ABSTRACT
Cosmic rays may have contributed to the start of life on the Earth. Here, we investigate the evolution of the Galactic cosmic ray spectrum at the Earth from ages t = 0.6−6.0 Gyr. We use a 1D ...cosmic ray transport model and a 1.5D stellar wind model to derive the evolving wind properties of a solar-type star. At $t=1\,$ Gyr, approximately when life is thought to have begun on the Earth, we find that the intensity of ∼GeV Galactic cosmic rays would have been ∼10 times smaller than the present-day value. At lower kinetic energies, Galactic cosmic ray modulation would have been even more severe. More generally, we find that the differential intensity of low-energy Galactic cosmic rays decreases at younger ages and is well described by a broken power law in solar rotation rate. We provide an analytic formula of our Galactic cosmic ray spectra at the Earth’s orbit for different ages. Our model is also applicable to other solar-type stars with exoplanets orbiting at different radii. Specifically, we use our Galactic cosmic ray spectrum at 20 au for $t=600\,$ Myr to estimate the penetration of cosmic rays in the atmosphere of HR 2562b, a directly imaged exoplanet orbiting a young solar-type star. We find that the majority of particles <0.1 GeV are attenuated at pressures ≳10−5 bar and thus do not reach altitudes below ∼100 km. Observationally constraining the Galactic cosmic ray spectrum in the atmosphere of a warm Jupiter would in turn help constrain the flux of cosmic rays reaching young Earth-like exoplanets.
Abstract
We assess the ionising effect of low energy protostellar cosmic rays in protoplanetary disks around a young solar mass star for a wide range of disk parameters. We assume a source of low ...energy cosmic rays located close to the young star which travel diffusively through the protoplanetary disk. We use observationally inferred values from nearby star-forming regions for the total disk mass and the radial density profile. We investigate the influence of varying the disk mass within the observed scatter for a solar mass star. We find that for a large range of disk masses and density profiles that protoplanetary disks are “optically thin” to low energy (∼3 GeV) cosmic rays. At R ∼ 10 au, for all of the disks that we consider (Mdisk = 6.0 × 10−4 − 2.4 × 10−2M⊙), the ionisation rate due to low energy stellar cosmic rays is larger than that expected from unmodulated galactic cosmic rays. This is in contrast to our previous results which assumed a much denser disk which may be appropriate for a more embedded source. At R ∼ 70 au, the ionisation rate due to stellar cosmic rays dominates in ∼50% of the disks. These are the less massive disks with less steep density profiles. At this radius there is at least an order of magnitude difference in the ionisation rate between the least and most massive disk that we consider. Our results indicate, for a wide range of disk masses, that low energy stellar cosmic rays provide an important source of ionisation at the disk midplane at large radii (∼70 au).
The interaction of plasma with magnetic field in the partially ionised solar atmosphere is frequently modelled via a single-fluid approximation, which is valid for the case of a strongly coupled ...collisional media, such as solar photosphere and low chromosphere. Under the single-fluid formalism the main non-ideal effects are described by a series of extra terms in the generalised induction equation and in the energy conservation equation. These effects are: Ohmic diffusion, ambipolar diffusion, the Hall effect, and the Biermann battery effect. From the point of view of the numerical solution of the single-fluid equations, when ambipolar diffusion or Hall effects dominate can introduce severe restrictions on the integration time step and can compromise the stability of the numerical scheme. In this paper we introduce two numerical schemes to overcome those limitations. The first of them is known as super time-stepping (STS) and it is designed to overcome the limitations imposed when the ambipolar diffusion term is dominant. The second scheme is called the Hall diffusion scheme (HDS) and it is used when the Hall term becomes dominant. These two numerical techniques can be used together by applying Strang operator splitting. This paper describes the implementation of the STS and HDS schemes in the single-fluid code MANCHA3D. The validation for each of these schemes is provided by comparing the analytical solution with the numerical one for a suite of numerical tests.
Abstract
Observations of non-thermal emission from several supernova remnants suggest that magnetic fields close to the blast wave are much stronger than would be naively expected from simple shock ...compression of the field permeating the interstellar medium (ISM).
We present a simple model which is capable of achieving sufficient magnetic field amplification to explain the observations. We propose that the cosmic ray pressure gradient acting on the inhomogeneous ISM upstream of the supernova blast wave induces strong turbulence upstream of the supernova blast wave. The turbulence is generated through the differential acceleration of the upstream ISM which occurs as a result of density inhomogeneities in the ISM. This turbulence then amplifies the pre-existing magnetic field.
Numerical simulations are presented which demonstrate that amplification factors of 20 or more are easily achievable by this mechanism when reasonable parameters for the ISM and supernova blast wave are assumed. The length scale over which this amplification occurs is that of the diffusion length of the highest energy non-thermal particles.
Abstract
It is believed that turbulence may have a significant impact on star formation and the dynamics and evolution of the molecular clouds in which this occurs. It is also known that non-ideal ...magnetohydrodynamic (MHD) effects influence the nature of this turbulence. We present the results of a numerical study of four-fluid MHD turbulence in which the dynamics of electrons, ions, charged dust grains and neutrals and their interactions are followed. The parameters describing the fluid being simulated are based directly on observations of molecular clouds. We find that the velocity and magnetic field power spectra are strongly influenced by multifluid effects on length-scales at least as large as 0.05pc. The probability density functions of the various species in the system are all found to be close to log-normal, with charged species having a slightly less platykurtic (flattened) distribution than the neutrals. We find that the introduction of multifluid effects does not significantly alter the structure functions of the centroid velocity increment.
