Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity

A truncated moment formalism for general relativistic radiation hydrodynamics, based on the Thorne's moment formalism, is derived. The fluid rest frame is chosen to be the fiducial frame for defining the radiation moments. Then, zeroth-, first-, and second-rank radiation moments are defined from the distribution function with a physically reasonable assumption for it in the optically thin and thick limits. The source terms are written, focusing specifically on the neutrino transfer and neglecting higher harmonic angular dependence of the reaction angle. Finally, basic equations for a truncated moment formalism for general relativistic radiation hydrodynamics in a closed covariant form are derived assuming a closure relation among the radiation stress tensor, energy density, and energy flux, and a variable Eddington factor, which works well.Comment: 33 pages, 2 figures, to be published in Prog. Theor. Phy

General Relativistic Ray-Tracing Method for Estimating the Energy and Momentum Deposition by Neutrino Pair Annihilation in Collapsars

Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation ($\nu + {\bar \nu} \rightarrow e^{-} + e^{+}$) in the vicinity of accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. For the neutrino opacity, the charged-current $\beta$-processes are taken into account, which are dominant in the vicinity of the accretion tori. The numerical accuracy of the developed code is certificated by several tests, in which we show comparisons with the corresponding analytic solutions. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the general relativistic effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percents. After the accretion disk settles into a stationary state (typically later than $\sim 9$ s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest the neutrino pair annihilation has a potential importance equal to the conventional magnetohydrodynamic mechanism for igniting the GRB fireballs.Comment: 33 pages, 15 figures, accepted to the Ap

Feasibility of methotrexate discontinuation following tocilizumab and methotrexate combination therapy in patients with long-standing and advanced rheumatoid arthritis: a 3-year observational cohort study

Objectives: Methotrexate (MTX) is associated with extensive side effects, including myelosuppression, interstitial pneumonia, and infection. It is, therefore, critical to establish whether its administration is required after achieving remission with tocilizumab (TCZ) and MTX combination therapy in patients with rheumatoid arthritis (RA). Therefore, the aim of this multicenter, observational, cohort study was to evaluate the feasibility of MTX discontinuation for the safety of these patients. Methods: Patients with RA were administered TCZ, with or without MTX, for 3 years; those who received TCZ+MTX combination therapy were selected. After remission was achieved, MTX was discontinued without flare development in one group (discontinued [DISC] group, n = 33) and continued without flare development in another group (maintain [MAIN] group, n = 37). The clinical efficacy of TCZ+MTX therapy, patient background characteristics, and adverse events were compared between groups. Results: The disease activity score in 28 joints-erythrocyte sedimentation rate (DAS28-ESR) at 3, 6, and 9 months was significantly lower in the DISC group (P < .05, P < .01, and P < .01, respectively). Further, the DAS28-ESR remission rate at 6 and 9 months and Boolean remission rate at 6 months were significantly higher in the DISC group (P < .01 for all). Disease duration was significantly longer in the DISC group (P < .05). Furthermore, the number of patients with stage 4 RA was significantly higher in the DISC group (P < .01). Conclusions: Once remission was achieved, MTX was discontinued in patients who responded favorably to TCZ+MTX therapy, despite the prolonged disease duration and stage progression