Quasi-normal modes of rotating relativistic stars - neutral modes for realistic equations of state

We compute zero-frequency (neutral) quasi-normal f-modes of fully relativistic and rapidly rotating neutron stars, using several realistic equations of state (EOSs) for neutron star matter. The zero-frequency modes signal the onset of the gravitational radiation-driven instability. We find that the l=m=2 (bar) f-mode is unstable for stars with gravitational mass as low as 1.0 - 1.2 M_\odot, depending on the EOS. For 1.4 M_\odot neutron stars, the bar mode becomes unstable at 83 % - 93 % of the maximum allowed rotation rate. For a wide range of EOSs, the bar mode becomes unstable at a ratio of rotational to gravitational energies T/W \sim 0.07-0.09 for 1.4 M_\odot stars and T/W \sim 0.06 for maximum mass stars. This is to be contrasted with the Newtonian value of T/W \sim 0.14. We construct the following empirical formula for the critical value of T/W for the bar mode, (T/W)_2 = 0.115 - 0.048 M / M_{max}^{sph}, which is insensitive to the EOS to within 4 - 6 %. This formula yields an estimate for the neutral mode sequence of the bar mode as a function only of the star's mass, M, given the maximum allowed mass, M_{max}^{sph}, of a nonrotating neutron star. The recent discovery of the fast millisecond pulsar in the supernova remnant N157B, supports the suggestion that a fraction of proto-neutron stars are born in a supernova collapse with very large initial angular momentum. Thus, in a fraction of newly born neutron stars the instability is a promising source of continuous gravitational waves. It could also play a major role in the rotational evolution (through the emission of angular momentum) of merged binary neutron stars, if their post-merger angular momentum exceeds the maximum allowed to form a Kerr black hole.Comment: 12 pages, 5 figures, submitted to Ap

Numerical Uncertainty Quantification for Radiation Analysis Tools

Recently a new emphasis has been placed on engineering applications of space radiation analyses and thus a systematic effort of Verification, Validation and Uncertainty Quantification (VV&UQ) of the tools commonly used for radiation analysis for vehicle design and mission planning has begun. There are two sources of uncertainty in geometric discretization addressed in this paper that need to be quantified in order to understand the total uncertainty in estimating space radiation exposures. One source of uncertainty is in ray tracing, as the number of rays increase the associated uncertainty decreases, but the computational expense increases. Thus, a cost benefit analysis optimizing computational time versus uncertainty is needed and is addressed in this paper. The second source of uncertainty results from the interpolation over the dose vs. depth curves that is needed to determine the radiation exposure. The question, then, is what is the number of thicknesses that is needed to get an accurate result. So convergence testing is performed to quantify the uncertainty associated with interpolating over different shield thickness spatial grids

Pion and Kaon Lab Frame Differential Cross Sections for Intermediate Energy Nucleus-Nucleus Collisions

Space radiation transport codes require accurate models for hadron production in intermediate energy nucleus-nucleus collisions. Codes require cross sections to be written in terms of lab frame variables and it is important to be able to verify models against experimental data in the lab frame. Several models are compared to lab frame data. It is found that models based on algebraic parameterizations are unable to describe intermediate energy differential cross section data. However, simple thermal model parameterizations, when appropriately transformed from the center of momentum to the lab frame, are able to account for the data

Radiation Shielding Optimization on Mars

Future space missions to Mars will require radiation shielding to be optimized for deep space transit and an extended stay on the surface. In deep space, increased shielding levels and material optimization will reduce the exposure from most solar particle events (SPE) but are less effective at shielding against galactic cosmic rays (GCR). On the surface, the shielding provided by the Martian atmosphere greatly reduces the exposure from most SPE, and long-term GCR exposure is a primary concern. Previous work has shown that in deep space, additional shielding of common materials such as aluminum or polyethylene does not significantly reduce the GCR exposure. In this work, it is shown that on the Martian surface, almost any amount of aluminum shielding increases exposure levels for humans. The increased exposure levels are attributed to neutron production in the shield and Martian regolith as well as the electromagnetic cascade induced in the Martian atmosphere. This result is significant for optimization of vehicle and shield designs intended for the surface of Mars

