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Revisit NGC 5466 tidal stream with Gaia , SDSS/SEGUE, and LAMOST

ABSTRACT By mining the data from Gaia Early Data Release 3, Sloan Digital Sky Survey/Sloan Extension for Galactic Understanding and Exploration Data Release 16, and Large Sky Area Multi-Object Fiber Spectroscopic Telescope Data Release 8, 11 member stars of the NGC 5466 tidal stream are detected and 7 of them are newly identified. To reject contaminators, a variety of cuts are applied in sky position, colour–magnitude diagram, metallicity, proper motion, and radial velocity. We compare our data to a mock stream generated by modelling the cluster’s disruption under a smooth Galactic potential plus the Large Magellanic Cloud (LMC). The concordant trends in phase space between the model and observations imply that the stream might have been perturbed by the LMC. The two most distant stars among the 11 detected members trace the stream’s length to 60° of sky, supporting and extending the previous length of 45°. Given that NGC 5466 is so distant and potentially has a longer tail than previously thought, we expect that the NGC 5466 tidal stream could be a useful tool in constraining the Milky Way gravitational field.

79 ASTRONOMY AND ASTROPHYSICS↗

DESI Early Data Release Milky Way Survey value-added catalogue

We present the stellar value-added catalogue based on the Dark Energy Spectroscopic Instrument (DESI) Early Data Release. The catalogue contains radial velocity and stellar parameter measurements for $\simeq$ 400 000 unique stars observed during commissioning and survey validation by DESI. These observations were made under conditions similar to the Milky Way Survey (MWS) currently carried out by DESI but also include multiple specially targeted fields, such as those containing well-studied dwarf galaxies and stellar streams. The majority of observed stars have $16\lt r\lt 20$ with a median signal-to-noise ratio in the spectra of $\sim$ 20. In the paper, we describe the structure of the catalogue, give an overview of different target classes observed, as well as provide recipes for selecting clean stellar samples. We validate the catalogue using external high-resolution measurements and show that radial velocities, surface gravities, and iron abundances determined by DESI are accurate to 1 km s −1 , 0.3 dex, and $\sim$ 0.15 dex respectively. We also demonstrate possible uses of the catalogue for chemo-dynamical studies of the Milky Way stellar halo and Draco dwarf spheroidal. The value-added catalogue described in this paper is the very first DESI MWS catalogue. The next DESI data release, expected in less than a year, will add the data from the first year of DESI survey operations and will contain approximately 4 million stars, along with significant processing improvements.

Galaxy: general↗

Exploring the interaction between the MW and LMC with a large sample of blue horizontal branch stars from the DESI survey

The Large Magellanic Cloud (LMC) is a Milky Way (MW) satellite that is massive enough to gravitationally attract the MW disc and inner halo, causing significant motion of the inner MW with respect to the outer halo. In this work, we probe this interaction by constructing a sample of 9866 blue horizontal branch (BHB) stars with radial velocities from the DESI spectroscopic survey out to 120 kpc from the Galactic centre. This is the largest spectroscopic set of BHB stars in the literature to date, and it contains four times more stars with Galactocentric distances beyond 50 kpc than previous BHB catalogues. Using the DESI BHB sample combined with SDSS BHBs, we measure the bulk radial velocity of stars in the outer halo and observe that the velocity in the Southern Galactic hemisphere is different by 3.7σ from the North. Modelling the projected velocity field shows that its dipole component is directed at a point 22 deg away from the LMC along its orbit, which we interpret as the travel direction of the inner MW. The velocity field includes a monopole term that is –24 km s –1 ⁠, which we refer to as compression velocity. This velocity is significantly larger than predicted by the current models of the MW and LMC interaction. This work uses DESI data from its first 2 yr of observations, but we expect that with upcoming DESI data releases, the sample of BHB stars will increase and our ability to measure the MW–LMC interaction will improve significantly.

