## The Hertzsrung-Russell Diagram (HR Diagram)

as related to Stellar Radius
and Temperature

*This page uses ***Java Script** for the
Calculations

##### 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 =
kR^{2}T_{eff}^{4}
- 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

The form below allows you to enter T and R and then allows you to calculate

L, BC and CI which gives M_{bol} and M_{v}.

*© Larry Bogan - Cambridge Station, N.S. Canada - June 1998*