Quark Matter in

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Eighth International Conference on STRANGENESS
IN QUARK MATTER Cape Town, South
Africa, September 15 - 20, 2004
Quark Matter in Compact Stars
Ignazio Bombaci
Dipartimento di Fisica "E. Fermi" Università di
Pisa
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Plan of the talk
Why strangeness is expected in Neutron
stars(compact stars) ? Confined form of
strangeness Hyperons, Kaons Deconfined
form of strangeness Strange Quark Matter
Role of strangeness on the bulk properties of
Neutron Stars
Astrophysical implications of strangeness in
Compact Stars existence of two families of
Neutron Stars pure
hadronic stars quark
stars, Quark-Deconfinement Nova ? engine
for GRBs bimodal nature of the kick
velocity distribution of radio PSRs
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Neutron Stars or Hyperon Stars

• Why is it very likely to have hyperons in the
  core of a Neutron Star?
• The central density of a Neutron Star is high
  ?c ? (4 8)
  ?0 (?0 0.17 fm-3)
• The nucleon chemical potentials increase very
  rapidly as function of density.

Above a threshold density (?c ? (2 3) ?0 )
hyperons are created in the stellar
interior.
A. Ambarsumyan, G.S. Saakyan, (1960)
V.R. Pandharipande
(1971)
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Baryon chemical potentials in dense hyperonic
matter
I. Vida
I. Vidaña, Ph.D. thesis (2001)
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Microscopic EOS for hyperonic matter extended
Brueckner theory
V is the baryon--baryon interaction for the
baryon octet (n, p, ?, ?-, ?0, ?, ?
-, ? 0 ) (e.g. the Nijmegen potential).
? Energy per baryon in the BHF approximation
Baldo, Burgio, Schulze, Phys.Rev. C61 (2000)
055801
Vidaña, Polls, Ramos, Engvik,
Hjorth-Jensen, Phys.Rev. C62 (2000) 035801
Vidaña, Bombaci, Polls, Ramos, Astron.
Astrophys. 399, (2003) 687.
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?-stable hadronic matter

• Equilibrium with respect to the weak interaction
  processes

• Charge neutrality

For any given value of the total baryon number
density nB
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The Equation of State of Hyperonic Matter
The presence of hyperons produces a softening in
the EOS
NSC97e
I. Vidaña et al., Phys. Rev C62 (2000) 035801
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Structure equations for compact stars
Hydrostatic equilibrium in General
Relativity Tolman Oppenheimer Volkov
equations (TOV)
Boundary conditions
m(r0) 0 P(rR) Psurf
R stellar radius
The solutions of the TOV eq.s depend
parametrically on the central density ?c
?(r0)
P P(r, ?c ) m m(r, ?c )
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Composition of hyperonic beta-stable matter
Baryon number density ?b fm-3
Particle fractions
Hyperonic Star MB 1.34 M?
I. Vidaña, I. Bombaci, A. Polls, A. Ramos,
Astron. and Astrophys. 399 (2003) 687
Radial coordinate km
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Composition of hyperonic beta-stable matter
Baryon number density ?b fm-3
Particle fractions
Hyperonic Star MB 1.34 M?
Hyperonic core
NM shell
crust
I. Vidaña, I. Bombaci, A. Polls, A. Ramos,
Astron. and Astrophys. 399 (2003) 687
Radial coordinate km
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M. Baldo, G.F. Burgio, H.-J. Schulze, Phys.Rev.
C61 (2000)
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PSR B191316
M. Baldo, G.F. Burgio, H.-J. Schulze, Phys.Rev.
C61 (2000)
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Measured Neutron Star Masses
Mmax ? 1.44 M?
very soft EOS are ruled out
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GM3 EOS Glendenning, Moszkowsky, PRL
67(1991) Relativistic Mean Field Theory of
hadrons interacting via meson exchange
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Hyperons in Neutron Stars implications for the
stellar structure
The presence of hyperons reduces the maximum
mass of neutron stars ?Mmax ? (0.5 0.8)
M? Therefore, to neglect hyperons always leads
to an overstimate of the maximum mass of neutron
stars
Microscopic EOS for hyperonic matter very
soft EOS non compatible with measured NS
masses.
Improved NY, YY two-body interaction Three-body
forces NNY, NYY, YYY
Need for extra pressure at high density
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Strange quark matter in Neutron Stars
QCD Ultra-Relativistic
Heavy Ion
Collisions
Quark-deconfinement phase transition expected
at ?c ? (3 5) ?0
The core of the most massive neutron stars is one
of the best candidates in the Universe where such
a deconfined phase of quark matter can be found

