adsabs/AstroCLIMB huggingface dataset:
Paper: On the Singularity Structure of Alfvénic Turbulence
Authors: N. H. Bian, Gang Li
Figure caption: P(Δz⊥, l⊥) deriving from T. S. Horbury & A. Balogh (1997)’s model.
Paper: On the Singularity Structure of Alfvénic Turbulence
Authors: N. H. Bian, Gang Li
Figure caption: P(Δz⊥, l⊥) deriving from B. D. G. Chandran et al. (2015)’s model.
Paper: Distinct Acceleration Relations of Galaxies and Galaxy Clusters from Hyperconical Modified Gravity
Authors: Robert Monjo, Indranil Banik
Figure caption: Galaxy rotation curves (squares; S. S. McGaugh et al. 2007) compared with the cluster RAR (circles; P. Li et al. 2023). Top left: fitting of galaxy rotation curves according to the HMG model (Equation (C16); R. Monjo 2023), where γ0 is modeled by Equation (6) with ϵH the only free parameter and γcen = 0.48π (dashed lines), or with two parameters (ϵH and γcen; solid lines). Top right: performance of the one-parameter (dashed gray lines) and two-parameter (solid gray lines) model for the ratio of predicted (apred) and observed (aobs) centripetal acceleration for the 60 galaxies (light gray lines). Results are compared with the McGaugh-Lelli-Schombert (MLS ), simple, standard, and sharp MOND interpolation functions fitted to 153 suitable galaxies. The 1σ confidence intervals for all functions (upper and lower lines of each color) are found as in Figure 23 of I. Banik et al. (2024). Bottom left: global fitting of the data set according to Equations (2) and (6). Bottom right: zoom-in on the theoretical prediction made for galaxies fitted using Equation (6) with ﹩{\varepsilon }_{{\rm{H}}}=2{1}_{-11}^{+32}﹩. As in Figure 1, the general model prediction for galaxies (gray band) corresponds to the parameter ﹩{\varepsilon }_{{\rm{H}}}=5{6}_{-12}^{+22}﹩ as an average value of the cluster fitting, with fixed γcen = π/2 and γU = π/3. To compare, the MOND-like model and the observational constraint of the general HMG model are also shown, with the shaded area representing the 90% confidence interval. Taking into account that the density of the surrounding system (ρnei) is mainly represented by the fitting parameter ﹩{\epsilon }_{{\rm{H}}}^{2}\sim {\rho }_{\rm{nei}\,}/{\rho }_{\,\rm{vac}}\sim 2{v}_{{\rm{N}}}^{2}({r}_{\,\rm{nei}\,})/{v}_{{\rm{H}}}^{2}({r}_{\,\rm{nei}\,})﹩ for a certain rnei, the interpretation of the abscissa axis (Newton–Hubble ratio) is ﹩\sqrt{2}{v}_{{\rm{N}}}(r)/[{\epsilon }_{{\rm{H}}}{v}_{{\rm{H}}}(r)]\sim [{v}_{{\rm{N}}}(r)/{v}_{{\rm{H}}}(r)]/[{v}_{{\rm{N}}}({r}_{\,\rm{nei}\,})/{v}_{{\rm{H}}}({r}_{\,\rm{nei}\,)}]﹩. Therefore, the abscissa axis represents how far this is from unity, so it is closely related to vN/vH, but this ratio is modulated by the factor 1/ϵH, so the maximum RAR anomaly occurs at unity.
