adsabs/AstroCLIMB huggingface dataset:
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: grz-band DECaLS images of the final sample of dwarf galaxies with X-ray AGNs. The positions of the X-ray sources from eRASS1 are shown as magenta crosses, with magenta circles showing the positional uncertainties. The smaller green circles identify the locations of the SDSS spectral fibers (with 1﹩\mathop{.}\limits^{\unicode{x02033}}﹩5 radii) for galaxies with corresponding SDSS spectra.
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: Stellar masses and SFRs of the host galaxies in our final sample of AGNs (black) and the full population of dwarf galaxies in the NSA (gray). One galaxy (ID 7) has an SFR that falls above the typical distribution of SFRs for dwarf galaxies. The remaining AGN hosts have similar SFRs to the general population with a slight bias toward lower SFRs, possibly the result of star formation being suppressed by AGNs.
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: Stellar masses and g − r colors of the host galaxies in our final sample of AGNs (black) and the full population of dwarf galaxies in the NSA (gray). The AGN hosts largely have similar masses and colors to the general population, with notable exceptions being IDs 7 and 18, which have notably redder and bluer g − r colors than the full population, respectively.
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: Ratio of SFRs derived from IR-corrected FUV luminosities (Equation (4)) to those derived from FUV luminosities alone (Equation (8)) for the galaxies in our final sample.
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: Ratio of the IR correction applied to the FUV luminosities (see Equation (5)) relative to the observed FUV luminosities for galaxies in our final sample.
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: The (inverse) concentration indices of the AGN sample compared to all dwarf galaxies in the NSA. The two populations are similar, with no clear difference in concentrations between AGN hosts and the parent dwarf galaxy population.
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: Comparison of stellar masses from the NSA to stellar masses estimated using mass-to-light ratios as a function of g − i color, following S. Zibetti et al. (2009). The red line shows the one-to-one relation.
Paper: A New Sample of Dwarf Galaxies with X-Ray-selected Active Galactic Nucleus Candidates from the eROSITA All-Sky Survey
Authors: John-Michael Eberhard, Amy E. Reines
Figure caption: X-ray luminosity in the 0.2–2.3 keV band vs. redshift for the sources in our AGN sample. The average detection limit of eRASS is shown as a dashed blue line.
Paper: Exploring the Signature of Assembly Bias and Modified Gravity Using Small-scale Clusterings of Galaxies
Authors: Yirong Wang, 艺蓉 王, Zhongxu Zhai, 忠旭 翟, Xiaohu Yang, 小虎 杨, Jeremy L. Tinker
Figure caption: Constraints on γf (upper half of each panel) from unity and Bayesian Evidence (lower half of each panel) for GR and four modified gravity methods with the same cosmological parameter setting at z = 0.55. Five panels correspond to five different HOD models. The error bars denote 1σ distributions. The meaning of cases “TT and TF” with different colors is shown in Table 3. It’s worth noting that the true underlying velocity field is different in these MG models. We isolate an effective true γf value of these MG simulations using the velocity bias as explained in the text. The thick and thin symbols show the raw constraint and velocity bias normalized results, respectively.
Paper: Exploring the Signature of Assembly Bias and Modified Gravity Using Small-scale Clusterings of Galaxies
Authors: Yirong Wang, 艺蓉 王, Zhongxu Zhai, 忠旭 翟, Xiaohu Yang, 小虎 杨, Jeremy L. Tinker
Figure caption: Fractional change of clustering measurement (projected wp for the left panel and monopole ξ0 for the right panel) for galaxy mocks with and without assembly bias effect. Different colors are used for 10 different HOD models, and seven test cosmology models for each HOD model have the same color. The maximum change occurs at ∼10h−1 Mpc for most of the models we have considered. The black dashed and dotted lines are associated with the left and right panels in Figure 1, respectively.
Paper: Exploring the Signature of Assembly Bias and Modified Gravity Using Small-scale Clusterings of Galaxies
Authors: Yirong Wang, 艺蓉 王, Zhongxu Zhai, 忠旭 翟, Xiaohu Yang, 小虎 杨, Jeremy L. Tinker
Figure caption: Average velocity bias measured from the MG simulation compared with the GR result, as a function of halo mass at redshift z = 0.55. Different MG methods are represented by their respective distinct colors. In the calculation of the true value of γf for four MG methods in Figure 5, the average value of the ratio VMG/VGR is taken into account as a multiplicative factor to give an effective γf parameter for these MG models. The error is estimated using a jackknife method by splitting the simulation into 1000 subsamples.
