Acceleration Constant and Superposition in Modified Newtonian Dynamics(1/3)

As an alternative to Newtonian dynamics at small acceleration regime, MOdified Newtonian Dynamics(MOND) is very competitive against dark matter in elucidating dynamical phenomena related to galaxy-scaleobjects. MOND has been very successful in interpreting the flat rotation curve and Tully-Fisher relation ofspiral galaxies. However, much less attentions have been dedicated to elliptical galaxies.The nonlinearity in MOND leads to the conundrum of how to superpose the influences by different massdistributions. Most of the baryons (a.k.a. “normal matter”) in elliptical galaxies reside in stars, thus we canmodel an elliptical galaxy as a one component mass distribution. However, for spiral galaxy we need at leasttwo components (a disk and a bulge, and perhaps a gaseous disk as well). We deem that elliptical galaxiesprovide a clean (or cleaner) experiment for MOND. A large part of the project will be devoted to thedynamics of elliptical galaxies in the framework of MOND.Observationally, the essence of MOND is the luminous mass is the same as the dynamical mass. Thedynamical mass of an elliptical galaxy can be measured by its stellar kinematics (velocity dispersion) or bythe images of a background source if the galaxy is the gravitational lens. We worked out the formulations forboth phenomena for spherical mass distribution. We apply these methods to publicly available data on stronglensing and stellar kinematics of elliptical galaxies, and then obtain stellar mass of each galaxy. Our maingoal is to estimate the acceleration constant (the utmost important quantity) in MOND solely from ellipticalgalaxies.The next step is to go beyond spherical model. We will develop corresponding formulations for slightlydeformed spherical distribution. This will enable us, for the first time, to do some detail mass modelling“freely”, which is not easy in MOND. Moreover we will have a handle on the uncertainty of the accelerationconstant found by the spherical model.We also want to study two more topics related to the nonlinearity of MOND: strong gravitational lensing byspiral galaxies and cosmological weak gravitational lensing. Both are potentially important for MOND butlargely ignored. The difficult and interesting part of both topics is the same old problem on how to sum upthe contributions of different mass distributions. For spiral galaxies we need a disk and a bulge (and perhapsa gaseous disk), and for weak lensing we have layers of perturbations.