Zwicky was wrong: a multi-length scale application of the virial theorem to galactic clusters shows no need for Dark Matter.

There are three legs on which the claims over the past 50 years for the need of Dark Matter to explain galaxy observations stands: the huge difference between observed baryonic mass and that inferred from application of the virial equation using the measured rotational velocities; the non-planetary behavior of the rotational velocities with increasing radius; and the anomalous behavior (at least compared to models) of recessional velocities of galaxies and clusters. The first began with Zwicky’s observations about the Como cluster ninety years ago, the second with the pioneering work of Rubin and co-workers in the 60’s; and the third, the current `Crisis in Cosmology’ in which different methodologies give highly accurate but different results for the for the Hubble `constant’. Many have confirmed these original findings, so it is generally assumed that Dark Matter must exist. We treated both legs 2 and 3 extensively in presentations at this meeting last year [1,2] (see also poster [3] in this meeting), and offered alternative theories which needed neither Dark Energy nor Dark Matter nor alternative physics to account for all the data.

This talk focuses on the first leg, the virial theorem and the way it was applied by Zwicky and most since. By using multi-length scale physical analysis and a packed sphere model we show that the mass he (and almost everyone since) inferred from the rotational velocities was too large by a factor of N^1/3, where N is the number of galaxies in the cluster. For the Coma cluster, N ~1000, hence Zwicky’s need for 90% invisible matter. We also show good agreement with recent data from the Virgo cluster and a compendium of merging groups and clusters, neither needing Dark Matter or Dark Energy but consistent with our theories for the other two legs.

[1] George, W.K and Johansson, T. J. (2023) http://www.turbulence-online.com/Publications/WKGeorge_APS_MAS_2023_U_Delaware.pdf

[2] George, W.K. and Johansson, T.J. (2023) “http://www.turbulence-online.com/Publications/A_Fluid_Mechanics_Solution_Galaxy_Rotation_Problem.pdf”

[3] George, W.K and Johansson, T.J.. (2024) Poster in this meeting about the implications JWST findings and our predictions of what it would find.