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Paper: ALMA 0.5 kpc Resolution Spatially Resolved Investigations of Nuclear Dense Molecular Gas Properties in Nearby Ultraluminous Infrared Galaxies Based on HCN and HCO+ Three Transition Line Data
Authors: Masatoshi Imanishi, 昌俊 今西, Shunsuke Baba, 俊介 馬場, Kouichiro Nakanishi, 康一郎 中西, Takuma Izumi, 拓磨 泉
Figure caption: Fitting results for the high-J to low-J emission line flux ratios of HCN and HCO+ derived from the 1 kpc beam-sized spectra, displayed in the same way as in Figure 10. The result for IRAS 16090−0139 is shown in Figure 11(d).
Paper: ALMA 0.5 kpc Resolution Spatially Resolved Investigations of Nuclear Dense Molecular Gas Properties in Nearby Ultraluminous Infrared Galaxies Based on HCN and HCO+ Three Transition Line Data
Authors: Masatoshi Imanishi, 昌俊 今西, Shunsuke Baba, 俊介 馬場, Kouichiro Nakanishi, 康一郎 中西, Takuma Izumi, 拓磨 泉
Figure caption:                         Same as Figure 28, but for the 2 kpc beam-sized spectra. The result for IRAS 16090−0139 is shown in Figure 11(e). LIRG NGC 1614 is not shown, for the same reason as explained in the caption of Figure 2.
Paper: ALMA 0.5 kpc Resolution Spatially Resolved Investigations of Nuclear Dense Molecular Gas Properties in Nearby Ultraluminous Infrared Galaxies Based on HCN and HCO+ Three Transition Line Data
Authors: Masatoshi Imanishi, 昌俊 今西, Shunsuke Baba, 俊介 馬場, Kouichiro Nakanishi, 康一郎 中西, Takuma Izumi, 拓磨 泉
Figure caption: Adopted Gaussian fit (solid curved line) of the HC3N J = 21–20 (for IRAS 22491−1808) or J = 18–17 (for other ULIRGs with a significant detection) emission line extracted from the 0.5 kpc beam-sized spectrum. The abscissa is the optical LSR velocity in km s−1, and the ordinate is the flux density in mJy. The horizontal thin dotted straight line indicates the zero-flux level.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Contour maps of perturbations (36 modes) in Type A models best-fitted to the ALMA data, MIR flux ratios, and VLBA positions of a core component q. The plotted maps show the potential perturbation δ ψ, convergence perturbation δ κ, and shear perturbation δ γ reconstructed with L = 3.″6 and the homogeneous weighting (top column), L = 3.″6 and the magnification weighting (middle column), L = 4.″2 and the magnification weighting (bottom column). Light brown curves denote the boundaries of regions in which the signals are larger than 3σ. The centers of the square region are (−0.4, 0.3) (top), (−0.4, 0.3) (middle), and (−0.7, 0.3), (bottom). The coordinates are J2000 centered at the centroid of the primary lensing galaxy G. The slight difference between the best-fitted potential wells around A1, A2, and B images of the quasar core reconstructed with L = 3.″6 and the magnification weighting (middle left) and that with L = 4.″2 and the magnification weighting (bottom left) may be due to the slight difference in the angular scales of the Fourier modes (see also Figure 24).