Paper: Exploring the Signature of Assembly Bias and Modified Gravity Using Small-scale Clusterings of Galaxies
Authors: Yirong Wang, 艺蓉 王, Zhongxu Zhai, 忠旭 翟, Xiaohu Yang, 小虎 杨, Jeremy L. Tinker
Figure caption: Two examples of the constraints on Ωm, σ8, and γf for two different HOD models using MG simulations. Different colors in each panel stand for different modified gravity methods, which are listed in Table 1. Here we focus on the deviation of γf from 1, which can approximately characterize the intensity of the modified gravitational effect compared with GR, as well as constraints and degeneracies with other parameters.
Paper: Exploring the Signature of Assembly Bias and Modified Gravity Using Small-scale Clusterings of Galaxies
Authors: Yirong Wang, 艺蓉 王, Zhongxu Zhai, 忠旭 翟, Xiaohu Yang, 小虎 杨, Jeremy L. Tinker
Figure caption: Galaxy clustering results for mocks with and without assembly bias. Two illustrative cases from Figure 1 are represented by thick dashed and dotted lines in two distinct colors. The ensemble of 70 mock (7 cosmologies × 10 HOD models) catalogs is depicted with thin light lines, while black lines denote BOSS dataset measurements for comparison.
Paper: Exploring the Signature of Assembly Bias and Modified Gravity Using Small-scale Clusterings of Galaxies
Authors: Yirong Wang, 艺蓉 王, Zhongxu Zhai, 忠旭 翟, Xiaohu Yang, 小虎 杨, Jeremy L. Tinker
Figure caption: Galaxy clustering results are presented for modified gravity mock catalogs across five HOD models sharing identical cosmological parameters, which correspond to the five panels in Figure 5. GR and four modified gravity methods are distinguished via distinct line styles. For comparison, measurements from the BOSS dataset are overlaid as black lines.
Paper: Exploring the Signature of Assembly Bias and Modified Gravity Using Small-scale Clusterings of Galaxies
Authors: Yirong Wang, 艺蓉 王, Zhongxu Zhai, 忠旭 翟, Xiaohu Yang, 小虎 杨, Jeremy L. Tinker
Figure caption: Constraints on the redshift dependence of w for GR and MG models under identical cosmological parameter settings at redshifts z = 0.25, 0.4,  and 0.55 with assembly bias parameters free. The five panels correspond to five distinct HOD models, consistent with those in Figure 5. The error bars represent 1σ uncertainties.
Paper: Fe Abundances of Early Galaxies at z = 9–12 Derived with Deep JWST Spectra
Authors: Minami Nakane, Masami Ouchi, Kimihiko Nakajima, Yoshiaki Ono, Yuichi Harikane, Yuki Isobe, Ken'ichi Nomoto, Miho N. Ishigaki, Hiroto Yanagisawa, Daichi Kashino, Nozomu Tominaga, Koh Takahashi, Moka Nishigaki, Yui Takeda, Kuria Watanabe
Figure caption: Comparison of the stellar population synthesis model spectra. The three panels show the differences in the spectra with respect to [Fe/H] and the following factors: stellar age (top), dust extinction (middle), and IMF (bottom). Each panel shows the flux ratio relative to the reference model with [Fe/H] = −1.0 dex, t = 10 Myr, E(B − V) = 0.0, and an E. E. Salpeter (1955) IMF (α  =  2.35; upper) and normalized model spectra at 2200 Å (lower). The black lines represent the reference models. The red, blue, orange, green, and purple lines indicate the same models as the black lines but for [Fe/H] = 0.0 dex, t = 100 Myr, E(B − V) = 0.1, an IMF with α  =  2.7, and an IMF with α  =  2.0, respectively. For display purposes, the purple and green lines are shifted by −5 and +5 Å in the x-axis, respectively. The faint lines show the wavelength regions excluded from the spectral fitting to avoid the impacts of nebular emission lines. A change in age does not affect the spectral shape in the same way as a change in [Fe/H] (top). A change in extinction flattens the spectra, which differs totally from a change in [Fe/H] (middle). A change in IMF does not make as large a difference as a change in [Fe/H] (bottom).
