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Stars

… how I wonder what you are.

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Goals

• Stars are Suns.• Are they:

– Near? Far?– Brighter? Dimmer?– Hotter? Cooler?– Heavier? Lighter?– Larger? Smaller?

• What categories can we place them in?

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Angular Size• Linear size = how big something really is

– Meters, inches, light years, feet• Angular size = how big something looks

– Degrees, arcminutes, arcseconds, milliarcseconds

Circle = 360 degrees

1 degree = 60 arcmin

1 arcmin = 60 arcsec

1 arcsec = 1000 mas

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Distance• One proof of a heliocentric

Universe is stellar parallax.– Tycho Brahe saw no parallax. – Copernicus: stars too far

away.• Nearest star: Proxima

CentauriParallax angle = 0.76 arcsec

– Tycho’s precision = 1 arcmin

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The Parsec

• What is the distance of an object with a parallax angle of 1 arcsec?

Distance = 206,265 AU

• This distance is 1 parsec (pc)1 pc = 206,265 AU = 3.3 ly

• 1 lightyear = distance light travels in one year.

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Concept Test• If Star A has a parallax of 2

arcseconds, and Star B has a parallax of 0.25 arcseconds:a. Star A is closer to us than Star B. Both are

farther from us than 1 pc.b. Star A is closer to us than Star B. Both are

closer to us than 1 pc.c. Star A is closer to us than 1 pc. Star B is

farther than 1 pc.d. Star B is closer to us than 1 pc. Star A is

farther than 1 pc.e. Star B is closer to us than Star A. Both are

farther away than 1 pc.

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Distances

• Closest star: Proxima Centauriparallax = 0.76 arcsecDistance = 1.3 pc or 4.3 lightyears

arcsec)(in parallax

1 parsecs)(in Distance

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Terms

• Brightness = How intense is the light I see from where I am.– Magnitude is

numerical term for this.

• Luminosity = how much light is the thing really giving off.

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Magnitude Scale

• The SMALLER the number the BRIGHTER the star!– Every difference of 1

magnitude = 2.5x brighter or dimmer.

– Difference of 2 magnitudes = 2.5x2.5 = 6.3x brighter or dimmer

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Magnitude vs. Brightness

Mag. Difference

Factors of 2.5 Brightness Diff.

1 2.51 = 2.5 2.5

2 2.52 = 2.5 X 2.5 6.3

3 2.53 = 2.5 X 2.5 X 2.5 16

4 2.54 = 2.5 X 2.5 X 2.5 X 2.5 40

5 2.55 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5

100

6 2.56 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5 X 2.5

250

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Star light, star bright

• Sirius is magnitude -1.5 Polaris is magnitude 2.5

• Is Sirius really more luminous than Polaris?

• No, Sirius is just closer.

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Apparent and Absolute

• Apparent Magnitude = brightness (magnitude) of a star as seen from Earth. m– Depends on star’s total energy radiated

(Luminosity) and distance• Absolute Magnitude = brightness

(magnitude) of a star as seen from a distance of 10 pc. M– Only depends on a star’s luminosity

10pc

distancelog5 10Mm

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Concept Test• Polaris has a an apparent magnitude

of 2.5. It’s absolute magnitude is 3.1. Polaris is:a. Closer to us than 10pc.b. Farther from us than 10 pc.c. Exactly 10 pc away.d. Can’t know without the parallax angle.e. None of these is correct.

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Concept Test• Polaris has a parallax angle of 0.01

arcsconds. Polaris is therefore:a. Closer to us than 1pc.b. Farther from us than 1pc.c. Exactly 1pc away.

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Concept Test• Polaris has a parallax angle of 0.01

arcsconds. Polaris is therefore:a. 1pc.b. 10pc.c. 100pc.d. 1000pc.e. None of the above.

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example

• Our Sun:– m = -26.8,– distance = 4.8 x 10-6 pcSo: M = 4.8

• Polaris:– m = 2.5,– distance = ~100 pcSo: M = -3.1

• Polaris is 1500 times more luminous than the Sun!