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Lensing power spectra for potential (left), astrometric shift (middle), and convergence (right) perturbations for small bins. The measured values were obtained from the ALMA image, the MIR flux ratios, the HST positions of galaxies, and the VLBA positions of lensed images of a core component q. Blue (red) vertical and horizontal bars centered at filled diamonds show ∼1σ errors in the square root of power and the bin range of angular wavenumber l used for a Type A model obtained with the homogeneous weighting and L = 4.″2 (L = 3.″6), respectively. Blue (red) horizontal bars centered at empty diamonds show the bin range of angular wavenumber l and the best-fitted values for a Type B model obtained with the homogeneous weighting and L = 4.″2 (L = 3.″6), respectively. The power spectra at the smallest, intermediate, and largest angular bins were obtained from seven low-to-intermediate-frequency modes, 11 intermediate-to-high-frequency modes, and seven high-frequency modes. The highest one ((m, n) = (6, 6)) was not included (see Figure 9). Note that the errors in the three (potential, shift, and convergence) lensing power spectra are not independent as they are given by common Fourier modes with an angular scale of 360°/l.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Image residual in the lens plane. The left panel shows the contour map of the residual intensity: smoothed (corresponding to a pixel size of 0.″05 ) intensity of an unperturbed background Type A model is subtracted by the intensity of the ALMA image with robust = 0. The middle panel shows the contour map of the residual intensity: smoothed intensity of a perturbed Type A model obtained with the magnification weighting with L = 3.″6 and c q + c p = 0.95 is subtracted by the intensity of the ALMA image with robust = 0. The right panel shows the intensity of the unperturbed background Type A model subtracted by the intensity of the perturbed Type A model. The red symbols represent the positions of p, q, r, and s observed at 5  GHz, as in Figure 14. The contours start from a −4σ level and increase with a step of 1σ. Green curves denote the boundary inside, for which the signal is >3σ. The thick black curve in the right panel shows the critical curve.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: De-lensed peak-subtracted source images for unperturbed and perturbed models, and caustics overlaid with critical curves in the perturbed model. The intensity of de-lensed peak-subtracted images is shown in contours for an unperturbed Type A model (left) and a perturbed (middle) Type A model obtained with the magnification weighting with L = 3.″6 and c q + c p = 0.95. The red curves in all of the panels show the caustics in the corresponding model. In the left and middle panels, the black symbols represent the positions of p, q, r, and s observed at 5  GHz as in Figure 14. In the right panel, the caustics and critical curves in the perturbed best-fitted model are shown: The red curves are the caustics, the black curves are the critical curve, the blue circled dot is the centroid of object X, the red “X” symbols are the best-fit positions of q in the lens plane, and the green “X” is the best-fitted position of q in the source plane.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Contour maps of convergence perturbations δ κ (36 modes) in Type B models in which object Y is explicitly modeled. The left row shows the convergence perturbations in which the contribution from object Y is subtracted. The right row represents the total convergence perturbations (object Y plus Fourier modes). The model was obtained with the source plane fits with L = 3.″6 and the homogeneous weighting (top column), L = 3.″6 and the magnification weighting (middle column), L = 4.″2 and the homogeneous weighting (bottom column). Green curves denote the boundaries of regions in which the signals are larger than 3σ. The centers of the square region that determines the Dirichlet boundary condition are (−0.4, 0.3) (top), (−0.4, 0.3) (middle), and (−0.7, 0.3), (bottom). The coordinates are J2000 centered at the centroid of the primary lensing galaxy G.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Convergence of object Y (left) and caustics overlaid with critical curves in a perturbed Type B model in which object Y is explicitly modeled (right). The left panel shows a contour map of the convergence of a modeled object Y in the background Type B model. Green curves denote the boundary inside which the signal is >3σ. The right panel shows the caustics, cuts (black), and critical curves (red) in a perturbed Type B model with the magnification weight and L = 3.″6. The red “X” symbols are the best-fitted positions of q in the lens plane, and the green “X” is the best-fitted position of q in the source plane. Blue circled dots are the centroid of object X and the position of the peak intensity of object Y.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Contour maps of low-frequency modes of the best-fitted convergence perturbations for the three Type A models shown in Figure 20. The plotted maps show the lowest mode (monopole; left), the sum of the second- and third-lowest two modes (dipole; middle), and the sum of the fourth- to sixth-lowest three modes (quadrupole; right). The symbols are the same as in Figure 20.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Comparison between observed and model (Type A) visibilities. The blue dots show the amplitude of visibilities on circular grids observed at 335.3 GHz vs. the uv distance ﹩(=\sqrt{{u}^{2}+{v}^{2}})﹩. The radial separation of adjacent grids is 100 m, and the azimuthal separation is δ θ = 90°. The green, orange, and red curves show best-fitted Type A model visibilities at v = 0 m for the total, extended source, point-source components, respectively.
Paper: ALMA Measurement of 10 kpc Scale Lensing-power Spectra toward the Lensed Quasar MG J0414+0534
Authors: Kaiki Taro Inoue, Takeo Minezaki, Satoki Matsushita, Kouichiro Nakanishi
Figure caption: Improvement in fitting with respect to no (null) model. The red filled circles show the reduced χ 2 in a perturbed Type A model divided by that in no (null) model. δ θ is the angular separation between the centers of adjacent grids.
