Here is my
List of Bulk Lorentz Factor (BLF) measurements:
I. HE/ME Delay (Limit) Method (and model-dependence):
Done by comparing the time delay between the MeV photons and GeV photons to get a BLF lower limit. Basically, if you follow the literature, you get high BLF limit if you have a one-zone model but can get lower BLF if you have multi-zones (e.g. Chang+12 ApJ 759,129 http://iopscience.iop.org/0004-637X/759/2/129/pdf/apj_759_2_129.pdf and Zhao, X+11 ApJ 726,89 http://iopscience.iop.org/0004-637X/726/2/89/pdf/0004-637X_726_2_89.pdf ). A theory-dependent parameter value isn't very satisfying! Another:
II. Pair Opacity/ Variability Timescale Method:
I note that Abdo et al. 2009 Science, 323 (5922): 1688-1693 , apparently gets a lower limit via
(1) the variability time scale for the particular pulse
(2) requiring the optical depth for high-energy photons to be ≤ 1 to determine BLF_min.
(Supplemental material, eqns. 3-9)
Apparently, the requirements for this are to
(i)show that there is no delay between the low and high-E photons, which argues that they are all produced at the same location. (I think this is so you can use a single set of spectral parameters to get photon density.)
(ii) there is no HE cutoff, i.e. that tau (Emax) < 1.
(inquiry idea: Is there a burst with some pulses with correlated variability, and some with lags? How much variation can you get in the same burst?) SCIENCE: is a BLF a property of a jet or a pulse? i.e. do they increase in time obviously or show randomness?
III. Afterglow Peak Time method:
A “nearly” model-independent measure of BLF from just the rise time of the afterglow, it essentially says the peak comes from the transition from coasting to deceleration phase.
====Use of Afterglow Peak time method:
'Optical Measurements': Molinari et al. 2007, A&A 469,13. http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/full/2007/25/aa7388-07/aa7388-07.html Molinari+ claims that they measure the initial gamma factor, not a limit.
Nava+12 has her own model, http://arxiv.org/pdf/1211.2806.pdf with a factor of 1.65 difference, and compares this to other models. They calculate L_bol, and state that any band that gives a proxy for this is OK. Generally speaking, the sensitivity to the profile of the circumburst medium is small.
Liang+12 http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1210.5142 is a big study of optical afterglows presenting distributions and correlations of this optical afterglow peak time method. He also has his own slightly different formula for initial BLF differing very slightly from Nava et al.
'X-ray Measurements:'
Liang+12 say that they could not measure the X-ray afterglow BLF since there were always flares during the X-ray peak. Nava+12 says that any measurement at nu > nu_cooling should represent her curves for the bolometric luminosity, therefore should make a good measurement, although she clearly states that she hasn't modeled this yet.
'Gamma-Ray Measurements'
Ackerman+13 http://arxiv.org/pdf/1303.2908v1.pdf First LAT Catalog (*) - Can get BLF by setting LAT t_peak = t_fireball_deceleration to measure BLF. I believe this is exactly the same thing.
(* Note the distribution of LAT BLFs is given in this paper.)
Papers
<Table border=1> <tr>
<th>Subject </th>
<th>Ref</th>
<th>Conceptual Feature</th>
</tr> <tr>
<td>HE/ME time delay method</td>
<td>ApJ 726 (2011) 89 Zhao, X+ http://iopscience.iop.org/0004-637X/726/2/89</td>
<td>You can get lower BLFs with 2-zone model</td> </tr> <tr>
<td>HE/ME time delay method</td>
<td>Chang+12 ApJ 759,129 http://iopscience.iop.org/0004-637X/759/2/129/pdf/apj_759_2_129.pdf</td>
<td>Extends to three zones</td>
</tr>
<tr>
<td>t_var time scale</td>
<td>Abdo et al. 2009 Science, 323 (5922): 1688-1693</td>
<td>First classic paper</td>
</tr><tr>
<td>HE Peak (deceleration) Time Method </td>
<td>Ackerman+13 http://arxiv.org/pdf/1303.2908v1.pdf First LAT Catalog;</td>
<td>Set t_peak,LAT = t_fireball_deceleration to measure BLF (distribution of BLFs given in this paper)</td>
</tr><tr>
<td>Subject </td>
<td>Ref</td>
<td>Conceptual Feature</td>
</tr><tr>
<td>Subject </td>
<td>Ref</td>
<td>Conceptual Feature</td>
</tr><tr>
<td>Subject </td>
<td>Ref</td>
<td>Conceptual Feature</td>
</tr>
</table>
