Colors and Magnitudes

1
Colors and Magnitudes

• Physical Astronomy
• Professor Lee Carkner
• Lecture 2

2
Light

• All we have is light
• Can measure
• Wavelength (color)
• We can measure how bright the star looks, we want
  how bright the star is

3
Stellar Spectral Energy Distributions

• Stellar spectra
• absorption lines (superimposed)
• Start with the simplest data we can get

4
Parallax

• Find position of star relative to fixed
  background stars 6 months apart
• Convert from radians to arcsec and use small
  angle approximation
• Define 206265 AU as 1 parsec
• d 1/p (d in pc, p in arcsec)
• 1 pc 3.26 lightyears

5
Parallax Issues

• Very hard to measure
• About 1/1000 the field of a typical telescope
  view
• Hipparcos space mission can get to 0.001 or 1000
  pc

6
Flux and Luminosity

• Flux
• W/m2
• Luminosity
• W
• From inverse square law
• F L/4pr2
• Sometimes use units of Lsun 3.839 X 1026 W

7
Magnitude

• Rank all visible stars in sky by brightness 1st
  to 6th by eye
• Can extend to all objects and formalize with 5
  magnitudes lower is 100 times brighter
• apparent bolometric magnitude m
• apparent
• bolometric
• Flux easy, magnitude hard

8
Magnitude and Flux

• F2/F1 100(m1-m2)/5
• m1-m2 -2.5 log (F1/F2)
• M (absolute magnitude) is like luminosity
• m-M -2.5 log (F/F10pc)
• m-M -2.5 log (L/4pd2)/(L/4p102)
• m-M 5 log (d/10pc)
• m-M is called the distance modulus

9
Colors

• We cant measure the real bolometric magnitude
• We use a filter to define a specific wavelength
  band and use that magnitude
• Difference between two filtered apparent
  magnitudes is the color index
• e.g., B-V, U-V

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Bolometric Correction

• The smaller the color index, the more important
  the wavelengths of the first filter are
• low U-B
• low B-V
• We can also apply the bolometric correction (BC)
  to get the bolometric magnitude
• Where BC is constant for a specific spectral type
• BC tells us what fraction of the total energy
  distribution V is

11
Apparent and Absolute

• For filters
• MV (or MB, MU, etc) is absolute magnitude
• e.g., B-V MB-MV

12
Questions

• Which looks brighter, a star with mbol 10 or a
  star with V 10?
• Which looks brighter, a star with B 10 or a
  star with V 10?

13
Sensitivity Function

• Depends on
• filters
• Varies with wavelength
• instrumental sensitivity

14
Flux and Sensitivity

• We wan to relate
• sensitivity function
• Integrating over all wavelengths (for V band)
• V -2.5 log (? FlSV dl) CV
• It is chosen to define zero magnitude as being
  equal to the flux from a group of key calibration
  stars

15
Flux and Color

• mbol -2.5 log (? Fl dl) Cbol
• B-V -2.5 log (? FlSV dl) / (? FlSB dl) CB-V
• Where CB-V CB-CV

16
Color-Color Diagram

• The color index tells us something about the
  shape of a stars spectral energy distribution
• Is an estimate of temperature
• Location on color-color diagram gives us an
  estimate of a stars spectral type

17
Next Time

• Read 3.3-3.5
• Homework 3.4, 3.5, 3.8, 3.9a-3.9d