New Probability Distributions in Astrophysics: XII. Truncation for the Gompertz Distribution

Analytical functions which fit the probability distributions of stars and galaxies can provide insight into how these distributions originate. In order to introduce a truncated version of the Gompertz distribution, we derive its probability density function, its distribution function, its average value, its second moment about the origin, its median, its random generation of values and a maximum likelihood estimator for its two unknown parameters. The astrophysical applications of the Gompertz distribution are the initial mass function for stars, the luminosity function for the galaxies of the Sloan Digital Sky Survey, the photometric maximum of galaxies visible in the GLADE+ catalog and a model for the mean absolute magnitude in the GLADE+ catalog as a function of the redshift.

New Probability Distributions in Astrophysics: XIII. Truncation for the Benini Distribution

In order to introduce a right truncated version of the Benini distribution, we derive its probability density function, its distribution function, its average value, its kth moment about the origin, its median, how to randomly generate its values, and the maximum likelihood estimator for its three unknown parameters. The astrophysical application of the Benini distribution and its right truncated version is to the initial mass function for stars.

New Probability Distributions in Astrophysics: XI. Left Truncation for the Topp-Leone Distribution

The Topp-Leone (T-L) distribution has aided the modeling of scientific data in many contexts. We demonstrate how it can be adapted to model astrophysical data. We analyse the left truncated version of the T-L distribution, deriving its probability density function (PDF), distribution function, average value, rth moment about the origin, median, the random generation of its values, and its maximum likelihood estimator, which allows us to derive the two unknown parameters. The T-L distribution, in its regular and truncated versions, is then applied to model the initial mass function for the stars. A comparison is made with specific clusters and between proposed functions for the IMF. The Topp-Leone distribution can provide an excellent fit in some cases.

New Probability Distributions in Astrophysics: VI. The Truncated Sujatha Distribution

The truncated version of the two-parameter Sujatha distribution is analysed. In particular, its probability density function and distribution function are obtained. The results are applied to the initial mass function for stars, to the luminosity function for galaxies, to the number of galaxies as a function of the redshift and to the average absolute magnitude of a galaxy as a function of its redshift.

Long-period eclipsing binaries:towards the true mass-luminosity relation.I.the test sample,observations and data analysis

The mass-luminosity relation is a fundamental law of astrophysics.We have suggested that the currently used mass-luminosity relation is not correct for the M/M⊙>2.7 range of mass since it was created utilizing double-lined eclipsing binaries,where the components are synchronized and consequently change each other's evolutionary path.To exclude this effect,we have started a project to study longperiod massive eclipsing binaries in order to construct radial velocity curves and determine masses for the components.We outline our project and present the selected test sample together with the first HRS/SALT spectral observations and the software package,FITTING BINARY STARS(FBS),that we developed for the analysis of our spectral data.As the first result,we present the radial velocity curves and best-fit orbital elements for the two components of the FP Car binary system from our test sample.

Evaluating Helium Variations By Modeling Red Giant Branch Bump of Large Magellanic Cluster NGC 1978

Many evidences show that the Multiple Population(MP)features exist not only in old clusters but also in intermediate-age clusters in the Megallanic Clouds(MCs),which are characterized by star-to-star abundance scatter of several elements,including helium(He).The red giant branch bump(RGBB)’s photometric properties are proved to be related to the variation in helium abundances of the member stars in star clusters.We use the"Modules for Experiments in Stellar Astrophysics"(MESA)stellar evolution code to calculate the evolution sequences of stars along the red giant branch(RGB)with changing helium content.Following the RGB sequences,we then generate a luminosity function of the RGB stars within the grid of input helium abundances,which are compared with the observational data of an intermediate-age MC cluster NGC 1978.

The simplest way to get a cluster's parameters in the Gaia era(Dolidze 41)

The astro-photometric parameters of the open star cluster Dolidze 41, which is located in the constellation Cygnus, have been investigated using the Gaia DR2 large survey that is merged with the near infrared Two Micron All Sky Survey(2 MASS) database.The radial density distribution(limited,core and tidal radii), color-magnitude diagrams, galactocentric coordinates, distances, color excess and age of Dolidze 41 are presented.The Gaia DR2 astrometry helped us to define the membership of the cluster stars easily.The luminosity and mass functions, the entire luminosity and mass, and the relaxation time of the cluster have been estimated as well.

Do protostellar fountains shape the regional core mass function?

The emerging massive binary system associated with AFGL 961 signifies the latest generation of massive star and cluster formation in the Rosette Molecular Complex. We present the detection of a compact cluster of dusty cores toward the AFGL 961 region based on continuum imaging at 1.3 mm by the Submillimeter Array. The binary components of AFGL 961 are associated with the most intensive millime- ter emission cores or envelopes, confirming that they are indeed in an early stage of evolution. The other massive cores, however, are found to congregate in the close vicinity of the central high-mass protostellar binary. They have no apparent infrared counterparts and are, in particular, well aligned transverse to the bipolar molecular outflows originating from AFGL 961. This provides evidence for a likely triggered origin of the massive cores. All 40 individual cores with masses ranging between 0.6 and 15 Mo were detected above a 3 σ level of 3.6 mJy beam-1 （or 0.4 M⊙）, based on which we derive a total core mass of 107 M⊙ in the AFGL 961 region. As compared to the stellar initial mass function, a shallow slope of 1.8 is, however, derived from the best fit to the mass spectrum of the millimeter cores with a prestellar and/or protostel- lar origin. The flatter core mass distribution in the AFGL 961 region is attributed here to dynamic perturbations from the massive molecular outflows that originated from the massive protostellar binary, which may have altered the otherwise more quiescent conditions of core or star formation, enhanced the formation of more massive cores and, as a result, influenced the core mass distribution in its close vicinity.

New Probability Distributions in Astrophysics: X. Truncation and Mass-Luminosity Relationship for the Frèchet Distribution

The Frèchet distribution has aided the modelling of scientific data in many contexts. We demonstrate how it can be adapted to model astrophysical data. We analyze the truncated version of the Frèchet distribution deriving the probability density function (PDF), the distribution function, the average value, the rth moment about the origin, the median, the random generation of values and the maximum likelihood estimator, which allows us to derive the two unknown parameters. This first PDF in the regular and truncated version is then applied to model the mass of the stars. A canonical transformation from the mass to the luminosity allows us to derive a new PDF, which is derived in its regular and truncated version. Finally, we apply this new PDF model on the distribution in luminosity of NGC 2362.