Article

Quark Stars as inner engines for Gamma Ray Bursts?

Astronomy and Astrophysics (Impact Factor: 4.38). 03/2001; 387(2). DOI: 10.1051/0004-6361:20020409
Source: arXiv
ABSTRACT
A model for Gamma ray bursts inner engine based on quark stars (speculated to exist in nature) is presented. We describe how and why these objects might constitute new candidates for GRB inner engines. At the heart of the model is the onset of exotic phases of quark matter at the surface of such stars, in particular the 2-flavor color superconductivity. A novel feature of such a phase is the generation of particles which are unstable to photon decay providing a natural mechanism for a fireball generation; an approach which is fundamentally different from models where the fireball is generated during collapse or conversion of neutron star to quark star processes. The model is capable of reproducing crucial features of Gamma ray bursts, such as the episodic activity of the engine (multiple and random shell emission) and the two distinct categories of the bursts (two regimes are isolated in the model with \sim 2 s and \sim 81 s burst total duration). Comment: 8 pages, 3 figures, new and more appropriate title. Major changes in the text (aspects of the models discussed in more details), better quality Figure 1 and Figure 2 and added Figure 3, version to appear in Astronomy&Astrophysics

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Available from: Francesco Sannino, Nov 17, 2012
arXiv:astro-ph/0103022v3 20 Mar 2002
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Quark Stars as inner engines for Gamma Ray Bursts?
Rachid Ouyed and Francesco Sannino
Nordic Institute for Theoretical Physics, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
Received/Accepted
Abstract. A model for Gamma ray bursts inner engine based on quark stars (speculated to exist in nature) is
presented. We describe how and why these objects might constitute new candidates for GRB inner engines. At
the heart of the model is the onset of exotic phases of quark matt er at the surface of such stars, in particular the
2-flavor color superconductivity. A novel feature of such a phase is the generation of particles which are unstable
to photon decay providing a natural mechanism for a fireball generation; an approach which is fundamentally
different from models where the fireball is generated during collapse or conversion of neutron star to quark star
processes. The model is capable of reproducing crucial features of Gamma ray bursts, such as the episodic activity
of the engine (multiple and random shell emission) and the two distinct categories of the bursts (two regimes are
isolated in the model with 2 s and 81 s burst total duration).
Key words. dense matter Gamma rays: bursts stars: interior
1. Introduction
A central problem contributing to the Gamma -ray bursts
(GRBs) mystery is the unknown nature of the engine pow-
ering them (Kouveliotou et al. 1995; Kulkarni et al. 1999;
Piran 1999a; Piran 1999b). Ma ny have been suggested but
it is fair to say that we are still fa r from a definite an-
swer. Regardless of the nature of the engine, however, it is
widely accepted that the most conventional interpretation
of the observed GRBs result from the conversion of the ki-
netic energy of ultra-relativistic particles to radiation in
an optically thin region. The particles being accelerated
by a fireball mechanism (or explosion of radiation) taking
place near the central engine (Goodman 1986; Shemi &
Piran 1990; Paczy´nski 1990).
The firs t challenge is to conceive of circumstances that
would create a sufficiently energe tic fireball. Conversion of
neutron s tars to quark stars (Olinto 1987; Cheng & Dai
1996; Bombaci & Datta 2000) has been sug gested as one
possibility. Other models also involve the compact object
element; such as black holes (Blandford & Znajek 1977)
and coalescing neutron stars (Eichler et al. 1989; Ruffert
& Janka 1999; Janka et al. 1999). We show in this work
that the plausible existence of quark stars combined with
the onset of a newly revived state of quark matter - called
color superconductivity - in these objects offers a new way
of tackling the GRB puzzle (Ouyed 2002). Here we will
argue that quar k sta rs might constitute new candidates
for GRB inner engines.
Send offprint requests to: ouyed@nordita.dk
Quark matter at very high density is expected to be-
have as a color superc onductor (see Raja gopal & Wilczek
2000 for a review). Associated with superconductivity is
the so-called gap energy inducing the quark-quark pair-
ing and the critical temperature (T
c
) above which thermal
fluctuations will wash out the s uper conductive state. A
novel feature of such a phase is the generation of glueball
like particles (hadrons made of gluons) which as demon-
strated in Ouyed & Sannino (2001) immediately decay
into photons. If color superc onductivity se ts in at the sur-
face of a quark star the glueball decay b ecomes a na tur al
mechanism for a fireball generation.
