chapter 11: stars · brightness: amount of starlight that reaches earth expressed in energy per...

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Chapter 11: Stars

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Fundamental Properties of Stars

• Luminosity• Surface Temperature• Mass

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The brightness of a star depends on both its distance and luminosity

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Luminosity: Amount of power a star radiates.

Expressed in units of energy per second (e.g. Watts)

Apparent brightness: Amount of starlight that reaches Earth

Expressed in energy per second per surface area (e.g. Watts/sq. meter).

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Relationship between luminosity and apparent brightness

• Luminosity passing through each imaginary sphere is the same.

• Area of sphere = 4 (radius)π 2

• Divide luminosity by area to get brightness.

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Luminosity Brightness = 4 (distance)π 2

This is the inverse square law for light.

Can use this to determine a star’s luminosity:

Luminosity = 4 (distance)π 2 x (Brightness)

Relationship between luminosity and apparent brightness

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QUESTION: How would the apparent brightness of Alpha Centauri change if it were three times farther away?

A. It would be only 1/3 as brightB. It would be only 1/6 as brightC. It would be only 1/9 as brightD. It would be three times brighter

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QUESTION: How would the apparent brightness of Alpha Centauri change if it were three times farther away?

A. It would be only 1/3 as brightB. It would be only 1/6 as brightC. It would be only 1/9 as brightD. It would be three times brighter

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• We observe the apparent brightness of stars.• To determine the luminosities (total energy output per

second), we need to know the distances to stars.• How do we measure the distances to stars?

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Parallax = apparent motion of an object relative to the background due to change in viewing positions.

More distant stars have smaller parallaxes.

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Units of stellar distances

• d = 1/p (for very small angles p)• 1 parsec is distance when parallax

angle (p) is measured in arcseconds• 1 parsec = 3.26 light years

Example: a star with p = 1/10 arcsec, is d = 10 parsecs away, or 32.6 light years away.

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Parallaxis the apparent shift in position of a nearby object against a background of more distant objects.

Parallax

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Apparent positions of the nearest stars shift by about an arcsecond as Earth orbits the Sun.

Parallaxes of the nearest stars

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Parallax angle is directly proportional to distance.

More distant stars have smaller parallaxes.

Parallax Angle as a Function of Distance

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Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star.

Measuring Parallax Angle

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There is a large spread in stellar luminosities.

Use the luminosity of the Sun LSun as a reference

Most luminous stars:

~106 LSun

Least luminous stars:

~10-4 LSun

(Lsun = Sun’s luminosity)

Factor of 10 billion spread.

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How hot are the stars?

• Every object emits thermal radiation:Hotter objects emit more light at shorter wavelengths (bluer colors).

• So by measuring the colors of stars, we can determine their surface temperature.

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Measuring a star’s surface T

• Astronomers measure the surface temperature because the interior temperature can only be inferred from models.

• Surface T is easier to measure than its luminosity because it does not depend on distance.

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Two Properties of Thermal Radiation

• Hotter objects emit more light at all wavelengths per unit area.• Hotter objects emit photons with a higher average energy (bluer).

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Hottest stars: 50,000 K

Coolest stars: 3,000 K

The Sun: 5,800 K.

(All these temperatures refer to the star’s surface.)

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Luminosity of an object depends both on its size and temperature

• An object of fixed size grows more luminous as temperature rises.

• An object of fixed temperature grows more luminous as it gets bigger.

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The types of absorption lines in a star’s spectrumalso tell us about its temperature.

(Hot interior emits a continuous spectrum,which is partly absorbed by the cool outer layers.)

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Solid

Molecules

Neutral Gas

IonizedGas(Plasma)

10 K

102 K

103 K

104 K

105 K

106 K The level of ionization depends on a star’s surface temperature.

Therefore, stars of different temperatures will show different absorption lines in their spectra.

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Spectral type = classification of stellar spectra based on the absorption lines

(hence, another way of determining stellar temperature)

OBAFGKM

30,000 K

20,000 K

10,000 K

7,000 K

6,000 K

4,000 K

3,000 K

Examples

Stars of Orion’s Belt

Rigel

Sirius

Polaris

Sun, Alpha Centauri A

Arcturus

Betelgeuse, Proxima Centauri

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(Hottest) O B A F G K M (Coolest)

Remembering Spectral Types

= “Oh, Be A Fine Girl, Kiss Me”

= “Only Boys Accepting Feminism Get Kissed Meaningfully”

• Spectral classes are further broken down into sub-classes, numbered from 0 to 9 (warmer to cooler). For example, the Sun is a G2 star, meaning it is warmer than a G5 star.

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QUESTION: Which kind of star is hottest?

A. M starB. F starC. A starD. K star

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QUESTION: Which kind of star is hottest?

A. M starB. F starC. A starD. K star

“Oh, Be A Fine Girl, Kiss Me”

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Pioneers of Stellar ClassificationAnnie Jump

Cannon and the “calculators” at Harvard laid the foundation of modern stellar classification.

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Pioneers of Stellar ClassificationWilliamina Fleming (1857-1911) classified stellar spectra according to the strength of their hydrogen lines: A strongest, B slightly weaker, and O for the weakest. She classified more than 10,000 stars, which Pickering published in 1890.

Annie Jump Cannon joined Pickering’s group in 1896. Building on the work of Fleming and Antonia Maury, she realized that the spectral classes fell into a natural order – but not the alphabetical order determined by hydrogen lines alone.

She also found that some of the original classes overlapped others and could be eliminated.

She discovered that the natural sequence was OBAFGKM. She added subdivisions by number.

Jump Cannon personally classified 400,000 stars.

In 1925, Cecilia Payne-Gaposchkin showed that the differences in spectral lines from star to star reflected changes in the ionization of the emitting atom. She published her findings in her doctoral thesis.

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How do we determine the masses of stars?

Use binary stars (pairs of stars held together by gravity).

About ~1/2 of all stars are binaries.

Relative sky positions of Sirius A & B over 70 years

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We measure mass using gravity (Newton’s version of Kepler’s Third Law).

Direct mass measurements are possible only for stars in binary star systems

p = period a = average separation M1, M2 = mass of the 2 stars

We measure the binary’s period and separation to get the sum of the stellar masses.

Isaac Newton

p2 = a3 4π2

G (M1 + M2)

€

p2= 4π2

G

a3

(M1+M

2)

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