Luminous Mass Research Articles

The Physical Origin of the Stellar Initial Mass Function

Stars are among the most fundamental structures of our Universe. They comprise most of the baryonic and luminous mass of galaxies; synthesize heavy elements; and inject mass, momentum, and energy into the interstellar medium. They are also home to the planets. Because stellar properties are primarily decided by their mass, the so-called stellar initial mass function (IMF) is critical to the structuring of our Universe. We review the various physical processes and theories that have been put forward as well as the numerical simulations that have been carried out to explain the origin of the stellar IMF. Key messages from this review include the following: ▪Gravity and turbulence most likely determine the power-law, high-mass part of the IMF.▪Depending of the Mach number and the density distribution, several regimes are possible, including ΓIMF ≃ 0, −0.8, −1, or −1.3, where dN/d log M ∝ M ΓIMF . These regimes are likely universal; however, the transition between these regimes is not.▪Protostellar jets can play a regulating influence on the IMF by injecting momentum into collapsing clumps and unbinding gas.▪The peak of the IMF may be a consequence of dust opacity and molecular hydrogen physics at the origin of the first hydrostatic core. This depends weakly on large-scale environmental conditions such as radiation, magnetic field, turbulence, or metallicity. This likely constitutes one reason for the relative universality of the IMF.

Giant molecular cloud G18.1-0.3+51 associated with H ii regions and supernova remnant in the 3-kpc expanding ring

ABSTRACT Analysing the high-resolution CO line survey of the Galactic plane with the Nobeyama 45-m telescope (FUGIN), we show that the star-forming complex G18.15-0.30+51 (G18) at radial velocity of 51 km s−1 is a tight triple association of a giant molecular cloud (GMC), H ii regions, and a supernova remnant (SNR). The radial velocity of G18 allows three possible kinematic distances of d = 3.9 ± 0.2 kpc for near solution or 12 ± 0.2 kpc for far solution, if we assume circular Galactic rotation, or d = 6.1 ± 0.1 kpc, if it is moving with the 3-kpc expanding ring at an expanding velocity of 50 km s−1. The H i line absorption of radio continuum from the H ii region constrains the distance to 5.6 ≲ dSNR ≤ 7.6 kpc. The Σ−D (radio brightness–diameter) relation yields the distance to the SNR of $d_{\rm SNR}=10.1^{+11.5}_{-4.7}$ kpc, allowing for a minimum distance of 5.4 kpc. From these, we uniquely determined the distance of G18 to be 6.07 ± 0.13 kpc in the 3-kpc expanding ring with the SNR being physically associated. The molecular mass of the GMC is estimated to be Mmol ∼ 3 × 105 M⊙. The ratio of virial to luminous molecular masses is greater than unity in the central region and decreases outward to ≲0.2 at the cloud edge, indicating that the central region is dynamic, while the entire cloud is stable. We discuss the origin of the G18 triple system and propose a sustainable GMC model with continuous star formation.

Modeling lens potentials with continuous neural fields in galaxy-scale strong lenses

Strong gravitational lensing is a unique observational tool for studying the dark and luminous mass distribution both within and between galaxies. Given the presence of substructures, current strong lensing observations demand more complex mass models than smooth analytical profiles, such as power-law ellipsoids. In this work, we introduce a continuous neural field to predict the lensing potential at any position throughout the image plane, allowing for a nearly model-independent description of the lensing mass. We applied our method to simulated Hubble Space Telescope imaging data containing different types of perturbations to a smooth mass distribution: a localized dark subhalo, a population of subhalos, and an external shear perturbation. Assuming knowledge of the source surface brightness, we used the continuous neural field to model either the perturbations alone or the full lensing potential. In both cases, the resulting model was able to fit the imaging data, and we were able to accurately recover the properties of both the smooth potential and the perturbations. Unlike many other deep-learning methods, ours explicitly retains lensing physics (i.e., the lens equation) and introduces high flexibility in the model only where required, namely, in the lens potential. Moreover, the neural network does not require pretraining on large sets of labeled data and predicts the potential from the single observed lensing image. Our model is implemented in the fully differentiable lens modeling code HERCULENS.

An infrared transient from a star engulfing a planet.

