Mass and temperature relation in stars

[jamespompey2109]

Hoping someone can help me here, I'm only a student so I'm sorry if my question is badly worded.

I'm doing my maths dissertation on a binary eclipsing star and I'm trying to work out the mass of one of my stars. I know the B-V value and effective temperature, and I believe the equation I need to be using is
log(M/Msun)=(((-1.744951 X + 30.31681) X - 196.2387) X + 562.6774) X - 604.076, where X=log(T), but I'm not getting anywhere near the required value. I don't understand this equation or where the constants come from in the first place, but it's one that I've been given.

I'll add that I'm observing RT And, and if anyone can help me get to the right values in the next few hours that would be amazing!

 

[mfb]

Plot.

If we take the logarithm with base 10 (an odd choice), the lower root corresponds to 5451 K, which roughly matches the surface temperature of Sun.

Google finds the first two numbers in a Greek MSc thesis - and nowhere else.

 

[Ken G]

What's more, there is only a connection between the mass of a star, and its surface temperature, for main-sequence stars. And even for main-sequence stars, it is absurd to use a formula that involves 7 decimal places, given that the surface temperature of a main-sequence star will vary by more than 10% over its lifetime, and additional variation comes from other variables like composition and rotation rate. So all the numbers in that formula should be rounded off to 2 decimal places at the most, or it's kind of a silly formula. But more to the point, if the eclipsing binary is not two main-sequence stars, then the formula really means nothing at all.

 

[mfb]

There are large cancellations in the formula, rounding everything to two digits leads to a completely different shape in the relevant X range.

Here is a plot of both.

 

[Ken G]

How bizarre, a fit using a polynomial whose low-order derivatives are all set to be close to zero. You're right, the precision is needed to get those tiny derivatives, the number of decimal places is constrained by the degree of the polynomial. That pretty much guarantees the formula has no physics in it, I'd prefer something that's more approximate but does reflect the actual physics that sets the temperature, but I realize it is only intended as an analytic fit.

 

[Jenab2]

Here's a table you can interpolate from.
http://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt

These are main sequence stars. The effective temperature is in the 2nd column. The B-V color index is in the 7th column. The estimated mass for the star (in solar masses) is in the 16th column.

I've made curve-fits to data such as these in the past. Unless one is careful, the ends of the interpolation functions won't meet up and there will be jump discontinuities. For that matter, if one isn't careful, the function might trace a curve that the data don't follow.