adsabs/AstroCLIMB huggingface dataset:
Paper: Complexity of the Upper Solar Atmosphere Revealed from Spectropolarimetry during a Solar Eclipse
Authors: Z. Q. Qu, L. Chang, G. T. Dun, Z. Xu, X. M. Cheng, L. H. Deng, X. Y. Zhang, Y. H. Jin
Figure caption: Comparison of SE204-4 Q/I spectra deduced from the different demodulation methods mentioned in the text. The top panel shows the Stokes I image and the other panels the Q/I images. It is evident that their dispersion distribution patterns from the RPOS demodulation methods are very similar but the amplitudes differ greatly.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Top panel: cumulative distribution of mass lost from the inspiraled globular clusters and mass from the remnants of the disrupted globular clusters. The orange markers show the observational constraints on the mass of the Milky Way nuclear star cluster (Launhardt et al. 2002; Schödel et al. 2014a, 2014b). Bottom panel: cumulative number of MSPs from the disrupted globular clusters, including MSPs that were ejected initially. The black curve is calculated from the averages of Equation (4). The blue dashed curve is the 1σ upper limit from Equation (3), while the green dotted–dashed curve shows an extreme upper limit taking into account that 70% of the MSPs in a cluster can be formed from giant star collisions with NSs and tidal capture interactions (in addition to the 1σ upper limit), which were not considered in the catalog models. The vertical line marks 2 kpc.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Top panel: number density of globular clusters as a function of the Galactocentric distance in the Milky Way. The orange and purple dots show the observations from the Harris catalog (Harris 1996, 2010 edition) and the Gaia EDR3 (Baumgardt & Vasiliev 2021), respectively. The black dots show the survived globular clusters at 11.5 Gyr from our cluster samples. Bottom panel: mass distribution of globular clusters in the Milky Way. The orange histogram is from the Harris catalog (Harris 1996, 2010 edition) assuming a mass-to-light ratio of 1.5. The purple histogram is from N-body fits to the observed cluster surface brightness profiles and velocity dispersion profiles (Baumgardt 2017; Baumgardt & Hilker 2018). The mass distribution of the survived sample clusters is shown in the black histogram.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Gamma-ray surface brightness of MSPs from disrupted globular clusters and the gamma-ray excess detected around the Galactic center as a function of the angular distance to the Galactic center (Hooper & Slatyer 2013; Calore et al. 2015; Daylan et al. 2016; Horiuchi et al. 2016; Di Mauro 2021). The gamma-ray surface brightness of MSPs corresponds to the average number of MSPs shown by the black curve in Figure 6 (bottom panel). Black stars show the case where the MSP gamma-ray luminosities are calculated using Equation (2), while gray diamonds assume that all MSPs have a gamma-ray luminosity of 4.8 × 1033 erg s−1.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Same as Figure 2 but for models with a metallicity Z = 0.0002 and Galactocentric distance R  g  = 2 kpc.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Same as Figure 2 but for models with a metallicity Z = 0.0002 and Galactocentric distance R  g  = 20 kpc.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Same as Figure 2 but for models with a metallicity Z = 0.002 and Galactocentric distance R  g  = 20 kpc.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Same as Figure 2 but for models with a metallicity Z = 0.002 and Galactocentric distance R  g  = 2 kpc.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Same as Figure 2 but for models with a metallicity Z = 0.0002 and Galactocentric distance R  g  = 8 kpc.
