adsabs/AstroCLIMB huggingface dataset:
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of in-situ characteristics and footpoint estimates for the SASW stream spanning from 2021 April 30 10:00:00 to 2021 May 01 00:00:00 during E8.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of in-situ characteristics and footpoint estimates for the FSW stream spanning from 2020 January 27 04:55:00 to 2020 January 27 05:15:00 during E4.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of in-situ characteristics and footpoint estimates for the FSW stream spanning from 2021 April 27 01:00:00 to 2021 April 27 04:00:00 during E8.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of in-situ characteristics and footpoint estimates for the FSW stream spanning from 2021 April 27 06:00:00 to 2021 April 27 08:30:00 during E8.
Paper: Multifluid Theory of Electrostatic Ion Cyclotron Waves in Partially Ionized Plasmas
Authors: Wenlong Huang, Yu Liu, Pengcheng Yu, Jiuhou Lei
Figure caption: The normalized mode frequency and damping rate as a function of k ρ  s  with ﹩{\hat{\nu }}_{{in}}=0.4﹩ and δ  n  = 0.01 ((a) and (b)), ﹩{\hat{\nu }}_{{in}}=4﹩ and δ  n  = 0.01 ((c) and (d)), and ﹩{\hat{\nu }}_{{in}}=4﹩ and δ  n  = 0.1 ((e) and (f)). In addition, τ = 0 is used here. The red and blue solid curves are numerical results calculated from Equation (40); the red and blue dotted curves represent solutions of Equations (41) and (49), respectively. In panels (a), (c), and (e), the red dashed and dotted–dashed curves are ﹩{\hat{\omega }}_{r}=\sqrt{1+{k}^{2}{\rho }_{s}^{2}}﹩ and ﹩{\hat{\omega }}_{r}=1﹩, whereas the blue curves are ﹩{\hat{\omega }}_{r}={\hat{\omega }}_{{ci}}^{\mathrm{eff}}﹩ and ﹩{\hat{\omega }}_{r}={\hat{\omega }}_{{ci}}^{* }﹩, respectively. Similarly, in panels (b), (d), and (f), the red dashed and dotted–dashed curves satisfy ﹩-\hat{\gamma }=(1+{\delta }_{n}){\hat{\nu }}_{{in}}﹩ and ﹩-\hat{\gamma }={\hat{\nu }}_{{in}}/2﹩, whereas the blue curves satisfy ﹩-\hat{\gamma }={\delta }_{n}{\hat{\nu }}_{{in}}/\left[1+{\left(1+{\delta }_{n}\right)}^{2}{\hat{\nu }}_{{in}}^{2}\right]﹩ and ﹩-\hat{\gamma }={\delta }_{n}{\hat{\nu }}_{{in}}﹩, respectively.
