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StarsStars

… how I wonder what you are.

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GoalsGoals

Tie together some topics from earlier in the semester to learn about stars:

• How do we know how far away stars are?• How do we know how bright they really

are?• What are they like?

– Temperature– Radius– Mass

• What categories can we place them in?

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Distances

• How do we perceive distances here on Earth?

• How do we know A is closer than B?• Can we apply these to objects in space?• Can we apply these to objects beyond

the solar system?• How do we know how far away the

stars are?

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Stellar Parallax

• One proof of a heliocentric Universe is stellar parallax.– Tycho Brahe saw no parallax

of stars. – Copernicus thought stars

must be too far away.

• Nearest star: Proxima Centauri

Parallax angle = 0.76 arcsec– Tycho’s precision = 1 arcmin

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The Parsec• Triangles:

tan = opposite/adjacent

• For small angles: tan = = (1 AU)/Distance

Distance = (1 AU)/• What is the distance of an

object with = 1 arcsec?Distance = 206,265

AU• Call this distance 1 parsec

(pc)• 1 pc = 206,265 AU = 3.3

lightyears

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Distances

• 1 parsec = distance with a parallax of 1 arcsecond.

• 1 lightyear = distance light travels in one year.

• 1 pc = 206,265 AU = 3.3 lightyears• Closest star: Proxima Centauri

= 0.76 arcsecDistance = 1.3 pc or 4.3 lightyears

arcsec)(in parallax

1 parsecs)(in Distance

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How far is this?

The Sun

New York

Alpha Centauri

Hawaii

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Star light, star bright

• In lecture 5 we talked about stellar magnitudes.

• Sirius is magnitude –1.5 Polaris is magnitude 2.5

• While Sirius is brighter than Polaris, Sirius is also a lot closer to us.

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Apparent and Absolute

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

(Luminosity) and its distance

• Absolute Magnitude = the brightness (magnitude) of a star at a distance of 10 pc. M– Only depends on a star’s luminosity

10pc

distancelog5 10Mm

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example

• Our Sun:– m = -26.8,– distance = 1/206,265 = 4.8 x 10-6 pcSo: M = 4.8

• Polaris:– m = 2.5,– distance = 132 pcSo: M = -3.1

• Polaris is 1500 times more luminous than the Sun!

10pc

distancelog5 10Mm

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Ste

llar

Sp

ectr

a

Stellar Temperatures

How hot are stars?

• In Lecture 3 we learned about blackbody spectra and temperature.

• Since different stars have different colors, different stars must be different temperatures.

Hot

Cool

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Spectral Classificati

ons

77Orion Copyright – Tyler Nordgren

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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

32

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Binary Stars• Most stars in

the sky are in multiple systems.

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

• The Sun is in the minority by being single.

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Spectroscopic Binaries

• Sometimes you can’t see both stars.– Too close– Too far– Too faint

• But if a star is orbiting something it must be moving.

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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

0.01 arcsec

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Stellar MassesHow massive are stars?

• Where M is the Total Mass of the binary.• Most stars have masses calculated this

way.• Result:

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

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

M

aP

32

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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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Stars are small

• Betelgeuse is the only star big enough to directly see its surface with a normal telescope.

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Interferometry

• Combine the light from two or more telescopes to simulate the RESOLUTION of one giant telescope.

VLA - radio

NPOI - optical

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Optical Interferometry

• NPOI simulates a single optical telescope 65 meters in diameter.

• Resolve stars as small as 1.5 mas!PTI - infrared

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Angular versus Linear

Supergiants, Giants and Dwarfs

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H-R Diagram• Can order the stars we see by the

property of temperature and luminosity (or absolute magnitude).

Prominent stars

Nearby Stars

Brightest Stars

1000 pc Stars