Paper: Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6
Authors: Junya Arita, Nobunari Kashikawa, Yoshiki Matsuoka, Wanqiu He, Kei Ito, Yongming Liang, Rikako Ishimoto, Takehiro Yoshioka, Yoshihiro Takeda, Kazushi Iwasawa, Masafusa Onoue, Yoshiki Toba, Masatoshi Imanishi
Figure caption: The DMH mass from clustering analysis as a function of redshift. Our result from the projected correlation function is represented as a red circle. Other symbols represent the DMH masses from previous studies. The circle, square, and triangle show studies that derive the projected, angular, and redshift–space correlation function, respectively. The filled symbols denote estimates from ACF signal, while others from CCF signal. The references are shown in the upper right of the figure. These masses are recalculated based on each bias parameter by using the cosmology in the study and the bias model of Tinker et al. (2010). The solid line with gray shade denotes the DMH mass evolution with its error based on the extended Press–Schechter theory. The three dashed lines represent the mass evolution of DMHs with M halo = 1013, 1012, 1011 h −1 M ⊙ at z ∼ 6 from the top. The red-shaded region represents the DMH mass range where most of quasars are expected to reside.
Paper: Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6
Authors: Junya Arita, Nobunari Kashikawa, Yoshiki Matsuoka, Wanqiu He, Kei Ito, Yongming Liang, Rikako Ishimoto, Takehiro Yoshioka, Yoshihiro Takeda, Kazushi Iwasawa, Masafusa Onoue, Yoshiki Toba, Masatoshi Imanishi
Figure caption: Evolution of the quasar bias parameter. This figure is the extension of Figure 12 in Timlin et al. (2018). The red circle represents our result of the projected correlation function, and the other symbols show the result of previous studies. Three black lines represent the bias parameters as a function of redshift based on the theoretical models: efficient feedback (solid line), inefficient feedback (dashed line), and maximal growth (dashed–dotted line). The efficient feedback model assumes that the growth of quasars only occurs in their active phase. The inefficient feedback model presumes that quasars continue growing periodically even after their active phase until z ∼ 2. The maximal growth model premises that quasars keep growing with their host DMH until z ∼ 2. In these models, as the feedback becomes inefficient, the DMH mass gets more massive.
Paper: Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6
Authors: Junya Arita, Nobunari Kashikawa, Yoshiki Matsuoka, Wanqiu He, Kei Ito, Yongming Liang, Rikako Ishimoto, Takehiro Yoshioka, Yoshihiro Takeda, Kazushi Iwasawa, Masafusa Onoue, Yoshiki Toba, Masatoshi Imanishi
Figure caption: The top, middle, and bottom panels show the projected correlation function, the angular correlation function, and the redshift–space correlation function, respectively. The error bars represent the 1σ error from the Jackknife resampling. The black solid lines represent the power-law functions, which are fitted by χ 2 fit.
Paper: Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6
Authors: Junya Arita, Nobunari Kashikawa, Yoshiki Matsuoka, Wanqiu He, Kei Ito, Yongming Liang, Rikako Ishimoto, Takehiro Yoshioka, Yoshihiro Takeda, Kazushi Iwasawa, Masafusa Onoue, Yoshiki Toba, Masatoshi Imanishi
Figure caption: Detection completeness map of the HSC-SSP S20A region. The color represents the detection completeness at m  z  = 24.5 of each tract. The red and black stars represent the SHELLQs and other quasars, respectively.
Paper: Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6
Authors: Junya Arita, Nobunari Kashikawa, Yoshiki Matsuoka, Wanqiu He, Kei Ito, Yongming Liang, Rikako Ishimoto, Takehiro Yoshioka, Yoshihiro Takeda, Kazushi Iwasawa, Masafusa Onoue, Yoshiki Toba, Masatoshi Imanishi
Figure caption: Detection completeness as a function of z-band magnitude. The black solid line denotes the median completeness of all patches. The thin gray solid lines show the detection completeness of each patch. Each median parameter and 1σ error are denoted in the left of the figure.
Paper: Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6
Authors: Junya Arita, Nobunari Kashikawa, Yoshiki Matsuoka, Wanqiu He, Kei Ito, Yongming Liang, Rikako Ishimoto, Takehiro Yoshioka, Yoshihiro Takeda, Kazushi Iwasawa, Masafusa Onoue, Yoshiki Toba, Masatoshi Imanishi
Figure caption: The CCF between quasars and LBGs at z ∼ 6 (red) and ACF of LBGs (blue). The solid line and the dashed line show the power-law function fitted to the CCF and the ACF by χ 2 fit, respectively. For visibility, CCF plots are offset toward x-axis direction.
Paper: The Crucial Role of Perpendicular Diffusion in the Longitude Distribution of >10 MeV Solar Energetic Protons
Authors: Yang Wang, Gang Qin
Figure caption: From top to bottom: the energetic proton intensities (panels 1–4), magnetic field intensity (panel 5), and solar wind speed (panel 6) in OMNI data are used instead of the plasma data observed by SOHO to improve the statistics. The horizontal dashed lines represent the peak intensities of the reference, which have the same ratios in each panel.
