris AIfA, University of Bonn Max-Planck-Institut für Radioastronomie, Bonn Evolution of Compact Binaries, ESO Chile, March 6-11, 2011

2 Millisecond pulsars - an introduction Mass transfer in X-ray binaries Stability Modes of mass transfer / loss Formation of millisecond pulsars 1) LMXB P orb > P bif 2) LMXB P orb < P bif 3) IMXB Common Envelope 4) IMXB Early case B 5) IMXB Case A Summary - PSR J For a review: Tauris & van den Heuvel (2006) Chile March 6-11, Thomas Tauris, Bonn

3 Pulsars are key probes of fundamental physics Particle physics Nuclear physics Condense matter physics Atom physics Plasma physics Relativity Chile March 6-11, Thomas Tauris, Bonn

4 Equations-of-state for high density nuclear matter Chile March 6-11, Thomas Tauris, Bonn

5 Detection of low frequency gravitational waves using pulsars Chile March 6-11, Thomas Tauris, Bonn

6 Tests of theories of gravity Chile March 6-11, Thomas Tauris, Bonn

7 1669 radio pulsars Chile March 6-11, Thomas Tauris, Bonn

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9 Chile March 6-11, Thomas Tauris, Bonn

10 Characteristics of a binary millisecond pulsar (BMSP): Rapid spin: P spin < 50 ms Small period derivative: dp/dt < s s -1 Ingridients needed for spin-up: Increase of spin ang. mom. Decrease of period derivative Solution: Accretion of mass d N J I M GM r dt * * * * A Lamb, Pethick & Pines (1973) Ghosh & Lamb (1979, 1992) 2 B c 1 v B B t 4 B 3 3c I 2 8 R NS 6 NS PP Chile March 6-11, 2011 Geppert & Urpin (1994); Konar & Bhattacharya (1997) 10 Magnetic-dipole model Thomas Tauris, Bonn

11 Formation of a BMSP Chile March 6-11, Thomas Tauris, Bonn

12 ZAMS LMXB cartoon Roche-lobe overflow P orb age 1200 days 0.0 Myr 1538 days Myr eccentricity: 0.0 common envelope + spiral-in helium star supernova days Myr 1.10 days Myr neutron star LMXB millisecond pulsar days 15 Myr days 2.29 Gyr days 2.39 Gyr Thomas Tauris, white Bonn dwarf eccentricity: 0.93 eccentricity: 0.0

13 LMXB cartoon Accretion? super-eddington? jet? B-field, spin? Stability? response of donor star? response of Roche-lobe? dynamically stable? Mode of mass loss? specific orbital angular momentum?

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15 donor Stability criteria for mass transfer exponents of radius to mass: ln R ln M 2 2 L ln R ln M L 2 R M adiabatic or thermal response of the donor star to mass loss initial stability criteria: L donor R 2 R t 2 M R 2 donor M 2 M 2 2 R L R t L M R L L M 2 M 2 2 R nuclear burning 2 R L yields mass loss rate! tidal spin-orbit couplings gravitational wave radiation Chile March 6-11, Thomas Tauris, Bonn

16 Stability criteria for mass transfer II - Isotropic re-emission model ln a M 2 ln q M Orbital evolution: q ( q 0) NS max M M M 2 Edd, orbit widens (a>0) 1 17 q orbit shrinks (a<0) unstable? (Tauris & Savonije 1999, 2001) light donor heavy donor Chile March 6-11, Thomas Tauris, Bonn

17 The Orbital Angular Momentum Balance Equation J orb M M M a 1 e orbital angular momentum a a logarithmic differentiation (e=0, tidal circularization) 2 J J M M M M M M M orb orb 1 2 J orb r p J J orb orb J J gwr orb J J mb orb J J ls orb J J ml orb J J ml orb 2 q (1 q) 1 q 2 M M 2 2 2( 1) a q q q ls a0 q0 q0 1 q0 1 2 (1 ) 2 32 (1 ) Chile March 6-11, Thomas Tauris, Bonn

18 LMXB bifircation period P orb < P bif : LMXB shorten their orbital period Donor star still on main sequence RLO driven by loss of J orb (gwr, mb) Tutukov et al. (1985) Pylyser & Savonije (1988, 1989) Ma & Li (2009) Pbif 1day Black widow millisecond pulsars: P 10 hrs M 0.1 M orb comp. Evaporation single millisecond pulsars Lazaridis, Verbiest, Tauris, et al. (2011) Chile March 6-11, Thomas Tauris, Bonn

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20 LMXB BMSPs with He-WD P orb > P bif : LMXB widen their orbital period Donor star is a (sub)giant RLO driven by nuclear expansion Formation of BMSPs with He-WD: P orb 1 day 0.18 M 0.46 M WD Unique relation between P orb and M WD Savonije (1987) Joss, Rappaport & Lewis (1987) Rappaport et al. (1995) Tauris & Savonije (1999) M WD P orb / days 5 M / Chile March 6-11, Thomas Tauris, Bonn

