Many astrophysical phenomena are modeled by an inverse power law distribution at high values of the random variable but often at low values of the random variable we have a departure from an inverse power law. In order to insert a continuous transition from low to high values of the random variable we analyse the truncated gamma-Pareto distribution in two versions by deriving the most important statistical parameters. The application of the results to the distribution in energy of cosmic rays allows deriving an analytical expression for the average energy, which is 2.6 GeV.

This study will see the resurgence of interest in precise velocity dispersion measurements, both for the study of galactic and active nuclei kinematics. As several works suggest, an excellent tactic to measure σ is to use the absorption lines of the calcium triplet, as it is a spectral region relatively free from complications. The discovery of an empirical relationship between the mass of the central black hole (M•) and σ was the leading guide of my detailed study of the calcium triplet region. This search for more accurate methods to calculate the dispersion of velocities, in addition to the careful study of uncertainties. After investing so much time in the development and improvement of the method and its application to so many galaxies, it is time to reap the rewards of this effort, using my results to address a series of questions concerning the physics of galaxies.

Observed spiral galaxy rotation curves allow a measurement of the warm dark matter particle velocity dispersion and mass. The measured thermal relic mass mh ≈ 100 eV is in disagreement with limits, typically in the range 1 to 4 keV. We review the measurements, update the no freeze-in and no freeze-out scenario of warm dark matter, and try to identify the cause of the discrepancies between measurements and limits.

The root-mean-square of non-relativistic warm dark matter particle velocities scales as vhrms(a)=vhrms(1)/a , where a is the expansion parameter of the universe. This velocity dispersion results in a cut-off of the power spectrum of density fluctuations due to dark matter free-streaming. Let kfs (teq) be the free-streaming comoving cut-off wavenumber at the time of equal densities of radiation and matter. We obtain , and , at 68% confidence, from the observed distributions of galaxy stellar masses and rest frame ultra-violet luminosities. This result is consistent with reionization. From the velocity dispersion cut-off mass we obtain the limits vhrms(1)kfs (teq) >1.5 Mpc-1. These results are in agreement with previous measurements based on spiral galaxy rotation curves, and on the formation of first galaxies and reionization. These measured parameters determine the temperature-to-mass ratio of warm dark matter. This ratio happens to be in agreement with the no freeze-in and no freeze-out warm dark matter scenario of spin 0 dark matter particles decoupling early on from the standard model sector. Spin 1/2 and spin 1 dark matter are disfavored if nature has chosen the no freeze-in and no freeze-out scenario. An extension of the standard model of quarks and leptons, with scalar dark matter that couples to the Higgs boson that is in agreement with all current measurements, is briefly reviewed. Discrepancies with limits on dark matter particle mass that can be found in the literature are addressed.

We derive the truncated version of the Weibull—Pareto distribution, deriving the probability density function, the distribution function, the average value, the rth moment about the origin, the media, the random generation of values and the maximum likelihood estimator which allows deriving the three parameters. The astrophysical applications of the Weibull—Pareto distribution are the initial mass function for stars, the luminosity function for the galaxies of the Sloan Digital Sky Survey, the luminosity function for QSO and the photometric maximum of galaxies of the 2 MASS Redshift Survey.

The discovery of a giant comet (C/2014 UN271) at a distance of 29 AU in October 2014 and the later discovery in September 2021 of a dramatic brightening episode offers an ideal opportunity for verifying the predictions of a “biological” comet. The eruptions of the comet at a heliocentric distance of 20 AU are plausibly explained as due to high pressure venting of the products of microbial metabolism in radioactively heated subsurface lakes. The standard non-biological model of comets is woefully inadequate to account for eruptions at such large distances from the sun where surface temperatures are as low as 60 K.

Through an analytical approach, we show that the Hubble constant is not unique and has two distinct values. The first of these values is consistent with the measurements by Riess et al., while the second value is consistent with the measurements by the Planck Collaboration. This is a new alternative approach that does not depend on the standard ΛCDM model and its constraints. Our analysis shows that the tension is due to a geometric mismatch in the comparison of the measurements which is equal to the temporal diameter of the surface of last scattering. Since the calculated values are essentially identical to the corresponding measured values, we conclude that the non-congruency of the ending point of the Riess et al. measurement and the starting point of the Planck Collaboration measurement, on the surface of last scattering, is the source of tension in the measurements. Further, the surprising consistency of the calculated values of the Hubble constant with the corresponding measured values confirms both the extreme fidelity of the measurements and the validity of the proposed approach.

The Sun would be subject to a significant variation of orbital motion about the solar system barycentre if a small planet is orbiting at a very large distance. This paper assesses if the Planet 9 hypothesis, the existence of a ninth planet, is consistent with the planetary hypothesis: the synchronisation of sunspot emergence to solar inertial motion (SIM) induced by the planets. We show that SIM would be profoundly affected if Planet 9 exists and that the hypothesised effect of SIM on sunspot emergence would be radically different from the effect of SIM due to the existing eight planets. We compare the frequency and time variation of Sun to barycentre distance, RB, calculated for both the eight and nine planet systems, with the frequency and time variation of sunspot number (SSN). We show that including Planet 9 improves the coherence between RB and SSN in the decadal, centennial and millennial time range. Additionally, as the variation of RB is sensitive to the longitude and period of Planet 9, it is possible to adjust both parameters to fit the variation of RB to the SSN record and obtain new estimates of the period and present longitude of Planet 9. Finally, we develop the hypothesis that planetary induced solar acceleration reduces meridional flow and consequently sunspot emergence thereby providing an explanation for the observed coincidence of grand solar minima with intervals of extreme solar acceleration.

This study is concerned with determining the altitude of the sun under the horizon to the beginning and the end of the true and pseudo dawn and dusk. In 2007 and 2008, the Sky Quality Meter (SQM) was used in four regions in Malaysia to measure the brightness at night, pseudo dawn, true dawn, true dusk and pseudo dusk. The measurements were taken when the device was directed to the position of sunrise and sunset at the horizontal angle of the sunrise or sunset and at five degrees above the horizon during the entire monitoring period. The altitude of the sun for the true dusk was found to be -14.38° ± 0.91° and for the beginning of the pseudo dusk was found to be -14.86° ± 0.91° and the end of the pseudo dusk is -17.8° ± 0.7°, while for the beginning of the true dawn it was found to be -14.19° ± 0.52° (for high confidence -14.71°) and for the pseudo dawn was found to be -18.62° ± 0.82°. The light magnitude of the full night after the pseudo dusk was found to be 20.77 ± 0.93 mag./arcsec2, while it was found to be 22.17 ± 0.1 mag./arcsec2 before the pseudo dawn.

Herein is introduced a simple scalar field model derived from classical based kinetic energy, gravitational potential energy, and Special Relativity’s rest mass energy. By applying a classical orbit over the scalar field, relativistic effects are predicted. The scalar field is then applied to a classical model of the Hydrogen atom resulting in a relativistic effect equal to the binding energy of the Hydrogen atom. In addition, the model derives the fine structure constant due to the gravitational effect. The relativistic effects are then discretized in increments equal to the model’s gravitational induced constant. The discretization produces the Hydrogen atom spectral emissions and an angular momentum equal to Planck’s reduced constant. The model is not presented as a replacement for current theory, rather it is for inspection and illustration of how a simplistic model may offer a fundamental bridge between the more complex, time proven theories of General Relativity and Quantum Mechanics.