adsabs/AstroCLIMB huggingface dataset:
Paper: Stellar Distributions around Supermassive Black Holes in Gas-rich Nuclear Star Clusters
Authors: Mor Rozner, Enrico Ramirez-Ruiz
Figure caption: Left: color map of the ratio of fluxes (color) as calculated for different gas-to-stars mass ratios and gas density power law γ. The solid line is the contour where ﹩| {{ \mathcal F }}_{{\rm{gas}}}/{{ \mathcal F }}_{\star }| \,=\,1﹩. The energies are evaluated at 0.1 pc and the power law for the phase-space distribution is taken to be α  = 1/4. The dashed line is the profile at the limit of gas domination for the given α. Right: color map of the ratio of fluxes (color) as calculated for different phase-space density power laws α and gas density power laws γ. The solid line is the contour where ﹩| {{ \mathcal F }}_{{\rm{gas}}}/{{ \mathcal F }}_{\star }| \,=\,1﹩, the dashed line is the profile at the limit of gas domination, and the dotted–dashed line is the Bahcall–Wolf profile. The energies are evaluated at 0.1 pc and the gas-to-stars mass ratio is set to be 10%.
Paper: Stellar Distributions around Supermassive Black Holes in Gas-rich Nuclear Star Clusters
Authors: Mor Rozner, Enrico Ramirez-Ruiz
Figure caption: Left: color map of the ratio of fluxes (color) as calculated for different gas-to-stars ratios and phase-space density power laws α. The solid line is the contour where ﹩| {{ \mathcal F }}_{{\rm{gas}}}/{{ \mathcal F }}_{\star }| =1﹩. The energies are evaluated at 0.1 pc and the power law for the gas density profile is taken to be γ = −2. Right: color map of the ratio of fluxes (color) as calculated for different gas-to-stars ratios and energies relative to the energy at the radius of influence. The solid line is the contour where ﹩| {{ \mathcal F }}_{\mathrm{gas}}/{{ \mathcal F }}_{\star }| =1﹩. The power laws for the phase-space distribution and gas density are taken to be α = 1/4, γ = −2 correspondingly.
Paper: Little Red Dots as the Very First Activity of Black Hole Growth
Authors: Kohei Inayoshi
Figure caption: Left: the distribution of UV absolute magnitudes for LRDs with the total sample (purple) and subsets at z ≥ 6 (green), z ≥ 7 (blue), and z ≥ 8 (orange). The vertical line indicates a reference threshold of MUV = −18 mag, fainter than which the observed decline in number is likely due to flux limits. Right: the LRD occurrence rate for the total sample (purple) and subsets at MUV < −18 (green) and MUV < −19 (blue) overlaid with best-fit log-normal distributions (solid curves).
Paper: Little Red Dots as the Very First Activity of Black Hole Growth
Authors: Kohei Inayoshi
Figure caption: The LRD occurrence-rate models: the log-normal case (magenta) and the decay cases driven by mergers: p = 0 (gray), p = 0.2 (cyan), and p = 0.5 (blue).
Paper: Stellar Distributions around Supermassive Black Holes in Gas-rich Nuclear Star Clusters
Authors: Mor Rozner, Enrico Ramirez-Ruiz
Figure caption: The ratio between gas-induced and scattering energy fluxes, at different locations at the cluster, or equivalently, different specific energies, for different mass ratios between gas and stars. The energies are normalized by the specific energy at the radius of influence ﹩{E}_{0}\,=\,G{M}_{\bullet }/{R}_{\inf }﹩. The power laws of the phase-space distribution and gas density are taken to be α  = 1/4, γ  = −2 correspondingly.
