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<jats:title>Abstract</jats:title> <jats:p>The fluctuations observed in the slow solar wind at 1 au by the WIND spacecraft are shown by recent studies to consist of mainly magnetic-field directional turning and magnetic-velocity alignment structure (MVAS). How these structures are created has been a question because the nature of the fluctuations in the near-Sun region remains unknown. Here, we present an analysis of the measurements in the slow solar wind from 0.1−0.3 au by Parker Solar Probe during its first six orbits. We present the distributions in the <jats:inline-formula> <jats:tex-math> <?CDATA ${C}_{\mathrm{vb}}^{{\prime} }\mbox{--}{\sigma }_{r}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>vb</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>–</mml:mo> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac3331ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> plane of both the occurrence and average amplitudes of the fluctuations, including the magnetic field, the velocity, and the Elsässer variables, where <jats:inline-formula> <jats:tex-math> <?CDATA ${C}_{\mathrm{vb}}^{{\prime} }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>vb</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac3331ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> is the correlation coefficient between the magnetic and velocity fluctuations multiplied by the opposite sign of the radial component of the mean magnetic field and <jats:italic>σ</jats:italic> <jats:sub> <jats:italic>r</jats:italic> </jats:sub> is the normalized residual energy. We find that the dominant composition is the outward-propagating Alfvénic fluctuations. We find Alfvénic fluctuations with <jats:inline-formula> <jats:tex-math> <?CDATA ${C}_{\mathrm{vb}}^{{\prime} }\gt 0.95$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>vb</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>&gt;</mml:mo> <mml:mn>0.95</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac3331ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>, in which the amplitudes of <jats:bold> <jats:italic>z</jats:italic> </jats:bold> <jats:sup>+</jats:sup> reach 60 km s<jats:sup>−1</jats:sup> and those of <jats:bold> <jats:italic>z</jats:italic> </jats:bold> <jats:sup>−</jats:sup> are close to the observational uncertainty. We also find a region with high <jats:inline-formula> <jats:tex-math> <?CDATA ${C}_{\mathrm{vb}}^{{\prime} }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>vb</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac3331ieqn4.gif" xlink:type="simple" /> </jats:inline-formula> and moderate minus <jats:italic>σ</jats:italic> <jats:sub> <jats:italic>r</jats:italic> </jats:sub> in which the fluctuations are considered MVAS being magnetic dominated with the amplitude of magnetic fluctuations reaching 60 km s<jats:sup>−1</jats:sup>. We provide empirical relations between the velocity fluctuation amplitude and <jats:inline-formula> <jats:tex-math> <?CDATA ${C}_{\mathrm{vb}}^{{\prime} }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>vb</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac3331ieqn5.gif" xlink:type="simple" /> </jats:inline-formula>. The comparison between these results and those observed at 1 au may provide some clues as to the nature and evolution of the fluctuations.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Several lines of evidence suggest that the Milky Way underwent a major merger at <jats:italic>z</jats:italic> ∼ 2 with the Gaia-Sausage-Enceladus (GSE) galaxy. Here we use H3 Survey data to argue that GSE entered the Galaxy on a retrograde orbit based on a population of highly retrograde stars with chemistry similar to the largely radial GSE debris. We present the first tailored <jats:italic>N</jats:italic>-body simulations of the merger. From a grid of ≈500 simulations we find that a GSE with <jats:italic>M</jats:italic> <jats:sub>⋆</jats:sub> = 5 × 10<jats:sup>8</jats:sup> <jats:italic> M</jats:italic> <jats:sub>⊙</jats:sub>, <jats:italic>M</jats:italic> <jats:sub>DM</jats:sub> = 2 × 10<jats:sup>11</jats:sup> <jats:italic> M</jats:italic> <jats:sub>⊙</jats:sub> best matches the H3 data. This simulation shows that the retrograde stars are stripped from GSE’s outer disk early in the merger. Despite being selected purely on angular momenta and radial distributions, this simulation reproduces and explains the following phenomena: (i) the triaxial shape of the inner halo, whose major axis is at ≈35° to the plane and connects GSE’s apocenters; (ii) the Hercules-Aquila Cloud and the Virgo Overdensity, which arise due to apocenter pileup; and (iii) the 2 Gyr lag between the quenching of GSE and the truncation of the age distribution of the in situ halo, which tracks the lag between the first and final GSE