adsabs/AstroCLIMB huggingface dataset:
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: The densities of positions where a return-to-disk photon reaches the accretion disk. The photon number is normalized to the seed photon number. The lines with different colors correspond to simulations with different jet velocities.
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: The simulated spectra at inclination angle 55°. The red lines are the thermal component emitted by the accretion disk; the yellow lines are the Compton component; the green lines are the reflection component; the blue lines are the sum of all components, i.e., the observed spectra. Panels (a)–(f) correspond to jet velocity 0c, 0.1c, 0.2c, 0.4c, 0.7c, and 0.99c, respectively.
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: Variation of reflection fraction with inclinations. The lines with different colors correspond to simulations with different jet velocities.
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: The simulated spectra at inclination angle 35°. The red lines are the thermal component emitted by the accretion disk; the yellow lines are the Compton component; the green lines are the reflection component; the blue lines are the sum of all components, i.e., the observed spectra. Panels (a)–(f) correspond to jet velocity 0c, 0.1c, 0.2c, 0.4c, 0.7c, and 0.99c, respectively.
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: The left panel shows comparisons between a cutoffpl (red) and our input spectrum (blue). The right panel shows the reflection spectra obtained by convolving both the cutoff power-law spectrum and the return-to-disk photons spectrum with the xilconv model.
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: The simulated spectra at inclination angle 45°. The red lines are the thermal component emitted by the accretion disk; the yellow lines are the Compton component; the green lines are the reflection component; the blue lines are the sum of all components, i.e., the observed spectra. Panels (a)–(f) correspond to jet velocity 0c, 0.1c, 0.2c, 0.4c, 0.7c, and 0.99c, respectively.
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: The simulated spectra at inclination angle 75°. The red lines are the thermal component emitted by the accretion disk; the yellow lines are the Compton component; the green lines are the reflection component; the blue lines are the sum of all components, i.e., the observed spectra. Panels (a)–(f) correspond to jet velocity 0c, 0.1c, 0.2c, 0.4c, 0.7c, and 0.99c, respectively.
Paper: Monte Carlo Simulation of the Compton Scattering and Disk Reflection of a Cylinder with Hot Electrons Moving Away from a Black Hole
Authors: Wei Meng, Yuan You, Shuang-Nan Zhang, Jia-Ying Cao
Figure caption: The simulated spectra at inclination angle 65°. The red lines are the thermal component emitted by the accretion disk; the yellow lines are the Compton component; the green lines are the reflection component; the blue lines are the sum of all components, i.e., the observed spectra. Panels (a)–(f) correspond to jet velocity 0c, 0.1c, 0.2c, 0.4c, 0.7c, and 0.99c, respectively.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Mass ratio (q) distribution as a function of χeff. Top left: results from our default setup for a E. Sirko & J. Goodman (2003) disk with BH mass distribution power-law index γ = 2, run sg_default. Gold points represent 1g–1g mergers (see text). Inverted purple triangles indicate either 2g–1g or 2g–2g mergers. Red triangles indicate ≥3g–Ng mergers. The solid and dashed lines are fit through (χeff, q) = (0, 1) and entire and ≥2g populations, respectively. Teal points with error bars are a representative sample of GW sources chosen to avoid cluttering and provide context for our results: GW190412,GW190521, GW190814, GW200115_042309, GW200208_222617, and GW200210_092254. The red-orange data point with an “×” represents GW231123. Bottom left: default setup for a T. A. Thompson et al. (2005) disk, run tqm_default. Right column: same as SG and TQM defaults but with a shallower IMF index of γ = 1 that increases the probability for high-mass BHs. Each experiment was performed for 100 galaxies. See Table 1 for setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Final mass of merger remnants vs. radius (left column) and time (right column) in SG disks (top row) and TQM disks (bottom row). Strong migration torques and traps in SG disks near 103 Rg accelerate hierarchical mergers, whereas weaker torques in TQM disks cause traps to be less important, leading to a maximum of 3g remnants and lower masses. SG disks take ∼0.2 Myr to regularly produce 1g mergers, with 2g mergers starting at 0.25 Myr and 3g+ mergers at 0.33 Myr, while final mass increases steadily with time and reaches ∼120 M⊙. TQM disks quickly merge the initial embedded BH population in the first 0.25 Myr and reach a steady state as the disk captures more BHs. The mass range of remnants stays relatively even between 20 and 70 M⊙ throughout time. Markers are as in Figure 1.