Paper: Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel–Lidov–Kozai Cycles: Implications in the HD 41004 System
Authors: Zhizhen Qin, 至臻 秦, Shang-Fei Liu, 尚飞 刘, Bo Ma, 波 马, Fabo Feng, 发波 冯
Figure caption: MEGNO stability maps for the HD 41004 system under varying binary eccentricities and observational inclinations. Each panel depicts the dynamical stability of planet Ab for specific combinations of binary eccentricity (e2) and inclination (I2). The x-axis represents the binary semimajor axis a2, and the left y-axis shows the mutual inclination iinitial. The right y-axis displays the true mass m1 inferred from ﹩{m}_{1}\sin {I}_{1}=2.54\,{M}_{\,\rm{J}\,}﹩. The color shading indicates MEGNO values: blue (﹩\bar{Y}\simeq 2﹩) represents stable, quasiperiodic motion, while yellow-white (﹩\bar{Y}\gt 2﹩) denotes chaotic behavior. The red dashed line marks iinitial = 75°, and the solid line represents the critical inclination of 39﹩\mathop{.}\limits^{\unicode{x000b0}}﹩2 for vZLK excitation. For e2 = 0, stability is maintained up to 75° across all a2. At e2 = 0.4 and e2 = 0.8, instability emerges at smaller a2 and near iinitial = 39﹩\mathop{.}\limits^{\unicode{x000b0}}﹩2 due to enhanced eccentric vZLK forcing. The top left panel is blank, as a2 is fixed for I2 = 0 and e2 = 0, making simulations unnecessary.
Paper: Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel–Lidov–Kozai Cycles: Implications in the HD 41004 System
Authors: Zhizhen Qin, 至臻 秦, Shang-Fei Liu, 尚飞 刘, Bo Ma, 波 马, Fabo Feng, 发波 冯
Figure caption: Dynamical RV fitting of HD 41004 A under different orbital configurations. In each plot, the top panel displays the combined RV signal of HD 41004 A, incorporating contributions from both the planetary companion (Ab) and the stellar companion (B). The middle panel presents the isolated planetary signal after subtracting the RV contribution of companion B. The bottom panel shows the O − C residuals for each fit. Different colors and line styles represent varying eccentricities of the stellar companion (e2) or different initial mutual inclinations (iinitial), depending on the scenario. The top figure corresponds to a2 = 22 au with different e2 and fixed iinitial = 0°, while the bottom figure shows a2 = 22 au with e2 = 0 and varying iinitial. The legend in each panel provides the rms values of the O − C residuals for each configuration. Observed RV data points are plotted with error bars, and the systemic velocity of 42.513 km s−1 is subtracted for consistency (S. Zucker et al. 2004). The time axis is referenced to JD 2451902.77432 (2000 December), marking the epoch of the first published RV measurement.
Paper: Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel–Lidov–Kozai Cycles: Implications in the HD 41004 System
Authors: Zhizhen Qin, 至臻 秦, Shang-Fei Liu, 尚飞 刘, Bo Ma, 波 马, Fabo Feng, 发波 冯
Figure caption: Schematic geometry of a hierarchical three-body system and projected separation s of HD 41004 B. Left panel: the blue plane represents the plane of the sky, perpendicular to the observer’s line of sight (black arrow). Red and blue arrows denote the orbital angular momentum vectors of the outer and inner orbits, respectively. The angles I1 and I2 are their inclinations relative to the plane of the sky, while iinitial is the mutual inclination between the two orbits. The green angle ΔΩ represents the difference in the longitudes of ascending nodes. Although I1 and I2 depend on the observer’s orientation, both iinitial and ΔΩ are intrinsic dynamical parameters of the system. Right panel: the red ellipse shows a representative orbit of component B with eccentricity e2 and inclination I2. The gray sectors illustrate the orbital phase angle ω2 + f2 within ±60° around periastron and apoastron. The projected separation s, instantaneous distance r, and inferred semimajor axis a2 follow the definitions in Equation (3).
Paper: Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel–Lidov–Kozai Cycles: Implications in the HD 41004 System
Authors: Zhizhen Qin, 至臻 秦, Shang-Fei Liu, 尚飞 刘, Bo Ma, 波 马, Fabo Feng, 发波 冯
Figure caption: Simulated RV curves of HD 41004 Ab for various initial mutual inclinations (iinitial) at a2 = 22 au and ﹩{m}_{1}\sin {I}_{1}=2.54\,{M}_{{\rm{J}}}﹩, with e2 = 0 (top panel) and e2 = 0.4 (bottom panel). The RV signals are plotted over a 40 yr baseline, illustrating the influence of different initial mutual inclinations (iinitial). In the top panel, the configuration with e2 = 0 is shown for iinitial ranging from 0° to 75°. The distinct color curves represent varying inclinations, with higher inclinations displaying larger RV amplitudes. The bottom panel presents the corresponding configurations for e2 = 0.4, with the same range of initial inclinations.
