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A Short Walk Through the Physics of Neutron Stars

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A Short Walk Through the Physics of Neutron Stars A short walk through the physics of neutron stars Isaac Vidaña, INFN Catania ASTRA: Advanced and open problems in low-energy nuclear and hadronic STRAngeness physics October 23rd-27th 2017, Trento (Italy) This short talk is just a brush-stroke on the physics of neutron stars. Three excellent monographs on this topic for interested readers are: Neutron stars are different things for different people ² For astronomers are very little stars “visible” as radio pulsars or sources of X- and γ-rays. ² For particle physicists are neutrino sources (when they born) and probably the only places in the Universe where deconfined quark matter may be abundant. ² For cosmologists are “almost” black holes. ² For nuclear physicists & the participants of this workshop are the biggest neutron-rich (hyper)nuclei of the Universe (A ~ 1056-1057, R ~ 10 km, M ~ 1-2 M ). ¤ But everybody agrees that … Neutron stars are a type of stellar compact remnant that can result from the gravitational collapse of a massive star (8 M¤< M < 25 M¤) during a Type II, Ib or Ic supernova event. 50 years of the discovery of the first radio pulsar ² radio pulsar at 81.5 MHz ² pulse period P=1.337 s Most NS are observed as pulsars. In 1967 Jocelyn Bell & Anthony Hewish discover the first radio pulsar, soon identified as a rotating neutron star (1974 Nobel Prize for Hewish but not for Jocelyn) Nowadays more than 2000 pulsars are known (~ 1900 Radio PSRs (141 in binary systems), ~ 40 X-ray PSRs & ~ 60 γ-ray PSRs) Observables § Period (P, dP/dt) § Masses § Luminosity § Temperature http://www.phys.ncku.edu.tw/~astrolab/mirrors/apod_e/ap090709.html § Magnetic Field § Gravitational Waves ü NS-NS or BH-NS mergers ü NS oscillation modes: r-, f-, … modes The 1001 Astrophysical Faces of Neutron Stars Observation of Neutron Stars X- and γ-ray telescopes Space telescopes Chandra Fermi HST (Hubble) Atmospheric opacity opacity Atmospheric Optical telescopes Radio telescopes VLT (Atacama, Chile) Arecibo (Puerto Rico): d= 305 m Green Banks (USA): d= 100 m Nançay (France): d ~ 94 m GW: A New Way of Observing Neutron Stars GW170817: Binary Neutron Star Merger LIGO/VIRGO GW detection with associated electromagnetic events observed by over 70 observatories August 17th 2017 12:41:04 UTC + 1.7 seconds GW from a BNS merger detected GRB (GRB170817A) detected by FERMI γ-ray by Adv. LIGO & Adv. VIRGO Burst Monitor & INTEGRAL + 10h 52 min New bright source of optical light (SSS17a) detected in the galaxy NGC 4993 in the Hydra constellation + 11h 36 min Infrared emission observed + 15h Bright ultraviolet emission detected + 9 days X-ray emission detected + 16 days Radio emission detected PRL 119, 161101 (2017) Importance of the Event GW170817 Detecting GW from a NS merger allows us to learn more about the structure of these compact objects This multi-messenger event provides confirmation that NS mergers can produce short GRBs The observation of a kilonova allows us to show that NS mergers could be responsible for the production of most of the heavy elements, like gold and platinum, in the universe Multi-messenger Observations of the Event GW170817 Timeline of the discovery of GW170817, GRB170817A & the bright optical source SSS17a at NGC 4993 and the follow up observations For details see: PRL 119, 161101 (2017) Nature (2017) ApJ L12 848 (2017) ApJ L13 848 (2017) … First Analysis & Implications of GW170817 The very first analysis of the event GW170817 seem to indicate: ² NS radii should be R < 13 km or even smaller than 12 km. Some analysis suggest R < 11 km Constraint on the EoS: those predicting large radii excluded ? ² Low value of the upper limit of tidal deformability indicates a soft EoS The Fingerprint of a Pulsar Individual pulses are very different. But the average over 100 or more pulses is extremely stable and specific of each pulsar ² Top: 100 single pulses from the pulsar PSR B0950+08 (P=0.253 s) showing the pulse- to-pulse variability in shape and intensity ² Bottom: Average profiles of several pulsars Hobbs et al., Pub Astr. Soc. Aust., 202, 28 (2011) Pulsar Rotational Period The distribution of the Normal pulsars rotational period of pulsars shows two clear peaks that indicate the existence of two types of pulsars § normal pulsars with P ~ s Millisecond pulsars § millisecond pulsars with P ~ ms § First millisecond pulsar discovered in 1982 (Arecibo) § Nowadays more than 200 millisecond pulsars are known § PSR J1748-2446ad discovered in 2005 is until know the fastest one with P=1.39 Globular cluster Terzan 5 ms (716 Hz) Minimum Rotational Period of a Neutron Star Pulsar cannot spin arbitrarily fast. The absolute minimum rotational period is obtained when Centrifugal Force = Gravitational Force Keplerian Frequency In Newtonian Gravity In General Relativity 3 1/2 3/2 1/2 3/2 R " M sun % " R % ! M sun $ ! R $ Pmin = 2π ≈ 0.55$ ' $ ' ms Pmin = 0.96# & # & ms GM # M & #10km & " M % "10km % 2 ! 