Severe Limits on Variations of the Speed of Light with Frequency

Explosive astrophysical events at high red shift can be used to place severe limits on the fractional variation in the speed of light ($\Delta c/c$), the photon mass ($m_{\gamma}$), and the energy scale of quantum gravity ($E_{QG}$). I find $\Delta c/c < 6.3 \times 10^{-21}$ based on the simultaneous arrival of a flare in GRB 930229 with a rise time of $220 \pm 30 \mu s$ for photons of 30 keV and 200 keV. The limit on $m_{\gamma}$ is $4.2 \times 10^{-44} g$ for GRB 980703 from radio to gamma ray observations. The limit on $E_{QG}$ is $8.3 \times 10^{16}$ GeV for GRB 930131 from 30 keV to 80 MeV photons.Comment: 7 pages, Submitted to PR

The Thousand Star Magnitudes in the Catalogues of Ptolemy, Al Sufi, and Tycho Are All Corrected For Atmospheric Extinction

Three pre-telescopic star catalogues contain about a thousand star magnitudes each (with magnitudes 1, 2, 3, 4, 5, and 6), with these reported brightnesses as the original basis for what has become the modern magnitude scale. These catalogues are those of Ptolemy (c. 137, from Alexandria at a latitude of 31.2), Al Sufi (c. 960, from Isfahan at a latitude of 32.6), and Tycho Brahe (c. 1590, from the island of Hven at a latitude of 55.9). Previously, extensive work has been made on the positions of the catalogued stars, but only scant attention has been paid to the magnitudes as reported. These magnitudes will be affected by a variety of processes, including the dimming of the light by our Earth's atmosphere (atmospheric extinction), the quantization of the brightnesses into magnitude bins, and copying or influence from prior catalogues. This paper provides a detailed examination of these effects. Indeed, I find all three catalogues to report magnitudes that have near-zero extinction effects, so the old observers in some way extinction corrected their observations.Comment: Four appendices appear only in the on-line edition available to subscribers (see http://www.shpltd.co.uk/jha.html), or in the last half of this arXiv PDF fil

Explaining the Gamma-Ray Burst E_peak Distribution

The characteristic photon energy for Gamma Ray Bursts, E_peak, has a remarkably narrow distribution for bursts of similar peak flux, with values between 150 and 600 keV for most faint bursts. This result is surprising within the framework of internal shock models, since spectral shifts associated with the jet's blue shift (by a Lorentz factor of Gamma) and the cosmological red shift (by a factor of 1+z) should cause substantial smearing in the distribution of the spectral peak in the jet's co-moving frame, E_rest. For the general case where the luminosity (L) varies as Gamma^N and E_rest varies as Gamma^M, then the observed E_peak will vary as L^{(M+1)/N}(1+z)^{-1}. For two independent set of 20 and 84 bursts, E_peak(1+z) varies as a power law of the luminosity with an index of (M+1)/N=0.36+-0.03. With this measured value, the above functional dependence of E_peak on L and z results in E_peak being roughly constant for bursts of similar peak flux, P_256. Thus, the kinematic smearing will be small, hence allowing the E_peak distribution to be narrow. This model also predicts that bright bursts will have high E_peak values because they all have some combination of high luminosity (and hence a large blue shift Gamma) and a nearby distance (and hence a small cosmological red shift). Quantitatively, E_peak should vary roughly as P_256^0.36, and this model prediction is strikingly confirmed with BATSE data by Mallozzi et al. A prediction of this model is that GRBs at very high red shift z~10 should all appear with E_peak at ~200 keV. A further prediction of this model is that normal bursts with P_256 below the BATSE trigger threshold will appear as x-ray flashes with E_peak~70 keV; just as is reported by Kippen et al. and Heise et al.Comment: ApJ Letters in press, 16 pages, 3 figure

Disagreeing Over Agreements: A Cross-Sectional Analysis of No-Poaching Agreements in the Franchise Sector

In October 2016, the Department of Justice Antitrust Division announced its intent to proceed criminally against parties to no-poaching agreements, or agreements between or among employers not to hire each other’s workers. Consequently, a wave of class action antitrust lawsuits has raised questions about the legality of no-poaching or no-hire provisions that certain franchised food businesses use. Fast-food restaurant chains, including McDonald’s, Carl’s Jr., and Pizza Hut, have recently found themselves embroiled in such litigation. This Note examines prior antitrust litigation involving no-poaching agreements between companies and discusses the differences and similarities between these cases and the cases involving franchised businesses. In analyzing the key issues that courts must confront to resolve current and future cases specific to franchises, this Note proposes that courts should employ a per se rule against no-poaching agreements among franchisors and franchisees

All Known Hot RCB Stars Are Fading Fast Over the Last Century

The R Coronae Borealis (RCB) stars are cool supergiants that display irregular and deep dips in their light curves, caused by dust formation. There are four known hot RCB stars (DY Cen, MV Sgr, V348 Sgr, and HV 2671), with surface temperatures of 15,000--25,000 K, and prior work has suggested that three of these have secular fading in brightness. I have tested this result by measuring century-long light curves in the Johnson B-band with modern comparison star magnitudes, and I have extended this by measuring many magnitudes over a wide time range as well as for the fourth hot RCB star. In all four cases, the B-band magnitude of the maximum light is now fast fading. The fading rates (in units of magnitudes per century) are 2.5 for DY Cen after 1960, 1.3 for MV Sgr, 1.3 for V348 Sgr, and 0.7 for HV 2671. This secular fading is caused by the expected evolution of the star across the top of the HR diagram at constant luminosity, as the temperature rises and the bolometric correction changes. For DY Cen, the brightness at maximum light is rising from 1906 to 1932, and this is caused by the temperature increase from near 5,800 to 7,500 K. Before 1934 DY Cen had frequent dust dips, while after 1934 there are zero dust dips, so there is some apparent connection between the rising temperature and the formation of the dust. Thus, we have watched DY Cen evolve from an ordinary RCB star up to a hot RCB star and now appearing as an extreme helium star, all in under one century.Comment: Just published in Monthly Notices of the Royal Astronomical Society. 11 pages, 3 figure

A latitude comparison of N2 density measurements by mass spectrometer

Latitude comparison of N2 ion density measurement by experimental mass spectromete