Distributions of Long-Lived Radioactive Nuclei Provided by Star Forming Environments

Radioactive nuclei play an important role in planetary evolution by providing an internal heat source, which affects planetary structure and helps facilitate plate tectonics. A minimum level of nuclear activity is thought to be necessary --- but not sufficient --- for planets to be habitable. Extending previous work that focused on short-lived nuclei, this paper considers the delivery of long-lived radioactive nuclei to circumstellar disks in star forming regions. Although the long-lived nuclear species are always present, their abundances can be enhanced through multiple mechanisms. Most stars form in embedded cluster environments, so that disks can be enriched directly by intercepting ejecta from supernovae within the birth clusters. In addition, molecular clouds often provide multiple episodes of star formation, so that nuclear abundances can accumulate within the cloud; subsequent generations of stars can thus receive elevated levels of radioactive nuclei through this distributed enrichment scenario. This paper calculates the distribution of additional enrichment for $^{40}$K, the most abundant of the long-lived radioactive nuclei. We find that distributed enrichment is more effective than direct enrichment. For the latter mechanism, ideal conditions lead to about 1 in 200 solar systems being directly enriched in $^{40}$K at the level inferred for the early solar nebula (thereby doubling the abundance). For distributed enrichment from adjacent clusters, about 1 in 80 solar systems are enriched at the same level. Distributed enrichment over the entire molecular cloud is more uncertain, but can be even more effective.Comment: 24 pages, 8 figures, accepted for publication in Ap

Assessing the Feasibility of Cosmic-Ray Acceleration by Magnetic Turbulence at the Galactic Center

The presence of relativistic particles at the center of our galaxy is evidenced by the diffuse TeV emission detected from the inner $\sim$$2^\circ$ of the Galaxy. Although it is not yet entirely clear whether the origin of the TeV photons is due to hadronic or leptonic interactions, the tight correlation of the intensity distribution with the distribution of molecular gas along the Galactic ridge strongly points to a pionic-decay process involving relativistic protons. In earlier work, we concluded that point-source candidates, such as the supermassive black hole Sagittarius A* (identified with the HESS source J1745-290), or the pulsar wind nebulae dispersed along the Galactic plane, could not account for the observed diffuse TeV emission from this region. Motivated by this result, we consider here the feasibility that the cosmic rays populating the Galactic Center (GC) region are accelerated in situ by magnetic turbulence. Our results indicate that even in a highly conductive environment, this mechanism is efficient enough to energize protons within the intercloud medium to the \ga TeV energies required to produce the HESS emission.Comment: Accepted for publication in Ap

High Energy Cosmic-ray Diffusion in Molecular Clouds: A Numerical Approach

The propagation of high-energy cosmic rays through giant molecular clouds constitutes a fundamental process in astronomy and astrophysics. The diffusion of cosmic-rays through these magnetically turbulent environments is often studied through the use of energy-dependent diffusion coefficients, although these are not always well motivated theoretically. Now, however, it is feasible to perform detailed numerical simulations of the diffusion process computationally. While the general problem depends upon both the field structure and particle energy, the analysis may be greatly simplified by dimensionless analysis. That is, for a specified purely turbulent field, the analysis depends almost exclusively on a single parameter -- the ratio of the maximum wavelength of the turbulent field cells to the particle gyration radius. For turbulent magnetic fluctuations superimposed over an underlying uniform magnetic field, particle diffusion depends on a second dimensionless parameter that characterizes the ratio of the turbulent to uniform magnetic field energy densities. We consider both of these possibilities and parametrize our results to provide simple quantitative expressions that suitably characterize the diffusion process within molecular cloud environments. Doing so, we find that the simple scaling laws often invoked by the high-energy astrophysics community to model cosmic-ray diffusion through such regions appear to be fairly robust for the case of a uniform magnetic field with a strong turbulent component, but are only valid up to $\sim 50$ TeV particle energies for a purely turbulent field. These results have important consequences for the analysis of cosmic-ray processes based on TeV emission spectra associated with dense molecular clouds.Comment: Accepted for publication in The Astrophysical Journa

High-Energy Activity in the Unusually Soft TeV Source HESS J1804-216 toward the Galactic Center

In recent years, apparent anisotropies in the ~EeV cosmic ray (CR) flux arriving at Earth from the general direction of the galactic center have been reported from the analysis of AGASA and SUGAR data. The more recently commissioned Auger Observatory has not confirmed these results. HESS has now detected an unusually soft TeV source roughly coincident with the location of the previously claimed CR anisotropy. In this paper, we develop a model for the TeV emission from this object, consistent with observations at other wavelengths, and examine the circumstances under which it might have contributed to the $\sim$ EeV cosmic ray spectrum. We find that the supernova remnant G8.7-0.1 can plausibly account for all the known radiative characteristics of HESS J1804-216, but that it can accelerate cosmic rays only up to an energy $\sim 10^5$ GeV. On the other hand, the pulsar (PSR J1803-2137) embedded within this remnant can in principle inject EeV protons into the surrounding medium, but it cannot account for the broadband spectrum of HESS J1804-216. We therefore conclude that although G8.7-0.1 is probably the source of TeV photons originating from this direction, there is no compelling theoretical motivation for expecting a cosmic ray anisotropy at this location. However, if G8.7-0.1 is indeed correctly identified with HESS J1804-216, it should also produce a $\sim$ GeV flux detectable in a one-year all sky survey by GLAST

Charged Particle Dynamics in the Magnetic Field of a Long Straight Current-Carrying Wire

The article discusses the concept behind motion of a charged particle in a non-uniform filed of a wire carrying current. Topics discussed include possible types of motion in a current carrying field, vector analysis of velocity and magnetic field of the particle and Coupled differential equations

Diffusive Cosmic Ray Acceleration at the Galactic Centre

The diffuse TeV emission detected from the inner $\sim2^\circ$ of the Galaxy appears to be strongly correlated with the distribution of molecular gas along the Galactic ridge. Although it is not yet entirely clear whether the origin of the TeV photons is due to hadronic or leptonic interactions, the tight correlation of the intensity distribution with the molecular gas strongly points to a pionic-decay process involving relativistic protons. But the spectrum of the TeV radiation---a power law with index $\alpha\approx -2.3$---cannot be accommodated easily with the much steeper distribution of cosmic rays seen at Earth. In earlier work, we examined the possible sources of these relativistic protons and concluded that neither the supermassive black hole Sagittarius A* (identified with the HESS source J1745-290), nor several pulsar wind nebulae dispersed along the Galactic plane, could produce a TeV emission profile morphologically similar to that seen by HESS. We concluded from this earlier study that only relativistic protons accelerated throughout the inter-cloud medium could account for the observed diffuse TeV emission from this region. In this paper, we develop a model for diffusive proton acceleration driven by a turbulent Alfv\'enic magnetic field present throughout the gaseous medium. Though circumstantial, this appears to be the first evidence that at least some cosmic rays are accelerated diffusively within the inner $\sim300$ pc of the Galaxy.Comment: Accepted for publication in MNRAS letter