Andromeda’s Supermassive Black Hole Projected Long-term Accretion Rate

Universe Formation Home Page

Jon M. Wilson



A formula for calculating the half-life of galaxy clusters is proposed. A galactic half-life is the estimated amount of time that the most massive supermassive black hole (SMBH) in the galaxy cluster will have accreted one half of the mass in the cluster. In this study the SMBH in the center of the Andromeda Galaxy is used as an example.  The calculation is based on a projection of the SMBH continuing its exponentially decreasing rate of accretion that it had in its first 13 billion years. The calculated half-life for the Andromeda SMBH is approximately 1.4327e14 years from the Big Bang. If the growth rate continues to decrease exponentially for five half-lives, almost 97 percent of the Local Group galaxy cluster’s mass will be consumed by this supermassive black hole or ejected from the cluster. That is 1.00289 e15, or about one quadrillion years after the Big Bang.


Several proposals have suggested that black holes could be significant factors in the formation of new universes. Lee Smolin in “Life of the Cosmos” in 1997 and more recently a universe formation hypothesis,, describes the mechanism by which the most massive central supermassive black hole in a gravitationally-bound galaxy cluster could grow to become the dominant massive object in the cluster by accretion of stars, gas, and dust. Under certain conditions, such as an extremely massive SMBH becoming more massive than the rest of the cluster, a quantum fluctuation could be triggered in the massive singularity, causing a universe-forming big bang. Part of the verification or falsification of this hypothesis could be done by an N-body simulation. These simulations require an enormous amount of computer power and time. Some plausible projection of the growth of the supermassive black hole is needed to prepare an N-body simulation budget proposal. The Local Group of galaxies is used for these calculations as it is the only one with sufficient data at this time.



The two largest galaxies in the Local Group, Andromeda and Milky Way, are on a collision course and will merge in about four billion years. It is likely that their central black holes will orbit each other and eventually merge in this process. Trinagaium is the third largest galaxy in the cluster and will also become part of the merged galaxy. Andromeda’s central SMBH is by far the most massive object in the cluster; therefore, it will become the dominant object in the resulting galaxy that consolidates all the gravitationally-bound galaxies in the Local Group. It is what I call a dominant supermassive black hole. The calculation is done as if this SMBH will accrete most of the mass in the cluster that is not ejected, since the cluster will eventually be one galaxy. The total mass of the satellite galaxies is relatively small compared to that of the three largest galaxies. Their mass is less than the confidence level estimated for the mass of the entire cluster, so satellite galaxy mass has not been added to the total used in this calculation. Calculations are also done and displayed in the table for the Milky Way, Andromeda, and Trinagaium separately, but these results are moot, as all of these galaxies will merge long before their central SMBHs will accrete more than a small percentage of their galaxy. Trinagaium has a relatively small SMBH, so the calculation produces infinity as a half-life. Its half-life may not actually be infinite, but it is so large that the result is not meaningful.

The Local Group and the Andromeda SMBH were chosen for this study, as this combination has sufficient data available. When considering long-term cosmic events, the Local Group may be treated as an independent entity separate from the rest of the universe due the expansion of the universe driven by dark energy. In about 40 billion years, the local cluster of galaxies will be isolated from the rest of the universe as more distant galaxies disappear over the galactic event horizon. [11] The Great Attractor, a hypothesized and little understood object that is gravitationally pulling the Local Group, is not considered in these calculations.


For the purpose of these calculations, a common start date of 13 billion years ago is used even though the current galaxies, which were formed from the merger of two or more older galaxies, may not be that old. It is reasonable to assume that the older galaxies that merged to form Andromeda had SMBHs that may have formed about 13 billion years ago; therefore, 13 billion years is the elapsed time used for the half-life calculation. Galaxies can gain and lose mass over time, but for the purpose of the calculation, the net total mass change is assumed to accrete to the central SMBH of the galaxy. Thus, the mass of the central supermassive black hole is added to the present mass to get the galaxy starting mass. The equation used is as follows: Half life = (time * log 2) / log (beginning mass / ending mass).


