1. Colors and Magnitudes PHYS390 (Astrophysics) Professor Lee Carkner Lecture 2

2. Answers 1)On the summer solstice, what RA is on the meridian at midnight?  Sun’s RA is 6 hr, so when RA 6 is on the other side of the Earth, RA 18 (6+12) is overhead 2)On what date will a star with an RA of 15 hr be on the meridian at midnight?  Want sun to have RA of 15-12 = 3 hr, which is half way between Mar 20 and Jun 21 or ~May 4

3. Flux and Luminosity  Photometry   Flux   W/m 2  Luminosity  WW  From inverse square law F = L/4  r 2   Sometimes use units of L sun = 3.839 X 10 26 W

4. Magnitude   Eye has semi-log response, so a 1 magnitude difference is a brightness difference of about 2.5   apparent bolometric magnitude = m  apparent =  bolometric = a  Smaller m, brighter star  Flux = easy, magnitude = hard 

5. Magnitude and Flux  If m 1 -m 2 = 100 then F 2 /F 1 = 100 m 1 -m 2 = -2.5 log (F 1 /F 2 )  m (apparent magnitude)  M (absolute magnitude)  M is equal to the apparent magnitude the star would have if it were at 10 pc m-M = -2.5 log [(L/4  d 2 )/(L/4  10 2 )] m-M = 5 log (d/10pc)  m-M is called the distance modulus  n.b., sometimes distance is “r” and sometimes “d”

6. Colors   Can’t detect all wavelengths at once   Examples: UBVRI = apparent magnitude in ultraviolet, blue, visible (green), red, and infrared  We write apparent magnitude in a filter band with a capital letter (e.g., V or B)

7. Bolometric Correction   e.g., B-V, U-V  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

8. Apparent and Absolute  Apparent magnitude   m bol (for bolometric)  Absolute magnitude   M bol (for bolometric)  Note also that the color index is a the same for apparent or absolute magnitudes  e.g., B-V = M B -M V

9. Spectral Type Information  Stars are classified by spectral type   Tells us temperature   Absolute magnitudes (M U, M B, M V, M R, M I, M bol )   Color indices (B-V, U-B)

10. Color-Color Diagram  The color index tells us something about the shape of a star’s spectral energy distribution  Negative B-V =  Positive B-V =  A star’s color index tells us its temperature BV

11. Normalizing the Scale  We can also relate the magnitude to the flux integrated over some wavelength range and a constant C   C is a constant chosen to normalize the magnitude scale to standard stars  m bol = -2.5 log (∫ F d ) + C bol  Where the integral is now the total flux

12. Flux Comparisons  Note that our magnitude scale relates two magnitudes to two fluxes m 1 -m 2 = -2.5 log (F 1 /F 2 )   e.g., we could input absolute magnitudes and the flux at 10 pc M-M sun = -2.5 log [(L/4  10 2 ) / (L sun /4  10 2 )] M = M sun - 2.5 log (L / L sun ) 

13. Next Time  Read: 3.3-3.5  Homework: 3.4, 3.5, 3.8, 3.9a-3.9d