Paper: Multifluid Theory of Electrostatic Ion Cyclotron Waves in Partially Ionized Plasmas
Authors: Wenlong Huang, Yu Liu, Pengcheng Yu, Jiuhou Lei
Figure caption: Dependence of the normalized mode frequency (﹩{\hat{\omega }}_{r}﹩) and damping rate (﹩-\hat{\gamma }﹩) on the ion–neutral collision frequency (﹩{\hat{\nu }}_{{in}}﹩) with δ  n  = 0.01 ((a) and (b)), 0.1 ((c) and (d)), and 0.2 ((e) and (f)). Here, k ρ  s  = 0 is used. In this figure, the red and blue solid curves are numerical results calculated from Equation (29); the red and blue dotted–dashed curves are plotted from Equations (33) and (34); the red and blue dashed curves represent the asymptotic solutions of ﹩{\hat{\omega }}_{h}﹩ and ﹩{\hat{\omega }}_{l}﹩ in the regime where δ  n  ≪ 1; and the red and blue dotted curves are ﹩\hat{\omega }=1-i{\hat{\nu }}_{{in}}﹩ and ﹩\hat{\omega }={\hat{\omega }}_{{ci}}^{* }﹩, respectively.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Validation of our choice of source surface height (R ss) for the three different streams we have discussed in this section. The rows corresponding to the streams from E7, E6, and E10 from top to bottom respectively. The trajectory of Parker at the source surface is shown in blue (negative polarity) and red (positive polarity) based on the measurements from Parker/FIELDS. The heliospheric current sheet from the PFSS model is compared with the trajectory and we show the percentage of correct polarity the model predicted in the legend.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Overview of error on estimated PFSS footpoints due to noise in the velocity measurement used for ballistic propagation. We use three streams of different speeds to show how the effect varies based on v sw. The top row (Panels (a), (b), (c)) shows the overall error on the latitude and longitude of the footpoints. The middle row (Panels (d), (e), (f)) shows the error on the source surface longitude as a function of time. The bottom row (Panels (g)–(i)) shows the error on the footpoints compared with the associated AIA image.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of the error on the estimated footpoints due to changing the source surface height for streams of varying speeds. Panels (a)–(c) show the overall error on the footpoints as a box plot. Panels (d)–(f) show the footpoints associated with different source surface heights on the associated AIA image.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of the effect of the choice of input magnetogram for the lower PFSS boundary condition on the estimated footpoints for streams of varied speeds. Panels (a)–(c) show the overall error on the estimated footpoint for each of the wind streams of interest. Panels (d)–(f) show the footpoints and their error on the associated AIA images.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of in-situ characteristics and footpoint estimates for the FSW stream spanning from 2022 December 15 21:15:00 to 2022 December 15 22:15:00 during E14.
Paper: Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by Parker Solar Probe
Authors: Tamar Ervin, Kai Jaffarove, Samuel T. Badman, Jia Huang, Yeimy J. Rivera, Stuart D. Bale
Figure caption: Comparison of in-situ characteristics and footpoint estimates for the FSW stream spanning from 2021 November 20 05:30:00 to 2021 November 20 10:30:00 during E10.
Paper: Poynting Flux of MHD Modes in Magnetic Solar Vortex Tubes
Authors: Samuel J. Skirvin, Viktor Fedun, Marcel Goossens, Suzana S. A. Silva, Gary Verth
Figure caption: The percentage difference of the maximum value of S  z  for different modes in the presence of a background rotational flow when compared to the static case. Red, black, blue, green, and yellow crosses correspond to modes m = 0, 1, −1, 2, −2, respectively.
Paper: Quiescent Solar Wind Regions in the Near-Sun Environment: Properties and Radial Evolution
Authors: Benjamin Short, David M. Malaspina, Alexandros Chasapis, Jaye L. Verniero
Figure caption: Quiescent region finding algorithm. Panel (a) is the magnetic field radial component in time series for encounter 7 with quiescent times highlighted in orange. Panel (b) is the result for quality flag q rand after one iteration of this identification algorithm. Panel (c) is the result after five iterations of the algorithm. Figure (d) is the result after 300 iterations. The final result for q rand used in this study is taken after 300 iterations. For panel (a), the gray dashed line represents 0 nT. For panels (b)–(d), the gray dashed line represents the 0.5 threshold required for solar wind to be labeled quiescent.
Paper: Quiescent Solar Wind Regions in the Near-Sun Environment: Properties and Radial Evolution
Authors: Benjamin Short, David M. Malaspina, Alexandros Chasapis, Jaye L. Verniero
Figure caption: Bulk flow velocity span across the entire PSP mission inside of 65  R  ⊙ vs. radial distance. Each curve represents a 2D histogram of the solar wind velocity measured by either SPAN or SPC depending on the quality of the data as described in Section 2.3. The top and bottom solid black lines bounding the colored areas represent the first and third quartiles in each radial bin, while the dotted line in the center of each colored area is the median value for the solar wind speed. Quiescent region data are highlighted in orange, while nonquiescent wind is highlighted in blue. The velocity spread for quiescent regions is consistently lower for most altitudes.