21 Orbital period white dwarf mass correlation On the red giant branch (hydrogen shell burning) the growth of the degenerate core mass is directly related to the luminosity of the star Temperature is almost constant on the Hyashi track L R 2 Hence there is a relation between M core and R L R T eff The donor star fills its Roche-lobe during the mass transfer R is correlated with P orb correlation between (P orb, M WD ) Chile March 6-11, Thomas Tauris, Bonn

22 Detailed evolution of LMXBs - formation of MSPs Tauris & Savonije (1999) Dt = 200 Myr Mo 1.30 Mo 0.29 Mȯ 2.05 Mo P = 39 days. P = 3 days. super- Eddington sub-eddington Chile March 6-11, 2011 Thomas Tauris, Bonn 22

23 Orbital period white dwarf mass correlation At first sight the theoretical relation looks really crappy when compared with observations. Chile March 6-11, Thomas Tauris, Bonn

24 The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, Thomas Tauris, Bonn

25 The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, Thomas Tauris, Bonn

26 Orbital period white dwarf mass correlation At first sight the theoretical relation looks really crappy when compared with observations. But for each individual binary one must take into account: 1) Unknown orbital inclination angle 2) The mass of the pulsar (not always 1.35 M sun -- LMXBs allow for accretion!) Chile March 6-11, Thomas Tauris, Bonn

27 The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, Thomas Tauris, Bonn

28 The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, Thomas Tauris, Bonn

29 The search for low-mass neutron stars Bonn March, 2011 No problem!! Some uncertainties and broad scatter is expected in the correlation, e.g. from - core convective overshooting - mixing length - chemical composition of the donor star Chile March 6-11, Thomas Tauris, Bonn

30 Chile March 6-11, Thomas Tauris, Bonn

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32 IMXB case C (B) RLO BMSPs with CO/ONeMg-WD via Common Envelope and spiral-in phase Dynamically unstable mass transfer if: deep convective envelope of donor star Run-away (rapid expasion in response to mass loss) M donor > M accretor (orbit shrinks in response to mass loss) process! common envelope drag force dissipation of orb. ang. mom. + deposition of E orb in the envelope Outcome: huge reduction of orbital separation Explain tight BMSPs, P orb < 3 days! rejection of stellar envelope (NS orbiting a naked helium star) merging of NS + core (Thorne-Zytkow object / black hole) Chile March 6-11, Thomas Tauris, Bonn

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34 IMXB Early case B RLO BMSPs with CO-WD (He-WD) Alternative to CE-phase: - thermal timescale mass transfer - isotropic re-emission model Cyg X-2: King & Ritter (1999) Podsiadlowski & Rappaport (2000) Tauris, van den Heuvel & Savonije (2000) Chile March 6-11, Thomas Tauris, Bonn

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36 IMXB case A RLO BMSPs with CO/He-WD Podsiadlowski, Rappaport & Pfahl (2002) Tauris, Langer & Kramer (2011a,b), Tauris & Langer (2011) Pulsar mass: 1.97±0.04 M o WD mass: 0.500±0.006 M o Orbital period: 8.69 days Projected a psr : light s Eccentricity: 1.30± Inclination angle: 89.17±0.02 deg. DM distance: 1.2 kpc Was this pulsar born massive? Nature of progenitor binary?

37 IMXB case A Chile March 6-11, Thomas Tauris, Bonn

38 IMXB case A: thermal + nuclear timescale mass transfer Chile March 6-11, Thomas Tauris, Bonn

39 IMXB case A: thermal + nuclear timescale mass transfer Chile March 6-11, Thomas Tauris, Bonn

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41 WD chemical abundances phase AB Hydrogen shell burning Chile March 6-11, Thomas Tauris, Bonn

42 Chile March 6-11, Thomas Tauris, Bonn

43 PSR J Tauris, Langer & Kramer (2011) Pulsar mass: 1.97±0.04 M o 1.99 M o WD mass: 0.500±0.006 M o M o Orbital period: 8.69 days 8.67 days Dynamical instabilities L-S interactions Chile March 6-11, Thomas Tauris, Bonn

44 Podsiadlowski, Rappaport & Pfahl (2002) Chile March 6-11, Thomas Tauris, Bonn

45 PSR J Spin of the recycled pulsar? Chile March 6-11, Thomas Tauris, Bonn

46 PSR J : 0.11 M PSR J : 0.01 M (CE) Chile March 6-11, Thomas Tauris, Bonn

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48 LMXB case B IMXB early case B case A LMXB case A IMXB case C (CE) HMXB Chile March 6-11, Thomas Tauris, Bonn

49 AIC accretion induced collapse of a white dwarf J. Hurley et al. (2010): AIC route cannot be ignored Theory / simulations ( ) Attractive for GC MSPs Population synthesis? Exact outcome P spin, B (?) No observational evidence (although probably candidates ) Chile March 6-11, Thomas Tauris, Bonn

50 Formation of millisecond pulsars 1) LMXB P orb > P bif (case B) 2) LMXB P orb < P bif (case A) 3) IMXB Common Envelope (case C) 4) IMXB Early case B 5) IMXB Case A (PSR J : neutron star was born massive) 5½) AIC Great diversity in MSP zoo since discovery in 1982 Challenges remain intact! tauris@astro.uni-bonn.de Chile March 6-11, Thomas Tauris, Bonn