Paper: Breaking the Mass Inclination Degeneracy of Radial Velocity Measurements via Monitoring von Zeipel–Lidov–Kozai Cycles: Implications in the HD 41004 System
Authors: Zhizhen Qin, 至臻 秦, Shang-Fei Liu, 尚飞 刘, Bo Ma, 波 马, Fabo Feng, 发波 冯
Figure caption: Simulated RV curves of HD 41004 Ab for various configurations over 2 × 106 days (∼5479 yr). Panel (a) corresponds to a2 = 22 au, e2 = 0, and ﹩{m}_{1}\sin {I}_{1}=2.54\,{M}_{{\rm{J}}}﹩, with varying initial mutual inclinations (iinitial). Panel (b) shows the same configuration except with e2 = 0.4. In panel (c), the simulation explores a2 = 22, 25, 30, 40 au, e2 = 0, and ﹩{m}_{1}\sin {I}_{1}=2.54\,{M}_{{\rm{J}}}﹩, with iinitial = 75°. Panel (d) follows the same setup as the bottom left panel but with e2 = 0.4.
Paper: Is Earendel a Star Cluster?: Metal-poor Globular Cluster Progenitors at z ∼ 6
Authors: Massimo Pascale, Liang Dai, Brenda L. Frye, Aliza G. Beverage
Figure caption: NIRSpec PRISM spectra of Earendel and 1b with the best-fit BPASS model from SED fitting overplotted. We omit the BC03 and FSPS best-fit SEDs for clarity, as they appear similar to the result from BPASS. Spectra are taken from version 3 of the DJA (K. E. Heintz et al. 2024). Both Earendel and 1b have similar spectra indicative of stellar continuum from an evolved SSP. The fit is influenced by the shape of the continuum, the lack of significant absorption features, and the clear Balmer break seen in both spectra. SED fitting measures similar parameters for these two objects, which are labeled approximately. Left insets show stamps from a JWST false-color image with the NIRSpec MSA slits overplotted. Right insets show smoothed zoom-ins of the Earendel spectrum where we identify marginal detections of nebular line emission [O III] λ5007 ([O III] λ4959 nondetection also marked) and Hα, which are measured at 2.5σ and 1.6σ significance, respectively.
Paper: Is Earendel a Star Cluster?: Metal-poor Globular Cluster Progenitors at z ∼ 6
Authors: Massimo Pascale, Liang Dai, Brenda L. Frye, Aliza G. Beverage
Figure caption: Posterior distributions for the Earendel (left), 1b (right purple), and 1a (right black) physical parameters from fitting with the BPASS SSP library, which generally yielded the largest age and metallicity uncertainties. We omit the ionization parameter, covering factor, and velocity dispersion, as they go unconstrained. We also omit the white-noise scaling, which is ≲1.3 in all cases. 2D contours enclose 50% and 90% of the posterior samples. Refer to Table 1 for the 68% confidence intervals of the parameters.
Paper: Is Earendel a Star Cluster?: Metal-poor Globular Cluster Progenitors at z ∼ 6
Authors: Massimo Pascale, Liang Dai, Brenda L. Frye, Aliza G. Beverage
Figure caption: Massive star cluster AMR predicted for MW-, LMC-, and SMC-mass host galaxies predicted by the E-MOSAICS cosmological simulation (J. M. D. Kruijssen et al. 2019; D. Horta et al. 2021) compared to measurements from LMC and SMC clusters (see Table A1 of D. Horta et al. 2021, and references therein) and MW clusters (see Table A1 of J. M. D. Kruijssen et al. 2019, and references therein) from the Sparkler (z = 1.38; A. Adamo et al. 2023), the Cosmic Gems (z ≈ 10.2; A. Adamo et al. 2024), and Earendel and 1b (BPASS results which have the largest uncertainties) from this work. We note that the younger ages of some clusters within both the Sparkler and the Cosmic Gems imply that the best-fit metallicity is dictated in part by enhancement from nebular emission; however, we still approximate ﹩{\mathrm{log}}\,(Z/{Z}_{\odot })\approx [\mathrm{Fe}/{\rm{H}}]﹩. All three sets of clusters appear broadly consistent with the predictions of SMC/LMC mass host galaxies, with the Sunrise also showing consistency with an MW-mass host. This figure is adapted from Figure 4 of both A. Adamo et al. (2023) and D. Horta et al. (2021).
