adsabs/AstroCLIMB huggingface dataset:
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: Velocity arrows on top of the density maps of the spiraling-in simulation with jets in the y = 0 plane at t = 3.2 yr, when the NS orbits at a SR = 300 R ⊙. This plane cuts the low-density and high-outflow velocity bubbles that the jets inflate in two regions above and two regions below the equatorial plane. The older two regions (above and below the equatorial plane) are to the right of the center and appear as pale-blue zones surrounded by green regions; we point at these regions of the bubbles with yellow arrows. The two newer regions are to the left of the center and appear as two green zones surrounded by yellow (higher-density) regions; we point at these regions of the bubbles with red arrows. The velocity magnitude is proportional to the length of the arrows. The maximum velocity inside the old bubbles is 76 km s−1. At the time of this figure the NS is at (x, y, z)NS = (−151 R ⊙, 259 R ⊙, 0), i.e., outside the plane of the figure. The white dot is the projected location of the NS on the y = 0 plane.
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: The average radius of the tracers of two initial spherical shells of 800 R ⊙ < r < 850 R ⊙ (blue lines) and 600 R ⊙ < r < 650 R ⊙ (red lines) in the simulations without jets. The solid lines are for the high-resolution simulation and the dashed lines are for the regular-resolution simulation. For reference, the Keplerian orbital period on the surface of the unperturbed RSG is P Kep = 2.35 yr and ﹩{P}_{{\rm{D}}}\equiv {(G\bar{\rho })}^{-1/2}=0.76\,\,\mathrm{yr}﹩, where ﹩\bar{\rho }﹩ is the average density of the initial RSG model.
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: Velocity vectors on top of density maps in part of the x = 0 plane (left) and in part of the the z = 0 plane (right), at t = 4 yr (top), and t = 4.5 yr (bottom) for the regular-resolution no-jets simulations. The density scale and units of the axes are as in Figure 1. The flow speed at each point is according to the length of the arrow. The maximum velocities in the vortices at 700 R ⊙ ≃ 50 × 1012 cm are v con,3D ≃ 3–8 km s−1.
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: The quantity ﹩{(\overrightarrow{{\rm{\nabla }}}\times \overrightarrow{v})}_{z}﹩ in the z = 6 × 1012 cm = 86 R ⊙ plane for the simulations with jets. Values are given according to the color bar in units of s−1. From top to bottom are plots at t = 2 yr just as the NS reaches an orbital separation of a = 500 R ⊙, t = 3 yr when the NS reaches a SR = 300 R ⊙, and t = 4 yr as the NS continues to orbit at a SR = 300 R ⊙. The black spiral in the center indicates the trajectory of the spiraling-in NS.
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: Density maps of the regular-resolution (left column) and of the high-resolution (right column) simulations without any jets in the z = 0 plane and at three times of, from the top row to bottom, t = 0.7 yr, t = 1.6 yr, and t = 6.4 yr. The black circle in each panel marks the surface of the RSG model at t = 0, which is R RSG = 881 R ⊙ = 6.13 × 1013 cm. The density color coding is according to the upper color bar in logarithmic scale and in units of g cm–3, from 10−12 g cm−3 (deep blue) to 10−6g cm−3 (deep red).
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: Radial profiles of the density (top; density in g cm−3) and of ﹩{F}_{{\rm{S}}}=\mathrm{log}(P/{\rho }^{5/3})﹩, which is about proportional to the entropy (bottom; P/ρ 5/3 in units of g−2/3 cm4 s−2) at four times as indicated in the insets and for the regular-resolution no-jets simulation. Each scatterplot is the collection of the values in all cells at the given time (a total of about 43,000 points).
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: Similar to Figure 4 but for the high-resolution simulation.
