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We perform several nonparametric correlation tests on the BATSE 3B data to search for evidence of cosmological time dilation. These tests account for the effects of data truncation due to threshold effects in both limiting brightness and limiting duration, enabling us to utilize a larger number of bursts than in previous analyses. We find little significant evidence for correlation between various measures of peak intensity and duration, but the tests cannot conclusively rule out time dilation factors of 2 or less without more data. There is stronger evidence for a positive correlation between fluence and duration, which if confirmed would rule out simple no-evolution cosmological models unless there is a strong intrinsic correlation between the total radiant energy and the duration of bursts., 21 pages, 5 Postscript figures, uses aaspp4.sty and psfig.sty, to appear in ApJ volume 474. Paper also available at http://www-bigbang.stanford.edu/~ted/paper5.html

We present strong evidence of time stretching in the peak-to-peak timescales in the light curves of BATSE gamma-ray bursts (GRBs). Extensive tests are performed on artificially dilated bursts to verify that the procedure for extracting the peak-to-peak timescales correctly recovers the stretching of the bursts. The resulting robust algorithm is then applied to the 4B GRB database. We derive a stretching factor of 1.92 ± 0.13 between the brightest burst group (P > 7.7 photons cm-2 s-1) and the dimmest burst group (P=1.0-1.4 photons cm-2 s-1), with several independent peak-to-peak timescale definitions, and they agree within the uncertainties. Such an agreement strongly supports the interpretation of the observed time stretching as the time dilation caused by cosmological expansion rather than by physical selection effects. We fitted the result to cosmological models with Λ=0, Ω0 from 0.2 to 1.0, and constrained the standard candle luminosity to be L0=(7.0 ± 2.0 ± 2.7) × 1056 photons s-1. Our luminosity value is fully consistent with the value from the combined PVO and BATSE log N-log P curve with the BATSE bright bursts at low redshifts of zbright=0.11 ± 0.02 ± 0.025. This luminosity fit is definitely inconsistent with the larger distance scale implied from associating burst density with star formation rates.

Using the parameter V [ ≡ (64)max/(1024)max], the ratio of expected peak counts in 64 ms and 1024 ms, proposed by Che et al. recently, we find the cosmological time dilation in short gamma-ray bursts (t90 < 1.5 s) directly from the Burst and Transient Source Experiment catalog. The parameter V of short bursts shows a good correlation with the brightness B when we use (64)max as a measure of brightness B rather than (1024)max, introduced by Lamb et al. in 1993. In a Friedmann universe with Ω = 1 and Λ = 0, the estimated redshift is about 2 and the time dilation factor (TDF) with the energy correction is about 1.8. The fact that these results generally agree with those found in long bursts supports the same origin of long and short gamma-ray bursts.

The observed apparent time dilation of supernovae light curves claimed recently by Leibundgut et al. to establish directly the "expansion of the universe" is, rather, a general implication of fundamental physics. In particular, it applies to chronometric cosmology, in which it appears explicitly as a generalized Lorentz-Fitzgerald contraction. The dilation effect was earlier shown in the proper motion-to-redshift relation of superluminal sources, as analyzed in the frame of chronometric cosmology by Segal, providing an estimate of the cosmic distance scale.

We present a test to investigate cosmological time dilation in long gamma-ray bursts (t90 > 1.5 s) using V, the ratio of expected peak counts in 64 and in 1024 ms. The theoretical evolution of V with redshift shows that dimmer bursts have flatter peaks than brighter ones when we assume that (1) the bursters are at cosmological distances, (2) the bursts have standard exponential profiles, and (3) the burst peak duration follows a power law in narrowing with cosmological redshift energy. The calculated V-distribution of long bursts versus intensity in a Friedmann universe with Ω = 1 and Λ = 0 is consistent with that found from previous results for long bursts. The estimated redshift is z ~ 2, and the time dilation factor with energy correction is ~1.8.

The recently reported time dilation effect in Type Ia supernova SN 1995K has been claimed to rule out the static universe model of Narlikar & Arp. It is shown here that the variable mass hypothesis which accounts for the redshift phenomenon in the above static universe model does indeed predict the observed effect and that there is no conflict between the data of Leibundgut et al. and the predictions of this model.