Paper: Distinct Acceleration Relations of Galaxies and Galaxy Clusters from Hyperconical Modified Gravity
Authors: Robert Monjo, Indranil Banik
Figure caption: Model parameters fitted to the 60 high-quality galaxy rotation curves (squares), empirical relationships (black lines), and comparison with the fitting to the RAR data of 10 clusters (circles). Left: constraint on the one-parameter HMG model for galaxies, with fixed γcen = 0.48π and free εH. This shows an (almost) empirical identity between the single parameter ϵH and the square root of the relative density ρtyp/ρvac. In other words, in units of vacuum density ρvac ≡ 3/(8πGt2), an observed density ρtyp ≡ ρ(rtyp) is defined at a typical equilibrium distance of rtyp ∼ 50–200 kpc, whose fit has been found (R = 0.85, p-value < 0.0001) as 4 times the maximum radius (﹩{r}_{\mathrm{typ}}\approx 4\,{r}_{\max }﹩) for each galaxy rotation curve and equal to the minimum radius (﹩{r}_{\mathrm{typ}}\approx {r}_{\min }﹩) for the data of each cluster. Right: constraint on the two-parameter HMG model for galaxies, which shows a relationship between ϵH and γcen such that ﹩\cos ({\gamma }_{\mathrm{cen}})=\cos (0.460\pi )-0.020{\mathrm{ln}}\,{\varepsilon }_{{\rm{H}}}﹩ for 1 ≤ εH < 400, with a Pearson coefficient of R = 0.80 (p-value < 0.0001; black regression line).
Paper: Distinct Acceleration Relations of Galaxies and Galaxy Clusters from Hyperconical Modified Gravity
Authors: Robert Monjo, Indranil Banik
Figure caption: RAR modeling with HMG for the total acceleration (atot) compared to the Newtonian acceleration (aN). Left: individual fitting (Equations (4) and (5)) for the galaxy clusters considered (P. Li et al. 2023) using two parameters (εH and γcen; Table 1). Right: global fitting for all data according to three models: MOND-like constant (blue band), general model (gray band; Equations (2) and (6)), and cluster model (red band; Equations (2) and (5)). The MOND-like model with constant ﹩{\gamma }_{0}^{-1}={\gamma }_{\rm{sys}\,}^{-1}\cos {\gamma }_{\,\rm{sys}}﹩ was considered with ﹩{\gamma }_{\,\rm{sys}\,}=0.46{6}_{-0.01}^{+0.011}\pi ﹩, which corresponds to Milgrom’s constant ﹩{a}_{0}=2{\gamma }_{0}^{-1}c/t=1.0{1}_{-0.32}^{+0.33}\times 1{0}^{-10}\,{\rm{m}}\,{{\rm{s}}}^{-2}﹩ (R. Monjo 2023). In the right panel, both the general model and the specific approach for clusters use only one free parameter (εH), done by setting the projective angle of the galaxies to γcen = π/2 and γU = π/3. The general model (gray band) is represented by ﹩{\varepsilon }_{{\rm{H}}}=5{6}_{-12}^{+22}﹩, while the cluster approach (red band) considers an average of ﹩{\varepsilon }_{{\rm{H}}}=4{0}_{-6}^{+8}﹩, with εH being the value of vN/vH that leads to the maximum RAR anomaly. The shaded areas represent 90% confidence intervals.
Paper: Distinct Acceleration Relations of Galaxies and Galaxy Clusters from Hyperconical Modified Gravity
Authors: Robert Monjo, Indranil Banik
Figure caption: Conceptual model of the projective angle γsys as a function of the relative geometry (orbital speed vN over the Hubble flux εHvH) for each gravitational system (black curves) with respect to the maximum background spacetime (red curves). To simplify the scheme, the projection factor ﹩{\gamma }_{0}^{-1}\equiv {\gamma }_{\rm{sys}\,}^{-1}\cos {\gamma }_{\,\rm{sys}}﹩ is graphically represented by an auxiliary angle ϕ, defined as the arc between the hyperplane of the gravitational system (dashed black line) and the maximum background hyperplane (dashed red line) curved by the dominant system (purple), such that γsys = π/2 − ϕ. The distance scale r is represented by tsys (Equation (B11)). In addition to the cosmic scale, six gravitational systems are considered: (i) a small system (e.g., solar system), (ii) an early-type galaxy with a dominant nuclear bulge, (iii) a typical spiral galaxy, (iv) a late-type spiral galaxy, (v) an irregular cluster, and (vi) a homogeneous cluster. The dominant objects (purple text) are the star for a small system, the galactic center for galaxies, and the brightest galaxy for a given cluster.
