adsabs/AstroCLIMB huggingface dataset:
Paper: Direct Collapse to Precursors of Supermassive Black Hole Seeds: Radiation-feedback-generated Outflows
Authors: Yang Luo, Isaac Shlosman, Kentaro Nagamine
Figure caption: Sketch of the inflow/outflow simulated in Figure 4: expanding outer shell forming a hot bubble filled with the fast wind and shells formed by injections of the accretion material, enveloped by the ambient accretion flow and accretion disk. The shocked ambient accretion and the fast wind backflow onto the outer shell at t ∼ 3 × 103 yr. The expanding cavity is transformed into the funnel. In Figure 4, the bubble is expanding to the lower side of the accretion disk. Only one hemisphere is shown here.
Paper: Direct Collapse to Precursors of Supermassive Black Hole Seeds: Radiation-feedback-generated Outflows
Authors: Yang Luo, Isaac Shlosman, Kentaro Nagamine
Figure caption: Evolution of the ionization cones in the inflow/outflow within the DM halo hosting a sink particle represented by the SMS or a self-gravitating accretion disk. The outflow is driven by the radiation and thermal feedback. The slice snapshots are shown on the scale of 0.02 pc (top) to 1000 pc (bottom), with the accretion disk situated edge-on in all panels. At t = 0, the outflow does not exist, and the accretion dominates. Note the accretion shock at ∼500 pc that persists for the entire simulation (bottom panels). At t = 0, the outflow does not exist, and the accretion dominates. From t ≳ 600 yr, the snapshots show a biconical ionization structure that is visible up to ∼2 pc. See the main text for more details.
Paper: Direct Collapse to Precursors of Supermassive Black Hole Seeds: Radiation-feedback-generated Outflows
Authors: Yang Luo, Isaac Shlosman, Kentaro Nagamine
Figure caption: Radial profiles of density ρ (top), temperature T (middle), and inflow/outflow velocity v  R  (bottom) along the ray θ = π/4 (left column) and θ = π (right column) coinciding with the disk rotation axis in the lower hemisphere. The times correspond to the snapshots shown in Figure 4. Note that positive velocities represent the outflow and the negative ones represent the inflow.
Paper: Direct Collapse to Precursors of Supermassive Black Hole Seeds: Radiation-feedback-generated Outflows
Authors: Yang Luo, Isaac Shlosman, Kentaro Nagamine
Figure caption: Radial profiles of density (top) and density-weighted temperature (bottom) within the parent DM halo, calculated in spherical shells within the DM halo at t = 0, prior to triggering the radiation feedback, and at subsequent times with active feedback. The sink particle mass is ∼105 M ⊙.
Paper: A Titov–Démoulin Type Eruptive Event Generator for β > 0 Plasmas
Authors: Igor V. Sokolov, Tamas I Gombosi
Figure caption: External field inductance, ﹩{L}_{0}^{(\mathrm{ext})}﹩ (Equation (97), black line), self-inductance, ﹩{L}_{0}^{(\mathrm{int})}﹩ (Equation (101), blue line), and toroidal field inductance, ﹩{L}_{0}^{(\mathrm{tor})}﹩ (Equation (106), brown line), for the n = 0 harmonic. The normalized inductance coefficients are related to μ 0 R ∞ and are presented as functions of the ﹩a/{R}_{0}=2{\kappa }_{0}^{{\prime} }/(1+{\kappa }_{0}^{{{\prime} }^{2}})﹩ ratio. The functions and their arguments are all calculated in terms of the value of ﹩{\kappa }_{0}^{{\prime} }﹩ at the toroidal surface. For comparison, approximate solutions given by Equations (98), (102), and (107) are shown by the dashed lines.
Paper: A Titov–Démoulin Type Eruptive Event Generator for β > 0 Plasmas
Authors: Igor V. Sokolov, Tamas I Gombosi
Figure caption: Magnetic field lines from the current filament characterized by R ∞ = 0.2R ⊙, ﹩{\kappa }_{0}^{{\prime} }=0.1﹩, B  c  = 1, strapped by the field from a pair of positive and negative magnetic charges. The configuration center is at a depth of d = 0.025R ⊙ below the solar surface; the distance, 2D, between the charges is D = R ∞ for panel (a) and D = 0.7R ∞ for panels (b) and (c). Null points can be seen in panels (a) and (b), which show meridional cross sections of the configuration, similarly to Figures 4 and 5. In the 3D topology, shown in panel (c), the null line is marked with a thick blue line.
