Relativistic Radiation Mediated Shocks

The structure of relativistic radiation mediated shocks (RRMS) propagating into a cold electron-proton plasma is calculated and analyzed. A qualitative discussion of the physics of relativistic and non relativistic shocks, including order of magnitude estimates for the relevant temperature and length scales, is presented. Detailed numerical solutions are derived for shock Lorentz factors $\Gamma_u$ in the range $6\le\Gamma_u\le30$, using a novel iteration technique solving the hydrodynamics and radiation transport equations (the protons, electrons and positrons are argued to be coupled by collective plasma processes and are treated as a fluid). The shock transition (deceleration) region, where the Lorentz factor $\Gamma$ drops from $\Gamma_u$ to $\sim 1$, is characterized by high plasma temperatures $T\sim \Gamma m_ec^2$ and highly anisotropic radiation, with characteristic shock-frame energy of upstream and downstream going photons of a few~$\times\, m_ec^2$ and $\sim \Gamma^2 m_ec^2$, respectively.Photon scattering is dominated by e$^\pm$ pairs, with pair to proton density ratio reaching $\approx10^2\Gamma_u$. The width of the deceleration region, in terms of Thomson optical depths for upstream going photons, is large, $\Delta\tau\sim\Gamma_u^2$ ($\Delta\tau\sim1$ neglecting the contribution of pairs) due to Klein Nishina suppression of the scattering cross section. A high energy photon component, narrowly beamed in the downstream direction, with a nearly flat power-law like spectrum, $\nu I_\nu\propto\nu^0$, and an energy cutoff at $\sim \Gamma_u^2 m_ec^2$ carries a fair fraction of the energy flux at the end of the deceleration region. An approximate analytic model of RRMS, reproducing the main features of the numerical results, is provided

Cosmic rays from trans-relativistic supernovae

We derive constraints that must be satisfied by the sources of ~10^{15} to ~10^{18} eV cosmic rays, under the assumption that the sources are Galactic. We show that while these constraints are not satisfied by ordinary supernovae (SNe), which are believed to be the sources of <10^{15} eV cosmic rays, they may be satisfied by the recently discovered class of trans-relativistic supernovae (TRSNe), which were observed in association with gamma-ray bursts. We define TRSNe as SNe that deposit a large fraction, f_R>10^{-2}, of their kinetic energy in mildly relativistic, \gamma\beta>1, ejecta. The high velocity ejecta enable particle acceleration to ~10^{18} eV, and the large value of f_R (compared to f_R~10^{-7} for ordinary SNe) ensures that if TRSNe produce the observed ~10^{18} eV cosmic ray flux, they do not overproduce the flux at lower energies. This, combined with the estimated rate and energy production of TRSNe, imply that Galactic TRSNe may be the sources of cosmic rays with energies up to ~10^{18}eV .Comment: Accepted to ApJ. Expanded abstract, introduction, discussio

Deformations of Calabi-Yau hypersurfaces arising from deformations of toric varieties

There are easy "polynomial" deformations of Calabi-Yau hypersurfaces in toric varieties performed by changing the coefficients of the defining polynomial of the hypersurface. In this paper, we explicitly constructed the ``non-polynomial'' deformations of Calabi-Yau hypersurfaces, which arise from deformations of the ambient toric variety

Counting rational curves of arbitrary shape in projective spaces

We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by enumerating one-component rational curves with a triple point or a tacnodal point in the three-dimensional projective space and with a cusp in any projective space.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper16.abs.htm

Treatment Failure Among Infected Periprosthetic Patients at a Highly Specialized Revision TKA Referral Practice

Deep infection is a serious and costly complication of total knee arthroplasty (TKA), which can increase patient morbidity and compromise functional outcome and satisfaction. Two-stage revision with an interval of parental antibiotics has been shown to be the most successful treatment in eradicating deep infection following TKA. We report a large series by a single surgeon with a highly specialized revision TKA referral practice. We identified 84 patients treated by a two-stage revision. We defined “successful two-stage revision” as negative intraoperative cultures and no further infection-related procedure. We defined “eradication of infection” on the basis of negative cultures and clinical diagnosis. After a mean follow up of 25 months, eradication of the infection was documented in 90.5% of the patients; some had undergone further surgical intervention after the index two-stage procedure. Successful two-stage revision (e.g. no I&D, fusion, amputation) was documented only in 63.5% of the patients. We also observed a trend between presence of resistant staphylococcus (MRSA) (p=0.05) as well as pre-revision surgical procedures (p=0.08) and a lower likelihood of successfully two-stage revision. Factors affecting the high failure rate included multiple surgeries prior to the two-stage revision done at our institution, and high prevalence of MRSA present among failed cases. The relatively high rate of failure to achieve a successful two-stage revision observed in our series may be attributed to the highly specialized referral practice. Thus increasing the prevalence of patients with previous failed attempts at infection eradication and delayed care as well as more fragile and immune compromised hosts

