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Andy Goulding

Publications and source records attributed to Andy Goulding.

At least 19 recordsLinked to original sources
arXiv2026

Under Pressure: UV Emission Line Ratios as Barometers of AGN Feedback Mechanisms

Feedback from active galactic nuclei (AGN) is widely acknowledged to regulate the growth of massive galaxies, though its driving mechanisms are debated. Prevailing theories suggest that AGN-driven outflows are driven either by radiation pressure acting directly on the dusty interstellar medium (ISM) or by hot winds entraining cooler ISM gas, but the relative contribution of each mechanism remains uncertain. By combining optical emission line measurements with highly ionized UV emission lines, it is possible to constrain whether the pressure source applied to ionized clouds is primarily radiation or primarily hydrodynamic, and thus constrain the dominant driver. This study presents the first multi-object analysis of far-ultraviolet (FUV) spectra from galactic-scale AGN-driven outflows in obscured quasars, based on Cosmic Origins Spectrograph observations of five low-redshift targets. By comparing narrow-line region UV emission line ratios to theoretical models that vary the importance of the two pressure sources, we find three out of five targets fall within the radiation pressure-dominated regime. A fourth target exhibits intermediate emission-line ratios that suggest radiation pressure and pressure from a hot wind are both dynamically important. Finally, the lowest-luminosity object in our sample may have a dynamically important hot wind component, but non-detections prevent a clear conclusion in this case. These results suggest radiation pressure dominates circum-nuclear narrow-line region cloud dynamics, but pressure from a hot wind also plays a role in some cases. This is consistent with AGN feedback scenarios mediated by radiation pressure or a short-lived hot wind phase that dissipates after initially accelerating outflows.

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arXiv2026

Little Red Dot $-$ Host Galaxy $=$ Black Hole Star: A Gas-Enshrouded Heart at the Center of Every Little Red Dot

The central engines of Little Red Dots (LRDs) may be ``black hole stars" (BH*s), early stages of black hole growth characterized by dense gas envelopes. So far, the most direct evidence for BH*s comes from a handful of sources where the host galaxy is completely outshone as suggested by their remarkably steep Balmer breaks. Here we present a novel scheme to disentangle BH*s from their host galaxies assuming that the [OIII]5008\r{A} line arises exclusively from the host. Using a sample of 98 LRDs ($z$~$2-9$) with high quality NIRSpec/PRISM spectra, we demonstrate that the host-subtracted median stack displays a Balmer break $>2\times$ stronger than massive quiescent galaxies, with the rest-optical continuum resembling a blackbody-like SED ($T_{\rm{eff}}$~$4050$ K, $\log(L_{\rm{bol}})$~$43.9$ erg s$^{-1}$, $R_{\rm{eff}}$~$1300$ au). We measure a steep Balmer decrement (H$\alpha$/H$\beta>10$) and numerous density-sensitive features (e.g., FeII, HeI, OI). These are hallmark signatures of dense gas envelopes, providing population-level evidence that BH*s indeed power LRDs. In the median LRD, BH*s account for $\sim20\%$ of the UV emission, $\sim50\%$ at the Balmer break, and $\sim90\%$ at wavelengths longer than H$\alpha$ with the remainder arising from the host. BH*s preferentially reside in low-mass galaxies ($M_{\rm{\star}}$~$10^{8}\,{\rm M}_{\rm{\odot}}$) undergoing recent starbursts, as evidenced by extreme emission line EWs (e.g., [OIII]5008\r{A}~$1100$\r{A}, CIII]~$12$\r{A}), thereby favoring BH* origins linked to star-formation. We show V-shaped LRD selections are biased to high BH*/host fractions ($\gtrsim60\%$ at 5500\r{A}) -- less dominant BH*s may be powering JWST's blue broad-line AGN. We find BH*s are so commonplace and transient (duty cycle $\sim1\%$, lifetime $\sim10$ Myrs) that every massive black hole may have once shone as a BH*.