Paper: Millisecond Pulsars in Dense Star Clusters: Evolution, Scaling Relations, and the Galactic-center Gamma-Ray Excess
Authors: Claire S. Ye, Giacomo Fragione
Figure caption: Same as Figure 2 but for models with a metallicity Z = 0.02 and Galactocentric distance R  g  = 2 kpc.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: Radial migration timescale relative to the collisional lifetime of small grains as a function of gas surface density (solid line) following Marino et al. (2020) and using the derived parameters for HD 110058. The horizontal dashed line represents a migration timescale equal to the collisional timescale. The vertical dotted line shows the minimum gas surface density derived from the minimum CO gas mass and radial distribution (95% confidence). The red section of the solid line represents the regime ruled out by our observations. The green section represents the region consistent with the CO observations and where the outward migration would be faster than the collisional timescale. The blue section represents the region where the gas density is high enough (and dominated by other gas species than CO) that the migration is very slow as small dust becomes well coupled to the gas.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: Simulated evolution of CO and CI undergoing viscous spreading and CO photodissociation using EXOGAS. The surface densities of CO and CI are shown in the left and middle panels for different viscosities after 10 Myr of evolution, while the right panel shows the temporal evolution of the total CO and CI mass. The vertical dashed lines in the left panel indicate the region where CO is significantly detected (10–30 au). The gray shaded region in the left panel represents the rate at which CO is released per unit area as a function of radius. The horizontal dotted lines in the left and middle panels represent the surface density above which CO starts to become self-shielded and shielded by CI. The blue shaded region in the right panel represents the CO mass derived from observations (95% confidence level).
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: Normalized CO surface density distribution from the MCMC run. Coloring is based on R in < 3 (blue) and R in > 3 (red) au from the two best-fit solutions.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: Planet mass and semimajor axis required to produce a warp at 40 (blue) or 60 (orange) au. The width of the lines accounts for a secular evolution during 10–17 Myr.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: The 12CO(3–2) channel maps for HD 110058, best-fit disk model (middle), and residuals (bottom). The model image is generated by using GALARIO to Fourier transform the best-fit model image onto the same baselines as the ALMA visibility data and then imaged using a CLEAN implementation built into pdspy. The residual image is similarly made by subtracting the best-fit model visibilities from the data and then imaging. We show solid contours starting at 3σ, with increments of 3σ (the rms per channel is 1.11 mJy beam−1). Similarly, dashed contours show emission starting at −3σ and continuing in increments of −3σ.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: The PV diagram of 12CO optical depth from (3−2) (left) and CO(2−1) (right). The 12CO optical depth τ was obtained by solving R × (1 − e −τ/76) =1 − e −τ , where R is the 12CO/ 13CO line ratio.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: Top: PV diagram of 12CO (2−1) (left) and 13CO (2−1) (right). The red dots are the maximum Keplerian velocities, and the black contours are at levels 3, 6, 9, and 12 times the rms (0.79 and 0.73 mJy beam−1, respectively). Bottom: same for 12CO (3−2) and 13CO (3−2), left and right panels, respectively. The rms for 12CO (3−2) and 13CO (3−2) are 1.11 and 1.53 mJy beam−1.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: Ratios of the 12CO(3−2) and 12CO(2−1) PV diagrams (left) and 13CO (3−2) and 13CO (2−1) PV diagrams (right). The ratios are computed in spaxels where both PV diagrams have signal higher than 4σ.
Paper: ALMA Observations of the HD 110058 Debris Disk
Authors: Antonio S. Hales, Sebastián Marino, Patrick D. Sheehan, Silvio Ulloa, Sebastián Pérez, Luca Matrà, Quentin Kral, Mark Wyatt, William Dent, John Carpenter
Figure caption: The PV diagrams of 12CO(3−2)/13CO(3−2) (left) and 12CO(2−1)/13CO(2−1) (right). The ratios are computed in spaxels where both PV diagrams have signal higher than 4σ.
Paper: The Connection Between Galactic Outflows and the Escape of Ionizing Photons
Authors: Ramesh Mainali, Jane R. Rigby, John Chisholm, Matthew Bayliss, Rongmon Bordoloi, Michael D. Gladders, T. Emil Rivera-Thorsen, Håkon Dahle, Keren Sharon, Michael Florian, Danielle A. Berg, Soniya Sharma, M. Riley Owens, Karin Kjellgren, Keunho J. Kim, Julia Wayne
Figure caption: Comparison of the outflowing gas inferred from UV absorption lines and optical emission lines for the leaker (top panel) and the nonleaker (bottom panel). The velocity profiles from the narrow (red curve) and broad (blue curve) components of the [O III]λ5007 emission line are plotted against low-ionization absorption lines (left panel) and high-ionization absorption lines (right panel).
