Skip to main content# Calculating Local Group Dark Energy using Better Mass Data: Cosmological (and Pedagogical) Results

Published onJun 01, 2020

Calculating Local Group Dark Energy using Better Mass Data: Cosmological (and Pedagogical) Results

The Local Group (LG)’s mass is mostly in M31 and the Milky Way Galaxy(MW), a central 0.75 Mpc bound binary of ordinary and dark matter mass M. The LG’s M is condensed from a 3 Mpc sphere. Dark energy (DE) density “antigravity” causes an outward acceleration (greater with radius R) of the dwarf population relative to M’s inward gravitation. The LG’s dwarfs show an increasing outer velocity (V) component with radius (R) in observations. We compare the data to a local theoretical curve using cosmologically estimated “ΛCDM” values. The critical density is 9.5×10^{-30} g/cm^{3}. Observations by the WMAP and others give 1.0803 of critical density (expands forever). The cosmologically determined DE density is 7×10^{-30} g/cm^{3}. Recent larger LG masses give a better local DE curve agreement with data than our earlier studies. For the MW mass, Gaia used 34 globular clusters + Hubble’s 12 more distant clusters to get 1.5×10^{12} solar masses. (Watkins L. et al., 2020, ApJ). M31’s mass is less certain, ranging from a disk + halo mass of 1×10^{12} to a distant rotation curve “all halo” 4×10^{12} solar masses. The MW–M31 binary mass can be estimated from the members’ moving apart nearly radially and now approaching. Gaia observations predict a future almost head-on collision. This motion supports a Kahn-Woltjer binary mass estimate of ~5.3×10^{12} solar masses by Binney and Tremaine (2008 *Galactic Dynamics*) and McLeod et al (2017). We choose a conservative LG mass ~4×10^{12} to calculate a V versus R line using the cosmologically determined ΛCDM DE density, 7×10^{-30} g/cm^{3} (Saarinen and Terrikorpi, 2014, *Astronomy and Astrophysics*, **568**, A33), An excellent fit to the data is obtained. Smaller masses give poorer fits. Assuming the DE density is zero and a LG mass of 4×10^{12}, gives a bad fit to the data. It appears the DE local density certainly is not zero with no support for variation with time. Dark energy acceleration in the Local Group provides an alternative and perhaps more convincing demonstration on a local scale for students than cosmological estimates. The popular rubber band Hubble law is more than a relative motion demo of nearby galaxies. Stretching the band is dark energy.