Planets with short orbital periods (roughly under 10 days) are common around stars like the Sun1,2. Stars expand as they evolve and thus we expect their close planetary companions to be engulfed, possibly powering luminous mass ejections from the host star3-5. However, this phase has never been directly observed. Here we report observations of ZTF SLRN-2020, a short-lived optical outburst in the Galactic disk accompanied by bright and long-lived infrared emission. The resulting light curve and spectra share striking similarities with those of red novae6,7-a class of eruptions now confirmed8 to arise from mergers of binary stars. Its exceptionally low optical luminosity (approximately 1035 erg s-1) and radiated energy (approximately 6.5 × 1041 erg) point to the engulfment of a planet of fewer than roughly ten Jupiter masses by its Sun-like host star. We estimate the Galactic rate of such subluminous red novae to be roughly between 0.1 and several per year. Future Galactic plane surveys should routinely identify these, showing the demographics of planetary engulfment and the ultimate fate of planets in the inner Solar System.

Mass distribution in spiral galaxies

The study of kinematics and dynamics is of great importance in the study of spiral galaxies, they contributed to the proof of the existence of exotic dark matter (not baryonic), matter that interacts gravitationally, but does not interact electromagnetically with ordinary matter, that is, it does not emit light. The present research started from the bibliographic review of the galaxies NGC 3351 and NGC 3938. Followed by obtaining data from the Hα emission line and velocity maps from observations of the Hα line, made with a Fabry-Perot scanning, emitted by ionized gas (CeSAM / LAM database). A rotation curve (made with ADHOCw) and a brightness profile with photometric data (J-band of 2MASS, made as IRAF) were constructed. The dynamic (total) mass is obtained from the rotation curve, and the brightness profile estimates the luminous mass (bowl and disk). Starting from a mass decomposition model (modmass) and using a density profile for the dark halo (ISO), the best fit is made in a space of 4 parameters ( , , , and ). After comparing the results with the literature, a good agreement was verified.

Average Luminous Mass of Early Galaxies at <I>z</i> = 10 - 20 Predicted as ~10<sup>9</sup> Solar Masses

This paper predicts the average luminous mass of galaxies that will be detected by JWST space telescope at redshift z ≈ 10 - 20. The prediction, derived in the paper, is based on holographic analysis, developed from quantum mechanics, general relativity, thermodynamics, and Shannon information theory. Consistent with early JWST data, ~109 solar masses is the predicted average luminous mass of early galaxies at z ≈ 10 - 20 that will be detected by JWST.

Incorporating baryon-driven contraction of dark matter halos in rotation curve fits

The condensation of baryons within a dark matter (DM) halo during galaxy formation should result in some contraction of the halo as the combined system settles into equilibrium. We quantify this effect on the cuspy primordial halos predicted by DM-only simulations for the baryon distributions observed in the galaxies of the SPARC database. We find that the DM halos of high surface brightness galaxies (with Σeff ≳ 100 L⊙ pc−2 at 3.6 μm) experience strong contraction. Halos become more cuspy as a result of compression: the inner DM density slope increases with the baryonic surface mass density. We iteratively fit rotation curves to find the balance between initial halo parameters (constrained by abundance matching), compression, and stellar mass-to-light ratio. The resulting fits often require lower stellar masses than expected for stellar populations, particularly in galaxies with bulges: stellar mass must be reduced to make room for the DM it compresses. This trade off between dark and luminous mass is reminiscent of the cusp-core problem in dwarf galaxies, but occurs in more massive systems: the present-epoch DM halos cannot follow from cuspy primordial halos unless (1) the stellar mass-to-light ratios are systematically smaller than expected from standard stellar population synthesis models, and/or (2) there is a net outward mass redistribution from the initial cusp, even in massive galaxies widely considered to be immune from such effects.

Cosmo-Paleontology: Statistics of Fossil Groups in a Gravity-Only Simulation

We present a detailed study of fossil group candidates identified in "Last Journey", a gravity-only cosmological simulation covering a $(3.4\, h^{-1}\mathrm{Gpc})^3$ volume with a particle mass resolution of $m_p \approx 2.7 \times 10^9\, h^{-1}\mathrm{M}_\odot$. The simulation allows us to simultaneously capture a large number of group-scale halos and to resolve their internal structure. Historically, fossil groups have been characterized by high X-ray brightness and a large luminosity gap between the brightest and second brightest galaxy in the group. In order to identify candidate halos that host fossil groups, we use halo merger tree information to introduce two parameters: a luminous merger mass threshold ($M_\mathrm{LM}$) and a last luminous merger redshift cut-off ($z_\mathrm{LLM}$). The final parameter choices are informed by observational data and allow us to identify a plausible fossil group sample from the simulation. The candidate halos are characterized by reduced substructure and are therefore less likely to host bright galaxies beyond the brightest central galaxy. We carry out detailed studies of this sample, including analysis of halo properties and clustering. We find that our simple assumptions lead to fossil group candidates that form early, have higher concentrations, and are more relaxed compared to other halos in the same mass range.