Paper: Testing the Accuracy of Spectral Energy Distribution Modeling Techniques Using the NIHAO-SKIRT-Catalog
Authors: Nicholas Faucher, Michael R. Blanton
Figure caption: Distributions of inferred SFR residuals as a function of the true SFRs using UV–IR filters with all SFH parameters free. Face-on orientations are denoted by circles and edge-on orientations by squares, with the colors indicating their axis ratios as shown in Figure 1.
Paper: Testing the Accuracy of Spectral Energy Distribution Modeling Techniques Using the NIHAO-SKIRT-Catalog
Authors: Nicholas Faucher, Michael R. Blanton
Figure caption: Similar to Figure 10 but fit to UV–optical filters.
Paper: Testing the Accuracy of Spectral Energy Distribution Modeling Techniques Using the NIHAO-SKIRT-Catalog
Authors: Nicholas Faucher, Michael R. Blanton
Figure caption: Fit of the edge-on orientation of the galaxy that has −2.66 dex residual in ﹩{\mathrm{log}}_{10}(\mathrm{SFR}\ [{M}_{\odot }/\mathrm{yr}])﹩ using the Cardelli dust attenuation model, and UV–IR bands (see Figure 10 for reference). Error bars that extend to the bottom of the plot represent fluxes that are consistent with zero up to one sigma.
Paper: Testing the Accuracy of Spectral Energy Distribution Modeling Techniques Using the NIHAO-SKIRT-Catalog
Authors: Nicholas Faucher, Michael R. Blanton
Figure caption: Distributions of true (black circles) and inferred face-on (blueish circles) and edge-on (reddish squares) sSFRs as functions of the true and inferred total stellar masses with all SFH parameters free in the fits. The inferred colors indicate their axis ratios as shown in Figure 1. Best-fitting lines for the true values are shown in black, for face-on orientations in blue, and for edge-on orientations in red.
Paper: Testing the Accuracy of Spectral Energy Distribution Modeling Techniques Using the NIHAO-SKIRT-Catalog
Authors: Nicholas Faucher, Michael R. Blanton
Figure caption: Similar to Figure 9 but fit to UV–optical filters.
Paper: Testing the Accuracy of Spectral Energy Distribution Modeling Techniques Using the NIHAO-SKIRT-Catalog
Authors: Nicholas Faucher, Michael R. Blanton
Figure caption: Distributions of inferred mass residual standard deviations as a function of the inferred mass biases (top) and inferred SFR residual standard deviations as a function of the inferred SFR biases (bottom) for face-on (blue) and edge-on (red) orientations of high-mass (>109.5 M ⊙) galaxies.
Paper: Parametric Instability of Alfvén Waves and Wave Packets in Periodic and Open Systems
Authors: Maile Marriott, Anna Tenerani
Figure caption: Dispersion relation for different periodic Alfvén wave trains. The solid blue line shows the curve γ(k)/ω 0 obtained by solving the analytic dispersion relation for a monochromatic, circularly polarized wave (Equation (7)) with amplitude η = 0.8. The black squares show the validation of the linear solver for the monochromatic case. The hollow, colored symbols show the growth rate obtained from the linear solver for a selection of ϵ, η pairs with the arc-polarized phase given by Equation (16) and such that ϵ η = 0.8.
Paper: Parametric Instability of Alfvén Waves and Wave Packets in Periodic and Open Systems
Authors: Maile Marriott, Anna Tenerani
Figure caption: The arc-polarized wave with phase ﹩\phi (X)=\epsilon \sin {k}_{0}X﹩ varies for different values of ϵ and η. Panel (a) shows the parametric curve described by the magnetic field of the Alfvén pump wave: changing ϵ changes the arc length, while changing η changes the radius of the arc and, therefore, also the amplitude. Panel (b) shows the angle of propagation, θ, as calculated by Equation (17), as a function of η for ϵ = 0.1, 0.5, and 1. The angle is positively correlated with η, but inversely correlated with ϵ. We can also see that for small amplitude waves, the effect of ϵ is negligible.
