adsabs/AstroCLIMB huggingface dataset:
Paper: Kinematically Complex Circumgalactic Gas Around a Low-mass Galaxy: Filamentary Inflow and Counterrotation in J0910b
Authors: Zeren Lin, D. Christopher Martin, Mateusz Matuszewski, James D. Neill, Drew M. Miles, Vincent Picouet, Nikolaus Z. Prusinski, Keri Hoadley, Rosalie McGurk
Figure caption: Azimuthally averaged median radial profiles for [O III] λ5007, Hβ, Hα, [N II] λ6583, [O II] λλ3727, 3729, and [S II] λ6716 line emission. The shaded regions around each profile represent the 25th to 75th percentiles. Profiles observed in the KCWI NAS configuration ([O III], Hβ) are shown in shades of blue, while those observed in the non-NAS configuration (Hα, [N II], [O II], [S II]) are shown in shades of red for clarity. The dashed lines labeled “KCWI NAS Limit” and “KCWI non-NAS Limit” indicate estimated values based on the largest smoothing kernel sizes used in adaptive smoothing, assuming uniform line widths of 10 Å and covariance calibration. These values should be considered as reference, as the detection limit in adaptive smoothing significantly depends on the kernel size at that step and is not constant across the field. They are provided only to illustrate the faintest possible detection (if any) extracted with the largest smoothing kernels, highlighting the differences between the NAS and non-NAS observations. In some annuli (e.g., for Hα and [N II] at 20″–25″), the median profiles dip slightly below these reference lines due to overlapping pointings and smaller adaptive smoothing kernels, which yield locally deeper sensitivity.
Paper: Kinematically Complex Circumgalactic Gas Around a Low-mass Galaxy: Filamentary Inflow and Counterrotation in J0910b
Authors: Zeren Lin, D. Christopher Martin, Mateusz Matuszewski, James D. Neill, Drew M. Miles, Vincent Picouet, Nikolaus Z. Prusinski, Keri Hoadley, Rosalie McGurk
Figure caption: Velocity profile showing counterrotating gas. The left column presents the Hα and [O III] λ5007 emissions, each overlaid with a 5″ pseudo-slit. The right column shows the velocity profile across the slit, with x-marked points indicating the weighted mean velocity. The velocity profile exhibits a negative gradient in the inner regions (between −3″ and 3″, or −5.3 to 5.3 kpc), consistent with the galaxy’s rotation. In the inner CGM (around 3–10″ and −10″ to −3″, or 5.3–18 kpc and −18 to −5.3 kpc), the velocity gradient reverses, with a positive gradient suggesting counterrotation relative to the galaxy’s disk. The larger velocity amplitudes seen in [O III] compared to Hα are attributed to the lower spectral resolution of KCWI-blue, as discussed in Appendix C.2. These maps are rotated and mirrored relative to Figure 6: the direction of increasing R.A. in Figure 6 corresponds to +ΔY here, while the direction of increasing decl. corresponds to −ΔX.
Paper: Kinematically Complex Circumgalactic Gas Around a Low-mass Galaxy: Filamentary Inflow and Counterrotation in J0910b
Authors: Zeren Lin, D. Christopher Martin, Mateusz Matuszewski, James D. Neill, Drew M. Miles, Vincent Picouet, Nikolaus Z. Prusinski, Keri Hoadley, Rosalie McGurk
Figure caption: Azimuthally averaged median line ratio plots for the emission lines: [O III] λ5007/Hβ, Hα/[N II] λ6583, [O III] λ5007/Hα, Hα/Hβ, [O II] λλ3727, 3729/Hα, [O III] λ5007/[O II] λλ3727, 3729, and Hα/[S II] λ6716. The shaded areas represent the 25th to 75th percentiles of the line ratios within the KCWI-blue and KCWI-red observations. For line ratios between KCWI-blue and KCWI-red, the ratios are derived by interpolating the data onto a common grid and then computing the median and percentiles, as described in the main text. The y-axis is plotted on a logarithmic scale to emphasize relative radial trends and prevent the largest ratios from dominating the visualization.
