Mizuta 2008 坍缩星喷流的角分布

主要内容:
就是有一定的分布

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Title:		Angular Energy Distribution of Collapsar-Jets
Authors:		Mizuta, Akira; Aloy, Miguel A.
Publication:		eprint arXiv:0812.4813
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		41 pages, 19 figures, submitted to ApJ, high resolution figures are available at http://www.cfs.chiba-u.ac.jp/~mizuta/ms10.pdf
Bibliographic Code:		2008arXiv0812.4813M

Abstract

Collapsars are fast-spinning, massive stars, whose core collapse liberates an energy, that can be channeled in the form of ultrarelativistic jets. These jets transport the energy from the collapsed core to large distances, where it is dissipated in the form of long-duration gamma-ray bursts. In this paper we study the dynamics of ultrarelativistic jets produced in collapsars. Also we extrapolate our results to infer the angular energy distribution of the produced outflows in the afterglow phase. Our main focus is to look for global energetical properties which can be imprinted by the different structure of different progenitor stars. Thus, we employ a number of pre-supernova, stellar models (with distinct masses and metallicities), and inject in all of them jets with fixed initial conditions. We assume that at the injection nozzle, the jet is mildly relativistic (Lorentz factor $\sim 5$), has a finite half-opening angle ($5^\circ$), and carries a power of $10^{51} $erg s$^{-1}$. These jets arrive intact to the stellar surface and break out of it. A large Lorentz factor region $\Gamma\simmore 100$ develops well before the jet reaches the surface of the star, in the unshocked part of the beam, located between the injection nozzle and the first recollimation shock. These high values of $\Gamma$ are possible because the finite opening angle of the jet allows for free expansion towards the radial direction. We find a strong correlation between the angular energy distribution of the jet, after its eruption from the progenitor surface, and the mass of the progenitors. The angular energy distribution of the jets from light progenitor models is steeper than that of the jets injected in more massive progenitor stars. This trend is also imprinted in the angular distribution of isotropic equivalent energy.

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Ioka 2008 伽玛暴作为TeV谱上"超"的来源

主要内容:

只考虑了谱, 完全没考虑流量, 时标, 方向性... 而且谱也是假设伽玛暴有TeV的光子出来
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arXiv:0812.4851 [ps, pdf, other]

Title: A Gamma-Ray Burst for Cosmic-Ray Positrons with a Spectral Cutoff and Line

Authors: Kunihito Ioka (KEK)

Comments: 4 pages, 3 figures

Subjects: Astrophysics (astro-ph)

We propose that a nearby gamma-ray burst (GRB) about 10^{5-6} years ago may be responsible for the excesses of cosmic-ray positrons and electrons recently observed by the PAMELA and ATIC/PPB-BETS experiments. The spectra have a sharp cutoff that is similar to the dark matter predictions, possibly together with a line (not similar), since higher energy cosmic-rays cool faster where the cutoff/line energy marks the source age. The same is true if a source is GRB-like (old, single and short-lived). An astrophysical source is expected to have a small but finite spread in the cutoff/line as well as anisotropy in the cosmic-ray flux, providing a method for the Fermi and future CALET experiments to discriminate between dark matter and astrophysical origins.

Racusin 2008 Swift暴X射线余辉的jet break和能量

主要内容:
狂多光变和谱的数据. 但是好像根本都没有考虑光学. 那些和光学不同时break的光变也被当成jet break了.

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arXiv:0812.4780 [ps, pdf, other]

Title: Jet breaks and Energetics of Swift GRB X-ray Afterglows

Authors: J. L. Racusin, E. W. Liang, D. N. Burrows, A. Falcone, T. Sakamoto, B. B. Zhang, B. Zhang, P. Evans, J. Osborne

Comments: 73 pages, 19 figures, 8 tables, submitted to ApJ

Subjects: Astrophysics (astro-ph)