Treatment Failure Among Infected Periprosthetic Total Hip Arthroplasty Patients

Two-stage revision has been shown to be the most successful treatment in eradicating deep infection following total hiparthroplasty. We identified 62 patients treated by a two-stage revision. We defined “successful revision” as negative intraoperative cultures and no further infection-related procedure. We defined “eradication of infection” on the basis of negative cultures and clinical diagnosis at least one year after 2nd stage procedure. After a mean follow up of 2.7 years, eradication of the infection was documented in 91.1%, and a successful two-stage revision in 85.7% of patients. We observed no association between higher pre-reimplantation levels of ESR and C-reactive protein and lower likelihood of successful two-stage revision. We found an association between a history of another previous infected prosthetic joint and a failed 2nd stage procedure. Failure to achieve eradication of infection and successful two-stage revision occurs infrequently. Patients with prior history of a previous prosthetic joint infection are at higher risk of failure

The energy production rate & the generation spectrum of UHECRs

We derive simple analytic expressions for the flux and spectrum of ultra-high energy cosmic-rays (UHECRs) predicted in models where the CRs are protons produced by extra-Galactic sources. For a power-law scaling of the CR production rate with redshift and energy, d\dot{n} /dE\propto E^-\alpha (1+z)^m, our results are accurate at high energy, E>10^18.7 eV, to better than 15%, providing a simple and straightforward method for inferring d\dot{n}/dE from the observed flux at E. We show that current measurements of the UHECR spectrum, including the latest Auger data, imply E^2d\dot{n}/dE(z=0)=(0.45\pm0.15)(\alpha-1) 10^44 erg Mpc^-3 yr^-1 at E<10^19.5 eV with \alpha roughly confined to 2\lesseq\alpha<2.7. The uncertainty is dominated by the systematic and statistic errors in the experimental determination of individual CR event energy, (\Delta E/E)_{sys} (\Delta E/E)_{stat} ~20%. At lower energy, d\dot{n}/dE is uncertain due to the unknown Galactic contribution. Simple models in which \alpha\simeq 2 and the transition from Galactic to extra-Galactic sources takes place at the "ankle", E ~10^19 eV, are consistent with the data. Models in which the transition occurs at lower energies require a high degree of fine tuning and a steep spectrum, \alpha\simeq 2.7, which is disfavored by the data. We point out that in the absence of accurate composition measurements, the (all particle) energy spectrum alone cannot be used to infer the detailed spectral shapes of the Galactic and extra-Galactic contributions.Comment: 9 pages, 11 figures, minor revision

Fast radiation mediated shocks and supernova shock breakouts

We present a simple analytic model for the structure of non-relativistic and relativistic radiation mediated shocks. At shock velocities \beta_s\equiv v_s/c\gtrsim 0.1, the shock transition region is far from thermal equilibrium, since the transition crossing time is too short for the production of a black-body photon density (by Bremsstrahlung emission). In this region, electrons and photons (and positrons) are in Compton (pair) equilibrium at temperatures T_s significantly exceeding the far downstream temperature, T_s\gg T_d\approx 2(\varepsilon n_u \hbar^3c^3)^{1/4}. T_s\gtrsim 10 keV is reached at shock velocities \beta_s\approx 0.2. At higher velocities, \beta_s\gtrsim0.6, the plasma is dominated in the transition region by e^\pm pairs and 60 keV\lesssim T_s \lesssim 200 keV. We argue that the spectrum emitted during the breaking out of supernova shocks from the stellar envelopes (or the surrounding winds) of Blue Super Giants and Wolf-Rayet stars, which reach \beta_s>0.1 for reasonable stellar parameters, may include a hard component with photon energies reaching tens or even hundreds of keV. This may account for the X-ray outburst associated with SN2008D, and possibly for other SN-associated outbursts with spectra not extending beyond few 100 keV (e.g. XRF060218/SN2006aj).Comment: 12 pages, 3 figures, analysis of the case \beta_d\approx 0.1 correcte