H-R DIAGRAM OUTLINE


I.  Magnitude

A. apparent magnitude:  m2 - m1 = -2.5log(I2/I1)   [ where: m2 - m1 is the magnitude difference between star 2 and star 1 and I2/I1 is the ratio of the intensity of star 2 to star 1 ]

1.  equation above defined by Pogson (1856) matches the ancient magnitude scale as defined by Hipparchus, but uses the measured intensity to determine the magnitude
2.  Hipparchus defined the brightest stars to be 1st magnitude and the faintest he could see to be 6th magnitude; in order to match the ancient scale (small numbers indicating bright magnitudes and larger numbers indicating fainter magnitudes), a negative sign is defined before the log function
3.  since it turns out that a difference of 5 magnitudes in Hipparchus' magnitude scale is equivilent to a ratio of 100:1 in intensity; the constant 2.5 (before the log function in the definition) is included to transform a ratio of 100:1 in intensity into 5 "steps" of magnitude brightness

B. absolute magnitude:  apparent magnitude a star would have at a standard distance of 10 parsec

1.  the intensity of a star falls off as one over the square of the distance (I = I0/r2); combining this property with the definitions of apparent and absolute magnitude we get the follow relationship between apparent and absolute magnitude and distance in parsecs
2.  r = 10(0.2(m-M)+1.0)      where:  r = distance in parsec (pc)
                                                         (m-M) = distance modulus = apparent mag. - absolute mag

C.  stellar luminosity:  total radiative power output of a star; the absolute magnitude of a star is related to the luminosity through the definition of magnitude

II. Surface Temperature

A.  stellar spectral classification: OBAFGKM (hot -> cool)

B.  color index (eq: B-V, blue mag. minus visual mag.)

III.  The Hertzsprung-Russell Diagram 

A.  definition: plot of absolute magnitude verses spectral type

B.  Color-Magnitude Diagram (CMD): observational HR diagram, usually apparent mag. of co-distant stars in a cluster verses color index

C.  observations needed to produce a CMD

1.  photometry of cluster at the telescope
a.  using 2 or 3 filters
b.  program stars, standard stars
c.  CCD calibration frames
2.  standard CCD pre-processing
3.  photometric reductions of data
a.  program stars: instrumental mags
b.  standard stars: zero points, transformations, etc.
4.  transformation of program stars to standard system

D.  analysis of CMD
1.  MS fitting:  determine cluster distance (must correct for interstellar extinction, otherwise distance is over-estimated)
2.  2-color diagram:  use to measure "reddening" of  starlight by dust; then use reddening to determine the interstellar extinction (how much the starlight is dimmed by intervening dust)
3.  MS turn-off (bluest stars still on the MS):  these points on the CMD represent the most massive stars that are just ending their MS life-time; the length of time a given mass star spends in its MS stage can be estimated from stellar models and so the age of these turn-off stars can be estimated; since all the stars in a given cluster began life at approximately the same time, this is also the cluster's age as a whole