The Trigonometric Parallax

Bp

B = 1 AU = 1.496*1013 cmd = (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 IndexWe 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

M 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 sun100 times smaller than the sun

Rigel Betelgeuze

Sun

Polaris

Giants

Supergiants

White Dwarfs