ABSTRACT
Energetic particles, such as stellar cosmic rays, produced at a heightened rate by active stars (like the young Sun) may have been important for the origin of life on Earth and other ...exoplanets. Here, we compare, as a function of stellar rotation rate (Ω), contributions from two distinct populations of energetic particles: stellar cosmic rays accelerated by impulsive flare events and Galactic cosmic rays. We use a 1.5D stellar wind model combined with a spatially 1D cosmic ray transport model. We formulate the evolution of the stellar cosmic ray spectrum as a function of stellar rotation. The maximum stellar cosmic ray energy increases with increasing rotation, i.e. towards more active/younger stars. We find that stellar cosmic rays dominate over Galactic cosmic rays in the habitable zone at the pion threshold energy for all stellar ages considered ($t_*=0.6\!-\!2.9\,$ Gyr). However, even at the youngest age, $t_*=0.6\,$ Gyr, we estimate that $\gtrsim \, 80$ MeV stellar cosmic ray fluxes may still be transient in time. At ∼1 Gyr when life is thought to have emerged on Earth, we demonstrate that stellar cosmic rays dominate over Galactic cosmic rays up to ∼4 GeV energies during flare events. Our results for t* = 0.6 Gyr (Ω = 4 Ω⊙) indicate that ≲GeV stellar cosmic rays are advected from the star to 1 au and are impacted by adiabatic losses in this region. The properties of the inner solar wind, currently being investigated by the Parker Solar Probe and Solar Orbiter, are thus important for accurate calculations of stellar cosmic rays around young Sun-like stars.
The redistribution of angular momentum is a long standing problem in our understanding of protoplanetary disc (PPD) evolution. The magnetorotational instability (MRI) is considered a likely ...mechanism. We present the results of a study involving multifluid global simulations including Ohmic dissipation, ambipolar diffusion and the Hall effect in a dynamic, self-consistent way. We focus on the turbulence resulting from the non-linear development of the MRI in radially stratified PPDs and compare with ideal magnetohydrodynamics simulations. In the multifluid simulations, the disc is initially set up to transition from a weak Hall-dominated regime, where the Hall effect is the dominant non-ideal effect but approximately the same as or weaker than the inductive term, to a strong Hall-dominated regime, where the Hall effect dominates the inductive term. As the simulations progress, a substantial portion of the disc develops into a weak Hall-dominated disc. We find a transition from turbulent to laminar flow in the inner regions of the disc, but without any corresponding overall density feature. We introduce a dimensionless parameter, αRM, to characterize accretion with αRM ≳ 0.1 corresponding to turbulent transport. We calculate the eddy turnover time, t
eddy, and compared this with an effective recombination time-scale, t
rcb, to determine whether the presence of turbulence necessitates non-equilibrium ionization calculations. We find that t
rcb is typically around three orders of magnitude smaller than t
eddy. Also, the ionization fraction does not vary appreciably. These two results suggest that these multifluid simulations should be comparable to single-fluid non-ideal simulations.
Abstract
We investigate the ionizing effect of low-energy cosmic rays (CRs) from a young star on its protoplanetary disc (PPD). We consider specifically the effect of ∼3 GeV protons injected at the ...inner edge of the PPD. An increase in the ionization fraction as a result of these CRs could allow the magnetorotational instability to operate in otherwise magnetically dead regions of the disc. For the typical values assumed we find an ionization rate of ζCR ∼ 10−17 s−1 at 1 au. The transport equation is solved by treating the propagation of the CRs as diffusive. We find for increasing diffusion coefficients the CRs penetrate further in the PPD, while varying the mass density profile of the disc is found to have little effect. We investigate the effect of an energy spectrum of CRs. The influence of a disc wind is examined by including an advective term. For advective wind speeds between 1 and 100 km s−1 diffusion dominates at all radii considered here (out to 10 au) for reasonable diffusion coefficients. Overall, we find that low-energy CRs can significantly ionize the mid-plane of PPDs out to ∼1 au. By increasing the luminosity or energy of the CRs, within plausible limits, their radial influence could increase to ∼2 au at the mid-plane but it remains challenging to significantly ionize the mid-plane further out.
Observations of non-thermal emission from several supernova remnants suggest that magnetic fields close to the blastwave are much stronger than would be naively expected from simple shock compression ...of the field permeating the interstellar medium (ISM). We investigate in some detail a simple model based on turbulence generation by cosmic ray pressure gradients. Previously, this model was investigated using 2D magnetohydrodynamic simulations. Motivated by the well-known qualitative differences between 2D and 3D turbulence, we further our investigations of this model using both 2D and 3D simulations to study the influence of the dimensionality of the simulations on the field amplification achieved. Further, since the model implies the formation of shocks which can, in principle, be efficiently cooled by collisional cooling, we include such cooling in our simulations to ascertain whether it could increase the field amplification achieved. Finally, we examine the influence of different orientations of the magnetic field with respect to the normal of the blastwave. We find that dimensionality has a slight influence on the overall amplification achieved, but a significant impact on the morphology of the amplified field. Collisional cooling has surprisingly little impact, primarily due to the short time which any element of the ISM resides in the precursor region for supernova blastwaves. Even allowing for a wide range of orientations of the magnetic field, we find that the magnetic field can be expected to be amplified by, on average, at least an order of magnitude in the precursors of supernova blastwaves.
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