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
Flux and Luminosity Photometry
Flux W/m2
Luminosity W
From inverse square lawF = L/4r2
Sometimes use units of Lsun = 3.839 X 1026 W
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
Magnitude and Flux If m1-m2 = 100 then F2/F1 = 100
m1-m2 = -2.5 log (F1/F2) 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/4d2)/(L/4102)]m-M = 5 log (d/10pc)
m-M is called the distance modulus n.b., sometimes distance is “r” and sometimes “d”
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)
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
Apparent and Absolute
Apparent magnitude mbol (for bolometric)
Absolute magnitude Mbol (for bolometric)
Note also that the color index is a the same for apparent or absolute magnitudes e.g., B-V = MB-MV
Spectral Type Information Stars are classified by spectral type
Tells us temperature
Absolute magnitudes (MU , MB, MV, MR, MI, Mbol)
Color indices (B-V, U-B)
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
B V
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
mbol = -2.5 log (∫ F d) + Cbol
Where the integral is now the total flux
Flux Comparisons Note that our magnitude scale relates two
magnitudes to two fluxes
m1-m2 = -2.5 log (F1/F2)
e.g., we could input absolute magnitudes and the flux at 10 pc
M-Msun = -2.5 log [(L/4102) / (Lsun/4102)]
M = Msun - 2.5 log (L / Lsun)