Paper: Distinct Acceleration Relations of Galaxies and Galaxy Clusters from Hyperconical Modified Gravity
Authors: Robert Monjo, Indranil Banik
Figure caption: Observational constraints on the proposed models fitted to RAR data of the 10 galaxy clusters considered (P. Li et al. 2023). Left: best values (red points) and uncertainty area (green shaded regions showing the 1σ confidence level) of the two parameters (εH and γcen; see Table 1) used in fits to individual clusters according to the specific approach (Equation (C17) is used in Equation (C13)). Right: best fit of the single free parameter (εH) used in the general model (Equation (C18) used in Equation (C13)), with fixed γcen = 0.48π. In both cases (one or two free parameters), the projective angle of the neighborhood (γU) was fixed to γU = π/3. Notice that cluster A2029 did not pass the χ2 test even with the two-parameter model. However, it passed the test for γU = 0.235π, corresponding to ﹩{\gamma }_{U}^{-1}\cos {\gamma }_{U}\approx 1﹩.
Paper: Study of Neutron Capture Nucleosynthesis Based on Post–Asymptotic Giant Branch Stars
Authors: Miao Tian, Wenyuan Cui, Jian-Rong Shi, Jin-Xiao Qin, Hongjie Li, Fang Wen, Zhenyan Huo
Figure caption: The comparison of our elemental abundances with those from K. De Smedt et al. (2016) for IRAS 14325-6428.
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: Top left: regions chosen for the nuCrossARF analysis overlaid on an exposure-corrected, background-subtracted 4–25 keV image of A665 (OBSID 70201002002). The white regions cover the equilibration area. The pre-shock region and shock front are also labeled for clarity. Bottom left: exposure-corrected, background-subtracted 4–25 keV image of A665 (OBSID 70201003002). The black regions correspond to the equilibration area. Both images on the left are smoothed with a Gaussian kernel with an FWHM of 3 pixels, scaled logarithmically from 0 counts s–1 pix–1 (black) to 10+ counts s–1 pix–1 (white), have a pixel size of 2﹩\mathop{.}\limits^{\unicode{x02033}}﹩46, and have the same color bar in units of counts s–1 pix–1. Top right: temperature map displaying results from the nuCrossARF analysis, corresponding to the temperatures in Table 2, with an average error map shown below. The regions highlighted in blue cover the equilibration area. The color bar indicates the temperature in keV. The blue and gray outlined regions correspond to the data points in Figure 4. Bottom right: temperature error map showing the average error for each region’s temperature measurement in the nuCrossARF analysis, corresponding to the above temperature map. The regions highlighted in cyan indicate the equilibration area. The color bar indicates the average 90% uncertainty, in keV. The equilibration area (Regions 11 and 12), along with an additional post-shock region (Region 10) and the pre-shock region (Region 13), as highlighted in each of the panels, correspond to the four data points displayed in each panel of Figure 4.
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: An exposure-corrected, background-subtracted, and smoothed 4–25 keV NuSTAR image of A665 with regions overlaid. The four regions correspond to the data points in Figure 4, with the purple region corresponding to the pre-shock area, the two blue regions covering the equilibration area, and the white region corresponding to an additional post-shock region. The shock front is indicated by the dashed white line. LOFAR radio contours are overlaid in pink. The color bar is in units of counts per second per pixel. For more details of the processing and presentation of this image, see Section 2 and Figure 2.
Paper: Study of Neutron Capture Nucleosynthesis Based on Post–Asymptotic Giant Branch Stars
Authors: Miao Tian, Wenyuan Cui, Jian-Rong Shi, Jin-Xiao Qin, Hongjie Li, Fang Wen, Zhenyan Huo
Figure caption: The odd-isotope ratio of Ba vs. [Fe/H] is shown, with the short vertical lines representing the uncertainties. The three dashed lines represent the pure s-process of the solar system (0.11), the solar system (0.18), and the pure r-process of the solar system (0.46), respectively, according to C. Arlandini et al. (1999). Different symbols represent different stars (see legend).
