Colors and Magnitudes

PHYS390 (Astrophysics)

Professor Lee Carkner

Lecture 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

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)

Next Time

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