Crater counting on the Moon and other bodies is crucial to constrain the dynamical history of the Solar System. This has traditionally been done by visual inspection of images, thus limiting the scope, efficiency, and/or accuracy of retrieval. In this paper we demonstrate the viability of using convolutional neural networks (CNNs) to determine the positions and sizes of craters from Lunar digital elevation maps (DEMs). We recover 92% of craters from the human-generated test set and almost double the total number of crater detections. Of these new craters, 15% are smaller in diameter than the minimum crater size in the ground-truth dataset. Our median fractional longitude, latitude and radius errors are 11% or less, representing good agreement with the human-generated datasets. From a manual inspection of 361 new craters we estimate the false positive rate of new craters to be 11%. Moreover, our Moon-trained CNN performs well when tested on DEM images of Mercury, detecting a large fraction of craters in each map. Our results suggest that deep learning will be a useful tool for rapidly and automatically extracting craters on various Solar System bodies. We make our code and data publicly available at https://github.com/ silburt/DeepMoon.git and https://doi.org/10.5281/zenodo.1133969.

The internal rotation of post-main sequence stars is investigated, in response to the convective pumping of angular momentum toward the stellar core, combined with a tight magnetic coupling between core and envelope. The spin evolution is calculated using model stars of initial mass 1, 1.5, and M 5  , taking into account mass loss on the giant branches. We also include the deposition of orbital angular momentum from a sub-stellar companion, as influenced by tidal drag along with the excitation of orbital eccentricity by a fluctuating gravitational quadrupole moment. A range of angular velocity profiles r ( ) W is considered in the envelope, extending from solid rotation to constant specific angular momentum. We focus on the backreaction of the Coriolis force, and the threshold for dynamo action in the inner envelope. Quantitative agreement with measurements of core rotation in subgiants and post-He core flash stars by Kepler is obtained with a two-layer angular velocity profile: uniform specific angular momentum where the Coriolis parameter Co 1 con  t º W (here con t is the convective time), and r r ( ) 1 W µ -where Co 1  . The inner profile is interpreted in terms of a balance between the Coriolis force and angular pressure gradients driven by radially extended convective plumes. Inward angular momentum pumping reduces the surface rotation of subgiants, and the need for a rejuvenated magnetic wind torque. The co-evolution of internal magnetic fields and rotation is considered in Kissin & Thompson, along with the breaking of the rotational coupling between core and envelope due to heavy mass loss.

The magnetism and rotation of white dwarf (WD) stars are investigated in relation to a hydromagnetic dynamo operating in the progenitor during shell burning phases. The downward pumping of angular momentum in the convective envelope, in combination with the absorption of a planet or tidal spin-up from a binary companion, can trigger strong dynamo action near the core-envelope boundary. Several arguments point to the outer core as the source for a magnetic field in the WD remnant: the outer third of a ∼ 0.55 M ⊙ WD is processed during the shell burning phase(s) of the progenitor; the escape of magnetic helicity through the envelope mediates the growth of (compensating) helicity in the core, as is needed to maintain a stable magnetic field in the remnant; and the intense radiation flux at the core boundary facilitates magnetic buoyancy within a relatively thick tachocline layer. The helicity flux into the growing core is driven by a dynamical imbalance with a latitude-dependent rotational stress. The magnetic field deposited in an isolated massive WD is concentrated in an outer shell of mass 0.1 M ⊙ and can reach ∼ 10 MG. A buried toroidal field experiences moderate ohmic decay above an age ∼ 0.3 Gyr, which may lead to growth or decay of the external magnetic field. The final WD spin period is related to a critical spin rate below which magnetic activity shuts off, and core and envelope decouple; it generally sits in the range of hours to days. WD periods ranging up to a year are possible if the envelope re-expands following a late thermal pulse.

The internal rotation and magnetism of massive stars are considered in response to i) the inward pumping of angular momentum through deep and slowly rotating convective layers; and ii) the winding up of a helical magnetic field in radiative layers. Field winding can transport angular momentum effectively even when the toroidal field is limited by kinking. Magnetic helicity is pumped into a growing radiative layer from an adjacent convective envelope (or core). The receding convective envelope that forms during the early accretion phase of a massive star is the dominant source of helicity in its core, yielding a ∼ 10 13 G polar magnetic field in a collapsed neutron star (NS) remnant. Using MESA models of various masses, we find that the NS rotation varies significantly, from P NS ∼ 0.1−1 s in a 13 M model to P NS ∼ 2 ms in a 25 M model with an extended core. Stronger inward pumping of angular momentum is found in more massive stars, due to the growing thickness of the convective shells that form during the later stages of thermonuclear burning. On the other hand, stars that lose enough mass to form blue supergiants in isolation end up as very slow rotators. The tidal spin-up of a 40 M star by a massive binary companion is found to dramatically increase the spin of the remnant black hole, allowing a rotationally supported torus to form during the collapse. The implications for post-collapse decay or amplification of the magnetic field are also considered.

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