Galaxy: evolution↗

Galactic echoes

Gaia has revealed a variety of substructures in the phase space of stars in the Solar neighbourhood, including the vertical ‘Snail’ $(z, v_z)$ in space. Such substructures are often interpreted as the incompletely phase-mixed response of the disc stars to a single perturbation, such as an impulsive encounter with a satellite galaxy. In this paper, we consider the possibility that such structures contain manifestations of phase-space echoes. First established in plasma physics in the 1960s, echoes arise when a collisionless system is perturbed twice: the macroscopic responses to both perturbations mix to small scales in phase space, whereupon they couple non-linearly, producing a third macroscopic ‘echo’ response without the need for a third perturbation. We derive the galactic analogue of the plasma echo theory using angle-action variables and apply it to a one-dimensional model of vertical motion in the Milky Way. We verify the predicted echo behaviour using idealized test particle simulations, both with and without the inclusion of diffusion through orbital scattering off molecular clouds. While we conclude that the Gaia Snail itself is unlikely a (pure) echo effect, the basic physics we uncover is sufficiently generic that we expect phase-space echoes to be common in disc galaxies.

Galaxy: evolution↗

The Arecibo Galaxy Environment Survey. XII. Optically Dark H i Clouds in the Leo I Group

Using data from the Arecibo Galaxy Environment Survey, we report the discovery of five H i clouds in the Leo I group without detected optical counterparts. Three of the clouds are found midway between M96 and M95, one is only from the southeast side of the well-known Leo Ring, and the fifth is relatively isolated. H i masses range from 2.6 × 10 6 M ⊙ to 9.0 × 10 6 M ⊙ , and velocity widths (W50) range from 16 to 42 km s -1 . Although a tidal origin is the most obvious explanation, this formation mechanism faces several challenges. For the most isolated cloud, the difficulties are its distance from neighboring galaxies and the lack of any signs of disturbance in the H i disks of those systems. Some of the clouds also appear to follow the baryonic Tully–Fisher relation between mass and velocity width for normal, stable galaxies, which is not expected if they are tidal in origin. Three clouds are found between M96 and M95 that have no optical counterparts but have otherwise similar properties and locations to the optically detected galaxy LeG 13. While overall we favor a tidal debris scenario to explain the clouds, we cannot rule out a primordial origin. If the clouds were produced in the same event that gave rise to the Leo Ring, they may provide important constraints on any model attempting to explain that structure.

79 ASTRONOMY AND ASTROPHYSICS↗

SDSS-IV MaNGA: Understanding Ionized Gas Turbulence Using Integral Field Spectroscopy of 4500 Star-forming Disk Galaxies

The Sloan Digital Sky Survey MaNGA program has now obtained integral field spectroscopy for over 10,000 galaxies in the nearby universe. We use the final MaNGA data release DR17 to study the correlation between ionized gas velocity dispersion and galactic star formation rate, finding a tight correlation in which σ Hα from galactic H ιι regions increases significantly from ~18–30 km s –1 , broadly in keeping with previous studies. In contrast, σ Hα from diffuse ionized gas increases more rapidly from 20–60 km s –1 . Using the statistical power of MaNGA, we investigate these correlations in greater detail using multiple emission lines and determine that the observed correlation of σ Hα with local star formation rate surface density is driven primarily by the global relation of increasing velocity dispersion at higher total star formation rate, as are apparent correlations with stellar mass. Assuming H ιι region models consistent with our finding that σ [O III] < σ Hα < σ [O I] , we estimate the velocity dispersion of the molecular gas in which the individual H ιι regions are embedded, finding values σ Mol = 5–30 km s –1 consistent with ALMA observations in a similar mass range. Finally, we use variations in the relation with inclination and disk azimuthal angle to constrain the velocity dispersion ellipsoid of the ionized gas σ z /σ r = 0.84 ± 0.03 and σ Φ /σ r = 0.91 ± 0.03, similar to that of young stars in the Galactic disk. Our results are most consistent with the theoretical models in which turbulence in modern galactic disks is driven primarily by star formation feedback.

79 ASTRONOMY AND ASTROPHYSICS↗

The AGORA High-resolution Galaxy Simulations Comparison Project. V. Satellite Galaxy Populations in a Cosmological Zoom-in Simulation of a Milky Way–Mass Halo

