Physics of Neutron stars

Sanjay K. GhoshDepartment of Physics

AndCentre for Astroparticle Physics & Space Science

Bose InstituteKolkata

ATHIC November 14 – 17, 2012, PUSAN

Plan:1. Theory & Observation (a) Mass (b) Cooling (c) Gravitational Wave

2. Hadron - quark transition: (a) Consequences (b) Transition Mechanism

3. Neutron Star Physics at FAIR-CBM

3. Summary

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NS M R-3

SS M R3

SS vs. NS

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StrangeStar Neutron StarMade up of quarks (u, d, s) Nucleons. Hyperons, boson

condensates, quarks

Energy/baryon E 930 MeV E 930 MeV

Self bound Bound by gravity

Maximum mass limit similar

No Minimum mass Minimum mass ~ 0.1 M

May be smaller Radii ~ 10 – 12 Km

Surface P=0, E=4B P=0, E= 0

Lattimer2012

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Mallick et al. JPG2012

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Lattimer & Prakash 2007 ATHIC 2012

Mass versus spin period for 39 NSs. Horizontal line M = 1 M (3.2 M) measured minimum mass Vertical line at 20 ms separates the samples into two groups, MSP (<20 ms) and less recycled NS (>20 ms). Mass averages of two groups are found to be, respectively, 1.57 ± 0.35 M and 1.37 ± 0.23 M. The solid curve stands for the relation between accretion mass and spin period of recycled pulsar. Zhang et al. A&A 527 A83 (2011) .

Accreting massM=Ma (P/ms)-2/3

Ma = characteristic accretion mass when pulsar is spun-up to 1 ms

M= M0 + M

M0= 1.4 0.07 M

Ma= 0.43 23 M

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NS Cooling

• Cooling 1. Direct URCA Relativistic NM, Unpaired QM, pion and kaon condensates single flavour pairing

2. Modified URCA NM at lower density (proton fraction < 0.1)

3. CFL phase

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Jaikumar et al. PRD66 (2002)Reddy et al. NPA714 (2003)

Iwamoto, Ann. Phys. 141 (1982)Ghosh et al. MPLA9 (1994), IJMPE5 (1996)

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Observations of surface temperatures and upper bounds for several isolated neutron stars. The solid line is the basic theoretical cooling curve of a nonsuperfluidneutron star with M = 1.3 M Yakovlev &Pethick2004

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Global Thermal Balance

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Cassiopeia A (CAS A)• Youngest known supernovae remnant in milky way• Distance ~ 3.4 Kpc • Age ~ 340 Yrs.• Mass 1.5 – 2.4 M• radius 8 – 18 Km• Carbon Atmosphere• B 1011 G• Surface temperature Ts ~ 2 X 106 K• surface temperature drop last 10 Yrs. 4%Explanation:(1) n & p pair breaking- formation – Schternin et al., Page

et al. 2011(2) Nuclear medium cooling scenario – Blashke et al.2011

Blaschke et al Page et al.

Gravitational Waves (GW)- Ripples in space-time curvature propagating through space at the

speed of light

- Massive compact binary system – energy lose Grav. Waves – Change in orbital period (Hulse & Taulor 1993)

- NS of same mass, diff. radii will emit different Grav. Waveform in the late stage of binary spiral (Markakis et al. JPG conf. 2009)

- Correlation between frequency peak of postmerger GW emission and physical properties of nuclear EOS (Bauswein et al. PRL 2012)

- Dynamical behaviour of SS and NS merger are different

- Can be detected through their GW emission – proof of strange matter hypothesis (Bauswein et al. PRD2010) ATHIC 2012

Consequences• r – Mode instability - bulk flow known as Rossby

modes or r (rotational) mode - coriolis force effect - transfer the angular momentum

into gravitational radiation - so above a critical frequency spin slow down - critical frequency is limited by

viscous damping - r-mode rules out CFL quark

stars - may provide signature of hybrid

stars Madsen PRL85, Andersson et al.

IJMPD10, 381 (2001), Andersson et al. MNRAS337, 1224 (2002), Drago et al. Astron. Astrophys. 445, 053 (2006) ATHIC 2012

Hadron-quark phase transition – GRB connectionWhat happens in phase transition ?

1. Hadronic sector : small no. of strange baryons, small strangeness fraction (strange baryon density/total baryon density)

2. Quark sector : Strangeness fraction ~ 1Ghosh et al. Zphys C1995

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GRB connection…

µ = Cos polar angle

Sharp peak - µ = 0.1 and 0.24 ≈ 12 degrees

Bhattacharyya et al. PLB635 (2006) ATHIC 2012

GRB connection ….

