On the question of the amount of dark matter I want to raise an idea
that I had some 40 years ago and then dismissed a little later thinking
"surely someone must have thought of that". Has anyone in fact really
worked this out?

If a double log scale plot is made of number of objects per unit volume
within some mass range [strictly speaking, within some delta log mass
range](y axis) versus object mass range (x axis) over a very wide range
of sizes from atomic to stellar sizes then this serves as a basis for
considering how much matter is light and dark.

Over the short range of stellar masses that are visible, the graph seems
to have a slope of -1 up to the point at which very massive stars have
behaviour that prevents larger stars forming and the curve dips down
very rapidly.

For atomic/molecular sizes and dust, visibility is achieved by
observation of absorption lines in bright obect spectra. The amount of
material lies (according to my crude calculations at the time based on
insufficient data) quite close to the same -1 slope line.

If in fact a line of slope -1 exists over the entire range of the graph
from atomic scales to stellar scales then the actual amount of material
in each order of magnitude is the same, although this will vary
according to any variations from an exact -1 slope. Given that there are
some 56 orders of magnitude between a hydrogen atom and a star and we
only observe 1 or 2 of these 56 orders of magnitude then it might well
be the case that there is 28 to 56 times times as much matter as is visible.

I had intended to try and work out the dynamics of all the various sized
objects according to accumulation by electrical or chemical forces,
sticking together for dust and gravitation for larger objects, but never
got enough knowledge of some of those processes to be able to
calculate the graph of a theoretical basis. But it always seemed to me
that all those other sizes must exist, as certainly evidenced by
discoveries over the years within the solar system where they are of
course more densely packed.

Of course the shape of the curve would change over time as smaller
objects fall into larger ones and are forever lost. That is, unless this
just happened to be balanced by nova redistributing the matter from
large to small scales again and maintaining a balance. But we would
expect there to be variations in the proportion of these processes over
time and so different aged galaxies would have different amounts of halo.

For objects of size intermediate between dust and very dim stars there
was no means of detecting objects when I first had this thought. Since
then the detectable range has been extended by gravitational lensing,
occultation and possibly other means. How much of the range has been
examined, and what does the graph that I describe above look like with
the latest information?