The isotropic distribution of gamma-ray bursts as observed with the Burst and Transient Experiment (BATSE) strongly suggests that the bursts are at cosmological distances. At such distances, the expansion of the universe should redshift the spectra and stretch the temporal structure. We relate the observed peak intensities, spectral shapes, and time dilation to distance. We include the uncertainties in our knowledge of the intrinsic spectrum and correct for the coupling between the spectral shape and the temporal structure. The reported time dilation between the dimmest BATSE bursts and the bright BATSE bursts (a factor of 2) requires a redshift of about 6 for the BATSE dimmest bursts rather than a redshift of 1 or 2 as previously reported. The large luminosity and distance determined from the time dilation is inconsistent with the observed Log N-Log P distribution. unless there is very strong evolution. The implied distance for the dimmest bursts is beyond where galaxies are thought to form. If true, the gamma-ray bursts would be orphans: no known objects would have the same distance scale. We conclude that either a large fraction (65%) of the observed time dilation between the BATSE bright and dimmest bursts is intrinsic to the bursts or that there are strong evolutionary effects in the Log N-Log P distribution and that it is only a coincidence that Log N-Log P shows a -3/2 power law at high intensities., Comment: 41 pages including figures, uuencoded compressed Postscript. Accepted for publication in the Astrophysical Journal. The preprint can also be found in Postscript form at http://sstcx1.lanl.gov/~jsbloom/ or at ftp://sstcx1.lanl.gov/pub/grb/time_dilation.ps

If gamma-ray burst sources are cosmological in origin, then the time dilation at large z can correlate a burst's duration with its peak flux. Detection of this effect is thought by many to be strong evidence for a cosmological burst origin. In this Letter I show that an apparent time distortion--either a dilation or contraction--is generally expected for an ensemble of bursts that is spatially limited within Euclidean space. The appearance of this effect is correlated with the falling away of the log N-log P curve from a -3/2 slope line. An example of this effect is provided by the relativistic bulk motion model, which produces a strong time dilation when spatially limited in Euclidean space. As a consequence, envidence that weak bursts have longer durations than strong bursts is not evidence of a cosmological burst origin.

Norris et al. (1994) report that the temporal structure of faint gamma ray bursts is longer than that of bright bursts, as expected for time dilation in the cosmological models of burst origin. I show that the observed trends can easily be produced by a burst luminosity function and thus may not result from cosmological effects. A cosmological signature may be present, but the tests Norris et al. present are not powerful enough to detect these signatures.

If gamma-ray bursters are at cosmological distances - as suggested by their isotropic distribution on the sky and by their number-intensity relation - then the burst profiles will be stretched in time, by an amount proportional to the redshift, 1 + $z$. We have tested data from the {\it Compton} Gamma Ray Observatory's Burst and Transient Source Experiment (BATSE) for such time dilation. Our measures of time scale are constructed to avoid selection effects arising from intensity differences by rescale all bursts to fiducial levels of peak intensity and noise bias. The three tests involved total count rate above background, wavelet decomposition, and alignment of the highest peaks. In all three tests, the dim bursts are stretched by a factor of about two relative to the bright ones, over seven octaves of time scale. We calibrated the measurements by dilating synthetic bursts that approximate the temporal characteristics of bright BATSE bursts. Results are consistent with bursts of BATSE's peak-flux completeness limit being at cosmological distances corresponding to $z \sim 1$, and thus with independent cosmological interpretations of the BATSE number-intensity relation., in press: ApJ, Plain TeX: 18 pages, 4 figures, hard preprint available upon request, Report # RJNSISSA003

The "Breakthrough Starshot" program is planning to send transrelativistic probes to travel to nearby stellar systems within decades. Since the probe velocity is designed to be a good fraction of the light speed, \citet{zha18} recently proposed that these transrelativistic probes can be used to study astronomical objects and to test special relativity. In this work, we further propose some methods to test special relativity and constrain photon mass using the Doppler effect with the images and spectral features of astronomical objects as observed in the transrelativistic probes. We introduce more general theories to set up the framework of testing special relativity, including a parametric general Doppler effect and Doppler effect with massive photon. We find that by comparing the spectra of a certain astronomical object, one can test Lorentz invariance and constrain photon mass. Besides, using imaging and spectrograph capabilities of transrelativistic probes, one can test time dilation and constrain photon mass. For a transrelativistic probe with velocity $v\sim0.2c$, aperture $D\sim3.5~{\rm cm}$ and spectral resolution $R\sim100$ (or $1000$), we find that the probe velocity uncertainty can be constrained to $\sigma_v\sim0.01c$ (or $0.001c$), and the time dilation factor uncertainty can be constrained to $\Delta\gamma=|\hat\gamma-\gamma|\lesssim0.01$ (or $0.001$), where $\hat\gamma$ is the time dilation factor and $\gamma$ is the Lorentz factor. Meanwhile, the photon mass limit is set to $m_\gamma\lesssim10^{-33}~{\rm g}$, which is slightly lower than the energy of the optical photon., Comment: 8 pages, 3 figures, accepted for publication in ApJ