We present a systematic temporal and spectral study of all Swift -XRT observations of GRB afterglows discovered between 2005 January and 2007 December. After constructing and fitting all light curves and spectra to power-law models, we classify the components of each afterglow in terms of the canonical X-ray afterglow and test them against the closure relations of the forward shock models for a variety of parameter combinations. The closure relations are used to identify potential jet breaks with characteristics including the uniform jet model with and without lateral spreading and energy injection, and a power-law structured jet model, all with a range of parameters. With this technique, we survey the X-ray afterglows with strong evidence for jet breaks (~12% of our sample), and reveal cases of potential jet breaks that do not appear plainly from the light curve alone (another ~30%), leading to insight into the missing jet break problem. Those X-ray light curves that do not show breaks or have breaks that are not consistent with one of the jet models are explored to place limits on the times of unseen jet breaks. The distribution of jet break times ranges from a few hours to a few weeks with a median of ~1 day. On average Swift GRBs have lower isotropic equivalent gamma-ray energies, which in turn results in lower collimation corrected gamma-ray energies than those of pre-Swift GRBs. Finally, we explore the implications for GRB jet geometry and energetics.

Genet 2008 测试高维辐射

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考虑多个pulses的和之后, 下降指数可以很大. 指数见右图. 其根本原因是最后一个pulse的时间零点被提前了很多.

文章信息:

arXiv:0812.4677 [ps, pdf, other]

Title: Testing High Latitude Emission in GRBs

Authors: F. Genet, J. Granot

Subjects: Astrophysics (astro-ph)

Most gamma-ray bursts (GRBs) observed by the Swift satellite show an early rapid decay phase (RDP) in their X-ray lightcurve, which is usually a smooth continuation of the prompt gamma-ray emission, strongly suggesting that it is its tail. However, the mechanism behind it is still not clear. The most popular model for this RDP is High Latitude Emission (HLE). While HLE is expected in many models for the prompt GRB emission, such as the popular internal shocks model, there are models in which it is not expected, such as sporadic magnetic reconnection events. Therefore, testing whether the RDP is consistent with HLE can help distinguish between different prompt emission models. We address this question by modeling the prompt emission as the sum of its individual pulses with their HLE tails. Analytic expressions for the observed flux density are obtained for power-law and Band function emission spectra. For internal shocks the observed instantaneous spectrum is very close to the emitted one, and should be well described by a Band function also during the RDP. Our model naturally produces, the observed spectral softening and steepening of the flux decay. The observed flux during the RDP is initially dominated by the tail of the last pulse, but the tails of one or more earlier pulses can become dominant later on. Moreover, modeling several overlapping pulses as a single wider pulse would over-predict the emission tail. Thus, one should be very careful when testing the predictions of HLE and do a combined temporal and spectral fit of the prompt GRB emission and the RDP.

Dai 2008 Swift暴的光度函数

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Title:		Intensity Distribution and Luminosity Function of the Swift Gamma-Ray Bursts
Authors:		Dai, Xinyu
Publication:		eprint arXiv:0812.4466
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		11 pages, 3 figures, submitted to ApJ Letters
Bibliographic Code:		2008arXiv0812.4466D

Abstract

Using the sample of long Gamma-ray bursts detected by Swift-BAT before June 2007, we measure the Log N - Log P distribution of the Swift bursts. Compared with the BATSE sample, we find that the two distributions are consistent after correcting the bandpass difference suggesting that the two instruments are sampling the same population of bursts. We also compare the Log N - Log P distributions for sub-samples of the Swift bursts, and find evidence for a deficit (99.75% confident) of dark bursts at high peak flux levels suggesting different redshift or Gamma-ray luminosity distributions. The consistency between the Log N - Log P distributions for the optically detected bursts with and without redshift measurements indicates that the current sample of the Swift bursts with redshift measurements, although selected heterogeneously, represents a fare sample of the none-dark bursts. We calculate the luminosity functions of this sample in two redshift bins (z<1>1), and find a broken power-law is needed to fit the low redshift bin, where dN/dL \propto L^{-1.30\pm0.06} at the high luminosity range (L_{peak} > 5E48 erg/s) and dN/dL \propto L^{-2.5\pm0.3} at the low luminosity end confirming the existence of a population of low luminosity GRBs. For the high redshift bin, the normalization of the luminosity function is not higher than the low redshift counterpart challenging the hypothesis that GRB rate follows the star formation rate.

