adsabs/AstroCLIMB huggingface dataset:
Paper: Probing the Distinct Extinction Law of the Pillars of Creation in M16 with JWST
Authors: Jun Li, 军 李, Bingqiu Chen, 丙秋 陈, Biwei Jiang, 碧沩 姜, Jian Gao, 健 高, Xi Chen, 曦 陈
Figure caption: Color–color diagrams of F200W − F335M vs. F090W − F200W (panel (a)) and F335M − F444W vs. F200W − F335M (panel (b)), generated using color maps. The linear fits are shown with solid red lines, and the 3σ deviation ranges with dashed red lines. Outliers identified by LTS_LINEFIT are marked with gray points. Reddening vectors for A  V  = 10 mag, calculated using the WD01 R  V  = 5.5 extinction law, are superimposed.
Paper: Filter Design for Estimation of Stellar Metallicity: Insights from Experiments with Gaia XP Spectra
Authors: Kai Xiao, Bowen Huang, Yang Huang, Haibo Yuan, Timothy C. Beers, Jifeng Liu, Maosheng Xiang, Xue Lu, Shuai Xu, Lin Yang, Chuanjie Zheng, Zhirui Li, Bowen Zhang, Ruifeng Shi
Figure caption: Upper-left panel: the gray shadowed region (3360 Å–4640 Å) represents the window over which we search to find the optimal design of a metallicity-sensitive filter. The red rectangle shows the region examined for the best design according to the algorithm described in Section 2. Two synthetic spectra are plotted, one with ﹩({T}_{\mathrm{eff}},\mathrm{log}\,g,[\mathrm{Fe}/{\rm{H}}])=(5500\,{\rm{K}},4.5,0.0)﹩ (blue line), and the other with (5500 K, 4.5, −1.5) (green line), taken from Göttingen Spectral Library (Husser et al. 2013), in order to demonstrate the “blanketing effect”. The transmission curves of the SkyMapper v band, SAGES v band, and Pristine Ca HK band are also shown. The dark purple line represents the typical error of Gaia XP spectra taken from Huang et al. (2024; see the green line in their Figure 8). Upper-right panel: metallicity-dependent stellar loci of training-set stars in the plane of ﹩{(m-{G}_{\mathrm{BP}})}_{0}﹩ and ﹩{({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}})}_{0}﹩, color-coded by [Fe/H] as shown in the color bar. Here m represents the synthetic magnitudes from the red rectangle region in the upper-left panel. The black lines represent our best fits for [Fe/H], with values ranging from +0.5 (top) to −2.0 (bottom), in steps of 0.5 dex, as described by Equation (1). The standard deviation of the fitting residuals, marked as ﹩{ \mathcal R }﹩ (in magnitudes), is labeled in the bottom-right corner. Bottom-left panel: variations of the stellar loci ﹩{\rm{\Delta }}{(m-{G}_{\mathrm{BP}})}_{0}﹩, as a function of ﹩{({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}})}_{0}﹩, for different metallicities (as marked by different colors) relative to the locus at [Fe/H] = −0.5. Bottom-right panel: comparison of the metallicity estimated from this work and LAMOST DR10. The standard deviation σ [Fe/H] of the metallicity differences is marked in the top-left corner.
Paper: Filter Design for Estimation of Stellar Metallicity: Insights from Experiments with Gaia XP Spectra
Authors: Kai Xiao, Bowen Huang, Yang Huang, Haibo Yuan, Timothy C. Beers, Jifeng Liu, Maosheng Xiang, Xue Lu, Shuai Xu, Lin Yang, Chuanjie Zheng, Zhirui Li, Bowen Zhang, Ruifeng Shi
Figure caption: Left panel: the metallicity sensitivity ﹩{ \mathcal S }﹩ in the λ c and Δλ plane. The sensitivity is significantly higher in the region with ﹩{\lambda }_{{\rm{c}}}+\tfrac{{\rm{\Delta }}\lambda }{2}\leqslant 4250\,\mathring{\rm A} ﹩, indicated by the black dashed line. The peak sensitivity centers around the wavelength of the Ca II K line (as indicated by the white arrow). A cut at ﹩{\lambda }_{{\rm{c}}}\geqslant 3360+\tfrac{{\rm{\Delta }}\lambda }{2}﹩ (gray dashed line) is adopted, given the blue boundary of the Gaia XP spectra. Middle panel: similar to the left panel, but for the scatter of the fitting residuals ﹩{ \mathcal R }﹩. The smallest scatter (<1%) tends to be in the region with ﹩{\lambda }_{{\rm{c}}}+\tfrac{{\rm{\Delta }}\lambda }{2}\geqslant 4050﹩ Å. Right panel: similar to the left panel, but for the metallicity precision σ [Fe/H]. The shaded regions indicate the areas of poorer (largest) metallicity-precision estimate, while the nonshaded region indicates the better (lowest) metallicity-precision estimate. The yellow star marks the location of the optimal filter design with a central wavelength of 3790 Å and a width of 640 Å. The black, blue, and white stars indicate the locations of the SkyMapper v band, SAGES v band, and Pristine Ca HK band, respectively.