Paper: Jet-powered Turbulence in Common Envelope Evolution
Authors: Shlomi Hillel, Ron Schreier, Noam Soker
Figure caption: Similar to Figure 6 but for the high-resolution simulation where we have 1.1 × 106 points in each scatterplot.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: During a tear, the inner and outer subdisks collide, causing streamers of low-angular gas to rain down onto the inner subdisk. Panel (a): we plot contours of inward flowing mass in tilted coordinates at time t = 78854.3r g/c. The mass flux has been integrated in ﹩\varphi ^{\prime} ﹩ and is depicted in the plane of tilted cylindrical (﹩R^{\prime} ﹩) and vertical (﹩z^{\prime} ﹩) coordinates. At the tearing radius (r tear ≈ 10 r g), the mass flux is distributed roughly uniformly over a shell. Within the tear, gas plunges radially onto the inner disk, shocking it and increasing the disk mass. Panel (b): same as panel (a), except we depict the outward flowing mass flux. Panel (c): same as panel (a), except we plot the temperature of the gas. The streamer-populated region within the tear is roughly 2 orders of magnitude hotter than the inner subdisk. Panel (d): here, we plot the radial profile of the dimensionless circularization radius of the gas ≡r c/r. Values above (below) unity indicate that the orbital velocity is above (below) its value for a circular orbit. At r tear, r c/r is small, causing streamlines to plunge. Just above the tear, r c/r is above unity. Panel (e): here, we plot the radial profile of the gas pressure in the disk. Since the disk is depleted of gas at the tear, the gas pressure must have a positive radial gradient at r ≳ r tear. This causes an inward force that is compensated by the super-Keplerian motion in this region.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: The effective α parameter far exceeds both unity and the magnetic α parameter, suggesting that accretion is neither driven by local turbulence (where α ≲ 1) nor magnetic fields. We show this by plotting radial profiles of the effective α parameter, α eff (Equation (8)), and the α parameter associated with the Maxwell’s stress, α M (Equation (9)). These profiles are averaged from times ∼72–90 × 104 r g/c. For both quantities, we also plot their instantaneous profiles at each time, which are depicted in lighter colors. Our time averages are not true steady-state measures of α because disk tearing makes the accretion flow inherently transient. The imprint of disk tearing can be seen in the instantaneous α eff curves, where we have labeled the radius of the tear, which moves inward as the inner disk is accreted.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: Dissipation at the tearing radius causes the formation of low-angular momentum streams of gas (“streamers”) that plunge onto the inner subdisk, causing it to rapidly reduce in size. Panel (a): we depict a time series of the specific angular momentum of gas accreted at the tear (ℓ accr, Equation (18)) normalized to the specific angular momentum of a circular orbit at the tearing radius (ℓ c, Equation (7)). At all times during the depicted tearing cycle, ℓ accr < ℓ c, indicating that the gas will try to circularize at smaller and smaller radii. Panel (b): we show a time series of the mass of the inner subdisk (M disk), the mass accreted by the BH (∫dM BH, Equation (17)), and the mass accreted by the inner subdisk from the tear (∫dM tear, Equation (15)). Each is normalized to the initial mass of the inner subdisk during the depicted phase (M disk,0). At t ≈ 83000 r g/c, there is a transition, when low-angular momentum gas from the tear fully replenishes the initial mass of the inner subdisk. Panel (c): here, we plot a corresponding spacetime diagram of the tilt angle. The tear is delineated by the discontinuity between red and blue regions. By t ≈ 77500 r g/c, the inner subdisk fully aligns with BH spin. The inner subdisk is consumed by the BH at the end of the depicted phase and is quickly replaced by outer disk material that has tilt angle ≈60° − 65°. Panel (d): we show a spacetime diagram of the shell-integrated dissipation rate (∫QdA  θ φ ). There is generally dissipation at the tear and at radii r ≲ 5 − 6 r g, where streamers crash into the inner subdisk. Dissipation in these regions is correlated, since dissipation in the tear is associated with an increased formation rate of streamers.