Mass discrepancy–acceleration relation in Einstein rings

Abstract

We study the Mass Discrepancy-Acceleration Relation (MDAR) of 57 elliptical galaxies by their Einstein rings from the Sloan Lens ACS Survey (SLACS). The mass discrepancy between the lensing mass and the baryonic mass derived from population synthesis is larger when the acceleration of the elliptical galaxy lenses is smaller. The MDAR is also related to surface mass density discrepancy. At the Einstein ring, these lenses belong to high-surface-mass density galaxies. Similarly, we find that the discrepancy between the lensing and stellar surface mass density is small. It is consistent with the recent discovery of dynamical surface mass density discrepancy in disk galaxies where the discrepancy is smaller when surface density is larger. We also find relativistic modified Newtonian dynamics (MOND) can naturally explain the MDAR and surface mass density discrepancy in 57 Einstein rings. Moreover, the lensing mass, the dynamical mass and the stellar mass of these galaxies are consistent with each other in relativistic MOND.

Study of gravitational fields and globular cluster systems of early-type galaxies

“…A dedicated test of MOND in slow rotators based on weak lensing would be welcome (Rong et al 2018 had 144 slow rotators in their sample). Analysis of strong lensing by massive ETGs by Tian & Ko (2017) revealed that their dynamical masses agree with the MOND prediction and the interpolating function found for the LTGs. The small systematic deviation of around 20% could have easily been caused by a systematic error in the estimated stellar M/L.…”

The Imprint of Spiral Arms on the Galactic Rotation Curve

“…Whether it is caused by MOND (Milgrom 1983, 2016a, or is natural in ΛCDM (Keller & Wadsley 2017;Ludlow et al 2017;Navarro et al 2017), or not (McGaugh 2015Milgrom 2016b;Famaey et al 2018;Tian & Ko 2019), or maybe sort of (Di Cintio & Lelli 2016;Desmond 2017), is neither here nor there for the purposes of this paper. All that matters here is that there exists a relation between the observed and baryon-predicted accelerations in external spiral galaxies that has been calibrated empirically Lelli et al 2017;Tian & Ko 2017) without reference to or dependence on any particular theory hypothesized to explain the missing mass problem. The critical if obvious assumption is that the Milky Way adheres to the same relation that has been established for other galaxies.…”

Halo Acceleration Relation

“…Milgrom (2019) even extended it to galaxy groups down to 10 −14 m s −2 for baryonic acceleration. Moreover, the relation also holds in relativistic effect such as gravitational lensing (Tian & Ko 2017, showed the relation in 57 Einstein rings).…”

“…The observed acceleration for spirals is obtained by dynamics (McGaugh et al 2016) from SPARC database (Lelli et al 2016), and for ellipticals by gravitational lensing (Tian & Ko 2017) from SLACS database (Auger et al 2009). The baryonic acceleration comes from total baryonic mass via population synthesis and mass model of galaxies (Tian & Ko 2017). Altogether, our sample comprises: ii.…”

“…As the data of elliptical galaxies is important for the high acceleration regime of HAR, we need to be cautious in mass estimation. The baryonic mass of SLACS lenses is estimated from population synthesis with Salpeter IMF (e.g., Auger et al (2009); Tian & Ko (2017)). We apply 20% uncertainty in the stellar mass by Salpeter IMF to gauge the influence on the results.…”