Paper: A Titov–Démoulin Type Eruptive Event Generator for β > 0 Plasmas
Authors: Igor V. Sokolov, Tamas I Gombosi
Figure caption: Top left: GONG magnetogram as of 2013 April 11 with intensified weak field. Bottom left: zoomed in AR field with the chosen locations for the current filament footpoints (red and blue asterisks) and the center of configuration (green asterisk). Right panel: the magnetic configuration superposed with realistic magnetic field of the active region adjusted to simulate the CME event of 2013 April 11.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: Top: the light curve of V844 Her over sectors 24 and 25. The average count rate over a 1-day wide moving window has been converted to an approximate magnitude. The outburst ends on BTJD = 1972, but the system continues to fade exponentially until BTJD ≈ 1988. Middle: the time-resolved power spectrum focused on the frequency region that includes the 29-minute signal and the second harmonic of the SH signal. The 29-minute signal shows variability on a 2-day timescale. Data gaps are masked. Bottom: the amplitudes of the 29-minute (solid red line) and 80-minute SH (dashed blue line) oscillations from periodograms of a 1-day wide moving window. These oscillations occur at 49 and 18 days−1, respectively. Gaps in the TESS data have been masked. The black-dotted line indicates a 3σ detection threshold for the oscillations. The 29-minute oscillation is well detected out to BTJD ≈ 1991.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: An analysis of the TPF showing the location V844 Her and the location of the oscillations. Top-left: the average TPF over the first 9 days of the outburst. Top-right: the difference between the brightest 9 days and the average of the final 10 days of sector 24. As the outburst had faded significantly, the residuals isolate the light distribution of V844 Her during sector 24. Lower-left: the strength of the SH signal as measured by the S/N ratio of the periodogram peak. As expected, the strongest signal coincides with the light distribution of V844 Her. Lower-right: shows the strength of the 29-minute signal in the TPF images. The position of the highest S/N ratio of the 29-minute oscillation matches the location of V844 Her and the SH signal strength.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: Left: periodogram of the TESS data during the outburst (BTJD <1969) zoomed in on the 29-minute peak (top). The primary signal is concentrated in an unresolved peak at 29.34 minutes (49.085 days−1). A weak, resolved peak is also present at 29.57 minutes (48.7 days−1). A periodogram of a simulated light curve is shown at the bottom. The observed beat signal is approximated by adding cosines with frequencies of 48.65 and 48.75 days−1 (corresponding to periods of 29.60 and 29.54 minutes) to a cosine with a frequency of 49.085 days−1. Right: the time-resolved periodogram of the TESS data (top) during outburst and the simulated light curve (bottom). The simulated light curve shows a modulation similar to that seen in the observations.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: The L-S periodogram of the three nights of V844 Her photometry from the AAVSO database. The faint red line shows the dirty periodogram resulting from daily gaps in the sampling window. The heavy blue line represents the clean spectrum clearly showing the fundamental SH signal and its harmonics. The 29-minute periodicity is recovered in the cleaned spectrum, and its amplitude relative to the SH harmonics is similar to what was seen in the TESS sector 24 data.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: Top: the periodogram of four nights of MDM photometry obtained during quiescence. The dirty spectrum is shown in light red and the cleaned spectrum in dark blue. No excess power is detected at 29 minutes. A peak at 79 minutes likely corresponds to the orbital period of the binary. Bottom: a high-frequency extension of the periodogram without cleaning does not show evidence of super-Nyquist frequencies at 671 or 769 days−1 (1.87 to 2.15 minutes). Both plots suggest the presence of QPOs corresponding to periodicities between 10 and 15 minutes.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: Top: a portion of the TESS light curve of V844 Her during sector 24. The super-outburst is seen fading from a maximum at the start of the observations. The development of classical SH oscillations (Kato 2022) is seen. Bottom: the time-resolved power spectrum is displayed over sector 24. The amplitude of the SH oscillations decays with the fading of the super-outburst. The strength of the 29-minute signal fades over the sector, but more slowly than that of the SHs. By the end of the sector, the 29-minute oscillation is the strongest signal seen. The new signal and the primary SH oscillation are marked on the right side of the figure with their periods of 29 and 80 minutes, respectively.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: The L-S periodogram for V844 Her calculated from the sector 24 TESS light curve. The strong SH signal is seen at 18 days−1 (80 minutes), and its harmonics are detected out to 108 days−1 (13.3 minutes). The strong peak at 49 days−1 (29.34 minutes) has not been identified. A weak signal near 98 days−1 (14.7 minutes) may be a harmonic of the unidentified oscillation.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: The X-ray periodograms of V1025 Cen (top), DW Cnc (middle), and V844 Her (bottom) using 30 s binning. The spectra are normalized to the strength of the signal in V1025 Cen. A clear peak and subsequent harmonics can be seen in the power spectra of the known IPs, but the spectrum of V844 Her shows no distinctive peak at the 29-minute period or possible super-Nyquist frequencies.
