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Analysis of Elliptical Galaxies


This analysis is part of a sequence of logical steps that are described in Investigation.  The density/radius relationship of elliptical galaxies is not claimed to be evidence for antigravity matter.  However the objective of this page is to demonstrate that it is also not evidence against antigravity matter. 



According to the AGM Theory most elliptical galaxies should be a little below the large scale AGM Exclusion Density which should be independent of radius.  This is because :-

  • They are in the AGM Excluded phase as described in Behaviour > Phase Change.
  • Most of them are far bigger than the G/P limit and their density should not be affected by AGM Pressure or anti-gravity matter wind.
  • They extend outwards to some degree beyond their shared AGM Boundary.


Data Source and Calculation

To test this prediction elliptical galaxy data were acquired from Hyperleda using the sql statement “select * where objtype='G' and type='E'”.  Galaxies were removed from the sample with negative or no recession velocity data, or with no brightness or radius data.  This left 3408 galaxies.  The following calculations were performed:-


  • The distance to each galaxy was estimated from the recession velocity (vgsr) assuming a Hubble Constant of 70 km sec-1 Mpc-1.
  • The radius was calculated from the distance and the apparent angular diameter, taking the geometric mean of the long and short axes (but see the considerations below).
  • The equivalent number of suns of luminosity was calculated from the magnitude and the distance.
  • The mass of each galaxy was estimated by multiplying the luminosity (in sols) by 2 × 1030 kgs / sol.
  • The average density of each galaxy was estimated from the mass and radius.
  • For each galazy the degree of redshift z was calculated as vgsr / c.
  • The corrected colour of each galaxy was calculated using the same approach as used for globular clusters and described in Analysis of Globular Cluster Colour except that the correction parameters were adjusted to minimise the standard deviation of the corrected elliptical galaxy colour data.


Most of this calculation is well known and obvious but some special considerations are described below.


ExpansionPulseConsideration 1 - Geometric effect of Expansion of the Universe

In Figure 1 a pulse of light starts from a distant galaxy at the time of z = 1.  At that time the distance between the galaxy and the earth (D then) was half what it is now (D now).  At the time of z = 0 (the present) the light arrives at the earth and the luminance of the light pulse is measured.  It can be seen from Figure 1 that if we are to equate absolute brightness, apparent brightness and distance we must use D now.  D now dictates how much the pulse has spread out. 


This applies for any positive value of z.


Hubble’s Law has been validated using the apparent brightness of Cepheid variables and other bightness related techniques (source).  We therefore assume that Hubble’s Law gives an estimate of D now.


ExpansionRadiusIn Figure 2 two light beams are emitted from the extremities of the same galaxy heading towards the Earth at the time of z = 1.  A few stars happen to be in between source and destination.  These stars do not obstruct or divert the light beams.  They only serve to mark the route for the purpose of this analysis. 


The universe expands while the light beams are travelling.  Despite this expansion straight lines remain straight.  The light beams were moving in the direction of the Earth at the start, and arrive at the Earth at the time of z = 0.  The angle between the two light beams is measured.


It can be seen from Figure 2 that if we are to equate angular size, actual size and distance we must use D then.


This applies for any positive value of z.


As a result of the argument above the absolute brightness and therefore the mass of the galaxy is calculated using D now but the radius of the galaxy is calculated using D then.


RadiusLuminanceConsideration 2 – Radius / Luminance effect

In the original data the angular size of each galaxy is measured to the isophote (contour of constant luminance) at which luminance is 25 mag.arcsec-2.   However the length of a geometrically similar line of sight through a spherical object increases as the radius of the object increases as depicted in Figure 3 on the right.  As a result the average (3 dimensional) density along the line of sight that passes through the 25 mag.arcsec-2 isophote reduces as the galaxy radius increases.  To allow galaxies of different sizes to be compared the radius calculation must take account of this Radius / Luminance effect. 


