Effects of Lens Motion and Uneven Magnification on Image Spectra

Counter to intuition, the images of an extended galaxy lensed by a moving galaxy cluster should have slightly different spectra in any metric gravity theory. This is mainly for two reasons. One relies on the gravitational potential of a moving lens being time-dependent (the $\text{Moving}$ $\text{Cluster}$ $\text{Effect}$, $\text{MCE}$). The other is due to uneven magnification across the extended, rotating source (the $\text{Differential}$ $\text{Magnification}$ $\text{Effect}$, $\text{DME}$). The time delay between the images can also cause their redshifts to differ because of cosmological expansion. This Differential Expansion Effect is likely to be small. Using a simple model, we derive these effects from first principles. One application would be to the Bullet Cluster, whose large tangential velocity may be inconsistent with the $\Lambda CDM$ paradigm. This velocity can be estimated with complicated hydrodynamic models. Uncertainties with such models can be avoided using the MCE. We argue that the MCE should be observable with ALMA. However, such measurements can be corrupted by the DME if typical spiral galaxies are used as sources. Fortunately, we find that if detailed spectral line profiles were available, then the DME and MCE could be distinguished. It might also be feasible to calculate how much the DME should affect the mean redshift of each image. Resolved observations of the source would be required to do this accurately. The DME is of order the source angular size divided by the Einstein radius times the redshift variation across the source. Thus, it mostly affects nearly edge-on spiral galaxies in certain orientations. This suggests that observers should reduce the DME by careful choice of target, a possibility we discuss in some detail.Comment: 15 pages, 8 figures, 2 tables. This is the peer-reviewed version which has been accepted for publication in Monthly Notices of the Royal Astronomical Societ

A third family of super dense stars in the presence of antikaon condensates

The formation of $K^-$ and $\bar K^0$ condensation in $\beta$-equilibrated hyperonic matter is investigated within a relativistic mean field model. In this model, baryon-baryon and (anti)kaon-baryon interactions are mediated by the exchange of mesons. It is found that antikaon condensation is not only sensitive to the equation of state but also to antikaon optical potential depth. For large values of antikaon optical potential depth, $K^-$ condensation sets in before the appearance of negatively charged hyperons. We treat $K^-$ condensation as a first order phase transition. The Gibbs criteria and global charge conservation laws are used to describe the mixed phase. Nucleons and $\Lambda$ hyperons behave dynamically in the mixed phase. A second order phase transition to $\bar K^0$ condensation occurs in the pure $K^-$ condensed phase. Along with $K^-$ condensation, $\bar K^0$ condensation makes the equation of state softer thus resulting in smaller maximum mass stars compared with the case without any condensate. This equation of state also leads to a stable sequence of compact stars called the third family branch, beyond the neutron star branch. The compact stars in the third family branch have different compositions and smaller radii than that of the neutron star branch.Comment: 21 pages; RevTex; 5 figures include

A new line on the wide binary test of gravity

The relative velocity distribution of wide binary (WB) stars is sensitive to the law of gravity at the low accelerations typical of galactic outskirts. I consider the feasibility of this wide binary test using the `line velocity' method. This involves considering only the velocity components along the direction within the sky plane orthogonal to the systemic proper motion of each WB. I apply this technique to the WB sample of Hernandez et. al. (2019), carefully accounting for large-angle effects at one order beyond leading. Based on Monte Carlo trials, the uncertainty in the one-dimensional velocity dispersion is $\approx 100$ m/s when using sky-projected relative velocities. Using line velocities reduces this to $\approx 30$ m/s because these are much less affected by distance uncertainties. My analysis does not support the Hernandez et. al. (2019) claim of a clear departure from Newtonian dynamics beyond a radius of $\approx 10$ kAU, partly because I use $2\sigma$ outlier rejection to clean their sample first. Nonetheless, the uncertainties are small enough that existing WB data are nearly sufficient to distinguish Newtonian dynamics from Modified Newtonian Dynamics. I estimate that $\approx 1000$ WB systems will be required for this purpose if using only line velocities. In addition to a larger sample, it will also be important to control for systematics like undetected companions and moving groups. This could be done statistically. The contamination can be minimized by considering a narrow theoretically motivated range of parameters and focusing on how different theories predict different proportions of WBs in this region.Comment: 14 pages, 9 figures, 1 table. Accepted for publication in the Monthly Notices of the Royal Astronomical Society in this for