Thomas Tauris Bonn Uni. / MPIfR

Transcription

1 Thomas Tauris Bonn Uni. / MPIfR Heidelberg XXXI, Oct. 2013

2 1: Introduction Degenerate Fermi Gases Non-relativistic and extreme relativistic electron / (n,p,e - ) gases 2: White Dwarfs Structure, cooling models, observations 3: Neutron Stars Structure and Equation-of-state Radio Pulsars Characteristics, observations, spin evolution, magnetars 4: Binary Evolution and Interactions Accretion, X-ray Binaries, formation of millisecond pulsars Black Holes Observations, characteristics and spins 5: Testing Theories of Gravity Using Pulsars Gravitational Waves Sources and detection Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 2

3 Structure of WDs Basic characteristics Chandrasekhar mass and stability EoS below neutron drip (Harrison-Wheeler / Baym-Pethick-Sutherland (BPS)) Neutron-rich nuclei Neutron drip Semi-empirical mass formula Including shell effects and lattice energy Elementary treatment of WD cooling Photon diffusion equation Luminosity, L (M,T ) Residual ion thermal energy Cooling age Crystallization Observations Heidelberg XXXI, Oct.2013

4 EoS for Baym-Bethe-Pethick (BBP) EoS Stability of NSs EoS for drip nuc Nucleon-nucleon interactions Muons, hyperons, -resonances, pion/kaon condensation Superfluidity (glitches/cooling) Bethe-Johnson (BJ) EoS Quark (strange) stars / quark-novae Summary of EoS above neutron drip Structure of NSs Cross section Soft vs Stiff EoS Observational constraints on M and R nuc Heidelberg XXXI, Oct.2013

5 11 3 Neutron drip (nuclei, e - drip 410 g cm, n) 2 phase system Fairly well-known EoS (e.g. BBP) drip nuc g cm nuc not well understood. Problems: nucleon-nucleon interactions many-body problem hyperons (nucleon-like strange baryons) pion/kaon condensation 10 nuc ultra-high densities: no relativistic many-body Schrödinger equation is known meson clouds around nucleons - quark-drip (break-down of potential, no longer 2-body interactions) neutron lattice? n n n n Heidelberg XXXI, Oct.2013 n n n Thomas Tauris - Bonn Uni. / MPIfR repulsion

6 The exchange of vector mesons (S=1) induces repulsive NN forces, while the exchange of scalar mesons (S=0) induces attractive forces. V(r) The two lowest mass vector mesons are: (769 MeV), (783 MeV). The intermediate-range attractive NN force is caused by the (f 0 ) meson (600 MeV), and the long-range NN force by (140 MeV). r 2 e The Yukawa-like potential: V12 g r approximately describes the NN interactions. 1 EV Vi j (sum all pairs of NN interactions) 2 i j Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 6

7 Compressible liquid drop model Reid soft core: superposition of Yukawa-like potentials Includes many-body interactions and improved Coulomb lattice effects Minimizing the total energy density: for constant n with respect to A n An (1 V n ) n N N N n (baryon number density) n ( W W ) (1 V n ) ( n ) N N L n N N e e V 12 g 2 e r r fraction of volume which is gas Nuclei must be stable against -decay (Z const.) N N n p e e n p e ( 0, leaves the star) Free n-gas must be in equilibrium with neutrons inside nuclei: G n N n Pressure balance between n-gas and nuclei: P G n P N n Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 7

8 Fig (Bayn, Bethe & Pethick 1971). stable NS no stable NS neutron drip 3 ( g cm ) For stability: 4 GTR 3

9 Fig (Baym & Pethick 1979).

10 Fig.9.1 (c.f. Fig.6.2) dm 0 d c

11 Steiner, Lattimer & Brown (2012). Lattimer (2009). Note, deviation from 1/3 R M Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 14

12 Muon contribution to EoS: Charge neutrality: e equilibrium: e e n p e np ne n e mc (106 MeV, g cm ) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 15

13 Hyperons are nucleon-like strange baryons (i.e. at least one s-quark, e.g.: 0 ( uds) 1116 MeV ) uus uds dds uss dss sss n fm nuc 0 0 3,,,,, (,,,,, ) when 2 ( 10 ) Fig. 8.4 (Canuto 1975) The concentrations in a free hyperonic gas as a function of total baryon density, n. Bednarik et al. (2011).