Linearity: galaxy formation encounters an unanticipated empirical relation

ABSTRACT Measurements from galaxies spanning a broad range of morphology reveal a linear scaling of enclosed dark to luminous mass that is not anticipated by standard galaxy formation cosmology. The linear scaling is found to extend from the inner galactic region to the outermost data point. Uncertainties in the linear relation are narrow, with rms = 0.31 and σ = 0.31. It is unclear what would produce this linearity of enclosed dark to luminous mass. Baryonic processes are challenged to account for the linear scaling, and no dark matter candidate possesses a property that would result in a linear relation. The linear scaling may indicate new dark matter candidates, or an astrophysical process beyond the standard galaxy formation theory.

Dark and luminous mass components of Omega Centauri from stellar kinematics

ABSTRACT We combine proper motion data from Gaia EDR3 and HST with line-of-sight velocity data to study the stellar kinematics of the ω Cen globular cluster. Using a steady-state, axisymmetric dynamical model, we measure the distribution of both the dark and luminous mass components. Assuming both Gaussian and Navarro–Frenk–White mass profiles, depending on the data set, we measure an integrated mass of ≲106 M⊙ within the ω Cen half-light radius for a dark component that is distinct from the luminous stellar component. For the HST and radial velocity data, models with a non-luminous mass component are strongly statistically preferred relative to a stellar mass-only model with a constant mass-to-light ratio. While a compact core of stellar remnants may account for a dynamical mass up to ∼5 × 105 M⊙, they likely cannot explain the higher end of the range. This leaves open the possibility that this non-luminous dynamical mass component comprises non-baryonic dark matter. In comparison to the dark matter distributions around dwarf spheroidal galaxies, the ω Cen dark mass component is much more centrally concentrated. Interpreting the non-luminous mass distribution as particle dark matter, we use these results to obtain the J-factor, which sets the sensitivity to the annihilation cross-section. For the data sets considered, the range of median J-factors is ∼1022−1024 GeV2 cm−5, which is larger than that obtained for any dwarf spheroidal galaxy.

A Conceptual Model to Explain Dark Matter and Dark Energy

This paper considers a conceptual model that attempts to explain ‘Dark Matter’ and ‘Dark Energy’. The model is based on considering a gravitational field to be the result of a mass (a Higgs field) scattering pre-existing cosmic background space-time waves or ‘Uber-waves’. The term ‘Uber’ is used to denote an outstanding or supreme example of a particular kind of gravitational wave with cosmic-scale wavelengths that are far in excess of those associated with the gravitational waves generated by accelerating masses. Such waves are taken to be the very lowest frequency components associated with the spectrum of space-time waves generated by the ‘Big Bang’ and are supported by the expanding fabric of space-time produced at the point of the big bang, i.e. the lowest frequency components of a cosmological spectrum whose bandwidth is the a Planck frequency (～10∧43 Hz). Like electromagnetic waves, Uber waves are taken to propagate with an upper velocity consistent with the speed of light and interact with, and are scattered by, a Higgs field. This interaction produces the effect of a mass locally curving space-time, an idea that is contrary to the conventional model associated with General Relativity where mass is taken to curve space-time directly which otherwise remains ‘flat’. By assuming the pre-existence of background Uber waves, we consider the concave curvature of such waves to generate an apparent attractive gravitational force. This interaction produces the effect of a mass locally curving space-time, an idea that is contrary to the conventional model associated with General Relativity where mass is taken to curve space-time directly which otherwise remains ‘flat’. By assuming the pre-existence of background Uber waves, we consider the concave curvature of such waves to generate an apparent attractive gravitational force. This attractive force is taken to govern the formation of large scale structures of matter (galaxies and super-clusters of galaxies, for example) in the conventional sense but surrounded by a residual background gravitational field. It is this residual field that gives rise to the effect known as dark matter where more gravity (as an attractive only force) appears to be available than that which can be accounted for by the observed (luminous) mass, a luminosity that is generated primarily by nuclear fusion in stars. The convex curvature of Uber waves is considered to account for cosmic voids within which gravity is a repulsive force and where large scale structures of matter can therefore not be formed. This is considered to explain the super-large cosmic voids or super voids that are observed. These are regions of the universe where there is an absence of rich super clusters of matter. In these anti-gravity zones, only relatively small structures of matter can be formed by electrostatic forces alone which are then repelled from each other when their mass becomes significant enough for the force of anti-gravity to become significant. In such regions of an Uber wave, the matter generated from electrostatic forces builds up to produce a weak gravitational repulsive field due to the low mass density within a void. However, due to the immense size of these cosmic voids, they are taken to generate a net repulsive force which is considered to be the reason for the acceleration associated with the expansion of the universe; the effect of dark energy. This effect also accounts for the cosmic web structure in which luminescent matter appears to exist in relatively thin connective filaments. The purpose of this paper is to provide a conceptual model and not to investigate the ideas proposed in any significant mathematical detail. This is accomplished by building up the ideas on a case-by-case basis, coupled with a series of thought experiments but without resorting to specific physical scales or the physical parameters associated with these scales other than, by default, the speed of light and Newton’s gravitational constant.

