Should Zeros Count? Modeling the Galaxy–Globular Cluster Scaling Relation with(out) Zero-inflated Count Models

Galaxy stellar mass is known to be monotonically related to the size of the galaxy’s globular cluster (GC) population for Milky Way sized and larger galaxies. However, the relation becomes ambiguous for dwarf galaxies, where there is some evidence for a downturn in GC population size at low galaxy masses. Smaller dwarfs are increasingly likely to have no GCs, and these zeros cannot be easily incorporated into linear models. We introduce the Hierarchical Errors-in-variables ERrors-in-variables BAyesian Lognormal hurdle (HERBAL) model to represent the relationship between dwarf galaxies and their GC populations, and apply it to the sample of Local Group galaxies, where the luminosity range coverage is maximal. This bimodal model accurately represents the two populations of dwarf galaxies: those that have GCs and those that do not. Our model thoroughly accounts for all uncertainties, including measurement uncertainty, uncertainty in luminosity to stellar mass conversions, and intrinsic scatter. The hierarchical nature of our Bayesian model also allows us to estimate galaxy masses and individual mass-to-light ratios from luminosity data within the model. We find that 50% of galaxies are expected to host GC populations at a stellar mass of , and that the expected mass of GC populations remains linear down to the smallest galaxies. Our hierarchical model recovers an accurate estimate of the Milky Way stellar mass. Under our assumed error model, we find a nonzero intrinsic scatter of (95% credible interval) that should be accounted for in future models.

Statistical modelling for falls count data

We analyze the evolution of red and blue galaxies in different cosmic web environments from redshift z = 3 to z = 0 using the IllustrisTNG simulation. We use Otsu's method to classify the red or blue galaxies at each redshift and determine their geometric environments from the eigenvalues of the deformation tensor. Our analysis shows that initially, blue galaxies are more common in clusters followed by filaments, sheets and voids. However, this trend reverses at lower redshifts, with red fractions rising earlier in denser environments. At z < 1, most massive galaxies (log(M */M ⊙) > 10.5) are quenched across all environments. In contrast, low-mass galaxies (log(M */M ⊙) < 10.5) are more influenced by their environment, with clusters hosting the highest red galaxy fractions at low redshifts. We observe a slower mass growth for low-mass galaxies in clusters at z < 1. Filaments show relative red fractions (RRF) comparable to clusters at low masses, but host nearly 60% of low-mass blue galaxies, representing a diverse galaxy population. It implies that less intense environmental quenching in filaments allows galaxies to experience a broader range of evolutionary stages. Despite being the densest environment, clusters display the highest relative blue fraction (RBF) for high-mass galaxies, likely due to interactions or mergers that can temporarily rejuvenate star formation in some of them. The (u-r) colour distribution transitions from unimodal to bimodal by redshift z = 2 across all environments. At z < 1, clusters exhibit the highest median colour, with stellar mass being the primary driver of colour evolution in massive galaxies. The suppression of star formation rate (SFR) and specific SFR (sSFR) is also most pronounced in clusters during this period. Our study suggests that stellar mass governs quenching in high-mass galaxies, while a complex interplay of mass and environment shapes the evolution of low-mass galaxies.

