The Calibration of absolute magnitude M

1
The Calibration of absolute magnitude (M)
M m - 5 logd / 10pc
Spectra
like stars (Same T)
5 star formula (M)
Apparent magnitude (m)
Distance (d)
Parallax (P)
2
Distances to the stars

• Direct method stellar parallax
• no assumptions need be made about the star
• Observations measure the apparent shift in the
  position of a near-by star over a 6 month time
  interval
• The point! The Earth moves half way around its
  orbit in this time interval

3
Distant , fixed stars
Obs. 2
Earths orbit
Distance, d
1 AU
P
Sun
Near-by star
Obs. 1
Idea is that observations give P the angle of
parallax
4
Time from Obs. 1 to Obs. 2 6 months
View from Obs. 1
View from Obs. 2
Measure Angular shift 2 P
5

• Trigonometry Tan (P) 1 AU / distance (d)
• The clever bit
• for small angles Tan(P) ? P(radians)
• P(radians) (2 p / 360) P(degrees)
• P(arcsec.) P(degrees) x 3600
• Result
• d 206,265 AU / P(arcsec.)

purely from numerical conversion terms
6

• Notes definition
• if P 1 second of arc, then d 206,265 AU
• hence if the observed parallax is 1 second of
  arc the distance is defined to be 1 parsec
• so the conversion factor is 1 parsec 206,265 AU
• Final result (another 5 star general)
• d(parsec) 1 / P(arcsec.)

? OOTETK
7
Parallax aint easy

• Parallax shifts are fractions of an arc second
• ground based limits P gt 0.05 arcsec. (d lt 20 pc)
• space based limits P gt 0.002 arcsec. (d lt 500
  pc)
• Beyond about 500 pc must use indirect methods
• 5 star formula standard candles

Definition Objects of known luminosity (or M)
8
First parallax numbers (1837)
No need to copy table
9
M calibrations G2, A0 K5 stars
No need to copy table