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: The equilibration region that sits along the shock edge used in our analysis (known as Region 12) compared to a LOFAR image of A665, with data tapered to 100 kpc resolution and compact sources subtracted (σm = 228 μJy/beam), taken from LoTSS DR2 (A. Botteon et al. 2022). The color bar is in units of janskys per beam. The edge of the chosen shock region lies directly along the edge of the shock, as highlighted by the synchrotron radio emission due to particles accelerated by the shock, reaccelerated cosmic-ray electrons compressed by the shock, and subsequently reaccelerated electrons due to turbulence from the merger.
Paper: Study of Neutron Capture Nucleosynthesis Based on Post–Asymptotic Giant Branch Stars
Authors: Miao Tian, Wenyuan Cui, Jian-Rong Shi, Jin-Xiao Qin, Hongjie Li, Fang Wen, Zhenyan Huo
Figure caption: Panels (a) and (b) show the fitting results between the calculated (solid line) and observed abundances (filled red circles) for the three-component and five-component models of IRAS 14325-6428, respectively. The bottom of panels (a) and (b) represent the relative offsets (﹩\bigtriangleup {\mathrm{log}}\,\epsilon ={\mathrm{log}}{N}_{i,\mathrm{cal}}-{\mathrm{log}}{N}_{i,\mathrm{obs}}﹩) and the observed uncertainties, respectively.
Paper: Study of Neutron Capture Nucleosynthesis Based on Post–Asymptotic Giant Branch Stars
Authors: Miao Tian, Wenyuan Cui, Jian-Rong Shi, Jin-Xiao Qin, Hongjie Li, Fang Wen, Zhenyan Huo
Figure caption: Left panel: the best fit to the observed Ba II resonance line at 4554 Å for IRAS 14325-6428. Right panel: the relationship between ﹩{\chi }_{r}^{2}﹩ and fodd,Ba.
Paper: Study of Neutron Capture Nucleosynthesis Based on Post–Asymptotic Giant Branch Stars
Authors: Miao Tian, Wenyuan Cui, Jian-Rong Shi, Jin-Xiao Qin, Hongjie Li, Fang Wen, Zhenyan Huo
Figure caption: The best fit of Nd II line at 4061 Å. The red line represents the optimal synthesis of the Nd spectral line. The blue shaded area indicates the deviation of ±0.10 dex from the best precision.
Paper: Study of Neutron Capture Nucleosynthesis Based on Post–Asymptotic Giant Branch Stars
Authors: Miao Tian, Wenyuan Cui, Jian-Rong Shi, Jin-Xiao Qin, Hongjie Li, Fang Wen, Zhenyan Huo
Figure caption: The fitting of the Al I line.
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: Projected (blue) and deprojected (black) NuSTAR temperatures in the equilibration regions compared to collisional (solid) and collisionless (dashed) models. The colored squares signify the weighted average for each model in each region. The shock front is indicated by the solid gray vertical line. The Chandra pre-shock temperature is also included. The shaded areas represent the 1σ uncertainties for each model. The red models used a Mach number of ﹩{ \mathcal M }=3.4\pm 0.7﹩ (the measured Chandra density jump), the green models used ﹩{ \mathcal M }=3.0\pm 0.6﹩ (the Chandra temperature jump), the blue models used ﹩{ \mathcal M }=2.8\pm 0.7﹩ (the predicted NuSTAR temperature jump from Equation (7)), and the orange models used ﹩{ \mathcal M }=2.5\pm 0.7﹩ (the observed NuSTAR post-shock + Chandra pre-shock temperature jump without accounting for cross-calibration differences).
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: Left: background regions (black) used in the nuskybgd background analysis in Section 2, overlaid on raw count images (smoothed with a Gaussian kernel with an FWHM of 3 pixels) of A665, with the cluster emission exclusion region in red. The top two panels are for OBSID 70201002002, and the bottom two panels are for OBSID 70201003002. Within each pair, the top image corresponds to NuSTAR’s FPMA detector and the bottom image to the FPMB detector. The color bar is log scaled and represents raw counts. Right: joint fits of the background spectra extracted from NuSTAR’s FPMA and FPMB for both observations (OBSID 70201002002 for the top two panels, and OBSID 70201003002 for the bottom two panels). The individual colors correspond to each background region used in the extraction and fitting. The spectral bins are grouped to have a detection of at least 8σ, with a maximum of 12 bins.
