Measuring Stars What We Want to Know

•Brightness •Temperature •Composition •Distance •Luminosity •Size (Radius) •Mass Easy Hard Binary Stars l peak

T

= 2900 (

M

+

m

)

P

2 =

a

3 •Spectrum also tells you much more

Luminosity and Brightness

•The

Luminosity L

is how much power something is putting out •The

Brightness B

is how bright something appears •They are related:

d A

Sphere: = 4 

d

2

L

= 4 

d

2

B

• The brightness is always easy to determine • If we can get

one

of the distance or the luminosity, we can get the other.

Star A and star B are equally bright, but star A is farther away. Which one is actually more luminous?

A) Star A B) Star B C) They are equally luminous D) There is insufficient information

Finding the Distance

• If we can get the distance, we can get the luminosity too • We will use a new unit for measuring distance, the light year • The distance light goes in a year ly = 9.46  10 15 m = 63,240 AU •Brightness •Temperature •Composition •Distance •Luminosity •Size (Radius) •Mass Easy Hard • Real astronomers use parsecs • But we won’t

Methods for Finding Distance

•Radar •Solar System Only •Excellent accuracy •Parallax •Nearby Stars (< 300 ly) •Moderate accuracy •Spectroscopic Parallax •Main Sequence Stars only •Poor accuracy

Earth

Radar Distance

Venus

d 2d = ct,

solve for

d

•We know what an AU is •Effectively no error

Methods for Finding Distance

•Radar •Solar System Only •Excellent accuracy •Parallax •Nearby Stars (< 300 ly) •Moderate accuracy •Spectroscopic Parallax •Main Sequence Stars only •Poor accuracy

Parallax

•The distance to an object can be judged if you view it from two angles •The difference in the angle you see it from is called

parallax

•The more distant, the smaller the parallax  

Parallax

•The farther apart you put your “two eyes”, the better you can judge distance •The smaller

p

is, the farther away the star is.

d



3.26 ly

p d

•

p

in arc-

p p

seconds (The distance 3.26 ly is also known as a parallax second ) nearest stars several ly away  Centauri C = Proxima Centauri : 4.2 ly Sirius: 9 ly

Spectral Type

The following are all equivalent information: • The surface temperature of a star • The color of the star • The

spectral type

of the star • From hottest to coldest, OBAFGKM • Subdivided 0-9, with 0 the hottest • Sun is a G2 star • The

spectral type

is easy to determine Why I hate astronomers “Oh Be A Fine Girl, Kiss Me.” Which star is hottest?

A) G2 C) F3 B) G4 D) F7

Spectral Type

Spectra and Motion – Doppler Effect

Spectra and Motion – Doppler Effect

Star A Spectrum Hydrogen Spectrum Star A is A) Made of a hydrogen variant B) Moving towards us C) Moving away from us D) Rotating

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• Test 2 questions • Test 2 solutions • Midterm grades

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Spectra and Motion – Doppler Effect

Star B Spectrum •

Binary stars

are two stars Hydrogen Spectrum that are orbiting each other • A

spectroscopic binary

are Star B is A) Made of two kinds of hydrogen two stars that

look

like one but their binary nature can be deduced from their spectrum B) Moving away from us AND moving towards us C) Actually two stars moving at different speeds

Spectra and Motion – Doppler Effect

• Other object could be smaller in mass • This is the

Doppler method

whereby we discover planets around other stars Hydrogen Spectrum Star C is A) In orbit around an invisible companion B) Alternately expanding and contracting C) Alternately heating and cooling D) Rotating

Summary – What Spectra Tell Us

• Temperature • From the peak of the spectrum • Composition • From wavelengths and strength of dark lines • Motion • From the Doppler shift • Multiplicity • From the number of sets of spectral lines • Orbit and masses • From the changing Doppler shift • Pressure and rotation • From width of lines

Luminosity, Temperature, and Radius

•The spectrum of a star is pretty much a black body distribution •How bright each point on the surface is depends only on temperature •Multiply by the area to get the Luminosity

L = A

F F

=

4 = 

T

4 

R

2 

T

4 Star X is the same temp. as the Sun, but it is 4 times more

L L

 

T

 

R R

   2 luminous. How large is it?

A) 2 times the Sun B) 4 times the Sun 4  4   

R R

   2

R R

 4 C) 16 times the Sun D) 4 4 = 256 times the Sun

R

 2

R

Intrinsic Properties of Stars

•To describe stars, we want to talk about intrinsic properties •Luminosity •Composition •Temperature •Radius •Mass •Composition is almost always the same •Mass is difficult to measure •Radius can be deduced from Luminosity and Temperature

Temperature and

Luminosity

The Hertzsprung-Russell Diagram

•A plot of temperature vs. luminosity •Hot on left, cold on right •Luminous at top, dim at bottom •Stars fall into categories: •The

Main Sequence

contains about 90% of the bright stars •The

Giants

are rare but very bright •The

Supergiants

are very rare but extremely bright •The

White Dwarfs

are not uncommon but very dim

Main Sequence Stars

•Main Sequence stars have different sizes, masses, and luminosities •But spectral class determines everything else •This diagram shows correct relative sizes and approximate colors of stars •But not correct relative luminosities

Luminosity from Spectral Class

Suppose you have a G2 star. What is its luminosity?

• 90% of all stars are main sequence G2:

L



L

B5: K5:

L L

  800 0.1

L L

•For

main sequence stars

, the spectral type tells you the luminosity •Together with brightness, this tells you the distance •Spectroscopic parallax

Spectroscopic Parallax

•Another distance method •Has nothing to do with parallax •Works only on main sequence stars

How it works:

•Observe the star – determine it’s brightness

B

•Measure its spectral type from spectrum •Deduce its luminosity from the Hertzsprung Russell Diagram •Find its distance from:

L

= 4 

d

2

B

Stellar Masses

•Only some stars can have their masses measured •They need to be in binary systems •The masses of main sequence stars depends pretty much only on their spectral type T O5 B0 B5 A0 A5 M 60 18 5.9

2.9

2.0

T F0 F5 G0 G5 K0 M 1.6

1.3

1.05

.92

.85

T M K5 .74

M0 .51

M5 .21

M8 .06

The Main Sequence

•The mass of a main sequence star affects everything •Temperature •More massive is hotter •Luminosity •More massive is much 60

M

1

M

more luminous •Radius •More massive is bigger 0.1

M