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Hoffman 2008 高能中微子望远镜

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Title:		High Energy Neutrino Telescopes
Authors:		Hoffman, K. D.
Publication:		eprint arXiv:0812.3809
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		33 pages, 21 figures, accepted for publication in the New Journal of Physics
Bibliographic Code:		2008arXiv0812.3809H

Abstract

This paper presents a review of the history, motivation and current status of high energy neutrino telescopes. Many years after these detectors were first conceived, the operation of kilometer-cubed scale detectors is finally on the horizon at both the South Pole and in the Mediterranean Sea. These new detectors will perhaps provide us the first view of high energy astrophysical objects with a new messenger particle and provide us with our first real glimpse of the distant universe at energies above those accessible by gamma-ray instruments. Some of the topics that can be addressed by these new instruments include the origin of cosmic rays, the nature of dark matter, and the mechanisms at work in high energy astrophysical objects such as gamma-ray bursts, active galactic nuclei, pulsar wind nebula and supernova remnants.

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Socrates 2008 引力结合能的释放

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Title:		On the release of binding energy and accretion power in core collapse-like environments
Authors:		Socrates, Aristotle; Ramirez-Ruiz, Enrico
Publication:		eprint arXiv:0812.3917
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		6 page Aspen conference proceeding
Bibliographic Code:		2008arXiv0812.3917S

Abstract

All accretion models of gamma-ray bursts share a common assumption: accretion power and gravitational binding energy is released and then dissipated locally, with the mass of its origin. This is equivalent to the Shakura-Sunyaev 1973 (SS73) prescription for the dissipation of accretion power and subsequent conversion into radiate output. Since their seminal paper, broadband observations of quasars and black hole X-ray binaries insist that the SS73 prescription cannot wholly describe their behavior. In particular, optically thick black hole accretion flows are almost universally accompanied by coronae whose relative power by far exceeds anything seen in studies of stellar chromospheric and coronal activity. In this note, we briefly discuss the possible repercussions of freeing accretion models of GRBs from the SS73 prescription. Our main conclusion is that the efficiency of converting gravitational binding energy into a GRB power can be increased by an order of magnitude or more.

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Zalamea 2008 中微子湮灭的效率--看是否能作为伽玛暴的能源机制

主要内容:
如果吸积率足够高, 貌似就是可以的.

公式:
epislon = 0.05 (M_dot/M_sun s^-1)^5/4
其中效率epsilon定义为 L_GRB/L_tot, 前者是可湮灭的, 后者是中微子的总能量.
比如吸积率为1太阳质量每秒, 效率1/20, 也差不多啦. 前提是a=0.95, 表示黑洞的旋转的.

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Title:		Efficiency of Neutrino Annihilation around Spinning Black Holes
Authors:		Zalamea, Ivan; Beloborodov, Andrei M.
Publication:		eprint arXiv:0812.4041
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		3 pages, 4 figures, to appear in the proceedings of the 6th Huntsville Gamma-Ray Burst Symposium 2008
Bibliographic Code:		2008arXiv0812.4041Z

Abstract

A fraction of neutrino emission from GRB accretion disks annihilates above the disk, creating e+- plasma that can drive GRB explosions. We calculate the efficiency of this annihilation using the recent detailed model of hyper-accretion disks around Kerr black holes. Our calculation is fully relativistic and based on a geodesic-tracing method. We find that the efficiency is a well-defined function of (1) accretion rate and (2) spin of the black hole. It is practically independent of the details of neutrino transport in the opaque zone of the disk. The results help identify the accretion disks whose neutrino emission can power GRBs.

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Evans 2008 自动分析XRT的数据

主要内容:
分析方法不感兴趣. 不过文中列出来318个暴的XRT数据, 值得参考. 文中也说网上有数据, 但列的网站太多了, 估计是在XRT的官网上吧, 比如:
http://www.swift.ac.uk/xrt_curves/

