Transcript The Family of Stars
The Family of Stars
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The Family of Stars
We already know how to determine a star’s
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surface temperature
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chemical composition Now, see how we can determine its
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distance luminosity radius mass and how all the different types of stars make up the big family of stars.
Distances of Stars
d in parsec (pc) p in arc seconds d = __ p 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.
1 pc = 3.26 LY
The Trigonometric Parallax
Example: Nearest star, a 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 = 0.385 arc seconds . What is its distance from Earth?
1. 0.385 pc 2. 0.80 light years 3. 1.255 pc 4. 2.60 light years 5. 8.47 light years
The method of trigonometric parallaxes (from ground based telescopes) allows us to measure distances … 1.
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only to objects in our solar system.
only to stars in our solar neighborhood within the Milky Way.
to stars throughout the entire Milky Way.
to stars and galaxies throughout the Local Group.
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 ~ d 2
The stars A and B have the same intrinsic luminosity, but A is 5 times further away from Earth than B. Then:
Star A Star B Earth
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Both stars will appear equally bright.
A will appear 5 times brighter than B.
B will appear 5 times brighter than A.
A will appear 25 times brighter than B.
B will appear 25 times brighter than A.
Magn. Diff.
1 2 … 5
Distance and Intrinsic Brightness
Example: Intensity Ratio 2.512
2.512*2.512 = (2.512) 2 = 6.31
… (2.512) 5 = 100 Betelgeuze App. Magn. m V = 0.41
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!
Rigel App. Magn. m V = 0.14
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 absolute and apparent by comparing magnitudes.
Absolute Magnitude (II)
m V M V d Betelgeuze Rigel 0.41
0.14
-5.5
152 pc -6.8
244 pc Betelgeuze 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!
Rigel
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 560 2 ≈ 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.
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the same as 100 times larger than 100 times smaller than 10,000 times larger than 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 Luminosity versus Temperature (or spectral type) Hertzsprung-Russell Diagram Temperature Spectral type: O B A F G K M
The Hertzsprung Russell Diagram
The Hertzsprung-Russell Diagram (II)
Same temperature, but much brighter than MS stars → Must be much larger → Giant Stars
Radii of Stars in the Hertzsprung-Russell Diagram
Rigel Betelgeuze Polaris Sun 100 times smaller than the sun
Ia Bright Supergiants Ia Ib II III
Luminosity Classes
Ib Supergiants II Bright Giants III Giants IV Subgiants IV V V Main-Sequence Stars
Examples:
• Our Sun : G2 star on the Main Sequence: G2V • Polaris: G2 star with Supergiant luminosity: G2Ib