Bradley E. Schaefer (Yale):
In the last few days, the GCN has had several discussions about the
possibility that GRB990123 might be lensed with a high amplification.
This note is to provide balance and point out several problems with this
possibility. In particular, the arguments suggest that there will be no
repeat lens events on short (or long) time scales.
(1) The idea of GRB990123 lensing has weak motivation.
The motivation that GRB990123 is lensed is (A) to reduce the
deduced isotropic-equivalent energy (2.3x10^54 erg) to a level that can be
readily explained by models, (B) to account for the lack of previous
optical flash detection by LOTIS and ROTSE [GCN #216], (C) to account for
GRB970627 as a lensed image [GCN #234], and (D) to explain the large radio
variability [GCN #239].
(A) To claim that GRB990123 is too energetic requires a knowledge
of the burst energy budget, whereas no such answer is known.
Nevertheless, within current reasonable models (e.g., collapsars, merging
compact objects) the typical gamma ray energies range up to ~10^52 ergs.
[This forces the lens amplification, A, to be >200 or so.] Any such
argument would already require that GRB971214 [3x10^53 erg; Kulkarni et
al. 1998, Nature, 393, 35] and GRB980703 [2x10^53 erg; GCN #139, GCN #143]
must also be lensed with large amplitude. The likelihood of three high
amplitude lenses among the 17 SAX bursts is close to zero.
(B) The optical flash luminosity is indeed large [it would appear
brighter than our Sun at a distance of 1 kpc], but we have no idea of what
is expected, so with A=200 the source still has M~-30.7 and this is still
astounding. More to the point, no previous search would have detected an
optical flash with the E_gamma/E_opt ratio for GRB990123 (i.e., V~9 [GCN
#205] for a gamma ray fluence of 5.1x10^-4 erg cm^-2 [GCN #224]). For
example, the highest fluence event seen by GROCSE is 1.9x10^-5 erg cm^-2
with an optical limit of 8.1 mag [H. S. Park et al. 1997, ApJ, 490, 99].
For LOTIS, the strictest limit comes from GRB970223 with a fluence of
4.8x10^-5 erg cm^-2 and an optical limit of 11.0 mag [H. S. Park et al.
1997, ApJLett, 490, L21]. So there are no missing-optical-flashes to
motivate a lens suggestion.
(C) For GRB970627 to be a lensed image, it must have the same
light curve, spectrum, and position as GRB990123. [Microlensing could
conceivably make mild changes in the light curve or spectrum by imaging
different portions of the fireball, but then the time delay between images
cannot be 1.5 years without simultaneously invoking high amplitude
microlensing on top of high amplitude macrolensing.] The two bursts have
peak-to-peak times of 12s and 17s, have greatly different peak intensity
ratios, have greatly different peak shapes, and GRB970627 lacks the late
time flux prominent in GRB990123. The two bursts have greatly different
hardness ratio in BATSE channels 1, 2, and 3, with H21 equal 1.37 versus
0.56 and H32 equal 5.83 versus 1.14
GRB990123 OT position is 4.23 degrees away from the IPN annulus for
GRB970627 which has a 3-sigma width of 0.065 degrees [GCN #235]. Thus,
GRB970627 is certainly not a lensed image of GRB990123.
(D) The radio observations of GRB990123 to date show >10X
variations in flux [GCN #239], but this is not qualitatively different
from the 4X variations already known from GRB scintillation [e.g., Frail
et al. 1997, Nature, 389, 261]. Nevertheless, GCN #239 suggests that
normal variation of a GRB cannot account for this variation, and instead
propose that the radio detection is of an earlier lensed image of the same
GRB. However, this alternative suggestion has exactly the same problem as
what it was trying to replace, since then the earlier lensed image is
required to vary by >10X. That is, lensing does not solve the posed
problem. So logically, there is no motivation to invoke lensing.
(2) A GRB990123 lensing event is now extremely improbable.
Within the lensing hypothesis, for simple lenses, the time delay
between images will scale as the mass of the lens, with typical delays of
250 seconds for a 10^9 solar mass lens or 7 hours for a 10^11 solar mass
lens [see E. Turner et al. 1984, ApJ, 284, 1]. So for the simple case,
there can be no lensed event in the future. For more complex lenses, GCN
#236 points out that the time delay between the two brightest and roughly
equal images will be from tens of seconds to a fraction of a day. In
either case, the lack of a comparable sized lens argues strongly that
there will be no more images arriving in the future and that there has
been no lensing at all.
The fraction of quasars that are lensed with moderate
amplification is ~10^-3. The fraction of GRBs with multiple images is
<10^-3 (G. Marani 1998, Thesis, George Mason). For a GRB distance
of z=1.6, the expected lensing fraction is ~2x10^-3
(D. Holz et al. 1999, ApJ, 510, 54). [A correction for amplification bias
is needed for this theoretical estimate, but this will not be large due to
the turn over in the LogN-LogP curve.] So, for GRBs with A>~2 we expect
the lensing fraction to be ~10^-3. The lensing probability scales as
A^-2. For the 17 SAX bursts, we then expect a final probability of
<2x10^-6 that any burst will be amplified as much as required. This
probability calculation suggests strongly that GRB990123 is not lensed and
thus will not have future lensing events on short or long time scales.
(3) Beaming is a better model.
Observationally, we know that the burst emission is collimated (to
allow the escape of GeV photons) and that most of burst emission is coming
from very small angular beams (e.g., B. Schaefer & K. C. Walker 1998,
ApJLett, 511, in press; ASTRO-PH/9810271; ASTRO-PH/9802200).
Theoretically, recent models produce small cones of emission, for example
S. Woosley suggests a beaming factor of 0.015 while M. Rees suggests it
can be as low as 10^-4 [Rome GRB Conf.]. So we have every reason to
expect significant beaming factors. This expectation will immediately
lower the burst energy requirements and eliminate the motivation for a
GRB990123 lens. Why invoke an extremely improbable solution with no
positive evidence when everyone already knows that beaming solves the
problem and must be present.