Radial substructures have now been observed in a wide range of protoplanetary discs (PPDs), from young to old systems; however, their formation is still an area of vigorous debate. Recent magnetohydrodynamic (MHD) simulations have shown that rings and gaps can form naturally in PPDs when nonideal MHD effects are included. However, these simulations employ ad hoc approximations to the magnitudes of the magnetic diffusivities in order to facilitate ring growth. We replace the parametrization of these terms with a simple chemical network and grain distribution model to calculate the nonideal effects in a more selfconsistent way. We use a range of grain distributions to simulate grain formation for different disc conditions. Including ambipolar diffusion, we find that large grain populations (>1 $\mu$m), and those including a population of very small polyaromatic hydrocarbons (PAHs) facilitate the growth of periodic, stable rings, while intermediatesized grains suppress ring formation. Including Ohmic diffusion removes the positive influence of PAHs, with only large grain populations still producing periodic ring and gap structures. These results relate closely to the degree of coupling between the magnetic field and the neutral disc material, quantified by the nondimensional Elsasser number Λ (the ratio of magnetic forces to Coriolismore »
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Free, publiclyaccessible full text available March 14, 2024

Free, publiclyaccessible full text available November 1, 2023

The confluent hypergeometric equation, also known as Kummer's equation, is one of the most important differential equations in physics, chemistry, and engineering. Its two power series solutions are the Kummer function, M(a,b,z), often referred to as the confluent hypergeometric function of the first kind, and M ≡ z1bM(1+ab, 2b,z), where a and b are parameters that appear in the differential equation. A third function, the Tricomi function, U(a,b,z), sometimes referred to as the confluent hypergeometric function of the second kind, is also a solution of the confluent hypergeometric equation that is routinely used. Contrary to common procedure, all three of these functions (and more) must be considered in a search for the two linearly independent solutions of the confluent hypergeometric equation. There are situations, when a, b, and a  b are integers, where one of these functions is not defined, or two of the functions are not linearly independent, or one of the linearly independent solutions of the differential equation is different from these three functions. Many of these special cases correspond precisely to cases needed to solve problems in physics. This leads to significant confusion about how to work with confluent hypergeometric equations, in spite of authoritative referencesmore »

Abstract Magnetic fields have an important role in the evolution of interstellar medium and star formation 1,2 . As the only direct probe of interstellar field strength, credible Zeeman measurements remain sparse owing to the lack of suitable Zeeman probes, particularly for cold, molecular gas 3 . Here we report the detection of a magnetic field of +3.8 ± 0.3 microgauss through the H I narrow selfabsorption (HINSA) 4,5 towards L1544 6,7 —a wellstudied prototypical prestellar core in an early transition between starless and protostellar phases 8–10 characterized by a high central number density 11 and a low central temperature 12 . A combined analysis of the Zeeman measurements of quasar H I absorption, H I emission, OH emission and HINSA reveals a coherent magnetic field from the atomic cold neutral medium (CNM) to the molecular envelope. The molecular envelope traced by the HINSA is found to be magnetically supercritical, with a field strength comparable to that of the surrounding diffuse, magnetically subcritical CNM despite a large increase in density. The reduction of the magnetic flux relative to the mass, which is necessary for star formation, thus seems to have already happened during the transition from the diffuse CNM to the molecular gasmore »

Abstract We select 48 multiflare gammaray bursts (GRBs) (including 137 flares) from the Swift/XRT database and estimate the spectral lag with the discrete correlation function. It is found that 89.8% of the flares have positive lags and only 9.5% of the flares show negative lags when fluctuations are taken into account. The median lag of the multiflares (2.75 s) is much greater than that of GRB pulses (0.18 s), which can be explained by the fact that we confirm that multiflare GRBs and multipulse GRBs have similar positive lag–duration correlations. We investigate the origin of the lags by checking the E peak evolution with the two brightest bursts and find the leading models cannot explain all of the multiflare lags and there may be other physical mechanisms. All of the results above reveal that Xray flares have the same properties as GRB pulses, which further supports the observation that Xray flares and GRB promptemission pulses have the same physical origin.

Free, publiclyaccessible full text available October 1, 2023

ABSTRACT We report the phaseconnected timing ephemeris, polarization pulse profiles, Faraday rotation measurements, and RotatingVectorModel (RVM) fitting results of 12 millisecond pulsars (MSPs) discovered with the Fivehundredmeter Aperture Spherical radio Telescope (FAST) in the Commensal Radio Astronomy FAST survey (CRAFTS). The timing campaigns were carried out with FAST and Arecibo over 3 yr. 11 of the 12 pulsars are in neutron star–white dwarf binary systems, with orbital periods between 2.4 and 100 d. 10 of them have spin periods, companion masses, and orbital eccentricities that are consistent with the theoretical expectations for MSP–Helium white dwarf (He WD) systems. The last binary pulsar (PSR J1912−0952) has a significantly smaller spin frequency and a smaller companion mass, the latter could be caused by a low orbital inclination for the system. Its orbital period of 29 d is well within the range of orbital periods where some MSP–He WD systems have shown anomalous eccentricities, however, the eccentricity of PSR J1912−0952 is typical of what one finds for the remaining MSP–He WD systems.