Phillip Helbig---remove CLOTHES to reply
December 29th 05, 10:06 AM
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.
"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.