pericenters. We make the following predictions: (i) the inner halo has a “double-break” density profile with breaks at both ≈15–18 kpc and 30 kpc, coincident with the GSE apocenters; and (ii) the outer halo has retrograde streams awaiting discovery at &gt;30 kpc that contain ≈10% of GSE’s stars. The retrograde (radial) GSE debris originates from its outer (inner) disk—exploiting this trend, we reconstruct the stellar metallicity gradient of GSE (−0.04 ± 0.01 dex <jats:inline-formula> <jats:tex-math> <?CDATA ${r}_{50}^{-1}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>50</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac2d2dieqn1.gif" xlink:type="simple" /> </jats:inline-formula>). These simulations imply that GSE delivered ≈20% of the Milky Way’s present-day dark matter and ≈50% of its stellar halo.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Here we show that precise Gaia EDR3 proper motions have provided robust estimates of 3D velocities, angular momentum, and total energy for 40 Milky Way dwarfs. The results are statistically robust and are independent of the Milky Way mass profile. Dwarfs do not behave like long-lived satellites of the Milky Way because of their excessively large velocities, angular momenta, and total energies. Comparing them to other MW halo populations, we find that many are at first passage, ≤2 Gyr ago, i.e., more recent than the passage of Sagittarius, ∼4–5 Gyr ago. We suggest that this is in agreement with the stellar populations of all dwarfs, for which we find that a small fraction of young stars cannot be excluded. We also find that dwarf radial velocities contribute too little to their kinetic energy when compared to satellite systems with motions only regulated by gravity, and some other mechanism must be at work such as ram pressure. The latter may have preferentially reduced radial velocities when dwarf progenitors entered the halo until they lost their gas. It could also explain why most dwarfs lie near their pericenter. We also discover a novel large-scale structure perpendicular to the Milky Way disk, which is made by 20% of dwarfs orbiting or counter-orbiting with the Sagittarius dwarf.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>While collisional accumulation is nearly universally accepted as the formation mechanism of rock and ice worlds, the situation regarding gas giant planet formation is more nuanced. Gas accretion by solid cores formed by collisional accumulation is the generally favored mechanism, but observations increasingly suggest that gas disk gravitational instability might explain the formation of at least the massive or wide-orbit gas giant exoplanets. This paper continues a series aimed at refining three-dimensional (3D) hydrodynamical models of disk instabilities, where the handling of the gas thermodynamics is a crucial factor. Boss (2017, 2021) used the <jats:italic>β</jats:italic> cooling approximation to calculate 3D models of disks with initial masses of 0.091 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> extending from 4 to 20 au around 1 <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub> protostars. Here we employ 3D flux-limited diffusion (FLD) approximation models of the same disks, in order to provide a superior treatment of disk gas thermodynamics. The new models have quadrupled spatial resolution compared to previous 3D FLD models, in both the radial and azimuthal spherical coordinates, resulting in the highest spatial resolution 3D FLD models to date. The new models continue to support the hypothesis that such disks can form self-gravitating, dense clumps capable of contracting to form gas giant protoplanets, and suggest that the FLD models yield similar numbers of clumps as <jats:italic>β</jats:italic> cooling models with <jats:italic>β</jats:italic> ∼ 1 to ∼10, including the critical value of <jats:italic>β</jats:italic> = 3 for fragmentation proposed by Gammie.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We propose an algorithm, referred to as the pulsar phase and standard deviation (PPSD), to mitigate transient radio frequency interference (RFI) in pulsar observations. PPSD uses the model for pulsar time of arrival to identify pulsar phase and extract the pulse profile to protect the original pulsar profile. PPSD sets a threshold based on the statistics empirical rule to label the transient RFI in the off-pulse data until all unlabelled off-pulse data obeys the white Gaussian noise (WGN) distribution. The transient RFI data is then substituted with WGN. Finally, we use PPSD to process the pulsar observation data obtained from the NanShan 25 m Radio Telescope. Our results show that PPSD can effectively mitigate the transient RFI and improve the signal-to-noise ratio of the pulsar observations.