The paper is presented as follows: In Sect. 2 we briefly
describe the concept of color sup e rconductivity in quark
matter. Glueball formation and their subsequent two-
photon dec ay is described. Sect. 3 deals with quark stars
and the onset of color sup e rconductivity at their surface.
In Sect. 4, we explain how GRBs are powered in this pic-
ture and show that variability (multiple s hell emission) is
inherent to the inner engine. We isolate two GRB regimes
in Sect. 5 associated with sma ll and massive quark stars.
The model’s features and its predictions are summarized
in Sect. 6 while a discus sion and conclusion fo llows in Sect.
7 where the model’s assumptions and limitations are high-
lighted.
2. Color Superconductivity
While in this paper we deal mostly with the astrophysics
aspect of the model, we nevertheless give a brief overview
of color superco nductivity and the glueball-to-photon de-
Page 1
2 Rachid Ouyed and Francesco Sannino: Quark Stars as inner engines for Gamma Ray Bursts?
Fig. 1. A schematic representation of a possible QCD
phase diagram (Rajagopal & Wilczek 2000). At high tem-
perature and density, matter is believed to be in a quark-
gluon plasma phase (QGP). The hadronic pha se lies in
the region of low temperature and density. At very high
density but low temperature, when nuclei melt into each
other, it has been suggested that a color superconductive
phase might set in. 2 SC denotes a 2-flavor color super-
conductive regime. The arrow depicts a plausible cooling
path of a HQS surface leading to the onset of color super-
conductivity.
cay proc e ss which leads to the fireball. The interested
reader is referred to Ouyed & Sannino (2001) for the un-
derlying physics. For a recent review see Sannino (2002)
2.1. 2-flavour color superconductivity
A reasonable Q uantum Chromo-Dynamics (QCD) phase
diagram (in the µT plane, where µ is the chemical poten-
tial simply related to matter density) is shown in Fig. 1.
At high temperature and density, matter is believed to
be in a quark-gluon plasma phas e (QGP). The hadronic
phase lies in the region of low temperature and density. At
high densities but low temperatur e s, when nuclei melt into
each other, it is now believed that a color superconductive
phase sets in. This phase is characterized by the formation
of quark- quark condensate. In the 2- flavor color supercon-
ductivity (2SC) the up and down quark come into play
during pairing. Furthermore, 2SC is characterized by five
out of the eight gluons acquiring mass. We refer the inter-
ested reader to Rajagopal & Wilczek (2000) for a review
of the dynamical properties o f 2SC.
2.2. Light G lueBalls
The 3 mas sless gluons in the 2SC phase which bind into
light glueballs (LGBs) to gether with the quarks up and
down constitute the 2SC phas e mixture. In Ouyed &
Sannino (2001) we studied certain properties o f these
LGBs. Among the properties rele vant to our present study
we found, i) The LGBS decay into photons with an asso-
ciated lifetime of the order of 10
14
s; ii) The mass of the
LGBs is of the order o f 1 MeV.
3. Quark stars
We now turn to study the astrophysical consequences
when such a state sets in at the surface of quark stars.
As such, we fir st assume that quark stars exists in nature
(further discussed in Sect. 7.1) and c onstitutes the first
major assumption in our model.
3.1. Hot Quark s t ars
We are concerned with quark stars born with surface tem-
peratures above T
c
. We shall refer to these stars as hot”
quark stars (HQSs) in order to avoid any confusion with
strange stars which are conjectured to exist even at zero
pressure if strange matter is the a bsolute ground state of
strong interacting matter rather than iron (Bodmer 1971;
Witten 1984; Haensel et al. 1986; Alcock et al. 1986; Dey
et al. 199 8).