Paper: Is Earendel a Star Cluster?: Metal-poor Globular Cluster Progenitors at z ∼ 6
Authors: Massimo Pascale, Liang Dai, Brenda L. Frye, Aliza G. Beverage
Figure caption: Top: metallicities inferred from the 1b NIRSpec PRISM spectrum using the BPASS SSPs (black error bars) with an iterative masking of wavelengths from the rest-FUV to the rest-optical. Masking the FUV through NUV does not appear to significantly affect the inferred metallicity; however, masking beyond the Balmer break (green dashed line), which is clearly detected in the NIRSpec spectrum (Figure 2), results in the metallicity becoming effectively unconstrained. Bottom: metallicities inferred via the BPASS (black), BC03 (purple), and FSPS (green) SSPs from a mock BPASS model of ﹩{\mathrm{log}}\,(Z/{Z}_{\odot })=-2.15﹩, ﹩{\mathrm{log}}\,({t}_{{\rm{age}}}/{\rm{yr}})=7.7﹩, and AV = 0 with increasing uniform fractional Gaussian noise applied. While BPASS and BC03 recover the ground truth (gray dashed line), FSPS exhibits an offset of ∼0.8 dex toward higher metallicities.
Paper: Is Earendel a Star Cluster?: Metal-poor Globular Cluster Progenitors at z ∼ 6
Authors: Massimo Pascale, Liang Dai, Brenda L. Frye, Aliza G. Beverage
Figure caption: JWST NIRCam F090W+F200W+F444W false-color image of the Sunrise galaxy at z ≈ 5.93. The multiple images shown sweep out an angular extent of ∼16″. At the redshift of Sunrise, the compass 2″ corresponds to ∼11.8 kpc. Labeled are multiply imaged clumps of interest within the galaxy: Earendel, image 1, image 6, and the SFC, consisting of images 3, 4, 5, and 6. We note the JWST NIRSpec MSA slit ID that covers image b of the SFC, 2282_12001, which is used for the spectroscopic redshift measurement.
Paper: Is Earendel a Star Cluster?: Metal-poor Globular Cluster Progenitors at z ∼ 6
Authors: Massimo Pascale, Liang Dai, Brenda L. Frye, Aliza G. Beverage
Figure caption: Metallicities and ages posteriors from fitting the BPASS SSPs to 10 mock spectra constructed using a BPASS model of ﹩{\mathrm{log}}\,(Z/{Z}_{\odot })=-2.15﹩, ﹩{\mathrm{log}}\,({t}_{{\rm{age}}}/{\rm{yr}})=7.7﹩, and AV = 0 with noise realizations applied that approximate the wavelength-dependent noise of the 1b NIRSpec PRISM spectrum. 2D contours enclose 50% and 90% of the posterior sample. The ground truth (blue lines) is generally recovered to within 1σ; however, the metallicity exhibits a noticeable bias toward lower metallicities.
Paper: A Binary Origin for Ultralong-period Radio Pulsars
Authors: Ying-Han Mao, Xiang-Dong Li, Dong Lai, Zhu-Ling Deng, Hao-Ran Yang
Figure caption: The evolutionary path of the formation of ULPPs in a binary system. The initial phase is an MS binary system, where the more massive primary star on the left undergoes an SN explosion, forming an NS (Step 1–Step 2). This NS then accretes material from the wind of the companion star through a wind-fed process, resulting in angular momentum loss and spin-down (Step 3). When the companion star on the right eventually reaches the SN phase, a violent mass ejection disrupts the binary system (Step 4). At this point, the firstborn NS is left behind, eventually becoming an isolated NS (Step 5). Its slow rotation period makes it a potential candidate for ULPPs.
Paper: A Binary Origin for Ultralong-period Radio Pulsars
Authors: Ying-Han Mao, Xiang-Dong Li, Dong Lai, Zhu-Ling Deng, Hao-Ran Yang
Figure caption: The number distribution of the companion star mass (M2), orbital period (Porb), and eccentricity (e) of the binary systems selected from the BPS simulation results, after the primary star has exploded and become an NS. The left and right panels correspond to the results for Z = 0.002 and Z = 0.02, respectively. This distribution corresponds to the parameters of the initial binary systems in Step 2 of Figure 1 and reflects the statistical weight of the initial systems retained after the evolutionary simulation. The noticeable dip in the M2 distribution around 12 M⊙ is likely caused by the mass exchange within binary systems. Primaries with mass >10 M⊙ are more likely to initiate mass transfer. During this stage, the companion stars typically gain a significant amount of mass, shifting into the M2 > 15 M⊙ range.