14 Baryons with only u- and d-quarks: n uuu uud udd ddd MeV,,, (,,, ) p, p, n, n Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 17

15 n p ( 140 MeV > ) n p e nuc have spin S=0 (bosons) and can form a Bose-Einstein condensate. Thus in their lowest energy state (z=0) they have no momentum and therefore they do not contribute to the pressure P. Pion condensates therefore results in soft EoS Kaon condensates may form too Heidelberg XXXI, Oct.2013

16 A fermionic superfluid may form at low temperatures. Zero-viscosity due to Cooper pairs (BCS theory). Three types: Consequences: 1) Formation of vortices 2) Dynamical evolution: pulsar glitches 3) The cooling of NSs 4) The Meissner effect (B-flux tubes) S 0 P S 2 0 neutron superfluid - inner crust neutron superfluid - core proton superfluid - core Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR

17 Vela I I I c n Moment of inertia Weak coupling between c: crust + charged particles n: superfluid neutrons in core (Two component model). A glitch is quickly (minutes) communicated to the charged particles via the B-field, but very slowly (months) to the superfluid neutrons. Problem: the two-component is too simplified and does not explain data (healing parameter Q and relaxation time differ for different glitches from the same pulsar) t/ ( t) 0( t) 0 Q e (1 Q) a t b The relaxation depends on the pinning/unpinning between core superfluid vortices and the normal component of nuclei (lattices) in the inner crust, transferring angular momentum. Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 20

18 NS cooling depends on: EoS Neutrino emission Superfluidity Magnetic fields Light elements on surface Direct URCA: ( >2 ) n p e e e e p e n n n Modified URCA: n n n p e e e nuc p e n e In highly degenerate matter a bystander particle e e must be present to absorb momentum Also neutrino emission due to Cooper pairing and bremsstrahlung. n n n n Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 21

19 Superfluidity affects the neutrino emission processes and the heat capacity. neutrino cooling photon cooling Douchin & Haensel (2001) Yakolov & Pethick (2004) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 22

20 Lattimer (2009)

21 NS radii can be determined for a few young NSs (the magificent seven) by fitting blackbody spectra: 2 4 L 4R T F F R d T 4 L 4 d 2 Correction for the gravitational redshift: R R T T GM cr GM 12 2 cr The apparent (observed) radius is larger than the true radius In practice more difficult because of the unknown spectral hardening (atmospheric corrections), and uncertainties in distance estimates. Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 28

22 Trümper et al. (2004).

23 Lattimer (2009)

24 Antoniadis et al. (2013) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 31

25 Shapiro delay measurements of binary radio pulsars. Measurements of other post-keplerian parameters:,, Pb, e Dual-line spectroscopy (measurements of WD spectra Dopplershift, besides from radio pulsar timing). Earth Shapiro delay Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 32

26 Nice (2013) Any PK measurement yields a line in the (m 1,m 2 )-plane. Hence, two PK parametres determines m 1 and m 2 uniquely.

27 The double pulsar PSR J Kramer et al. (2006). Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 34

28 PSR J M= Antoniadis et al. (2013) Lattimer (2013)

29 Surface (few cm) outer crust inner crust

30 A soft equation of state has an average system energy which is attractive at nuclear densities. (e.g. a Reid potential). A stiff equation of state has a repulsive component at higher densities. For a given mass, M: soft stiff soft EoS: P is small ( is small) R is small, is large ( M is small) stiff EoS: P is large ( is large) R is large, is small ( M is large) P=K Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 38 c c max max

