On The Synchrotron Self-Compton Emission from Relativistic Shocks and Its Implications for Gamma-Ray Burst Afterglows

We consider the effects of inverse Compton scattering of synchrotron photons from relativistic electrons in GRB afterglows. We compute the spectrum of the inverse Compton emission and find that it can dominate the total cooling rate of the afterglow for several months or even years after the initial explosion. We demonstrate that the presence of strong inverse Compton cooling can be deduced from the effect it has on the time-evolution of the cooling break in the synchrotron spectral component, and therefore on the optical and X-ray afterglow lightcurves. We then show how the physical interpretation of the observed characteristics of the synchrotron spectrum must be modified to take into consideration this extra source of cooling, and give a revised prescription for computing physical parameters characterizing the expanding shock wave from the observed quantities. We find that for a given set of observables (synchrotron break frequencies and fluxes) there is either no consistent physical interpretation or two of them. Finally we discuss the prospects of directly detecting the inverse Compton emission with Chandra. We argue that such a detection is possible for GRBs exploding in a reasonably dense (n>1 cm^-3) medium.Comment: 21 pages, ApJ submitte

The prompt energy release of gamma-ray bursts using a cosmological k-correction

The fluences of gamma-ray bursts (GRBs) are measured with a variety of instruments in different detector energy ranges. A detailed comparison of the implied energy releases of the GRB sample requires, then, an accurate accounting of this diversity in fluence measurements which properly corrects for the redshifting of GRB spectra. Here, we develop a methodology to ``k-correct'' the implied prompt energy release of a GRB to a fixed co-moving bandpass. This allows us to homogenize the prompt energy release of 17 cosmological GRBs (using published redshifts, fluences, and spectra) to two common co-moving bandpasses: 20-2000 keV and 0.1 keV-10 MeV (``bolometric''). While the overall distribution of GRB energy releases does not change significantly by using a k-correction, we show that uncorrected energy estimates systematically undercounts the bolometric energy by ~5% to 600%, depending on the particular GRB. We find that the median bolometric isotropic-equivalent prompt energy release is 2.2 x 10^{53} erg with an r.m.s. scatter of 0.80 dex. The typical estimated uncertainty on a given k-corrected energy measurement is ~20%.Comment: Accepted to the Astronomical Journal. 21 pages (LaTeX) and 4 figure

Formation of Kuiper Belt Binaries

The discovery that a substantial fraction of Kuiper Belt objects (KBOs) exists in binaries with wide separations and roughly equal masses, has motivated a variety of new theories explaining their formation. Goldreich et al. (2002) proposed two formation scenarios: In the first, a transient binary is formed, which becomes bound with the aid of dynamical friction from the sea of small bodies (L^2s mechanism); in the second, a binary is formed by three body gravitational deflection (L^3 mechanism). Here, we accurately calculate the L^2s and L^3 formation rates for sub-Hill velocities. While the L^2s formation rate is close to previous order of magnitude estimates, the L^3 formation rate is about a factor of 4 smaller. For sub-Hill KBO velocities (v << v_H) the ratio of the L^3 to the L^2s formation rate is 0.05 (v/v_H) independent of the small bodies' velocity dispersion, their surface density or their mutual collisions. For Super-Hill velocities (v >> v_H) the L^3 mechanism dominates over the L^2s mechanism. Binary formation via the L^3 mechanism competes with binary destruction by passing bodies. Given sufficient time, a statistical equilibrium abundance of binaries forms. We show that the frequency of long-lived transient binaries drops exponentially with the system's lifetime and that such transient binaries are not important for binary formation via the L^3 mechanism, contrary to Lee et al. (2007). For the L^2s mechanism we find that the typical time, transient binaries must last, to form Kuiper Belt binaries (KBBs) for a given strength of dynamical friction, D, increases only logarithmically with D. Longevity of transient binaries only becomes important for very weak dynamical friction (i.e. D \lesssim 0.002) and is most likely not crucial for KBB formation.Comment: 20 pages, 3 figures, Accepted for publication in ApJ, correction of minor typo

The Ratio of Retrograde to Prograde Orbits: A Test for Kuiper Belt Binary Formation Theories

