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Astronomy and Cosmology
Astronomy and Astrophysics
Star Radius & Mass from Spectral Class, B-V, Luminosity
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[QUOTE="gunhed508, post: 5458359, member: 208900"] Wow - I guess there aren't many Astrophysicists reading this forum. :( I seemed to have found some answers on my own without resorting to cornering a very busy professor at my local college. :) For those interested in this subject, particularly what's involved in rendering the approximate color, size, and luminosity of local stars, I've done a lot of the legwork for you! In my searching, I found a couple of potential equations to estimate a star's Surface Temperature from its BV color index. I used good-old MS Excel to plot the [URL='http://skyserver.sdss.org/dr1/en/proj/advanced/hr/radius1.asp']simplified table[/URL] from my previous post to compare it to the two equations. The first is from Yahoo! Answers, of all places, from a person at UTK who left [URL='https://answers.yahoo.com/question/index?qid=20080809081008AA6mzdJ']this post[/URL]. The equation follows: If B-V > -0.0413, then T = 10^{ [14.551 - (B-V)] / 3.684 } If B-V < -0.0413, then T = 10^{ 4.945 - sqrt[ 1.087353 + 2.906977 (B-V) ] } The second post was from an individual at UNI, who had created an online http://www.uni.edu/morgans/stars/b_v.html to perform the calculation, which looks like a least-squares curve fit for a table using 6 or 7 data points. I gleaned this equation (using the provided table of constants) from the javascript code: C1=3.9791451067; C2=-0.6544992269; C3=1.7406900424; C4=-4.6088151541; C5=6.7925997799; C6=-5.3969098913; C7=2.1929703765; C8=-0.3594957393; logt=C1+C2*bmv+C3*pow(bmv,2)+C4*pow(bmv,3)+C5*pow(bmv,4)+C6*pow(bmv,5)+C7*pow(bmv,6)+C8*pow(bmv,7); t=pow(10,logt); As I said, I plotted both equations over the [URL='http://skyserver.sdss.org/dr1/en/proj/advanced/hr/radius1.asp']original table[/URL], and compared results. Despite the UTK method requiring an inequality, I found that its curve seemed to fit better. The UNI method fit OK, but at the endpoints, the curve seemed to become more exaggerated and less reliable. Once I knew the temperature, I could calculate the [URL='https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#Temperature_of_stars']Radius of the star[/URL] using equations derived from the Boltzmann Law: R/Rsol = (Tsol/T)^2 * SQRT(L/Lsol) Since I'm using the [URL='http://astronexus.com/node/34']HYG data set[/URL], the luminosity is already expressed in ratio to Sol, so it made at least one thing easy. Also, I attempted to use the spetrum data from the set (where possible) to infer the temperature, and, thus the radius using some [URL='http://www.isthe.com/chongo/tech/astro/HR-temp-mass-table-byhrclass.html']work already curated[/URL] by Landon Curt Noll. Some spectrum data was imcomplete, so I made my best guess. Those gaps in the data where I had no spectrum data, I used the B-V color index to calculate the temperature. Those stars with no spectrum or color index were dropped from my data set. The result, thusfar, is this: [URL]http://www.marsgate.net/stars/starmap.html[/URL] Please note this is a work in progress, and will only function smoothly on high-end computers; I doubt a tablet could handle it. Also, it's not designed to work with Internet Explorer, as I found it lacking in many respects. [/QUOTE]
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Star Radius & Mass from Spectral Class, B-V, Luminosity
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