31

32

33 MIT bagmodel degenerate Fermi sea of massless quarkes energy density B important physics parameters: B, m s, s (bag constant, mass of strange quark, strong interaction coupling constant) 1 P ( 4 B ) 3 EoS: See Weber (2005) Prog.Part.Nucl.Phys.54: , for a modern review. M(R) (quark stars with larger masses have larger radii) Difficult to confirm observationally (sub-ms pulsar: P 0.6 ms ) Hybrid stars are very popular: quark core + normal matter Quark-novae represent the transition from a normal NS to hybrid star

34 Alford & Reddy (2003)

35 Weber (2005)

36 A quark-nova is the violent explosion resulting from the conversion of a neutron star to a quark star (Oyued, Dey & Dey, A&A 390 L39-42, 2002). When a neutron star spins down, it may convert to a quark star through a process known as quark deconfinement. Direct evidence for quark-novae is lacking; however, recent observations of supernovae SN 2006gy, SN 2005gj and SN 2005ap have been suggested may point to their existence (Leahy & Ouyed, MNRAS 387, 1193, 2008). Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 46

37

38 1: Introduction Degenerate Fermi Gases Non-relativistic and extreme relativistic electron / (n,p,e - ) gases 2: White Dwarfs Structure, cooling models, observations 3: Neutron Stars Structure and Equation-of-state Radio Pulsars Characteristics, observations, spin evolution, magnetars 4: Binary Evolution and Interactions Accretion, X-ray Binaries, formation of millisecond pulsars Black Holes Observations, characteristics and spins 5: Testing Theories of Gravity Using Pulsars Gravitational Waves Sources and detection Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 48

39 Observational aspects of radio pulsars The radio pulsar population in the Milky Way Pulse profiles / Scintillation / Dispersion measure Emission properties Spin evolution of pulsars in the PP-diagram The magnetic dipole model Evolution with B-field decay Evolution with gravitational wave emission The braking index True ages of radio pulsars Magnetars Soft gamma-ray repeaters (SGRs) and Anomalous X-ray pulsars (AXPs) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 49

40 A pulsar is a perfect physics laboratory: = 700 Hz (P=1,4 ms 8 sec.) B = 10 Perfect clock: G E = 10 L (F = 10 F ) rot 13 5 M = 1.4 M R = 10 km Giant atomic nucleus: A=10 baryons, = 2-10 Magnetosphere: production of 10 TeV -rays _ 38 core nuclear + (e, e ) per second e accelerated to 10 ev, =10 _ 16 Volts Rotation axis P= seconds (PSR ) 16 B Radio signal period Time Particle physics Nuclear physics Solid state physics Atom physics Plasma physics Relativity Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 50

41 The surface intensity of the radio emission, I using a Planck function demonstrates that if the radio emission was caused by thermal black body radiation one would obtain an extremely high brightness temperature (leading to absurdly large particle energies) and therefore the radiation mechanism of a radio pulsar must be coherent (most models invoke curvature radiation or a maser mechanism). I 3 2h 1 I, h / kt c e 1 Crab : f MHz (1 Jansky 10 erg cm s Hz st ) kt ev T K ( 10 ) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 51

42 ~ 2400 radio pulsars ~ 50 X-ray pulsars ~ 300 neutron stars in X-ray binary systems - Pulsars are concentrated in the Galactic plane in star forming regions (OB star progenitors) - Large spread is caused by high velocities (kicks imparted to NS in supernova explosions) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 52

43 y (kpc) Sun Centre of Milky Way x (kpc) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 53

44 Duty cycle: 1-5% for slow pulsars pulsar Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 54

45 436, 660, 1420 MHz Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 55

46 57

47

48 Solar system emitted pulse observed pulse

49 452 MHz 256 channels * 125 khz ta DM 0 L 4 e m c n e e 2 3 dl DM n e L 436 MHz (70 cm) 420 MHz distance 1/slope Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 60

50 The magnetic-dipole model: E dipole m ~ 2 m 3c BR sin 1 2 Erot I NS 2 E rot I NS ( 2 / P) B 3 3c I 2 8 R NS 6 NS PP P 2P Characteristic age Active pulsar lifetime: million yr Millisecond pulsars