Paper: Filter Design for Estimation of Stellar Metallicity: Insights from Experiments with Gaia XP Spectra
Authors: Kai Xiao, Bowen Huang, Yang Huang, Haibo Yuan, Timothy C. Beers, Jifeng Liu, Maosheng Xiang, Xue Lu, Shuai Xu, Lin Yang, Chuanjie Zheng, Zhirui Li, Bowen Zhang, Ruifeng Shi
Figure caption: Standard deviations (after subtracting the internal error of the LAMOST metallicities) of the difference between the photometric metallicity estimated from the optimal passband in this work (red line), SAGES v band (saffron line), SkyMapper v band (dark blue line), Pristine Ca HK band (gray line), and the LAMOST metallicity estimate, as a function of G-band magnitude. Similar results are shown comparing the literature metallicities from Andrae et al. (2023; purple dashed curve), Martin et al. (2023; gray dashed curve), Zhang et al. (2023; green dashed curve), and Gaia broad bands (B. Huang et al. 2024, in preparation; yellow curve) to the LAMOST metallicity. The black boxes mark the theoretical precision predicted using the method in the Appendix.
Paper: Filter Design for Estimation of Stellar Metallicity: Insights from Experiments with Gaia XP Spectra
Authors: Kai Xiao, Bowen Huang, Yang Huang, Haibo Yuan, Timothy C. Beers, Jifeng Liu, Maosheng Xiang, Xue Lu, Shuai Xu, Lin Yang, Chuanjie Zheng, Zhirui Li, Bowen Zhang, Ruifeng Shi
Figure caption: External validation of the metallicity precision from member stars of the open cluster NGC2682. Left panel: color-absolute magnitude diagram of NGC2682 member stars, color-coded by our photometric-metallicity estimate, as indicated in the top-left color bar. The giant branch stars are excluded by the cut: ﹩{M}_{{\rm{G}}}\geqslant -{({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}}{)}_{0}^{2}+6.5\times ({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}})}_{0}-1.8﹩. Right panel: photometric metallicity estimated using the optimal filter design (blue) and the SkyMapper v band (black line), respectively. The red and green curves are best-fit Gaussians for the metallicity distributions from our work and the SkyMapper v band, respectively. The 1σ values from the fits are labeled in the upper-right corner.
Paper: Filter Design for Estimation of Stellar Metallicity: Insights from Experiments with Gaia XP Spectra
Authors: Kai Xiao, Bowen Huang, Yang Huang, Haibo Yuan, Timothy C. Beers, Jifeng Liu, Maosheng Xiang, Xue Lu, Shuai Xu, Lin Yang, Chuanjie Zheng, Zhirui Li, Bowen Zhang, Ruifeng Shi
Figure caption: Differences between the metallicity estimated from this work using the optimal metallicity-sensitive filter design (i.e., λ c = 3790 Å,  Δλ = 640 Å) and that estimated from LAMOST DR10, as a function of ﹩{({G}_{\mathrm{BP}}-{G}_{\mathrm{RP}})}_{0}﹩ (left), LAMOST [Fe/H] (middle), and E(B − V)SFD (right) for both the training (upper) and testing (lower) samples. The black and green lines in each panel are the median and 1σ values from Gaussian fitting, respectively.