Paper: No Evidence for a Dip in the Binary Black Hole Mass Spectrum
Authors: Christian Adamcewicz, Paul D. Lasky, Eric Thrane, Ilya Mandel
Figure caption: Posterior distributions for gap-related population hyperparameters inferred using GWTC-3 data (blue). The values listed above give the median and 90% credible intervals on these posteriors. The contours on the two-dimensional panels give the 50%, 90%, and 99% credible intervals. The green line shows the posterior for the gap depth A when constraining the gap edges to ﹩{\gamma }_{\mathrm{low}}={10}_{-1}^{+1}{M}_{\odot }﹩ and ﹩{\gamma }_{\mathrm{low}}={15}_{-1}^{+1}{M}_{\odot }﹩. The priors are overplotted in gray. Note that there are restrictions that γ low > μ 1 and γ high < μ 2. These peak locations (μ 1 and μ 2) are well measured.
Paper: No Evidence for a Dip in the Binary Black Hole Mass Spectrum
Authors: Christian Adamcewicz, Paul D. Lasky, Eric Thrane, Ilya Mandel
Figure caption: Posterior distributions for gap-related population hyperparameters inferred from mock catalogs with 250 perfectly measured (zero-uncertainty) events each. Each color shows the results for an individual catalog, while the true values are shown by gray dashed lines. The contours on the two-dimensional panels give 90% credible intervals. The legend gives the natural log one-dimensional Bayes factor and difference in maximum natural log-likelihood comparing the gap and no-gap hypotheses for each mock catalog, as well as the Bayes factor comparing the empty-gap and no-gap scenarios. Note that while the other four catalogs have a small amount of posterior support near A = 0, the purple catalog’s support for A = 0 is vanishingly small, explaining its anomalously high values of ﹩\mathrm{ln}{{ \mathcal B }}_{A}﹩ and ﹩\mathrm{ln}{{ \mathcal B }}_{\mathrm{empty}}﹩. This can be seen in the log-scale depth posterior in Appendix C.
Paper: No Evidence for a Dip in the Binary Black Hole Mass Spectrum
Authors: Christian Adamcewicz, Paul D. Lasky, Eric Thrane, Ilya Mandel
Figure caption: Population predictive distributions for primary mass m 1 (left) and secondary mass m 2 (right) black holes fit to GWTC-3 data. Blue shows the inferred distribution for the standard gap model, while green shows the inferred distribution when the gap’s edge locations are constrained to ﹩{\gamma }_{\mathrm{low}}={10}_{-1}^{+1}{M}_{\odot }﹩ and ﹩{\gamma }_{\mathrm{low}}={15}_{-1}^{+1}{M}_{\odot }﹩. The solid lines show the median distributions, while shaded regions give 90% credible intervals. For comparison, the 90% credible intervals inferred using a model with no gap are shown in gray dashed lines. Note the logarithmic vertical scale.
Paper: No Evidence for a Dip in the Binary Black Hole Mass Spectrum
Authors: Christian Adamcewicz, Paul D. Lasky, Eric Thrane, Ilya Mandel
Figure caption: Posterior distributions for the gap depth inferred with each mock catalog, constraining the gap location to ≈10–15M ⊙. Each color shows the results for an individual catalog. The legend gives the natural log one-dimensional Bayes factor comparing the gap and no-gap hypotheses, as well as the empty-gap and no-gap hypotheses for each mock catalog.
