adsabs/AstroCLIMB huggingface dataset:
Paper: Mind the Kinematics Simulation of Planet–Disk Interactions: Time Evolution and Numerical Resolution
Authors: Kan Chen, Ruobing Dong
Figure caption: Resolution convergence test of synthetic channel maps. For each V ch, the left and right columns present residuals (similar to Figures 8 panel (a-b)) and differences, respectively. Difference channel maps are obtained by subtracting residual channel maps at different resolutions. Residual or difference emission stronger than 3σ = ± 3.0 mJy beam−1 is marked with green contours. The disk rotation direction is marked in the top left panel. The color bar is in a linear scale. See Section 4.3 for discussions.
Paper: Mind the Kinematics Simulation of Planet–Disk Interactions: Time Evolution and Numerical Resolution
Authors: Kan Chen, Ruobing Dong
Figure caption: Azimuthally averaged τ = 1 surface of synthetic CO J = 2–1 emission (blue line) of the simulation with CPH = 20 at 1000 orbits. Dashed lines in magenta, cyan, and yellow represent 1, 2, and 3 scale heights, respectively. The gray dashed–dotted lines mark the inner and outer gap edges. The planet is at r = 100 au.
Paper: Mind the Kinematics Simulation of Planet–Disk Interactions: Time Evolution and Numerical Resolution
Authors: Kan Chen, Ruobing Dong
Figure caption: Similar to Figure 3 but for V  ϕ  − V Kep.
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: Left: comparison of DYNAMO (blue) and PHANGS (gray) σ mol and ΣSFR measurements to the prediction from the gas transport plus feedback model of M. R. Krumholz et al. (2018), where the yellow dashed line is the prediction for high-redshift galaxies and the yellow dotted line is for local spirals. This comparison shows that, for the fiducial parameters assumed by M. R. Krumholz et al. (2018), the transport+feedback models overpredict the DYNAMO and PHANGS velocity dispersions. Right: comparison of DYNAMO and PHANGS measurements to the results of the TIGRESS (solid purple line; E. C. Ostriker & C.-G. Kim 2022) and SILCC (dashed purple line; T.-E. Rathjen et al. 2023) simulations, which incorporate stellar feedback only, and the feedback-only model of M. R. Krumholz et al. (2018) assuming fixed Q and variable ϵ ff (dotted purple line).
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: Global values of velocity dispersion, using the median dispersion from the moment maps, and ΣSFR are compared to several samples for both cold gas tracers (CO and [C II]) on the left and ionized gas on the right. There is a significant correlation between ΣSFR and velocity dispersion, with a systematic offset to higher dispersion when measured with ions. In both panels, the solid line indicates a fit to ΣSFR and σ mol, and the dashed line represents 2.5 × σ mol. CO data from literature sources are taken from PHANGS (z ∼ 0; J. Sun et al. 2023), EDGE (z = 0.005−0.03; R. C. Levy et al. 2018), H. Übler et al. (2019; z ∼ 2), M. Girard et al. (2019; z ∼ 1–1.5), J. Molina et al. (2019; z ∼ 1.5), D. Liu et al. (2023; z ∼ 2), K. Tadaki et al. (2018; z ∼ 4); for [C II] they are taken from F. Lelli et al. (2021; z ∼ 5), F. Rizzo et al. (2021; z ∼ 4−5), R. Herrera-Camus et al. (2022; z ∼ 5.5), T. Tsukui & S. Iguchi (2021), and T. Tsukui et al. (2023; z ∼ 4.4). Ionized gas velocity dispersion measurements are taken from SAMI (z ∼ 0; M. R. Varidel et al. 2020), MASSIV (z ∼ 1–1.5; B. Epinat et al. 2012), and SINS (z ∼ 2; N. M. Förster Schreiber et al. 2011).
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: Beam-smearing-corrected molecular gas velocity dispersions as a function of molecular gas surface density (left) and star formation rate surface density (right), for individual ∼1–2 kpc-scale line-of-sight measurements in seven DYNAMO galaxies. The black squares correspond to the PHANGS–ALMA derived measurements of J. Sun et al. (2020) in 70 nearby galaxies, at a resolution of 1 kpc to match our observations (J. Sun 2024, private communication). Consistent with the PHANGS–ALMA results, velocity dispersions in DYNAMO galaxies increase with Σmol and ΣSFR. In contrast to PHANGS, DYNAMO galaxies populate the regime of high σ mol, Σmol, and ΣSFR of this parameter space. Furthermore, these high values are observed throughout the entire disks of DYNAMO galaxies, not just their central regions.