We analyze and compare the satellite halo populations at z ~ 2 in the high-resolution cosmological zoom-in simulations of a 10 12 M ⊙ target halo (z = 0 mass) carried out on eight widely used astrophysical simulation codes (Art-I, Enzo, Ramses, Changa, Gadget-3, Gear, Arepo-t, and Gizmo) for the AGORA High-resolution Galaxy Simulations Comparison Project. We use slightly different redshift epochs near z = 2 for each code (hereafter "z ~ 2") at which the eight simulations are in the same stage in the target halo's merger history. After identifying the matched pairs of halos between the CosmoRun simulations and the DMO simulations, we discover that each CosmoRun halo tends to be less massive than its DMO counterpart. When we consider only the halos containing stellar particles at z ~ 2, the number of satellite galaxies is significantly fewer than that of dark matter halos in all participating AGORA simulations and is comparable to the number of present-day satellites near the Milky Way or M31. The so-called "missing satellite problem" is fully resolved across all participating codes simply by implementing the common baryonic physics adopted in AGORA and the stellar feedback prescription commonly used in each code, with sufficient numerical resolution (≲100 proper pc at z = 2). We also compare other properties such as the stellar mass–halo mass relation and the mass–metallicity relation. Our work highlights the value of comparison studies such as AGORA, where outstanding problems in galaxy formation theory are studied simultaneously on multiple numerical platforms.

79 ASTRONOMY AND ASTROPHYSICS↗

Different Formation Scenarios for Counterrotating Stellar Disks in Nearby Galaxies

Using the integral field unit data from the Mapping Nearby Galaxies at Apache Point Observatory survey, we select a sample of 101 galaxies with counterrotating stellar disks and regularly rotating ionized gas disks. We classify the 101 galaxies into four types based on the features of their stellar velocity fields. The relative fractions and stellar population age radial gradients of the four types are different in the blue cloud, green valley, and red sequence populations. We suggest different formation scenarios for counterrotating stellar disks; the key factors in the formation of counterrotating stellar disks include (1) the abundance of preexisting gas in the progenitor and (2) the efficiency in angular momentum consumption.

79 ASTRONOMY AND ASTROPHYSICS↗

A New Member of the Milky Way’s Family Tree: Characterizing the Pontus Merger of Our Galaxy

We study the Pontus structure—a recently discovered merger that brought in ~7 globular clusters in the course of the hierarchical buildup of the Milky Way’s halo. Here, we analyze the stellar population of Pontus and examine (1) its phase-space distribution using the ESA/Gaia data set, (2) its metallicity and chemical abundances (i.e., [Fe/H], [ α /Fe], [Mg/Fe], and [Al/Fe]) using the spectroscopic catalog of APOGEE DR17, and (3) the color–magnitude diagram that shows interesting features, including a possibly double horizontal branch and a small population of blue stragglers. In sum, the Pontus stars show some unique properties that suggest they likely originated from the merging of an independent satellite galaxy; however, future analysis will shed more light on the true nature of this structure. This chemodynamical analysis of Pontus stars is another step forward in our bigger quest to characterize all the merging events of our Milky Way.

79 ASTRONOMY AND ASTROPHYSICS↗

Rotation curves and scaling relations of extremely massive spiral galaxies

We study the kinematics and scaling relations of a sample of 43 giant spiral galaxies that have stellar masses exceeding $10^{11} \, {\rm M}_\odot$ and optical discs up to 80 kpc in radius. We use a hybrid 3D–1D approach to fit 3D kinematic models to long-slit observations of the H α-$\rm{[N\, \small {II}]}$ emission lines and we obtain robust rotation curves of these massive systems. We find that all galaxies in our sample seem to reach a flat part of the rotation curve within the outermost optical radius. We use the derived kinematics to study the high-mass end of the two most important scaling relations for spiral galaxies: the stellar/baryonic mass Tully–Fisher relation and the Fall (mass-angular momentum) relation. All galaxies in our sample, with the possible exception of the two fastest rotators, lie comfortably on both these scaling relations determined at lower masses, without any evident break or bend at the high-mass regime. When we combine our high-mass sample with low-mass data from the Spitzer Photometry & Accurate Rotation Curves catalogue, we find a slope of α = 4.25 ± 0.19 for the stellar Tully–Fisher relation and a slope of γ = 0.64 ± 0.11 for the Fall relation. Our results indicate that most, if not all, of these rare, giant spiral galaxies are scaled up versions of less massive discs and that spiral galaxies are a self-similar population of objects up to the very high-mass end.