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigated the stable isotope fractionation of chromium (Cr) for a panorama of chondrites, including EH and EL enstatite chondrites and their chondrules and different phases (by acid leaching). We observed that chondrites have heterogeneous <jats:italic>δ</jats:italic> <jats:sup>53</jats:sup>Cr values (per mil deviation of the <jats:sup>53</jats:sup>Cr/<jats:sup>52</jats:sup>Cr from the NIST SRM 979 standard), which we suggest reflect different physical conditions in the different chondrite accretion regions. Chondrules from a primitive EH3 chondrite (SAH 97096) possess isotopically heavier Cr relative to their host bulk chondrite, which may be caused by Cr evaporation in a reduced chondrule-forming region of the protoplanetary disk. Enstatite chondrites show a range of bulk <jats:italic>δ</jats:italic> <jats:sup>53</jats:sup>Cr values that likely result from variable mixing of isotopically different sulfide-silicate-metal phases. The bulk silicate Earth (<jats:italic>δ</jats:italic> <jats:sup>53</jats:sup>Cr = –0.12 ± 0.02‰, 2SE) has a lighter Cr stable isotope composition compared to the average <jats:italic>δ</jats:italic> <jats:sup>53</jats:sup>Cr value of enstatite chondrites (–0.05 ± 0.02‰, 2SE, when two samples out of 19 are excluded). If the bulk Earth originally had a Cr isotopic composition that was similar to the average enstatite chondrites, this Cr isotope difference may be caused by evaporation under equilibrium conditions from magma oceans on Earth or its planetesimal building blocks, as previously suggested to explain the magnesium and silicon isotope differences between Earth and enstatite chondrites. Alternatively, chemical differences between Earth and enstatite chondrite can result from thermal processes in the solar nebula and the enstatite chondrite-Earth, which would also have changed the Cr isotopic composition of Earth and enstatite chondrite parent body precursors.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We reconstruct the history of reionization using Gaussian process regression. Using the UV luminosity data compilation from Hubble Frontiers Fields we reconstruct the redshift evolution of UV luminosity density and thereby the evolution of the source term in the ionization equation. This model-independent reconstruction rules out single power-law evolution of the luminosity density but supports the logarithmic double power-law parameterization. We obtain reionization history by integrating ionization equations with the reconstructed source term. Using the optical depth constraint from Planck cosmic microwave background observation, measurement of UV luminosity function integrated until truncation magnitude of −17 and −15, and derived ionization fraction from high redshift quasar, galaxies, and gamma-ray burst observations, we constrain the history of reionization. In the conservative case we find the constraint on the optical depth as <jats:italic>τ</jats:italic> = 0.052 ± 0.001 ± 0.002 at 68% and 95% confidence intervals. We find the redshift duration between 10% and 90% ionization to be <jats:inline-formula> <jats:tex-math> <?CDATA ${2.05}_{-0.21-0.30}^{+0.11+0.37}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>2.05</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.21</mml:mn> <mml:mo>−</mml:mo> <mml:mn>0.30</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.11</mml:mn> <mml:mo>+</mml:mo> <mml:mn>0.37</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac3251ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>. Longer duration of reionization is supported if UV luminosity density data with truncation magnitude of −15 is used in the joint analysis. Our results point out that even in a conservative reconstruction, a combination of cosmological and astrophysical observations can provide stringent constraints on the epoch of reionization.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Galaxy clusters are good targets for examining our understanding of cosmology. Apart from numerical simulations and gravitational lensing, X-ray observation is the most common and conventional way to analyze the gravitational structures of galaxy clusters. Therefore, it is valuable to have simple analytical relations that can connect the observed distribution of the hot, X-ray-emitting gas to the structure of the dark matter in the clusters as derived from simulations. In this article, we apply a simple framework that can analytically connect the hot gas empirical parameters with the standard parameters in the cosmological cold dark matter model. We have theoretically derived two important analytic relations, <jats:inline-formula> <jats:tex-math> <?CDATA ${r}_{s}\approx \sqrt{3}{r}_{c}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msqrt> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac32c4ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math> <?CDATA ${\rho }_{s}\approx 9\beta {kT}/8\pi {{Gm}}_{g}{r}_{c}^{2}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>ρ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>9</mml:mn> <mml:mi>β</mml:mi> <mml:mi mathvariant="italic">kT</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>8</mml:mn> <mml:mi>π</mml:mi> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">Gm</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> </mml:msub> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac32c4ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>, which can easily relate the dark matter properties in galaxy clusters with the hot gas properties. This can give a consistent picture describing gravitational astrophysics for galaxy clusters by the hot gas and cold dark matter models.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this paper, we investigate the structure of out-of-plane magnetic field in the reconnection event observed by Magnetospheric Multiscale Mission at the magnetopause of the Earth magnetosphere on 2015 October 21. We find that the perturbation of out-of-plane magnetic field in this event is different from previous observations of the quadrupolar Hall magnetic field. The distinct out-of-plane magnetic field is interpreted as a part of the hexapolar Hall magnetic field obtained in a recent simulation of asymmetric reconnection with the guide field. This is significant evidence of the hexapolar Hall magnetic field in collisionless magnetic reconnection from the observations in the magnetosphere. High-resolution measurements of particle and field are used to provide a comprehensive description of the features of the hexapolar Hall magnetic field. The results from this study offer an insight into the Hall effect in collisionless magnetic reconnection.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We present a new application of deep learning to reconstruct the cosmic microwave background (CMB) temperature maps from images of the microwave sky and to use these reconstructed maps to estimate the masses of galaxy clusters. We use a feed-forward deep-learning network, mResUNet, for both steps of the analysis. The first deep-learning model, mResUNet-I, is trained to reconstruct foreground and noise-suppressed CMB maps from a set of simulated images of the microwave sky that include signals from the CMB, astrophysical foregrounds like dusty and radio galaxies, instrumental noise as well as the cluster’s own thermal Sunyaev–Zel’dovich signal. The second deep-learning model, mResUNet-II, is trained to estimate cluster masses from the gravitational-lensing signature in the reconstructed foreground and noise-suppressed CMB maps. For SPTpol-like noise levels, the trained mResUNet-II model recovers the mass for 10<jats:sup>4</jats:sup> galaxy cluster samples with a 1<jats:italic>σ</jats:italic> uncertainty <jats:inline-formula> <jats:tex-math> <?CDATA ${\rm{\Delta }}{M}_{200{\rm{c}}}^{\mathrm{est}}/{M}_{200{\rm{c}}}^{\mathrm{est}}=$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>200</mml:mn> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>est</mml:mi> </mml:mrow> </mml:msubsup> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>200</mml:mn> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>est</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac32d0ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> 0.108 and 0.016 for input cluster mass <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{200{\rm{c}}}^{\mathrm{true}}={10}^{14}\,{M}_{\odot }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>200</mml:mn> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>true</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>14</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em" /> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac32d0ieqn2.gif" xlink:type="simple" /> </jats:inline-formula> and 8 × 10<jats:sup>14</jats:sup> <jats:italic>M</jats:italic> <jats:sub>⊙</jats:sub>, respectively. We also test for potential bias on recovered masses, finding that for a set of 10<jats:sup>5</jats:sup> clusters the estimator recovers <jats:inline-formula> <jats:tex-math> <?CDATA ${M}_{200{\rm{c}}}^{\mathrm{est}}=2.02\times {10}^{14}\,{M}_{\odot }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>200</mml:mn> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>est</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>2.02</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>14</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em" /> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac32d0ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>, consistent with the input at 1% level. The 2<jats:italic>σ</jats:italic> upper limit on potential bias is at 3.5% level.</jats:p>