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

Radius, R

The radius of the star's photosphere

Luminosity, L

The total electromagnetic power radiated by a star (Watts)
L = kR²T_eff⁴

Effective Temperature, T_eff

The temperature of the surface of the photosphere that give the total luminosity by Planck's Blackbody radiation

Bolometric Magnitude, M_bol

The total Luminosity expressed in Magnitudes relative to the sun [M_bol(sun) = +4.75]
M_bol(*) = M_bol(sun) - 2.5 log(L_*/L_sun) The bolometric magnitude can be related to the visible magnitude using a bolometric correction (BC)
M_bol = M_v + BC(T_eff)

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(T_eff)

Empirical Relationship between CI, M_bol and T_eff

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 [669] page36
has give an empirical fit of M_bol and CI to their T_eff 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