 ## The Hertzsrung-Russell Diagram (HR Diagram)as related to Stellar Radius and Temperature

##### written by Larry Bogan

The HR Diagrams plots stellar brightness versus surface temperature

• Luminosity vs. Surface Temperature
• Absolute Magnitude vs. Color Index
• Absolute Magnitude vs. Spectral Class
The radius of the star's photosphere
Luminosity, L
The total electromagnetic power radiated by a star (Watts)
L = kR2Teff4
Effective Temperature, Teff
The temperature of the surface of the photosphere that give the total luminosity by Planck's Blackbody radiation
Bolometric Magnitude, Mbol
The total Luminosity expressed in Magnitudes relative to the sun [Mbol(sun) = +4.75]
Mbol(*) = Mbol(sun) - 2.5 log(L*/Lsun) The bolometric magnitude can be related to the visible magnitude using a bolometric correction (BC)
Mbol = Mv + BC(Teff)
Color Index, B - V
The stars color as given by its blue magnitude minus visible magnitude. Since magnitudes are smaller for larger brightness, a brighter blue star will have a more negative Color Index.
Color Index ,CI, is monotonically related to the temperature of the star
B-V = CI(Teff)

### Empirical Relationship between CI, Mbol and Teff

.

Cameron Reed of Alma College (Michigan) in
"The Composite Observational-Theoretical HR Diagram"
The Journal of the Royal Astronomical Society of Canada
February/March 1998 Volume92 Number 1  page36
has give an empirical fit of Mbol and CI to their Teff dependence.

• B-V = -3.684 log(T) + 14.551
for log(T) < 3.961
• B-V = 0.344 [log(T)]2 -3.402 log(T) +8.037
for log(T) >3.961
• BC = -8.499 [log(T)- 4]4 + 13.421[log(T)- 4]3- 8.131[log(T)- 4]2 - 3.901 [log(T)- 4] - 0.438

The form below allows you to enter T and R and then allows you to calculate
L, BC and CI which gives Mbol and Mv.