Paper: Fe Abundances of Early Galaxies at z = 9–12 Derived with Deep JWST Spectra
Authors: Minami Nakane, Masami Ouchi, Kimihiko Nakajima, Yoshiaki Ono, Yuichi Harikane, Yuki Isobe, Ken'ichi Nomoto, Miho N. Ishigaki, Hiroto Yanagisawa, Daichi Kashino, Nozomu Tominaga, Koh Takahashi, Moka Nishigaki, Yui Takeda, Kuria Watanabe
Figure caption: Top: signal-to-noise ratio in the rest-frame wavelength range of 1300–3800 Å as a function of redshift. The filled red circles represent our sample galaxies with S/N(1300–3800 Å) > 60. The open red circles (diamond) denote the galaxies with S/N(1300–3800 Å) > 60, which we do not select due to the lack of sufficient emission lines to measure oxygen abundances (X-ray detection as a strong signature of an AGN; A. D. Goulding et al. 2023; Á. Bogdán et al. 2024). The open black circles show the galaxies with S/N(1300–3800 Å) ≤ 60. The double circles (diamond) indicate lensed galaxies whose magnification factors are μ > 5. The black solid line marks the S/N(1300–3800 Å) = 60 criterion in selecting our sample galaxies. Bottom: absolute UV magnitude distribution as a function of redshift. The symbols are the same as in the top panel.
Paper: Fe Abundances of Early Galaxies at z = 9–12 Derived with Deep JWST Spectra
Authors: Minami Nakane, Masami Ouchi, Kimihiko Nakajima, Yoshiaki Ono, Yuichi Harikane, Yuki Isobe, Ken'ichi Nomoto, Miho N. Ishigaki, Hiroto Yanagisawa, Daichi Kashino, Nozomu Tominaga, Koh Takahashi, Moka Nishigaki, Yui Takeda, Kuria Watanabe
Figure caption: Spectra of the seven galaxies in our sample. Each panel shows the two-dimensional spectrum (top) and the one-dimensional spectrum (bottom). The black solid lines and shaded regions represent the observed spectra and their 1σ uncertainties, respectively. The red dashed lines indicate Lyman-break features and other emission lines.
Paper: Fe Abundances of Early Galaxies at z = 9–12 Derived with Deep JWST Spectra
Authors: Minami Nakane, Masami Ouchi, Kimihiko Nakajima, Yoshiaki Ono, Yuichi Harikane, Yuki Isobe, Ken'ichi Nomoto, Miho N. Ishigaki, Hiroto Yanagisawa, Daichi Kashino, Nozomu Tominaga, Koh Takahashi, Moka Nishigaki, Yui Takeda, Kuria Watanabe
Figure caption: Fitting results of our sample galaxies with the stellar population synthesis models. Left: the upper panel compares the observed and model spectra. The black (gray) line shows the observed spectrum and its 1σ error, which are used (not used) for the fitting. The red line indicates the best-fit model spectrum. The lower panel presents the residuals from the best-fit model. The black lines and gray shaded regions denote the residuals and their 1σ errors, respectively. Right: posterior PDFs of the fitting parameters. The red solid lines and black dashed lines represent the mode and the boundaries of the 68% HPDI, respectively.
Paper: The Hot Circumgalactic Medium in Stacked X-Rays: Observations versus Simulations
Authors: Skylar Grayson, Evan Scannapieco, Johan Comparat, John A. ZuHone, Yi Zhang, Soumya Shreeram, Marcus Brüggen, Esra Bulbul
Figure caption: Radial profiles of the average mass-weighted metallicity (top), temperature (middle), and density squared (bottom) of M31-type central galaxies (11 < log(M*/M⊙) < 11.25, 12 < log(M200c/M⊙) < 14). These results only include gas particles with T > 106 K, as cooler particles will not significantly contribute to the soft X-ray emission (see Figure 6). Error bars represent the 95% confidence interval generated by bootstrapping the radial profiles for all galaxies in the sample. Metallicities are given as the mass fraction of elements heavier than helium normalized to a solar value of 0.02.
Paper: The Hot Circumgalactic Medium in Stacked X-Rays: Observations versus Simulations
Authors: Skylar Grayson, Evan Scannapieco, Johan Comparat, John A. ZuHone, Yi Zhang, Soumya Shreeram, Marcus Brüggen, Esra Bulbul
Figure caption: Total soft X-ray emissivity (0.5–2.0 keV) as a function of plasma temperature and metallicity relative to solar as given by APEC and pyatomdb (A. R. Foster & K. Heuer 2020). Here the different color curves represent changes in emission due to varying the O, Ne, and Fe (three species that contribute significantly to lines at this energy range) abundance relative to solar. The emission generated by pyXSIM is determined by this output from APEC and the density in the plasma.