Paper: A Surprising Periodicity Detected during a Super-outburst of V844 Herculis by TESS
Authors: Anousha Greiveldinger, Peter Garnavich, Colin Littlefield, Mark R. Kennedy, Jules P. Halpern, John R. Thorstensen, Paula Szkody, Arto Oksanen, Rebecca S. Boyle
Figure caption: The X-ray spectra of the two known IPs and V844 Her without the bandpass filter applied. The normalized counts s−1 keV−1 for V844 Her have been multiplied by 8 to scale the spectrum to the same height as the other two at 1 keV.
Paper: Beyond Ultra-diffuse Galaxies. I. Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny P. Greco, Song Huang, 崧 黄, Peter Melchior, Rachael Beaton, Kirsten Casey, Shany Danieli, Andy Goulding, Remy Joseph, Erin Kado-Fong, Ji Hoon Kim, Lauren A. MacArthur
Figure caption: Left panel: schematic diagram showing the UDG size cut (gray band), survey limit (blue shade), average mass–size relation (dark green dashed line), and 1.5σ above it (light green line). The solid lines are constant surface brightness cuts at ﹩{\overline{\mu }}_{\mathrm{eff}}(g)=25\ \mathrm{mag}\,{\mathrm{arcsec}}^{-2}﹩ for two different colors g − i = 0.4 (blue) and g − i = 0.8 (red). The constant surface stellar mass density line is in purple, which is parallel to the solid lines. The dotted part of the green lines indicates where we linearly extrapolate the mass–size relation to define UPGs. Right panel: The distributions of UDGs and UPGs on the mass–size plane. UDGs that are also classified as UPGs are shown as orange squares, while UDGs that do not satisfy the UPG definition are marked as red stars. Conversely, blue triangles are UPGs that are not classified as UDGs. The UDG sample includes a significant number of galaxies that are not mass–size outliers (falling below the 1.5σ line), which are red in color because the surface brightness cuts are different on the mass–size plane for blue and red galaxies.
Paper: Beyond Ultra-diffuse Galaxies. I. Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny P. Greco, Song Huang, 崧 黄, Peter Melchior, Rachael Beaton, Kirsten Casey, Shany Danieli, Andy Goulding, Remy Joseph, Erin Kado-Fong, Ji Hoon Kim, Lauren A. MacArthur
Figure caption: Completeness of our LSBG search as a function of the effective radius r  e  and the average surface brightness ﹩{\overline{\mu }}_{\mathrm{eff}}(g)﹩. The overall completeness (right panel) comprises the detection completeness (left panel) and deblending completeness (middle panel). The dashed lines in the right panel highlight the 70%, 50%, and 20% completeness contours. The completeness drops as we go to fainter surface brightness and smaller size. For the size range of 3″ < r  e  < 14″, we are >70% complete to ﹩{\overline{\mu }}_{\mathrm{eff}}(g)\lt 26.5\ \mathrm{mag}\,{\mathrm{arcsec}}^{-2}﹩ and >50% complete to ﹩{\overline{\mu }}_{\mathrm{eff}}(g)\leqslant 27.0\ \mathrm{mag}\,{\mathrm{arcsec}}^{-2}﹩.
Paper: Beyond Ultra-diffuse Galaxies. I. Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny P. Greco, Song Huang, 崧 黄, Peter Melchior, Rachael Beaton, Kirsten Casey, Shany Danieli, Andy Goulding, Remy Joseph, Erin Kado-Fong, Ji Hoon Kim, Lauren A. MacArthur
Figure caption: Measurement bias (defined as “truth minusmeasurement”) and uncertainty as a function of the measured angular size r  e  and surface brightness ﹩{\overline{\mu }}_{\mathrm{eff}}(g)﹩. The colors show the bias term while the dashed contours show the constant uncertainty lines. We derive the bias in the total magnitudes from the combined bias in r  e , ﹩{\overline{\mu }}_{\mathrm{eff}}(g)﹩, and color. We find that the bias and uncertainty in our measurement increase toward the fainter end. We apply the bias correction to the real LSBGs before studying their physical properties.
