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Pulsars and Neutron Stars Pulsars and neutron Stars J´erˆomeNovak Pulsars and neutron stars: an Introduction Models introduction to observations and Observations and current models constraints Pulsars Laboratories J´erˆome Novak for physics [email protected] Laboratoire Univers et Th´eories (LUTH) CNRS / Observatoire de Paris Exotic Nuclei: New Challenges, May 7-18, 2007 Outline Pulsars and neutron Stars J´erˆomeNovak Introduction 1 Introduction Models Observations and 2 Neutron star models and global properties constraints Pulsars Laboratories 3 Observations and constraints for physics 4 Magnetic field and pulsar models 5 Neutron stars as probes for modern physics Pulsars and neutron Stars J´erˆomeNovak Introduction Models Observations and constraints Pulsars Introduction Laboratories for physics Neutron stars or compact stars? Pulsars and neutron Stars A star made of neutrons... is the main idea. J´erˆomeNovak Introduction Models BUT Observations and constraints it is not the only feature: Pulsars Laboratories strong gravitational field for physics electro-magnetic field transition to the surface and/or accretion of matter from the interstellar medium (see also lecture by N. Sandulescu) many possibilities for nuclear matter: protons, electrons, muons, pions, s quarks, hyperons, ... ⇒self-gravitating object at nuclear density (not only neutrons) The concept Pulsars and neutron Stars J´erˆomeNovak In 1932, British scientist James Chadwick Introduction discovers the existence of neutrons. Models Observations and constraints Pulsars Laboratories for physics The legend says that, the very same evening, Lev Landau discusses about the possibility of dense stars made only of neutrons. Some orders of magnitude... Pulsars and neutron Stars J´erˆomeNovak Introduction 17 3 Models density = nuclear density ρnuc ' 1.66 × 10 kg / m , Observations 30 and let us take a mass M ' 1M = 2 × 10 kg, constraints s Pulsars 3M the radius should be R ' 3 ' 14 km, Laboratories 4πρnuc for physics and the surface gravity ∼ 1011 m /s2 (about 109 times that of the Sun). Discovery of pulsars Pulsars and neutron Stars J´erˆomeNovak In 1967, at Cambridge Introduction University Antony Hewish lead Models Observations an observational survey of and extra-galactic radio-sources. constraints Pulsars In august, his student Jocelyn Laboratories for physics Bell detects important signal fluctuations, which are observed to be periodic with a period of 1.337 s. ⇒pulsar or Pulsating Source of Radio (PSR) Pulsars are neutron stars Pulsars and Originally, the sources were associated with pulsations of neutron Stars J´erˆomeNovak neutron stars or white dwarfs after thinking of little green men: the first pulsar has been called LGM before PSR B1919+21... Introduction Models Observations and constraints Pulsars Laboratories Thomas Gold, in 1968 identifies pulsars with for physics rotating magnetized neutron stars and predicts a slight increase of their period due to energy loss. ⇒with the discovery of the Crab pulsar (PSR B0531+21) with a period of 33 ms, white dwarfs are ruled out... At maximal rotating speed, centrifugal and gravitational forces cancel s exactly: GM 3π RΩ2 = , and P ' R2 min Gρ Pmin ∼ 1 s for white dwarfs and Pmin ∼ 1 ms for neutron stars. How are they formed? Pulsars and neutron Stars J´erˆomeNovak In 1934, the astronomers Introduction Walter Baade and Fritz Zwicky Models make the hypothesis that Observations supernovæ could represent the and constraints transition between main Pulsars sequence (normal) stars and Laboratories neutron stars. for physics reasonable explanation for the source of energy of supernovæ in accordance with the discovery of Crab pulsar(supernovæ observed in 1054). Stellar evolution Pulsars and neutron Stars J´erˆomeNovak Introduction Models Observations and constraints Pulsars Laboratories for physics White dwarfs Pulsars and neutron Stars J´erˆomeNovak white dwarfs have been observed as Introduction very hot (white) and very small (dwarf) Models stars; Observations and e.g. Sirius B has been observed with constraints Teff = 24000K and R ∼ 5000 km; Pulsars the density is therefore ρ ∼ 109 kg/m3. Laboratories for physics gravity is balanced by degeneracy pressure of the electrons, if the mass is lower than some critical value, called Chandrasekhar mass ∼ 1.5M . If they do not accrete matter, white dwarfs cool down and become fainter and fainter. Black holes Pulsars and neutron Stars a black hole is a region of space-time causally J´erˆomeNovak disconnected from asymptotic observers. the (geometric) boundary is called event horizon. Introduction Models Observations and constraints Pulsars Laboratories for physics inside the horizon, no light ray can reach any outside observer (black); what falls inside the horizon is definitely lost (hole) ... Pulsars and neutron Stars J´erˆomeNovak Introduction Models Observations and constraints Pulsars Neutron star models Laboratories for physics Physical ingredients Pulsars