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arXiv2025

A Compact Symmetric Object Discovered by the VLA Low-band Ionosphere and Transient Experiment

We present new Very Long Baseline Array (VLBA) imaging of a MHz-peaked spectrum (MPS) source that was found using commensal low-frequency data taken with the Karl G. Jansky Very Large Array (VLA). The source, J0330-2730, was identified in multi-epoch data from the VLA Low-band Ionosphere and Transient Experiment (VLITE). VLITE continuously collects low-frequency data at 340 MHz during regular VLA observations. Our analysis of the VLITE light curve demonstrates that J0330-2730 has significant 340 MHz flux variability at the ~20% level over a timescale of approximately one year. Our VLBA images reveal a resolved, double-lobed morphology with a projected linear size of 64 pc. We consider plausible mechanisms that could explain the observed 340 MHz variability and the source properties on milliarcsecond scales. We rule-out variable Doppler boosting and conclude that refractive interstellar scintillation or variable free-free absorption are the most likely explanations. We argue that the properties of J0330-2730 are consistent with the class of compact symmetric objects (CSOs) and consider the evolutionary stage of the source. The extent of the resolved lobes revealed by the VLBA is significantly smaller than predictions based on the turnover-size relation for a standard synchrotron self-absorbed jet model. We discuss possible explanations for the departure from the turnover-size relation, including jet formation by a transient phenomenon such as a tidal disruption event or a "frustrated jet" impeded by the presence of dense gas or a high-pressure environment. This study highlights the potential of VLITE for the identification of compact and young radio sources.

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arXiv2025

A "Black Hole Star" Reveals the Remarkable Gas-Enshrouded Hearts of the Little Red Dots

The physical processes that led to the formation of billion solar mass black holes within the first 700 million years of cosmic time remain a puzzle. Several theoretical scenarios have been proposed to seed and rapidly grow black holes, but direct observations of these mechanisms remain elusive. Here we present a source 660 million years after the Big Bang that displays singular properties: among the largest Hydrogen Balmer breaks reported at any redshift, broad multi-peaked H$\beta$ emission, and Balmer line absorption in multiple transitions. We model this source as a "black hole star" (BH*) where the Balmer break and absorption features are a result of extremely dense, turbulent gas forming a dust-free "atmosphere" around a supermassive black hole. This source may provide evidence of an early black hole embedded in dense gas -- a theoretical configuration proposed to rapidly grow black holes via super-Eddington accretion. Radiation from the BH* appears to dominate almost all observed light, leaving limited room for contribution from its host galaxy. We demonstrate that the recently discovered "Little Red Dots" (LRDs) with perplexing spectral energy distributions can be explained as BH*s embedded in relatively brighter host galaxies. This source provides evidence that black hole masses in the LRDs may be over-estimated by orders of magnitude -- the BH* is effectively dust-free contrary to the steep dust corrections applied while modeling LRDs, and the physics that gives rise to the complex line shapes and luminosities may deviate from assumptions underlying standard scaling relations.

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arXiv2024

Rich and diverse molecular gas environments of closely-separated dual quasars viewed by ALMA

We present a study of the molecular gas in five closely-spaced ($R_{\perp}<20$ kpc) dual quasars ($L_{\rm bol}\gtrsim10^{44}~\mathrm{erg~s}^{-1}$) at redshifts $0.4<z<0.8$ with the Atacama Large Millimeter/submillimeter Array. The dual quasar phase represents a distinctive stage during the interaction between two galaxies for investigating quasar fueling and feedback effects on the gas reservoir. The dual quasars were selected from the Sloan Digital Sky Survey and Subaru/Hyper Suprime-Cam Subaru Strategic Program, with confirmatory spectroscopic validation. Based on the detection of the CO J=2--1 emission line with Band 4, we derived key properties including CO luminosities, line widths, and molecular gas masses for these systems. Among the ten quasars of the five pairs, eight have line detections exceeding $5\sigma$. The detected sources prominently harbor substantial molecular gas reservoirs, with molecular gas masses ($M_{\text{molgas}}$) between $10^{9.6-10.5}~\mathrm{M_{\odot}}$, and molecular gas-to-stellar mass ratios ($\mu_{\text{molgas}}$) spanning $18-97\%$. The overall $\mu_{\text{molgas}}$ of these dual quasars agrees with that of inactive star-forming main-sequence galaxies at comparable redshifts, indicating no clear evidence of quenching. However, intriguing features in each individual system show possible evidence of AGN feedback, matter transfer, and compaction processes.