Paper: Kinematically Complex Circumgalactic Gas Around a Low-mass Galaxy: Filamentary Inflow and Counterrotation in J0910b
Authors: Zeren Lin, D. Christopher Martin, Mateusz Matuszewski, James D. Neill, Drew M. Miles, Vincent Picouet, Nikolaus Z. Prusinski, Keri Hoadley, Rosalie McGurk
Figure caption: Integrated spectrum for [O III] λλ5007, 4959, Hβ, Hα, [N II] λ6583, [O II] λλ3727, 3729, and [S II] λ6716 across all detected regions defined by the 3D mask, excluding the inner 8″ radius around the galaxy, as shown in Figure 6. The area under each curve corresponds to the total line flux detected for each emission. The vertical dashed lines mark the expected positions of the emission lines, including [O III] λ5007, 4959, Hβ, Hα, [N II] λ6583, and [O II] λλ3727, 3729. The estimated line ratios are [O III] λ5007/Hα ∼ 0.47, [O II] λλ3727, 3729/Hα ∼ 1.25, and [O III] λ5007/[O II] λλ3727, 3729 ∼0.37, which are consistent with the results discussed in Section 4.1 and Figure 11.
Paper: Kinematically Complex Circumgalactic Gas Around a Low-mass Galaxy: Filamentary Inflow and Counterrotation in J0910b
Authors: Zeren Lin, D. Christopher Martin, Mateusz Matuszewski, James D. Neill, Drew M. Miles, Vincent Picouet, Nikolaus Z. Prusinski, Keri Hoadley, Rosalie McGurk
Figure caption: Similar to Figure 6, this figure displays the surface brightness, line-of-sight velocity, and velocity dispersion maps of [O II] λλ3727, 3729 (top) and [S II] λ6716 (bottom rows). The velocity dispersion of [O II] appears larger due to the blending of the two lines.
Paper: Kinematically Complex Circumgalactic Gas Around a Low-mass Galaxy: Filamentary Inflow and Counterrotation in J0910b
Authors: Zeren Lin, D. Christopher Martin, Mateusz Matuszewski, James D. Neill, Drew M. Miles, Vincent Picouet, Nikolaus Z. Prusinski, Keri Hoadley, Rosalie McGurk
Figure caption: Similar to Figure 5, this figure presents consecutive 4 Å narrowband images around [O II] λλ3727, 3729 (top) and [S II] λ6716 (bottom rows). The [O II] doublet is unresolved in our setup due to the spectral resolution of 〈R〉 = 900.
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Upper panel: measured periods with multicomponent fitting using Equation (2). The errors were evaluated using the Python Numpy package (C. R. Harris et al. 2020). The style and colors of the points represent the different ranges of exposure times. The horizontal lines indicate the mean value and error interval derived by H. H. Wang et al. (2024). Middle panel: the results (with the colors adopted in the upper panel) using simulated light curves in which the period is constant, to show the resulting scatter of the measured period in the simulation. The scatter is larger for the shorter exposure times. Lower panel: the whole, unbinned light curve for reference. (In Figure 1, we only showed the average count rate of each short exposure.)
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Comparison of high-count-rate vs. low-count-rate NICER spectra. On the left, the spectrum measured on day 96 PO (high count rate) vs. the one measured on day 102 (low count rate); on the right, the spectrum measured on day 135 (high count rate) vs. the one measured on day 118 (low count rate; see Table A2). In red, on the left, model fits with a temperature of T = 778,000 K and N(H) = 4.4 × 1021 cm–2 for the low count rate and N(H) = 3.4 × 1021 cm–2 for the high count rate, respectively; on the right, a model fit with a fixed value of the column density, N(H) = 4.7 × 1021 cm–2, and T = 782,000 K and 703,000 K for the high and low count rates, respectively. The logarithmic scale on the Y-axis shows the deviation from a pure atmosphere model, which in the grating observations turned out to be due mostly to emission lines.
