The Trigonometric Parallax

Bp

B = 1 AU = 1.496*1013 cm

d = (1/p[arcsec]) parsec

d

1 pc = 3.26 LY ≈ 3*1018 cm

The Moving Cluster Method

x

vvr

v

The magnitude scale system can be extended towards negative numbers (very bright) and

numbers > 6 (faint objects):

Sirius (brightest star in the sky): mv = -1.42

Full moon: mv = -12.5

Sun: mv = -26.5

Color and Temperature

Orion

Betelgeuze

Rigel

Stars appear in different colors,

from blue (like Rigel)

via green / yellow (like our sun)

to red (like Betelgeuze).

These colors tell us about the star’s

temperature.

Blackbody Radiation (I)

The light from a star is usually concentrated in a rather narrow

range of wavelengths.

The spectrum of a star’s light is approximately a thermal

spectrum called Blackbody Spectrum.

Blackbody Radiation

Fsurf = Teff4

= 5.67*10-5 erg/(cm2 s K4)

Wien’s displacement law:

max ≈ 0.29 cm / TK

(TK = temperature in Kelvin).

The Color Index (I)B band

V bandThe color of a star is measured by comparing its brightness in different wavelength bands:

The blue (B) band and the visual (V) band.

We define B-band and V-band magnitudes just as we did

before for total magnitudes.

Optical Wavelength Bands

U: 0 ≈ 3650 Å

B: 0 ≈ 4400 Å

V: 0 ≈ 5500 Å

The Color Index

We define the Color Index

B – V(i.e., B magnitude – V magnitude)

The bluer a star appears, the smaller the color index B – V.

The hotter a star is, the smaller its color index B – V.

B - V

Temperature

Example:

For our sun:

Absolute V magnitude: 4.83

Absolute B magnitude: 5.51

=> Color index:

B – V = 0.68

From standard tables:

B – V = 0.68 => T ≈ 5800 K.

The Color-Color Diagram

B - V

U -

B

-0.5 1.51.00.50.0 2.01.5

1.0

0.5

0.0

-0.5

-1.0

Blackbody

B0

A0F0 G0

K0

M0

The Hertzsprung-Russell Diagram

B - V

Teff

Mb

ol

Log

(L)

Most stars are found along the Main Sequence

Zero-Age Main Sequence (ZAMS)

Radii of Stars in the Hertzsprung-Russell Diagram

10,000 times the

sun’s radius

100 times the

sun’s radius

As large as the sun

100 times smaller than the sun

Rigel Betelgeuze

Sun

Polaris

Giants

Supergiants

White Dwarfs

Extinction and Reddening

Interstellar Extinction

Wavelength-Dependent Extinction