Paper: The Crucial Role of Perpendicular Diffusion in the Longitude Distribution of >10 MeV Solar Energetic Protons
Authors: Yang Wang, Gang Qin
Figure caption: Panels (a) and (b) represent the diffusion of >10 MeV energetic protons in the absence and presence of the acceleration of interplanetary shock, respectively. The solid black lines represent the MFLs. Spacecraft A, B, and C are near 1 AU in the ecliptic. The dotted lines represent the magnetic field line connected to the strongest acceleration part of the solar source region. The inner and outer dotted dashed lines represent the effects of perpendicular diffusion of particles near the Sun and in interplanetary space, respectively.
Paper: The Crucial Role of Perpendicular Diffusion in the Longitude Distribution of >10 MeV Solar Energetic Protons
Authors: Yang Wang, Gang Qin
Figure caption: Locations of the Earth (SOHO) and the two STEREO spacecraft in the ecliptic plane between 2010 January and 2015 June.
Paper: The Crucial Role of Perpendicular Diffusion in the Longitude Distribution of >10 MeV Solar Energetic Protons
Authors: Yang Wang, Gang Qin
Figure caption: As in Figure 2 for the 2013 March 5 event. The vertical dotted line indicates the moment when the shock passed STEREO B near 1 AU.
Paper: The Crucial Role of Perpendicular Diffusion in the Longitude Distribution of >10 MeV Solar Energetic Protons
Authors: Yang Wang, Gang Qin
Figure caption: As in Figure 2 for the 2011 November 3 event. The peaks observed by STEREO B and SOHO are so close that only one dashed line, rather than two, is used to represent the peaks observed by STEREO B and SOHO.
Paper: MFPIM: A Deep Learning Model Based on Multimodal Fusion Technology for Pulsar Identification
Authors: Yi Liu, Jing Jin, Hongyang Zhao, Xujie He, Yanan Guo
Figure caption: F1 score and loss curves for training and validation sets on the HTRU data set.
Paper: Evidence of Extended Dust and Feedback around z ≈ 1 Quiescent Galaxies via Millimeter Observations
Authors: Jeremy Meinke, Seth Cohen, Jenna Moore, Kathrin Böckmann, Philip Mauskopf, Evan Scannapieco
Figure caption: Dust radial profile and best-fit point source+King model as defined in Section 4.9, shown here with core radius r 0 = 3.0 comoving Mpc for the Overlap (black) and Wide-Area (blue) Samples. Shaded regions represent the 2σ uncertainty of the combined fit. Dashed lines correspond to the separate best-fit point-source and King components.
Paper: Evidence of Extended Dust and Feedback around z ≈ 1 Quiescent Galaxies via Millimeter Observations
Authors: Jeremy Meinke, Seth Cohen, Jenna Moore, Kathrin Böckmann, Philip Mauskopf, Evan Scannapieco
Figure caption: Observed intensity spectrum within a ﹩2\buildrel{\,\prime}\over{.} 0﹩ circular aperture for the (a) Overlap Sample (N = 94,452) and (b) Wide-Area Sample (N = 387,627). Measured ACT (black, circles) and SPT (black, triangles) values are placed at each frequency map bandcenter, determined by integrating over their respective response. Dust (red) and tSZ (blue) are shown with shaded 2σ bounds determined from the two-component fit of Equation (6).
Paper: Evidence of Extended Dust and Feedback around z ≈ 1 Quiescent Galaxies via Millimeter Observations
Authors: Jeremy Meinke, Seth Cohen, Jenna Moore, Kathrin Böckmann, Philip Mauskopf, Evan Scannapieco
Figure caption: Mollweide (equatorial) projected sky footprints showing the coverage of the DES (red), SPT-SZ (black), and ACT (blue) surveys used in this analysis. The Planck HFI 353 GHz data are shown in the background. This was made with the help of publicly available resources at https://lambda.gsfc.nasa.gov/toolbox/footprint/.
Paper: Evidence of Extended Dust and Feedback around z ≈ 1 Quiescent Galaxies via Millimeter Observations
Authors: Jeremy Meinke, Seth Cohen, Jenna Moore, Kathrin Böckmann, Philip Mauskopf, Evan Scannapieco
Figure caption: Compton-y parameter radial profile for our quiescent galaxy catalogs: Overlap (black, triangles) and Wide-Area (blue, circles). Alongside their best fit (solid), shaded 2σ bounds and the individual point-source and King components (dashed) are shown.
