The Family of Stars

Chapter 8:

We already know how to determine a star’s • surface temperature

• chemical composition

• surface density

In this chapter, we will learn how we can determine its

• distance• luminosity• radius• mass

and how all the different types of stars make up the big family of stars.

Motivation

Recent Picture from SDO

• A flare erupts from the sun's surface on March 30, in one of the first images sent back by NASA's Solar Dynamics Observatory. Launched in February, SDO is the most advanced spacecraft ever designed to study the sun. SDO provides solar images with clarity 10 times better than high-definition television.

Solar Flare -- SDO

Hipparchus -- ~ 150 BC

• Credited with first star catalog• Introduced 360° in a circle• Introduced use of trigonometry• Using data from solar eclipse was able to

calculate distance to moon.• Accurate star chart with 850 stars• Created magnitude scale of 1 to 6

Hipparcos

• High Precision Parallax Collecting Satellite• Mission – Map 100000 nearest stars to 2

milliseconds of arc• Map another 1000000 stars to 10 milliseconds

of arc along with color information. • Exceeded goals. 120000 stars to 1milliseconds• Launched 1989 - Ended 1993• Exceeded all goals. ESA European Space Agency

Hipparcos Satallite

Distances to Stars

Trigonometric Parallax:

A star appears slightly shifted from different positions of the Earth on its orbit.

The further away the star is (larger d), the smaller the parallax angle p.

d = __ p 1

d in parsec (pc) p in arc seconds

1 pc = 3.26 LY

The Trigonometric ParallaxExample:

Nearest star, Centauri, has a parallax of p = 0.76 arc seconds

d = 1/p = 1.3 pc = 4.3 LY

The Limit of the Trigonometric Parallax Method:

With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec

=> d ≤ 50 pc

=> This method does not work for stars further away than 50 pc.

Intrinsic Brightness / Absolute Magnitude

The more distant a light source is, the fainter it appears.

The same amount of light falls onto a smaller area at distance 1 than at distance 2 => smaller

apparent brightness

Area increases as square of distance => apparent brightness decreases as inverse of distance squared

Intrinsic Brightness / Absolute Magnitude

The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely

proportional to the square of the distance (d):

F ~ L__d2

Star AStar B Earth

Both stars may appear equally bright, although star A is intrinsically much brighter than star B.

Distance and Intrinsic Brightness

Betelgeuse

Rigel

Example:

App. Magn. mV = 0.41

Recall:

Magn. Diff. Intensity Ratio

1 2.512

2 2.512*2.512 = (2.512)2 = 6.31

… …

5 (2.512)5 = 100

App. Magn. mV = 0.14For a magnitude difference of 0.41 – 0.14 = 0.27, we find a flux ratio of (2.512)0.27 = 1.28

Distance and Intrinsic Brightness

Betelgeuse

Rigel

Rigel appears 1.28 times brighter than Betelgeuse.

Thus, Rigel is actually (intrinsically) 1.28*(1.6)2 = 3.3 times brighter than

Betelgeuse.

But, Rigel is 1.6 times further away than

Betelgeuse.

Absolute Magnitude

To characterize a star’s intrinsic brightness or luminosity, we

define the Absolute Magnitude (MV):

Absolute Magnitude MV = Magnitude that a star would have if it were at a distance of 10 pc.

Absolute Magnitude

Betelgeuse

Rigel

Betelgeuse Rigel

mV 0.41 0.14

MV -5.5 -6.8

d 152 pc 244 pc

Back to our example of Betelgeuse and Rigel:

Difference in absolute magnitudes: 6.8 – 5.5 = 1.3

=> Luminosity ratio = (2.512)1.3 = 3.3

The Distance ModulusIf we know a star’s absolute magnitude, we can infer its distance by comparing

absolute and apparent magnitudes:

Distance Modulus

= mV – MV

= -5 + 5 log10(d [pc])

Distance in units of parsec

Equivalent:

d = 10(mV – MV + 5)/5 pc

The Size (Radius) of a StarWe already know: flux increases with surface temperature (~ T4); hotter stars are brighter

But brightness also increases with size:

A BStar B will be brighter than

star A.

Absolute brightness is proportional to the surface area of the star, and thus its radius squared, L ~ R2.

Quantitatively: L = 4 R2 T4

Surface area of the starSurface flux due to a blackbody spectrum

Example:

Polaris has just about the same spectral type (and thus surface temperature) as our sun, but

it is 10,000 times brighter than our sun.

Thus, Polaris is 100 times larger than the sun.

This causes its luminosity to be 1002 = 10,000 times more than our sun’s.

Organizing the Family of Stars: The Hertzsprung-Russell Diagram

We know:

Stars have different temperatures, different luminosities, and different sizes.

To bring some order into that zoo of different types of stars: organize them in a diagram of:

Luminosity versus Temperature (or spectral type)

Lum

inos

ity

Temperature

Spectral type: O B A F G K M

Hertzsprung-Russell Diagram

orA

bsol

ute

mag

.

The Hertzsprung Russell Diagram

Most stars are found along the

Main Sequence

The Hertzsprung-Russell Diagram

Stars spend most of their active

life time on the M

ain Sequence.

Same temperature,

but much brighter than

MS stars

→ Must be much larger

→ Giant Stars

Same temp., but

fainter → Dwarfs

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