Paper: The Yarkovsky Effect on the Long-term Evolution of Binary Asteroids
Authors: Wen-Han Zhou, 文翰 周, David Vokrouhlický, Masanori Kanamaru, Harrison Agrusa, Petr Pravec, Marco Delbo, Patrick Michel
Figure caption: The principle of the YS effect. A binary system consists of a larger primary and a smaller secondary (satellite). The relative orbit is assumed circular, and the satellite has zero obliquity and a rotation synchronous with the motion about the primary; both periods are much smaller than the period of the binary heliocentric motion, such that during one satellite orbit about the primary, the Sun is assumed fixed and in the orbital plane of the satellite. The color-coded arrows attached to the satellite represent its thermal acceleration due to solar irradiation (see also the side bar); the tilt away from the opposite direction to the Sun is due to the satellite thermal inertia. The specific values were computed using the numerical model and binary parameters from Section 2.3. In the absence of the satellite passage through the primary’s shadow, the thermal acceleration would be constant. The orbit-averaged effect on the satellite distance from the primary would be zero. The essence of the YS effect is due to the satellite crossing the primary’s shadow. The interrupted solar irradiation results in the satellite cooling such that the thermal acceleration drops and tilts. Upon leaving the shadow, the satellite heats, slowly regaining the thermal state at the subsolar configuration. The net budget of the transverse component of the thermal acceleration may be nonzero, depending on the satellite rotation rate and obliquity, resulting in a secular change of its distance from the primary.
Paper: The Yarkovsky Effect on the Long-term Evolution of Binary Asteroids
Authors: Wen-Han Zhou, 文翰 周, David Vokrouhlický, Masanori Kanamaru, Harrison Agrusa, Petr Pravec, Marco Delbo, Patrick Michel
Figure caption: The Yarkovsky coefficient, f Y, as a function of m and ε, where m = ω/n is the ratio of the spin frequency to the orbital frequency and ε is the angle between the spin vector and the orbital vector. The sign of f Y is the same as the sign of ﹩{\dot{a}}_{{\rm{Y}}}﹩, and f Y = 0.005 corresponds to ﹩\dot{a}=1.4﹩ cm yr−1 for this system. The direction of the white arrows denotes the evolution direction under the Yarkovsky effect. For small values of ε, the Yarkovsky effect drives m toward 1; otherwise, the satellite is driven away from the primary.
Paper: The Yarkovsky Effect on the Long-term Evolution of Binary Asteroids
Authors: Wen-Han Zhou, 文翰 周, David Vokrouhlický, Masanori Kanamaru, Harrison Agrusa, Petr Pravec, Marco Delbo, Patrick Michel
Figure caption: The YS coefficient f YS as a function of the ratio of the spin velocity to the mean motion, ω/n. The blue dots show the numerical results of the zero-obliquity case compared with the analytical solution (orange). The secondary x-axis and y-axis indicate the corresponding rotation period and semimajor axis drift for the given binary system.
Paper: Improving Photometric Redshift Estimates with Training Sample Augmentation
Authors: Irene Moskowitz, Eric Gawiser, John Franklin Crenshaw, Brett H. Andrews, Alex I. Malz, Samuel Schmidt
Figure caption: The best-case photo-z estimation for single-, double-, and triple-feature augmentation (bottom row), with the corresponding augmented training samples (top row). Left: when only a single feature is used for augmentation, redshift augmentation produces the best photo-z estimates. The training sample was augmented with the unshifted Buzzard catalog, which in this case produced better photo-z statistics than the magnitude-shifted or flowed Buzzard catalog. Center: when a double-feature combination is used for selecting galaxies for augmentation, the combination of color+redshift produces the best results. The best results for this case came from using the magnitude-shifted Buzzard catalog. Right: the best photo-z estimates were produced when all three features are combined for selected galaxies for augmentation. The best results for this case came from using the magnitude-shifted Buzzard catalog.
Paper: Improving Photometric Redshift Estimates with Training Sample Augmentation
Authors: Irene Moskowitz, Eric Gawiser, John Franklin Crenshaw, Brett H. Andrews, Alex I. Malz, Samuel Schmidt
Figure caption: The results of partitioning our DC2 catalog into training (left) and application (center) samples. The training sample is redder and brighter than the bulk of the application sample. The right panel shows the Buzzard sample used for augmenting the training sample. The horizontal dotted line shows the i-band selection criterion, while the vertical dotted line shows the (g-z) color criterion. The dashed line indicates the section criterion for color+magnitude augmentation, which generally matches the shape of the DC2 training sample in the left panel. Open arrows indicate which regions of color–magnitude space are used for single-feature augmentation, while solid arrows indicate regions used for color+magnitude augmentation See Section 3.3 for more details on augmentation criteria.