We borrow the language of the MIT-bag model for-
malism at low temperature and high density to describe
HQSs (Farhi & Jaffe 1984). This gives a simple equation
of state
P = b(ρ ρ
HQS
)c
2
, (1)
where b is a constant of model-dependent value (close to,
but generally no t equal, to 1/3 of the MIT-bag model),
and ρ
HQS
is the density at ze ro-press ure (the star’s surface
density). We should keep in mind that T
c
1 as is
confirmed later.
Features of HQSs are - to a leading order in T
c
- iden-
tical to that of strange stars. The latter have been studied
in details (Alcock et al. 198 6; Glendenning & Weber 1992;
Glendenning 1997). Of impor tance to our model:
i) The “sur fa c e of a HQS is very different from the sur-
face of a neutron star, or any other type of stars. Because
it is bound by the strong force, the density at the surface
changes abruptly from zero to ρ
HQS
. The abrupt change
(the thickness of the quark s urface) occurs within about
1 fm, which is a typical strong interaction length scale.
ii) The electrons being b ound to the quark matter by
the electro-magnetic interaction and not by the str ong
force, are able to move freely across the quark surface
extending up to 10
3
fm above the surface of the star.
Associated with this electron layer is a strong electric field
(5 × 10
17
V/cm)- higher than the critical value (1 .3 × 10
16
V/cm) to make the vacuum region unstable to sponta-
neously create (e
+
, e
) pairs.
iii) The presence of normal matter (a crust made of
ions) at the surface of the quark star is subject to the enor-
mous elec tric dipole. The strong positive Coulomb barrier
prevents a tomic nuclei bound in the nuclea r crust from
coming into direct contact with the quark core. The crust
is suspended above the vacuum r e gion.
iv) One can show that the maximum mass of the crus t
cannot exceed M
crust
5 × 10
5
M
set by the require-
ment that if the density in the inner crust is above the neu-
tron drip density (ρ
drip
4.3 × 10
11
g/cc), free neutrons
will gravitate to the surfac e of the HQS and be converted
Page 2
Rachid Ouyed and Francesco Sannino: Quark Stars as inner engines for Gamma Ray Bursts? 3
to quark matter. This is due to the fact that neutrons
can easily penetra te the Coulomb barrier a nd are rea dily
absorbed.
3.2. Cooling and 2SC layer formation
The HQS surface layer might enter the 2SC phase as illus-
trated in Fig. 1. In the QCD phase diag ram (Fig. 2), (ρ
B
0
,
T
B
0
) is the critical point beyond which one re- e nters the
QGP phase (the extent of the 2SC layer into the star). The
star co ns ists of a QGP phas e surro unded by a 2SC layer
where the photons (from the LGB/photon decay) leaking
from the surface of the star provides the dominant cooling
source. This picture, as illustrated in Fig. 2, is only valid if
neutrino cooling in the 2SC phase is heavily suppressed as
to become slower than the photon cooling. Unfortunately,
the details of neutrino cooling in the 2SC phase is still a
topic of debate and studies (Carter & Reddy 2000; Schaab
et al. 2000 to cite only few). One can only assume such
a scenario which constitutes the second major assump-
tion in our model. In Sect. 7.2, we discuss the remaining
alternative when pho ton cooling is dwarfed by neutrino
cooling.
3.3. LGBs decay and photon thermali zation
The photons from LGB decay are generated at energy
E
γ
< T
c
and find themselves immersed in a degener-
ate quark gas. They quickly gain energy via the inverse
Compton process and b ecome thermalized to T
c
. We es-
timate the photon mean free path to be smaller than few
hundred Fermi (Rybicki & Lightman 1979; Long air 1992)
while the 2SC layer is measur e d in meters (see Sect. 5.2).
A local thermodynamic equilibrium is thus reached with
the photon luminosity given by that of a black b ody radi-
ation,
L
γ
= 3.23 × 10
52
ergs s
1
(
R
HQS
5 km
)
2
(
T
c
10 MeV
)
4
. (2)
The energy for a single 2SC event is thus
E
LGB
= δ
LGB
M
2SC
c
2
, (3)
where M
2SC
= δ
2SC
M
HQS
is the portion o f the star in
2SC. Here, δ
2SC
depends on the star ’s mass while δ