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arXiv2024

Evidence for Intrinsic X-ray Weakness Among Red Quasars at Cosmic Noon

Quasar feedback is a key ingredient in shaping galaxy evolution. A rare population of extremely red quasars (ERQs) at $z=2-3$ are often associated with high-velocity [O III]$\lambda5008$ outflows and may represent sites of strong feedback. In this paper, we present an X-ray study of 50 ERQs to investigate the link between the X-ray and outflow properties of these intriguing objects. Using hardness ratio analysis, we confirm that the ERQs are heavily obscured systems with gas column density reaching $N_\mathrm{H}=10^{23-24}\,\mathrm{cm^{-2}}$. We identify 20 X-ray-non-detected ERQs at high mid-infrared luminosities of $\nu L_\mathrm{\nu,6\mu m}\gtrsim3\times10^{46}\,\mathrm{erg\,s^{-1}}$. By stacking the X-ray observations, we find that the non-detected ERQs are on average underluminous in X-rays by a factor of $\sim10$ for their mid-infrared luminosities. We consider such X-ray weakness to be due to both heavy gas absorption and intrinsic factors. Moreover, we find that the X-ray-weak sources also display higher-velocity outflows. One option to explain this trend is that weaker X-rays facilitate more vigorous line-driven winds, which then accelerate the \oiii-emitting gas to kpc-scales. Alternatively, super-Eddington accretion could also lead to intrinsic X-ray weakness and more powerful continuum-driven outflow.

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arXiv2023

Outlier Detection in the DESI Bright Galaxy Survey

We present an unsupervised search for outliers in the Bright Galaxy Survey (BGS) dataset from the DESI Early Data Release. This analysis utilizes an autoencoder to compress galaxy spectra into a compact, redshift-invariant latent space, and a normalizing flow to identify low-probability objects. The most prominent outliers show distinctive spectral features such as irregular or double-peaked emission lines, or originate from galaxy mergers, blended sources, and rare quasar types, including one previously unknown Broad Absorption Line system. A significant portion of the BGS outliers are stars spectroscopically misclassified as galaxies. By building our own star model trained on spectra from the DESI Milky Way Survey, we have determined that the misclassification likely stems from the Principle Component Analysis of stars in the DESI pipeline. To aid follow-up studies, we make the full probability catalog of all BGS objects and our pre-trained models publicly available.

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arXiv2023

Little Red Dots: an abundant population of faint AGN at z~5 revealed by the EIGER and FRESCO JWST surveys

Characterising the prevalence and properties of faint active galactic nuclei (AGN) in the early Universe is key for understanding the formation of supermassive black holes (SMBHs) and determining their role in cosmic reionization. We perform a spectroscopic search for broad H$\alpha$ emitters at $z\approx4-6$ using deep JWST/NIRCam imaging and wide field slitless spectroscopy from the EIGER and FRESCO surveys. We identify 20 H$\alpha$ lines at $z=4.2-5.5$ that have broad components with line widths from $\sim1200-3700$ km s$^{-1}$, contributing $\sim30-90$ % of the total line flux. We interpret these broad components as being powered by accretion onto SMBHs with implied masses $\sim10^{7-8}$ M$_{\odot}$. In the UV luminosity range M$_{\rm UV}=-21$ to $-18$, we measure number densities of $\approx10^{-5}$ cMpc$^{-3}$. This is an order of magnitude higher than expected from extrapolating quasar UV luminosity functions. Yet, such AGN are found in only $<1$ % of star-forming galaxies at $z\sim5$. The SMBH mass function agrees with large cosmological simulations. In two objects we detect narrow red- and blue-shifted H$\alpha$ absorption indicative, respectively, of dense gas fueling SMBH growth and outflows. We may be witnessing early AGN feedback that will clear dust-free pathways through which more massive blue quasars are seen. We uncover a strong correlation between reddening and the fraction of total galaxy luminosity arising from faint AGN. This implies that early SMBH growth is highly obscured and that faint AGN are only minor contributors to cosmic reionization.

