Astronomical

In article ,
"Stupendous_Man" writes:

Philip Helbig wrote:

However, this doesn't take the redshift into account. Redshift means
the photons lose energy. This gives a factor of 1+z in the flux. This
is what the original poster suggested dropping if the detector just
counts photons and not energy. However, due to the redshift the arrival
rate of photons is also decreased by 1+z. Together, these two effects
give another factor of (1+z)**2 with relation to the flux, or 1+z with
relation to the distance. Thus, together with the geometric factor
above, the luminosity distance is greater than the angular-size distance
by the factor (1+z)**2.

Okay, I understand this so far. It agrees with the standard
textbook explanations. Good!

OK. Note the following: the geometric factor gives (1+z)**2 in flux or
(1+z) in distance. The reduced photon rate gives (1+z) in flux and the
reduced energy per photon another (1+z) in flux. That makes for
(1+z)**2 in flux or another (1+z) in distance, for a total of (1+z)**2
in distance. This is just a summary of all the stuff you agree with!

If one "just counts photons and not energy", then the "luminosity
distance" thus defined is greater than the angular-size distance by the
factor (1+z)**1.5, since their arrival rate is still decreased by 1+z
even if one doesn't worry about the energy of an individual photon.

Right. The total is (1+z)**2 in distance or (1+z)**4 in flux. If we
leave out the fact that the energy of each individual photon is reduced
and "just count photons", then we have to divide (1+z)**4 in flux by
(1+z) which gives us (1+z)**3 in flux or (1+z)**1.5 in distance.

Sorry, I don't quite get this part. If I follow your argument here,
then the "just-counting-photon-distance" method shares one factor
with the standard luminosity distance -- arrival times are dilated --
but not another -- the decreasing energy of each photon.

It shares THREE factors of (1+z) in flux with the standard luminosity
distance, and doesn't share one. Since distance goes like the
reciprocal of flux squared, that means 3/2 or 1.5.

It seems
to me that the result should be a dependence on redshift which
involves one fewer power of (1+z): the "just-counting-photons-distance"
should go like (1+z)**3.

Yes, IN FLUX. The 1.5 power is in DISTANCE.

But I see in your statement above that
the "just-counting-photons-distance" should go like the angular-size
distance, which is (1+z)**2, times a factor of (1+z)**1.5; that would
make the overall factor (1+z)**3.5.