In this thesis I address the formation and evolution of lowmass galaxies and investigate their importance in the general galaxy evolution/formation process. Currently favored models of galaxy formation, such as cold dark matter (CDM), suggest that the first galaxies to form in the universe have low masses and sizes, similar to modern dwarf galaxies, that later merge to form more massive systems. The most common galaxies in the nearby universe are dwarf ellipticals in clusters that could be descendants of these early galaxies. This thesis addresses two questions related to these objects: (1) Are the dwarf elliptical galaxies seen in clusters an old primordial population that survived since their initial formation, or are these dwarfs the end product of some evolutionary dynamical process? (2) Do galaxy mergers occur in the universe, and if so, how does this merging evolve through time? To determine whether dwarf elliptical galaxies are an old cluster population, kinematic, structural, and photometric information for these objects was obtained using the WisconsinIndiana-Yale-NOAO 3.5 m telescope. Radial velocities of dwarf elliptical galaxies in the Virgo Cluster suggest that these objects are not an old cluster population but were accreted sometime in the past (C. J. Conselice, J. S. Gallagher III, & R. F. G. Wyse 2001, ApJ, 559, 791). Kinematics also demonstrate that these objects could have originated from a more massive progenitor. Photometry of dwarf elliptical galaxies in the Perseus Cluster further suggests that the stellar populations of these objects are old, with little to no recent star formation or population gradients. The broadband UBR colors of these objects are also consistent with color differences originating from metallicity. Low-mass galaxies in the Perseus Cluster however do not follow the color-magnitude relationship found for the giant elliptical galaxies, with some too red and others too blue for their magnitudes. Through comparisons with LCDM models of galaxy formation, I show that the blue lowmass cluster objects in Perseus are consistent with being old CDM galaxies. Low-mass cluster galaxies that are redder than the color-magnitude relationship are shown to be composed of stars with high metallicities. These red low-mass cluster galaxies must have very high mass-to-light ratios near 250 in solar units or must be the remnants of higher mass galaxies whose stellar material was stripped during high-speed impulsive interactions with other cluster galaxies. To address the issue of galaxy mergers, I develop and use a morphological system to identify robustly, and unambiguously, objects undergoing major mergers (C. J. Conselice, M. A. Bershady, & A. Jangren 2000, ApJ, 529, 886; C. J. Conselice, M. A. Bershady, & J. S. Gallagher III 2000, A&A, 354, L21). This system uses an asymmetry index, such that galaxies undergoing mergers have asymmetry values , with the A 1 0.35 range of possible values being 0–2. When this is applied to the galaxies in the Hubble Deep Field–North, an increase with redshift of galaxies undergoing major mergers is found. Depending on the method of computation, the merger fraction evolution out to can be characterized as , where m m z ∼ 3.5 f p (1 z) ranges from 1 to 2.5. The best fit gives a variable m, such that . m p 2.96 0.32z I also investigate the properties of a nearby massive central cluster galaxy, NGC 1275 in the Perseus Cluster, whose unusual properties and structural aspects can be partially accounted for by recent and past mergers (C. J. Conselice, J. S. Gallagher III, & R. F. G. Wyse 2001, AJ, 122, 2281). Finally, after summarizing the results of this thesis, as well as previous work, I present a new galaxy classification system according to which all galaxies can be fitted based on the three most salient properties that drive galaxy evolution: dissipation, star formation, and galaxy interactions.

Multiple populations (MPs), characterized by variations in light elemental abundances, have been found in stellar clusters in the Milky Way, Magellanic Clouds, as well as several other dwarf galaxies. Based on a large number of observations, mass has been suggested to be a key parameter affecting the presence and appearance of MPs in stellar clusters. To further investigate the existence of MPs in low-mass clusters and explore the mass threshold for the formation of MPs, we carried out a project studying the composition of the stellar population in several low-mass Galactic globular clusters. Here we present our study on the cluster Eridanus. With blue-UV low-resolution spectra obtained with the OSIRIS/Multi-object spectrograph on the Gran Telescopio Canarias, we computed the spectral indices of CH and CN for a sample of giant stars and derived their carbon and nitrogen abundances using model spectra. A significant dispersion in the initial surface abundance of nitrogen was found in the sample, indicating the existence of MPs in Eridanus. Inspecting the age–initial mass distribution of in situ clusters with MPs, we find a slight trend that initial mass increases with increasing age, and the lowest initial masses of logMinitial ∼ 4.98 and 5.26 are found at the young and old end, respectively, which might provide a rough reference for the mass threshold for clusters to form MPs. However, more observations of clusters with low initial masses are still necessary before any firm conclusion can be drawn.