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: The same as the left panel of Figure 7; however, we now only include DYNAMO measurements at larger radii where the rotation curves are flat and the β = 0 assumption is valid. The range of t orb for the DYNAMO points in this case is ∼100–300 Myr. The black dashed (dotted) lines are the models of M. R. Krumholz et al. (2018) for the high-z (local spiral) case, assuming t orb = 300, 200, and 100 Myr (from left to right). Because DYNAMO galaxies are most similar to z ∼ 1 galaxies, we expect them to lie between the dotted and dashed model lines for this range of t orb. However, we find that while the shape of the transport+feedback models qualitatively matches DYNAMO, the observed velocity dispersions are still overpredicted.
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: The molecular gas mass surface density as a function of stellar mass surface density. The blue data points correspond to DYNAMO ∼1–2 kpc line-of-sight measurements, assuming a variable α CO conversion factor as described by Equation (4). For comparison, we include the PHANGS CO(2−1) ∼1 kpc line-of-sight measurements as black data points, and best-fit lines from local galaxy samples in EDGE–CALIFA (yellow dashed line; J. K. Barrera-Ballesteros et al. 2020; S. F. Sánchez et al. 2021) and ALMaQUEST (yellow dashed–dotted line; S. L. Ellison et al. 2021a). We also perform an ODR fit to the DYNAMO measurements (solid purple line), which shows that DYNAMO galaxies are fitted by a shallower slope and larger normalization. DYNAMO galaxies are fundamentally more gas-rich than local spirals at all disk positions.
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: The kiloparsec-scale resolved Kennicutt–Schmidt relation for DYNAMO galaxies with Σmol measured assuming a constant α CO (left panel) and a varying α CO (right panel). We include the ∼1 kpc-scale measurements of J. Sun et al. (2020) for PHANGS galaxies, using CO(2−1) maps and SFRs derived from Hα + 24 μm, as black squares. The solid yellow line shown in both panels is the best-fit line (determined using orthogonal linear regression) to the DYNAMO measurements. The dashed yellow line is the best-fit relation to the DYNAMO and PHANGS data combined. The dotted purple lines indicate constant molecular gas depletion times of 0.1, 1, and 10 Gyr (from top left to bottom right).
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: Gas fraction (f gas) as a function of orbital frequency (Ω = R/V). The green shaded region of this parameter space is where superbubbles created by clustered supernovae are expected to reach the scale height of the disk and break out to produce outflows before the final supernova goes off (“powered breakout”; M. E. Orr et al. 2022a, 2022b). The pink shaded region is where the superbubble expansion stalls within the disk before reaching the disk scale height and before the final supernova is produced (“powered stall”). DYNAMO line-of-sight measurements (colored circles) are shaded according to the distance of the region from the galaxy center. We find that ∼38% of our DYNAMO measurements lie in the region where outflows and/or fountains are expected to occur.
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: Observed and modeled velocity field and velocity dispersion maps of DYNAMO G04-1. Left: the observed velocity field (top) and velocity dispersion (bottom). Middle: the modeled velocity field (top) and velocity dispersion (bottom), derived from a model data cube. Right: the velocity field residuals we obtain by subtracting the model velocity field from the observations (top), and the corrected velocity dispersion map obtained by subtracting in quadrature the model velocity dispersion from our measured velocity dispersion. This simulates the effect of beam smearing and corrects for it.
Paper: Disk Turbulence and Star Formation Regulation in High-z Main-sequence Analog Galaxies
Authors: Laura Lenkić, Deanne B. Fisher, Alberto D. Bolatto, Peter J. Teuben, Rebecca C. Levy, Jiayi Sun, Rodrigo Herrera-Camus, Karl Glazebrook, Danail Obreschkow, Roberto Abraham
Figure caption: Beam-smearing-corrected molecular gas velocity dispersion as a function of the gas depletion time (t dep), measured along individual ∼1–2 kpc-sized lines of sight and assuming a variable α CO. Compared to PHANGS, DYNAMO disks have overall shorter depletion times. As we would expect, the shorter depletion times are at smaller galactocentric radii, where the velocity dispersions are greater. The yellow dashed line represents the best fit to the DYNAMO+PHANGS measurements.