With the discovery of Kuiper Belt binaries that have wide separations and roughly equal masses new theories were proposed to explain their formation. Two formation scenarios were suggested by Goldreich and collaborators: In the first, dynamical friction that is generated by a sea of small bodies enables a transient binary to become bound ($L^2s$ mechanism); in the second, a transient binary gets bound by an encounter with a third body ($L^3$ mechanism). We show that these different binary formation scenarios leave their own unique signatures in the relative abundance of prograde to retrograde binary orbits. This signature is due to stable retrograde orbits that exist much further out in the Hill sphere than prograde orbits. It provides an excellent opportunity to distinguish between the different binary formation scenarios observationally. We predict that if binary formation proceeded while sub-Hill velocities prevailed, the vast majority of all comparable mass ratio binaries have retrograde orbits. This dominance of retrograde binary orbits is a result of binary formation via the $L^2s$ mechanism, or any other mechanism that dissipates energy in a smooth and gradual manner. For super-Hill velocities binary formation proceeds via the $L^3$ mechanism which produces a roughly equal number of prograde and retrograde binaries. These predictions assume that subsequent orbital evolution due to dynamical friction and dynamical stirring of the Kuiper belt did not alter the sense of the binary orbit after formation.Comment: 18 pages, 4 figures, minor changes, added section on comparison with recent observations, accepted for publication in Ap

Pure and loaded fireballs in SGR giant flares

On December 27, 2004, a giant flare from SGR 1806$-$20 was detected on earth. Its thermal spectrum and temperature suggest that the flare resulted from an energy release of about $10^{47}$ erg/sec close to the surface of a neutron star in the form of radiation and/or pairs. This plasma expanded under its own pressure producing a fireball and the observed gamma-rays escaped once the fireball became optically thin. The giant flare was followed by a bright radio afterglow, with an observable extended size, implying an energetic relativistic outflow. We revisit here the evolution of relativistic fireballs and we calculate the Lorentz factor and energy remaining in relativistic outflow once the radiation escapes. We show that pairs that arise naturally in a pure pairs-radiation fireball do not carry enough energy to account for the observed afterglow. We consider various alternatives and we show that if the relativistic outflow that causes the afterglow is related directly to the prompt flare, then the initial fireball must be loaded by baryons or Poynting flux. While we focus on parameters applicable to the giant flare and the radio afterglow of SGR 1806$-$20 the calculations presented here might be also applicable to GRBs

Characterizing Long COVID in an International Cohort: 7 Months of Symptoms and Their Impact

Objective: To characterize the symptom profile and time course in patients with Long COVID, along with the impact on daily life, work, and return to baseline health. / Design: International web-based survey of suspected and confirmed COVID-19 cases with illness lasting over 28 days and onset prior to June 2020. / Setting: Survey distribution via online COVID-19 support groups and social media. / Participants: 3,762 respondents from 56 countries completed the survey. 1166 (33.7%) were 40-49 years old, 937 (27.1%) were 50-59 years old, and 905 (26.1%) were 30-39 years old. 2961 (78.9%) were women, 718 (19.1%) were men, and 63 (1.7%) were nonbinary. 8.4% reported being hospitalized. 27% reported receiving a laboratory-confirmed diagnosis of COVID-19. 96% reported symptoms beyond 90 days. / Results: Prevalence of 205 symptoms in 10 organ systems was estimated in this cohort, with 66 symptoms traced over seven months. Respondents experienced symptoms in an average of 9.08 (95% confidence interval 9.04 to 9.13) organ systems. The most frequent symptoms reported after month 6 were: fatigue (77.7%, 74.9% to 80.3%), post-exertional malaise (72.2%, 69.3% to 75.0%), and cognitive dysfunction (55.4%, 52.4% to 58.8%). These three symptoms were also the three most commonly reported overall. In those who recovered in less than 90 days, the average number of symptoms peaked at week 2 (11.4, 9.4 to 13.6), and in those who did not recover in 90 days, the average number of symptoms peaked at month 2 (17.2, 16.5 to 17.8). Respondents with symptoms over 6 months experienced an average of 13.8 (12.7 to 14.9) symptoms in month 7. 85.9% (84.8% to 87.0%) experienced relapses, with exercise, physical or mental activity, and stress as the main triggers. 86.7% (85.6% to 92.5%) of unrecovered respondents were experiencing fatigue at the time of survey, compared to 44.7% (38.5% to 50.5%) of recovered respondents. 45.2% (42.9% to 47.2%) reported requiring a reduced work schedule compared to pre-illness and 22.3% (20.5% to 24.3%) were not working at the time of survey due to their health conditions. / Conclusions: Patients with Long COVID report prolonged multisystem involvement and significant disability. Most had not returned to previous levels of work by 6 months. Many patients are not recovered by 7 months, and continue to experience significant symptom burden

