TITLE: GCN GRB OBSERVATION REPORT NUMBER: 241 SUBJECT: GRB990123, Probability of gravitational lensing DATE: 99/01/31 02:31:33 GMT FROM: Brad Schaefer at Yale U 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 [http://www.batse.msfc.nasa.gov/data/grb/catalog/flux.html]. The 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.