M. Bhuyan
Institute of Theoretical Physics
Chinese Academy of Sciences
Beijing-100190, China P.R
CUSTIPEN-2015
Introduction
Theoretical Formalisms
Relativistic mean field theory
Effective field theory motivated RMFT
Results and Discussions
Normal Nuclear Matter
Neutron Star Matter
Static Neutron Star (SNS)
Rotating Neutron Star (RNS)
Gravitational wave strain amplitude
Summary
According to Einstein's theory of gravity,
an accelerating mass causes the fabric of
space-time to ripple like a pond disturbed
by a rock. These ripples are Gravity
Waves.
http://focus.aps.org/story/v8
This picture represents Gravity Waves
produced by a pair of rotating neutron
stars.
Neutron stars radiate gravitationally in a number of
ways. The most promising scenarios involve:
 Inspiralling Binaries: Post Newtonian approximation
 Supernova core collapse: Violent dynamics
 Rotating compact stars: Shape asymmetry
 Oscilation and Instability: Superfluid core
There are also many other sources for the gravitational wave radiations. ….
The oscillation in the X and Y directions and the wave moves in the
Z direction.
Gravity waves have two polarizations like electromagnetic Waves.
The only difference is that Gravity Wave polarization lies in a
horizontal-vertical “+” shape and 45 degrees to that in a “x” shape.
a. The three US detectors, LIGO, have ofcially reached
their initial design sensitivity.
b. The Anglo-German detector GEO600 is at design
sensitivity at frequencies above 200 Hz.
c. The 6th science run, taking coincident data, began in
November, and will last about 18 months.
d. The Italian-French VIRGO is carrying out engineering
runs, but is getting close to science mode.
People are beginning to get jumpy...
To estimate the gravitational wave strain amplitude , it is
necessary to deal the neutron star fundamental correctly.
a. The structure and dynamics of a neutron star is
governed by the equation of state EoS of the dense
nuclear matter.
b. It is necessary to include other fundamental particles
as a function of density in prediction of nuclear EoS
of the neutron star or compact star.
c. The fundamental properties such as Mass, Radius,
rotational frequency
and elipticity etc. of the
rotating neutron star (RNS).
How to deal all these above properties???
To deal all above these properties, we need a standard
theoretical approach, which can explain the nuclear EoS
correctly.
Mass: 1.97 ± 0.4 M0
MAX υ: 716 Hz
Radius: 10-15 Km


The structure and dynamics of a neutron star is
governed by the equation of state EoS of the dense
nuclear matter
TYPICAL DENSITY: (3 – 10) TIMES NORMAL NUCLEAR
DENSITY. >>
CONSTRAINTS !!!
J. Antoniadis et al., Science 340, 6131 (2013).
Here we have introduced the effective field theory
relativistic mean field model (E-RMF) for the present
analysis. The form of the Lagrangian density expressed as:
Forces
NL3
Linear
σ, ω, ρ σ, ω, ρ
NonLinear
Cross
coupling
σ
G2+Λ
σ, ω
σ-ω,
σ-ρ,
ω-ρ
NL3
S. K. Singh, M. Bhuyan, P. Panda & S. K. Patra, J. Phys. G, 40, 085104 (2013)
M. Bhuyan, R. N. Panda, T. R. Routray & S. K. Patra, Phys. Rev. C 82, 064602 (2010)
The obtained results for the energy density as a function of
baryon for symmetric nuclear matter.
S. K. Singh, M. Bhuyan, P. Panda & S. K. Patra, J. Phys. G, 40, 085104 (2013)
M. Bhuyan, R. N. Panda, T. R. Routray & S. K. Patra, Phys. Rev. C 82, 064602 (2010)
The obtained results for the pressure density as a function
of baryon for symmetric nuclear matter.
S. K. Singh, M. Bhuyan, P. Panda & S. K. Patra, J. Phys. G, 40, 085104 (2013)
To see the variation of pressure and energy density with
respect to density with different constituents.
Nucleaonic Matter
Feed to TOV &
RNS EQUATIONS
NUCLEONS/
HYPERONS/
QUARKS
ε/P
ρ
Schematic diagram for EoS
M. Bhuyan & Shan-Gui Zhou, to be appeared in PRC
Here, we have shown the particle fraction or the Yield
product as a function of baryon density. Here, we have
considered all baryon octet family (n, p, Λ, Σ-, Σ0, Σ+, Ξ- & Ξ0).
M. Bhuyan, S. K. Patra & Shan-Gui Zhou, to be appeared in PRC
To estimate the gravitational wave strain amplitude , it is
necessary to deal the neutron star fundamental correctly.
Is attained when the OUTWARD
neutron
degeneracy
pressure
equal
to
the
INWARD
gravitational potential
The rotation stabilizes the system
as GRAVITATIONAL PULL is
counteracted by the PRESSURE +
CENTRIFUGAL FORCE
G
P
The neutron star mass and radius from E-RMFT for various
force parameters
M. Bhuyan et al., arxiv: 1312.5840, to be appeared in PRC
The realistic approximation that when neutron star is rotating
with static, axial symmetric, space-time, the time translational
invariant and axial-rotational invariant metric in spherical
polar coordinate,
For a perfect fluid, the energy momentum tensor can be given
by
with the four-velocity
The final expression for the maximum rotation i.e. the Kepler
frequency in the relativistic approximation is as,
N. K. Glendenning et al., Phys. Rev. D 50, 3836 (1994); M. Bhuyan et al., arxiv: 1312.5840
The comparison of static and rotating neutron star
properties from E-RMF Model for various forces.
M. Bhuyan et al., arxiv: 1312.5840, to be appear in PRC
The quadrupole moment of a rotating neutron star
depends on the maximum mass M and radius R with a
simple relation,
here σmax is called breaking strain of the crust.
The ellipticity of the rotating neutron star is connected to
the quadrupole moment by a simple relation
The moment of inertia along the z-axis and for
conventional rotating neutron star is given as
M. Bhuyan et al., arxiv: 1312.5840, to be appear in PRC
The maximum rotational frequency of the stable
rotationary neutron star can be given by the simple
relation
Finally, using these above calculated quantities, we can
estimate the gravitational wave strain amplitude,
a. Neutron stars are the natural laboratories to
understand cold dense matter interaction and their
compositions.
b. Hyperons constitutes a sizable population in dense
matter, where the –ve charged particles are more
favored over natural & +ve charged particles.
c. The estimation of gravitational wave strain amplitude
from rotating neutron / compact star is one step ahead
in the nuclear matter study.
d. Neutron stars are a promising candidate for
gravitational wave generation We are involved in a
variety of efforts to detect them and can give insight
into other fields of physics.
Shan-Gui Zhou, ITP-CAS, Beijing, China
S. K. Patra, Institute of Physics, India
S. K. Singh, Institute of Physics, India
X. Vi˜nas, University of Barcelona, Spain
Raj K. Gupta, Punjab University, India
P. Arumugam, Indian Institute of Technology, India
Thanks for your kind
attentions and welcome
for discussions
CUSTIPEN-2015