Paper: Quasi-linear Analysis of Proton-cyclotron Instability
Authors: Peter H. Yoon, Rodrigo A. López, Jungjoon Seough, Muhammad Rashid, Chadi S. Salem, Muhammad Sarfraz, Marian Lazar, Shaaban M. Shaaban
Figure caption: The plot of model dispersion relation z  r  = ∣q∣/(1 + ∣q∣/2) over both positive and negative ranges of q, as well as two sets of lines, 1 + qu and 1 − qu, for various values of u. The values for u corresponding to 0.1, 0.3, and 1 are roughly the parallel thermal speeds for the protons corresponding to cases 1, 2, and 3, respectively. Likewise, u = 0.4, 1.24, and 5 depict the same for cases 4, 5, and 6, respectively. We chose to plot the two groups of cases by way of differentiating the signs of 1 ± qu to prevent cluttering. The intersection points define the resonant wavenumber, q  r .
Paper: Quasi-linear Analysis of Proton-cyclotron Instability
Authors: Peter H. Yoon, Rodrigo A. López, Jungjoon Seough, Muhammad Rashid, Chadi S. Salem, Muhammad Sarfraz, Marian Lazar, Shaaban M. Shaaban
Figure caption: The plot of wave energy density ﹩\delta {B}^{2}/{B}_{0}^{2}=\int {dk}\,\delta {B}^{2}(k)/{B}_{0}^{2}﹩ ((a)–(c)) and β ⊥ and β ∥ ((d)–(f)) for cases 1–3, vs. normalized time Ω p  t. The same is plotted for cases 4–6, which are shown in panels (g)–(l). Blue curves represent solutions obtained from the parallel kinetic Equation (18), while light blue curves denote the same wave intensity computed from the velocity moment-based Equation (12).
Paper: Quasi-linear Analysis of Proton-cyclotron Instability
Authors: Peter H. Yoon, Rodrigo A. López, Jungjoon Seough, Muhammad Rashid, Chadi S. Salem, Muhammad Sarfraz, Marian Lazar, Shaaban M. Shaaban
Figure caption: The contour plots of the initial bi-Maxwellian distributions (dotted contours) and of the final distributions (solid contours) for six cases. Parts of the resonance contours defined by Equation (21) are also plotted as red curves. The resonance curves were constructed on the basis of v  ϕ  = ω  r /k corresponding to the maximum wave growth for each case, namely, v  ϕ  = ±0.69V A (case 1), ±0.74V A (case 2), ±0.82V A (case 3), ±0.75V A (case 4), ±0.83V A (case 5), and ±0.87V A (case 6). The final states of the proton velocity distribution function can clearly be identified as representing the “plateau” distribution in pitch-angle space, ∂f  p /∂μ ∼ 0, where μ is the cosine of the pitch angle defined in the wave frame. We have indicated the contour level for the final VDF in case 1, to aid the visualization and for a sense of reference, but omitted the contour levels in all other cases to avoid clutter.
Paper: Quasi-linear Analysis of Proton-cyclotron Instability
Authors: Peter H. Yoon, Rodrigo A. López, Jungjoon Seough, Muhammad Rashid, Chadi S. Salem, Muhammad Sarfraz, Marian Lazar, Shaaban M. Shaaban
Figure caption: Comparison of maximum growth rate computed from the exact dispersion relation of Equation (3) (solid contours) vs. approximated maximum growth rate, Equation (9), computed from the approximate analytic dispersion relation of Equation (10) (dashed contours). Six cases to be considered in the present analysis are indicated by dots. The contours are plotted against the backdrop of the two-dimensional solar wind proton data distribution.
Paper: Quasi-linear Analysis of Proton-cyclotron Instability
Authors: Peter H. Yoon, Rodrigo A. López, Jungjoon Seough, Muhammad Rashid, Chadi S. Salem, Muhammad Sarfraz, Marian Lazar, Shaaban M. Shaaban
Figure caption: Comparison of the exact dispersion relation, Equation (1) (solid curves), with the approximate dispersion computed from the combination of Equations (8) and (9), plus the adjustment factor f for each case (dashed curves). The top panel plots the real frequency and growth rate for cases 1–3, while the bottom panel shows the same for cases 4–6.
Paper: Quasi-linear Analysis of Proton-cyclotron Instability
Authors: Peter H. Yoon, Rodrigo A. López, Jungjoon Seough, Muhammad Rashid, Chadi S. Salem, Muhammad Sarfraz, Marian Lazar, Shaaban M. Shaaban
Figure caption: Comparison of hybrid, PIC, and quasi-linear results. The plot layout is analogous to Figure 4 and is self-explanatory. Note how similar the hybrid and PIC results are. For cases 1–3, we chose the kinetic equation-based quasi-linear theoretical results, as they provide better matches with the simulation results. For cases 4–6, we chose the velocity moment-based quasi-linear theoretical results, which seemed to produce marginally better comparisons (but we should note that we could have used either results).