10pc

distancelog5 10Mm

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Concept Test

• The most likely absolute magnitudes (M) for each is:a. A = 2.5, B = -2.5, C = 2.5b. A = 2.5, B = 2.5, C = -2.5c. A = -2.5, B = 2.5, C = 2.5d. A = 2.5, B = 2.5, C = 2.5e. None of the above.

Star Distance

m M

A 5 pc 1.0

B 10 pc 2.5

C 20 pc -1.0

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A Spectrum

• A spectrum = the amount of light given off by an object at a range of wavelengths.

Emission lines Absorption linesContinuum

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Three Reasons

All objects do one or more:1. Reflect light because of color or smoothness

(same as scatter)2. Emit light because of their temperature

(thermal radiation)

3. Emit or absorb light because of their composition(spectral lines)

A person, house, or the Moon: reflects visible light, and because each is warm, emits infrared light.

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Temperature and Light

• Warm objects emit light.– Thermal radiation

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Stellar Temperatures

How hot are stars?

• Thermal radiation and temperature.

• Different stars have different colors, different stars are temperatures.

• Different temp, different trace compositions

Ste

llar

Sp

ectr

a

Hot

Cool

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Spectral Classificati

on

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Stellar MassesHow massive are stars?• Kepler’s Laws – devised for the planets.• Apply to any object that orbits another object.• Kepler’s Third Law relates:

– Period: “how long it takes to orbit something”– Semimajor axis: “how far you are away from that

something”– Mass: “how much gravity is pulling you around in

orbit”

• Where M is the Total Mass.• Can calculate the mass of stars this way.

M

aP

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Binary Stars

• Most stars in the sky are in multiple systems.

• Binaries, triplets, quadruplets, etc….– Sirius– Alcor and Mizar– Tatooine

• The Sun is in the minority by being single.

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NPOI Observations of Mizar A (1 Ursa Majoris)

Mizar, 88 light years distant, is the middle star in the handle of the Big Dipper. It was the first binary star system to be imaged with a telescope. Spectroscopic observations show periodic

Doppler shifts in the spectra of Mizar A and B, indicating that they are each binary stars. But they were too close to be directly imaged -until 2 May 1996, when the NPOI produced the first

image of Mizar A. That image was the highest angular resolutionimage ever made in optical astronomy. Since then, the NPOI has

observed Mizar A in 23 different positions over half the binary orbit. These images have been combined here to make a movie of the orbit. As a reference point, one component has been fixed at the map center; in reality, the two stars are of comparable size

and revolve about a common central position.

Orbital Phase: 000o

0.005 arcsec

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Stellar MassesHow massive are stars?

• Most stars have masses calculated this way.

• Find:– The more massive the star, the more luminous

it is.– The more massive the star, the hotter it is.

M

aP

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Stellar Radii

How big are stars?• We see stars have

different luminosities and different temperatures.

• Stars have different sizes.• If you know:

– Distance– Angular size

• Learn real size.

50 mas

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Betelgeuse

• Angular size = 50 mas• Parallax = 7.6 mas = 0.0076 arcsec• Apparent mag = 0.6

• Distance = 1/parallax = 132 pc• True size = distance * angular size =

1400 Rsol

– Model solar system: 97 yards in radius.• Absolute Mag = m – 5log(d/10pc) = -5

– Our sun M ~5, Betelgeuse = 10,000x luminosity

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Angular versus Linear

Supergiants, Giants and Dwarfs

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H-R Diagram• Can order the stars by:

– Temperature (or spectral type)– Luminosity (or absolute magnitude).

• And see where other qualities fall:– Mass– Radius

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Luminosity Class

• The roman numerals.

• Stars at same temp can have different luminosities.

• Corresponds to different classes: MS, giant, supergiant.

V III

I

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Concept TestWhich star is:

1. Hottest?2. Coolest?3. Faintest as

seen from Earth?

4. Most luminous?

Of Main Seq. Stars?5. Most massive?6. Most like the

Sun?

Star Spec Type

m M

A F0 V 0.0 0.0

B G2 V 10.0 4.4

C K5 III 0.0 -2.0

D F7 I -1.0 -5.0

E K3 V 5.0 6.5

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The Main Sequence• Stars characterized

by what holds them up.

• 90% held up by heat of Hydrogen fusion?

4H He + Energy