Compact stars as laboratories to test matter at extreme conditions. Alessandro Drago Otranto, June 2009

Transcription

1 Compact stars as laboratories to test matter at extreme conditions Alessandro Drago Otranto, June 2009

2 Plan of the lectures Introduction: the discovery of neutron stars and pulsars; main facts about their structure; how are they observed; how are they born Two classical observational limits: the Mass-Radius relation and the cooling curve The structure and stability of rapidly rotating compact stars Their origin: Supernovae (and GRBs)

3 Introduction to compact stars Their invention and their discovery Main problems concerning their structure Their life: birth, death and recycling Main references: Black Holes, White Dwarfs and Neutron stars, Shapiro & Teukolsky Compact Stars, Glendenning Neutron Stars 1, Haensel, Potekhin & Yakovlev 2007.

4 The invention of neutron stars Invented by Landau in 1931 before the discovery of neutrons (Chadwick 1932)! (giant nucleus ) The real neutron star, Baade and Zwicky 1934 (extremely closed packed neutrons) The equation of hydrostatic equilibrium (spherically symmetric) in General Relativity, Tolman Oppenheimer & Volkoff 1939). For a non-interacting gas of neutrons M max = 0.71 M sun. 1. Nuclear interaction provides larger masses (Cameron 1959) 2. Superfluidity (Ginzburg & Kirzhnits 1964) 3. Neutrino emission (Chiu & Salpeter 1964) and cooling

5 Pulsars! X-ray astronomy (detectors on rockets and baloons) First non-solar X-ray source Sco X-1 (Giacconi et al. 1962) Emission from Crab Nebula (1964) too large to be a neutron star (it is a plerion) Invention of pulsars (Pacini 1967) (magnetized and rapidly rotating neutron stars) Little Green Men: Jocelyn Bell (supervised by Hewish) discovers a radio source pulsating at s (1967) Discovery of Crab pulsar (1968) P= 33 ms!! Pulsars are neutron stars!

6 Neutron star matter Charge neutral: r p = r e b-stable: m n =m p +m e Can be computed at T=0 Proto-Neutron star matter Neutrino trapping: m ve not vanishing Has to be computed at various lepton fractions Has to be computed at finite temperature or entropy

7 TOV equations of matter equilibrium in General Relativity and for a spherical object

8 Main points concerning compact star structure 1. Outer crust. Few hundred meters thick. Density up to neutron drip density r ND = 4X10 11 g/cm 3. Made of ions and electrons. It can be solid. 2. Inner crust. A km thick. Density above neutron drip and up to 0.5 r 0. Made of electrons, free neutrons and neutron rich nuclei. Free neutrons can be superfluid. 3. Outer core. A few km thick (maybe ). Density up to 1-2 r 0. Made of neutrons, protons, electrons and maybe muons. 4. Inner core. Occupies the bulk of the star. The central density can be very large, up to several times r 0, depending on the softness of the Equation of State. The composition is unknown. Could contain hyperons, pion or kaon condensates, deconfined quarks either in a pure or in a mixed phase.

9 Quark stars? Bodmer (1971) proposed stars composed of collapsed nuclei, reaching densities much larger than the normal ones. One possible scenario was matter made of uds quarks. Witten (1984) advanced the hypothesis of absolutely stable strange quark matter. He suggested that quark nuggets could be formed in the early universe. Quark stars can have masses and radii similar to those of neutron stars. Farhi and Jaffe (1984) discussed the possibility of strangelets and of absolutely stable quark matter using the MIT bag model. Haensel et al. (1986) and Alcock et al. (1986) propose detailed models for quark stars and possible formation scenarios.

10 Strangelets in the MIT bag model

11 If Quark Stars exist, are ALL compact stars Quark Stars? Madsen (1988) says yes!. And therefore quark stars cannot exist Janka et al. (2008) say maybe no. And therefore quark stars and neutron stars can both exist. If both quark stars and neutron stars exist: 1. Observational data on masses, radii and cooling times (and other) are more easy to interpret 2. When a neutron star collapses into a quak star a huge amount of energy can be released! (order of erg)

12 How do we observe compact stars now? Electromagnetic emission: Radiotelescopes Optical telescopes (weak emission) X-ray telescopes (Rosat, Beppo SAX, Chandra, XMM, RXTE ) gamma-ray telescopes (HETE, HETE-2, INTEGRAL ) Neutrino detectors (Sudbury, Kamioka, Gran Sasso) Gravitational wave detectors (LIGO, VIRGO)