More than 60% of accidents in Iran occur within 30 kilometers of cities entrance roads. Therefore the number of accidents per kilometer in these regions, in contrast to the other parts of roads is very considerable. The city of Tehran, as the capital of Iran, is the cross point of major arterials of passenger and freight transportation. Thus the evaluation of road safety, entering and exiting the city in the 30 kilometers buffer, can be considered to improve countrywide road safety. To investigate the effects of roadway characteristics and traffic conditions, including number of traffic violations, on accident frequency within 30 km of Tehran entrance roads, Poisson and Negative Binomial regression model were calibrated in this study. Although the goodness of fit index in Poisson model is much greater than the Negative Binomial model, the accident data dispersion in this study implies that Negative Binomial model is more appropriate to show the influences of effective variables. According to results of modeling, the variables including average daily volume, share of heavy vehicles, average daily speed violations and number of direct accesses and interchanges have effective influence on accident frequencies. Controlling access to roads and using effective actions to reduce the speed and number of speed violation can be accounted as effective policies to reduce accident frequencies within 30 km of Tehran entrance roads.

Crash prediction based on random effect negative binomial model considering data heterogeneity

We investigate X-ray binary (XRB) luminosity function (XLF) scaling relations for Chandra-detected populations of low-mass XRBs (LMXBs) within the footprints of 24 early-type galaxies. Our sample includes Chandra and Hubble Space Telescope observed galaxies at Mpc that have estimates of the globular cluster (GC) specific frequency (S N ) reported in the literature. As such, we are able to directly classify X-ray-detected sources as being coincident with unrelated background/foreground objects, GCs, or sources that are within the fields of the galaxy targets. We model the GC and field LMXB population XLFs for all galaxies separately and then construct global models characterizing how the LMXB XLFs vary with galaxy stellar mass and S N . We find that our field LMXB XLF models require a component that scales with S N and has a shape consistent with that found for the GC LMXB XLF. We take this to indicate that GCs are “seeding” the galactic field LMXB population, through the ejection of GC LMXBs and/or the diffusion of the GCs in the galactic fields themselves. However, we also find that an important LMXB XLF component is required for all galaxies that scales with stellar mass, implying that a substantial population of LMXBs are formed “in situ,” which dominates the LMXB population emission for galaxies with S N ≲ 2. For the first time, we provide a framework quantifying how directly associated GC LMXBs, GC-seeded LMXBs, and in situ LMXBs contribute to LMXB XLFs in the broader early-type galaxy population.

The foliage in a fully-leafed deciduous forest canopy is clumped. Consequently, theory indicates that the probability of beam penetration will be estimated more accurately with a model based on the negative binomial distribution than with a model based on the Poisson distribution, incorporating an assumption of a spherical leaf inclination angle distribution. Flux densities of photosynthetically active radiation (PAR) were measured in and above a deciduous forest canopy and were computed with the canopy radiative transfer models based on the negative binomial and Poisson distributions. These radiation values were used to compute canopy photosynthesis and stomatal conductance. Canopy photosynthesis and stomatal conductance, based on the negative binomial model, overestimated values computed from measured PAR profiles by 8 and 9%. respectively. The canopy photosynthesis and stomatal conductance values computed with the spherical Poisson model under-estimated measured values by 17 and 10%, respectively. Thus, the negative binomial radiative transfer model improves estimates of canopy photosynthesis and, to a lesser extent, stomatal conductance, inside a deciduous forest.

A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data

We study the relations between stellar mass, star formation history, size and internal structure for a complete sample of 122 808 galaxies drawn from the Sloan Digital Sky Survey. We show that low-redshift galaxies divide into two distinct families at a stellar mass of 3 × 1010 M⊙. Lower-mass galaxies have young stellar populations, low surface mass densities and the low concentrations typical of discs. Their star formation histories are more strongly correlated with surface mass density than with stellar mass. A significant fraction of the lowest-mass galaxies in our sample have experienced recent starbursts. At given stellar mass, the sizes of low-mass galaxies are lognormally distributed with dispersion δ (ln R50) ∼ 0.5, in excellent agreement with the idea that they form with little angular momentum loss through cooling and condensation in a gravitationally dominant dark matter halo. Their median stellar surface mass density scales with stellar mass as µ* ∝ M0.54*, suggesting that the stellar mass of a disc galaxy is proportional to the three halves power of its halo mass. All of this suggests that the efficiency of the conversion of baryons into stars in low-mass galaxies increases in proportion to halo mass, perhaps as a result of supernova feedback processes. At stellar masses above 3 × 1010 M⊙, there is a rapidly increasing fraction of galaxies with old stellar populations, high surface mass densities and the high concentrations typical of bulges. In this regime, the size distribution remains lognormal, but its dispersion decreases rapidly with increasing mass and the median stellar mass surface density is approximately constant. This suggests that the star formation efficiency decreases in the highest-mass haloes, and that little star formation occurs in massive galaxies after they have assembled.

