Early-type galaxies (ETGs) are supposed to follow the virial relation M = ke2 Re=G, with M being the mass,  being the stellar velocity dispersion, Re being the eective radius, G being Newton's constant, and ke being the virial factor, a geometry factor of order unity. Applying this relation to (a) the ATLAS3D sample of Cappellari et al. (2013) and (b) the sample of Saglia et al. (2016) gives ensemble- averaged factors hkei = 5:15  0:09 and hkei = 4:01  0:18, respectively, with the dierence arising from dierent denitions of eective velocity dispersions. The two datasets reveal a statistically signicant tilt of the empirical relation relative to the theoretical virial relation such that M / (2 Re)0:92. This tilt disappears when replacing Re with the semi-major axis of the projected half-light ellipse, a. All best-t scaling relations show zero intrinsic scatter, implying that the mass plane of ETGs is fully determined by the virial relation. Whenever a comparison is possible, my results are consistent with, and conrm, the results by Cappellari et al. (2013). The difference between the relations using either a or Re arises from a known lack of highly elliptical high-mass galaxies; this leads to a scaling (1-) / M0:12, with  being the ellipticity and Re = a p 1 - . Accordingly, a, not Re, is the correct proxy for the scale radius of ETGs. By geometry, this implies that early-type galaxies are axisymmetric and oblate in general, in agreement with published results from modeling based on kinematics and light distributions.

The masses of supermassive black holes in active galactic nuclei (AGN) can be derived spec- troscopically via virial mass estimators based on selected broad optical/ultraviolet emission lines. These estimates commonly use the line width as a proxy for the gas speed and the monochromatic continuum luminosity, λLλ, as a proxy for the radius of the broad line region. However, if the size of the broad line region scales with the bolometric AGN luminosity rather than λLλ, mass estimates based on different emission lines will show a systematic discrepancy which is a function of the color of the AGN continuum. This has actually been observed in mass estimates based on Hα/Hβ and Civ lines, indicating that AGN broad line regions indeed scale with bolometric luminosity. Given that this effect seems to have been overlooked as yet, currently used single-epoch mass estimates are likely to be biased.

Massive gravity provides a natural solution for the dark energy problem of cosmology and is also a candidate for resolving the dark matter problem. I demonstrate that, assuming reasonable scaling relations, massive gravity can provide for Milgrom’s law of gravity (or “modified Newtonian dynamics”) which is known to remove the need for particle dark matter from galactic dynamics. Milgrom’s law comes with a characteristic acceleration, Milgrom’s constant, which is observationally constrained to a0 ≈ 1.1×10−10ms−2. In the derivation presented here, this constant arises naturally from the cosmologically required mass of gravitons like a0 ∝ c√ ∝ cH0√3 , with , H0, and  being the cosmological constant, the Hubble constant, and the third cosmological parameter, respectively. My derivation suggests that massive gravity could be the mechanism behind both, dark matter and dark energy.

The jet production efficiency of radio galaxies can be quantified by comparison of their kinetic jet powers Pjet and Bondi accretion powers PB. These two parameters are known to be related linearly, with the jet power resulting from the Bondi power by multiplication with an efficiency factor of order 1%. Using a recently published (Nemmen & Tchekhovskoy 2014) high-quality sample of 27 radio galaxies, I construct a PB − Pjet diagram that includes information on optical AGN types as far as available. This diagram indicates that the jet production efficiency is a function of AGN type: Seyfert 2 galaxies seem to be systematically (with a false alarm probability of 4.3 × 10−4) less efficient, by about one order of magnitude, in powering jets than Seyfert 1 galaxies, LINERs, or the remaining radio galaxies. This suggests an evolutionary sequence from Sy 2s to Sy 1s and LINERs, controlled by an interplay of jets on the one hand and dust and gas in galactic nuclei on the other hand. When taking this effect into account, the PB − Pjet relation is probably much tighter intrinsically than currently assumed.