Paper: No Evidence for a Dip in the Binary Black Hole Mass Spectrum
Authors: Christian Adamcewicz, Paul D. Lasky, Eric Thrane, Ilya Mandel
Figure caption: Posterior distributions for gap-related population hyperparameters inferred from mock catalogs with 250 events each. Each color shows the results for an individual catalog, while the true values are shown by gray dashed lines. The contours on the two-dimensional panels give 90% credible intervals. The legend gives the natural log one-dimensional Bayes factor, the natural log Bayes factor between the empty- and no-gap hypotheses, and the difference in the maximum natural log-likelihood comparing the gap and no-gap hypotheses for each mock catalog.
Paper: Digging into the Ultraviolet Luminosity Functions of Galaxies at High Redshifts: Galaxies Evolution, Reionization, and Cosmological Parameters
Authors: Yi-Ying Wang, Lei Lei, Shao-Peng Tang, Guan-Wen Yuan, Yi-Zhong Fan
Figure caption: Posterior distributions of the SFE parameters for the UV LFs presented in Figure 2. The contours are at the 68%, 95%, and 99% credible levels, respectively. The reported values are at the 68% credible level.
Paper: Digging into the Ultraviolet Luminosity Functions of Galaxies at High Redshifts: Galaxies Evolution, Reionization, and Cosmological Parameters
Authors: Yi-Ying Wang, Lei Lei, Shao-Peng Tang, Guan-Wen Yuan, Yi-Zhong Fan
Figure caption: Complete posterior distributions of the SFE parameters and cosmological parameters for Case 1, Case 2, and Case 3. All of the ranges are at the 90% credible level.
Paper: Digging into the Ultraviolet Luminosity Functions of Galaxies at High Redshifts: Galaxies Evolution, Reionization, and Cosmological Parameters
Authors: Yi-Ying Wang, Lei Lei, Shao-Peng Tang, Guan-Wen Yuan, Yi-Zhong Fan
Figure caption: The posterior distribution of ﹩{\dot{M}}_{* }/{\dot{M}}_{{\rm{h}}}﹩. The GALLUMI results use the same HST observations as N. Sabti et al. (2022b). The solid lines indicate the best-fit values, while the colored regions represent the 90% credible intervals, corresponding to the observed magnitude range.
Paper: Scylla. II. The Spatially Resolved Star Formation History of the Large Magellanic Cloud Reveals an Inverted Radial Age Gradient
Authors: Roger E. Cohen, Kristen B. W. McQuinn, Claire E. Murray, Benjamin F. Williams, Yumi Choi, Christina W. Lindberg, Clare Burhenne, Karl D. Gordon, Petia Yanchulova Merica-Jones, Karoline M. Gilbert, Martha L. Boyer, Steven Goldman, Andrew E. Dolphin, O. Grace Telford
Figure caption: Comparison of our global SFHs to recent literature results. For the top two rows, the left column compares CSFHs and the right column compares star formation rate vs. look-back time. In each plot, the three panels represent the three different evolutionary models we assume for our fits. Top row: our results are compared with SMASH results from their LMC North area (T. Ruiz-Lara et al. 2020), including only our fields in the same footprint (see text for details). Middle row: comparison with VMC results from A. Mazzi et al. (2021), normalized to our field distribution over the VMC tiles. Bottom row: comparison of our global combined CSFH with the LMC CSFH from D. R. Weisz et al. (2013).
Paper: Scylla. II. The Spatially Resolved Star Formation History of the Large Magellanic Cloud Reveals an Inverted Radial Age Gradient
Authors: Roger E. Cohen, Kristen B. W. McQuinn, Claire E. Murray, Benjamin F. Williams, Yumi Choi, Christina W. Lindberg, Clare Burhenne, Karl D. Gordon, Petia Yanchulova Merica-Jones, Karoline M. Gilbert, Martha L. Boyer, Steven Goldman, Andrew E. Dolphin, O. Grace Telford
Figure caption: Best-fit AMR from all of our LMC fields combined. Each panel compares our best-fit AMR assuming one of the stellar evolutionary libraries (black lines, with uncertainties shown with gray shading) with literature values. These include LMC field disk and bar AMRs from R. Carrera et al. (2008), shown in red and orange, respectively, and the LMC field AMR based on Washington photometry from A. E. Piatti & D. Geisler (2013), shown in blue. The LMC cluster AMR from G. I. Perren et al. (2017) is overplotted with its uncertainty interval using green lines. Our recovered global LMC AMR is in good agreement with previous measurements, especially given differences in spatial coverage of the LMC.