Two models of the gamma ray burst population, one with a standard candle luminosity and one with a power law luminosity distribution, are chi^2-fitted to the union of two data sets: the differential number versus peak flux distribution of BATSE's long duration bursts, and the time dilation and energy shifting versus peak flux information of pulse duration time dilation factors, interpulse duration time dilation factors, and peak energy shifting factors. The differential peak flux distribution is corrected for threshold effects at low peak fluxes and at short burst durations, and the pulse duration time dilation factors are also corrected for energy stretching and similar effects. Within an Einstein-de Sitter cosmology, we place strong bounds on the evolution of the bursts, and these bounds are incompatible with a homogeneous population, assuming a power law spectrum and no luminosity evolution. Additionally, under the implied conditions of moderate evolution, the 90% width of the observed luminosity distribution is shown to be < 10^2, which is less constrained than others have demonstrated it to be assuming no evolution. Finally, redshift considerations indicate that if the redshifts of BATSE's faintest bursts are to be compatible with that which is currently known for galaxies, a standard candle luminosity is unacceptable, and in the case of the power law luminosity distribution, a mean luminosity < 10^57 ph s^-1 is favored., Accepted to the Astrophysical Journal, 18 pages, LaTex

The pulses that compose gamma-ray bursts (GRBs) are hypothesized to have the same shape at all energies, differing only by scale factors in time and amplitude. This "Pulse Scale Conjecture" is confirmed here between energy channels of the dominant pulse in GRB 930214c (BATSE trigger 2193), the single most fluent single-pulsed GRB that occurred before May 1998. Furthermore, pulses are hypothesized to start at the same time independent of energy. This "Pulse Start Conjecture" is also confirmed in GRB 930214c. Analysis of GRB 930214c also shows that, in general, higher energy channels show shorter temporal scale factors. Over the energy range 100 KeV - 1 MeV, it is found that the temporal scale factors between a pulse measured at different energies are related to that energy by a power law, possibly indicating a simple relativistic mechanism is at work. To test robustness, the Pulse Start and Pulse Scale Conjectures were also tested on the four next most fluent single-pulse GRBs. Three of the four clearly passed, with a second smaller pulse possibly confounding the discrepant test. Models where the pulse rise and decay are created by different phenomena do not typically predict pulses that satisfy both the Pulse Start Conjecture and the Pulse Scale Conjecture, unless both processes are seen to undergo common time dilation., Comment: 19 pages, 9 figures, analysis revised and extended, accepted to ApJ

Power density spectra (PDSs) of long gamma-ray bursts (GRBs) provide useful information on GRBs, indicating their self-similar temporal structure. The best power-law PDSs are displayed by the longest bursts (T90 > 100 s) in which the range of self-similar timescales covers more than 2 decades. Shorter bursts have apparent PDS slopes more strongly affected by statistical fluctuations. The underlying power law can then be reproduced with high accuracy by averaging the PDSs for a large sample of bursts. This power law has a slope α ≈ -5/3 and a sharp break at ~1 Hz. The power-law PDS provides a new sensitive tool for studies of GRBs. In particular, we calculate the PDSs of bright bursts in separate energy channels. The PDS flattens in the hard channel (hν > 300 keV) and steepens in the soft channel (hν < 50 keV), while the PDS of bolometric light curves approximately follows the -5/3 law. We then study dim bursts and compare them to the bright ones. We find a strong correlation between the burst brightness and the PDS slope. This correlation shows that the bursts are far from being standard candles and dim bursts should be intrinsically weak. The time dilation of dim bursts is probably related to physical processes occurring in the burst rather than to a cosmological redshift.

A likelihood statistic constructed from positions and positional uncertainties identifies 82 associations of BATSE sources with rich, concentrated Abell clusters. Random simulations indicate that 42 ± 9 of these pairs are chance associations. Among the approximately 40 physically associated cluster-gamma-ray burst (GRB) pairs (the nearest containing the Coma Cluster and GRB 2193), we find (1) a plateau between 15.8 and 16.2 mag in the integral (observed-minus-random) number distribution of mR(10), the magnitude of 10th brightest cluster member, which may indicate the presence of two burst populations with different characterstic intrinsic luminosities; (2) the dispersion in GRB fluences between 100 and 300 keV (represented as apparent magnitude, m[100-300 keV]) is smaller for bursts paired with mR(10) ≤ 16.2 clusters than for those with mR(10) > 16.2; (3) the average 100-300 keV isotropic intrinsic energy of GRBs associated with mR(10) ≤ 16.2 clusters with known redshift z 99.9% confidence level). The slope of this relation indicates t90∝L−11024. These results suggest that the anticorrelation of apparent burst magnitude with duration is an intrinsic property of the bursts and is not caused by cosmological time dilation.