79 ASTRONOMY AND ASTROPHYSICS↗

The Velocity Map Asymmetry of Ionized Gas in MaNGA. I. The Catalog and General Properties

The SDSS-IV MaNGA survey has measured two-dimensional maps of emission-line velocities for a statistically powerful sample of nearby galaxies. The asymmetric features of these kinematics maps reflect the nonrotational component of a galaxy’s internal motion of ionized gas. In this study, we present a catalog of kinematic asymmetry measurements of the H α velocity map of a sample of 5353 MaNGA galaxies. Based on this catalog, we find that “special” galaxies (e.g., merging galaxies, barred galaxies, and active galactic nucleus host galaxies) contain more galaxies with highly asymmetric velocity maps. However, we notice that more than half of galaxies with high kinematic asymmetry in our sample are quite “regular.” For those “regular” galaxies, kinematic asymmetry shows a significant anticorrelation with stellar mass at log M * < 9.7 , while such a trend becomes very weak at log M * > 9.7 . Moreover, at a given stellar mass, the kinematic asymmetry shows weak correlations with photometric morphology, star formation rate, and environment, while it is independent of H i gas content. We also have quantified the observational effects in the kinematic asymmetry measurement. We find that both the signal-to-noise ratio of H α flux and disk inclination angle contribute to the measures of kinematic asymmetry, while the physical spatial resolution is an irrelevant factor inside the MaNGA redshift coverage.

79 ASTRONOMY AND ASTROPHYSICS↗

Different higher order kinematics between star-forming and quiescent galaxies based on the SAMI, MAGPI, and LEGA-C surveys

We present the first statistical study of spatially integrated non-Gaussian stellar kinematics spanning 7 Gyr in cosmic time. We use deep, rest-frame optical spectroscopy of massive galaxies (stellar mass $M_\star \gt 10^{10.5} \, \mathrm{M_\odot }$) at redshifts z = 0.05, 0.3, and 0.8 from the SAMI, MAGPI, and LEGA-C surveys, to measure the excess kurtosis h 4 of the stellar velocity distribution, the latter parametrized as a Gauss–Hermite series. We find that at all redshifts where we have large enough samples, h 4 anticorrelates with the ratio between rotation and dispersion, highlighting the physical connection between these two kinematic observables. In addition, and independently from the anticorrelation with rotation-to-dispersion ratio, we also find a correlation between h 4 and M ⋆ , potentially connected to the assembly history of galaxies. In contrast, after controlling for mass, we find no evidence of independent correlation between h 4 and aperture velocity dispersion or galaxy size. These results hold for both star-forming and quiescent galaxies. For quiescent galaxies, h 4 also correlates with projected shape, even after controlling for the rotation-to-dispersion ratio. At any given redshift, star-forming galaxies have lower h 4 compared to quiescent galaxies, highlighting the link between kinematic structure and star-forming activity.

79 ASTRONOMY AND ASTROPHYSICS↗

The dynamical state of RXCJ1230.7+3439: A multi-substructured merging galaxy cluster

We analyse the kinematical and dynamical state of the galaxy cluster RXCJ1230.7+3439 (RXCJ1230), at $z$ = 0.332 using 93 new spectroscopic redshifts of galaxies acquired at the Telescopio Nazionale Galileo and from SDSS DR16 public data. We study the density galaxy distribution retrieved from photometric SDSS multiband data and find that RXCJ1230 appears as a clearly isolated peak in the redshift space, with a global line-of-sight (LOS) velocity dispersion of $σ$ v = 1004 -122 +147 km s -1 . Several tests applied to the spatial and velocity distributions reveal that RXCJ1230 is a complex system with the presence of three subclusters, located to the southwest, east, and south with respect to the main body of the cluster, containing several bright galaxies (BGs) in their respective cores. Our analyses confirm that the three substructures are in a pre-merger phase, where the main interaction takes place with the southwest subclump, almost in the plane of the sky. We compute a velocity dispersion of $σ$ v ~ 1000 and $σ$ v ~ 800 km s -1 for the main cluster and the southwest substructure, respectively. The central main body and southwest substructure differ by ~870 km s -1 in the LOS velocity. From these data, we estimate a dynamical mass of $M$ 200 = 9.0 ± 1.5 × 1014 $M$ ⊙ and 4.4 ± 3.3 × 1014 $M$ ⊙ for the RXCJ1230 main body and southwest clump, respectively, which reveals that the cluster will undergo a merger characterised by a 2:1 mass ratio impact. We solve a two-body problem for this interaction and find that the most likely solution suggests that the merging axis lies ~17° from the plane of the sky and the subcluster will fully interact in ~0.3 Gyr. However, a slight excess in the X-ray temperature observed in the southwest clump confirms a certain degree of interaction already. The comparison between the dynamical masses and those derived from X-ray data reveals good agreement within errors (differences ~15%), which suggests that the innermost regions (< r 500 ) of the galaxy clumps are almost in hydrostatical equilibrium. In summary, RXCJ1230 is a young but also massive cluster in a pre-merging phase accreting other galaxy systems from its environment.