Paper: Improving Photometric Redshift Estimates with Training Sample Augmentation
Authors: Irene Moskowitz, Eric Gawiser, John Franklin Crenshaw, Brett H. Andrews, Alex I. Malz, Samuel Schmidt
Figure caption: Normalized redshift distributions of the DC2 training sample (blue solid line), DC2 application sample (orange dashed line), and Buzzard sample (green dotted line). The DC2 training sample is biased to lower redshifts than the application sample. The vertical dashed line indicates the selection criterion for redshift augmentation, with the arrow indicating the region of redshift space used for augmentation. The black dotted–dashed line shows the redshift distribution of the best-performing, postaugmentation training sample shown in the top right panel of Figure 4.
Paper: Improving Photometric Redshift Estimates with Training Sample Augmentation
Authors: Irene Moskowitz, Eric Gawiser, John Franklin Crenshaw, Brett H. Andrews, Alex I. Malz, Samuel Schmidt
Figure caption: Top: photo-z's estimated from the realistic, nonrepresentative DC2 training sample shown in Figure 1. Solid black lines indicate the boundary for outliers. Bottom: photo-z's estimated from a fully representative training sample drawn randomly from the DC2 application sample in Figure 1.
Paper: A Millisecond Pulsar Binary Embedded in a Galactic Center Radio Filament
Authors: Marcus E. Lower, Shi Dai, Simon Johnston, Ewan D. Barr
Figure caption: A 1.28 GHz radio image of the region around the major kink in the Snake (Heywood et al. 2022). The ∼5′ diameter beam of Murriyang at 4 GHz is shown by the large blue circle centered on G359.13142−0.20005. The red circle is centered on the MeerKAT S-band localization of PSR J1744−2946.
Paper: A Millisecond Pulsar Binary Embedded in a Galactic Center Radio Filament
Authors: Marcus E. Lower, Shi Dai, Simon Johnston, Ewan D. Barr
Figure caption: The top panel shows the pulsar timing residuals of PSR J1744−2946 as a function of the orbital phase after applying the timing model in Table 1. The bottom panel assumes a binary semimajor axis of zero to demonstrate the influence of the companion object.
Paper: Discovering the Mass-Scaled Damping Timescale from Microquasars to Blazars
Authors: Haoyang Zhang, Shenbang Yang, Benzhong Dai
Figure caption: The mass-scaled damping timescale of our sample. The red and pink data points indicate the blazars and microquasars, respectively. The orange solid line and shaded region represent the best fit and 1σ confidence interval for all jetted systems, respectively. The blue dashed–dotted line shows a linear fit to the blazar data. The gray data points, star points, and dashed line represent the data and the fitted results for nonjetted systems from Burke et al. (2021).
Paper: Discovering the Mass-Scaled Damping Timescale from Microquasars to Blazars
Authors: Haoyang Zhang, Shenbang Yang, Benzhong Dai
Figure caption: Characteristic timescales as a function of the model timescales. The black solid line and the orange shaded region indicate the dynamic and thermal timescales at the UV-emitting radius of the accretion disk, respectively. The upper and lower edges of the orange shaded region correspond to a viscosity parameter of 0.01 to 0.1, respectively. The red data points and pink triangles represent blazars and microquasars, respectively.
Paper: A Millisecond Pulsar Binary Embedded in a Galactic Center Radio Filament
Authors: Marcus E. Lower, Shi Dai, Simon Johnston, Ewan D. Barr
Figure caption: Flux density of PSR J1744−4429 as a function of observing frequency. Overplotted in black is our best-fit spectral model and 68% confidence interval (gray shading).
Paper: A Millisecond Pulsar Binary Embedded in a Galactic Center Radio Filament
Authors: Marcus E. Lower, Shi Dai, Simon Johnston, Ewan D. Barr
Figure caption: Linear polarization position angle swing (top), time and frequency averaged polarization profile (middle), and the total intensity spectrum (bottom) of PSR J1744−2946. Note, the average profile in the middle panel excluded data below 1900 MHz.