Massive Black Holes Regulated by Luminous Blue Variable Mass Loss and Magnetic Fields

Abstract We investigate the effects of mass loss during the main-sequence (MS) and post-MS phases of massive star evolution on black hole (BH) birth masses. We compute solar metallicity Geneva stellar evolution models of an 85 star with mass-loss rate ( ) prescriptions for MS and post-MS phases and analyze under which conditions such models could lead to very massive BHs. Based on the observational constraints for of luminous stars, we discuss two possible scenarios that could produce massive BHs at high metallicity. First, if a massive BH progenitor evolves from the observed population of massive MS stars known as WNh stars, we show that its average post-MS mass-loss rate has to be less than . However, this is lower than the typical observed mass-loss rates of luminous blue variables (LBV). Second, a massive BH progenitor could evolve from a yet undetected population of 80–85 stars with strong surface magnetic fields, which could quench mass loss during the evolution. In this case, the average mass-loss rate during the post-MS LBV phase has to be less than 5 × 10−5 to produce 70 BHs. We suggest that LBVs that explode as SNe have large envelopes and small cores that could be prone to explosion, possibly evolving from binary interaction (either mergers or mass gainers that do not fully mix). Conversely, LBVs that directly collapse to BHs could have evolved from massive single stars or binary-star mergers that fully mix, possessing large cores that would favor BH formation.

The two body problem in the presence of dark energy and modified gravity: application to the Local Group

We explore mass estimation of the Local Group via the use of the simple, dynamical `timing argument' in the context of a variety of theories of dark energy and modified gravity: a cosmological constant, a perfect fluid with constant equation of state w, quintessence (minimally coupled scalar field), MOND, and symmetrons (coupled scalar field). We explore generic coupled scalar field theories, with the symmetron model as an explicit example. We find that theories which attempt to eliminate dark matter by fitting rotation curves produce mass estimates in the timing argument which are not compatible with the luminous mass of the galaxies alone. Assuming that the galaxies are approaching their first encounter, MOND gives a mass of around 2.7× 1010 M⊙, roughly 10% of the luminous mass of the LG, although a higher mass can be obtained in the case of a previous fly-by event between the MW and M31. The symmetron model suggests a mass too high to be explained without additional dark matter (\U0001d4aa(1012) M⊙), suggesting that there is a missing mass problem in this model. We also demonstrate that tensions in measurements of H0 can produce an uncertainty in the Local Group mass estimate comparable to observational uncertainties on the separation and relative velocity of the galaxies, with values for the mass ranging from 4.4–5.3 × 1012 M⊙ varying h between 0.63 and 0.76.

Paradigms and Scenarios for the Dark Matter Phenomenon

Well known scaling laws among the structural properties of the dark and the luminous matter in disc systems are too complex to be arisen by two inert components that just share the same gravitational field. This brings us to critically focus on the 30-year-old paradigm, that, resting on a priori knowledge of the nature of Dark Matter (DM), has led us to a restricted number of scenarios, especially favouring the collisionless Λ Cold Dark Matter one. Motivated by such observational evidence, we propose to resolve the dark matter mystery by following a new Paradigm: the nature of DM must be guessed/derived by deeply analyzing the properties of the dark and luminous mass distribution at galactic scales. The immediate application of this paradigm leads us to propose the existence of a direct interaction between Dark and Standard Model particles, which has finely shaped the inner regions of galaxies.

