{
  "bibcode": "1999GCN...241....1S",
  "body": "Bradley E. Schaefer (Yale):\n\nIn the last few days, the GCN has had several discussions about the\npossibility that GRB990123 might be lensed with a high amplification.\nThis note is to provide balance and point out several problems with this\npossibility.  In particular, the arguments suggest that there will be no\nrepeat lens events on short (or long) time scales.\n\n(1) The idea of GRB990123 lensing has weak motivation.\n\tThe motivation that GRB990123 is lensed is (A) to reduce the\ndeduced isotropic-equivalent energy (2.3x10^54 erg) to a level that can be\nreadily explained by models, (B) to account for the lack of previous\noptical flash detection by LOTIS and ROTSE [GCN #216], (C) to account for\nGRB970627 as a lensed image [GCN #234], and (D) to explain the large radio\nvariability [GCN #239].\n\t(A) To claim that GRB990123 is too energetic requires a knowledge\nof the burst energy budget, whereas no such answer is known.\nNevertheless, within current reasonable models (e.g., collapsars, merging\ncompact objects) the typical gamma ray energies range up to ~10^52 ergs.\n[This forces the lens amplification, A, to be >200 or so.]  Any such\nargument would already require that GRB971214 [3x10^53 erg; Kulkarni et\nal. 1998, Nature, 393, 35] and GRB980703 [2x10^53 erg; GCN #139, GCN #143]\nmust also be lensed with large amplitude.  The likelihood of three high\namplitude lenses among the 17 SAX bursts is close to zero.\n\t(B) The optical flash luminosity is indeed large [it would appear\nbrighter than our Sun at a distance of 1 kpc], but we have no idea of what\nis expected, so with A=200 the source still has M~-30.7 and this is still\nastounding.  More to the point, no previous search would have detected an\noptical flash with the E_gamma/E_opt ratio for GRB990123 (i.e., V~9 [GCN\n#205] for a gamma ray fluence of 5.1x10^-4 erg cm^-2 [GCN #224]).  For\nexample, the highest fluence event seen by GROCSE is 1.9x10^-5 erg cm^-2\nwith an optical limit of 8.1 mag [H. S. Park et al. 1997, ApJ, 490, 99].\nFor LOTIS, the strictest limit comes from GRB970223 with a fluence of\n4.8x10^-5 erg cm^-2 and an optical limit of 11.0 mag [H. S. Park et al.\n1997, ApJLett, 490, L21].  So there are no missing-optical-flashes to\nmotivate a lens suggestion.\n\t(C) For GRB970627 to be a lensed image, it must have the same\nlight curve, spectrum, and position as GRB990123.  [Microlensing could\nconceivably make mild changes in the light curve or spectrum by imaging\ndifferent portions of the fireball, but then the time delay between images\ncannot be 1.5 years without simultaneously invoking high amplitude\nmicrolensing on top of high amplitude macrolensing.]  The two bursts have\npeak-to-peak times of 12s and 17s, have greatly different peak intensity\nratios, have greatly different peak shapes, and GRB970627 lacks the late\ntime flux prominent in GRB990123.  The two bursts have greatly different\nhardness ratio in BATSE channels 1, 2, and 3, with H21 equal 1.37 versus\n0.56 and H32 equal 5.83 versus 1.14\n[http://www.batse.msfc.nasa.gov/data/grb/catalog/flux.html].  The\nGRB990123 OT position is 4.23 degrees away from the IPN annulus for\nGRB970627 which has a 3-sigma width of 0.065 degrees [GCN #235].  Thus,\nGRB970627 is certainly not a lensed image of GRB990123.\n\t(D) The radio observations of GRB990123 to date show >10X\nvariations in flux [GCN #239], but this is not qualitatively different\nfrom the 4X variations already known from GRB scintillation [e.g., Frail\net al. 1997, Nature, 389, 261].  Nevertheless, GCN #239 suggests that\nnormal variation of a GRB cannot account for this variation, and instead\npropose that the radio detection is of an earlier lensed image of the same\nGRB.  However, this alternative suggestion has exactly the same problem as\nwhat it was trying to replace, since then the earlier lensed image is\nrequired to vary by >10X.  That is, lensing does not solve the posed\nproblem.  So logically, there is no motivation to invoke lensing.\n\n(2) A GRB990123 lensing event is now extremely improbable.\n\tWithin the lensing hypothesis, for simple lenses, the time delay\nbetween images will scale as the mass of the lens, with typical delays of\n250 seconds for a 10^9 solar mass lens or 7 hours for a 10^11 solar mass\nlens [see E. Turner et al. 1984, ApJ, 284, 1].  So for the simple case,\nthere can be no lensed event in the future.  For more complex lenses, GCN\n#236 points out that the time delay between the two brightest and roughly\nequal images will be from tens of seconds to a fraction of a day.  In\neither case, the lack of a comparable sized lens argues strongly that\nthere will be no more images arriving in the future and that there has\nbeen no lensing at all.\n\tThe fraction of quasars that are lensed with moderate\namplification is ~10^-3.  The fraction of GRBs with multiple images is\n<10^-3 (G. Marani 1998, Thesis, George Mason).  For a GRB distance \nof z=1.6, the expected lensing fraction is ~2x10^-3\n(D. Holz et al. 1999, ApJ, 510, 54).  [A correction for amplification bias\nis needed for this theoretical estimate, but this will not be large due to\nthe turn over in the LogN-LogP curve.]  So, for GRBs with A>~2 we expect\nthe lensing fraction to be ~10^-3.  The lensing probability scales as\nA^-2.  For the 17 SAX bursts, we then expect a final probability of\n<2x10^-6 that any burst will be amplified as much as required.  This\nprobability calculation suggests strongly that GRB990123 is not lensed and\nthus will not have future lensing events on short or long time scales.\n\n(3) Beaming is a better model.\n\tObservationally, we know that the burst emission is collimated (to\nallow the escape of GeV photons) and that most of burst emission is coming\nfrom very small angular beams (e.g., B. Schaefer & K. C. Walker 1998,\nApJLett, 511, in press; ASTRO-PH/9810271; ASTRO-PH/9802200).\nTheoretically, recent models produce small cones of emission, for example\nS. Woosley suggests a beaming factor of 0.015 while M. Rees suggests it\ncan be as low as 10^-4 [Rome GRB Conf.].  So we have every reason to\nexpect significant beaming factors.  This expectation will immediately\nlower the burst energy requirements and eliminate the motivation for a\nGRB990123 lens.  Why invoke an extremely improbable solution with no\npositive evidence when everyone already knows that beaming solves the\nproblem and must be present.",
  "circularId": 241,
  "createdOn": 917749893000,
  "email": "brad@grb2.physics.yale.edu",
  "subject": "GRB990123, Probability of gravitational lensing",
  "submitter": "Brad Schaefer at Yale U  <brad@grb2.physics.yale.edu>",
  "eventId": "GRB 990123"
}