Paper: Modeling the X-Ray Emission of the Boomerang Nebula and Implication for Its Potential Ultrahigh-energy Gamma-Ray Emission
Authors: Xiao-Bin Chen, Xuan-Han Liang, Ruo-Yu Liu, Xiang-Yu Wang
Figure caption: The corner plot of the MCMC fitting for the diffusion-dominated scenario.
Paper: Assessing Core-powered Mass Loss in the Context of Early Boil-off: Minimal Long-lived Mass Loss for the Sub-Neptune Population
Authors: Yao Tang, Jonathan J. Fortney, Ruth Murray-Clay
Figure caption: We evaluate the importance of advective cooling by getting rid of the initial entropy effect from the setup in Figure B1. We start both planets with the same initial entropy (bottom left), which gives different initial radii (middle left) with the 30% model larger, the same as the sonic point radius. In the top-right panel, we find that advective cooling generates an enhancement by another factor of 2, compared to the initial entropy effect, demonstrating that both effects are equally important with such an extreme initial radius. However, we argue that the advective cooling effect is typically minor if planets are born smaller, only 10%–20% of the sonic point radius R  s  with the self-consistent initial conditions. The same physical quantities are plotted in each panel, as in Figure 9.
Paper: Characterizing the Nanohertz Gravitational Wave Background Using a t-process Power Spectral Density
Authors: Shashwat C. Sardesai, Joseph Simon, Sarah J. Vigeland
Figure caption: Combined posterior plot for all 50 simulations of ﹩{\rm{log}}\,{A}_{{\rm{gw}}}﹩, γ gw, and ﹩\mathrm{log}{\alpha }_{1}﹩ for the power-law recovery (blue) and t-process recovery (green). We see that the standard power law recovers the injected amplitude and spectral index value very accurately. The t-process is also able to recover the injected values but underestimates the amplitude and overestimates the spectral index. We also see that ﹩\mathrm{log}{\alpha }_{1}﹩ is centered at 0, implying there is no deviation from a power-law PSD at that frequency. The other α  i  values not shown have similar distributions, with increasing variance as we go to higher frequencies.
Paper: Assessing Core-powered Mass Loss in the Context of Early Boil-off: Minimal Long-lived Mass Loss for the Sub-Neptune Population
Authors: Yao Tang, Jonathan J. Fortney, Ruth Murray-Clay
Figure caption: We examine the importance of the initial entropy effect in affecting the final mass fraction at the end of boil-off by switching off advective cooling from the setup in Figure B1, with other conditions the same. This eliminates the advective cooling effect. In the top-right panel, we find that the initial entropy effect accounts for a factor of 2 difference, implying that it is another important physical effect, in addition to advective cooling, in explaining the different final mass fractions found in J. E. Owen & Y. Wu (2016). The same physical quantities are plotted in each panel, as in Figure 9.
Paper: Characterizing the Nanohertz Gravitational Wave Background Using a t-process Power Spectral Density
Authors: Shashwat C. Sardesai, Joseph Simon, Sarah J. Vigeland
Figure caption: Reconstructed GWB PSD for power-law simulations using a t-process model (blue), free spectral model (red), and power-law model (green). The violins and shaded region show the 90% confidence interval. The injected PSD is shown as the black dashed line. The standard power law recovers the injected PSD the best, although all three models recover the injected PSD accurately at low frequencies.
Paper: Characterizing the Nanohertz Gravitational Wave Background Using a t-process Power Spectral Density
Authors: Shashwat C. Sardesai, Joseph Simon, Sarah J. Vigeland
Figure caption: The recovered log-PSD values (top) and the distribution of Hellinger distances (bottom) comparing the 3f bump simulations in blue to the pure power-law simulations (null hypothesis) in red of all 50 simulations. The black curve indicates the convolution of the ﹩{\rm{log}}\,{A}_{{\rm{gw}}}﹩, γ gw posteriors and the inverse gamma prior. The posterior is overestimated from the injected value but still presents a clear distinction from the prior, implying that the α 3 parameter is adjusted for the excess noise at 5.93 nHz. The null distribution has a 90% confidence interval between 0.114 and 0.184, while the excess noise simulations have a 90% confidence interval between 0.182 and 0.201 at 5.93 nHz.
Paper: Characterizing the Nanohertz Gravitational Wave Background Using a t-process Power Spectral Density
Authors: Shashwat C. Sardesai, Joseph Simon, Sarah J. Vigeland
Figure caption: Reconstructed GWB PSD for excess power simulation using a t-process model (blue), free spectral model (red), and power-law model (green). The violins and shaded region show the 90% confidence interval. The injected is shown in the black dashed line. For these simulations, the PSD follows a power-law PSD with excess power at 5.93 nHz. The t-process and the free spectral are able to recover the bump as well as the rest of the injection, whereas the standard power law overestimates the amplitude of the entire PSD.