Cosmic Reionization On Computers: The Galaxy–Halo Connection between 5 ≤ z ≤ 10

Abstract We explore the connection between the stellar component of galaxies and their host halos during the epoch of reionization (5 ≤ z ≤ 10) using the CROC (Cosmic Reionization on Computers) simulations. We compare simulated galaxies with observations and find that CROC underpredicts the abundance of luminous galaxies when compared to observed UV luminosity functions, and analogously the most massive galaxies when compared to observed stellar mass functions. We can trace the deficit of star formation to high redshifts, where the slope of the star formation rate to stellar mass relation is consistent with observations, but the normalization is systematically low. This results in a star formation rate density and stellar mass density that are systematically offset from observations. However, the less luminous or lower stellar mass objects have luminosities and stellar masses that agree fairly well with observational data. We explore the stellar-to-halo mass ratio (SHMR), a key quantity that is difficult to measure at high redshifts and that models do not consistently predict. In CROC, the SHMR decreases with redshift, a trend opposite to some abundance-matching studies. These discrepancies uncover where future effort should be focused in order to improve the fidelity of modeling cosmic reionization. We also compare the CROC galaxy bias with observational measurements using Lyman-break galaxy samples, finding reasonable consistency.

Enigmatic velocity dispersions of ultradiffuse galaxies in light of modified gravity theories and the radial acceleration relation

Recent observations of anomalous line-of-sight velocity dispersions of two ultra-diffuse galaxies (UDGs) provide a stringent test for modified gravity theories. While NGC 1052-DF2 exhibits an extremely low dispersion value ($\sigma \sim 7.8_{-2.2}^{+5.6}$ km/s), the reported dispersion value for NGC 1052-DF44 is quite high ($\sigma \sim 41.0 \pm 8$ km/s). For DF2, the dynamical mass is almost equal to the luminous mass suggesting the galaxy have little to no `dark matter' in $\Lambda$CDM whereas DF4 requires a dynamical mass-to-light ratio of $\sim 30$ making it to be almost entirely consists of dark matter. It has been claimed that both these galaxies, marking the extreme points in terms of the estimated dynamical mass-to-light ratio among known galaxies, would be difficult to explain in modified gravity scenarios. Extending the analysis presented in \cite{islam2019modified}, we explore the dynamics of DF2 and DF44 within the context of three popular alternative theories of gravity [Modified Newtonian Dynamics (MOND), Weyl Conformal gravity and Modified gravity (MOG)] and examine their viability against the dispersion data of DF2 and DF44. We further show that the galactic `Radial Acceleration Relation' (RAR) is consistent with DF44 dispersion data but not with DF2.

Suppression of luminosity and mass–radius relation of highly magnetized white dwarfs

ABSTRACT We explore the luminosity L of magnetized white dwarfs and its effect on the mass–radius relation. We self-consistently obtain the interface between the electron degenerate-gas dominated inner core and the outer ideal gas surface layer or envelope by incorporating both the components of gas throughout the model white dwarf. This is obtained by solving the set of magnetostatic equilibrium, photon diffusion, and mass conservation equations in the Newtonian framework, for different sets of luminosity and magnetic field. We appropriately use magnetic opacity, instead of Kramer’s opacity, wherever required. We show that the Chandrasekhar limit is retained, even at high luminosity up to about $10^{-2}\, L_\odot$ but without magnetic field, if the temperature is set constant inside the interface. However, there is an increased mass for large-radius white dwarfs, an effect of photon diffusion. Nevertheless, in the presence of strong magnetic fields, with central strength of about 1014 G, super-Chandrasekhar white dwarfs, with masses of about $1.9\, {\rm M}_{\odot }$, are obtained even when the temperature inside the interface is kept constant. Most interestingly, small-radius magnetic white dwarfs remain super-Chandrasekhar even if their luminosity decreases to as low as about $10^{-20}\, L_{\odot }$. However, their large-radius counterparts in the same mass–radius relation merge with Chandrasekhar’s result at low L. Hence, we argue for the possibility of highly magnetized, low luminous super-Chandrasekhar mass white dwarfs that, owing to their faintness, can be practically hidden.