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: The black dots in the top panel show the light curve of NICER observation 6203910103, binned every 5 s for better visualization. The lower panel shows the corresponding Lomb–Scargle periodogram (black line). The colored lines represent the model fitting (in the upper panel) and derived corresponding periods (in the lower panel); the blue lines are for the single-sine model with constant periodicity and constant amplitude (Equation (1)), while the red lines show the result of the multicomponent model with two sine functions, constant periodicity with its first harmonics, and variable amplitude (Equation (2)).
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Fit to the spectrum taken on 2023 October 21 with the model described in the text. The blue line indicates the fit with only the atmosphere model. The BVAPEC model (included in the red line) adds emission lines of N VII and O, but it does not significantly improve the fit, as most emission lines are not fitted. A thorough analysis on the origin of the emission lines—confirming the result on the atmospheric temperature—is presented in detail in the spectral paper.
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Upper panel: light curve of Nova V1716 Sco over 300 days of Swift observations in the 0.3–10 keV range. The epochs of the Chandra exposures are denoted with dashed red lines. Lower panel: light curve obtained with NICER, with count rate in the 0.2–0.8 keV range, the energy band in which the flux is significant.
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Light-curve comparison of day 99 (red) vs. day 128 PO (blue). In these segments, for the day 99 exposure the average count rate is ∼17 ct s−1, and the average count rate for day 128 is ∼47 ct s−1. We fit Equation (2) to both light-curve segments (black lines) to estimate the modulation amplitude for each. We note that the fitting here is intended only to estimate the amplitudes, and is not used in our timing analysis, since both segments are ∼400 s, below our 500 s threshold. The modulation amplitude for day 99 is 34% ± 5% of the average count rate vs. a modulation amplitude of 18% ± 4% of the average count rate for day 128. Various NICER light curves with largely different average count rates show this discorrelation when compared, and we suggest that the amplitude of the modulation on the periodic signal is not correlated with variations in observed flux from the source.
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Periodograms of two Chandra light curves. ObsID 28048 in the upper panel in black represents the observations during the NICER interval in Figure 7; ObsID 28049 is shown in the bottom panel in red. The horizontal dashed lines mark the corresponding 99.9% confidence level. The inset in the upper panel is a zoom in of the two observations, showing a comparison of the detected period around 77.9 s.
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Selected light curves to show the variability over timescales of minutes and of hours. The NICER data from day 97 postoutburst (PO), in 5 s bins (top panel), and two Chandra/HRC (zeroth-order) light curves, respectively: ObsID 28048 (2023 August), binned every 20 s (middle panel), and ObsID 28049 (2023 October), binned every 20 s (lower panel). There is still some aperiodic variability in the NICER data of the same day, but the average in each pulsation does not vary by more than 30%, while we observe fluctuations as large as >100% over timescales of days after the first peak.
Paper: X-Ray Observations of Nova Scorpii 2023 (V1716 Sco) in Outburst
Authors: John T. Worley, Marina Orio, Andrej Dobrotka, Jozef Magdolen, Kim Page, Ehud Behar, Jeremy J. Drake, Sharon Mitrani
Figure caption: Top panel: comparison of the ±1 orders average spectra of August 27 (black) and October 20 (red). Middle panel: comparison of the August 26 (red) and August 27 (black)  ±1 orders spectra, with the second shifted by 0.375 ct s−1. Bottom panel: comparison of the October 20 (red), 21 (blue), 22 (black)  ±1 order spectra with successive shifts by 0.375 ct s−1. Note how the difference is significant only between August and October, but not in spectra taken on sequential days.