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: The phase offset of the m = 2 scale height oscillations is equal to the precession angle (set to ﹩\varphi ^{\prime} =0﹩) in the outer disk but not in the inner disk. We depict this with spacetime diagrams of ﹩{H}_{{p}_{{\rm{g}}}}/r﹩ at fixed r = 10 r g (panel (b)) and r = 40 r g (panel (d)). In the time period visualized, the tearing radius is initially 10 r g < r tear < 40 r g, but drifts inward, crossing r = 10 r g at t ≈ 79 × 104 r g/c. This is reflected in the warp amplitude (ψ) plots accompanying each spacetime diagram. In panel (a), we have drawn a red line when the disk tears. We have also drawn a blue dotted ψ c = 0.089 line as an estimate for when extreme scale height oscillations begin occurring, calculated using Equation (154) of Fairbairn & Ogilvie (2021a). When t < 79 × 104 r g/c, panel (b) shows the inner disk, which exhibits radially dependent phase offsets (depicted in dark blue) due to strong differential precession. At all times at r = 40 r g, the depicted annulus is part of the outer disk, and the phase of the scale height oscillations is locked with the precession angle. At r = 10 r g, the scale height is also generally larger than the target scale height (=0.02, depicted in white) due to the enhanced dissipation and because vertical oscillations cause a departure from hydrostatic equilibrium.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: Low-angular momentum streamers produced at the tear crash into the inner subdisk, shocking it and leading to significant dissipation. Panel (a): we depict the fluid frame entropy density (ρ κ g) at radius r = 6 r g and time t = 81, 062r g/c. Streamers that originated at r tear = 7.8 r g rain down onto a transiently aligned, unwarped inner subdisk, shocking and dissipating their kinetic energy. Panel (b): we depict the cumulative dissipation, analogous to Figure 6(b), except we show the dissipation in each direction (﹩r,\theta ^{\prime} ,\varphi ^{\prime} ﹩). We see that we get dissipation of a similar strength to a nozzle shock, except the dissipation is more spread out on the inner disk. The dissipation is still centered at two points along the annulus, but is no longer located at ﹩\varphi ^{\prime} \approx 0﹩ and π. Panel (c): we depict a 3D rendering of ρ κ g at the same time. Here, we have excised gas at radii >20 r g to focus on the inner regions. We can see that streamers from the outer subdisk rain down onto the inner subdisk from either side, and then “spill” over the top.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: Dissipation in nozzle shocks can mostly account for the measured mass accretion rate everywhere except the innermost regions of the disk. Panel (a): here, we compare ﹩\dot{M}﹩ to the estimated mass accretion rate due to nozzle shocks, ﹩{\dot{M}}_{\mathrm{NZ}}﹩ (Equation (13)). We do this for multiple values of f (Equation (12)), where higher f indicates a stricter cutoff for the degree of compression. Each quantity is averaged from times ∼72–90 × 104 r g/c. Panel (b): here, we show what percentage of a given annulus passes our compression criterion when calculating ﹩{\dot{M}}_{\mathrm{NZ}}﹩, for each value of f. Panel (c): here, we show our fits for the dimensionless mean (﹩{\tilde{H}}_{{p}_{{\rm{g}}}}^{(\mathrm{mean})}/r﹩) and amplitude (﹩{\tilde{H}}_{{p}_{{\rm{g}}}}^{(\mathrm{amp})}/r﹩) of the scale height oscillations (Equation (3)). The quantities are time-averaged over the same period as the other panels, with the corresponding instantaneous curves depicted in lighter colors.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: The vertical compressions of the warped disk lead to “nozzle shocks” twice an orbit, where significant dissipation occurs. Panel (a): here, we depict the fluid frame entropy (κ g), at radius r = 21 r g and time t = 115923.3 r g/c in the ﹩\theta ^{\prime} -\varphi ^{\prime} ﹩ plane. We see that the entropy spikes at ﹩\varphi ^{\prime} \approx 0﹩ (or 2π) and π, where the disk is most compressed. Panel (b): we plot the cumulative fraction of dissipated energy along the annulus (Equation (11) and following text), normalized to the orbital energy of the annulus. Across the ﹩\varphi ^{\prime} =\pi ﹩ nozzle shock, ≈1.8% of the orbital energy is dissipated.
Paper: Nozzle Shocks, Disk Tearing, and Streamers Drive Rapid Accretion in 3D GRMHD Simulations of Warped Thin Disks
Authors: Nicholas Kaaz, Matthew T. P. Liska, Jonatan Jacquemin-Ide, Zachary L. Andalman, Gibwa Musoke, Alexander Tchekhovskoy, Oliver Porth
Figure caption: We depict the conversion of global (“true”) coordinates to our radially dependent tilted coordinates. We do so by showing snapshots of ρ in both coordinate systems. The tilted coordinates are indicated by primes and are a function of the local tilt and precession angles (Equation (A1)). At all radii in the tilted coordinate system, ﹩\hat{z}^{\prime} ﹩ is parallel to the local angular momentum vector, ﹩\varphi ^{\prime} =0﹩ is set to the local precession angle, and ﹩\theta ^{\prime} =\pi /2﹩ is set to the local midplane of the disk.
