Astro 105: The Milky Way

Lecture VIII
Measuring Stars

 

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"Stars are the Golden fruit of a tree beyond reach"
George Elliot
 

"There is no easy way to the stars from the Earth"
Seneca

Today we will learn how we learn anything about the stars.

They are so distant they we can not travel to them... how do we know what we know?

How can we build their stories?

Distances

 So much of our knowledge of astrophysics depends on knowing how far away objects are.

Any tool which allows the determination of distance in astronomy is hailed as a great breakthrough.

We constantly learn new methods (standard candles!) which allow us to go the ever farther distances or to measure distances more accurately.

The most direct distance determination  method is the geometrical means of -

STELLAR PARALLAX

The relative movement of nearby stars relative to distant stars when the Earth moves across a 2 AU baseline.

Simple trigonometry gets you the answer.

If d is the distance and p is the angular shift

d = 1/p


when p is measured in arcsec and d is measured in parsecs.

1 arcsec ('') of parallax yields a distance of 1 parsec.

1 parsec (pc) = 206,265 AU = 3.26 light-year (ly)

Very difficult to measure parallax.

Closest star: Alpha Centuri has p = 0.76 ''

What is d?

For distant stars it is even harder.

Hipparcos Satellite  measured more than 100,000 stellar parallaxes down to p = .002 '' or d = 500 pc.


The Solar Hood

About 3 lightyears in radius



Proper Motion

We can watch the motion of the stars across the plane of the sky.

Some move faster than others.   Why?

1) Stars do move at different speeds.
2) Same speeds different distances.

Nearby objects moving at the same angular velocity (''/year) as distant object.

Which one is actually covering more "linear" space?  Use the small angle formula

p1 = 206,265'' L1/d1
p2 = 206,265'' L2/d2

If p1 = p2 but d1 > d2
Then L1 > L2 

 


Stellar Temperature

You know this one already.

Color is related to temperature via the Blackbody Law.
 

You measure the Spectral Energy Distribution
(SED) and fit it to a blackbody curve

B(l) = Brightness (wavelength)
Read this as B as a function of l

Stellar Classification

In the early 1900's astronomers found that stars could be classified via the strength of different absorption lines in the spectra.

Some stars had many Hydrogen Lines, some had none.

Some stars had many lines from calcium, some had none.

Astronomers grouped the stars according to their spectral line strengths

O, B, A, F, G, K, M


 

O, B, A, F, G, K, M 

This is the spectral classification 

O stars are blue and hot.
M stars are red and cold.


Luminosity

Blackbodies have a special relationship between their energy output and their temperature.

Energy Output is Energy/time = Luminosity

L = 4 pi R2 s T4 

where R is the radius of the star and T is its temperature.
s = the stefan boltzman constant.

Divide by quantities for the sun

(L/Lsun) = (R/Rsun)2 (T/Tsun)4

If a star has R = Rsun but T = 2 Tsun
then L = (2)4 L sun = 16 Lsun

This is also a way to MEASURE STAR SIZES!!

Rearrange the formula 

(R/Rsun)2 = (L/Lsun)/(T/Tsun)4

If we know L and T then we can sort stars by the sizes: R

Stars with big R: Giants
Stars with little R: Dwarfs
 

In this diagram Barnards star and Betelgeuse have the same T but the differ in L by 7 orders in magnitude.

Using the  L proportional to  R2 T4 relation  Betelgeuse must have much larger radius.

(how much larger?)
 


The HR Diagram

Once astronomers had the spectral classification down and they knew about stellar temperatures and luminosities then they could look for PATTERNS in the properties of stars.

The Hertzsprung-Russel diagram is place where astronomers discovered the essential patterns

HR Diagram= L vs T


 

Notice the relationship between T and spectral classification.

Most stars lie on the MAIN SEQUENCE.
Stars below the Main Sequence are Dwarfs.
Stars above the Main Sequence are Giants.
 


 

What is the main sequence?

They are the "normal" stars

We shall see that "normal" for a star on the HR diagram means middle aged.


Luminosity Classification

In the 40s astronomers found that the width of a stars spectral lines depended on its luminosity.
This lead to a luminosity classification

 

  • Ia         Bright Supergiant
  • Ib         Superginat
  • II         Bright Giant
  • III        Giant
  • IV        Subgiant
  • V         Dwarf

 

The width of a line occurs via "collisonal broadening" as atoms in the atmosphere of a star get jiggled
around.

Thus the width of lines told astronomers how intrinsically bright a star should be.

Recall

B = Io/(4 pi D2 )

For what we have been doing L = Io

So the spectral classification gives astronomers a way to know distance to a star since the have B (how bright it appears) and L (how bright it should be).

This way of determining distance is called spectroscopic parallax.
(it really has nothing to do with parallax).

This allows you to measure larger distances than regular parallax.

Stellar Masses

We measure stellar masses via BINARY STARS.
We need to get P and R for two orbiting
stars.
 

Recall Newton's version of Keplers 3rd law for the solar system gave us


 
 

For the two stars we have M star1 and Mstar2
 

With these measurements we find a relation between mass and location on the HR Diagram's main sequence.

Why should this be?