Paper: Beyond Ultra-diffuse Galaxies. I. Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny P. Greco, Song Huang, 崧 黄, Peter Melchior, Rachael Beaton, Kirsten Casey, Shany Danieli, Andy Goulding, Remy Joseph, Erin Kado-Fong, Ji Hoon Kim, Lauren A. MacArthur
Figure caption: Demonstration of the deblending step described in Section 3.2 and Appendix B. Here we show two objects from our initial sample: the one shown in the top panels is a blue LSBG, whereas the one shown in the bottom is a false positive, which is a blend between a high-z galaxy and galaxy outskirts. The first columns show the griz color-composite images with the bounding boxes overlaid. The objects covered by the gray shades are masked during fitting. The remaining columns show the initial model, the optimized model (PSF convolved), the residual image, and the optimized model of the target galaxy only. The red dashed circle in the rightmost column denotes the measured half-light radius.
Paper: Beyond Ultra-diffuse Galaxies. I. Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny P. Greco, Song Huang, 崧 黄, Peter Melchior, Rachael Beaton, Kirsten Casey, Shany Danieli, Andy Goulding, Remy Joseph, Erin Kado-Fong, Ji Hoon Kim, Lauren A. MacArthur
Figure caption: Distribution of UDGs (left) and UPGs (right) on the size–surface brightness plane. The UPGs are defined to be galaxies that are 1.5σ above the average mass–size relation in Carlsten et al. (2021). The samples are split into two color bins and shown in red (g − i > 0.8) and blue (g − i < 0.8). The marginal histograms are not normalized to highlight the relative number of red and blue galaxies. Compared with the UDG sample, the UPG sample includes blue galaxies with surface brightness higher than the UDG cut (﹩{\overline{\mu }}_{\mathrm{eff}}(g)\lt 25\ \mathrm{mag}\,{\mathrm{arcsec}}^{-2}﹩) and excludes red galaxies at ﹩25\lt {\overline{\mu }}_{\mathrm{eff}}(g)\lt 26\ \mathrm{mag}\,{\mathrm{arcsec}}^{-2}﹩, due to the color–M ⋆/L dependence.
Paper: Flares from Merged Magnetars: Their Prospects as a New Population of Gamma-Ray Counterparts of Binary Neutron Star Mergers
Authors: Shu-Xu Yi, Zhen Zhang, Xilu Wang
Figure caption: Plot of the absorption factor ξ vs. time (τ) for four different energy bands: 45 keV–10 MeV (black); 10–100 keV (blue); 100 keV–1 MeV (green); 1 MeV–10 MeV (red). The solid lines are the absorption results for a 0.01 M ⊙ BNS ejecta with 0.3c expansion velocity and robust main r-process components, the color shades indicate uncertainties due to the variations in the BNS ejecta properties including mass, velocity, and composition; the dashed lines denote boundaries of 1 − ξ for four different energy bands. We include two reference lines: τ = 1 day (vertical) and 1 − ξ = 0.1 (horizontal). These lines represent the fiducial spin-down timescale and the point at which the ejecta transitions from being optically thick to optically thin, respectively.
Paper: Flares from Merged Magnetars: Their Prospects as a New Population of Gamma-Ray Counterparts of Binary Neutron Star Mergers
Authors: Shu-Xu Yi, Zhen Zhang, Xilu Wang
Figure caption: Same plot as the band for GW counterpart in Figure 2, but with absorption considered for energy ranges from 1 MeV to 10 MeV and from 100 keV to 1 MeV. The orange dashed line is the estimated Fermi/GBM detector fluence limit for a 1 s burst; while the vertical shaded region is the estimated fluence limit range for next-generation megaelectronvolt detectors like MeVGRO with ∼1 s exposure time.
Paper: Beyond Ultra-diffuse Galaxies. I. Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny P. Greco, Song Huang, 崧 黄, Peter Melchior, Rachael Beaton, Kirsten Casey, Shany Danieli, Andy Goulding, Remy Joseph, Erin Kado-Fong, Ji Hoon Kim, Lauren A. MacArthur
Figure caption: Distribution of scarlet morphological measurements for the LSBG candidates from our initial sample. The sample after the color–size–surface brightness cuts is shown in the top panels. We further remove false positives (junk; highlighted in red) by selecting their morphological parameters (dashed boxes). Morphology cuts (bottom panels) remove another 82% of junk. In total, 98% of false positives are removed in the deblending step.