79 ASTRONOMY AND ASTROPHYSICS↗

The Atacama Cosmology Telescope: Detection of the pairwise kinematic Sunyaev-Zel’dovich effect with SDSS DR15 galaxies

We present a 5.4$\sigma$ detection of the pairwise kinematic Sunyaev-Zel'dovich (kSZ) effect using Atacama Cosmology Telescope (ACT) and $\it{Planck}$ CMB observations in combination with Luminous Red Galaxy samples from the Sloan Digital Sky Survey (SDSS) DR15 catalog. Results are obtained using three ACT CMB maps: co-added 150 GHz and 98 GHz maps, combining observations from 2008-2018 (ACT DR5), which overlap with SDSS DR15 over 3,700 sq. deg., and a component-separated map using night-time only observations from 2014-2015 (ACT DR4), overlapping with SDSS DR15 over 2,089 sq. deg. Comparisons of the results from these three maps provide consistency checks in relation to potential frequency-dependent foreground contamination. A total of 343,647 galaxies are used as tracers to identify and locate galaxy groups and clusters from which the kSZ signal is extracted using aperture photometry. We consider the impact of various aperture photometry assumptions and covariance estimation methods on the signal extraction. Theoretical predictions of the pairwise velocities are used to obtain best-fit, mass-averaged, optical depth estimates for each of five luminosity-selected tracer samples. A comparison of the kSZ-derived optical depth measurements obtained here to those derived from the thermal SZ effect for the same sample is presented in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗

Galaxy properties as revealed by MaNGA – III. Kinematic profiles and stellar population gradients in S0s

ABSTRACT This is the third paper of a series where we study the stellar population gradients (SP; ages, metallicities, α-element abundance ratios, and stellar initial mass functions) of early-type galaxies (ETGs) at $z$ ≤ 0.08 from the Mapping Nearby Galaxies at APO Data Release 15 (MaNGA-DR15) survey. In this work, we focus on the S0 population and quantify how the SP varies across the population as well as with galactocentric distance. We do this by measuring Lick indices and comparing them to SP synthesis models. This requires spectra with high signal-to-noise ratio which we achieve by stacking in bins of luminosity (Lr) and central velocity dispersion (σ0). We find that: (1) there is a bimodality in the S0 population: S0s more massive than $3\times 10^{10}\, \mathrm{M}_\odot$ show stronger velocity dispersion and age gradients (age and σr decrease outwards) but little or no metallicity gradient, while the less massive ones present relatively flat age and velocity dispersion profiles, but a significant metallicity gradient (i.e. [M/H] decreases outwards). Above $2\times 10^{11}\, \mathrm{M}_\odot$, the number of S0s drops sharply. These two mass scales are also where global scaling relations of ETGs change slope. (2) S0s have steeper velocity dispersion profiles than fast-rotating elliptical galaxies (E-FRs) of the same luminosity and velocity dispersion. The kinematic profiles and SP gradients of E-FRs are both more similar to those of slow-rotating ellipticals (E-SRs) than to S0s, suggesting that E-FRs are not simply S0s viewed face-on. (3) At fixed σ0, more luminous S0s and E-FRs are younger, more metal rich and less α-enhanced. Evidently for these galaxies, the usual statement that ‘massive galaxies are older’ is not true if σ0 is held fixed.