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Title:		Methods and results of an automatic analysis of a complete sample of Swift-XRT observations of GRBs
Authors:		Evans, P. A.; Beardmore, A. P.; Page, K. L.; Osborne, J. P.; O'Brien, P. T.; Willingale, R.; Starling, R. L. C.; Burrows, D. N.; Godet, O.; Vetere, L.; Racusin, J.; Goad, M. R.; Wiersema, K.; Angelini, L.; Capalbi, M.; Chincarini, G.; Gehrels, N.; Kennea, J. A.; Margutti, R.; Morris, D. C.; Mountford, C. J.; Pagani, C.; Perri, M.; Rol, E.; Romano, P.; Tanvir, N.
Publication:		eprint arXiv:0812.3662
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		Submitted to MNRAS. 21 pages inc. 11 figures, plus 38 pages of tables
Bibliographic Code:		2008arXiv0812.3662E

Abstract

We present a homogeneous X-ray analysis of all 318 Gamma Ray Bursts detected by the X-ray Telescope on the Swift satellite up to 2008 July 23; this represents the largest sample of X-ray GRB data published to date. In Sections 2--3 we detail the methods which the Swift-XRT team has developed to produce the enhanced positions, light curves, hardness ratios and spectra presented in this paper. Software using these methods continues to create such products for all new GRBs observed by the Swift-XRT. We also detail web-based tools allowing users to create these products for any object observed by the XRT, not just GRBs. In Sections 4--6 we present the results of our analysis of GRBs, including probability distribution functions of the temporal and spectral properties of the sample. We demonstrate evidence for a consistent underlying behaviour which can produce a range of light curve morphologies, and attempt to interpret this behaviour in the framework of external forward shock emission. We find several difficulties, in particular that reconciliation of our data with the forward shock model requires energy injection to continue for days to weeks.

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Ohno 2008 GRB 061007的随时间演化的E_p-L关系

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在Youlitouku关系上的点(红色)

把061007按时间分段(可以分出这么多段? 时间分辨率挺高的吗)后在E_p-L_iso上的图.
如果能把每个点所对应的时间也加上就更好了, 可以看到点在这个图上的演化. 不过其中有个表列了这些点, 估计包含了这些信息.
另外这个图上有一个比较明显的界线, 就是右下角是空白的. 不知道是物理上有什么限制, 还是观测上的(不像).

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Title:		Time-evolution of Peak Energy and Luminosity Relation within Pulses for GRB 061007: Probing Fireball Dynamics
Authors:		Ohno, Masanori; Ioka, Kunihito; Yamaoka, Kazutaka; Tashiro, Makoto; Fukazawa, Yasushi; Nakagawa, Yujin E.
Publication:		eprint arXiv:0812.3737
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		21 pages, 16 figures, accepted for publication in PASJ
Bibliographic Code:		2008arXiv0812.3737O

Abstract

We perform a time-resolved spectral analysis of bright, long Gamma-ray burst GRB 061007 using Suzaku/WAM and Swift/BAT. Thanks to the large effective area of the WAM, we can investigate the time evolution of the spectral peak energy, Et_peak and the luminosity Lt_iso with 1-sec time resolution, and we find that luminosity Lt_iso with 1-sec time resolution, and we find that the time-resolved pulses also satisfy the Epeak-Liso relation, which was found for the time-averaged spectra of other bursts, suggesting the same physical conditions in each pulse. Furthermore, the initial rising phase of each pulse could be an outlier of this relation with higher Et_peak value by about factor 2. This difference could suggest that the fireball radius expands by a factor of 2-4 and/or bulk Lorentz factor of the fireball is decelerated by a factor of 4 during the initial phase, providing a new probe of the fireball dynamics in real time.

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Ziaeepour 2008 GRB cook book I: 公式

主要内容:
挺不错的伽玛暴入门讲义(不过我们中文有南京伽玛暴组更好的, 戴老师笔记, 吴雪峰, 范一中博士论文等等).