Paper: The IR Compactness of Dusty Galaxies Sets Star Formation and Dust Properties at z ∼ 0–2
Authors: Jed McKinney, Alexandra Pope, Allison Kirkpatrick, Lee Armus, Tanio Díaz-Santos, Carlos Gómez-Guijarro, Maximilien Franco, David Elbaz, Christopher C. Hayward, Hanae Inami, Gergö Popping, Mengyuan Xiao
Figure caption: Left: the ratio of AGN-corrected IR luminosity to total dust mass, a tracer of the star formation efficiency, as a function of IR surface density. Labeling follows Figure 4. A best-fit linear trend to all galaxies on the figure is shown in solid gray. Hatched regions show the fit beyond the domain of our data. The dashed and dotted–dashed lines show the star formation efficiency and IR size relation from Elbaz et al. (2018) derived from 870 μm imaging of Herschel-selected (U)LIRGs, and from millimeter-selected galaxies in Franco et al. (2020), respectively, each over their respective domains in ΣIR. Both literature trends are normalized to the locus of our data as differences in SFR and gas mass derivations can change the absolute normalization of the trend. We find a redshift-independent relation between the IR size and L IR,SF/M dust ratio where higher IR surface density galaxies exhibit evidence for higher star formation efficiencies. Right: distance from the specific star-forming main sequence for each galaxy’s redshift and stellar mass as a function of ΣIR,SF. The black hatched region encases the ±0.3 dex canonical main-sequence scatter (Whitaker et al. 2014), and the dashed black line indicates the threshold above which galaxies are considered starbursts (Puglisi et al. 2021). (U)LIRGs at high IR surface density tend to be further above the main sequence, a trend that is more pronounced at z ∼ 0 (shaded pink line) than at z ∼ 2 (shaded blue line) where the data are well fit with no ΣIR,SF dependence (hatched blue region).
Paper: The IR Compactness of Dusty Galaxies Sets Star Formation and Dust Properties at z ∼ 0–2
Authors: Jed McKinney, Alexandra Pope, Allison Kirkpatrick, Lee Armus, Tanio Díaz-Santos, Carlos Gómez-Guijarro, Maximilien Franco, David Elbaz, Christopher C. Hayward, Hanae Inami, Gergö Popping, Mengyuan Xiao
Figure caption: PAH/L IR,SF vs. IR surface density. GOALS galaxies (circles) are colored by the ratio of the radiation field strength G in units of G 0 (G 0 = 1.6 × 10−3erg s−1 cm−2; Habing 1968) to neutral gas density (n H/cm−3) in PDRs, derived from far-IR find-structure line modeling (Díaz-Santos et al. 2017). For comparison, we also show the trend in [C II]neutral/L IR from Díaz-Santos et al. (2017) as a black line, which has not been scaled. KINGFISH (gray diamonds) cluster at lower ΣIR,SF about this trend. (U)LIRGs at z ∼ 2 (blue squares) follow the local trend in PAH/L IR,SF vs. ΣIR,SF, which exhibits a comparable turnover as found for the deficit observed in [C II] emission at ﹩\mathrm{log}{{\rm{\Sigma }}}_{\mathrm{IR}}/[{L}_{\odot }\,{\mathrm{kpc}}^{-2}]﹩  > 10 accompanied by high G/n H. This suggests a change in the ISM conditions with ΣIR,SF for z ∼ 2 dusty star-forming galaxies comparable to the trends found with IR surface density in GOALS galaxies (McKinney et al. 2021a).
Paper: The IR Compactness of Dusty Galaxies Sets Star Formation and Dust Properties at z ∼ 0–2
Authors: Jed McKinney, Alexandra Pope, Allison Kirkpatrick, Lee Armus, Tanio Díaz-Santos, Carlos Gómez-Guijarro, Maximilien Franco, David Elbaz, Christopher C. Hayward, Hanae Inami, Gergö Popping, Mengyuan Xiao
Figure caption: IR surface density not corrected for AGNs (top) and IR size (bottom) vs. the fractional contribution of AGNs to the integrated mid-IR emission (f AGN,MIR). GOALS galaxies are shown with purple circles, and blue squares indicate the z ∼ 2 ALMA-detected sample from this work. At z ∼ 2, dust-obscured galaxies tend to have smaller R eff and higher ΣIR with increasing f AGN,MIR on average, exhibiting a factor of ∼2 difference in the average sizes between f AGN,MIR < 0.2 and 0.2 < f AGN,MIR < 0.8 (red symbols).
Paper: The IR Compactness of Dusty Galaxies Sets Star Formation and Dust Properties at z ∼ 0–2
Authors: Jed McKinney, Alexandra Pope, Allison Kirkpatrick, Lee Armus, Tanio Díaz-Santos, Carlos Gómez-Guijarro, Maximilien Franco, David Elbaz, Christopher C. Hayward, Hanae Inami, Gergö Popping, Mengyuan Xiao
Figure caption: ALMA contours (red levels) over JWST/NIRCam F150W imaging from the JADES survey (Eisenstein et al. 2023; JADES Team 2023; Rieke & the JADES Collaboration 2023) where available, and HST/F160W otherwise. We also show the ALMA contours over Spitzer/IRAC4 images. The ALMA contours are drawn at 3σ, 4σ, 5σ, 10σ, 15σ, and 20σ. Tick marks are spaced on each cutout by 1.″0.
