Explanation of Two Important Empirical Relations for Galaxies

The phenomenon of “missing mass” in galaxies has triggered new theoretical exploration, forming a competition between dark matter assumption, modified Newtonian dynamics and modified gravity. Over the past forty years, various versions of the modified scenario have been proposed to simulate the effects of missing mass. These schemes replace the dynamic effect of dark matter by introducing some tiny extra force terms in the dynamic equations. Such extra forces have mainly interactions on large scales of galaxies, such as fitting the Tully-Fisher relation or asymptotically flat rotation curves. The discussion in this paper shows that the evidence of taking the modified schemes as fundamental theory is still insufficient. In this paper, we display a system of simplified galactic dynamical equations derived from weak field and low-speed approximations of Einstein field equations, and then we use it to discuss two important empirical relations in galactic dynamics, namely the Faber-Jackson relation and Tully-Fisher relation, as well as the related fundamental plane. These discussions provide a reference scheme for improving the dispersion of the empirical relations, and also provide a theoretical foundation to analyze the properties of dark matter and galactic structures.

Astrophysical Applications of a Variant to Kepler’s Third Law

It is verified that the Nebula Hypothesis is applicable to the Solar System by way of a straightforward generalization of Kepler’s third law which also confirms that angular momentum transport is achieved by way of the self-gravity of the protoplanetary disk itself as it coalesces into planetesimals. The masses of the planets may then be approximately determined (within 10% error, for three planets) by way of this methodology, using the radius as well as the rate of rotation of the particular planet being considered. This would only be possible, not only in light of the Nebula Hypothesis, but also due to angular momentum transport (as these three planets most ideally express the expectations of angular momentum conservation from the protoplanetary disk). Also in this regard, the rotation of the Sun at its equator is discussed as it is found to be closely related to the planetary issue as it pertains to the evolution and structure of the body. A modified technique from that used in planetary study is then applied to the Galaxy for the purpose of the calculation of dark matter mass, presupposes treating the Galaxy as a homogeneous sphere (of dark matter) that is rotating. The model provides clear evidence of not only flat rotation-curves, but also the lack of centrifugal ejection of stars from galaxies as well as the configuration of the arms of spiral galaxies, along with a sound basis for black hole creation at the center of spiral galaxies.

Star formation properties of galaxy cluster A1767

Abell 1767 is a dynamically relaxed, c D cluster of galaxies with a redshift of 0.0703. Among 250 spectroscopically confirmed member galaxies within a projected radius of 2.5r200, 243 galaxies（ Digital Sky Survey. Based on this ～97%） are spectroscopically covered by the Sloanhomogeneous spectral sample, the stellar evolutionary synthesis code STARLIGHT is applied to investigate the stellar populations and star formation histories of galaxies in this cluster. The star formation properties of galaxies, such as mean stellar ages, metallicities, stellar masses, and star formation rates, are presented as functions of local galaxy density. A strong environmental effect is found such that massive galaxies in the high-density core region of the cluster tend to have higher metallicities, older mean stellar ages, and lower specific star formation rates（SSFRs）, and their recent star formation activities have been remarkably suppressed. In addition, the correlations of the metallicity and SSFR with stellar mass are confirmed.