Paper: Subkiloparsec Scaling Relations between Hot Gas, Dense Gas, and Star Formation Rate in Five Nearby Star-forming Galaxies
Authors: Chunyi Zhang, Junfeng Wang, Qing-Hua Tan, Yu Gao, Shuting Lin, Xiaoyu Xu
Figure caption: Correlations between the diffuse X-ray emission (﹩{L}_{0.5-2\,\mathrm{keV}}^{\mathrm{gas}}﹩) and the dense gas tracers. The colored circles represent the spatially resolved subkiloparsec regions where HCN and HCO+ are detected at S/N ≥ 3. Top panels: ﹩{L}_{0.5-2\,\mathrm{keV}}^{\mathrm{gas}}﹩ as a function of ﹩{L}_{\mathrm{HCN}(4-3)}^{{\prime} }﹩ (left) and ﹩{L}_{{\mathrm{HCO}}^{+}(4-3)}^{{\prime} }﹩ (right), respectively. The solid lines in the panels indicate the best-fit relations derived from the Bayesian method for linear regression (Kelly 2007). Arrows denote the 3σ upper limits and are not included in the fitting. The inset shows the probability density distribution of the slope obtained by the Bayesian fitting. Bottom panels: similar to the top panels, but the luminosities of HCN and HCO+ are normalized by ﹩{L}_{\mathrm{CO}(1-0)}^{{\prime} }﹩, defined as f dense (see Section 3.1). The 3σ upper limits of f dense are not displayed in these panels due to the relatively large scatter of the upper limits. The best-fit slope and the Spearman rank correlation coefficient for the ﹩{L}_{0.5-2\,\mathrm{keV}}^{\mathrm{gas}}﹩− ﹩{L}_{\mathrm{dense}}^{{\prime} }﹩ and the ﹩{L}_{0.5-2\,\mathrm{keV}}^{\mathrm{gas}}﹩−f dense relations are listed in the top left of each panel, but note that the f dense of M82 is ignored for HCN J = 4 → 3 due to its weak HCN emission.
Paper: Subkiloparsec Scaling Relations between Hot Gas, Dense Gas, and Star Formation Rate in Five Nearby Star-forming Galaxies
Authors: Chunyi Zhang, Junfeng Wang, Qing-Hua Tan, Yu Gao, Shuting Lin, Xiaoyu Xu
Figure caption: Top row: the R-band images for NGC 6946 (6450 Å), IC 342 (6450 Å), M82 (6450 Å), NGC 253 (6400 Å), and M83 (6400 Å). Data downloaded from NASA/IPAC Extragalactic Database (NED). The purple box in each panel represents central ∼1.6 kpc region of each galaxy. Middle row: the Chandra broadband (0.5−7 keV) X-ray images of the central ∼1.6 kpc regions (purple box). Bottom row: the JCMT observing positions of the central 50″ × 50″ regions of our sample galaxies overlaid on spitzer MIPS 70 μ m emission on a logarithmic stretch. The 70 μ m images also show the central ∼1.6 kpc regions of our sample galaxies. The white cross in each panel indicates the center of the galaxy. The colored circles denote positions observed in jiggle mode, with 14″ diameters representing the FWHM of JCMT at about 350 GHz. The red circles in each panel indicate positions where HCN and HCO+ are detected at signal-to-noise ratio (S/N) ≥ 3, and the derived properties of these positions are listed in Table 2.
Paper: Subkiloparsec Scaling Relations between Hot Gas, Dense Gas, and Star Formation Rate in Five Nearby Star-forming Galaxies
Authors: Chunyi Zhang, Junfeng Wang, Qing-Hua Tan, Yu Gao, Shuting Lin, Xiaoyu Xu
Figure caption: Correlations between X-ray luminosities and SFRs at the different spatial scales. The colored circles represent the spatially resolved subkiloparsec positions in the central 50″ × 50″ regions of our sample galaxies and the black circles represent the entire galaxies. The solid line indicates the best fit of the ﹩{L}_{0.5-2\,\mathrm{keV}}^{\mathrm{gas}}﹩−SFR relation at the subkiloparsec scale (not including the black circles), with the fitting parameters listed in the top left corner of this plot. The dotted line shows the global linear relation between the intrinsic bolometric luminosity of hot gas and the SFR, as found by Mineo et al. (2012b).
