Homework: Parallax

• Given p in arcseconds (”), use d=1/p to calculate the distance which will be in units “parsecs”

• By definition, d=1pc if p=1”, so convert d to A.U. by using trigonometry

• To calculate p for star with d given in lightyears, use d=1/p but convert ly to pc.

• Remember: 1 degree = 3600”• Note: p is half the angle the star

moves in half a year

Our Stellar Neighborhood

Scale Model

• If the Sun = a golf ball, then– Earth = a grain of sand

– The Earth orbits the Sun at a distance of one meter

– Proxima Centauri lies 270 kilometers (170 miles) away

– Barnard’s Star lies 370 kilometers (230 miles) away

– Less than 100 stars lie within 1000 kilometers (600 miles)

• The Universe is almost empty!

• Hipparcos satellite measured distances to nearly 1 million stars in the range of 330 ly

• almost all of the stars in our Galaxy are more distant

Reminder: Three Things Light Tells Us

• Temperature – from black body spectrum

• Chemical composition– from spectral lines

• Radial velocity– from Doppler shift

Luminosity and Brightness

• Luminosity L is the total power (energy per unit time) radiated by the star, actual brightness of star, cf. 100 W lightbulb

• Apparent brightness B is how bright it appears from Earth– Determined by the amount of

light per unit area reaching Earth– B L / d2

• Just by looking, we cannot tell if a star is close and dim or far away and bright

Brightness: simplified

• 100 W light bulb will look 9 times dimmer from 3m away than from 1m away.

• A 25W light bulb will look four times dimmer than a 100W light bulb if at the same distance!

• If they appear equally bright, we can conclude that the 100W lightbulb is twice as far away!

Same with stars…

• Sirius (white) will look 9 times dimmer from 3 lightyears away than from 1 lightyear away.

• Vega (also white) is as bright as Sirius, but appears to be 9 times dimmer.

• Vega must be three times farther away

• (Sirius 9 ly, Vega 27 ly)

Distance Determination Method

• Understand how bright an object is (L)is (L)• Observe how bright an object appears (B)appears (B)

• Calculate how far the object is away:

B L / d2

So

L/B d2 or d √L/B

Homework: Luminosity and Distance

• Distance and brightness can be used to find the luminosity:

L d2 B

• So luminosity and brightness can be used to find Distance of two stars 1 and 2:

d21 / d2

2 = L1 / L2 (since B1 = B2 )

i.e. d1 = (L1 / L2)1/2 d2

The Magnitude Scale• A measure of the apparent

brightness

• Logarithmic scale • Notation: 1m.4 (smaller brighter)• Originally six groupings

– 1st magnitude the brightest

– 6th magnitude is 100x dimmer

• So a difference of 5mag is a difference of brightness of 100

• Factor 2.512=1001/5 for each mag.

Absolute Magnitude

• The absolute magnitude is the apparent magnitude a star would have at a distance of 10 pc.

• Notation example: 2M.8

• It is a measure of a star’s actual or intrinsic brightness called luminosity

• Example: Sirius: 1M.4, Sun 4M.8– Sirius is intrinsically brighter than the Sun

Finding the absolute Magnitude• To figure out absolute magnitude, we need to

know the distance to the star

• Then do the following Gedankenexperiment:– In your mind, put the star from its actual position to a

position 10 pc away– If a star is actually closer than 10pc, its absolute

magnitude will be a bigger number, i.e. it is intrinsically dimmer than it appears

– If a star is farther than 10pc, its absolute magnitude will be a smaller number, i.e. it is intrinsically brighter than it appears

Measuring the Sizes of Stars

• Direct measurement is possible for a few dozen relatively close, large stars– Angular size of the disk and known distance

can be used to deduce diameter

Indirect Measurement of Sizes

• Distance and brightness can be used to find the luminosity:

L d2 B (1)

• The laws of black body radiation also tell us that amount of energy given off depends on star size and temperature:

L R2 T4 (2)

• We can compare two values of absolute luminosity L to get the size

Sizes of Stars• Dwarfs

– Comparable in size, or smaller than, the Sun

• Giants– Up to 100 times

the size of the Sun

• Supergiants– Up to 1000 times

the size of the Sun

• Note: Temperature changes!

Classification of the Stars: Temperature

Class Temperature Color Examples

O 30,000 K blue

B 20,000 K bluish Rigel

A 10,000 K white Vega, Sirius

F 8,000 K white Canopus

G 6,000 K yellow Sun, Centauri

K 4,000 K orange Arcturus

M 3,000 K red Betelgeuse

Mnemotechnique: Oh, Be A Fine Girl/Guy, Kiss Me

The Key Tool to understanding Stars: the Hertzsprung-Russell diagram

• Hertzsprung-Russell diagram is luminosity vs. spectral type (or temperature)

• To obtain a HR diagram: – get the luminosity. This is your y-coordinate. – Then take the spectral type as your x-coordinate, e.g.

K5 for Aldebaran. First letter is the spectral type: K (one of OBAFGKM), the arab number (5) is like a second digit to the spectral type, so K0 is very close to G, K9 is very close to M.

Constructing a HR-Diagram• Example: Aldebaran, spectral type K5III,

luminosity = 160 times that of the Sun

O B A F G K M Type… 0123456789 0123456789 012345…

1

10

100

1000

L

Aldebaran

Sun (G2V)

160

The Hertzprung-

Russell Diagram• A plot of absolute

luminosity (vertical scale) against spectral type or temperature (horizontal scale)

• Most stars (90%) lie in a band known as the Main Sequence

Hertzsprung-Russell diagrams … of the closest stars …of the brightest stars