Paper: The Connection Between Galactic Outflows and the Escape of Ionizing Photons
Authors: Ramesh Mainali, Jane R. Rigby, John Chisholm, Matthew Bayliss, Rongmon Bordoloi, Michael D. Gladders, T. Emil Rivera-Thorsen, Håkon Dahle, Keren Sharon, Michael Florian, Danielle A. Berg, Soniya Sharma, M. Riley Owens, Karin Kjellgren, Keunho J. Kim, Julia Wayne
Figure caption: Intrinsic line flux (magnification-corrected) of the outflow component measured from the broad component in the [O III] 5007 line for the leaker (the blue square) and three individual nonleakers (the red squares) probed by the FIRE slits. On the x-axis, we plot the physical distances between the leaker and the three nonleakers in the source plane, as given by the lens model (Sharon et al. 2022).
Paper: The Connection Between Galactic Outflows and the Escape of Ionizing Photons
Authors: Ramesh Mainali, Jane R. Rigby, John Chisholm, Matthew Bayliss, Rongmon Bordoloi, Michael D. Gladders, T. Emil Rivera-Thorsen, Håkon Dahle, Keren Sharon, Michael Florian, Danielle A. Berg, Soniya Sharma, M. Riley Owens, Karin Kjellgren, Keunho J. Kim, Julia Wayne
Figure caption: [O III]λ5007 emission line profile in leaking (left) and nonleaking (right) regions. The black curve represents the FIRE spectra. We fit the data with a two-component Gaussian model, where the dashed red line represents the narrow component and the dashed blue line represents the broad line. The dashed green line represents the best-fit model.
Paper: Effects of Inner Halo Angular Momentum on the Peanut/X Shapes of Bars
Authors: Sandeep Kumar Kataria, Juntai Shen
Figure caption: This figure shows radial dependence of the following quantities: (a) circular rotation curve for all the galaxy models along with the contribution from various components; (b) surface density of the disk; (c) velocity of dispersion of stars in the disk; and (d) Toomre parameter of the disk.
Paper: VERTICO. IV. Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals
Authors: Vicente Villanueva, Alberto D. Bolatto, Stuart Vogel, Tobias Brown, Christine D. Wilson, Nikki Zabel, Sara Ellison, Adam R. H. Stevens, María Jesús Jiménez Donaire, Kristine Spekkens, Mallory Tharp, Timothy A. Davis, Laura C. Parker, Ian D. Roberts, Dhruv Basra, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Bumhyun Lee, Adam Watts
Figure caption: Left: the resolved molecular-to-atomic gas ratio R mol = Σmol/Σatom vs. galactocentric radius, with circles colored by H I-Class. The black contours enclose, from outside in, 66% and 33% of the points. Middle: the molecular-to-atomic gas ratio, in logarithmic space, computed using the molecular and atomic gas masses within R  e , R mol(r < R  e ) = M mol(r < R  e )/M atom(r < R  e ), vs. H I-Class. The black bars show the R mol values obtained from the M mol/M atom–M ⋆ relation for xGASS-CO MS galaxies from Saintonge & Catinella (2022) using the mean stellar masses for the Yoon et al. (2017) H I-Classes listed in Table 2. There is an increase of R mol(r < R  e ) that is up to about an order of magnitude going from lower to higher H I-Classes (e.g., from Class I to III); the more disturbed the H I, the higher the molecular-to-atomic ratio within R  e . Right: R mol(r < R  e ) vs. H I-Class groups as in the right panel of Figure 7. Conventions and symbols are as in Figure 7.