Paper: A Binary Origin for Ultralong-period Radio Pulsars
Authors: Ying-Han Mao, Xiang-Dong Li, Dong Lai, Zhu-Ling Deng, Hao-Ran Yang
Figure caption: MC simulation results for subsolar metallicity (Z = 0.002) and fixed values of f and Lcrit/L0 (top panels) and for solar metallicity (Z = 0.02) and randomized values of f and Lcrit/L0 (bottom panels). All other settings are the same as in Figure 4.
Paper: A Binary Origin for Ultralong-period Radio Pulsars
Authors: Ying-Han Mao, Xiang-Dong Li, Dong Lai, Zhu-Ling Deng, Hao-Ran Yang
Figure caption: The distribution of the final NS spin period (Ps) as a function of magnetic field strength (B) and orbital period (Porb). The orange triangles, green squares, and blue dots denote systems in phases b, c, and d, respectively. The small red circles are the systems that remain gravitationally bound after the second SN explosion. Several known ULPPs are displayed in the left panel, with their magnetic fields representing the upper limits of the dipole field. The red dashed line marks Ps = 1000 s.
Paper: A Binary Origin for Ultralong-period Radio Pulsars
Authors: Ying-Han Mao, Xiang-Dong Li, Dong Lai, Zhu-Ling Deng, Hao-Ran Yang
Figure caption: Evolutionary tracks of spin period (Ps) and magnetic field (B) for a system with M2 = 10 M⊙ and Porb = 5000 day. The solid, dashed, and dashed–dotted lines represent three different magnetic field evolution scenarios: exponential decay, power-law decay, and constant field, respectively. In the left panel, the black, orange, and blue lines correspond to phases a, b, and d, respectively. In the right panel, the red dashed box highlights the range of magnetic field strengths corresponding to the time interval shown in the left panel.
Paper: A Binary Origin for Ultralong-period Radio Pulsars
Authors: Ying-Han Mao, Xiang-Dong Li, Dong Lai, Zhu-Ling Deng, Hao-Ran Yang
Figure caption: The distribution of final spin period (Ps) and X-ray luminosity (LX) in the parameter space of companion zero-age main-sequence star mass and orbital period. The magnitudes of Ps and LX are displayed with different colors. The white area indicates systems that experience Roche-lobe overflow.
Paper: Solar Alfvénic Pulses and Mesoscale Solar Wind
Authors: Jeongwoo Lee, Manolis K. Georgoulis, Rahul Sharma, Nour E. Raouafi, Qin Li, Haimin Wang
Figure caption: Tracking NBP motions in a magnetogram. In the top panel, NBPs are marked with cyan circles with equivalent area, and their total displacements during their lifetimes are indicated by cyan lines (same in both plots), with length 3 times longer than actual displacements for visual convenience. The equivalent areas (cyan dots) and velocities (cyan lines) of these NBPs are further shown against the corresponding NIRIS LOS magnetogram, used to calculate the electric field vectors (red lines) shown in the bottom image.
Paper: Solar Alfvénic Pulses and Mesoscale Solar Wind
Authors: Jeongwoo Lee, Manolis K. Georgoulis, Rahul Sharma, Nour E. Raouafi, Qin Li, Haimin Wang
Figure caption: Illustration of the energy calculation and the associated parameters (top) and the distribution of the results. (a) Parameters in the photosphere and chromosphere. (b) Parameters of a magnetic switchback. (c) Number distributions of electric field, magnetic flux, and energy of Alfvénic pulses. (d) Energies of Alfvénic pulses (yellow) and those associated with magnetic reconnection (blue) in comparison with six switchback energies (red arrows). SB#1–6 refer to the PSP switchbacks with ID: E2S4, E2S6, E1S5, E1S6, E1S1, and E2S3, defined in R. Laker et al. (2021).