Paper: From Wide Triples to Ultracompact X-ray Binaries: Multimessenger Signatures of Dynamically Formed Black Hole–White Dwarf Systems in the LISA Band
Authors: Zeyuan Xuan, Cheyanne Shariat, Smadar Naoz
Figure caption: Time evolution of an example BH–WD system that undergoes strong EKL oscillations during the dynamical formation stage (left column) and transitions into a mass-transferring UCXB (right column). Here, we show the time evolution of a representative BH–WD system from our simulation, with initial mass m1 = 10 M⊙, m2 = 0.6 M⊙, orbit separation a0 = 95.3 au, eccentricity e0 = 0.199. This binary is orbited by a tertiary companion with mass m3 = 0.836 M⊙, outer orbit separation a2 = 4997 au, eccentricity e2 = 0.602, and mutual inclination i = 91﹩\mathop{.}\limits^{\unicode{x000b0}}﹩8 to the inner binary. We define tc as the time when the BH–WD binary becomes fully circularized (e < 0.01). The system’s evolution during the dynamical formation stage is shown in the left column as a function of tc − t (log-scale), while its post-circularization evolution is shown in the right column as a function of t − tc. The first row shows the inner binary’s orbital eccentricity, as 1 – e. The second row shows the inner orbital separation (red solid line, a), the WD–BH mass ratio (blue dashed–dotted line, m2/m1), the Roche lobe radius (black dashed line, Rlobe, see, e.g., Equation (28) in C. S. Ye et al. (2023)), and the WD radius (black dotted line, R2). The third row plots two ratios: the tidal energy dissipation rate (red solid line, see Equation (4)) to the GW radiation power (see, e.g., Equation (5.4) in P. C. Peters (1964)), and the WD spin angular frequency Ωs to the binary’s pericenter frequency Ωp = Ω(1 – e)−3/2 (blue dashed–dotted line). The bottom row shows the expected GW signal-to-noise ratio at distance Dl = 8 kpc (red solid line) for a 4 yr LISA observation, and the binary’s X-ray luminosity LX (blue dashed–dotted line), normalized by 0.1% of the BH Eddington luminosity, L0 = 10−3LEdd ∼ 1.26 × 1036erg s−1.
Paper: From Wide Triples to Ultracompact X-ray Binaries: Multimessenger Signatures of Dynamically Formed Black Hole–White Dwarf Systems in the LISA Band
Authors: Zeyuan Xuan, Cheyanne Shariat, Smadar Naoz
Figure caption: Comparison between the energy transfer rate of dynamical tides and GW radiation, for a highly eccentric BH–WD system. Here, we consider a 10–0.6 M⊙ BH–WD binary with e = 0.95, WD radius R2 = 5.3 × 10−5 au, and WD dimensionless tidal torque ﹩\hat{F}(\omega )\sim 150{\omega }^{5}﹩. The energy transfer rates from WD dynamical tides and from GW radiation are plotted as functions of the binary’s pericenter distance rp. We show two cases for dynamical tides: the zero-spin case (red solid line, fixing Ωs = 0) and the synchronized-spin case (blue dashed line, when Ωs synchronizes with pericenter frequency and satisfies ﹩{\dot{J}}_{{\rm{tide}}}=0﹩). The energy loss due to GW radiation is shown as the gray dashed–dotted line. We note that when eccentricity is nonzero, there will be a residual tidal heating rate (blue dashed line) even when there is no net torque on the WD. This rate will vanish in the circular limit.
Paper: From Wide Triples to Ultracompact X-ray Binaries: Multimessenger Signatures of Dynamically Formed Black Hole–White Dwarf Systems in the LISA Band
Authors: Zeyuan Xuan, Cheyanne Shariat, Smadar Naoz
Figure caption: The population of BH–WD systems from the simulated Milky Way Galactic field, and their estimated GW signal-to-noise ratio as a function of semimajor axis and eccentricity (for a 4 yr LISA observation). Here, we plot the semimajor axis, a, and eccentricity, as 1 − e, of each simulated BH–WD system (see the white stars). The left panel shows the initial conditions, while the right panel represents the final state of each system, either when its dynamical evolution ends at the Hubble time or when the orbit separation shrinks to ≲10−3 au and triggers the mass transfer. The background color maps the binary’s expected GW signal-to-noise ratio, assuming a fixed distance Dl = 8 kpc and a 4 yr LISA observation. In the right panel, we also plot intermediate evolutionary stages (pink dots) for binaries that eventually evolve into UCXBs. These dots represent the evolution track of UCXBs formed via the wide triple channel, and highlight the region of parameter space where they may become detectable.
