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Register a new userApplying Modified Gravity (MOG) to the Lensing and Einstein Ring in Abell 3827
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The lensing and Einstein ring at the core of the galaxy cluster Abell 3827 are reproduced in the modified gravity theory MOG. The estimated effective lensing mass $M_L=(1+alpha)M_b=5.2times 10^{12} M_odot$ within $R=18.3$~kpc for a baryon mass $M_b=1.0times 10^{12} M_odot$ within the same radius produces the observed Einstein ring angular radius $theta_E=10$. A detailed derivation of the total lensing mass is based on modeling of the cluster configuration of galaxies, intracluster light and X-ray emission. The MOG can fit the lensing and Einstein ring in Abell 3827 without dark matter as well as General Relativity with dark matter.
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A covariant modified gravity (MOG) is formulated by adding to general relativity two new degrees of freedom, a scalar field gravitational coupling strength $G= 1/chi$ and a gravitational spin 1 vector field $phi_mu$. The $G$ is written as $G=G_N(1+alpha)$ where $G_N$ is Newtons constant, and the gravitational source charge for the vector field is $Q_g=sqrt{alpha G_N}M$, where $M$ is the mass of a body. Cosmological solutions of the theory are derived in a homogeneous and isotropic cosmology. Black holes in MOG are stationary as the end product of gravitational collapse and are axisymmetric solutions with spherical topology. It is shown that the scalar field $chi$ is constant everywhere for an isolated black hole with asymptotic flat boundary condition. A consequence of this is that the scalar field loses its monopole moment radiation.
The modified gravity (MOG) theory is applied to the gravitational wave binary merger GW190814 to demonstrate that the modified Tolman-Oppenheimer-Volkoff equation for a neutron star can produce a mass $M=2.6 -2.7 M_odot$, allowing for the binary secondary component to be identified as a heavy neutron star in the hypothesized mass gap $2.5 - 5 M_odot$.
The equation of motion in the generally covariant modified gravity (MOG) theory leads, for weak gravitational fields and non-relativistic motion, to a modification of Newtons gravitational acceleration law. In addition to the metric $g_{mu u}$, MOG has a vector field $phi_mu$ that couples with gravitational strength to all baryonic matter. The gravitational coupling strength is determined by the MOG parameter $alpha$, while parameter $mu$ is the small effective mass of $phi_mu$. The MOG acceleration law has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train Wreck Cluster mergers. For the SPARC sample of rotationally supported spiral and irregular galaxies, McGaugh et al. [24] (MLS) have found a radial acceleration relation (RAR) that relates accelerations derived from galaxy rotation curves to Newtonian accelerations derived from galaxy mass models. Using the same SPARC galaxy data, mass models independently derived from that data, and MOG parameters $alpha$ and $mu$ that run with galaxy mass, we demonstrate that adjusting galaxy parameters within $pm 1$-sigma bounds can yield MOG predictions consistent with the given rotational velocity data. Moreover, the same adjusted parameters yield a good fit to the RAR of MLS, with the RAR parameter $a_0=(5.4pm .3)times 10^{-11},{rm m/s^2}$.
The non-detection of dark matter (DM) particles in increasingly stringent laboratory searches has encouraged alternative gravity theories where gravity is sourced only from visible matter. Here, we consider whether such theories can pass a two-dimensional test posed by gravitational lensing -- to reproduce a particularly detailed Einstein ring in the core of the galaxy cluster Abell 3827. We find that when we require the lensing mass distribution to strictly follow the shape (ellipticity and position angle) of the light distribution of cluster member galaxies, intracluster stars, and the X-ray emitting intracluster medium, we cannot reproduce the Einstein ring, despite allowing the mass-to-light ratios of these visible components to freely vary with radius to mimic alternative gravity theories. Alternatively, we show that the detailed features of the Einstein ring are accurately reproduced by allowing a smooth, freely oriented DM halo in the lens model, with relatively small contributions from the visible components at a level consistent with their observed brightnesses. This dominant DM component is constrained to have the same orientation as the light from the intracluster stars, indicating that the intracluster stars trace the gravitational potential of this component. The Einstein ring of Abell 3827 therefore presents a new challenge for alternative gravity theories: not only must such theories find agreement between the total lensing mass and visible mass, but they must also find agreement between the projected sky distribution of the lensing mass and that of the visible matter, a more stringent test than has hitherto been posed by lensing data.
We extend a recent work on weak field first order light deflection in the MOdified Gravity (MOG) by comprehensively analyzing the actual observables in gravitational lensing both in the weak and strong field regime. The static spherically symmetric black hole (BH) obtained by Moffat is what we call here the Schwarzschild-MOG (abbreviated as SMOG) containing repulsive Yukawa-like force characterized by the MOG parameter $alpha>0$ diminishing gravitational attraction. We point out a remarkable feature of SMOG, viz., it resembles a regular textit{brane-world} BH in the range $-1<alpha <0$ giving rise to a negative tidal charge $Q$ ($=frac{1}{4}frac{alpha }{1+alpha}$) interpreted as an imprint from the $5D$ bulk with an imaginary source charge $q$ in the brane. The Yukawa-like force of MOG is attractive in the brane-world range enhancing gravitational attraction. For $-infty <alpha <-1$, the SMOG represents a naked singularity. Specifically, we shall investigate the effect of $alpha $ or Yukawa-type forces on the weak (up to third PPN order) and strong field lensing observables. For illustration, we consider the supermassive BH SgrA* with $alpha =0.055$ for the weak field to quantify the deviation of observables from GR but in general we leave $alpha$ unrestricted both in sign and magnitude so that future accurate lensing measurements, which are quite challenging, may constrain $alpha$.
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