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
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 J1614-2230 For a review: Tauris & van den Heuvel (2006) Chile March 6-11, 2011 2 Thomas Tauris, Bonn
Pulsars are key probes of fundamental physics Particle physics Nuclear physics Condense matter physics Atom physics Plasma physics Relativity Chile March 6-11, 2011 3 Thomas Tauris, Bonn
Equations-of-state for high density nuclear matter Chile March 6-11, 2011 4 Thomas Tauris, Bonn
Detection of low frequency gravitational waves using pulsars Chile March 6-11, 2011 5 Thomas Tauris, Bonn
Tests of theories of gravity Chile March 6-11, 2011 6 Thomas Tauris, Bonn
1669 radio pulsars Chile March 6-11, 2011 7 Thomas Tauris, Bonn
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Characteristics of a binary millisecond pulsar (BMSP): Rapid spin: P spin < 50 ms Small period derivative: dp/dt < 10-18 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
Formation of a BMSP Chile March 6-11, 2011 11 Thomas Tauris, Bonn
ZAMS LMXB cartoon Roche-lobe overflow 15.0 1.6 13.1 1.6 P orb age 1200 days 0.0 Myr 1538 days 13.87 Myr eccentricity: 0.0 common envelope + spiral-in helium star supernova 4.86 3.99 1.6 0.83 days 13.87 Myr 1.10 days 14.95 Myr neutron star LMXB millisecond pulsar 80.75 days 15 Myr 1.3 1.6 4.11 days 2.29 Gyr 1.3 1.595 58 days 2.39 Gyr 1.6 0.303 Thomas Tauris, white Bonn dwarf eccentricity: 0.93 eccentricity: 0.0
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?
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, 2011 15 Thomas Tauris, Bonn
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,0 0 0 2 orbit widens (a>0) 1 17 q 1.28 4 orbit shrinks (a<0) unstable? (Tauris & Savonije 1999, 2001) light donor heavy donor Chile March 6-11, 2011 16 Thomas Tauris, Bonn
The Orbital Angular Momentum Balance Equation J orb M M M 1 2 2 2 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 2 1 2 2 1 2 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) 1 1 1 a q q q ls a0 q0 q0 1 q0 1 2 (1 ) 2 32 (1 ) Chile March 6-11, 2011 17 Thomas Tauris, Bonn
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, 2011 18 Thomas Tauris, Bonn
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 1.210 1 / 4.50 0.120 Chile March 6-11, 2011 20 Thomas Tauris, Bonn
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 2 4 4 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, 2011 21 Thomas Tauris, Bonn
Detailed evolution of LMXBs - formation of MSPs Tauris & Savonije (1999) Dt = 200 Myr. 1.60 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
Orbital period white dwarf mass correlation At first sight the theoretical relation looks really crappy when compared with observations. Chile March 6-11, 2011 23 Thomas Tauris, Bonn
The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, 2011 24 Thomas Tauris, Bonn
The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, 2011 25 Thomas Tauris, Bonn
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, 2011 26 Thomas Tauris, Bonn
The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, 2011 27 Thomas Tauris, Bonn
The search for low-mass neutron stars Bonn March, 2011 Chile March 6-11, 2011 28 Thomas Tauris, Bonn
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, 2011 29 Thomas Tauris, Bonn
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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, 2011 32 Thomas Tauris, Bonn
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, 2011 34 Thomas Tauris, Bonn
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 : 11.29 light s Eccentricity: 1.30±0.04 10-6 Inclination angle: 89.17±0.02 deg. DM distance: 1.2 kpc Was this pulsar born massive? Nature of progenitor binary?
IMXB case A Chile March 6-11, 2011 37 Thomas Tauris, Bonn
IMXB case A: thermal + nuclear timescale mass transfer Chile March 6-11, 2011 38 Thomas Tauris, Bonn
IMXB case A: thermal + nuclear timescale mass transfer Chile March 6-11, 2011 39 Thomas Tauris, Bonn
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WD chemical abundances phase AB Hydrogen shell burning Chile March 6-11, 2011 41 Thomas Tauris, Bonn
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PSR J1614-2230 Tauris, Langer & Kramer (2011) Pulsar mass: 1.97±0.04 M o 1.99 M o WD mass: 0.500±0.006 M o 0.501 M o Orbital period: 8.69 days 8.67 days Dynamical instabilities L-S interactions Chile March 6-11, 2011 43 Thomas Tauris, Bonn
Podsiadlowski, Rappaport & Pfahl (2002) Chile March 6-11, 2011 44 Thomas Tauris, Bonn
PSR J1614-2230 Spin of the recycled pulsar? Chile March 6-11, 2011 45 Thomas Tauris, Bonn
PSR J1614-2230: 0.11 M PSR J1802+2224: 0.01 M (CE) Chile March 6-11, 2011 46 Thomas Tauris, Bonn
LMXB case B IMXB early case B case A LMXB case A IMXB case C (CE) HMXB Chile March 6-11, 2011 48 Thomas Tauris, Bonn
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, 2011 49 Thomas Tauris, Bonn
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 J1614-2230: 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, 2011 50 Thomas Tauris, Bonn