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arXiv2023

Varstrometry for Off-nucleus and Dual sub-Kpc AGN (VODKA): Investigating the Nature of J0823+2418 at $z=1.81$: a Likely Lensed Quasar

Dual quasars at small physical separations are an important precursor phase of galaxy mergers, ultimately leading to the coalescence of the two supermassive black holes. Starting from a sample of dual/lensed quasar candidates discovered using astrometric jitter in Gaia data, we present a pilot case study of one of the most promising yet puzzling candidate dual quasars at cosmic noon (z$\sim$1.8). Using multi-wavelength imaging and spectroscopy from X-ray to radio, we test whether the J0823+2418 system is two individual quasars in a bound pair at separation$\sim$0.64'', or instead a single quasar being gravitationally lensed by a foreground galaxy. We find consistent flux ratios ($\sim$1.25-1.45) between the two sources in optical, NIR, UV, and radio, and thus similar spectral energy distributions, suggesting a strong lensing scenario. However, differences in the radio spectral index, as well as changing X-ray fluxes, hint at either a dual quasar with otherwise nearly identical properties, or perhaps lensing-based time lag of $\sim$3 days paired with intrinsic variability. We find with lens mass modeling that the relative NIR positions and magnitudes of the two quasars and a marginally detected central galaxy are consistent with strong lensing. Archival SDSS spectra likewise suggest a foreground absorber via Mg II absorption lines. We conclude that J0823+2418 is likely a lensed quasar, and therefore that the VODKA sample contains a population of these lensed systems (perhaps as high as 50%) as well as dual quasars.

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arXiv2023

Evidence for heavy seed origin of early supermassive black holes from a z~10 X-ray quasar

Observations of quasars reveal that many supermassive black holes (BHs) were in place less than 700 million years after the Big Bang. However, the origin of the first BHs remains a mystery. Seeds of the first BHs are postulated to be either light (i.e., $10-100~\rm{M_{\odot}})$, remnants of the first stars or heavy (i.e., $10^4-10^5~\rm{M_{\odot}})$, originating from the direct collapse of gas clouds. Harnessing recent data from the Chandra X-ray Observatory, we report the detection of an X-ray-luminous massive BH in a gravitationally-lensed galaxy identified by JWST at $z\approx10.3$ behind the cluster lens Abell 2744. This heavily-obscured quasar with a bolometric luminosity of $L_{\rm bol}\sim5\times10^{45}~\rm{erg\ s^{-1}}$ harbors a $M_{\rm BH}\sim10^7-10^8~\rm{M_{\odot}}$ BH assuming accretion at the Eddington limit. This mass is comparable to the inferred stellar mass of its host galaxy, in contrast to what is found in the local Universe wherein the BH mass is $\sim0.1\%$ of the host galaxy's stellar mass. The combination of such a high BH mass and large BH-to-galaxy stellar mass ratio just $\sim$500 Myrs after the Big Bang was theoretically predicted and is consistent with a picture wherein BHs originated from heavy seeds.

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arXiv2023

The Spitzer Coverage of HSC-Deep with IRAC for Z studies (SHIRAZ) I: IRAC mosaics

We present new Spitzer Infrared Array Camera (IRAC) 3.6 and 4.5{\mu}m mosaics of three fields, E-COSMOS, DEEP2-F3, and ELAIS-N1. Our mosaics include both new IRAC observations as well as re-processed archival data in these fields. These fields are part of the HSC-Deep grizy survey and have a wealth of additional ancillary data. The addition of these new IRAC mosaics is critical in allowing for improved photometric redshifts and stellar population parameters at cosmic noon and earlier epochs. The total area mapped by this work is {\sim} 17 deg2 with a mean integration time of {\sim}1200s, providing a median 5{\sigma} depth of 23.7(23.3) at 3.6(4.5){\mu}m in AB. We perform SExtractor photometry both on the combined mosaics as well as the single-epoch mosaics taken {\sim}6 months apart. The resultant IRAC number counts show good agreement with previous studies. In combination with the wealth of existing and upcoming spectro-photometric data in these fields, our IRAC mosaics will enable a wide range of galactic evolution and AGN studies. With that goal in mind, we make the combined IRAC mosaics and coverage maps of these three fields publicly available. counts show good agreement with previous studies.

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arXiv2023

Morphological asymmetries of quasar host galaxies with Subaru Hyper Suprime-Cam

How does the host galaxy morphology influence a central quasar or vice versa? We address this question by measuring the asymmetries of 2424 SDSS quasar hosts at $0.2 45$). This then manifests itself into quasar hosts being more asymmetric, on average, when they harbor a more massive and highly accreting black hole. The merger fraction also positively correlates with $L_{\rm bol}$ and reaches up to 35\% for the most luminous. Compared to control galaxies, quasar hosts are marginally more asymmetric (excess of 0.017 in median at 9.4$\sigma$ level) and the merger fractions are similar ($\sim 16.5\%$). We quantify the dependence of asymmetry on optical band which demonstrates that mergers are more likely to be identified with the bluer bands and the correlation between $L_{\rm bol}$ and asymmetry is also stronger in such bands. We stress that the band dependence, indicative of a changing stellar population, is an important factor in considering the influence of mergers on AGN activity.