Modified gravity theories in light of the anomalous velocity dispersion of NGC1052-DF2

Recent observations of ultra-dwarf galaxy NGC1052-DF2 started an interesting discussion between dark matter hypothesis and modified gravity theories. Reported low velocity dispersion (< 10.5 km/s at 90% confidence level) derived from the kinematic data of 10 globular clusters in the galaxy points towards an extraordinarily low dynamical mass ($\sim$ $3.4 \times 10^{8} M_{\odot}$) which is of the same order of the luminous mass ($\sim$ $2.0 \times 10^{8} M_{\odot}$) in the galaxy. This has been interpreted as the first evidence of a galaxy `without Dark Matter'. It has been argued that dark matter is not necessarily coupled to the the baryonic mass on the galactic scale and poses a challenge to modified gravity theories. We explore the dynamics of NGC1052-DF2 within the context of four popular alternative theories of gravity [Modified Newtonian Dynamcies (MOND), Weyl Conformal gravity, Modified gravity (MOG)/Scalar-Tensor-Vector Gravity (STVG) and Verlinde's Emergent gravity] and present the analysis of detailed radial variation of the velocity dispersion. We demonstrate that the dispersion data of NGC1052-DF2 is fully consistent with modified gravity paradigm (as well as with general relativity without dark matter). We reach similar conclusion for the ultra-dwarf NGC1052-DF4 which has been claimed to be the second candidate for galaxies `without Dark Matter'.

ALMA Observations of Giant Molecular Clouds in the Starburst Dwarf Galaxy Henize 2-10

Abstract We present new 12CO (J = 1−0) observations of He 2-10, a blue compact dwarf galaxy about 8.7 Mpc away, taken with the Atacama Large Millimeter Array. These are the highest spatial and spectral resolution observations, to date, of the molecular gas in this starburst galaxy. We measure a molecular mass of (1.2 ± 0.4) × 108 M ⊙ in He 2-10, and 75% of the molecular gas mass is contained within the northern region of the galaxy near the previously identified young super star clusters, which has a projected size of about 300 pc. We use the CPROPS algorithm to identify 119 resolved giant molecular clouds distributed throughout the galaxy, and the molecular gas contained within these clouds makes up between 45% and 70% of the total molecular mass. The molecular clouds in He 2-10 have similar median sizes (∼26 pc), luminous masses (∼4 × 105 M ⊙), and surface densities (∼180 M ⊙ pc−2) to Milky Way clouds. However, He 2-10 clouds have velocity dispersions (∼3 km s−1) about 50% higher than those in the Milky Way. We provide evidence that He 2-10 clouds tend to be in virial equilibrium, with the virial and luminous masses scaling according to ∝ , similar to clouds in the Milky Way. However, we measure a scaling relationship between luminous mass and size, ∝ R 3.0±0.3, that is steeper than what is observed in Milky Way clouds. Assuming that He 2-10 molecular clouds are virialized, we infer values of the CO-to- conversion factor ranging from 0.5 to 13 times the standard value in the solar neighborhood. Given star formation efficiencies as low as 5%, the most massive molecular clouds in He 2-10 currently have enough mass to form the next generation of super star clusters in the galaxy.

Denuded dwarfs demystified: gas loss from dSph progenitors and implications for the minimum mass of galaxies

The placement of early-type dwarf galaxies (dSphs and dEs) with respect to the Potential Plane defined by pressure-supported late-type dwarf galaxies (dIs and BCDs) has been determined from surface brightness profiles. dEs and the most luminous dSphs lie on the Plane, suggesting that they emerged from late-type dwarfs that converted most of their gas into stars. However, there is a critical value of the potential at which dSphs start to fall systematically below the Plane, with the deviation growing as the potential becomes shallower. The displacements are attributed to depletion of baryons through gas loss, smaller galaxies having lost proportionately more gas. The critical potential corresponds to an escape velocity of 50 $\pm$ 8 km/s, which is what is expected for gas with a temperature of 13,000 $\pm$ 4,000 K, typical of a low-metallicity HII region. This suggests that photoionization was responsible for instigating the loss of gas by galaxies with potentials shallower than the critical value, with evacuation occurring over a few tens of millions of years. Extreme ratios of dynamical to luminous masses observed for the smallest dSphs are an artifact of mass loss. Because the efficiency with which gas was converted into stars was lower for dSphs with shallower potentials, there should be a minimum baryonic mass for a galaxy below which the stellar mass is negligible. Gross extrapolation of the trend of inferred gas masses with stellar masses suggests a value between 500 and 10,000 M$_\odot$. The corresponding dynamical mass is below 10$^6$ M$_\odot$.