Transcript Document

Nuclear Physics from the sky
Vikram Soni
CTP
Strongly Interacting matter @high
density (> than saturation density)
Extra Terrestrial
From the Sky
No experiments
No Lattice Gauge Theory
From the Sky - Stars
The great Neutron Star(2010) ~ 2 Solar masses
The Binary star :PSR J 1614-2230
*
The strong interaction Ground State : New Physics
Neutron Star is the only laboratory at a High Density ( No
lattice either)
i) The discovery (2010) of a new 2 solar mass binary
neutron star
PSR J 1614-2230 : Mass 1.97 M_solar
ii) Neutron stars with a non relativistic n, p, e exterior
and ( soft ) quark matter interior:
M_max ~1.6 solar mass
Lattimer, J. M. and Prakash,M., 2001, ApJ, 550, 426
Soni, and Bhattacharya,, 2006, Phys. Lett. B, 643, 158
ii) However, we have purely nuclear stars made up of
entirely from n, p, e
which can have : M_max > 2 solar mass ( eg Pandharipande et al)
New Implications for high density strong interactions
Nuclear EOS APR Akmal, Pandharipande, Ravehall ( PhyRevC,58, 1804 (1998)
Quark Matter EOS Soni, and Bhattacharya,, 2006, Phys. Lett. B, 643, 158
THE NUCLEAR EQUATION OF STATE
Going Back to the Akmal, Pandharipande, Ravenhall nuclear phase in in fig 11 of APR ( PRC,58,
1804 (1998)) we find that for the APR [A18 + dv +UIX] the central density of a star of 1.8 solar
mass is ( n_B ~0.62 /fm^3), very close to the initial density at which the phase transition begins.
The reason we are taking a static star mass of 1.8 solar mass from APR ( PRC,58, 1804 (1998)) is that for
PSR -1614 ,the star is rotating fast at a period of 3 millisec and we expect a ~ 15% diminution of the central
density from the rotation( Haensel et al….).
the central density of a fast rotating 1.97 solar mass star ~ the central density of a static 1.8 solar mass star.
Frpm the figure below ,, MAXWELL CONSTRUCTION
.
the common tangent in the two phases starts at , 1/n_B ~ 1.75 fm^3 ( n_B ~0,57/fm^3) in the
nuclear (APR [A18 + dv +UIX]) phase
and ends up at1/n_B ~ 1.25 fm^3 (n_B ~ 0.8/ fm^3) in the quark matter phase (tree level sigma mass
~850 Mev)
If the central density of the star (0.62/fm^3) ~ < density at which the phase transition begins ( n_B
~0,57/fm^3 we can conclude the star is NUCLEAR - Borderline
Effective ( Intermediate) Theory
Chiral sigma model with quarks and pions and sigma and gluons
It plausibly describes quark matter and the nucleon as a soliton with
quark bound states in Mean Field Theory
• One place to find the quark matter phase is in figure 2 of
(Soni, V. and Bhattacharya, D., 2006, Phys. Lett. B, 643,
158)).
• This is based on an effective chiral symmetric theory that
is QCD coupled to a chiral sigma model. The theory thus
preserves the symmetries of QCD. In this effective
theory chiral symmetry is spontaneously broken and the
degrees of freedom are constituent quarks which couple
to colour singlet, sigma and pion fields as well as gluons.
Quark matter and the nucleon
Quark Matter ( already Shown )
Such an effective theory has a range of validity
up to centre of mass energies ( or quark
chemical potentials) of ~ 800 Mev. For details
we refer the reader to (Soni, V. and
Bhattacharya, D., 2006, Phys. Lett. B, 643,
158))
This is the simplest effective chiral symmetric
theory for the strong interactions at
intermediate scale and we use this consistently
to describe, both, the composite nucleon of
quark boundstates and quark matter .
>>
Nuclear Equation of State?
Chiral Quark matter Equation of state
Beyond the Maxwell construction
The Maxwell construction assumes
point particle quark degrees of freedom
and also
point particle nucleon degtees of freedom (APR)
It does not take the structure of the nucleon into account -needed at nucleon
overlap/higher than nuclear density
We need to move to higher resolution
The ‘nucleon’
The ‘nucleon’ in such a theory is a colour singlet quark soliton with
three valence quark bound states ( Ripka, Kahana, Soni)Nucl.