• Hybrid Neutron Stars
• Strange Stars (Bodmer-Witten hypotesis for
  SQM)

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Neutron Stars
traditional Neutron
Stars
Hadronic Stars
Hyperon Stars
Hybrid Stars
Quark Stars
Strange Stars
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Hybrid Star
GM3Bag model ms150 MeV,
B13.6.6Mev/fm3
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Hybrid Star
Pure quark matter core
Mixed hadron-quark phase
crust
NM shell
GM3Bag model ms150 MeV,
B13.6.6Mev/fm3
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The EOS for Hybrid Stars

• Hadronic phase Relativistic Mean Field
  Theory of hadrons interacting via meson exch.
  e.g. Glendenning, Moszkowsky, PRL 67(1991)
• Quark phase EOS based on the MIT bag model
  for hadrons. Farhi, Jaffe, Phys. Rev.
  D46(1992)
• Mixed phase Gibbs construction for a
  multicomponent system with two conserved
  charges. Glendenning, Phys. Rev. D46 (1992)

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Strange Quark Matter in compact stars and Gamma
Ray Bursts
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Gamma Ray Bursts (GRBs)

• Spatial distribution isotropic
• Distance cosmological d (1 10) 10 9 ly
• Energy range 100 keV a few MeV
• Emitted energy 10 51 erg (beamed / jets)
  J.S. Bloom,
  D.A. Frail, S.R. Kulkarni, ApJ 594, 2003
• Duration 1 300 s
  Two different types short GRBs
  and long GRBs

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NATURE, vol. 423, 19 june 2003
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SN GRB connection
Evidence for atomic lines in the spectra of the
X-ray afterglow
time delay ?T between the SN expl. and the GRB

• GRB 990705 ?T ? 10 yr
  Amati et al., Science 290, 2000, 953
• GRB 030227 ?T ? 3 80 days
  Watson et al., ApJ 595, 2003, L29
• GRB 030813 ?T ? 2 months
  Butler et al. ApJ 597, 2003, 1010
• GRB 011211 ?T ? 4 days
• Reeves et al. , Nature 2002

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A two-step scenario
1st explosion Supernova
(birth of a NS) 2nd explosion (ass.
with the NS)
central engine of the GRB

• What is the origin of the 2nd
  explosion ?
• How to explain the long time delay between
  the two events?

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The delayed collapse
of an Hadronic Star to a Quark Star

• pure Hadronic Star
  Quark Star
• The conversion process can be delayed due to
  the effects of the surface tension between the
  H-phase and the Q-phase.
• The nucleation time depends dramaticaly on the
  central pressure of the Hadronic Star
• As a critical-size drop of QM is formed the HS
  is converted to a QS (HyS or SS)
• The conversion process liberates Econv 10
  52 10 53 erg
• Central engine for a GRB.

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Supernova-GRB connection the
Quark-Deconfinement Nova model
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Hadron-Quark phase transition in bulk matter
In bulk matter the H-Q phase transition
begins at the static transition point
defined according to the Gibbs criterion
for phase equilibrium
?H ?Q ? ?0 P(?H) P(?Q) ? P(?0)
? P0 TH TQ ? T (T 0, we consider cold
matter)
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Finite size effects on the H-Q phase transition
The formation of a critical-size drop of QM is
not immediate ?P P P0

overpressure with respect to the
static transition point P0
Quantum nucleation of a drop of QM in HM at T
0 I.M. Lifshitz and Y. Kagan, 1972