2π R6 $ log P = log#( ) B2 sin2 α&− log P 3 P log P = log P − log(2τ ) Pulsar distribution "# 6c I %& in the . Magnetars P-P plane Normal pulsars Pulsar equivalent of the Hertzprung-Russell diagram for ordinary stars Millisecond pulsars Magnetic Field of a Pulsar Type of Pulsar Surface magnetic field Millisecond 108 – 109 G Normal 1012 G Magnetar 1014 – 1015 G Extremely high compared to … Magnetars Earth Magnet Sun spots 0.3− 0.5G 103 −104 G 105G Magnetars € € € Largest continuous Largest magnetic field in lab. (USA) pulse in lab. (Russia) Normal pulsars 4.5x105G 2.8x107G Millisecond pulsars € € Where the NS magnetic field comes from ? A satisfactory answer does not exist yet. Several possibilities have been considered: 2 ² Conservation of the $ R ' φ = φ ⇒ B = B i magnetic flux during the i f f i& ) % R f ( gravitational collapse of the 2 iron core For a progenitor star with Bi ~ 10 G 6 12 & Ri ~ 10 km we have Bf ~ 10 G ² Electric currents flowing€ in the highly conductive NS interior ² Spontaneous transition to a ferromagnetic state due to the nuclear interaction Neutron Star Structure: General Relativity or Newtonian Gravity ? Surface gravitational ~ 10−10 potential tell us how much compact an object is ~ 10−5 2GM c 2R € ~ 10−4 −10−3 è Relativistic effects are € ~ 0.2 − 0.4 very important in Neutron Stars and General Relativity € must be used to describe their€ 1 structure € € Neutron Stars Structure Equations Ø The structure of a static (i.e., non-rotating) star with spherical symmetry in General Relativity is described by the Tolman-Oppenheimer-Volkoff (TOV) Equations −1 dP m(r)ε(r)" P(r) %" 4πr3P(r)m(r)%" 2Gm(r)% = −G $1+ '$1+ '$1− ' dr r2 # c2ε(r)&# c2 &# c2r & dm = 4πr2ε(r) dr § boundary conditions € P(0) = Po , m(0) = 0 P(R) = 0, m(R) = M € Ø€ Rotation breaks spherical symmetry and makes the structure equations “slightly” more complicated Stability solutions of the TOV equations ² The solutions of the TOV eqs. represent static equilibrium configurations ² Stability is required with respect to small perturbations dM dM G > 0, or G < 0 dρc dr The role of the Equation of State The only ingredient needed Matter constituents to solve the TOV equations is the (poorly known) EoS (i.e., p(ε)) of dense matter Interactions EoS “stiff” EoS TOV “stiff” EoS “soft” EoS “soft” EoS Upper limit of the Maximum Mass Mmax depends mainly on the behaviour of EoS, P(ε), at high densities. Any realistic EoS must satisfy two conditions: dP dP § Causality: ≤ c 2 § Stability: > 0 dρ dρ If the EoS is known up to ρ, these conditions imply: 1/2 " 5x1014 g / cm3 % € M max ≤ 3M $ € ' ¤ # ρ & If rotation is taken into account Mmax can increase up to 20%: 1/2 " 5x1014 g / cm3 % M max ≤ 3.89M $ ' ¤ # ρ & How to Measure Neutron Star Masses § 5 Keplerian orbital parameters can normaly be determined in a binary system: ü orbital period: P ü time of periastron passage: T0 ü eccentricity: e ü projected semi-major axis: a sin i ü angle of periastron: ω § 3 unknown: M1, M2, i Kepler’s 3rd law 2 3 2 3 3 ! $ M 2 sini " 2π % a sin i G(M1 + M 2 ) 2π f M , M ,i ( ) = ( 1 2 ) ≡ 2 = $ ' 3 # & M M # P & G a " P % ( 1 + 2 ) mass function In few cases small deviations from Keplerian orbit due to GR effects can be detected Measure of at least 2 post- High precision NS mass Keplerian parameters determination −5/3 2/3 2/3 " Pb % 1 ω = 3T⊗ $ ' (M p + Mc ) # 2π & 1−ε Periastron precession 1/3 M M 2M 2/3 " Pb % c ( p + c ) γ = T $ ' ε Time dilation and grav. redshift ⊗ # 2π & 4/3 (M p + Mc ) Shapiro delay “range” r = T⊗Mc 2/3 −2/3 M M −1/3 " Pb % ( p + c ) s = sini = T⊗ $ ' x Shapiro delay “shape” # 2π & Mc " %−5/3 M M 192π 5/3 Pb p c Orbit decay due to GW emission Pb = − T $ ' f (ε) 5 ⊗ # 2π & 1/3 (M p + Mc ) An example: the mass of the Hulse-Taylor pulsar (PSR J1913+16) Recent measurements of high masses § PSR J164-2230 (Demorest et al. 2010) ü binary system (P=8.68 d) ü low eccentricity (ε=1.3 x 10-6) ü companion mass: ~ 0.5M ¤ ü pulsar mass: M =1.928± 0.017M ¤ § PSR J0348+0432 (Antoniadis et al. 2013) ü binary system (P=2.46 h) ü very low eccentricity ü companion mass: 0.172 ± 0.003M ¤ ü pulsar mass: M = 2.01± 0.04M¤ Formation of Binary Systems Figure by P.C.C.
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