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Varying the disk lifetime. Top row: SG disk setups with τAGN = 0.25, 0.5, and 0.75 Myr. Bottom row: TQM disk setups with τAGN = 2.5, 3, and 5 Myr. The anticorrelation steepens with lifetime in dense SG disks as more hierarchical mergers with large χeff occur, but τAGN has little impact on low-density TQM disks. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Merger remnant mass vs. disk lifetime. Top row: SG disk setups with τAGN =  0.25, 0.5, and 0.75 Myr. Bottom row: TQM disk setups with τAGN = 2.5, 3, and 5 Myr. Hierarchical mergers drive up the mass of remnants in SG disks with increased lifetime, whereas TQM disks quickly merge BHs on near-circular orbits, but low migration rates suppress subsequent interactions that would increase remnant masses beyond ∼80 M⊙. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Primary mass vs. χeff. Hierarchical mergers drive primary masses higher and produce mergers with larger values of χeff. Markers are as in Figure 1.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Varying the retrograde BBH fraction. Left column: default SG and TQM disk setups where no retrograde BBHs form (fret = 0, sg_default). Center column: retrograde fraction set to fret = 0.1 (sg_fr0p1). Right column: half of BBHs are set to retrograde, fret = 0.5 (sg_fr0p5). Increasing the allowed retrograde fraction splits the hierarchical population to negative χeff and flattens the slopes of the anticorrelation for SG-like disks. The TQM model (bottom row; tqm_default, tqm_fr0p1, tqm_fr0p5) reflects this behavior but the hierarchical population still suffers from low numbers. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Initially circular orbits with varying AGN lifetimes. Left: TQM disk evolved for τAGN = 1 Myr (tqm_e0_t1). Center: setup same as tqm_default but with circular BH orbits (τAGN = 3 Myr; tqm_e0). Right: default TQM setup where τAGN = 3 Myr and the initial eccentricity is capped at ﹩{e}_{{\rm{\max }}}=0.05﹩ (tqm_default). Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Varying the width of the Gaussian distribution for initial BH spin magnitude. Top left: SG disk with spin magnitude distribution σχ = 0.02 (sg_0p02). Top center: default SG disk with σχ = 0.1 (sg_default). Top right: SG disk with σχ = 0.2 (sg_0p2). Bottom row: same as top row but for a TQM disk model (tqm_0p02, tqm_default, tqm_0p2). Narrower (wider) spin magnitude distributions primarily affect the 1g population by narrowing (widening) the distribution in χeff. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Varying the initial maximum orbital eccentricity. SG disk with NSC initial eccentricity capped at ﹩{e}_{{\rm{\max }}}=0.1﹩ (left, sg_e0p1), 0.3 (center, sg_default), and 0.5 (right, sg_0p5). The number of mergers is inversely proportional to the initial eccentricity. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Varying the initial maximum orbital eccentricity. TQM disk with NSC initial eccentricity capped at ﹩{e}_{{\rm{\max }}}=0.015﹩ (left, tqm_e0p015), 0.05 (center, tqm_default), and 0.1 (right, tqm_e0p1). The number of mergers is inversely proportional to the initial eccentricity, and an extremely low eccentricity is required for the TQM model to produce an appreciable number of hierarchical mergers, as opposed to the SG model. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Thermal population with varying lifetimes. Left: default SG disk with ﹩{e}_{{\rm{\max }}}=0.3﹩ (sg_default). Center: SG disk interacting with a thermal NSC with ﹩{e}_{{\rm{\max }}}=0.7﹩ (sg_e0p7). Right: thermal NSC with SG disk lifetime increased to τAGN = 0.75 Myr (sg_e0p7_t0p75). A more eccentric initial BH population takes longer to circularize, which increases the time to produce mergers. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Varying disk radius. SG and TQM disks with radii r = [2 × 104, 5 × 104,  105] Rg. Both decreases and increases in disk radius result in fewer mergers. Model names, from left to right, top to bottom: sg_r2e4, sg_default, sg_r7e4, tqm_r2e4, tqm_default, and tqm_r7e4. Markers are as in Figure 1. See Table 1 for unique setup parameters and Table 2 for population statistics.
