The bivariate gas-stellar mass distributions and the mass functions of early- and late-type galaxies at z∼0z\sim0

We report the bivariate HI- and H$_2$-stellar mass distributions of local galaxies in addition of an inventory of galaxy mass functions, MFs, for HI, H$_2$, cold gas, and baryonic mass, separately into early- and late-type galaxies. The MFs are determined using the HI and H$_2$ conditional distributions and the galaxy stellar mass function, GSMF. For the conditional distributions we use the compilation presented in Calette et al. 2018. For determining the GSMF from $M_{\ast}\sim3\times10^{7}$ to $3\times10^{12}$ $M_{\odot}$, we combine two spectroscopic samples from the SDSS at the redshift range $0.0033<z<0.2$. We find that the low-mass end slope of the GSMF, after correcting from surface brightness incompleteness, is $\alpha\approx-1.4$, consistent with previous determinations. The obtained HI MFs agree with radio blind surveys. Similarly, the H$_2$ MFs are consistent with CO follow-up optically-selected samples. We estimate the impact of systematics due to mass-to-light ratios and find that our MFs are robust against systematic errors. We deconvolve our MFs from random errors to obtain the intrinsic MFs. Using the MFs, we calculate cosmic density parameters of all the baryonic components. Baryons locked inside galaxies represent 5.4% of the universal baryon content, while $\sim96$% of the HI and H$_2$ mass inside galaxies reside in late-type morphologies. Our results imply cosmic depletion times of H$_2$ and total neutral H in late-type galaxies of $\sim 1.3$ and 7.2 Gyr, respectively, which shows that late type galaxies are on average inefficient in converting H$_2$ into stars and in transforming HI gas into H$_2$. Our results provide a fully self-consistent empirical description of galaxy demographics in terms of the bivariate gas--stellar mass distribution and their projections, the MFs. This description is ideal to compare and/or to constrain galaxy formation models.Comment: 37 pages, 17 figures. Accepted for publication in PASA. A code that displays tables and figures with all the relevant statistical distributions and correlations discussed in this paper is available here https://github.com/arcalette/Python-code-to-generate-Rodriguez-Puebla-2020-result

Soft clustering analysis of galaxy morphologies: A worked example with SDSS

Context: The huge and still rapidly growing amount of galaxies in modern sky surveys raises the need of an automated and objective classification method. Unsupervised learning algorithms are of particular interest, since they discover classes automatically. Aims: We briefly discuss the pitfalls of oversimplified classification methods and outline an alternative approach called "clustering analysis". Methods: We categorise different classification methods according to their capabilities. Based on this categorisation, we present a probabilistic classification algorithm that automatically detects the optimal classes preferred by the data. We explore the reliability of this algorithm in systematic tests. Using a small sample of bright galaxies from the SDSS, we demonstrate the performance of this algorithm in practice. We are able to disentangle the problems of classification and parametrisation of galaxy morphologies in this case. Results: We give physical arguments that a probabilistic classification scheme is necessary. The algorithm we present produces reasonable morphological classes and object-to-class assignments without any prior assumptions. Conclusions: There are sophisticated automated classification algorithms that meet all necessary requirements, but a lot of work is still needed on the interpretation of the results.Comment: 18 pages, 19 figures, 2 tables, submitted to A

Comparing PyMorph and SDSS photometry. II. The differences are more than semantics and are not dominated by intracluster light

The Sloan Digital Sky Survey pipeline photometry underestimates the brightnesses of the most luminous galaxies. This is mainly because (i) the SDSS overestimates the sky background and (ii) single or two-component Sersic-based models better fit the surface brightness profile of galaxies, especially at high luminosities, than does the de Vaucouleurs model used by the SDSS pipeline. We use the PyMorph photometric reductions to isolate effect (ii) and show that it is the same in the full sample as in small group environments, and for satellites in the most massive clusters as well. None of these are expected to be significantly affected by intracluster light (ICL). We only see an additional effect for centrals in the most massive halos, but we argue that even this is not dominated by ICL. Hence, for the vast majority of galaxies, the differences between PyMorph and SDSS pipeline photometry cannot be ascribed to the semantics of whether or not one includes the ICL when describing the stellar mass of massive galaxies. Rather, they likely reflect differences in star formation or assembly histories. Failure to account for the SDSS underestimate has significantly biased most previous estimates of the SDSS luminosity and stellar mass functions, and therefore Halo Model estimates of the z ~ 0.1 relation between the mass of a halo and that of the galaxy at its center. We also show that when one studies correlations, at fixed group mass, with a quantity which was not used to define the groups, then selection effects appear. We show why such effects arise, and should not be mistaken for physical effects.Comment: 15 pages, 17 figures, accepted for publication in MNRAS. The PyMorph luminosities and stellar masses are available at https://www.physics.upenn.edu/~ameert/SDSS_PhotDec

Numerical valuation of two-asset options under jump diffusion models using Gauss-Hermite quadrature

In this work a finite difference approach together with a bivariate Gauss–Hermite quadrature technique is developed for partial integro-differential equations related to option pricing problems on two underlying asset driven by jump-diffusion models. Firstly, the mixed derivative term is removed using a suitable transformation avoiding numerical drawbacks such as slow convergence and inaccuracy due to the appearance of spurious oscillations. Unlike the more traditional truncation approach we use 2D Gauss–Hermite quadrature with the additional advantage of saving computational cost. The explicit finite difference scheme becomes consistent, conditionally stable and positive. European and American option cases are treated. Numerical results are illustrated and analysed with experiments and comparisons with other well recognized methods.FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) Ministerio de Economía y Competitividad Spanish grant MTM2013-41765-

The high mass end of the stellar mass function: Dependence on stellar population models and agreement between fits to the light profile

We quantify the systematic effects on the stellar mass function which arise from assumptions about the stellar population, as well as how one fits the light profiles of the most luminous galaxies at z ~ 0.1. When comparing results from the literature, we are careful to separate out these effects. Our analysis shows that while systematics in the estimated comoving number density which arise from different treatments of the stellar population remain of order < 0.5 dex, systematics in photometry are now about 0.1 dex, despite recent claims in the literature. Compared to these more recent analyses, previous work based on Sloan Digital Sky Survey (SDSS) pipeline photometry leads to underestimates of rho_*(> M_*) by factors of 3-10 in the mass range 10^11 - 10^11.6 M_Sun, but up to a factor of 100 at higher stellar masses. This impacts studies which match massive galaxies to dark matter halos. Although systematics which arise from different treatments of the stellar population remain of order < 0.5 dex, our finding that systematics in photometry now amount to only about 0.1 dex in the stellar mass density is a significant improvement with respect to a decade ago. Our results highlight the importance of using the same stellar population and photometric models whenever low and high redshift samples are compared.Comment: 18 pages, 17 figures, accepted for publication in MNRAS. The PyMorph luminosities and stellar masses are available at https://www.physics.upenn.edu/~ameert/SDSS_PhotDec

An ETD method for multi-asset American option pricing under jump-diffusion model

In this paper, we propose a numerical method for American multi-asset options under jump-diffusion model based on the combination of the exponential time differencing (ETD) technique for the differential operator and Gauss–Hermite quadrature for the integral term. In order to simplify the computational sten- cil and improve characteristics of the ETD-scheme mixed derivative eliminating transformation is applied. The results are compared with recently proposed methods