The Radius / Luminance relationship of an elliptical galaxy can be predicted by the de Vaucouleurs’ Law (source).  A typical plot of elliptical galaxy luminance against radius is shown in Figure 4.  Re is the radius that contains half the galaxy’s brightness and Ie is the luminance at that radius.  When R = Re the luminance is inversely proportional to the square of radius.  On the right of this graph luminance is inversely proportional to approximately tenth power of radius.  The value in this power function continues to increase as radius increases.


Therefore we apply a correction to the radius such that:-


Corrected Radius = Radius × (10000 ly / Radius (ly))Fr


Where Fr is a correction parameter with a starting guess of ¼.  This value corresponds with a guess that for a 10000 ly radius galaxy the radius of the 25 mag.arcsec-2 isophote is somewhat greater than Re at a radius where luminance is inversely proportional to the forth power of radius.  Later we investigate the effect of adjusting the value of Fr.


The figure 10000 ly is chosen arbitrarily.  This means that the definition of radius is also arbitrary, but since the original definition of radius (the 25 mag.arcsec-2 isophote) was also arbitrary this has no real effect.  We are generating a radius value that allows galaxies of different size to be compared.  This is not the radius of the AGM Boundary, though we are assuming that the AGM Boundary is nearby in the outer extremities of the galaxy.


Consideration 3 – Redshifting

A typical star has approximately the radiation spectrum of a black body at a temperature of 5523 K (source).  As the light from a star is redshifted it moves out of the visible range.  In addition each photon loses energy as its wavelength increases.  Figure 5 shows several spectra from such a black body that have been redshifted by varying amounts.  The amount of energy in the visible range between blue and red vertical lines reduces as z increases.  We use this graph to explore the relationship between visible light and redshifting.  This leads to the points on the graph shown in Figure 6.  We derive a forth power polynomial to define the trendline fitted to the data points as shown.


This polynomial is then used to generate a Brightness Multiplication Factor which is used in the calculation of the absolute brightness and therefore the mass of the galaxies.


If galaxy brightness is increased by the above argument then galaxy radius must also be increased because radius is measured at a particular isophote as described above.  The following is included in the radius calculation:-


Corrected Radius = Radius calculated so far × (Brightness Multiplication Factor)Fr


Where Fr is the correction parameter with a starting guess of ¼ as described in Consideration 2 above.



The following graphs are produced.





Observations and Concerns

The concerns listed from 3) onwards below are not believed to be evidence against the antigravity matter theory.  They all relate to observations over very large distances and may be clues to other cosmological effects.

1)      Figure 7 shows that with the guessed value of Fr = 0.25 the range of most elliptical galaxy densities is less than one decade.  Figure 10 shows that with a higher value of Fr = 0.4 the majority of elliptical galaxies are even more tightly grouped.  Figure 12 shows them in the context of the red Dnx line as generated in Investigation.  The Dnx line runs vertically to the right of the elliptical galaxies because the AGM Boundary is assumed to be within the calculated radius of the galaxy.

2)      When Fr = 0.4 smaller elliptical galaxies are less dense.  It may be that these galaxies are actually falling apart.  This would be consistent with Figure 11 which shows that below a galaxy radius of about 1 ×1020 m (~10000 ly) dispersion velocity appears to fall dramatically, suggesting that the stars in these galaxies are less constrained by gravity.  If this were the case the majority of the stars in these galaxies are in the AGM Mixed state as described in Behaviour.

3)      It is worrying that the majority of the galaxies also appear to have a limited range of radii.

4)      It is also worrying that maximum galaxy radius and maximum galaxy mass appear to increase with distance as shown in Figures 8 and 9.  For the most distant galaxies z ~ 0.8 so we are observing these as they were when the universe was significantly younger.  This suggests the maximum size of elliptical galaxies has been getting smaller for a long time.

5)      It is also worrying that if the amount of antigravity matter in the universe was constant and if Gnn, Gna and Gaa remained constant we would actually expect the AGM Exclusion Density to be higher in the distant past.  At z = 1 we would expect the AGM Exclusion Density to be 8 times higher.  This does not come out of the data.


© Copyright Tim E Simmons 2008 to 2015. Last updated 28th July 2015.  Major changes are logged in AGM Change Log.