Stability of quark matter and quark stars

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Stability of quark matter and quark stars
Manuel Malheiro, Fluminense Federal University,
Niterói (RJ, Brazil) André Taurines, Federal
University of Rio Grande do Sul, Porto Alegre
(RGS, Brazil) Manuel Fiolhais, Coimbra
University (Portugal)
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OBJECTIVES

• Study strange quark matter in the framework of
  the chromo-dielectric model with a quartic
  potential
• Investigate quark stars within the model
• Predict properties for such objects (there are
  recent observations of the compact objects as RX
  J1856.5-3754 )

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Outline

• The chromodielectric model (CDM)
• Quark matter
• Application to compact objects (quark stars)

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I - CDM model
Nielsen, Patkós Pirner Banerjee
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Potentials in the CDM
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Dynamical quark mass (after ChSM) mqg fp / c
Parameters of the CDM
g parameter in potential U(c) h parameter
in potential U(c), related to bag constant B ms
0.6 1.2 GeV sigma mass mp 0
pion mass fp 0.093 GeV pion
decay constant M gt 1.2 GeV c mass g
0.023 GeV coupling constant
gu, gd, gs coupling constants for each
flavour (depend on g)
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Nucleon as a soliton in the CDM
Projected hedgehog approach 3 quarks in 1s
state, surrounded by boson clouds (coherent
states)
Radial functions u(r), v(r), c(r), s(r), f(r)
determined variationally
P angular momentum-isospin projector (PY)
Quarks are confined
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Quadratic vs. quartic potential
Best nucleon properties are obtained for quartic
potentials, or for double minimum potentials with
small c (c close to zero).
One free parameter
Nucleon electric form factors
Nucleon magnetic form factors
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II - Strange quark matter in the CDM model
Homogeneous system of u, d, s, quarks (plane
waves), interacting with (constant) s and c
fields plus electrons (plane waves)
Mean field energy density
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Two four self-consistent equations
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For the same set of parameters we found two
distinct solutions
Solution I - chiral broken phase quark
masses are large (Drago, Fiolhais,
Tambini, 1996) Solution II - chiral restored
phase mu , md , ms ? 0 ?u ? ?d ?
?s and ?e ? 0 (almost no electrons)
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EOS
B ? 4 M4
0.08 ? ? ? 0.15 0.150 ? B1/4 ? 0.250 GeV
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I Normal II Nova
e/r (fm-1) vs. r (fm-3)
M1.7 GeV, g0.023 GeV (G0.2 GeV)
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EOS - Pressure vs. energy density
B ? 4 M4 0.150 ? B1/4 ? 0.250 GeV 0.08 ? ?
? 0.15
Similar results already obtained in a
perturbative QCD calculation, E. S. Fraga, R. D.
Pisarski, J. Schaffner-Bielich, Phys. Rev. D63,
121702 (2001)
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III - Quark stars

• Tolman-Oppenheimer-Volkov (TOV) equations

star mass, M star radius, R
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Solution I Hybrid stars

• M ? 1. to 1.6 solar masses, R ? 10 to 12 km and
  a small hadron mantle
• Similar results already obtained by
• Drago, Tambini, Hjorth-Jensen, Phys. Lett. B380,
  13 (1996)

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Solution II pure quark stars
Smaller and denser stars R ? 4 to 7 km, M ?
0.6 to 1.0 solar mass
RX J 1856.5-3754
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• Recent observations of a nearby compact object
  RX J1856.5-3754
• At a distance of 61 pc, the best fit is M 0.9
  solar mass and R 6 km
• J. A. Pons, F. M. Walter, J. M. Lattimer, M.
  Prakash, R. Neuhäuser, P. An, Astrophys. J.564,
  981 (2002)

From NASA press release 02-65, April 10th
2002 NASA's Chandra X-ray Observatory has
found two stars - one too small, one too cold -
that reveal cracks in our understanding of the
structure of matter. These discoveries open a new
window on nuclear physics, offering a link
between the vast cosmos and its tiniest
constituents. Chandra's observations of RX
J1856.5-3754 and 3C58 suggest that the matter in
these stars is even denser than nuclear matter
found on Earth. This raises the possibility these
stars are composed of pure quarks
Chandra X-ray image
http//chandra.harvard.edu/press/02_releases/press
_041002.html
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RX J1856 in Optical Light This optical image of
RX J1856.5-3754 portrays a crowded region of star
formation. In comparison, the Chandra X-ray image
shows that RX J1856 outshines all of the other
sources in the field (Credit European Southern
Observatory Very Large Telescope)
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Conclusions

• Two phases for quark matter in the CDM

• Both are metastable with respect to iron

• CDM yields hybrid stars as well as to pure quark
  stars

• Quark stars with a phenomenology compatible with
  recent observations of compact objects

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