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1. Photometric mass estimation and the stellar mass–halo mass relation for low mass galaxies

   https://doi.org/10.1093/mnras/stac3610  

   Zaritsky, Dennis; Behroozi, Peter (December 2022, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We present a photometric halo mass estimation technique for local galaxies that enables us to establish the stellar mass–halo mass (SMHM) relation down to stellar masses of 105 M⊙. We find no detectable differences among the SMHM relations of four local galaxy clusters or between the cluster and field relations and we find agreement with extrapolations of previous SMHM relations derived using abundance matching approaches. We fit a power law to our empirical SMHM relation and find that for adopted NFW dark matter profiles and for M* < 109 M⊙, the halo mass is Mh = 1010.35 ± 0.02(M*/108 M⊙)0.63 ± 0.02. The normalization of this relation is susceptible to systematic modelling errors that depend on the adopted dark matter potential and the quoted uncertainties refer to the uncertainties in the median relation. For galaxies with M* < 109 M⊙ that satisfy our selection criteria, the scatter about the fit in Mh, including uncertainties arising from our methodology, is 0.3 dex. Finally, we place lower luminosity Local Group galaxies on the SMHM relationship using the same technique, extending it to M* ∼ 103 M⊙ and suggest that some of these galaxies show evidence for additional mass interior to the effective radius beyond that provided by the standard dark matter profile. If this mass is in the form of a central black hole, the black hole masses are in the range of intermediate mass black holes, 10(5.7 ± 0.6) M⊙, which corresponds to masses of a few percent of Mh, well above values extrapolated from the relationships describing more massive galaxies. 

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2. Solitary waves in mass-in-mass lattices

   https://doi.org/10.1007/s00033-020-01384-8  

   Faver, Timothy E.; Goodman, Roy H.; Wright, J. Douglas (December 2020, Zeitschrift für angewandte Mathematik und Physik)

   null (Ed.)
3. Mass, Capacitary Functions, and the Mass-to-Capacity Ratio

   https://doi.org/10.1007/s42543-023-00071-7  

   Miao, Pengzi (June 2023, Peking Mathematical Journal)
4. Satellite mass functions and the faint end of the galaxy mass–halo mass relation in LCDM

   https://doi.org/10.1093/mnras/stac2057  

   Santos-Santos, Isabel M. E.; Sales, Laura V.; Fattahi, Azadeh; Navarro, Julio F. (July 2022, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT The abundance of the faintest galaxies provides insight into the nature of dark matter and the process of dwarf galaxy formation. In the LCDM scenario, low-mass haloes are so numerous that the efficiency of dwarf formation must decline sharply with decreasing halo mass in order to accommodate the relative scarcity of observed dwarfs and satellites in the Local Group. The nature of this decline contains important clues to the mechanisms regulating the onset of galaxy formation in the faintest systems. We explore here two possible models for the stellar mass (M*)–halo mass (M200) relation at the faint end, motivated by some of the latest LCDM cosmological hydrodynamical simulations. One model includes a sharp mass threshold below which no luminous galaxies form, as expected if galaxy formation proceeds only in systems above the hydrogen-cooling limit. In the second model, M* scales as a steep power law of M200 with no explicit cut-off, as suggested by recent semi-analytical work. Although both models predict satellite numbers around Milky Way-like galaxies consistent with current observations, they predict vastly different numbers of ultrafaint dwarfs and of satellites around isolated dwarf galaxies. Our results illustrate how the satellite mass function around dwarfs may be used to probe the M*–M200 relation at the faint end and to elucidate the mechanisms that determine which low-mass haloes ‘light up’ or remain dark in the LCDM scenario. 

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5. Galaxy cluster matter profiles: I. Self-similarity, mass calibration, and observable-mass relation validation employing cluster mass posteriors

   https://doi.org/10.1051/0004-6361/202451516  

   Singh, A; Mohr, J J; Davies, C T; Bocquet, S; Grandis, S; Klein, M; Marshall, J L; Aguena, M; Allam, S S; Alves, O; et al (March 2025, Astronomy & Astrophysics)

   We present a study of the weak lensing inferred matter profiles ΔΣ(R) of 698 South Pole Telescope (SPT) thermal Sunyaev-Zel’dovich effect (tSZE) selected and MCMF optically confirmed galaxy clusters in the redshift range 0.25 <  z <  0.94 that have associated weak gravitational lensing shear profiles from the Dark Energy Survey (DES). Rescaling these profiles to account for the mass dependent size and the redshift dependent density produces average rescaled matter profiles ΔΣ(R/R_200c)/(ρ_critR_200c) with a lower dispersion than the unscaled ΔΣ(R) versions, indicating a significant degree of self-similarity. Galaxy clusters from hydrodynamical simulations also exhibit matter profiles that suggest a high degree of self-similarity, with RMS variation among the average rescaled matter profiles with redshift and mass falling by a factor of approximately six and 23, respectively, compared to the unscaled average matter profiles. We employed this regularity in a new Bayesian method for weak lensing mass calibration that employs the so-called cluster mass posteriorP(M₂₀₀|ζ̂, λ̂,z), which describes the individual cluster masses given their tSZE (ζ̂) and optical (λ̂,z) observables. This method enables simultaneous constraints on richnessλ-mass and tSZE detection significanceζ-mass relations using average rescaled cluster matter profiles. We validated the method using realistic mock datasets and present observable-mass relation constraints for the SPT×DES sample, where we constrained the amplitude, mass trend, redshift trend, and intrinsic scatter. Our observable-mass relation results are in agreement with the mass calibration derived from the recent cosmological analysis of the SPT×DES data based on a cluster-by-cluster lensing calibration. Our new mass calibration technique offers a higher efficiency when compared to the single cluster calibration technique. We present new validation tests of the observable-mass relation that indicate the underlying power-law form and scatter are adequate to describe the real cluster sample but that also suggest a redshift variation in the intrinsic scatter of theλ-mass relation may offer a better description. In addition, the average rescaled matter profiles offer high signal-to-noise ratio (S/N) constraints on the shape of real cluster matter profiles, which are in good agreement with available hydrodynamical ΛCDM simulations. This high S/N profile contains information about baryon feedback, the collisional nature of dark matter, and potential deviations from general relativity. 

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