Massive compact stars

Physics department, South China University of TechnologyDehua Wen

2016.6 Beijing

OutlineI. Background

II. The discrepancy between the EOSsand the observations

III. The mechanism to support massivecompact stars by soft EOS

I. Background

Neutron star： a gold mine for the study of physicalphenomena including particle physics, nuclear physics,astrophysics and general relativity.

Nature 467, 1081 (2010)；Science 341, 365 (2013)；Science 340,(2013)；Nature 514,202 (2014)；Nature 505, 520 (2014)； NaturePhysics 10, 116(2014)； Nature 505,62(2014)； Science 346, 614(2014); Nature, 523, 189 (2015)； Nature, 531, 202 (2016).

（A） NEUTRON STARS

1. The outermost surface of the neutron star contains a very thinatmosphere of only a few centimeters thick that is composed ofHydrogen, but may also contain heavier elements such as Helium andCarbon.

2. Just below the atmosphere lies the 100m thick envelope that actsas “blanket” between the hot interior (with T ×108 K) and the “cold”surface (with T × 106 K). (outer crust)

3. Further below lies the non-uniform crust, a 1 km region that isbelieved to be involved in pulsar glitches—the sudden increase inrotational frequency of the star. (inner crust)

4. Below the non-uniform crust sits a uniform liquid core thatconsists of neutrons, protons, electrons, and muons. The core accountsfor practically all the mass and for about 90% of the size of a neutronstar. There is also a possibility of an inner core made of exotic particles,such as hyperons, meson condensates, and quark matter

J. Piekarewicz, arXiv:1311.7046v1

Basic Structure

Equation of states (EOS) of neutron star matters

•If the composition and the interaction of the matters in neutronstar core are determined (not certain yet), the relation betweenpressure p and energy density ε (e.g. EOS) can be determined.

APJ, 550(2001)426

EOS and M-R Relations

A large sample of proposed equations of state calculated under different physical assumptions.

1603.02698v1

—— the general relativistic equations of hydrostatic equilibrium

Basic Structure Equations

(TOV Eqs.)

white dwarf (WD)： another kind of compact stars.

• Chandrasekhar set a famous mass limit for the white

dwarf——the mass of a white dwarf cannot exceed

1.44M ⊙. This limit is obtained from the fact that in a

white dwarf the inward gravitational force is balanced by

the outward pressure produced by the degenerate

electrons.

(B) White Dwarfs

• Accelerated expanding Universe was established through

the observations of SNeIa (2011 Nobel prize).

arXiv:1411.1515v1

• Ia supernovae (SNeIa): the violent thermonuclear

explosion when the mass of an accreting WD in a binary

system approaches the Chandrasekhar limit of 1.44M⊙.

This character can be used as standard candles in

measuring cosmic distances.

New observations for the massive compact stars

For neutron stars:

• PSR J1614+2230: 1.97± 0.04 M⊙,

• PSRJ0348+0432: 2.01± 0.04 M ⊙;

For white dwarfs:

• The progenitors of Ia supernovae SN2003fg, SN2006gz,

SN2007if and SN2009dc: in a range of 2.1M ⊙ ~ 2.8M ⊙

Nature 467, 1081 (2010)

Science 340: 448 (2013)

Nature 443, 308 (2006); Astrophys. J. 713, 1073 (2010).

Most of the observed NSs with masses around 1.4M⊙

Most of the observed WDs with masses below 1M⊙

• The classical equation of state (EOS) of white dwarf and many of theEOS of neutron star matters are not stiff enough to support a WD/NSwith a mass over 2.8M ⊙.

• These situations promote a discrepancy between the compact starobservations and the theories of the compact star matters.

Super strong B

Normal EOS

White dwarf

PRL 110, 071102 (2013)Nature 467, 1081 (2010).

II. The discrepancy between the EOSs and the observations

For neutron stars:

• Theoretically, hyperons ( or Kaon condensates, or quark matters)might be present in the core of neutron stars, and the appearance ofnew particles will results in the softening of matters. For example,the contribution to the pressure from energetic nucleons is replacedby that of the slowly-moving, massive hyperons .

• As to the unconfined quark matters, if a higher bag constant ispreferred (such as B1/4 = 170 MeV) in the MIT bag model, the EOSof the quark matter is also soft.

Glendenning N K, Moszkowski S A. Phys Rev Lett, 1991, 67: 2414.

J. Xu, L.W. Chen, C.M. Ko, B.A. Li, Phys. Rev. C 81 (2010) 055803.

Glendenning N K, Moszkowski S A. Phys Rev Lett, 1991, 67: 2414.