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: Left: joint spectral fits for the nuCrossARF analysis (Section 3.3) using the regions shown in Figure 2. A combined model accounting for the contribution from each region for each observation (solid) is compared to spectral data combined from each of the four observations (points). This is purely for illustrative purposes, as each observation was fit individually. Each set of data and a corresponding model is shifted vertically on a logarithmic scale for illustrative purposes (×10shift). Right: the ratio showing the goodness of the fit for each region. The region numbers are listed on the y-axis, and the colors correspond with the data and models on the left.
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: A rough temperature map of A665 (left: OBSID 70201002002; right: OBSID 70201003002) calculated through the spectral fitting of predefined pixel areas, as described in Section 3.1. The green contours outline the LOFAR radio emission in Figure 3, matching the contours shown in Figure 1. The color bar indicates the temperature in keV.
Paper: Electron–Ion Equilibration in the Merging Galaxy Cluster A665
Authors: Christian T. Norseth, Daniel R. Wik, Craig L. Sarazin, Ming Sun, Fabio Gastaldello
Figure caption: A comparison of the projected Chandra temperature measurements in the pre-shock and post-shock regions in A665. The green points correspond to the measurements made in S. Dasadia et al. (2016b), the red points represent an analysis carried out using CIAO v4.7, and the black points represent the measurements using CIAO v4.13. The vertical gray line shows the location of the shock front relative to these regions. All analyses agree with each other with some uncertainty in the immediate post-shock region.
Paper: HST Proper Motions of Andromeda V and Andromeda VI
Authors: Dana I. Casetti-Dinescu, Marcel S. Pawlowski, Terrence M. Girard, Kosuke Jamie Kanehisa, Max Martone, Alexander Petroski
Figure caption: Overlap between the early WFPC2 exposures (red symbols) and the late ACS/WFC exposures (blue symbols). Coordinates are a gnomonic projection of R.A. and decl. with the tangent point (ξ, η) = (0, 0) at the satellite’s center. The one half-light ellipses are also shown according to the parameters in A. W. McConnachie (2012).
Paper: HST Proper Motions of Andromeda V and Andromeda VI
Authors: Dana I. Casetti-Dinescu, Marcel S. Pawlowski, Terrence M. Girard, Kosuke Jamie Kanehisa, Max Martone, Alexander Petroski
Figure caption: Proper-motion uncertainty as a function of instrumental magnitude in F814W for both ACS catalogs/chips and satellites. A moving median (1 mag bin) is represented with a solid line for each sample. The horizontal branch of each system is at magF814W ∼ 21.5, where a higher stellar density is apparent.
Paper: HST Proper Motions of Andromeda V and Andromeda VI
Authors: Dana I. Casetti-Dinescu, Marcel S. Pawlowski, Terrence M. Girard, Kosuke Jamie Kanehisa, Max Martone, Alexander Petroski
Figure caption: Backward orbit integrations of And V around M31 over the last 5 Gyr for a high-mass (Mvir = 2 × 1012 M⊙) and low-mass (Mvir = 1.5 × 1012 M⊙) M31 model, in solid and dashed lines, respectively. The blue orbits assume the HST+Sats M31 proper motion, while the black orbits adopt the fiducial choice of a weighted average with M31’s EDR3 proper motion. Andromeda’s disk lies along the X–Y plane, while the Milky Way lies toward the negative X-axis. Present-time positions and orbital trajectories are also shown for Monte Carlo realizations of And V in the fiducial model (high-mass M31 and HST+Sats+EDR3 proper motion). Note that the present-time position distribution (top, right panel) has a width orthogonal to the line-of-sight direction due to contributions from uncertainties in M31’s distance.
