canopus56 wrote:

In using Schaefer's alogrithm (as implemented by Bogan), I notice that
if you put in red color stars - those with positive color indices
between 0.75 and 2.0 - the calculator returns a brighter TLM and not a
fainter TLM.

This is counter to my understanding of how the human eye sees faint
stars. The human eye should see red colored K and M stars at a fainter
TLM than white colored 0 index stars.

Are you sure about that? Schaefer makes the opposite assumption.

...[C]onsider the case of two stars with equal V magnitude but
different color. An observer using day vision would pronounce the
two stars to be of equal brightness, whereas if night vision were
being used the redder of the two stars would appear fainter. (1990
p. 212)

This is what I'd expect, since the scotopic sensitivity peak is bluer
than the photopic peak.

Keep in mind what this implies about limiting magnitude. The limiting
magnitude is the dimmest thing you can see. As you turn the magnitude
dial toward the dim end, the red stars disappear first. These red stars
have the same V magnitude as bluer stars you can still see, meaning that
your limiting magnitude is *brighter* for redder stars.

I have compared Schaefer's code with Bogan's Javascript port and I am
reasonably certain is a faithful translation.

In comparing Schaefer's 1990 paper with Bogan's Javascript port with
respect to color index, I notice the following difference:

Bogan's code: FC=Math.pow(10,0.4*(CI/2-1)); // COLOR OF STAR

Equation 13 in Schaefer 1990 at 215
-2.5 log (Fc) = 1-(B-V)/2 if log(B)3.17

which implies:

Fc = 10 ^ (0.4 * (1-(CI/2))

Is CI handled properly in the calculator?

You're missing a minus sign in that last equation. It should be

Fc = 10 ^ (-0.4 * (1 - ( CI / 2 )))

which is identical to the equation you've attributed to Bogan.

Fc is larger for redder stars and smaller for bluer ones.

B-V Fc
mu Cep 2.35 1.17
alp Ori 1.85 0.93
alp Tau 1.50 0.79
bet Gem 1.00 0.63
alp CMi 0.38 0.47
bet Ori -0.03 0.39
gam Ori -0.22 0.36

This is consistent with Schaefer's assertion. Using his nomenclature,
the V brightness I* is proportional to the perceived brightness I
multiplied by his color correction factor Fc,

I* ~ IFc

in some linear brightness units (e.g. lamberts), not magnitude. Turning
this around, the perceived brightness is the V brightness divided by Fc,
so bigger Fc (redder stars) implies dimmer perceived brightness for the
same V brightness.

Converting to magnitudes, the limiting magnitude for redder stars is a
smaller number.

- Ernie http://home.comcast.net/~erniew