Paper: VERTICO. IV. Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals
Authors: Vicente Villanueva, Alberto D. Bolatto, Stuart Vogel, Tobias Brown, Christine D. Wilson, Nikki Zabel, Sara Ellison, Adam R. H. Stevens, María Jesús Jiménez Donaire, Kristine Spekkens, Mallory Tharp, Timothy A. Davis, Laura C. Parker, Ian D. Roberts, Dhruv Basra, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Bumhyun Lee, Adam Watts
Figure caption: Left: the molecular-to-stellar mass ratio within R  e , ﹩{R}_{\star }^{\mathrm{mol}}(r\lt {R}_{e})={M}_{\mathrm{mol}}(r\lt {R}_{e})/{M}_{\star }(r\lt {R}_{e})﹩ (top), and the atomic-to-stellar mass ratio within R  e , ﹩{R}_{\star }^{\mathrm{atom}}(r\lt {R}_{e})={M}_{\mathrm{atom}}(r\lt {R}_{e})/{M}_{\star }(r\lt {R}_{e})﹩ (bottom), vs. H I-Class defined by Yoon et al. (2017). The black bars show the values obtained from the M mol/M ⋆–M ⋆ and M atom/M ⋆–M ⋆ relations for xGASS-CO MS galaxies from Saintonge & Catinella (2022) using the mean stellar masses for the Yoon et al. (2017) H I-Classes listed in Table 2. The violin error bars represent the distribution of values for each H I-Class. The white circle is the median value of the distribution. The green shaded area in the top panel is the ﹩{R}_{\star }^{\mathrm{mol}}(r\lt {R}_{e})﹩ range covered by EDGE-CALIFA spiral galaxies within 1σ scatter. Right: ﹩{R}_{\star }^{\mathrm{mol}}(r\lt {R}_{e}))﹩ (top) and the ﹩{R}_{\star }^{\mathrm{atom}}(r\lt {R}_{e})﹩ (bottom) vs. H I-Class after clustering them in three broader groups: (i) unperturbed galaxies (H I-Class 0), (ii) asymmetric galaxies (H I-Classes I and II galaxies), and (iii) symmetric-truncated galaxies (H I-Classes III and IV galaxies). Conventions are as in the left panel. While ﹩{R}_{\star }^{\mathrm{mol}}(r\lt {R}_{e})﹩ values for VERTICO galaxies are within the ranges covered by the xGASS-CO MS galaxies, ﹩{R}_{\star }^{\mathrm{atom}}(r\lt {R}_{e})﹩ values show a systematic decrease with increasing H I-Class.
Paper: VERTICO. IV. Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals
Authors: Vicente Villanueva, Alberto D. Bolatto, Stuart Vogel, Tobias Brown, Christine D. Wilson, Nikki Zabel, Sara Ellison, Adam R. H. Stevens, María Jesús Jiménez Donaire, Kristine Spekkens, Mallory Tharp, Timothy A. Davis, Laura C. Parker, Ian D. Roberts, Dhruv Basra, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Bumhyun Lee, Adam Watts
Figure caption: Left: the resolved SFE of the molecular gas, SFEmol, vs. galactocentric radius. The black contours enclose, from outside in, 66% and 33% of the points. Middle: the SFE of the molecular gas within R  e , SFEmol(r < R  e ), vs. H I-Class. The horizontal black bars are the SFR/M mol median values for H I-Class 0, I, II, III, and IV VERTICO galaxies using the SFR/M mol–M ⋆ relation derived from the molecular depletion times, τ dep = M mol/SFR, for xGASS-CO MS galaxies by Saintonge & Catinella (2022). The green shaded area is the SFEmol(r < R  e ) range covered by EDGE-CALIFA spiral galaxies within 1σ scatter. Right: SFEmol(r < R  e ) vs. H I-Groups. Conventions are as in the left panel of Figure 7. The results shown in Figures 9 and 10 suggest that the systematic decrease of SFEmol(r < R  e ) is a consequence of changes to the state of the gas or the star formation process caused by the source of the morpho-kinematic perturbations that affect the H I in the outer disks of VERTICO galaxies.
Paper: VERTICO. IV. Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals
Authors: Vicente Villanueva, Alberto D. Bolatto, Stuart Vogel, Tobias Brown, Christine D. Wilson, Nikki Zabel, Sara Ellison, Adam R. H. Stevens, María Jesús Jiménez Donaire, Kristine Spekkens, Mallory Tharp, Timothy A. Davis, Laura C. Parker, Ian D. Roberts, Dhruv Basra, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Bumhyun Lee, Adam Watts
Figure caption: The SFE of the molecular mass within R  e , SFEmol(r < R  e ), vs. the best-fit power-law index of the resolved Kennicutt–Schmidt, N rKS, from Jimenez-Donaire et al. (submitted). However, without a significant correlation between SFEmol(r < R  e ) and N rKS (Pearson r  p  = 0.3), H I-Classes III and IV (blue circles) seem to group at both lower N rKS and SFEmol(r < R  e ) than H I-Classes 0 and I (red circles), and vice versa.