Paper: The IR Compactness of Dusty Galaxies Sets Star Formation and Dust Properties at z ∼ 0–2
Authors: Jed McKinney, Alexandra Pope, Allison Kirkpatrick, Lee Armus, Tanio Díaz-Santos, Carlos Gómez-Guijarro, Maximilien Franco, David Elbaz, Christopher C. Hayward, Hanae Inami, Gergö Popping, Mengyuan Xiao
Figure caption: Continuation of Figure 10.
Paper: In Search of Infall Motion in Molecular Clumps. IV. Mapping of the Global Infall Sources
Authors: Yang Yang, Xi Chen, Zhibo Jiang, Zhiwei Chen, Shuling Yu, Jun Li
Figure caption: HCO+ (1–0) and H13CO+ (1–0) average spectra obtained from RATRAN modeling of a collapsing cloud (see text). The observed HCO+ (1–0) spectrum is plotted in black, and the averaged area is the red boxed area of each target in Figure B1. The green line is the spectrum obtained by the RATRAN model, while the dashed green line is the result of Gaussian fitting of HCO+ (1–0) and H13CO+ (1–0). The dashed red line indicates the central radial velocity of H13CO+.
Paper: Beyond Ultra-diffuse Galaxies. II. Environmental Quenching of Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny Greco, Rachael Beaton, Shany Danieli, Andy Goulding, Song Huang, 崧 黄, Erin Kado-Fong
Figure caption: Quenched fractions of UDGs (gray) and UPGs (green) as a function of their stellar masses. The results from ELVES (Carlsten et al. 2022a) and SAGA (Mao et al. 2021) are also shown for comparison, where the quenched fractions are all defined based on the mass-dependent color cut and corrected for incompleteness following Mao et al. (2021). We find that UDGs have a high quenched fraction that changes little over a wide range of stellar mass. On the contrary, the quenched fraction of UPGs is lower and decreases with increasing satellite stellar mass. Given their large sizes, UPGs have a similar quenched fraction to the normal satellites of MW analogs in ELVES.
Paper: Beyond Ultra-diffuse Galaxies. II. Environmental Quenching of Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny Greco, Rachael Beaton, Shany Danieli, Andy Goulding, Song Huang, 崧 黄, Erin Kado-Fong
Figure caption: Left: quenched fractions of UPGs in this work and the ELVES survey. We select UPGs from the ELVES sample and calculate the quenched fraction, shown as the brown line. The quenched fraction of UPGs in this work is highlighted in green, while the quenched fraction of the whole ELVES sample is shown in orange. We do not find a significant dependence of the quenched fraction on the size of the satellites by comparing UPGs with the bulk of the satellites. Right: comparisons with simulations of satellites in MW analogs. The purple and pink lines show the quenched fractions produced in the ARTEMIS (Font et al. 2022) and FIRE-2 (Samuel et al. 2022) simulations, respectively. The quenched fraction of UPGs agrees quite well with that of normal-sized satellites in simulations.
Paper: Beyond Ultra-diffuse Galaxies. II. Environmental Quenching of Mass–Size Outliers among the Satellites of Milky Way Analogs
Authors: Jiaxuan Li, 嘉轩 李, Jenny E. Greene, Johnny Greco, Rachael Beaton, Shany Danieli, Andy Goulding, Song Huang, 崧 黄, Erin Kado-Fong
Figure caption: Size distribution of UDGs (left) and UPGs (right) hosted by MW analogs. The contribution from the foreground and background contaminants (gray dots) is subtracted, and the completeness effect has been corrected. We fit a power law to the size distribution of UDGs and get a power law ﹩{dn}/d\mathrm{log}{r}_{e}\propto {r}_{e}^{-1.45\pm 0.20}﹩. By comparing with the size distributions of UDGs in van der Burg et al. (2016, 2017), we find that the power law becomes steeper as the average halo mass increases. It is possible that denser environments provide stronger tidal forces and thus produce more small UDGs. The UPG size distribution is suppressed at the smaller-size end because small galaxies are not 1.5σ above the mass–size relation and thereby not included as UPGs.