51 n k the deceleration law, n 2 is the braking index n n 3 pure dipole 5 pure gravitar (only spin-down by gravitational wave radiation) P P0 true age of pulsars: t 1 ( n 1) P P 2 2 E m dipole 3 3c Erot I Edipole Eplasma Egw For example: B() t B e 0 t/ D n1 32 G 5 c ~ m BR sin Egw I 5 second derivative of magnetic moment / t 1 2 D D P P( t) P0 B0D 1 e t ln 1 2 k 2 D 2P a b ( a b) / 2 ellipticity (asymmetry rotation axis) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 64

52 Tauris & Konar (2001)

53 B-field decay in neutron stars, via crustal ohmic dissipation and diffusion, and its dependence on input physics. 2 B c 1 v B B t 4 B 3 3c I 2 8 R NS 6 NS PP

54 Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 67

55 A magnetar is a type of neutron star with an extremely high B-field, the decay of which powers the highenergy emission of anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs). Duncan & Thompson & (1992) developed the theory to explain these objects. Support for this extreme B-field picture comes from: 1) Location in P-P dot diagram 2) Cannot be radio pulsars b/c LX Erot 3) Cannot be X-ray binaries b/c absence of Doppler modulation in timing data 4) Cannot be neutron stars accreting from a fall-back disk b/c of detection of flares 5) Bursts can be explained by magnetic giant flares Magnetars are detected both as persistent (quiescent) sources and burst sources. There are currently 26 known magnetars: 13 SGRs and 13 AXPs according to McGill SGR/AXP online catalogue: with various burst, transient and persistent properties Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 68

56

57 The famous March 5, 1979 event (the largest burst of gamma-rays ever detected) Notice, the 8.0 sec cycle (spin period of NS). 16 additional small bursts seen between and since then no burst have been detected. The source was located in an LMC SN remnant Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 70

58 Another famous giant flare (burst) is the August 27, 1998 event (most intense flux of gamma-ray ever detected) Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 71

59 A magnetic twist gives rise to X-ray emissions from a magnetar. Robert C. Duncan, University of Texas at Austin Twisted B-fields support of excess currents in the magnetosphere. Detection of resonant cyclotron scattering reveals the B-field strengths. E GM c R B G proton cyclotron / ( /10 ) kev

60 Giant flares a fireball model Huge tension builds up in the crust from magnetic stress - when released this energy produces a giant flare. A trapped fireball (orange zone) on the surface of a neutron star (brown). The fireball, containing positrons ( e + ), electrons ( e - ), and high-energy photons (γ), is confined by the magnetic field (dark, arched lines). It loses energy by emitting hard X-ray photons (orange squiggley arrows) from its surface. The fireball also contains a trace of heavy particles (protons and ions) which were blown off the surface of the star. These heavy particles settle down along field lines as the fireball loses energy and shrinks. Robert C. Duncan, University of Texas at Austin

61 B 3 3c I 2 8 R NS 6 NS PP Kaspi et al. (2001), ApJ. 558, 253

62 NS EoS above neutron drip Baym-Bethe-Pethick (BBP) EoS Stability of NSs, exotic particles, quark stars Exotic particles Structure of NSs Cross section, soft vs.stiff EoS, observational constraints Radio pulsars Observational properties The magnetic dipole model Spin evolution of pulsars in the PP-diagram True ages Magnetars Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 77

63 1: Introduction Degenerate Fermi Gases Non-relativistic and extreme relativistic electron / (n,p,e - ) gases 2: White Dwarfs Structure, cooling models, observations 3: Neutron Stars Structure and Equation-of-state Radio Pulsars Characteristics, observations, spin evolution, magnetars 4: Binary Evolution and Interactions Accretion, X-ray Binaries, formation of millisecond pulsars Black Holes Observations, characteristics and spins 5: Testing Theories of Gravity Using Pulsars Gravitational Waves Sources and detection Heidelberg XXXI, Oct.2013 Thomas Tauris - Bonn Uni. / MPIfR 78