13 How are they born? Core collapse of stars having a mass larger than 10 M s Progenitors with smaller masses end up as white dwarf; the mass upper limit of the progenitor depends on the metallicity and on rotation. Too heavy progenitors end up as back hole. White dwarf: M<M s ; R=10-2 R s ; r=10 7 g/cm 3 ; GM/Rc 2 =10-4 Neutron stars: M<3M s ; R=10-5 R s ; r=10 15 g/cm 3 ; GM/Rc 2 =10-1

14 From: How massive single stars end their life Heger, Fryer, Woosley and Langer 2003

15 Rotation-powered pulsars The rotational energy can be very large: 2 x erg for Crab (P=33 ms) An estimate of the magnetic field can be obtained assuming that the slow-down is due to dipole emission: I (dw/dt) = -2 W 3 B eff2 R 6 / 3 c 3 where B eff = B sina For Crab B eff = 3.8 x G Solving the diff. equation of slow down and assuming that the pulsar was initially rotating much faster, one gets the characteristic pulsar age: t pulsar = P/(2 dp/dt) For Crab t pulsar = 1240 years. Crab actually exploded in 1054.

16 Rotation powered pulsars from Lamb and Boutloukos 2007

17 X-ray binaries If there is mass transfer in a compact binary system, we obtain a X-ray source. The compact stellar object receiving mass can be either a neutron star or a black-hole. Mass accretion can transfer angular momentum to the compact star. The typical timescale of the spin-up is very long, of the order of a few ten million years. Depending on the mass of the companion (high or low) the evolution of the system can be rather different. Low Mass X-ray Binaries are probably among the oldest stellar objects.

18 High mass X-ray binary Low mass X-ray binary

19 Disk accretion d(iw)/dt = (dm/dt) l(r 0 )+N l is the angular momentum of the accreting plasma N magnetic and viscous torque outside r 0. Using di/dt = (di/dm) (dm/dt) and dw/dt=-(w/p)(dp/dt) we get: (dp/dt)/p=(dm/dt)/m [(M/I)(dI/dM)-(l/l s )]-(N/IW) wherel s =IW/M. Since (M/I)(dI/dM) is order 1 and l>l s the star angular velocity can increase.

20 Accreting and nuclear powered Millisecond pulsars from Lamb and Boutloukos 2007

21 Rotational history of a compact star 1) SN progenitor: not a rigid rotator. Induced magnetic fields can limit the initial angular velocity of the core. Open question: can a proto-neutron star rotate at millisecond period? 2) Rapid rotation of the proto-neutron would be braked by bar instabilities and by r-mode instabilities. 3) The star continues slowing down due to magnetic braking and r-mode instabilities. 4) Death-line: large P, small dp/dt the pulsar is no more emitting 5) If the star is in a binary system and it accretes mass, then it can be re-accelerated Open question: all observed millisecond pulsars have been recycled?

22 Thermal history of a compact star 1) Born hot: initial temperature of a proto-neutron star is of a few ten MeV (a few K) 2) The cooling takes place initially mainly via neutrino-antineutrino emission 3) In some 10 seconds it cools down to less then 1 MeV 4) At T<0.1 MeV the cooling time is strongly influenced by the composition: DT mod.urca = 1 yr T 9-6 DT quarks = 1 hr T 9-4 5) After some 1 Myr the cooling due to photon emission from the surface becomes dominant 6) The star is no more observable But if it accretes mass its temperature increases again

23 What is new since 1983? (what was not yet in Shapiro-Teukolsky?) Observations: 1) SN1987a!!! 2) Lower limits on thermal emissions (ROSAT) 3) Much larger statistics concerning fast rotators 4) Estimates of compactness M/R from red-shifted emissions 5) Evidence of vibration of the surface 6) (magnetars, Gamma-Ray-Bursts connection to Sne, ) Theory 1) Sophisticated EOS of matter (Wiringa-Ficks-Fabrocini, Akmal-Pandharipande-Ravenhall, Lattimer-Swesty) 2) Realistic simulations of SN explosions 3) Hyperons! (Glendenning-Moszkowski) 4) Quarks! (color superconductivity) 5) R-mode instabilities

24 Conclusions: Compact Stars are Superstars! (Haensel, Potekhin & Yakovlev 2007) They are: Superdense Superfast Superfluid and Superconducting They contain superstrong magnetic fields and are made of super- isospin rich matter