Individual gamma-ray bursts (GRBs) have very diverse time behavior—from a single pulse to a long complex sequence of chaotic pulses of different timescales. I studied time profiles of GRBs using data from the Compton Gamma Ray Observatory's Burst and Transient Source Experiment (BATSE) and found that the postpeak slope of the average peak-aligned time profile of GRBs obeys a unique and simple analytical law, I ~ exp [-(t/t0)1/3], where t is the time measured from the peak of the event and t0 is a constant ranging from 0.3 s for strong bursts to ~1 s for weak bursts. The average peak-aligned time profile follows this law with good accuracy in the whole time range available for analysis (from fractions of a second to ~120 s after the peak). Such a law (a stretched exponential) appears in processes associated with fractals (e.g., turbulence). The same analysis for solar flares gives a different shape for the average time profile. The dependence of t0 on the brightness of GRBs is presented. The time dilation of the dimmest GRBs relative to the brightest GRBs is at least a factor ~2 and possibly ~3. The statistics (600 GRBs), however, still does not allow us to rule out an intrinsic anticorrelation between intensity and duration of GRBs as a possible explanation of the effect. Probably, it is possible to confirm (or disprove) the cosmological origin of GRBs using the total existing statistics of strong bursts.

The parameters T(sub 90) and T(sub 50) have recently been introduced as a measurement of the duration of gamma-ray bursts. We present here a description of the method of measuring T(sub 90) and T(sub 50) and its application to gamma-ray bursts observed with the Burst and Transient Source Experiment (BATSE) onboard the Compton Gamma-Ray Observatory (CGRO). We use simulated as well as observed time profiles to address some of the possible systematic effects affecting individual T(sub 90) (T(sub 50)) measurements. We show that these systematic effects do not mimic those effects that would result from time dilation if the burst sources are at distances of several Gpc. We discuss the impact of these systematic effects on the T(sub 90) (T(sub 50)) distributions for the gamma-ray bursts observed with BATSE. We distinguish between various types of T(sub 90) (T(sub 50)) distributions, and discuss the ways in which distributions observed with different experiments can vary, even though the measurements for commonly observed bursts may be the same. We then discuss the distributions observed with BATSE and compare them to those observed with other experiments.

Statistical studies of BATSE gamma-ray bursts are presented: we average the time profiles, aligning the events at their highest peaks. Using the time histories in different energy channels, we summarize the general features of the average intensity and spectral evolution of gamma-ray bursts (GRBS) and compare the average evolution of bright and dim events. While no differences are found between the average intensity histories, the average hardness ratio histories demonstrate a hardness/brightness correlation. The observed lack of differences between the intensity histories of bright and dim bursts is incompatible with cosmological time dilation effects predicted by simple cosmological models. The combined results of no intensity history difference but a hardness history difference between bright and dim bursts places constraints on galactic models for the origin of GRBS.

We find that dim gamma-ray bursts (GRBs) are softer than bright GRBs, as indicated on average by data from the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory. We show that this correlation is statistically significant with respect to variations due to random differences between GRBs. This effect is discernable using a variety of methods and data sets, including public domain data. We analyze several types of systematic errors and selection effects in the BATSE data and conclude that the observed effect is not dominated by any of them. We therefore assert that this dim/soft effect is a real property of GRBs. It is possible that this correlation is a consequence of the time dilation detected by Norris et al. (1994) and that this is additional evidence that burst sources are located at cosmological distances., in press: The Astrophysical Journal (Letters), 15 pages of Plain TEX version 3.0. Postscript text and figures available through RJN's Home Page URL of http://enemy.gsfc.nasa.gov/htmltest/rjn.html

Supernovae can perhaps be found at Zapprox. =1 using the Space Telescope and the Focal Plane Camera (cryogenic charge coupled devices) at a rate of approximately four per week using 3 hours per week of viewing time. If Type II supernovae are used as a self-calibrating candle at Zvery-much-less-than1, then Type I's can be calibrated from Type II's as a secondary standard candle (2 mag brighter) and used instead of Type II's for a less difficult determination of q/sub 0/. This assumes all Type I's are the same independent of Z whereas each Type II is self-calibrated. Adequate statistics of supernovae in nearby galaxies Z< or approx. =1 can further verify the uniqueness of Type I's. Three-color wide-band photometry performed over the period of the maximum luminosity of a Type I gives the time dilation proportional (1+Z)/sup -1/, color shift proportional (1+Z)/sup -1/, and apparent luminosity proportionalZ/sup -2/(1+0.5(1+q/sub 0/) Z+O (Z))/sup -2/ (1+Z)/sup -2/. A Type I supernova at maximum and Z=1, H/sub 0/=50, should give rise to a statistically meaningful maximum single pixel signal of approx.250 photoelectrons compared to an average galaxy center background of approx.25 photoelectrons for an 80 s integration time. An average of approx.100 large galaxiesmore » (10/sup 10/L/sub sun/) per field allows approx.10/sup 4/ galaxies to be monitored using 3 hours of viewing time. Z can be determined by time dilation and color shift sufficiently accurately that the determination of q/sub 0/ will have twice the error of the calibration of Type I as a standard candle.« less

The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.