Polarization is a basic property of light and is fundamentally linked to the internal geometry of a source of radiation. Polarimetry complements photometric, spectroscopic, and imaging analyses of sources of radiation and has made possible multiple astrophysical discoveries. In this article I review (i) the physical basics of polarization: electromagnetic waves, photons, and parameterizations; (ii) astrophysical sources of polarization: scattering, synchrotron radiation, active media, and the Zeeman, Goldreich- Kylafis, and Hanle effects, as well as interactions between polarization and matter (like birefringence, Faraday rotation, or the Chandrasekhar-Fermi effect); (iii) observational methodology: on-sky geometry, influence of atmosphere and instrumental polarization, polarization statistics, and observational techniques for radio, optical, and X/γ wavelengths; and (iv) science cases for astronomical polarimetry: solar and stellar physics, planetary system bodies, interstellar matter, astrobiology, astronomical masers, pulsars, galactic magnetic fields, gamma-ray bursts, active galactic nuclei, and cosmic microwave background radiation.

The empirical mass discrepancy–acceleration (MDA) relation of disk galaxies provides a key test for models of galactic dynamics. In terms of modified laws of gravity and/or inertia, the MDA relation quantifies the transition from Newtonian to modified dynamics at low centripetal accelerations ac ≤ 10−10ms−2. As yet, neither dynamical models based on dark matter nor proposed modifications of the laws of gravity/inertia have predicted the functional form of the MDA relation. In this work, I revisit the MDA data and compare them to four different theoretical scaling laws. Three of these scaling laws are entirely empirical; the fourth one – the “simple μ” function of Modified Newtonian Dynamics – derives from a toy model of gravity based on massive gravitons (the “graviton picture”). All theoretical MDA relations comprise one free parameter of the dimension of an acceleration, Milgrom’s constant aM. I find that the “simple μ” function provides a good fit to the data free of notable systematic residuals and provides the best fit among the four scaling laws tested. The best-fit value of Milgrom’s constant is aM = (1.06 ± 0.05) × 10−10ms−2. Given the successful prediction of the functional form of the MDA relation, plus an overall agreement with the observed kinematics of stellar systems spanning eight orders of magnitude in size and 14 orders of magnitude in mass, I conclude that the “graviton picture” is sufficient (albeit probably not a necessary nor unique approach) to describe galactic dynamics on all scales well beyond the scale of the solar system. This suggests that, at least on galactic scales, gravity behaves as if it was mediated by massive particles.

Modified Newtonian Dynamics (MOND) is a possible solution for the missing mass problem in galac- tic dynamics; its predictions are in good agreement with observations in the limit of weak accelerations. However, MOND does not derive from a physical mechanism and does not make predictions on the transitional regime from Newtonian to modified dynamics; rather, empirical transition functions have to be constructed from the boundary conditions and comparisons with observations. I compare the formalism of classical MOND to the scaling law derived from a toy model of gravity based on virtual massive gravitons (the “graviton picture”) which I proposed recently. I conclude that MOND naturally derives from the “graviton picture” at least for the case of non-relativistic, highly symmetric dynamical systems. This suggests that – to first order – the “graviton picture” indeed provides a valid candidate for the physical mechanism behind MOND and gravity on galactic scales in general.

I present a simple scheme for the treatment of gravitational interactions on galactic scales. In anal- ogy with known mechanisms of quantum field theory, I assume ad hoc that gravitation is mediated by virtual exchange particles – gravitons – with very small but non-zero masses. The resulting den- sity and mass profiles are proportional to the mass of the gravitating body. The mass profile scales with the centripetal acceleration experienced by a test particle orbiting the central mass, but this comes at the cost of postulating a universal characteristic acceleration a0 ≈ 4.3 × 10−12msec−2 (or 8πa0 ≈ 1.1×10−10msec−2). The scheme predicts the asymptotic flattening of galactic rotation curves, the Tully-Fisher/Faber-Jackson relations, the mass discrepancy–acceleration relation of galaxies, the surface brightness–acceleration relation of galaxies, the kinematics of galaxy clusters, and “Renzo’s rule” correctly; additional (dark) mass components are not required. Given that it is based on various ad-hoc assumptions and given further limitations, the scheme I present is not yet a consistent theory of gravitation; rather, it is a “toy model” providing a convenient scaling law that simplifies the description of gravity on galactic scales.