Paper: McFACTS. II. Mass Ratio–Effective Spin Relationship of Black Hole Mergers in the Active Galactic Nucleus Channel
Authors: Harrison E. Cook, Barry McKernan, K.E. Saavik Ford, Vera Delfavero, Kaila Nathaniel, Jake Postiglione, Shawn Ray, Emily J. McPike, Richard O'Shaughnessy
Figure caption: Merger remnant mass vs. radius. Left column shows the outer disk radius set to 2 × 104 Rg, compared to the default 5 × 104 Rg in the center column and 7 × 104 Rg in the right column. SG disks (top row) produce fewer mergers with both changes for SG. Shrinking TQM disks (bottom row) also produces fewer mergers, but extending this disk includes more of the optically thick outskirts that drives migration in this model, so the number of mergers is the same as the default case. Markers are as in Figure 1.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Evolution of the normalized harmonics amplitude, Eℓ/E0, measured in N-body runs (dotted lines, averaged over 19 runs), in collisionless KRIOS runs (full lines, averaged over 10 runs, with time step Δtsys = 0.01 HU) and (collisionless) EXP runs (dashed–dotted lines, averaged over 10 runs). The growth rate prediction by linear theory using the Julia package JuliaStellarDynamics (https://github.com/JuliaStellarDynamics) is shown as a dashed black line along the curve. All runs contain N = 105 particles of equal masses. We centered the time axis at the peak of the ℓ = 2 amplitude for each realization before ensemble average. The ROI drives the amplification of the quadrupole ℓ = 2 and, in a lesser fashion, that of the ℓ = 4 component, until saturation occurs. Two-body relaxation tends to counteract ROI, leading to a slightly lower quadrupole amplitude and a slow decrease over time similar to N-body measurements (as opposed to the constant saturation in collisionless runs). The other harmonics are not impacted by the ROI, and therefore remain at the noise level ∼1/N = 10−5. Finally, collisionless runs (KRIOS w/o two-body relaxation and EXP) closely recover the ROI observed in direct N-body runs. This is because the two-body relaxation timescale computes to ﹩{\hat{T}}_{{\rm{rel}}}\sim 200\,{\rm{HU}}﹩ (at t = 0), which is much longer than the dynamical timescale over which the ROI occurs.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Illustration of the two-body gravitational scattering in the plane of deflection for the particles i and i + 1, which are selected by a predetermined pairing scheme (see Section 3.1). We defined the relative position Δr = ri − ri+1 and the relative velocity w = vi − vi+1 of the two interacting particles. These two particles are deflected by an angle βe and follow hyperbolic trajectories during their interaction. This results in a modification of their velocities, which exactly conserves energy, but only approximately conserves angular momentum.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Profile of the potential (top panel, ψ) and radial density (bottom panel, ρr) for a cluster nearing core collapse. The instantaneous potential and density are represented in green, while the SCF expansions are represented in red (using an optimized Z96 family) and in purple (using the CB73 family). Although both radial expansions are limited by ﹩{n}_{{\rm{\max }}}=10﹩, it is clear that the CB73 expansion struggles to converge toward the instantaneous potential-density pair, whereas the optimized Z96 expansion quickly converges toward it, illustrating both its necessity and effectiveness.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Evolution of the Z96 basis parameters, α and b, as an isotropic Plummer sphere with N = 106 particles undergoes core collapse. In order for the Z96 basis functions to make it possible to accurately reproduce the mean field potential of the cluster as it becomes more and more cuspy over the course of its relaxation, higher values of α and lower values of b are necessary. The dashed red line corresponds to the CB73 family (α = 1/2), whereas the dashed purple line corresponds to the HO92 family (α = 1). The colored triangles represent the best-fit parameters corresponding to a Plummer sphere (in red) and a Hernquist sphere (in purple) in Hénon units.