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Title:		Gamma Ray Bursts Cook Book I: Formulation
Authors:		Ziaeepour, Houri
Publication:		eprint arXiv:0812.3277
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		34 pages, 1 figure
Bibliographic Code:		2008arXiv0812.3277Z

Abstract

Since the suggestion of relativistic shocks as the origin of gamma-ray bursts (GRBs) in early 90's, the mathematical formulation of this process has stayed at phenomenological level. One of the reasons for the slow development of theoretical works in this domain has been the simple power-law behaviour of the afterglows hours or days after the prompt gamma-ray emission. Nowadays with the launch of the Swift satellite, gamma-ray bursts can be observed in multi-wavelength from a few tens of seconds after trigger onward. These observations have leaded to the discovery of features unexplainable by the simple formulation of the shocks and emission processes used up to now. But "devil is in details" and some of these features may be explained with a more detailed formulation of phenomena and without adhoc addition of new processes. Such a formulation is the goal of this work. We present a consistent formulation of the collision between two spherical relativistic shells. The model can be applied to both internal and external shocks. Notably, we propose two phenomenological models for the evolution of the emitting region during the collision. One of these models is more suitable for the internal shocks and the other for the external collisions. We calculate radiation flux, lags, and hardness ratios. One of our aims has been a formulation enough complex to include the essential processes, but enough simple such that the data can be directly compared with the theory to extract the value and evolution of physical quantities. To accomplish this goal, we also suggest a procedure for extracting parameters of the model from data. In a following paper we numerically calculate the evolution of some simulated models and compare their features with the properties of the observed gamma-ray bursts.(abbreviated)

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Bissaldi 2008 Fermi GBM的地面校准

主要内容:
没看明白 :(

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Title:		Ground-based calibration and characterization of the Fermi Gamma-Ray Burst Monitor Detectors
Authors:		Bissaldi, Elisabetta; von Kienlin, Andreas; Lichti, Giselher G.; Steinle, Helmut; Narayana Bhat, P.; Briggs, Michael S.; Fishman, Gerald J.; Hoover, Andrew S.; Kippen, R. Marc; Krumrey, Michael; Gerlach, Martin; Connaughton, Valerie; Diehl, Roland; Greiner, Jochen; van der Horst, Alexander J.; Kouveliotou, Chryssa; McBreen, Sheila; Meegan, Charles A.; Paciesas, William S.; Preece, Robert D.; Wilson-Hodge, Colleen A.
Publication:		eprint arXiv:0812.2908
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		36 pages, 28 figures, accepted for publication in Experimental Astronomy; doi:10.1007/s10686-008-9135-4
Bibliographic Code:		2008arXiv0812.2908B

Abstract

One of the scientific objectives of NASA's Fermi Gamma-ray Space Telescope is the study of Gamma-Ray Bursts (GRBs). The Fermi Gamma-Ray Burst Monitor (GBM) was designed to detect and localize bursts for the Fermi mission. By means of an array of 12 NaI(Tl) (8 keV to 1 MeV) and two BGO (0.2 to 40 MeV) scintillation detectors, GBM extends the energy range (20 MeV to > 300 GeV) of Fermi's main instrument, the Large Area Telescope, into the traditional range of current GRB databases. The physical detector response of the GBM instrument to GRBs is determined with the help of Monte Carlo simulations, which are supported and verified by on-ground individual detector calibration measurements. We present the principal instrument properties, which have been determined as a function of energy and angle, including the channel-energy relation, the energy resolution, the effective area and the spatial homogeneity.

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Kuin 2008 UVOT对GRB081203A的观测

主要内容:
观测了一些氢线. 可以定红移为2. 对于V band星等亮于14, 红移在0.5到3.5之间的, UVOT就可以通过谱线定红移. (氢的Ly-alpha, Ly-break)

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UVOT的光变, 很平滑, 应该是余辉. 可以和X-ray比较一下.

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Title:		Swift-UVOT captures the earliest ultraviolet spectrum of a Gamma Ray Burst
Authors:		Kuin, N. P. M.; Landsman, W.; Page, M. J.; Schady, P.; Still, M.; Breeveld, A. A.; De Pasquale, M.; Brown, P. J.; Carter, M.; James, C.; Curran, P. A.; Cucciara, A.; Gronwall, C.; Holland, S. T.; Hoversten, E.; Hunsberger, S.; Kennedy, T.; Koch, S.; Lamoureux, H.; Marshall, F. E.; Oates, S. R.; Parsons, A.; Palmer, D.; Roming, P.; Smith, P. J.
Publication:		eprint arXiv:0812.2943
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		4 pages, 4 figures, submitted to MNRAS letters
Bibliographic Code:		2008arXiv0812.2943K