Paper: Damping Obliquities of Hot Jupiter Hosts by Resonance Locking
Authors: J. J. Zanazzi, Janosz Dewberry, Eugene Chiang
Figure caption: Projected stellar obliquities λ (as distinct from deprojected or true 3D obliquities ψ) vs. host star effective temperature T eff of hot Jupiter systems (selecting for planet masses M p ≥ 0.3 M J and semimajor axes a ≤ 10 R ⋆, where R ⋆ is the host star radius; data from Albrecht et al. 2022; Rice et al. 2022a, 2022b; Espinoza-Retamal et al. 2023; Sedaghati et al. 2023; Siegel et al. 2023; Hu et al. 2024). Obliquities are larger for hot high-mass stars (stellar effective temperature T eff > 6100 K; red points) than for cool low-mass stars (blue points). This correlation (Winn et al. 2010) is statistically significant according to a two-sided Kolmogorov–Smirnov test, which yields a p = 1.6 × 10−3 probability that the cumulative obliquity distributions for cool and hot stars are drawn from the same underlying distribution (right panel).
Paper: Damping Obliquities of Hot Jupiter Hosts by Resonance Locking
Authors: J. J. Zanazzi, Janosz Dewberry, Eugene Chiang
Figure caption: Coordinate system used to analyze the coupling between stellar spin and planet orbit. The z-axis is chosen to always point in the direction of the stellar spin ﹩{\hat{{\boldsymbol{j}}}}_{\star }﹩, and the y-axis is chosen to always point normal to ﹩{\hat{{\boldsymbol{j}}}}_{\star }﹩ and ﹩{\hat{{\boldsymbol{j}}}}_{\mathrm{orb}}﹩. The obliquity ψ is the angle between ﹩{\hat{{\boldsymbol{j}}}}_{\star }﹩ and ﹩{\hat{{\boldsymbol{j}}}}_{\mathrm{orb}}﹩. In this Letter, we consider only the components of the tidal torque  T  that act to change ψ, i.e., only the x- and z-components.
Paper: Damping Obliquities of Hot Jupiter Hosts by Resonance Locking
Authors: J. J. Zanazzi, Janosz Dewberry, Eugene Chiang
Figure caption: Projected obliquities vs. eccentricities for hot Jupiters (identical sample to Figure 1). Obliquities and eccentricities are lower for cool stars than for hot stars.
Paper: Damping Obliquities of Hot Jupiter Hosts by Resonance Locking
Authors: J. J. Zanazzi, Janosz Dewberry, Eugene Chiang
Figure caption: Parametric instability assuming the child modes behave as standing waves that do not break. We integrate Equations (B1) using the ﹩{U}_{202}^{2}﹩ component of the gravitational potential of a Jupiter-mass planet on a circular (e = 0), polar (ψ = 90°) orbit of semimajor axis a. The parent stellar g-mode, of oscillation period P  α  = 1.5 days, is computed from GYRE using a 4 Gyr old, solar-mass star of radius R ⋆ modeled with MESA. Equations (B1) are integrated to a time ﹩{t}_{\mathrm{end}}=1.1\times {10}^{10}\ {\omega }_{\alpha }^{-1}﹩, with c  α (0) set by Equation (A16), and c  β (0) = 10−6 c  α (0). Left: energies of the parent mode and one of the twin child modes vs. time for frequency detuning Δ α  = 3.3 × 10−4 ω  α . Parent and child energies evolve to their equilibrium standing-wave energies ﹩{E}_{\alpha }^{\mathrm{thr},\mathrm{sw}}﹩ (Equation (B5)) and ﹩{E}_{\beta }^{\mathrm{sw}}﹩ (Equation (B6)), respectively. Middle: parent and child energies (crosses) at times t > t end/2 vs. forcing frequency. Both parent and child energies are independent of Δ α , in contrast to the Lorentzian resonant response of the parent mode neglecting child modes (﹩{E}_{\alpha }^{\mathrm{lin}}﹩; Equation (B4)). Right: the child mode energy ﹩{E}_{\beta }^{\mathrm{sw}}﹩ exceeds the child breaking energy ﹩{E}_{\beta }^{\mathrm{brk}}﹩ (Equation (B8)) for values of a/R ⋆ relevant to hot Jupiter systems. Breaking of standing child modes might help restore the resonant response of the parent mode; see Figures 14 and 15.