HZETRN Radiation Transport Validation Using Balloon-Based Experimental Data

The deterministic radiation transport code HZETRN (High charge (Z) and Energy TRaNsport) was developed by NASA to study the effects of cosmic radiation on astronauts and instrumentation shielded by various materials. This work presents an analysis of computed differential flux from HZETRN compared with measurement data from three balloon-based experiments over a range of atmospheric depths, particle types, and energies. Model uncertainties were quantified using an interval-based validation metric that takes into account measurement uncertainty both in the flux and the energy at which it was measured. Average uncertainty metrics were computed for the entire dataset as well as subsets of the measurements (by experiment, particle type, energy, etc.) to reveal any specific trends of systematic over- or under-prediction by HZETRN. The distribution of individual model uncertainties was also investigated to study the range and dispersion of errors beyond just single scalar and interval metrics. The differential fluxes from HZETRN were generally well-correlated with balloon-based measurements; the median relative model difference across the entire dataset was determined to be 30%. The distribution of model uncertainties, however, revealed that the range of errors was relatively broad, with approximately 30% of the uncertainties exceeding 40%. The distribution also indicated that HZETRN systematically under-predicts the measurement dataset as a whole, with approximately 80% of the relative uncertainties having negative values. Instances of systematic bias for subsets of the data were also observed, including a significant underestimation of alpha particles and protons for energies below 2.5 GeV/u. Muons were found to be systematically over-predicted at atmospheric depths deeper than 50 g/cm(sup 2) but under-predicted for shallower depths. Furthermore, a systematic under-prediction of alpha particles and protons was observed below the geomagnetic cutoff, suggesting that improvements to the light ion production cross sections in HZETRN should be investigated

Faster and More Accurate Transport Procedures for HZETRN

Several aspects of code verification are examined for HZETRN. First, a detailed derivation of the numerical marching algorithms is given. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of various coding errors is also given, and the impact of these errors on exposure quantities is shown. Finally, a coupled convergence study is conducted. From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is also determined that almost all of the discretization error in HZETRN is caused by charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons are given for three applications in which HZETRN is commonly used. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations

Recent Developments in Three Dimensional Radiation Transport Using the Green's Function Technique

In the future, astronauts will be sent into space for longer durations of time compared to previous missions. The increased risk of exposure to dangerous radiation, such as Galactic Cosmic Rays and Solar Particle Events, is of great concern. Consequently, steps must be taken to ensure astronaut safety by providing adequate shielding. In order to better determine and verify shielding requirements, an accurate and efficient radiation transport code based on a fully three dimensional radiation transport model using the Green's function technique is being develope

Predicting Cell Death and Mutation Frequency for a Wide Spectrum of LET by Assuming DNA Break Clustering Inside Repair Domains

Cosmic radiation, which is composed of high charged and energy (HZE) particles, is responsible for cell death and mutation, which may be involved in cancer induction. Mutations are consequences of mis-repaired DNA breaks especially double-strand breaks (DSBs) that induce inter- and intra-chromosomal rearrangements (translocations, deletions, inversion). In this study, a computer simulation model is used to investigate the clustering of DSBs in repair domains, previously evidenced by our group in human breast cells [1]. This model is calibrated with experimental data measuring persistent 53BP1 radiation-induced foci (RIF) and is used to explain the high relative biological effectiveness (RBE) of HZE for both cell death and DNA mutation frequencies. We first validate our DSB cluster model using a new track structure model deployed on a simple geometrical configuration for repair domains in the nucleus; then we extend the scope from cell death to mutation induction. This work suggests that mechanism based on DSB repair process can explain several biological effects induced by HZE particles on different type of living cell

Simulation of the Formation of DNA Double Strand Breaks and Chromosome Aberrations in Irradiated Cells

The formation of DNA double-strand breaks (DSBs) and chromosome aberrations is an important consequence of ionizing radiation. To simulate DNA double-strand breaks and the formation of chromosome aberrations, we have recently merged the codes RITRACKS (Relativistic Ion Tracks) and NASARTI (NASA Radiation Track Image). The program RITRACKS is a stochastic code developed to simulate detailed event-by-event radiation track structure: [1] This code is used to calculate the dose in voxels of 20 nm, in a volume containing simulated chromosomes, [2] The number of tracks in the volume is calculated for each simulation by sampling a Poisson distribution, with the distribution parameter obtained from the irradiation dose, ion type and energy. The program NASARTI generates the chromosomes present in a cell nucleus by random walks of 20 nm, corresponding to the size of the dose voxels, [3] The generated chromosomes are located within domains which may intertwine, and [4] Each segment of the random walks corresponds to approx. 2,000 DNA base pairs. NASARTI uses pre-calculated dose at each voxel to calculate the probability of DNA damage at each random walk segment. Using the location of double-strand breaks, possible rejoining between damaged segments is evaluated. This yields various types of chromosomes aberrations, including deletions, inversions, exchanges, etc. By performing the calculations using various types of radiations, it will be possible to obtain relative biological effectiveness (RBE) values for several types of chromosome aberrations

Differential Cross Sections for Proton-Proton Elastic Scattering

Proton-proton elastic scattering is investigated within the framework of the one pion exchange model in an attempt to model nucleon-nucleon interactions spanning the large range of energies important to cosmic ray shielding. A quantum field theoretic calculation is used to compute both differential and total cross sections. A scalar theory is then presented and compared to the one pion exchange model. The theoretical cross sections are compared to proton-proton scattering data to determine the validity of the models