simple MOND question

In article , "Phillip Helbig (undress to
reply)" writes:

But the equation immediately before Eq. (2),

F_N = ma^2/a_0,

can be rewritten as

F_N = ma(a/a_0).

The standard expression, of course, is

F_N = ma.

In the "deep MOND regime", where a is much smaller than a_0, the factor
in parentheses is much less than 1. So, the force in this case is the
standard force multiplied by a factor much less than 1. In other words,
at low acceleration ("deep MOND regime"), the MOND force should be
LESS than the standard force. However, this regime corresponds to the
outskirts of galaxies, where the observed orbital velocity is much MORE
than expected from the standard force law (which is why, if one assumes
the standard force law, one is led to dark matter to explain the
additional force).

OK, answering my own question here. F_N is the NEWTONIAN force. What
is confusing is that since the Newtonian force is known (F_N=ma), it is
somewhat confusing to write an expression for it which includes a_0, the
new constant (units of acceleration) introduced by MOND, and where a is
NOT the NEWTONIAN acceleration, but rather the "total" acceleration.
Presumably, the interesting thing is the acceleration predicted by MOND,
which is "a" above. So, in the "deep MOND regime", we have

a = sqrt(a_0*F_N/m).

Since

F_N = GMm/(r^2),

we have

a = sqrt(GMa_0)/r.

Contrasting this with the Newtonian acceleration, it falls off as 1/r
instead of 1/r^2 (in the low-acceleration regime), so the MOND
acceleration is of course larger.

Since the acceleration in a circular orbit is sqrt(GM/r^2), we get

v^4 = GMa_0.

In other words, the circular velocity is (in the low-acceleration
regime) independent of the radius, leading to the famous flat rotation
curves of spiral galaxies.

Mond introduces a new constant with the dimensions of acceleration, but
spiral galaxies don't have a constant ACCELERATION in the
low-acceleration regime, but rather a constant CIRCULAR VELOCITY.