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<jats:title>Abstract</jats:title> <jats:p>Electron-scale magnetic holes filled with high-energy electrons can provide a seed population of electrons in the magnetosphere and might play an important role in the interaction between the magnetosphere and solar wind. Theoretical studies have investigated their generation mechanisms based on the 1D or 2D geometry of the structure. However, the generation mechanism is still unclear. Here we report on the 3D geometry of the electron-scale magnetic hole in the solar wind based on the Magnetospheric Multiscale mission. We find that the cross section of the magnetic hole with a size of ∼0.2–0.6 <jats:italic>ρ</jats:italic> <jats:sub>i</jats:sub> (ion gyroradius) is either circular or 2D sheet-like. Electron vortices exist in both kinds of cross sections. The ellipse is a possible candidate for the geometry of the magnetic hole in the plane including its axis. Surprisingly, such an elliptical geometry suggests that the axial lengths of all our selected magnetic holes are ∼1–2 <jats:italic>ρ</jats:italic> <jats:sub>i</jats:sub>. This 3D geometry might shed some light on the generation mechanism and role of the electron-scale magnetic hole in the astrophysical plasma.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>The Jovian-sized object WD 1856 b transits a white dwarf (WD) in a compact 1.4 day orbit. Unlikely to have endured stellar evolution in its current orbit, WD 1856 b is thought to have migrated from much wider separations. Because the WD is old, and a member of a well-characterized hierarchical multiple, the well-known Kozai mechanism provides an effective migration channel for WD 1856 b. The tidal dissipation that makes this mechanism possible is sensitive to the mass of WD 1856 b, which remains unconstrained by observations. Moreover, the lack of tides in the star allows us to directly connect the current semimajor axis to the pre-migration one, from which we can infer the initial conditions of the system. By further requiring that planets must survive all previous phases of stellar evolution before migrating, we are able to constrain the main-sequence semimajor axis of WD 1856 b to have been ∼2.5 au, and its mass to be ≃0.7–3<jats:italic>M</jats:italic> <jats:sub>J</jats:sub>. These mass limits put WD 1856 b firmly within the planet category. Furthermore, our inferred values imply that WD 1856 b was born a typical gas giant. We further estimate the occurrence rate of Kozai-migrated planets around WDs to be <jats:inline-formula> <jats:tex-math> <?CDATA ${ \mathcal O }({10}^{-3}-{10}^{-4})$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlabc564ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, suggesting that WD 1856 b is the only one in the TESS sample, but implying <jats:inline-formula> <jats:tex-math> <?CDATA ${ \mathcal O }({10}^{2})$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlabc564ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> future detections by the LSST survey. In a sense, WD 1856 b was an ordinary Jovian planet that underwent an extraordinary dynamical history.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Energy supply sources for the heating process in the slow solar wind remain unknown. The Parker Solar Probe (PSP) mission provides a good opportunity to study this issue. Recently, PSP observations have found that the slow solar wind experiences stronger heating inside 0.24 au. Here for the first time we measure in the slow solar wind the radial gradient of the low-frequency breaks on the magnetic trace power spectra and evaluate the associated energy supply rate. We find that the energy supply rate is consistent with the observed perpendicular heating rate calculated based on the gradient of the magnetic moment. Based on this finding, one could explain why the slow solar wind is strongly heated inside 0.25 au but expands nearly adiabatically outside 0.25 au. This finding supports the concept that the energy added from the energy-containing range is transferred by an energy cascade process to the dissipation range, and then dissipates to heat the slow solar wind. The related issues for further study are discussed.</jats:p>