Paper: From Wide Triples to Ultracompact X-ray Binaries: Multimessenger Signatures of Dynamically Formed Black Hole–White Dwarf Systems in the LISA Band
Authors: Zeyuan Xuan, Cheyanne Shariat, Smadar Naoz
Figure caption: Parameters of detached BH–WD systems in triples after MS evolution. Here, we plot the semimajor axis of inner (a1) and outer orbits (a2) for the BH–WD binaries and their tertiary companions, immediately after the inner binary has evolved into a BH–WD configuration. Red circles represent all systems, while blue triangles indicate those that later form UCXBs in our simulations. The dashed line indicates a2/a1 = 1.
Paper: An AI Superresolution Field Emulator for Cosmological Hydrodynamics: The Lyα Forest
Authors: Fatemeh Hafezianzadeh, Xiaowen Zhang, Yueying Ni, Rupert A. C. Croft, Tiziana DiMatteo, Mahdi Qezlou, Simeon Bird
Figure caption: Comparison of the one-dimensional flux power spectra from HydroEmu (solid red) and HR-HydroSim (dashed blue) with observational measurements. Green circles indicate data from V. Iršič et al. (2017; XQ-100) at z = 3.0; purple squares represent measurements from M. Walther et al. (2019) at z = 3.0; black circles show data from A. Day et al. (2019) averaged over the redshift range z = 2.6–3.0; and orange triangles correspond to large-scale measurements from DESI (N. G. Karaçaylı et al. 2024) at z = 3.0. The upper panel displays the dimensionless flux power spectrum, kP(k)/π, while the lower panel shows the relative difference between HydroEmu and HR-HydroSim. Shaded regions denote the standard deviation across simulation realizations.
Paper: An AI Superresolution Field Emulator for Cosmological Hydrodynamics: The Lyα Forest
Authors: Fatemeh Hafezianzadeh, Xiaowen Zhang, Yueying Ni, Rupert A. C. Croft, Tiziana DiMatteo, Mahdi Qezlou, Simeon Bird
Figure caption: Comparison between HR-HydroSim outputs and HydroEmu predictions for key physical quantities in the Lyα forest. Each panel shows a two-dimensional hexbin scatter plot of the HydroEmu prediction versus the HR-HydroSim ground truth for: (a) overdensity ﹩\rho /\bar{\rho }﹩, (b) temperature T [K], (c) velocity component Vy [km s−1], (d) optical depth τ, and (e) transmitted flux. The dashed black line indicates one-to-one correspondence. RMSE values are shown in the top-left of each panel. Red contours enclose 90% of the data.
Paper: An AI Superresolution Field Emulator for Cosmological Hydrodynamics: The Lyα Forest
Authors: Fatemeh Hafezianzadeh, Xiaowen Zhang, Yueying Ni, Rupert A. C. Croft, Tiziana DiMatteo, Mahdi Qezlou, Simeon Bird
Figure caption: Scale-dependent flux decoherence, 1 − r2(k), between the high-resolution simulation and each of the emulator (HydroEmu, red) and low-resolution simulation (LR-HydroSim, green). Shaded regions show the standard deviation across four test sets. The vertical dashed line marks the Nyquist frequency kNyq.
