The Family of Stars Please press “1” to test your transmitter.

The Family of Stars We already know how to determine a star’s surface temperature chemical composition Now, see how we can determine its distance luminosity radius mass and how all the different types of stars make up the big family of stars.

Distances of Stars Trigonometric Parallax: Star appears slightly shifted from different positions of the Earth on its orbit The further away the star is (larger d), the smaller the parallax angle p. d = __ p 1 d in parsec (pc) p in arc seconds 1 pc = 3.26 LY

The Trigonometric Parallax Example: Nearest star,  Centauri, has a parallax of p = 0.76 arc seconds d = 1/p = 1.3 pc = 4.3 LY With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec => d ≤ 50 pc This method does not work for stars further away than 50 pc.

Sirius, the brightest star in the sky, has a trigonometric parallax of p = arc seconds. What is its distance from Earth? pc light years pc light years light years

The method of trigonometric parallaxes (from ground based telescopes) allows us to measure distances … 1.only to objects in our solar system. 2.only to stars in our solar neighborhood within the Milky Way. 3.to stars throughout the entire Milky Way. 4.to stars and galaxies throughout the Local Group. 5.even to other clusters of galaxies.

Intrinsic Brightness / Absolute Magnitude The further away a light is, the fainter it appears.

Intrinsic Brightness / Absolute Magnitude (II) More quantitatively: The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): F ~ L __ d2d2

The stars A and B have the same intrinsic luminosity, but A is 5 times further away from Earth than B. Then: 1.Both stars will appear equally bright. 2.A will appear 5 times brighter than B. 3.B will appear 5 times brighter than A. 4.A will appear 25 times brighter than B. 5.B will appear 25 times brighter than A. Earth Star BStar A

Distance and Intrinsic Brightness Betelgeuze Rigel Example: App. Magn. m V = 0.41 Magn. Diff.Intensity Ratio *2.512 = (2.512) 2 = 6.31 …… 5(2.512) 5 = 100 App. Magn. m V = 0.14 For a magnitude difference of 0.41 – 0.14 = 0.27, we found: Rigel appears 1.28 times brighter than Betelgeuze But Rigel and Betelgeuze may be at quite different distances from us!

Absolute Magnitude To characterize a star’s intrinsic brightness, define Absolute Magnitude (M V ): Absolute Magnitude = Magnitude that a star would have if it were at a distance of 10 pc. If we know a star’s absolute magnitude, we can infer its distance by comparing absolute and apparent magnitudes.

Absolute Magnitude (II) Betelgeuze Rigel BetelgeuzeRigel mVmV MVMV d152 pc244 pc Difference in absolute magnitudes: 6.8 – 5.5 = 1.3 => Luminosity ratio = (2.512) 1.3 = 3.3 Rigel is actually 3.3 times brighter than Betelgeuze!

The Size (Radius) of a Star We already know: flux increases with surface temperature (~ T 4 ); hotter stars are brighter. But brightness also increases with size: A B Star B will be brighter than star A. Specifically: Absolute brightness is proportional to radius (R) squared, L ~ R 2.

Example: Both Spica B and Sirius B are B-type stars, but Sirius B is a white dwarf star, with a radius ~ 560 times smaller than Spica B. Thus, since L ~ R 2, Sirius B is intrinsically ≈ 320,000 times fainter than Spica B.

Polaris has just about the same spectral type (and surface temperature) as our sun, but it is 10,000 times brighter. Thus, Polaris’ radius is … the sun’s radius. 1.the same as times larger than times smaller than 4.10,000 times larger than 5.10,000 times smaller than

Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of LuminosityversusTemperature (or spectral type) Luminosity Temperature Spectral type: O B A F G K M Hertzsprung-Russell Diagram

The Hertzsprung Russell Diagram Most stars are found along the Main Sequence

The Hertzsprung-Russell Diagram (II) Stars spend most of their active life time on the Main Sequence (MS). Same temperature, but much brighter than MS stars → Must be much larger → Giant Stars Same temp., but fainter → Dwarfs

Radii of Stars in the Hertzsprung-Russell Diagram 10,000 times the sun’s radius 100 times the sun’s radius As large as the sun 100 times smaller than the sun RigelBetelgeuze Sun Polaris

Luminosity Classes Ia Bright Supergiants Ib Supergiants II Bright Giants III Giants IV Subgiants V Main-Sequence Stars Ia Ib II III IV V

Examples: Our Sun: G2 star on the Main Sequence: G2V Polaris: G2 star with Supergiant luminosity: G2Ib