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# Lecture Notes:

## Properties of Stars: Distance, Temperature, Luminosity

text: Chapter 12 (sections 12.1 and 12.2)

Here is a discussion of similar material: http://www.astronomynotes.com/starprop/s1.htm

### Introduction and scale

What properties can we learn about?

• Distance
• Luminosity
• Size
• Mass
• Composition
• Temperature
• Rotation
• Speed of motion
• Magnetic Field

Use these to determine:

• How do stars work?
• How do stars change during their lives?

Typical Ranges of values:

• Luminosity: 1/1000 of the Sun ---> 1,000,000 x Sun
• Surface temperature: 3000 - 30,000 K (Sun = 6000K)
• Size (volume): 1/1,000,000 of the Sun ---> 1 billion x Sun
• Mass: 1/10 of the Sun ---> 30 x Sun
• composition - similar to Sun

### Distances

For nearby stars, we can measure distance by parallax:

parallax = apparent motion of a star caused by motion of the Earth

[DEMO: hold thumb up a arms length in front of your face. Close one eye and then switch eyes, your thumb appears to move relative to a distance background.]

Same happens as Earth orbit the Sun. Examine position of star at two different times about 6 months apart and examine the apparent change of position of the nearby star relative to the distant stars.

In January, the star appears in the sky near the right hand distant star. In July, it appears in the sky near the left hand distant star.

We can measure parallax to get distance information:

Geometry says that if I know all three angles of a triangle and the length of one side, I know the other side.

We can measure all of the angles, and we know the distance from Earth to Sun, so we know the distance to the star.

(These pictures show the star much too close to us. The parallax angles are really VERY small since even nearby stars are quite far away.)

Click on the button to bring up an animation of parallax from Ohio State University. It will appear on a separate window in the upper right corner of your screen. You can close the new window by clicking on the small box in the upper corner - or just click on this main window to return here.

Here is a similar JAVA applet on parallax: http://instruct1.cit.cornell.edu/courses/astro101/java/parallax/parallax.html

This link has a JAVA applet which shows the concept of parallax: http://www.astro.washington.edu/labs/parallax/solar.html

Define a distance unit related to the parallax angle:

1 parsec = distance of a star with a parallax angle of 1 arcsecond
= 3.26 light years = 3 x 1013 km

1 arcsecond = 1/3600 of a degree

Parallax angles are ALWAYS VERY SMALL (< 1 arc second)

this makes them hard to measure

this technique only works for the closest stars

measuring from Earth, we can measure about 1000 stars at distances < 100 pc away

measuring from satellites in orbit we can measure about 100,000 stars out to about 1000 pc

This animation shows a picture of stars with the motion from parallax (sped up considerably!): http://www.astro.washington.edu/labs/parallax/parallax_distance.html

We will need other methods for measuring stars which are farther away (MOST STARS).

One method which we will discuss in more detail later is to use objects whose actual brightness we think we know.

"method of standard candles"

if brightness is known then brighter stars are closer

### Temperature

hot stars emit more blue and ultra-violet light

cool stars emit more red and infrared light

the line spectra of stars also contain information about temperature (more on this later)

hard to measure directly since most stars appear as points of light in telescopes
can not measure angular size of image for most stars

can make direct measurements (using interferometry or Space Telescope) for a few nearby stars and a few very large stars (< 50 total)

Link to a photograph of red supergiant star Betelgeuse: http://antwrp.gsfc.nasa.gov/apod/ap980419.html

Link to an exercise allowing you to calculate the size of Betelgeuse: http://imagine.gsfc.nasa.gov/YBA/HTCas-size/betelgeuse.html

will learn an indirect method in the next section

### Luminosity and Brightness

luminosity = amount of energy per second emitted by an object

the wattage of a light bulb is an example of measuring luminosity

luminosity depends on

• temperature
• hotter star has more luminosity
• Stefan-Boltzmann Law
• size
• larger star has more luminosity

Examples:

brightness = how bright something appears to us

depends on temperature, size and distance of a star

PROBLEM : The Brightness we can measure from Earth depends on the distance to the star

greater distance = less brightness (inverse square law)

for nearby stars, we can measure the distance from parallax and determine the luminosity from the brightness

### Measuring Brightness and Luminosity

use a system developed by Hipparchus in about 150 BC

Brightness from Apparent Magnitude

let the "brightest star" have magnitude = 1

let the faintest star visible by eye have magnitude = 6

Each magnitude is 2.5 times fainter than the previous one.

There are brighter stars (not visible in Mediteranean region) - so use negative numbers

magnitude of -1 is BRIGHTER than magnitude of 1

 OBJECT APPARENT MAGNITUDE Sun -26.7 brightest star (Sirius) -1.4 faintest star observable with telescopes +30

Apparent magnitude measures brightness which depends on both Luminosity and Distance.

Luminosity from Absolute Magnitude

Define something that does NOT depend on distance

absolute magnitude = apparent magnitude of a star if it was a distance of 10 pc away

If we know brightness (apparent magnitude) (look at the sky) and luminosity (absolute magnitude) - we can find DISTANCE - discuss this further soon (Method of Standard Candles)

If we know brightness (apparent magnitude) (look at the sky) and distance - we can find luminosity (absolute magnitude) - possible for stars close enough to use parallax (about 100,000 of them)

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