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arXiv2023

Beyond Ultra-diffuse Galaxies. II. Environmental Quenching of Mass-Size Outliers among the Satellites of Milky Way Analogs

Recent observations have reignited interest in a population of dwarf galaxies that are large and diffuse for their mass, often called ultra-diffuse galaxies. However, the origin and evolution of these mass-size outliers and the role of the environment are still unclear. Using the exquisitely deep and wide Hyper Suprime-Cam Strategic Survey images, we search for ultra-puffy galaxies, defined as being $1.5\sigma$ larger than the average size for their mass, around Milky Way-like galaxies. We present the sizes and radial distributions of mass-size outliers and derive their quenched fraction to explore the impact of the environment. Surprisingly, despite being outliers in size, the ultra-puffy galaxies have a similar quenched fraction as normal-sized satellites of Milky Way analogs in both observations and simulations, suggesting that quenching is not tied to being a mass-size outlier. The quenched fraction is higher for the ultra-puffy galaxies associated with redder hosts, as well as those that are closer to the host in projection. In contrast, the ultra-diffuse galaxies are overall redder and more quiescent compared with normal satellites. We show that the classic definition of ultra-diffuse galaxies is heavily weighted toward quenched galaxies and thus cannot be used for a study of quenching of mass-size outliers.

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arXiv2023

The eROSITA Final Equatorial-Depth Survey (eFEDS): Host-galaxy Demographics of X-ray AGNs with Subaru Hyper Suprime-Cam

We investigate the physical properties, such as star-forming activity, disk vs. bulge nature, galaxy size, and obscuration of 3796 X-ray selected AGNs at $0.2<z<0.8$ in the eFEDS field. Using Subaru Hyper Suprime-Cam imaging data in the $grizy$ bands for SRG/eROSITA-detected AGNs, we measure the structural parameters for AGN host galaxies by performing a 2D AGN-host image decomposition. We then conduct spectral energy distribution fitting to derive stellar mass and rest-frame colors for AGN hosts. We find that (1) AGNs can contribute significantly to the total optical light down to ${\rm log}\,L_{\rm X}\sim 42.5\ \rm erg\,s^{-1}$, thus ignoring the AGN component can significantly bias the structural measurements; (2) AGN hosts are predominately star-forming galaxies at ${\rm log}\,\mathcal{M}_\star \lesssim 11.3\ M_\odot$; (3) the bulk of AGNs (64%) reside in galaxies with significant stellar disks, while their host galaxies become increasingly bulge dominated and quiescent at ${\rm log}\,\mathcal{M}_\star \gtrsim 11.0\ M_\odot$; (4) the size-stellar mass relation of AGN hosts tends to lie between that of inactive star-forming and quiescent galaxies, suggesting that the physical mechanism responsible for building the central stellar density also efficiently fuel the black hole growth; (5) the hosts of X-ray unobscured AGNs are biased towards face-on systems and the average $E(B-V)/N_{\rm H}$ is similar to the galactic dust-to-gas ratio, suggesting that some of the obscuration of the nuclei could come from galaxy-scale gas and dust, which may partly account for (up to 30%) the deficiency of star-forming disks as host galaxies for the most massive AGNs. These results are consistent with a scenario in which the black hole and galaxy grow in mass while transform in structure and star-forming activity, as desired to establish the local scaling relations.

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arXiv2023

Observational Signatures of Carbon-Oxygen White Dwarf Merger Remnants

Many double white dwarf (WD) mergers likely do not lead to a prompt thermonuclear explosion. We investigate the prospects for observationally detecting the surviving remnants of such mergers, focusing on the case of mergers of double Carbon-Oxygen WDs. For $\sim 10^4$ yr, the merger remnant is observationally similar to an extreme AGB star evolving to become a massive WD. Identifying merger remnants is thus easiest in galaxies with high stellar masses (high WD merger rate) and low star formation rates (low birth rate of $\sim 6-10 \,{\rm M_{\odot}}$ stars). Photometrically identifying merger remnants is challenging even in these cases because the merger remnants appear similar to He stars and post-outburst classical novae. We propose that the most promising technique for discovering WD merger remnants is through their unusual surrounding photoionized nebulae. We use CLOUDY photoionization calculations to investigate their unique spectral features. Merger remnants should produce weak hydrogen lines and strong carbon and oxygen recombination and fine-structure lines in the UV, optical and IR. With narrow-band imaging or integral field spectrographs, we predict that multiple candidates are detectable in the bulge of M31, the outskirts of M87 and other nearby massive galaxies, and the Milky Way. Our models roughly reproduce the WISE nebula surrounding the Galactic WD merger candidate IRAS 00500+6713; we predict detectable [Ne\,VI] and [Mg\,VII] lines with JWST but that the mid-IR WISE emission is dominated by dust not fine-structure lines.