J. Xu, L.W. Chen, C.M. Ko, B.A. Li, Phys. Rev. C 81 (2010) 055803.

III. The mechanism to support massive compact stars by soft EOS

1. Non-Newtonian gravity

Wen D H, Li B A, Chen L W， Phys Rev Lett, 2009, 103: 211102

( ) ( )2 2

21 2 1 2 2

1 1 2 4 2

r

UBg e gx x dx dx

V r

µ

ρ ρ ρπ

εµ

−

= =∫ 2 2 2/ 2UBP g ρ µ= （ ）

( )2 2/ 4 bg Gmα π= ±

( )/1 2( ) 1 rGm mV r er

λα −= − +

1/λ µ=

For neutron stars:

2. Electrically charged

Einstein-Maxwell stress-energy tensor:

charged TOV equations

Modelling the charge distribution:

where ρq is the charge density, k is proportionality factor, Mp is the mass of a proton, e is the charge of an electron/proton.

where k0 is the charge fraction, a is a constant describing the width of the Gaussian.

Equation of state (EOS) and mass-radiusrelation for the uncharged hybrid stars,where the EOS is taken from J. Xu, et al.,PRC 81 (2010) 055803 with B1/4 = 170MeV.

The mass-radius relations for the charge

distributing as and the

corresponding total charge

Jing Z Z, Wen D H, Zhang X D. Sci China-Phys Mech Astron, 2015, 58: 109501

3. EIBI gravity

41 2= ( ) ,16 M MS d x g R g S gµν µνκ λπ κ

− + − − + Ψ∫

3

223(2 )

4dm c a rdr G abbκ

= + −

2 2 3 3 2

2 2 2 2 2 2 2 2

( )[(1 2 )(1 2) 2 ](1 2 )[4 3 ( ) ( ) ]q

db ab a b ab a b r Gm cdr r Gm c r ab a a b b a b c

κ− + − +=

− + − − −

generalized TOV equations

PRL 105, 011101 (2010)；PRL 107, 031101 (2011); PRL 109, 021101 (2012)PHYSICAL REVIEW D 85, 084020 (2012); PHYSICAL REVIEW D 86, 064015 (2012); PHYSICAL REVIEW D 88, 044032 (2013); PHYSICAL REVIEW D 87, 061503(R) (2013)

action:

αβγΓ

λ is related to cosmological constant as Λ=(λ-1)/κ, normally λ=1

matter actionnew

The mass-radius relations for the EIBI gravity.

1. Electrically charged

Liu H.L., Zhang X.D. and Wen D.H., PRD 89, 104043 (2014)

In the Newtonian framework:

the hydrostatic equilibrium equation

charge distribution

For white dwarfs:

Liu H.L., Zhang X.D. and Wen D.H., PRD 89, 104043 (2014)

The charge density and the total charge as functions of radius

The mass-radius relations of thecharged white dwarf. The insetshows the equation of state of freeelectron gas.

2. EIBI gravity

Kepler frequency - the stellar mass

Mass-radius

CHIN. PHYS. LETT. 33. 5 (2016) 050401

Future work

• Considering the noncommutativity effect in compact stars;

• Considering the lighter dark matter particles in compact stars.

SummaryThe mechanism to support massive compact stars by soft EOS:

• For neutron stars:

1. Non-Newtonian gravity2. Electrically charged3. EiBI gravity

• For white dwarfs:

1. Electrically charged2. EiBI gravity

Thanks!

• Non-Newtonian Gravity and weakly interacting light boson

1. E. G. Adelberger et al., Annu. Rev. Nucl. Part. Sci. 53, 77(2003).2. M.I. Krivoruchenko, et al., hep-ph/0902.1825v1

The inverse square-law (ISL) of gravity is expected to be

violated, especially at less length scales due to either the

geometrical effect of the extra space-time dimensions predicted

by string theories and/or the exchange of the weakly interacting

bosons newly proposed in the super-symmetric extension of the

standard model.

In stable neutron stars, the gravity has to be balanced by the

strong interaction. Neutron stars are thus provided a natural

testing ground for the non-Newtonian gravity.

The deviation from the Inverse-Square-Law of gravity can be characterizedeffectively by adding a Yukawa term to the normal gravitational potential

In the scalar/vector boson (U-boson ) exchange picture,

Within the mean-field approximation, the extra energy density andthe pressure due to the Yukawa term is

E. G. Adelberger et al., Annu. Rev. Nucl. Part. Sci. 53, 77(20

and

Hep-ph\0810.4653v3

PRL-2005,94,e240401 Hep-ph\0902.1825

Constraints on the couplingstrength with nucleons g2/(4π)and the mass μ (equivalently αand λ) of hypothetical weaklyinteracting light bosons.

Constraints on the coupling strength by the stability and observed global properties of neutron stars