and neutron Stars J´erˆomeNovak First one builds equilibrium models: Introduction assume that nuclear matter is a fluid; Models assume chemical equilibrium; Observations and constraints give the gravitational law (self-gravitating body); Pulsars write the hydrostatic equilibrium; Laboratories for physics give a law for the pressure as a function of nuclear matter density (temperature?) ⇒equation of state (EOS). The EOS specifies the nuclear matter properties and, in particular the strength of the strong interaction between particles, which is to equilibrate gravity. Compactness The need for relativistic gravity Pulsars and Let us compare the escape velocity v from a self-gravitating neutron Stars e J´erˆomeNovak body to the speed of light c: Introduction 1 GMm v2 2GM mv2 = and e = = Ξ Models 2 e R c2 Rc2 Observations and constraints Ξ is called the compactness parameter of the body, and also Pulsars measures the ratio between the gravitational potential energy Laboratories and the mass energy. It value is for physics 10−6 for our Sun, 10−3 for a white dwarf, 0.4 for a neutron star and 1 for a black hole ⇒it gives the influence of relativistic effects on the gravitational force: one needs general relativity (GR) to describe neutron stars! Tolman-Oppenheimer-Volkov system Pulsars and To describe the gravitational field in GR, one needs the metric gαβ neutron Stars (static and spherically symmetric): J´erˆomeNovak 2 α β 2 2 2 2 2 2 2 2 2 ds = gαβdx dx = −N c dt + A dr + r dθ + sin θdϕ Introduction Models The matter is assumed to be a perfect fluid and is given by its αβ Observations stress-energy tensor T : and p constraints αβ α β αβ T = ρ + 2 u u + pg . c −1 Pulsars 2Gm Laboratories Defining m(r) and Φ(r) from A = 1 − 2 and for physics rc N = exp Φ/c2, Einstein and hydrostatic equations write: dm = 4πr2ρ dr dΦ 2Gm−1 Gm p = 1 − + 4πG r dr rc2 r2 c2 dp p dΦ = − ρ + dr c2 dr Simple equations of state: polytropes Pulsars and neutron Stars In order to integrate the TOV system, one must specify an J´erˆomeNovak EOS: Introduction soon after their birth in supernovæ, neutron stars cool Models down below their Fermi temperature; Observations and constraints temperature effects can be neglected and nuclear reactions Pulsars are at equilibrium; Laboratories cold catalyzed matter at the endpoint of thermonuclear for physics evolution. ⇒all state variables are functions of only one parameter, chosen to be e.g. the baryonic density n. n dp Defining the adiabatic index Γ(n) = , a family of simple p dn EOSs, called polytropic EOSs, is obtained by assuming Γ = const. Numerical results Pulsars and The TOV system is integrated specifying (in addition to the neutron Stars J´erˆomeNovak EOS): a value of the central density (to vary the resulting mass); Introduction regularity conditions at r = 0; Models Thus, the system can be integrated until p = 0 at the surface Observations and (r = R), where it is matched with vacuum spherical static constraints Pulsars solution (Birkhoff’s theorem). Laboratories for physics Global quantities Pulsars and neutron Stars J´erˆomeNovak In GR, one must be cautious when defining global quantities: Introduction the gravitational mass can be defined for an isolated R Models Z system, and here as M = 4πr2ρ(r)dr = m(R). Observations g and 0 constraints the baryon mass is given by the number of baryons Pulsars Z R 2 Laboratories contained in the star Mb = mb 4πr A(r)n(r)dr. for physics 0 the gravitational redshift is the frequency relative redshift undergone by a signal emitted at the surface of the star and measured by a distant observer 2GM −1/2 z = 1 − − 1 = (1 − 2Ξ)−1/2 − 1. Rc2 Maximal mass Pulsars and Contrary to white dwarfs, where Γ → 4/3 near maximal mass, neutron Stars J´erˆomeNovak neutron star models exhibit a maximal mass as a general relativistic effect: more mass ⇒more pressure to equilibrate Introduction ⇒more gravity ⇒more mass ... Models Observations and constraints Pulsars Laboratories for physics 4 40 Γ=3 3 30 Γ=3 Γ=2.5 Γ=2.5 2 20 Γ=2 M in solar masses M in solar masses 1 10 Γ=2 0 0 0 10 20 30 0 5 10 15 n in nuclear density c nc in nuclear density dM if g < 0, the equilibrium is unstable. dnc note: if the pressure is supposed to come only from neutron degeneracy pressure, the maximal mass is 0.7 M ... Rotating models: more complications Pulsars and Next step: take into account rotation; two possibilities neutron Stars J´erˆomeNovak Analytically perturb spherical models; Numerically compute full models in axisymmetry. Introduction Assumption of circularity (no meridional convective currents), Models ⇒four gravitational potentials, depending on (r, θ). Two more Observations and differences with spherical models: constraints Pulsars need to specify the rotation law as Ω = f(r sin θ), Laboratories f = const being rigid rotation; for physics no more Birkhoff’s theorem: the gravitational potentials must be integrated up to spatial infinity, where space-time is asymptotically flat.
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