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arXiv2023

Autoencoding Galaxy Spectra II: Redshift Invariance and Outlier Detection

We present an unsupervised outlier detection method for galaxy spectra based on the spectrum autoencoder architecture spender, which reliably captures spectral features and provides highly realistic reconstructions for SDSS galaxy spectra. We interpret the sample density in the autoencoder latent space as a probability distribution, and identify outliers as low-probability objects with a normalizing flow. However, we found that the latent-space position is not, as expected from the architecture, redshift invariant, which introduces stochasticity into the latent space and the outlier detection method. We solve this problem by adding two novel loss terms during training, which explicitly link latent-space distances to data-space distances, preserving locality in the autoencoding process. Minimizing the additional losses leads to a redshift-invariant, non-degenerate latent space distribution with clear separations between common and anomalous data. We inspect the spectra with the lowest probability and find them to include blends with foreground stars, extremely reddened galaxies, galaxy pairs and triples, and stars that are misclassified as galaxies. We release the newly trained spender model and the latent-space probability for the entire SDSS-I galaxy sample to aid further investigations.

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arXiv2022

Autoencoding Galaxy Spectra I: Architecture

We introduce the neural network architecture SPENDER as a core differentiable building block for analyzing, representing, and creating galaxy spectra. It combines a convolutional encoder, which pays attention to up to 256 spectral features and compresses them into a low-dimensional latent space, with a decoder that generates a restframe representation, whose spectral range and resolution exceeds that of the observing instrument. The decoder is followed by explicit redshift, resampling, and convolution transformations to match the observations. The architecture takes galaxy spectra at arbitrary redshifts and is robust to glitches like residuals of the skyline subtraction, so that spectra from a large survey can be ingested directly without additional preprocessing. We demonstrate the performance of SPENDER by training on the entire spectroscopic galaxy sample of SDSS-II; show its ability to create highly accurate reconstructions with substantially reduced noise; perform deconvolution and oversampling for a super-resolution model that resolves the [OII] doublet; introduce a novel method to interpret attention weights as proxies for important spectral features; and infer the main degrees of freedom represented in the latent space. We conclude with a discussion of future improvements and applications.

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arXiv2022

Beyond Ultra-diffuse Galaxies. I. Mass--Size Outliers among the Satellites of Milky Way Analogs

Large diffuse galaxies are hard to find, but understanding the environments where they live, their numbers, and ultimately their origins, is of intense interest and importance for galaxy formation and evolution. Using Subaru's Hyper Suprime-Cam Strategic Survey Program, we perform a systematic search for low surface brightness galaxies and present novel and effective methods for detecting and modeling them. As a case study, we surveyed 922 Milky Way analogs in the nearby Universe ($0.01 < z < 0.04$) and build a large sample of satellite galaxies that are outliers in the mass-size relation. These ``ultra-puffy'' galaxies (UPGs), defined to be $1.5\sigma$ above the average mass-size relation, represent the tail of the satellite size distribution. We find that each MW analog hosts $N_{\rm UPG} = 0.31\pm 0.05$ ultra-puffy galaxies on average, which is consistent with but slightly lower than the observed abundance at this halo mass in the Local Volume. We also construct a sample of ultra-diffuse galaxies (UDGs) in MW analogs and find an abundance of $N_{\rm UDG} = 0.44\pm0.05$ per host. With literature results, we confirm that the UDG abundance scales with the host halo mass following a sublinear power law. We argue that our definition for ultra-puffy galaxies, which is based on the mass-size relation, is more physically-motivated than the common definition of ultra-diffuse galaxies, which depends on surface brightness and size cuts and thus yields different surface mass density cuts for quenched and star-forming galaxies.

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