Paper: VERTICO. IV. Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals
Authors: Vicente Villanueva, Alberto D. Bolatto, Stuart Vogel, Tobias Brown, Christine D. Wilson, Nikki Zabel, Sara Ellison, Adam R. H. Stevens, María Jesús Jiménez Donaire, Kristine Spekkens, Mallory Tharp, Timothy A. Davis, Laura C. Parker, Ian D. Roberts, Dhruv Basra, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Bumhyun Lee, Adam Watts
Figure caption: Top: the molecular gas mass within R  e , M mol(r < R  e ) (M ⊙), vs. H I-Class. Bottom: the SFR within R  e , SFR (r < R  e ) (M ⊙ yr−1), vs. H I-Class. Conventions are as in left panel of Figure 7. While M mol(r < R  e ) remains almost constant, there is a systematic decrease of SFR (r < R  e ) with H I-Class (particularly from H I-Classes II to IV).
Paper: VERTICO. IV. Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals
Authors: Vicente Villanueva, Alberto D. Bolatto, Stuart Vogel, Tobias Brown, Christine D. Wilson, Nikki Zabel, Sara Ellison, Adam R. H. Stevens, María Jesús Jiménez Donaire, Kristine Spekkens, Mallory Tharp, Timothy A. Davis, Laura C. Parker, Ian D. Roberts, Dhruv Basra, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Bumhyun Lee, Adam Watts
Figure caption: The SFE of the molecular mass within the radius of the bulge R  b , SFEmol(r < R  b ), vs. the bulge mass M  b  (in units of the total stellar mass) for H I-Classes II, III, and IV. Symbols are color-coded by H I-Class as in Figure 11. The horizontal arrows are upper limits for M  b  since no clear breaks in the stellar radial profiles due to bulges are identified; therefore, M  b  in these cases is the mass enclosed within 0.1r 25, which corresponds to r gal ≈ 1.0 kpc at the Virgo Cluster distance (16.5 Mpc; Mei et al. 2007).
Paper: VERTICO. IV. Environmental Effects on the Gas Distribution and Star Formation Efficiency of Virgo Cluster Spirals
Authors: Vicente Villanueva, Alberto D. Bolatto, Stuart Vogel, Tobias Brown, Christine D. Wilson, Nikki Zabel, Sara Ellison, Adam R. H. Stevens, María Jesús Jiménez Donaire, Kristine Spekkens, Mallory Tharp, Timothy A. Davis, Laura C. Parker, Ian D. Roberts, Dhruv Basra, Alessandro Boselli, Barbara Catinella, Aeree Chung, Luca Cortese, Bumhyun Lee, Adam Watts
Figure caption: Left: the resolved molecular-to-stellar mass ratio ﹩{R}_{\star }^{\mathrm{mol}}﹩ colored by H I-Class vs. galactocentric radius for annuli within the 38 VERTICO galaxies analyzed in this work. The black contours enclose, from outside in, 66% and 33% of the ﹩{R}_{\star }^{\mathrm{mol}}﹩ of the points. The green shaded area is the range covered by EDGE-CALIFA spiral galaxies within 1σ scatter about the mean values for radial bins of 0.1r 25 wide. Right: the resolved atomic-to-stellar mass ratio ﹩{R}_{\star }^{\mathrm{atom}}﹩ vs. galactocentric radius. Conventions are as in left panel.
Paper: Redshift-evolutionary X-Ray and UV Luminosity Relation of Quasars from Gaussian Copula
Authors: Bao Wang, Yang Liu, Zunli Yuan, Nan Liang, Hongwei Yu, Puxun Wu
Figure caption: The histogram of 2421 quasar data points in the z and z * spaces with the vertical axis representing the probability density. In the up and down panels, the solid lines represent the gamma distribution in the z space and the Gaussian distribution in the z * space, respectively.