Magnitudes
Magnitudes
This set of notes by Nick Strobel covers: the magnitude system and the relation
between the color index and temperature. Vocabulary terms are italicized.
- Fainter things have larger, more positive magnitudes.
- Can have negative magnitudes (really bright objects).
- Equal ratios of intensity correspond to equal intervals of
magnitude. NOT equal intervals of intensity corresponding to equal
intervals of magnitude.
Rule: Change magnitude by interval of 5 corresponds to change of
brightness of a factor of 100 times.
If change in magnitude = 1, then there is 2.512 factor change of brightness.
If change in magnitude = 2, then there is 2.512 
2.512 factor change
of brightness NOT 2 2.512!
If change in magnitude = 2, then there is 2.512 2.512 2.512
factor change of brightness NOT 3 2.512!
- Apparent magnitude--brightness we see from Earth.
- Absolute magnitude--brightness we would see if object was at 10
parsecs (measures Luminosity!).
- Flux--amount of energy reaching every square centimeter of our
detector every second. The flux of starlight we measure =
(FLUX at star surface), where 
= star radius and 
=
distance to the star.
FLUX at star surface = 
, where 
is the Stefan-Boltzmann
constant and 
is the
temperature at the surface.
- Luminosity--amount of energy radiated by object every second.
Luminosity = (surface area)
FLUX, i.e.,
.
From inverse square law we have: 
(flux we measure) =
Hot stars appear bluer than cooler stars. Cooler stars are redder than hotter
stars. The B-V color is a way of quantifying this using two different filters;
one a blue (B) filter that only lets a narrow range of colors or wavelengths
through (the blue ones), and a ``visible'' (V) filter that only lets the
wavelengths close to the green-yellow band through.
A hot star has a B-V color index close to 0 or negative, while a cool
star has a B-V color index close to 2.5. Other stars are somewhere in between.
So here are the steps to determine the B-V color index:
- Measure flux with two different filters (B, V).
- Flux tells you the magnitude (brightness) at the wavelength of the filter.
- Find magnitude difference in the two filters, B-V.
last updated 29 Aug 95
Nick Strobel --
Email:
strobel@astro.washington.edu
(206) 543-1979
University of Washington
Astronomy
Box 351580
Seattle, WA 98195-1580