Paper: Solar Alfvénic Pulses and Mesoscale Solar Wind
Authors: Jeongwoo Lee, Manolis K. Georgoulis, Rahul Sharma, Nour E. Raouafi, Qin Li, Haimin Wang
Figure caption: Filling factor of NBPs. (a) The areas of mobile NBPs (red circles) and filigree (blue contours). The filling factor is calculated by dividing the sum of the NBP areas by the total area of the filigree at each time. (b) Time–distance (T–R) map of the NBPs. At each time, the NBP areas along the T-axis is obtained by adding up the NBPs along the R-axis. (c) Average filling factor as a function of time. The error bars are based on the uncertainty in the filigree area, and the dashed line at ∼8% is the mean value of the filling factor over time.
Paper: Solar Alfvénic Pulses and Mesoscale Solar Wind
Authors: Jeongwoo Lee, Manolis K. Georgoulis, Rahul Sharma, Nour E. Raouafi, Qin Li, Haimin Wang
Figure caption: Transmission of Alfvénic pulses. (a) Transmission coefficient in energy as a function of period for selected values of the Alfvén speed contrast, ﹩\alpha ={V}_{{{\rm{A}}}_{2}}/{V}_{{{\rm{A}}}_{1}}﹩ calculated for two density scale heights, Hρ. (b) Transmission coefficient as a function of Hρ and α at a fixed period of 40 s. Different contours between 0.1% and 90% are labeled with these percentage values. Darker contours denote stronger wave reflection.
Paper: Solar Alfvénic Pulses and Mesoscale Solar Wind
Authors: Jeongwoo Lee, Manolis K. Georgoulis, Rahul Sharma, Nour E. Raouafi, Qin Li, Haimin Wang
Figure caption: Spicules and NBPs in a GST/VIS Hα–1.0 Å blue wing image. A few field lines inferred from the selective spicule trajectories are marked in color together with NBPs outlined by a blue contour underneath. The inset magnifies the white box region, in which the color-filled masks represent the NBPs and associated field lines are colored in the same code. Using SWAMIS, we track each NBP in subsequent frames to determine its velocity (arrows in the inset).
Paper: Langmuir-wave Excitation in Solar Wind Magnetic Holes
Authors: Jingting Liu, 婧婷 刘, Daniel Verscharen, Jesse Coburn, Georgios Nicolaou, Xiangyu Wu, 翔宇 吴, Wence Jiang, 文策 蒋, Oreste Pezzi, Francesco Pucci, Matteo Zuin, Christopher J. Owen, Hamish Reid
Figure caption: Solar Orbiter observations of an MH on 2022 January 2 from 00:08:01 UT to 00:08:03 UT (case 2). The horizontal axis shows the time in UT (hh:mm). (a) Magnetic field strength B in green and electron number density ne in blue. (b) Components of the magnetic field in RTN coordinates. (c) Electron pitch-angle distribution of electrons from 69 eV to 2000 eV. (d) Electron pitch-angle distribution from 100 eV to 250 eV. The blue and olive colored dots indicate angles beyond which Equations (9) and (12) are violated for E = Ecrit = 150 eV. (e) Dynamic spectrum of wave flux vs. time in spectral flux units. (f) Illustration of a possible magnetic field configuration based on a feather plot of our in situ magnetic field measurements. In this panel, time is displayed in hh:mm:ss format.
Paper: Langmuir-wave Excitation in Solar Wind Magnetic Holes
Authors: Jingting Liu, 婧婷 刘, Daniel Verscharen, Jesse Coburn, Georgios Nicolaou, Xiangyu Wu, 翔宇 吴, Wence Jiang, 文策 蒋, Oreste Pezzi, Francesco Pucci, Matteo Zuin, Christopher J. Owen, Hamish Reid
Figure caption: Illustration of changes in the electron VDF when passing through an MH. The variation in magnetic field strength as a function of time is shown on the right, with the times of interest indicated by pink lines. Time t0 corresponds to the time before entering the MH. Electrons with v∥ > 0 stream toward the MH with a core and strahl configuration, while the distribution at v∥ < 0 consists of core electrons that have already crossed the MH. For the subsequent times, the loss-cone angle α is represented by black dashed lines. The distribution functions at t1, t2, and t3 illustrate the VDFs at their respective locations within the MH. Near the minimum of ∣B∣ at t3, strahl electrons with velocities within the shaded area violate their μ conservation. These electrons have energy greater than the critical energy Ecrit and form a bump in the form of a positive gradient in velocity space.