Physics A 415, 351 (1984). The quark meson couplings are set by
matching mass of the nucleon to its experimental value and the
meson self coupling which sets the tree level sigma particle mass is
set from pi-pi scattering to be of order 800 Mev.
Bound Quarks in A Nucleon
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Figure uses
Dimensionless Units : X = R. g fπ
•
The effective radius of the squeezed nucleon at which the bound state
quarks are liberated to the continuum. this translates to nucleon density of
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n_B = 1/(6 R^3) ~ 0.77 fm^{-3}
\
Thus the quark bound states in nucleon persist until a much higher density
~ 0.8/fm^3$ than the density at which the nuclear – quark matter
transition begins (0.57/fm^3) or the maximum central density of the APR
star,(0.62/fm^3) .
• In other words, nucleons can survive well above the density at which
the Maxwell phase transition begins and appreciably above the
central density of the APR 2-solar-mass star.
The binding energy of the quark in the nucleon,.
• E/(g f_pi) = ({3.12/X} N - 0.94. N) + 24 {X/g^2}
•
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Minimizing this with respect to , X
E_{min}/(g f_{\pi}) = \sqrt[3.12 N .24 /g^2 ] - 0.94N
For the nucleon we must set , $N = 3$ .We can now evaluate the coupling,
g, by setting the nucleon mass to $ ~960 MeV $. This yields a value for , $ g
\sim 6.9$.
E_{min/}(N g f_{\pi}) = ~ 0.5 for N = 3\\
~ 0.83 for N =2\\
~ 1.27 for N =1
Binding energy of a quark in the Nucleon
• regardless of the value of $f_\pi $ we have bound states for N =2
and 3.
•
$ g ~\sim 6.9$,
the energy required to liberate a quark from such a nucleon. The
energy of a two quark bound state and a free quark is $1707 $MeV
in comparision to
the energy of a 3 quark bound state nucleon which is , $~962 $ MeV.
• The difference gives the binding energy of the quark in
the nucleon, $ ~ 745 $ MeV.
.T
3)Another feature of the skyrme/ soliton model is the the N-N repulsion
This is an indication that nucleon - nucleon potential becomes strongly
repulsive.
It thus follows that the phase transition from nuclear to quark matter will
encounter a potential barrier before the quarks can go free. This effect
cannot be seen by the coarse Maxwell construction which does not track
their transition.
This will modify the simple minded Maxwell construction which
assumes only the energy and pressure that exist independently
of nucleon structure and binding in the 2 phases. Here is where
the internal structure of the nucleon will delay the transition.
Nuclear Stars
• All in all this produces a very plausible
scenario of how the ~ 2 solar mass star
can be achieved in a purely nuclear
phase.
• Since this high mass is close to the
maximum allowed mass of neutron
stars it means that stars with quark
interiors may not exist at all.
A new idea from this - Phase Diagram of QCD
• At chiral restoration, T_\Xi ~ 150 MeV
• thermal energy in a nucleon of size ~ 1 fermi which is
approximately ~ 250 Mev
• the cost in gradient energy of decreasing the meson VEV 's from $
f _\pi $ at the boundary of a single soliton nucleon to 0 in chiral
symmetry restored value outside of the nucleon over a size of
1 fermi is about 150 Mev
• .
• The sum of these energies is around 350 -400 Mev,
• whereas the binding energy of the quark in such a nucleon is $ \sim
750 Mev,
• indicating that at chiral restoration, T_\Xi ~ 150 Mev, the nucleon
may yet be intact.
Changes the T, µ phase diagram
• At finite but small baryon density and T_\Xi ~ 150
Mev, there may emerge a new intermediate mixed
phase in which nucleons will exist as bound states
of locally spontaneously broken chiral symmetry
(SBCS) in a sea of chirally restored quark matter.
• This is quite the opposite to the popular bag notions
of the nucleon as being islands of restored chiral
symmetry in a SBCS sea.
• CHEERS for Prof Usmani and Lunch