Rigel wrote:in V1.2 I've put Hipparcos stars with a parallax < 0.0002" to this limit value, because I don't think it could be possible to detect stars more distant than 5000 pc, or am I wrong in this supposition ?
No, you're right! But that doesn't mean you must exclude this star from the catalogue, for reasons I explained in the previous post. It may not be possible to detect stars 5000 pc away in Tycho, but
this star was detected! This means that the star is
not 5000 pc away, but much closer. I'll make a try to put the logic simple:
A) The Tycho catalogue is magnitude limited, not distance limited. It is only complete to about V=10.5.
B) A class III source of V=10.5 and (for example!!) B=12.0
B-V=1.5
absolute V magnitude ~ -1.5, this translates to a distance of about 2000 pc. Thus, class III sources of B-V=1.5 can be seen out to a distance of about 2000 pc in the Tycho catalogue.
C) A class V source of V=10.5 and (for example!!) B=12.0
B-V=1.5
absolute V magnitude ~ 9, this translates to a distance of about 20 pc. Thus, class V sources of B-V=1.5 can be seen out to a distance of about
20 pc in the Tycho catalogue.
Assume, for the sake of argument, that you find a star at the limiting magnitude V=10.5 with B-V=1.5 and the oddly small parallax 0.0002" with standard error 0.010". Should you disregard this star? No! Because even if you add the parallax error to the parallax, and get the parallax 0.0102", the corresponding distance is still 100 pc. That is, we say that the star with one-sigma confidence is further away than 100 pc. Similarly, we have that on the two-sigma level (parallax 0.0202"), the star is further away than 50 pc. But according to C) we wouldn't be able to see this star if it was of class V and at the distance of 100 pc or even 50 pc, because the furthest we can see class V sources with B-V=1.5 is 20 pc. Thus the star is not of class V but class III => we derive with B) the "colour" distance 2000 pc corresponding parallax 0.0005" which is consistent with 0.0002"+/-0.010".
I hope you now see that it is generally wrong to dismiss stars with small parallaxes. We only use the parallaxes to differentiate between class III and class V stars, and then a small parallax tells us at least that the star is distant, which is useful information.
Rigel wrote:And I've rejected all Tycho stars only with a new calculated parallax from the B-V color index < 0.0002 " for the same reason...
Well... The faintest stars in Tycho have about V=12. A parallax of 0.0002"
a distance of 5000 pc
an absolute magnitude of Mv = -1.5. A smaller parallax
an even brighter absolute magnitude (Mv < -1.5), but I don't see how you could possibly deduce such a bright absolute magnitude. According to the fit P3 you sent me, the brightest Mv seems to be ~ -1.
To deduce a larger distance than 5000 pc from a V = 12 mag star you need the absolute magnitude to be Mv < -1.5. If you do find stars with deduced "colour" parallaxes as small or smaller than 0.0002", this suggests an error somewhere in your code!
Regarding finding a fitting function Mv = f(B-V) for various classes, I think the best you can do is to use the Hipparcos data (as you've already done). There will always be a spread due to, for example, variable extinction, which you cannot correct for with only B-V colours. That's why it's important to find the RMS of your fit to determine how accurate your "colour" parallaxes are. With more colours it would be possible to correct for extinction as well and get a more accurate fit, but this involves more work since you need to check other sources than the Hipparcos and Tycho catalogues and make (somewhat difficult) cross identifications. Currently I estimate that the derived distances using your procedure have an error of about 50%. Not too bad
OK, I realise that all this may seem like difficult stuff, and maybe I'm not too good at explaining it, but don't give up. You've come a long way already, so don't hesitate to ask me about specifics. And the reward is a larger and more accurately simulated universe!
/Alexis
Great work, and good luck with your students..!