Optical Spectropolarimetry of the GRB 020813 Afterglow

The optical afterglow of gamma-ray burst 020813 was observed for 3 hours with the LRIS spectropolarimeter at the Keck-I telescope, beginning 4.7 hours after the burst was detected by HETE-2. The spectrum reveals numerous metal absorption lines that we identify with two systems at z=1.223 and z=1.255. We also detect an O II 3727 emission line at z=1.255 and we identify this galaxy as the likely host of the GRB. After a correction for Galactic interstellar polarization, the optical afterglow has a linear polarization of 1.8-2.4% during 4.7-7.9 hours after the burst. A measurement of p = 0.80% +/- 0.16% on the following night by Covino et al. demonstrates significant polarization variability over the next 14 hours. The lack of strong variability in the position angle of linear polarization indicates that the magnetic field in the jet is likely to be globally ordered rather than composed of a number of randomly oriented cells. Within the framework of afterglow models with collimated flows, the relatively low observed polarization suggests that the magnetic field components perpendicular and parallel to the shock front are only different by about 20%.Comment: To appear in ApJ Letters. 6 pages including 2 figure

Enhanced articular cartilage by human mesenchymal stem cells in enzymatically mediated transiently RGDS-functionalized collagen-mimetic hydrogels

Recapitulation of the articular cartilage microenvironment for regenerative medicine applications faces significant challenges due to the complex and dynamic biochemical and biomechanical nature of native tissue. Towards the goal of biomaterial designs that enable the temporal presentation of bioactive sequences, recombinant bacterial collagens such as Streptococcal collagen-like 2 (Scl2) proteins can be employed to incorporate multiple specific bioactive and biodegradable peptide motifs into a single construct. Here, we first modified the backbone of Scl2 with glycosaminoglycan-binding peptides and cross-linked the modified Scl2 into hydrogels via matrix metalloproteinase 7 (MMP7)-cleavable or non-cleavable scrambled peptides. The cross-linkers were further functionalized with a tethered RGDS peptide creating a system whereby the release from an MMP7-cleavable hydrogel could be compared to a system where release is not possible. The release of the RGDS peptide from the degradable hydrogels led to significantly enhanced expression of collagen type II (3.9-fold increase), aggrecan (7.6-fold increase), and SOX9 (5.2-fold increase) by human mesenchymal stem cells (hMSCs) undergoing chondrogenesis, as well as greater extracellular matrix accumulation compared to non-degradable hydrogels (collagen type II; 3.2-fold increase, aggrecan; 4-fold increase, SOX9; 2.8-fold increase). Hydrogels containing a low concentration of the RGDS peptide displayed significantly decreased collagen type I and X gene expression profiles, suggesting a major advantage over either hydrogels functionalized with a higher RGDS peptide concentration, or non-degradable hydrogels, in promoting an articular cartilage phenotype. These highly versatile Scl2 hydrogels can be further manipulated to improve specific elements of the chondrogenic response by hMSCs, through the introduction of additional bioactive and/or biodegradable motifs. As such, these hydrogels have the possibility to be used for other applications in tissue engineering. Statement of Significance Recapitulating aspects of the native tissue biochemical microenvironment faces significant challenges in regenerative medicine and tissue engineering due to the complex and dynamic nature of the tissue. The ability to take advantage of, mimic, and modulate cell-mediated processes within novel naturally-derived hydrogels is of great interest in the field of biomaterials to generate constructs that more closely resemble the biochemical microenvironment and functions of native biological tissues such as articular cartilage. Towards this goal, the temporal presentation of bioactive sequences such as RGDS on the chondrogenic differentiation of human mesenchymal stem cells is considered important as it has been shown to influence the chondrogenic phenotype. Here, a novel and versatile platform to recreate a high degree of biological complexity is proposed, which could also be applicable to other tissue engineering and regenerative medicine applications