Paper: An AI Superresolution Field Emulator for Cosmological Hydrodynamics: The Lyα Forest
Authors: Fatemeh Hafezianzadeh, Xiaowen Zhang, Yueying Ni, Rupert A. C. Croft, Tiziana DiMatteo, Mahdi Qezlou, Simeon Bird
Figure caption: Flux PDF from the HydroEmu(solid red) and HR-HydroSim (dashed navy), compared to observational data from E. Rollinde et al. (2013) and (T.-S. Kim et al. 2007). The bottom panel displays the relative error between HydroEmu and HR-HydroSim results, with shaded bands indicating the standard deviation across sight lines.
Paper: Bright Siren without an Electromagnetic Counterpart Detected by the LISA-Taiji-TianQin Network
Authors: Yejing Zhan, David Izquierdo-Villalba, Xiao Guo, Qing Yang, Daniele Spinoso, Fa-Yin Wang
Figure caption: The merger rate of all population models across varying redshift (left) and binary mass (right). The MBHB population at high redshift (z > 4) is predominated in the LightSeed-Nodelay and HeavySeed-Nodelay models, whereas the IV24 and QY25 models predict a significant MBHB population at low redshifts (z < 4). In the HeavySeed-Delay model, the population is largely uniformly distributed in a redshift range of 1–6. Regarding binary mass, the LightSeed-Nodelay model predicts a prevalence of low-mass MBHBs with total masses below 105M⊙, while the HeavySeed-Delay and HeavySeed-Nodelay models show a dominance of MBHBs with masses in the range of 106–107M⊙. The mass distribution of IV24 is largely uniform in the range of 104–108M⊙. The QY25 model favors high-mass MBHBs with mass over 106M⊙.
Paper: Bright Siren without an Electromagnetic Counterpart Detected by the LISA-Taiji-TianQin Network
Authors: Yejing Zhan, David Izquierdo-Villalba, Xiao Guo, Qing Yang, Daniele Spinoso, Fa-Yin Wang
Figure caption: The GND in different models as the redshift changes. The blue line represents the filter in the mass range of 108–109M⊙, defined by Equation (2), while the orange line represents the filter in the mass range of 109–1014M⊙.
Paper: Continuous Gravitational Waves from Magnetized White Dwarfs: Quantifying the Detection Plausibility by LISA
Authors: Mayusree Das, Banibrata Mukhopadhyay, Tomasz Bulik
Figure caption: Top panel: decay of ν (red solid) and χ (blue dashed) as functions of time for initial ν = 0.05 Hz, χ = 3∘ for a toroidally dominated WD—WD1+BP ( ﹩{B}_{max}^{{\rm{Toroidal}}}=4\times 1{0}^{13}﹩ G, ﹩{B}_{p}^{{\rm{Poloidal}}}=8\times 1{0}^{8}﹩ G) with a magnetosphere. For the same WD, the middle panel shows the variation of luminosities, and the bottom panel shows GW strain decay with time.
Paper: Continuous Gravitational Waves from Magnetized White Dwarfs: Quantifying the Detection Plausibility by LISA
Authors: Mayusree Das, Banibrata Mukhopadhyay, Tomasz Bulik
Figure caption: Density (top panels) and magnetic field (bottom panels) are shown in the color bar for two models: WD1 (M = 1.83 M⊙, toroidal field; left panels); and WD2 (M = 1.42 M⊙, poloidal field; right panels). The isocontour lines are drawn for density, toroidal magnetic field (having magnetic field perpendicular to the plane of the paper) and the poloidal magnetic field lines (with arrow). The detailed properties of those WDs are mentioned in Table 1.
Paper: Continuous Gravitational Waves from Magnetized White Dwarfs: Quantifying the Detection Plausibility by LISA
Authors: Mayusree Das, Banibrata Mukhopadhyay, Tomasz Bulik
Figure caption: A cartoon diagram of a magnetized rotating WD with misalignment between the magnetic field axis and the rotation axis. Here i is the angle between the rotation axis of the source and the detector, and χ is the misalignment between the magnetic and rotation axes.