Paper: Unusually Powerful Flare Phenomenon of the Water Maser in W51 and the Possibility of Detecting Gravitational Radiation from It
Authors: A. E. Volvach, L. N. Volvach, M. G. Larionov
Figure caption: The spectra of the features near 60 km s−1 for Flare 5 (top panel, (a)) and Flare 0 along with Flare 5 (bottom panel, (b)). Gaussian Flare 0 approximation (bottom panel (b), red line). The amplitude of Flare 5 on panel (b) is limited by the flux-density level of 20 kJy, at which Flare 0 is more clearly visible.
Paper: Unusually Powerful Flare Phenomenon of the Water Maser in W51 and the Possibility of Detecting Gravitational Radiation from It
Authors: A. E. Volvach, L. N. Volvach, M. G. Larionov
Figure caption: Powerful flare phenomenon of the water maser near 60 km s−1. Individual flares are numbered.
Paper: Unusually Powerful Flare Phenomenon of the Water Maser in W51 and the Possibility of Detecting Gravitational Radiation from It
Authors: A. E. Volvach, L. N. Volvach, M. G. Larionov
Figure caption: (a) The dependence between the spectral line width in the power of −2(Δv)−2 km s−1 and the natural logarithm of the flux density ln(S) kJy for Flares 1–5. (b) Powerful flare phenomenon of the water maser near 60 km s−1. Flux densities of Flares 1–9 are plotted at a scale of natural logarithms.
Paper: Unusually Powerful Flare Phenomenon of the Water Maser in W51 and the Possibility of Detecting Gravitational Radiation from It
Authors: A. E. Volvach, L. N. Volvach, M. G. Larionov
Figure caption: Spectra of features near 60 km s−1 for Flare 0 and background flares (before, the bottom panel, and after the flare phenomenon, the top panel).
Paper: Unusually Powerful Flare Phenomenon of the Water Maser in W51 and the Possibility of Detecting Gravitational Radiation from It
Authors: A. E. Volvach, L. N. Volvach, M. G. Larionov
Figure caption: The frequency drift of maxima of Flares 1–9.
Paper: Study of Advective Energy Transport in the Inflow and Outflow of Super-Eddington Accretion Flows
Authors: Cheng-Liang Jiao, 承亮 焦
Figure caption: Self-similar solution for α = 0.1, M = 10M ⊙, and ρ(π/2) = 0.5 g cm−2.5 (for n = 1/2; ρ(π/2) is a coefficient defined in our calculation; see Equation (6)), which corresponds to the density on the equatorial plane ρ eq = 9.2 × 10−6 g cm−3, the mass-inflow rate ﹩{\dot{M}}_{\mathrm{in}}=6800{L}_{\mathrm{Edd}}/{c}^{2}﹩, and the mass-outflow rate ﹩{\dot{M}}_{\mathrm{out}}=853{L}_{\mathrm{Edd}}/{c}^{2}﹩ at r = 1000r S. Note that the normalization factor for velocities, v K, is defined as ﹩\sqrt{{GM}/r}﹩, independent of θ. All these normalized profiles are independent of r.
Paper: Study of Advective Energy Transport in the Inflow and Outflow of Super-Eddington Accretion Flows
Authors: Cheng-Liang Jiao, 承亮 焦
Figure caption: Heating/cooling rates normalized by (GM)3/2 r −n−5/2 in the left panel and the advective factor in the right panel for the solution presented in Figure 1. In the left panel, the solid line represents the heating caused by viscous dissipation, q vis, which is always positive; the dashed line represents the radiative energy transport, q rad; the dotted line represents the advective energy transport in r direction, ﹩{q}_{\mathrm{adv}}^{r};﹩ and the dotted–dashed line represents the advective energy transport in θ direction, ﹩{q}_{\mathrm{adv}}^{\theta }﹩. The values of q rad, ﹩{q}_{\mathrm{adv}}^{r}﹩, and ﹩{q}_{\mathrm{adv}}^{\theta }﹩, can be either positive or negative, while positive values represent energy loss (cooling) and negative values represent energy gain (heating), and the sum of these values should equal q vis in order to maintain energy conservation. In the right panel, the solid line represents the local advective factor, f, while the dashed line represents the cumulative advective factor, f cum. The solid gray line in each panel indicates where the function values equal 0.