It is assumed that SMBH growth rate decreases exponentially as it consumes the closest material first and adds mass from gas, dust, stars, and stellar black holes [9] whose galactic orbits have been perturbed. Perturbance events become rarer over time as the universe expands. SMBHs also grow in spurts or cycles in which high rates of feeding on mass are followed by periods of low or almost no consumption, possibly caused by some of the unconsumed mass being flung outward taking other nearby stars, gas, and other matter away from the galaxy enter. Galaxy mergers are major contributors to perturbance by disrupting the orbits of stars and black holes by gravitational reflex and other means. It is plausible that when galaxies merge, few, if any, stars collide or even become accreted by the SMBH at first. Rather, galaxy collisions increase the perturbance rate that will cause the galactic orbits of more stars to be sent to the galaxy center. This is sometimes caused when a star, for example, has a close encounter with a larger body, causing it to be redirected toward the galaxy center or accelerate by gravitational reflex to greater than the escape velocity of the galaxy. Two- and three-star pairs may be more likely to have one star accreted by the SMBH and also have one of the pair or group accelerated out of the galaxy. As the approximately 50 satellite galaxies continue to merge, perturbance will provide a continuous environment in which orbits of stars, black holes, dust, and gas that are perturbed all provide a regular diet for the dominant SMBH over many trillions of years. Mass that is ejected from the galaxy by gravitational reflex and reaches escape velocity contributes to the percent of the galaxy mass in the SMBH, as ejected material is no longer in the galaxy.


All central SMBHs have not had the same history, so they have had different growth rates. It is plausible that the early history positions one or more SMBHs to accrete faster and thus become the dominant SMBH in a cluster. For example, the Milky Way data would produce a half-life result by more than an order of magnitude longer than Andromeda, as its SMBH is much smaller. Once a SMBH becomes the dominant feature in its galaxy cluster, it will likely continue to dominate, and its successful growth contributes to more growth. Hence, the SMBH in Andromeda will be the dominant SMBH in the combined galaxy that will form from all the galaxies in the Local Group.


For the purpose of this calculation, dark matter is treated in the same way as baryonic matter. This assumption is not certain, and more information about dark matter is needed to determine if dark and baryonic matter function the same gravitationally. This half-life equation may become less accurate in estimating galactic mass accretion to SMBHs after several half-lives, as the calculation does not consider certain energy components, such as the loss of mass from the galaxy to neutrinos and photons or the potential gain in mass from dark energy in the later stages of the galaxy.


One verification method for the galactic half-life hypothesis would be to compare a continuum of equivalent type galaxies and their masses relative to their SMBHs from many different eras, since using information from more distant galaxies is, in effect, looking back in time. The hypothesis that dominant SMBHs grow at an exponentially decreasing rate based upon their early growth may be verified at some time in the future with accurate measurements of mass of very distant galaxies and their SMBHs.


Table for Calculating Galactic Half-Life

Name of galaxy in cluster

NGC number



galaxy mass M

SMBH mass


Galaxy mass remaining after loss to smbh in 13 billion years

Half-life years

Years for five half-lives or 96.75 % of the mass of the future Local Group galaxy to be accreted by the dominant SMBH or ejected from the galaxy.

Milky Way























Local Group Combined










The calculated half-life for the Andromeda SMBH is approximately 1.4327e14 years from the Big Bang. If the growth rate of this SMBH continues to decrease exponentially for five half-lives, almost 97 percent of the galaxy cluster will be consumed by this supermassive black hole or ejected from the future Local Group galaxy cluster. That time needed is 1.00289e15 or one about quadrillion years. Even with the fastest computers and a very large budget, it is not feasible to run a standard N-body simulation at this time in order to validate or falsify the universe formation from gravitationally-bound galaxies hypothesis. However, for now this method provides an estimate for the growth rate of the Andromeda SMBH and deposition of the outcome of most of the galaxy cluster’s mass which is either accreted by the SMBH, lost by ejection from the cluster, or lost in the form of energy.


References will be added.


Copyright © 2013 - John M. Wilson