Paper: Scylla. II. The Spatially Resolved Star Formation History of the Large Magellanic Cloud Reveals an Inverted Radial Age Gradient
Authors: Roger E. Cohen, Kristen B. W. McQuinn, Claire E. Murray, Benjamin F. Williams, Yumi Choi, Christina W. Lindberg, Clare Burhenne, Karl D. Gordon, Petia Yanchulova Merica-Jones, Karoline M. Gilbert, Martha L. Boyer, Steven Goldman, Andrew E. Dolphin, O. Grace Telford
Figure caption: As in the left column of Figure 8, but assuming the isopleth-based LMC center location from R. P. van der Marel & M.-R. L. Cioni (2001). The median age–radius relation from J. T. Povick et al. (2024) is overplotted as a brown curve in the bottom panel.
Paper: Scylla. II. The Spatially Resolved Star Formation History of the Large Magellanic Cloud Reveals an Inverted Radial Age Gradient
Authors: Roger E. Cohen, Kristen B. W. McQuinn, Claire E. Murray, Benjamin F. Williams, Yumi Choi, Christina W. Lindberg, Clare Burhenne, Karl D. Gordon, Petia Yanchulova Merica-Jones, Karoline M. Gilbert, Martha L. Boyer, Steven Goldman, Andrew E. Dolphin, O. Grace Telford
Figure caption: As in Figure 16, but assuming BaSTI18 evolutionary models.
Paper: Scylla. II. The Spatially Resolved Star Formation History of the Large Magellanic Cloud Reveals an Inverted Radial Age Gradient
Authors: Roger E. Cohen, Kristen B. W. McQuinn, Claire E. Murray, Benjamin F. Williams, Yumi Choi, Christina W. Lindberg, Clare Burhenne, Karl D. Gordon, Petia Yanchulova Merica-Jones, Karoline M. Gilbert, Martha L. Boyer, Steven Goldman, Andrew E. Dolphin, O. Grace Telford
Figure caption: As in Figure 15, but assuming the MIST evolutionary models and adopting the isopleth-based center (left column) or the H I kinematic center (right column).
Paper: Impulsively Accelerated Ions as the Source of Ion Acoustic Waves in Solar Wind
Authors: R. E. Ergun, L. G. Strus, D. M. Malaspina, I. H. Cairns, C. A. Cattell
Figure caption: (a) The real parts of ϵ, χ  i , and χ  e  (solid lines) as a function of k for a fixed frequency of 1 kHz with T  e /T  i  = 2. There is no root (ϵ ≠ 0). The plasma conditions are on the plot. The dashed lines show a solution with T  e /T  i  > 4, in which case the ion acoustic root appears (ϵ = 0, marked on plot). (b) A Maxwellian electron distribution is used. (c) The real parts of ϵ, χ  i , and χ  e  (solid lines) as a function of k for a fixed frequency with T  e /T  i  = 3 and a (d) flat-top electron distribution. The root (ϵ = 0) is marked on the plot. (e) The real parts of ϵ, χ  i , and χ  e  (solid lines) as a function of k for a fixed frequency using the plasma conditions in Figure 1. Even though T  e /T  i  = 1.3, a root appears in the real part of the dispersion if the ion distribution (f) has a sufficiently sharp positive slope. (g) The growth rate (color) as a function of frequency and of k. The dispersion relation is a straight line. (h) The growth rate as a function of k.