Domínguez Sánchez, H.↗

Barless flocculent galaxies: a dynamic puzzle

We draw attention to the bright galaxies that do not show a bar in their structure but have a flocculent spiral structure. Using the THINGS and HERACLES kinematic data for four barless galaxies (NGC 2841, NGC 3512, NGC 5055, NGC 7331), we built their mass models including dark haloes. We concluded that the fraction of the dark matter does not exceed 50 per cent within the optical radii of the galaxies. This is too little to explain the lack of a bar in these galaxies. In an attempt to understand the featureless structure of these galaxies, we constructed several N-body models with an initially reduced content of dark matter. We concluded that, in addition to the low mass of the dark halo, the decisive factor that leads to a barless disc is the start from an initially unstable state. An isolated dynamically cold disc (with the Toomre parameter Q < 0.5) settled into rotational equilibrium passes through the short stage of violent instability with fragmentation and formation of stellar clumps. After that, it evolves passively and ends up with a featureless structure. We assume that the barless flocculent galaxies studied in this work may be descendants of galaxies at high redshifts with rotation curves that are consistent with the high mass fraction of baryons relative to the total dark matter halo.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing cosmic velocities with the pairwise kinematic Sunyaev-Zel’dovich signal in DESI Bright Galaxy Sample DR1 and ACT DR6

We present a measurement of the pairwise kinematic Sunyaev-Zel’dovich (kSZ) signal using the Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Sample (BGS) Data Release 1 (DR1) galaxy sample overlapping with the Atacama Cosmology Telescope (ACT) CMB temperature map. Our analysis makes use of 1.6 million galaxies with stellar masses log⁡ 𝑀 ⋆ /𝑀 ⊙ >10, and we explore measurements across a range of aperture sizes (2.1′ <𝜃 ap <3.5′) and stellar mass selections. This statistic directly probes the velocity field of the large-scale structure, a unique observable of cosmic dynamics and modified gravity. In particular, at low redshifts, this quantity is especially interesting, as deviations from General Relativity are expected to be largest. Notably, our result represents the highest-significance low-redshift (𝑧 ∼ 0.3) detection of the kSZ pairwise effect yet. In our most optimal configuration (𝜃 ap =3.3′, log⁡ 𝑀 ⋆ >11), we achieve a 5⁢𝜎 detection. Assuming that an estimate of the optical depth and galaxy bias of the sample exists via e.g., external observables, this measurement constrains the fundamental cosmological combination 𝐻 0 ⁡𝑓⁡𝜎$^2_8$. A key challenge is the degeneracy with the galaxy optical depth. We address this by combining CMB lensing, which allows us to infer the halo mass and galaxy population properties, with hydrodynamical simulation estimates of the mean optical depth, $\bar{𝜏}$ . We stress that this is a proof-of-concept analysis; with BGS DR2 data we expect to improve the statistical precision by roughly a factor of two, paving the way toward robust tests of modified gravity with kSZ-informed velocity-field measurements at low redshift.

Hadzhiyska, Boryana [Institute of Astronomy; Kavli↗

The Extended Baryonic Tully–Fisher Relation for SDSS MaNGA Galaxies

The baryonic Tully–Fisher relation (BTFR), a relationship between the rotational velocity and baryonic mass in spiral galaxies, probes the relative content of baryonic and total mass in galaxies and thus provides a good test of dark matter content in galaxies. Using Hα kinematics, we model the rotation curves of the Sloan Digital Sky Survey MaNGA DR17 spiral galaxies. To extend the BTFR to higher masses with elliptical galaxies, we estimate their total masses from their stellar velocity dispersions using the virial theorem and define the effective rotational velocity as the velocity a rotation-supported galaxy would exhibit given this mass. The baryonic mass of spiral galaxies is composed of stellar, H I , H 2 , and He mass, while only the stellar mass is used for the baryonic content of ellipticals. We construct joint BTFRs for 5743 MaNGA spiral and elliptical galaxies, TNG100 simulated galaxies with baryonic masses greater than 10 9 M ⊙ , and a cross-matched subsample between these two datasets (3149 spiral and 1423 elliptical galaxies). For the cross-matched subsample, we find agreement in the slopes between observed and simulated galaxies. We find a slope of $3.8{6}_{-0.62}^{+0.92}$ for the full MaNGA sample, which agrees well with the slope of 4.0 predicted by MOND and the fitted slope of $3.5{8}_{-0.38}^{+0.48}$ for the TNG100 galaxies. We find that a sample of lower-mass galaxies is necessary to differentiate between the two models.

79 ASTRONOMY AND ASTROPHYSICS↗