Abstract

We present the earliest ever ultraviolet spectrum of a gamma-ray burst (GRB) as observed with the Swift-UVOT. The spectrum of GRB 081203A was observed for 50 seconds with the UV grism starting 251 seconds after the Swift-BAT trigger when the GRB was of u ~13.4 mag and still rising to its peak optical brightness. The UV grism spectrum shows a damped Ly-alpha line, Ly-beta, and the Lyman continuum break at a redshift z = 2.05 +/- 0.01. A model fit to the Lyman absorption implies log N(HI) = 22.0 +/- 0.2 cm-2, which is typical for GRB host galaxies with damped Ly-alpha absorbers. This observation of GRB 081203A demonstrates that for GRBs brighter than v ~14 mag and with 0.5 <> Bibtex entry for this abstract Preferred format for this abstract (see Preferences)

Starling 2008 GRB 080721的观测

主要内容:
虽然打着这个暴的总能量的牌子, 但实际上就是给出这个暴的观测. 能量本身多少也不重要(不是很多也不是很少).

貌似观测的文章不能只是给一下观测, 总得说点儿啥, 不然不好发表.

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Title:		Constraining the energy budget of GRB 080721
Authors:		Starling, R. L. C.; Rol, E.; van der Horst, A. J.; Yoon, S. -C.; Pal'shin, V.; Ledoux, C.; Page, K. L.; Fynbo, J. P. U.; Wiersema, K.; Tanvir, N. R.; Jakobsson, P.; Guidorzi, C.; Curran, P. A.; Levan, A. J.; O'Brien, P. T.; Osborne, J. P.; Svinkin, D.; de Ugarte Postigo, A.; Oosting, T.
Publication:		eprint arXiv:0812.2490
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		11 pages, 6 figures, submitted to MNRAS
Bibliographic Code:		2008arXiv0812.2490S

Abstract

We follow the bright, highly energetic afterglow of Swift-discovered GRB 080721 out to 36 days or 3e6 s since the trigger in the optical and X-ray bands. We do not detect a break in the late-time light curve inferring a limit on the opening angle of theta_j >= 7.22 deg and setting tight constraints on the total energy budget of the burst of E_gamma >= 9.88e51 erg within the fireball model. To obey the fireball model closure relations the GRB jet must be expanding into a homogeneous surrounding medium. The energy constraint we derive can be used as observational input for models of the progenitors of long gamma-ray bursts: we discuss how such high collimation-corrected energies could be accommodated with certain parameters of the standard massive star core-collapse models. We can, however, most probably rule out a magnetar progenitor for this GRB which would require 100% efficiency to reach the observed total energy.

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Curran 2008 多参数拟合余辉

主要内容:
为解释Swift的早期余辉(就是一系列的新问题), 考虑多个参数: 电子指数p, 能量注入参数q, 星风参数k. 貌似解释的还不错, 但也有不能解释的.

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Title:		Testing the blast wave model with Swift GRBs
Authors:		Curran, P. A.; Starling, R. L. C.; van der Horst, A. J.; Wijers, R. A. M. J.
Publication:		eprint arXiv:0812.2813
Publication Date:		12/2008
Origin:		ARXIV
Keywords:		Astrophysics
Comment:		14 pages, submitted to MNRAS
Bibliographic Code:		2008arXiv0812.2813C

Abstract

The complex structure of the light curves of Swift GRBs has made the identification of breaks, and the interpretation of the blast wave caused by the burst, more difficult than in the pre-Swift era. We aim to identify breaks, which are possibly hidden, and to constrain the blast wave parameters; electron energy distribution, p, density profile of the circumburst medium, k, and the continued energy injection index, q. We do so by comparing the observed multi-wavelength light curves and X-ray spectra of our sample to the predictions of the blast wave model. We can successfully interpret all of the bursts in our sample of 10, except two, within this framework and we can estimate, with confidence, the electron energy distribution index for 6 of the sample. Furthermore we identify jet breaks in a number of the bursts. A statistical analysis of the distribution of p reveals that, even in the most conservative case of least scatter, the values are not consistent with a single, universal value. The values of k suggest that the circumburst density profiles are not drawn from only one of the constant density or wind-like media populations.

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