• Time scale seconds1010 13

Normally small energy deposition The high gravity environment might enhance the deposition

(Salmonson & Wilson APJ, 517 (1999) 859

Result of two effects1. Path bending of neutrinos2. Gravitational red shift 10% energy deposit

Effect of rotation and gravitation : Increase in deposition rate Asymmetry in deposition

Bhattacharyya et al. IJP 2012

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Mechanism of phase transition: Conversion

Two step process: (a) Strong – Nuclear 2 flavour (b) Weak 2 Flavour 3 flavour

(a) Nuclear to 2-flavour conversion

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Bhattacharyya et al. PRC74, 065804 (2006) Drago et. al. Astrophys. J.659, 1519 (2007)

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I. Tokareva, A. Nusser, V. Gurovich, and V. Folomeev, Int. J., Mod. Phys. D 14, 33 (2005).

Bhattacharyya et al. PRC74, 065804 (2006)

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• (b) 2- flavour to 3-flavour conversion

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Mechanism of phase transition• Two step process (a) hadronic matter to two flavour matter - deconfinement - t ~ milliseconds

(b) two flavour to three flavour matter - s quark via weak process - t ~ 100 seconds Presence of two fronts ?

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Rotating Star: Density Profile :

R/Re = s/(1-s)R: radius Re = equatorial radius

AB, SKG, SRPL B635 (2006) 195

R/Re = s/(1 − s)Equator s = 0.5

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General relativistic effects Bhattacharyya et al. PRC76, 052801(R) (2007)

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http://www.atnf.csiro.au/research/pulsar/psrcat ATHIC 2012

http://www.atnf.csiro.au/research/pulsar/psrcat ATHIC 2012

Equation of continuiy

Euler equation

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First we perform our calculation for the static star considering both poloidal and toroidal field configuration following Colaiuda et al. (2008), for the field extending throughout the star

where provides the relative weight factor for the contribution of toroidal field. The force is purely poloidal if = 0, and both poloidal and toroidal contribute if = 1. For both the cases the hydrodynamic equation gets modified due to the inclusion of the magnetic field.

Static Star

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Rotating star

Canonical picture: we assume that the magnetic field of the NS is due to a dipole at the center of the star.

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Alternate field configurationsBocquet et al. 1995

Field configuration proposed for magnetars

Chakraborty et al. 1997

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Variation of the velocity of the conversion front with a different magnetic fieldconfiguration obtained from (Bocquet et al 1995; Konno et al. 1999)

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Variation of the velocity of the conversion front with a different magnetic fieldconfiguration given by (Chakrabarty et al. 1997).

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Summary• High density physics has interesting posssibilities

• Better radius measurements and next generation Gravitational wave detectors are expected to put very strong constraints on EOS.

• CBM experiment may help us to understand the physics of Neutron stars.

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Thank you

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PNJL MODEL

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ATHIC 2012Comparison of charge neutral trajectory in NJL and PNJL model

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The contour of scaled baryon number density nB/n0; (scaled by normal nuclear matter density) along with phasediagram at μe=40 for (a) NJL model and (b) for PNJL model; (From left nB/n0 = 0.5, 1, 3, 5, 10 respectively)

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The contour of net strangeness fraction (ns/nB) along with nB/n0 at μe=40 for (a) NJL model and (b) PNJL model;the values of nB/n0 are 0.5, 1, 3, 5 and 10 (from left).

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The isentropic trajectories along with phase diagram for (a) at μe=0, 2+1-flavor PNJL, (b) at μe=40, 2+1-flavor PNJL, (c) at μe=0, 2-flavor PNJL and (d) at μe=40, 2+1-flavor NJL model. s/nB=300,100,30,10,5,3.5 (from left).

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Magnetic field – Magnetar - SS connection • Initial association – to explain the SGR burst intensity -

much larger than Eddington limit Eddington limit does not apply to bare strange star –

self bound Present Scenario: To explain large magnetic field For example – quark phase with pion condensate – carries large

magnetic moment and hance can give magnetized core Bhattacharyya & Soni – astro-ph/0705.0592

Ferromagnetism in quark phase – OGE interactionTatsumi – 2000, Maruyama et al. NPA Other problems exist - High frequency quasi periodic oscillation in giant flares from SGR1806-20

and SGR1900+14 can not be explained by quark star - Watts & Reddy astro-ph/0609364 ATHIC 2012

Origin of magnetic field

Flux conservation • generation of magnetic fluxes earlier in progenitor stars and then

its subsequent trapping inside the compact objects.

• But fields inside a main sequence progenitor may not be enough to yield the needed magnetic field inside a neutron star as the neutron star contains only aound 15% of the progenitor mass

(Spruit ) 2008 (Rudderman 1972; Reisenegger 2001; Ferrario & Wickramasinghe 2005a,b, 2006) .

Dynamo processes • astrophysical dynamo (electric + kinetic = magnetic field)

• Pulsars - rotating and convecting fluid. (Thompson & Duncan 1993) (Duncan & Thompson 1992; Thompson & Duncan 1995, 1996). ATHIC 2012