Paper: The Hot Circumgalactic Medium in Stacked X-Rays: Observations versus Simulations
Authors: Skylar Grayson, Evan Scannapieco, Johan Comparat, John A. ZuHone, Yi Zhang, Soumya Shreeram, Marcus Brüggen, Esra Bulbul
Figure caption: Radial profiles of the average mass-weighted metallicity (top), temperature (middle), and density squared (bottom) of galaxies with ﹩12\lt {\rm{log}}({M}_{200c}/{M}_{\odot })\lt 14﹩ and 10.5 < log(M*/M⊙) < 11 (left) and 12 < log(M200c/M⊙) < 14 (right). These results only include gas particles with T > 106 K, as cooler particles will not significantly contribute to the soft X-ray emission (see Figure 6).
Paper: The Hot Circumgalactic Medium in Stacked X-Rays: Observations versus Simulations
Authors: Skylar Grayson, Evan Scannapieco, Johan Comparat, John A. ZuHone, Yi Zhang, Soumya Shreeram, Marcus Brüggen, Esra Bulbul
Figure caption: Soft X-ray surface brightness profiles of simulated galaxies stacked by stellar mass, compared against observed CGM emission from Y. Zhang et al. (2024a). Vertical dashed lines represent R200c. From left to right, the bins are 10 < log(M*/M⊙)<11, 11 < log(M*/M⊙) < 11.25, and 11.25 < log(M*/M⊙) < 11.5. All samples have additional cuts on halo mass, such that 12 < log(M200c/M⊙) < 14.
Paper: The Hot Circumgalactic Medium in Stacked X-Rays: Observations versus Simulations
Authors: Skylar Grayson, Evan Scannapieco, Johan Comparat, John A. ZuHone, Yi Zhang, Soumya Shreeram, Marcus Brüggen, Esra Bulbul
Figure caption: Surface brightness profiles of simulated galaxies stacked by stellar mass from the EAGLE and SIMBA simulations. Solid lines show emission from hot plasma, while dashed lines show forward-modeled XRB emission. From left to right, the bins are 10 < log(M*/M⊙) < 11 , 11 < log(M*/M⊙) < 11.25, and 11.25 < log(M*/M⊙) < 11.5.
Paper: The Hot Circumgalactic Medium in Stacked X-Rays: Observations versus Simulations
Authors: Skylar Grayson, Evan Scannapieco, Johan Comparat, John A. ZuHone, Yi Zhang, Soumya Shreeram, Marcus Brüggen, Esra Bulbul
Figure caption: Surface brightness profiles of simulated galaxies stacked by stellar mass and SFR. Here we compare the contribution of the CGM (solid lines) to that from XRBs (dashed lines). The top row shows results from SIMBA, and the bottom row shows results from EAGLE. From left to right, the bins are 10.5 < log(M*/M⊙)<11 , 11 < log(M*/M⊙) < 11.25, and 11.25 < log(M*/M⊙) < 11.5. Galaxies with an sSFR < 0.01 Gyr−1 are considered quiescent.
Paper: The Hot Circumgalactic Medium in Stacked X-Rays: Observations versus Simulations
Authors: Skylar Grayson, Evan Scannapieco, Johan Comparat, John A. ZuHone, Yi Zhang, Soumya Shreeram, Marcus Brüggen, Esra Bulbul
Figure caption: Radial profiles of X-ray surface brightness using galaxies from five simulations stacked by M200c. Vertical dashed lines represent R200c.
Paper: Interpreting Cosmological Information from Neural Networks in the Hydrodynamic Universe
Authors: Arnab Lahiry, Adrian E. Bayer, Francisco Villaescusa-Navarro
Figure caption: Overdensity cut inference. The R2 scores (left) and average variance ﹩\bar{{\sigma }^{2}}﹩ (right) of the predicted cosmological parameters Ωm (circles in blue) and σ8 (squares in red) as a function of ﹩{\rho }_{{\rm{\max }}}﹩. The solid lines represent the maps from the hydrodynamic simulations, and the dashed lines represent the maps from the N-body simulations. At low ﹩{\rho }_{{\rm{\max }}}﹩ there is a sharp increase in the R2 and a decrease in variance, but already with ﹩{\rho }_{{\rm{\max }}}\simeq 0.25\bar{\rho }﹩ the inference precision and accuracy are saturated, implying that much of the information is in underdense regions.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Snapshots of the magnetic field evolution are shown for aligned (↑ ↑, left two columns) and antialigned (↑ ↓, right two columns) magnetic moments on the z − x plane in the corotating frame. Black streamlines indicate the magnetic field direction on the poloidal plane, while the color denotes the normalized magnitude of the magnetic field component perpendicular to it (first and third column) and the magnitude of the magnetic field (second and fourth column). Dashed vertical lines indicate the characteristic distance c/Ω.