The globular cluster (GC) systems of galaxies are well known to extend to large galactocentric radii. Here, we quantify the size of GC systems using the half number radius of 22 GC systems around early-type galaxies (ETGs) from the literature. We compare GC system sizes to the sizes and masses of their host galaxies. We find that GC systems typically extend to 4 times that of the host galaxy size; however, this factor varies with galaxy stellar mass from about 3 times for M* galaxies to 5 times for the most massive galaxies in the universe. The size of a GC system scales approximately linearly with the virial radius (R200) and with the halo mass (M200) to the 1/3 power. The GC system of the Milky Way follows the same relations as for ETGs. For ultra diffuse galaxies (UDGs), their GC system size scales with halo mass and virial radius as for more massive, larger galaxies. UDGs indicate that the linear scaling of GC system size with stellar mass for massive galaxies flattens out for low stellar mass galaxies. Our scalings are different to those reported recently by Hudson &amp; Robison.

Application of the Conway–Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes

Observations of massive galaxies at low redshift have revealed approximately linear scaling relations between the mass of a supermassive black hole (SMBH) and properties of its host galaxy. How these scaling relations evolve with redshift and whether they extend to lower-mass galaxies, however, remain open questions. Recent galaxy formation simulations predict a delayed, or ‘two-phase,’ growth of SMBHs: slow, highly intermittent BH growth due to repeated gas ejection by stellar feedback in low-mass galaxies, followed by more sustained gas accretion that eventually brings BHs on to the local scaling relations. The predicted two-phase growth implies a steep increase, or ‘kink,’ in BH-galaxy scaling relations at a stellar mass $\rm {M}_{*}\sim 5\times 10^{10}$ M⊙. We develop a parametric, semi-analytic model to compare different SMBH growth models against observations of the quasar luminosity function (QLF) at z ∼ 0.5−4. We compare models in which the relation between SMBH mass and galaxy mass is purely linear versus two-phase models. The models are anchored to the observed galaxy stellar mass function, and the BH mass functions at different redshifts are consistently connected by the accretion rates contributing to the QLF. The best fits suggest that two-phase evolution is significantly preferred by the QLF data over a purely linear scaling relation. Moreover, when the model parameters are left free, the two-phase model fits imply a transition mass consistent with that predicted by simulations. Our analysis motivates further observational tests, including measurements of BH masses and active galactic nuclei activity at the low-mass end, which could more directly test two-phase SMBH growth.

Thanks to its exceptional near-infrared photometry, JWST can effectively contribute to the discovery, characterisation, and understanding of multiple stellar populations in globular clusters, especially at low masses where the Hubble Space Telescope (HST) faces limitations. This paper continues the efforts of the JWST GO-1979 programme in exploring the faintest members of the globular cluster NGC 6397. In this work, we show that the combination of HST and JWST data allows us to identify two groups of MS stars: MSa, the first-generation group, and MSb, the second-generation group. We measured the ratio between the two groups and combined it with measurements from the literature focused on more central fields and more massive stars compared to our study. Our findings suggest that the MSa and MSb stars are present in a ≈30−70 ratio regardless of the distance from the centre of the cluster and the mass of the stars used so far. However, considering the limited areal coverage of our study, a more comprehensive spatial analysis is necessary to definitively confirm complete spatial mixing.