A Census of the Stellar Populations in the Sco-Cen Complex*

I have used high-precision photometry and astrometry from the early installment of the third data release of Gaia (EDR3) to perform a survey for members of the stellar populations within the Sco-Cen complex, which consist of Upper Sco, UCL/LCC, the V1062 Sco group, Ophiuchus, and Lupus. Among Gaia sources with σ π < 1 mas, I have identified 10,509 candidate members of those populations. I have compiled previous measurements of spectral types, Li equivalent widths, and radial velocities for the candidates, which are available for 3169, 1420, and 1740 objects, respectively. In a subset of candidates selected to minimize field star contamination, I estimate that the contamination is ≲1% and the completeness is ∼90% at spectral types of ≲M6–M7 for the populations with low extinction (Upper Sco, V1062 Sco, UCL/LCC). I have used that cleaner sample to characterize the stellar populations in Sco-Cen in terms of their initial mass functions, ages, and space velocities. For instance, all of the populations in Sco-Cen have histograms of spectral types that peak near M4–M5, which indicates that they share similar characteristic masses for their initial mass functions (∼0.15–0.2 M ⊙). After accounting for incompleteness, I estimate that the Sco-Cen complex contains nearly 10,000 members with masses above ∼0.01 M ⊙. Finally, I also present new estimates for the intrinsic colors of young stars and brown dwarfs (≲20 Myr) in bands from Gaia EDR3, the Two Micron All Sky Survey, the Wide-field Infrared Survey Explorer, and the Spitzer Space Telescope.

Virial Halo Mass Function in the Planck Cosmology

We study halo mass functions with high-resolution N-body simulations under a ΛCDM cosmology. Our simulations adopt the cosmological model that is consistent with recent measurements of the cosmic microwave backgrounds with the Planck satellite. We calibrate the halo mass functions for 108.5 ≲ M vir/(h −1 M ⊙) ≲ 1015.0–0.45 z , where M vir is the virial spherical-overdensity mass and redshift z ranges from 0 to 7. The halo mass function in our simulations can be fitted by a four-parameter model over a wide range of halo masses and redshifts, while we require some redshift evolution of the fitting parameters. Our new fitting formula of the mass function has a 5%-level precision, except for the highest masses at z ≤ 7. Our model predicts that the analytic prediction in Sheth & Tormen would overestimate the halo abundance at z = 6 with M vir = 108.5–10 h −1 M ⊙ by 20%–30%. Our calibrated halo mass function provides a baseline model to constrain warm dark matter (WDM) by high-z galaxy number counts. We compare a cumulative luminosity function of galaxies at z = 6 with the total halo abundance based on our model and a recently proposed WDM correction. We find that WDM with its mass lighter than 2.71 keV is incompatible with the observed galaxy number density at a 2σ confidence level.

Galaxy Stellar Mass Functions from z ∼ 10 to z ∼ 6 using the Deepest Spitzer/Infrared Array Camera Data: No Significant Evolution in the Stellar-to-halo Mass Ratio of Galaxies in the First Gigayear of Cosmic Time

We present new stellar mass functions at z ∼ 6, z ∼ 7, z ∼ 8, z ∼ 9 and, for the first time, z ∼ 10, constructed from ∼800 Lyman-break galaxies previously identified over the eXtreme Deep Field and Hubble Ultra-Deep Field parallel fields and the five Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey fields. Our study is distinctive due to (1) the much deeper (∼200 hr) wide-area Spitzer/Infrared Array Camera (IRAC) imaging at 3.6 μm and 4.5 μm from the Great Observatories Origins Deep Survey Re-ionization Era Wide-area Treasury from Spitzer program (GREATS) and (2) consideration of z ∼ 6–10 sources over a 3× larger area than those of previous Hubble Space Telescope+Spitzer studies. The Spitzer/IRAC data enable ≥2σ rest-frame optical detections for an unprecedented 50% of galaxies down to a stellar mass limit of ∼ 10 8  ⊙ across all redshifts. Schechter fits to our volume densities suggest a combined evolution in the characteristic mass  * and normalization factor ϕ * between z ∼ 6 and z ∼ 8. The stellar mass density (SMD) increases by ∼1000× in the ∼500 Myr between z ∼ 10 and z ∼ 6, with indications of a steeper evolution between z ∼ 10 and z ∼ 8, similar to the previously reported trend of the star formation rate density. Strikingly, abundance matching to the Bolshoi–Planck simulation indicates halo mass densities evolving at approximately the same rate as the SMD between z ∼ 10 and z ∼ 4. Our results show that the stellar-to-halo mass ratios, a proxy for the star formation efficiency, do not change significantly over the huge stellar mass buildup occurred from z ∼ 10 to z ∼ 6, indicating that the assembly of stellar mass closely mirrors the buildup in halo mass in the first ∼1 Gyr of cosmic history. The James Webb Space Telescope is poised to extend these results into the “first galaxy” epoch at z ≳ 10.

Press-Schechter primordial black hole mass functions and their observational constraints

We present a modification of the Press-Schechter (PS) formalism to derive general mass functions for primordial black holes (PBHs), considering their formation as being associated to the amplitude of linear energy density fluctuations. To accommodate a wide range of physical relations between the linear and non-linear conditions for collapse, we introduce an additional parameter to the PS mechanism, and that the collapse occurs at either a given cosmic time, or as fluctuations enter the horizon. We study the case where fluctuations obey Gaussian statistics and follow a primordial power spectrum of broken power-law form with a blue spectral index for small scales. We use the observed abundance of super-massive black holes (SMBH) to constrain the extended mass functions taking into account dynamical friction. We further constrain the modified PS by developing a method for converting existing constraints on the PBH mass fraction, derived assuming monochromatic mass distributions for PBHs, into constraints applicable for extended PBH mass functions. We find that when considering well established monochromatic constraints there are regions in parameter space where all the dark matter can be made of PBHs. Of special interest is the region for the characteristic mass of the distribution ∼102 M⊙, for a wide range of blue spectral indices in the scenario where PBHs form as they enter the horizon, where the linear threshold for collapse is of the order of the typical overdensities, as this is close to the black hole masses detected by LIGO which are difficult to explain by stellar collapse.

Learning Numerosity Representations with Transformers: Number Generation Tasks and Out-of-Distribution Generalization

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here, we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

Learning Numerosity Representations with Transformers

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

On a stochastic order induced by an extension of Panjer’s family of discrete distributions

We factorize probability mass functions of discrete distributions belonging to Panjer’s family and to its certain extensions to define a stochastic order on the space of distributions supported on $${\mathbb {N}}_0$$ N 0 . Main properties of this order are presented. Comparison of some well-known distributions with respect to this order allows to generate new families of distributions that satisfy various recurrrence relations. The recursion formula for the probabilities of corresponding compound distributions for one such family is derived. Applications to various domains of reliability theory are provided.