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Behavior of the radial basis function, ﹩{U}_{n}^{\ell }(r)﹩, of the lowest Zhao potential basis elements n = ℓ = 0, defined in Equation (A3a). We display four α values (shown in blue, red, green, and purple by increasing order) and two b values (0.1 in dashed lines, 1.0 in solid lines). The α parameter is a power-law index that sets the “cuspiness” of the potential-density profile. For example, α = 1/2 corresponds to a Plummer sphere, and α = 1 to the Hernquist potential. The b parameter can be qualitatively related to the scale length of the system.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: KRIOS uses two frames to describe the dynamics of the cluster: (i) a fixed reference frame (in black), centered at 0 and attached to a fixed set of Cartesian coordinates (x, y, z); (ii) a time-dependent frame called the SCF frame (in purple), centered at the density center of the cluster rc(t), attached to a translation of the same Cartesian coordinates, and to which we add a set of spherical coordinates (r, ϑ, ϕ). Frame (i) is used to integrate the dynamics in an inertial frame, while frame (ii) is adapted to the description of the cluster and is used to expand its potential-density pair using the SCF method.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Schematic flowchart of the KRIOS code during one time step. The sections describing each entries are given within brackets.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Top panel: evolution of the core radius (Equation (24)) of an initial isotropic, nonrotating Plummer sphere (with identical masses) using N-body simulations (in transparent colors, N = 104) and the KRIOS code (in red, N = 106 and nneigh = 30, ﹩{\ell }_{{\rm{\max }}}=0﹩ and ﹩{n}_{{\rm{\max }}}=15﹩). Bottom panel: evolution of a few Lagrange radii for the same system using N-body simulations (transparent lines), the KRIOS code (solid lines). The dotted lines corresponds to the RAGA run described in Figure 2 of E. Vasiliev (2015) and rescaled to our units. Time is expressed in units of initial half-mass relaxation time (see Equation (23)). We show a sample of 50 realizations of N-body simulations. The SCF approach is consistent with measurements made in N-body simulations over the course of the cluster’s relaxation up to the deeper stages of core collapse. Using the SCF method, KRIOS is able to reach core collapse in a reasonable time (tcc ∼ 18 trh) —a value that weakly depends on the run parameters.
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Evolution of the fractional energy change (bottom panel) and of the absolute error in angular momentum (in Hénon units), ∣ΔL∣, ∣ΔLz∣, during the cluster’s evolution shown in Figure 8, in the SCF frame. Energy conservation is satisfactory due to the Stodółkiewicz scheme adjustment, and stays well below 1% relative error at core collapse. Similarly, angular momentum conservation remains below ∣δL∣ ≤ 0.06 HU—despite the Stodółkiewicz prescription and the approximate conservation in two-body collisions (see Section 2.3)—provided we use the density-pairing scheme (see Section 3.1).
Paper: KRIOS: A New Basis-expansion N-body Code for Collisional Stellar Dynamics
Authors: Kerwann Tep, Brian T. Cook, Carl L. Rodriguez, Jiya Jolly, Eddie Sawin, Michael S. Petersen, Christoph Gaffud
Figure caption: Evolution of the rotation curve, 〈vϕ〉(R), along the relaxation of an isotropic, rotating cluster with αr = 1/2. We compare KRIOS runs with N = 105 particles averaged over 5 realizations (solid lines) against N-body runs with N = 104 particles averaged over 50 realizations (dashed lines). The red dotted line is the theoretical prediction at t = 0. As the cluster undergoes secular relaxation, its internal angular momentum is slowly reorganized. This phenomenon is captured both in N-body measurements and in KRIOS measurements.