Paper: Interpreting Cosmological Information from Neural Networks in the Hydrodynamic Universe
Authors: Arnab Lahiry, Adrian E. Bayer, Francisco Villaescusa-Navarro
Figure caption: Random pixel augmentation inference. The R2 scores (left) and average variance ﹩\bar{{\sigma }^{2}}﹩ (right) of Ωm (green circles) and σ8 (orange squares) as a function of the fraction of unrandomized pixels for each of the ﹩{\rho }_{{\rm{\min }}}﹩ (solid lines) and ﹩{\rho }_{{\rm{\max }}}﹩ (dashed lines) cases for hydrodynamic maps. It can be seen for R2 that the ﹩{\rho }_{{\rm{\min }}}﹩ lines are either above or equal to the corresponding ﹩{\rho }_{{\rm{\max }}}﹩ lines, implying that there is more information per pixel in overdense regions, particularly for σ8.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: A schematic diagram illustrating the parameters defining the configuration realizations. Each panel depicts the two magnetic moments (in red and blue) along with their opposite vectors (shown with low opacity). The orbital angular frequency, Ω, is represented by the magenta vector aligned with the z-axis. The primary, i.e., stronger magnetic moment, m1, is always confined to the x–z plane, making the azimuthal angle difference, ΔΦ, between the two magnetic moments equivalent to the azimuthal angle of the second magnetic moment, m2. Each set of parameters corresponds to two possible configurations, which are, however, physically equivalent. The left (right) panels represent the two configurations for the λ > 0 (λ < 0) cases. In our simulations, only one of these equivalent configurations is implemented.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Mollweide projection of the Poynting flux distribution of an isolated pulsar with 45° inclination angle, calculated at a sphere of radius 1.3 of the light cylinder. The color indicates the norm of the radial Poynting vector. (Left) The corotating anisotropic pattern is shown at a specific time. (Right) The total Poynting flux integrated over five pulsar rotations.
Paper: Interpreting Cosmological Information from Neural Networks in the Hydrodynamic Universe
Authors: Arnab Lahiry, Adrian E. Bayer, Francisco Villaescusa-Navarro
Figure caption: The variation in R2 values for cross-testing case studies conducted for overdensity and underdensity cuts.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: The total Poynting flux that crosses a surface of radius 13 r⋆ during system evolution starting from the initial separation of 3.3 r⋆ (red line) and 8 r⋆ (black line). Both simulations show similar flux evolution in the case of α1 = 0°,  α2 = 45°, and λ = −1 (↑ ↙).
Paper: Interpreting Cosmological Information from Neural Networks in the Hydrodynamic Universe
Authors: Arnab Lahiry, Adrian E. Bayer, Francisco Villaescusa-Navarro
Figure caption: Scatter plots of predicted vs. true Ωm and σ8 for representative R2 values corresponding to selected density cuts. High R2 values correspond to points closely aligned along the diagonal, while lower R2 values show increased scatter.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: The evolution of high-energy emission skymaps for BNS systems with α1 = 0, α2 = 45°, ΔΦ = 0, and λ = 1 (↑ ↗), left, and λ = −1 (↑ ↙), right. Notably, the horizontal axis labeled ϕ does not represent phase, as is typically the case in skymaps of isolated pulsars. Instead, ϕ corresponds to the azimuthal angle measured from the x-axis, meaning each point in these diagrams represents a fixed absolute direction in the sky relative to the BNS system. Additionally, the values of τ indicate the relative time at which these skymaps will reach the observational sphere, referenced to a photon emitted from the center of the system at the moment of the merger.
Paper: Magnetosphere Evolution and Precursor-driven Electromagnetic Signals in Merging Binary Neutron Stars
Authors: Dimitrios Skiathas, Constantinos Kalapotharakos, Zorawar Wadiasingh, Demosthenes Kazanas, Alice K. Harding, Paul T. Kolbeck
Figure caption: Top row: evolution of the torque in the y-direction of the corotating frame over a short period before merger for positive (left) and negative (right) λ, with B⋆ = 3.16 × 1015 G. The cases correspond to α1 = 0° with α2 = 0° (dotted line), α2 = 45° (solid line), and α2 = 90° (dashed line). Bottom row: evolution of the angle θ of the orbital plane’s deviation from its fixed position, resulting from the torque in y-direction, for negative (left) and positive (right) λ, following the same cases as in the top row.