Paper: Characterizing the Nanohertz Gravitational Wave Background Using a t-process Power Spectral Density
Authors: Shashwat C. Sardesai, Joseph Simon, Sarah J. Vigeland
Figure caption: Corner plot of all 50 simulations of the 3rd frequency bump simulations. The blue contours and histograms are for the t-process, while the green histograms and contours are for the standard power-law recovery. We can clearly see that the standard power-law model is completely skewed toward higher log A values, whereas the t-process captures the injected values, as well as recovers the deviation at 5.93 nHz. We see that since ﹩\mathrm{log}{\alpha }_{3}=1.0﹩, the t-process detects the presence of excess power. The other ﹩\mathrm{log}{\alpha }_{i}﹩ distributions not shown here all peak around 0, and as we increase frequency, the variance increases as well.
Paper: Characterizing the Nanohertz Gravitational Wave Background Using a t-process Power Spectral Density
Authors: Shashwat C. Sardesai, Joseph Simon, Sarah J. Vigeland
Figure caption: The log-PSD values (top) and the distribution of Hellinger distances for the first frequency (1.98 nHz) of the pure power-law injection (bottom) of all 50 simulations. The black curve indicates the convolution of the ﹩{\rm{log}}\,{A}_{{\rm{gw}}}﹩, γ gw posteriors and the inverse gamma prior. We see that the PSD is accurately recovered at the maximum PDF of the convoluted prior, implying that there is no adjustment of the α 1 parameter. This is the null distribution of Hellinger distances (no deviations from the power law), and at 1.98 nHz the 90% confidence interval is between 0.146 and 0.163.
Paper: WTP 19aalnxx: Discovery of a Bright Mid-infrared Transient in the Emerging Class of Low-luminosity Supernovae Revealed by Delayed Circumstellar Interaction
Authors: Charlotte Myers, Kishalay De, Lin Yan, Jacob E. Jencson, Nicholas Earley, Christoffer Fremling, Daichi Hiramatsu, Mansi M. Kasliwal, Ryan M. Lau, Morgan MacLeod, Megan Masterson, Christos Panagiotou, Robert Simcoe, Samaporn Tinyanont
Figure caption: Comparison of the optical and MIR light curves for a sample of SNe, selected to include known SNe exhibiting signs of early or late-time CSM interaction. The comparison sample includes the Type IIb SN 2020jfv (J. Sollerman et al. 2021), the Type Ib SN 2019oys (J. Sollerman et al. 2020), the Type IIn SN 2015da (L. Tartaglia et al. 2020), the Type Ib SN 2019tsf (J. Sollerman et al. 2020), the Type Ic SN 2017dio (H. Kuncarayakti et al. 2018), the Type IIn SN 2014C (S. Tinyanont et al. 2016), the Type Ic-BL SN 2017ens (T. W. Chen et al. 2018), the Type Ic-BL SN 2018ijp (L. Tartaglia et al. 2020) and the Type II SN 2020yzq (J. Zhang et al. 2020). The optical light curves were obtained from the respective publications, and the MIR W2 light curves were obtained from our forced photometry pipeline. While the majority of events exhibit sustained bright MIR emission comparable in flux to the optical peak, a small sample of sources exhibit dramatic MIR brightenings at ≳1 yr after and >1 mag brighter than the optical peak (including WTP 19aalnxx; shown in the gray shaded region).
Paper: Simulation of Thermal Nonequilibrium Cycles in the Solar Wind
Authors: Roger B. Scott, Jeffrey W. Reep, Mark G. Linton, Stephen J. Bradshaw
Figure caption: Additional profiles of plasma number density and temperature (topmost panel), pressure and wind speed (second panel), and rates of heating per particle (lower two panels) for three steady-state solutions with increased footpoint heating rates. The global heating in each case is unchanged from ﹩{{ \mathcal H }}_{g}=2\times {10}^{-6}\,\mathrm{erg}\,{\mathrm{cm}}^{-3}\,{{\rm{s}}}^{-1}﹩. The values of ﹩\alpha \in \{2.0,3.0,3.45\}﹩ correspond to footpoint heating rates of ﹩{{ \mathcal H }}_{b}\in \{4.0,6.0,6.9\}\times {10}^{-4}\,\mathrm{erg}\,{\mathrm{cm}}^{-3}\,{{\rm{s}}}^{-1}﹩.