Measuring StarsWhat We Want to Know

•Brightness•Temperature•Composition•Distance•Luminosity•Size (Radius)•Mass

Easy

Hard

Binary Stars

•Spectrum tells you composition

(M+m)P2 = a3

peakT = 2900 Km

•Spectrum also tells you much more

•The Luminosity L is how much power something is putting out•The Brightness B is how brightsomething appears•They are related:

Sphere:A = 4d2

L = 4d2B

d

Luminosity and Brightness

•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 BC) They are equally luminousD) There is insufficient information

Finding the Distance•Brightness•Temperature•Composition•Distance•Luminosity•Size (Radius)•Mass

Easy

Hard

•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 1015 m = 63,240 AU

•Real astronomers use parsecs•But we won’t

•Radar•Solar System Only•Excellent accuracy

•Parallax•Nearby Stars (< 300 ly)•Moderate accuracy

•Spectroscopic Parallax•Main Sequence Stars only•Poor accuracy

Methods for Finding Distance

Earth Venus

d

2d = ct, solve for d

•We know what an AU is•Effectively no error

Radar Distance

•Radar•Solar System Only•Excellent accuracy

•Parallax•Nearby Stars (< 300 ly)•Moderate accuracy

•Spectroscopic Parallax•Main Sequence Stars only•Poor accuracy

Methods for Finding Distance

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

pp

•The smaller p is, the farther away the star is.

d

3.26 lyd

p

•p in arc-seconds

(The distance 3.26 ly isalso known as a parallax second)parsec

nearest stars several ly away

Centauri C = Proxima Centauri : 4.2 ly

Sirius: 9 ly

Spectral Type

Why I hate astronomers

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

“Oh Be A Fine Girl, Kiss Me.”

Which star is hottest?A) G2 B) G4C) F3 D) F7

Spectral Type

Spectra and Motion – Doppler Effect

Spectra and Motion – Doppler EffectStar A Spectrum

Hydrogen Spectrum

Star A isA) Made of a hydrogen variantB) Moving towards usC) Moving away from usD) Rotating

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Spectra and Motion – Doppler EffectStar B Spectrum

Hydrogen Spectrum

Star B isA) Made of two kinds of hydrogenB) Moving away from us AND moving towards usC) Actually two stars moving at different speeds

•Binary stars are two stars that are orbiting each other•A spectroscopic binary are two stars that look like one but their binary nature can be deduced from their spectrum

Spectra and Motion – Doppler EffectStar C Spectrum – Day 0

Hydrogen Spectrum

Star C Spectrum – Day 50Star C Spectrum – Day 100Star C Spectrum – Day 150Star C Spectrum – Day 200

Star C isA) In orbit around an invisible companionB) Alternately expanding and contractingC) Alternately heating and coolingD) Rotating

•Other object could be smaller in mass •This is the Doppler method whereby we discover planets around other stars

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

=T4

•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 = 4R2T4 4 2L T R

L T R

Star X is the same temp. as the Sun, but it is 4 times more luminous. How large is it?A) 2 times the SunB) 4 times the SunC) 16 times the SunD) 44 = 256 times the Sun

2

44 1

R

R

4R

R

2R R

•To describe stars, we want to talk about intrinsic properties•Luminosity•Composition•Temperature

•Composition is almost always the same•Mass is difficult to measure•Radius can be deduced from Luminosity and Temperature

•Radius•Mass

Temperature and Luminosity

Intrinsic Properties of Stars

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 sizesand approximate colors of stars•But not correct relative luminosities

Luminosity from Spectral Class

L L

800L L

0.1L L

G2:B5:K5:

Suppose you have a G2 star. What is its luminosity?•90% of all stars are main sequence

•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 = 4d2B

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 M T M T MO5 60 F0 1.6 K5 .74B0 18 F5 1.3 M0 .51B5 5.9 G0 1.05 M5 .21A0 2.9 G5 .92 M8 .06A5 2.0 K0 .85

The Main Sequence

60M

1M

0.1M

•The mass of a main sequence star affects everything•Temperature

•More massive is hotter•Luminosity

•More massive is much more luminous

•Radius•More massive is bigger