Paper: HST Proper Motions of Andromeda V and Andromeda VI
Authors: Dana I. Casetti-Dinescu, Marcel S. Pawlowski, Terrence M. Girard, Kosuke Jamie Kanehisa, Max Martone, Alexander Petroski
Figure caption: Distribution of calculated orbital poles of And V (top) and VI (bottom) relative to M31 in Galactic coordinates from 105 Monte Carlo realizations. The orbital pole corresponding to the measured-value position and velocity, i.e., ignoring uncertainties, is shown as a red cross. The peak in the density distribution when including the uncertainties is shown as a magenta circle. The black diamond indicates the spin of the galactic disk of M31, while the blue plus sign indicates the normal vector to the GPoA aligned with its direction of corotation. And VI is consistent with co-orbiting along the galactic disk spin of M31, while And V is counterorbiting and less well aligned.
Paper: HST Proper Motions of Andromeda V and Andromeda VI
Authors: Dana I. Casetti-Dinescu, Marcel S. Pawlowski, Terrence M. Girard, Kosuke Jamie Kanehisa, Max Martone, Alexander Petroski
Figure caption: Sky projection of the M31 satellite system as seen from M31. The M31 disk is aligned with the equator, and the Milky Way lies along ϕ = 0°. The yellow star represents the present-time position of And V (top) and And VI (bottom), while the thick line represents their most likely orbits colored by M31-centric distance. The thin lines plot 1000 Monte Carlo realizations of the orbit, with each realization’s present-time position marked with a small black dot. The other M31 satellites and the GPoA are also shown for reference.
Paper: The z ≳ 9 Galaxy UV Luminosity Function from the JWST Advanced Deep Extragalactic Survey: Insights into Early Galaxy Evolution and Reionization
Authors: Lily Whitler, Daniel P. Stark, Michael W. Topping, Brant Robertson, Marcia Rieke, Kevin N. Hainline, Ryan Endsley, Zuyi Chen, William M. Baker, Rachana Bhatawdekar, Andrew J. Bunker, Stefano Carniani, Stéphane Charlot, Jacopo Chevallard, Emma Curtis-Lake, Eiichi Egami, Daniel J. Eisenstein, Jakob M. Helton, Zhiyuan Ji, Benjamin D. Johnson, Pablo G. Pérez-González, Pierluigi Rinaldi, Sandro Tacchella, Christina C. Williams, Christopher N. A. Willmer, Chris Willott, Joris Witstok
Figure caption: The F200W footprint of the imaging used in this work. The color bar shows the 5σ depth of F200W measured as described in Section 2.2, where darker gray corresponds to deeper depths. The shallowest region with F200W exposure time of <5000 s primarily falls in GOODS-N and has typical 5σ depths of mAB ∼ 29 mag, while the deepest, >40,000 s region lies exclusively in GOODS-S and reaches mAB ∼ 30.8.
Paper: HST Proper Motions of Andromeda V and Andromeda VI
Authors: Dana I. Casetti-Dinescu, Marcel S. Pawlowski, Terrence M. Girard, Kosuke Jamie Kanehisa, Max Martone, Alexander Petroski
Figure caption: Spatial distribution and motions of satellite galaxies around M31. The position and orientation of the M31 disk is indicated with a black ellipse; the white area indicates the extent of the PAndAS footprint. Red upward triangles mark dwarf galaxies with receding line-of-sight velocities relative to that of M31, blue downward triangles those with approaching velocity. The on-sky velocities relative to M31 for satellite galaxies with measured proper motions are marked with green arrows, with And V and VI, whose proper motions are presented in this work, highlighted with yellow outlines. The Great Plane of Andromeda (GPoA) and its rms width are shown with dashed and dotted lines, respectively.
Paper: HST Proper Motions of Andromeda V and Andromeda VI
Authors: Dana I. Casetti-Dinescu, Marcel S. Pawlowski, Terrence M. Girard, Kosuke Jamie Kanehisa, Max Martone, Alexander Petroski
Figure caption: Proper-motion catalogs: spatial distribution (top), and relative proper motions for stars with proper-motion uncertainties ≤0.5 mas yr−1 (bottom). In the top panels, we mark the direction of the satellite proper motion relative to that of M31 (red arrow) together with its error ellipse and the direction toward M31. The half-light ellipse, according to the parameters in A. W. McConnachie (2012), is represented with a dashed line. In the bottom panels, the blue curves represent the proper-motion histograms in each coordinate.