Paper: Evidence of Extended Dust and Feedback around z ≈ 1 Quiescent Galaxies via Millimeter Observations
Authors: Jeremy Meinke, Seth Cohen, Jenna Moore, Kathrin Böckmann, Philip Mauskopf, Evan Scannapieco
Figure caption: Measured radial profiles as detailed in Section 4.3 for (a) all N = 94,452 galaxies within the overlap field as measured on the SPT frequency maps of 95, 150, and 220 GHz. (b) Profile of estimated bias in the same SPT maps and overlap field, calculated from bootstrap resampling a catalog of randomly generated positions (Section 4.5).
Paper: Evidence of Extended Dust and Feedback around z ≈ 1 Quiescent Galaxies via Millimeter Observations
Authors: Jeremy Meinke, Seth Cohen, Jenna Moore, Kathrin Böckmann, Philip Mauskopf, Evan Scannapieco
Figure caption: (a) Redshift and (b) log10 stellar mass distributions of our Overlap Sample (black) that overlaps with both the SPT and ACT fields, and the Wide-Area Sample (blue, dashed) that utilizes the larger ACT field. Distributions shown are after SED selection, normalized by count N and bin width.
Paper: Evidence of Extended Dust and Feedback around z ≈ 1 Quiescent Galaxies via Millimeter Observations
Authors: Jeremy Meinke, Seth Cohen, Jenna Moore, Kathrin Böckmann, Philip Mauskopf, Evan Scannapieco
Figure caption: Overlap Sample galaxy stacks (N = 94,452) for their respective SPT and ACT frequency maps, processed according to Section 4.2. A gradient was also removed from each image. Dashed circles correspond to radii of ﹩2\buildrel{\,\prime}\over{.} \,0﹩ and ﹩10^{\prime} ﹩.
Paper: Simulation of Head-on Collisions between Filamentary Molecular Clouds Threaded by a Lateral Magnetic Field and Subsequent Evolution
Authors: Raiga Kashiwagi, Kazunari Iwasaki, Kohji Tomisaka
Figure caption: One-dimensional profiles on the x- and y-axes for the radial collapse model β01M at four different epochs: t = 0.350 (red), 0.670 (yellow), 0.710 (green), and 0.735 (blue). The density and velocity profiles on the x- and y-axes are shown in (a) and (b), respectively, in which the solid lines represent the density distributions (ρ(x) in (a) and ρ(y) in (b)) in the upper panels, whereas these solid lines represent the velocity profiles (v  x  in (a) and v  y  in (b)) in the lower panels. The gas and magnetic pressure profiles on the x- and y-axes are shown in (c) and (d), respectively. In (c) and (d), the solid and dashed lines in the upper panel represent the gas and magnetic pressure, respectively. The solid lines in the lower panels represent the plasma beta values.
Paper: Simulation of Head-on Collisions between Filamentary Molecular Clouds Threaded by a Lateral Magnetic Field and Subsequent Evolution
Authors: Raiga Kashiwagi, Kazunari Iwasaki, Kohji Tomisaka
Figure caption: Time evolution of the radial collapse model β01M. This figure shows the cross-section of the colliding filaments on the x–y plane, and the plot area is restricted to ±2.5 from the box size (±5). Each panel shows the cross-section at different epochs: t = 0.350 (a), 0.670 (b), 0.710 (c), and 0.735 (d). The color scale represents the density, and the white lines are the magnetic field lines.
Paper: Simulation of Head-on Collisions between Filamentary Molecular Clouds Threaded by a Lateral Magnetic Field and Subsequent Evolution
Authors: Raiga Kashiwagi, Kazunari Iwasaki, Kohji Tomisaka
Figure caption: Same as Figure 2, but for the stable model (β01S). Each panel shows the cross-section at different epochs: t = 0.900 (a), 1.300 (b), 1.900 (c), and 3.500 (d).
Paper: Simulation of Head-on Collisions between Filamentary Molecular Clouds Threaded by a Lateral Magnetic Field and Subsequent Evolution
Authors: Raiga Kashiwagi, Kazunari Iwasaki, Kohji Tomisaka
Figure caption: Same as Figure 3, but for the stable model (β01S). Color represents different epochs: t = 0.900 (red), 1.300 (yellow), 1.900 (green), and 3.500 (blue).
Paper: Simulation of Head-on Collisions between Filamentary Molecular Clouds Threaded by a Lateral Magnetic Field and Subsequent Evolution
Authors: Raiga Kashiwagi, Kazunari Iwasaki, Kohji Tomisaka
Figure caption: Maximum density ﹩({\rho }_{\max })﹩ as a function of the elapsed time (t). The red and blue lines represent the radial collapse (β01M) and stable (β01S) models, respectively.