K. Iida and K. Sato, 1998 For more details
see talk by Isaac Vidaña


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Potential energy barrier between
the metastable
hadronic phase and the quark phase
U(R) (4/3)? R3 nQ (?Q - ?H ) 4?? R2
av(P) R3 asR2
log(?/sec)
P2 gt P1 gt P0
Pres.
The nucleation time depends dramaticaly on the
value of the Hadronic Stars
central pressure (on the HS mass)
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The critical mass of metastable Hadronic Stars
Def. Mcr MHS(?1yr)
HS with MHS lt Mcr are metastable
with ? 1 yr ? The accretion of
Maccr ? 0.01 M? reduces the HS
mean-life time ? gtgt age of the
Universe ? ? a few years
HS with MHS gt Mcr are very unlikely to
be observed The critical mass Mcr plays
the role of an effective maximum mass for the
hadronic branch of compact stars
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Hadronic Stars nucleons hyperons
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Total energy released in the stellar conversion
Assuming that the stellar baryonic mass is
conserved during the stellar conversion the total
energy released in the process is Econv Mcr
MQS(Mbcr)
I.B., B. Datta, 2000, ApJ 530, L69
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Total energy released in the stellar conversion

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The kick velocity of neutron stars
A new born neutron star receives a considerable
kick during (or shortly after) the SN
explosion. (Lai,
Chernoff, Cordes, 2001, ApJ, 549)
From obseravtional data one infers
Vkick
(100 1000) km/s Lyne, Lorimer, 1994, Nature,
369, 127 Lorimer et al.,
1997, Mont. Not. Royal Astr. Soc., 289, 592 Hobbs
et al., 2003, astro-ph/0309219
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A possible explanation the hydrodynamical kick
model
asymmetry in the Supernova explosion
(matter or/and neutrino jets)
Vkick
NS
NS
Progenitor star
SN explosion
SN remnant after a few (103 104) yr
In the progenitor stars rest reference frame
(figure panels not in the same scale)
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Vkick
?

V?
s
d
PSR
?
SNR G292 / PRS J1124-59
observer
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The velocity distribution of isolated radio PSRs
Bimodal distribution! (two maxwellian
distributions)
?1 90 km/s ?2 500 km/s w1 0.4
Arzoumanian, Chernoff, Cordes, 2002, ApJ 568
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The velocity distribution of isolated radio PSRs
The bimodal nature of the kick velocity
distribution of radio PSRs could be connected
with the dichotomy between Hadronic Stars and
Quark Stars
Hadronic Stars one natal kick during the SNE
Quark Stars second kick during
the HS ? QS conversion
I.B., S. Popov, 2004, AA, 424, 627
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The second kick in the QDN model
?E energy unbalance between
the ?-ray two jets
?E ?E? ? ? Econv ?P ?E/c Vkick/c
?E /(MNSc2)
Assuming ? 0.1 ? ?E 1050 --
1051 erg Vkick a few (10 102) km/s
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Conclusions (of the last part of the talk)
M
QS
Metastable HS
GRB
R

• Neutron stars (HS) are metastable to
  HS ? SS or to HS ?
  HyS the HS mean-life time range
  within ? gtgt age univ. ? ? yr-days
• Econv 1052 1053 erg
  GRBs
• Our model explains the SN-GRB connection and
  the time delay ?T(SN-GRB) days --
  years or nearly simultaneus events
  (SN2003dh GRB030329)

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• Implications of our scenario
  existence of two different families of
  compact stars
• pure Hadronic Stars (metastable)
  which could have large radii (R 12
  15 km), as e.g., 1E
  1207.4-5209
• (2) Strange Stars or Hybrid Stars
  with small radii (R 7 9
  km), as e.g.,
  SAX J1808.4-3658 (X-D. Li et al, PRL 83,
  1999)

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Collaborators
Z. Berezhiani (LN Gran Sasso, INFN)
A. Drago (Univ.di Ferrara)
F. Frontera (Ist.
TESRE CNR, Bologna) A. Lavagno
(Politecnico di Torino)
Ref. Z. Berezhiani, I.B., A. Drago, F. Frontera,
A. Lavagno,
2003, Astrophys. J., 586, 1250
I. Parenti (Univ. Pisa now at Univ. Ferrara)
I. Vidaña (INFN, sez. di Pisa
now at GSI, Germ.)
Ref. I.B., I. Parenti, I. Vidaña, 2004,
Astrophys. J., 614 (in press october 10, 2004)
S.B. Popov (Sternberg Astronomical Institute,
Moscow)
Ref. I.B., S.B. Popov, 2004, AA, 424, 627