A Compact Binary Merger Model for the Short, Hard GRB 050509b Page: 4 of 4
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Lee, Ramirez-Ruiz & Granot
v > max(v,,, v,) which is above 300 keV at 20 ms. This results
in overproducing the flux at 200 s by a factor of ~ 10-20 for
p = 2.5. The observed flux is reproduced for p ~ 2.8. Alter-
natively, lower values of p might still be possible if, e.g., there
are significant radiative losses or a much higher EB in the very
early afterglow.
4. DISCUSSION AND PROSPECTS
From the inferred energy per solid angle, simple blast-wave
models seem able to accommodate the data on the afterglow
of GRB 050509b. Constraints on the angle-integrated --ray
energy are not very stringent - the outflow could be con-
centrated in a high Lorentz factor beam only a few degrees
across, or actually be wider. Standard arguments concerning
the opacity of a relativistically expanding fireball (Paczynski
1986) indicate that Lorentz factors F > 102 are required, with
a baryon loading no larger than ~ 10-4M. As we have ar-
gued in 3.1, for GRB 050509b internal shocks face the prob-
lem of explaining the observed peak energy. With an external
shock, the required Lorentz factor is high by usual standards,
and such accelerations would accordingly require a remark-
ably low baryon loading close to the central engine.
Only detailed numerical simulations in full GR will pro-
vide us with the details of the merger process in a compact
binary. However, an approximate treatment using variable
compressibility in the equation of state and a range of mass
ratios frequently leads to similar outcomes, suggesting that
the creation of a dense torus is a robust result. If the central
engine involves such a configuration, is it possible to discrim-
inate between the alternate modes for its formation: compact
merger or collapsar? Accurate localizations of further events
should help to confirm or reject the latter option, since a col-
lapsar would occur in or near a region of recent star forma-
tion, contrary to the expectations concerning compact object
mergers (see 1). A more direct test would obviously be
a detection, or lack thereof, of a supernova-like signature4
(Bloom et al. 2005; Hjorth et al. 2005). Definitive and spec-
tacular confirmation could come from the detection of a coin-
cident gravitational wave signal in the 0.1-1 kHz range, since
mass determinations in X-ray binaries and the binary pulsars
4 It is important to note that the natural time scale for a collapsing envelope
to produce a GRB is given by the fall-back time, which is longer than a fewindicate that in NS-NS systems mass ratios should be close
to unity, whereas in BH-NS binaries they should be smaller
than 1/3. Accurate measurement of the inspiral waveform in
the LIGO band would allow simultaneous determination of
the ratio of reduced to total system mass, p/(mI +m2) and of
the so-called "chirp" mass M, = (mlm2)3/5/(ml +m2)1/5, from
which the mass ratio can be derived.
GRB 050509b is the first event in the short class of bursts
for which we have an accurate localization and a tentative
distance indicator, based on an association with an elliptical
galaxy at z = 0.2248. At the inferred distance of ~ 1 Gpc, we
have shown here that the energetics and duration can be ac-
counted for by small, dense disks around stellar mass black
holes, based on dynamical modeling of such systems. Putting
GRB 050509b at a significantly higher redshift places more
serious constraints due to the energetics, but particularly be-
cause of the short duration: at z = 3, Eiso ~ 2 x 1050 erg and
t50 ~ 8 ms (see Figures 1 and 2). This is hard to reconcile
with the current models. The observed duration distribution
of bursts may be affected by the mechanism responsible for
the production of the relativistic outflow, with magnetically
powered events more faithfully reflecting the intrinsic popu-
lation. GRB 050509b is in many respects an unusual event,
being so short and apparently sub-energetic.
Much progress has been made in understanding how --rays
can arise in fireballs produced by brief events depositing a
large amount of energy in a small volume, and in deriving the
generic properties of the long wavelength afterglows that fol-
low from this. The identity of short-burst progenitors remains
one of the standing mysteries, which further observations of
events similar to GRB 050509b will hopefully help elucidate.
We thank J. Bloom, J. Hjorth, C. Kouveliotou, P. Kumar,
D. Page, D. Pooley, J. Prochaska and S. Rosswog for helpful
conversations. This work is supported by CONACyT-36632E
(WHL), the DoE under contract DE-AC03-76SF00515 (JG),
and NASA through a Chandra Fellowship award PF3-40028
(ER-R).
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Lee, William H.; /Princeton, Inst. Advanced Study /UNAM, Inst. Astron.; Ramirez-Ruiz, Enrico; /Princeton, Inst. Advanced Study; Granot, Jonathan & /Princeton, Inst. Advanced Study /KIPAC, Menlo Park. A Compact Binary Merger Model for the Short, Hard GRB 050509b, article, June 15, 2005; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc876315/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.