Astonishing Astronomy 101With Doctor Bones (Don R. Mueller,

Ph.D.)

EducatorEntertainer

JU

G G LE

RPLANETARY

Scientist

ScienceExplorer

Chapter 17 – The Stars

Nearby Stars

Proxima-Centauri(4.23 ly)

Alpha-Centauri A, B

(4.32 ly)

Barnard’s Star(5.9 ly)

Sirius A, B(8.60 ly)

Ross 128(10.9 ly)

The Sun’s stellar neighborhood

Sun

Measuring the distances to the stars: Parallax to Stellar Parallax

• As an observer’s viewing location changes, foreground objects appear to shift relative to background objects.

• This effect is called parallax and it can be used to measure the distance to closer astronomical objects.

A star's apparent motion against a stellar background of more distant stars (as the Earth revolves around the Sun) is known as stellar parallax.

A star with a parallax of 1 arc-second has a distance of 1 Parsec.

Parallax decreases with Distance.

Example of Parallax Distance:

Alpha Centauri has a parallax of p = 0.742 arc-seconds

d = 1/p = 1/0.742 = 1.35 parsecs

Earth (December)

Earth (June)

SunDistance d is in parsecs:( 1 parsec ≈ 3.26 light-years)

d = 1/p

p

d

1 AU

The distance d to the star is inversely proportional to the parallax p:

Parallax angle p: Measured in arc-seconds

Some Trigonometry

d = 1 parsec (pc) = 3.3 ly

Circumference = 2p x 1 pc = 2p d

p = 1 arc-second

360arcsecond1AU1

nceCircumfere

360arcsecond1

2AU1dp

1,296,0001

arcseconds1,296,000arcsecond1

2AU1

dp

d = 206,265 AU = 3.09 x 1013 kmπ2AU1,296,000d

The Effect of Distance on Light

• Light from distant objects appears to be very dim:

• Why? Because light spreads out as it travels from source to destination.

• The further you are from the source, the dimmer the light.

• The object’s brightness or amount of light received from a source, is decreasing.

• The amount of light reaching us is a star’s brightness.

2d4OutputLight TotalBrightness

p

This is an inverse-square law : The brightness decreases with the square of the distance (d) from the source.

The Inverse-Square Law

Inverse-Square Law

• Stars, like light bulbs, emits light in all directions: called isotropic radiation. We see the photons that are heading in our direction.

• As you move away from the star, fewer and fewer photons are headed toward you, thus the star appears to dim.

• The total amount of energy a star emits into space is its luminosity (power) and is measured in Watts.

• Some types of stars have a known luminosity and we can use the standard candle to calculate the distance to the stars.

• The brightness decreases with the square of the distance from the star.

• When you move twice as far from the star, its brightness decreases by a factor of 22 = 4.

• If we know the total energy output of a star (luminosity L) and we can count the number of photons we receive from the star (brightness b), we can calculate its distance d:

b4Ldp

The Hipparchus Star Magnitude Scale

• We can quantify the brightness of a star by assigning it an apparent magnitude or number in this case:

• Brighter stars have lower numbers.• Dimmer stars have higher numbers.• Differences in magnitudes correspond to

ratios in brightness.

• Hipparchus classified the naked-eye stars into 6 star classes: the brightest being 1st-class (magnitude) stars and the faintest being 6th class stars.

• The “brightness” numbers in the star ranking system of Hipparchus are called apparent magnitudes.

Absolute Magnitude

• It’s easier to compare the respective luminosities of two stars if they are at the same distance from the Sun.

• We can calculate how bright the stars would appear if they were all the same distance from us. Solely as a matter of convenience we choose 10 parsecs (pc).

• The magnitude of a star “moved” to 10 pc from us is referred to as its absolute magnitude.

• For example, when a star that is actually closer to 100 pc from us is placed at the 10 pc standard, its distance d has decreased by 10 times. In turn, the star’s apparent brightness would increase by a factor of d2 = 102 =100 (the inverse square law). The star’s apparent magnitude has decreased by a factor of 5.

• Years ago, astronomers in their refinement of the star magnitude scale of Hipparchus, established that a difference of 5 orders in magnitude corresponded to a factor of 100 times in brightness (intensity).

Relating Magnitude to Brightness RatioMagnitude Difference Ratio of Brightness

0 2.5120 = 1:1

0.1 2.5120.1 = 1.10:1

0.5 2.5120.5 = 1.58:1

1 2.5121 = 2.512:1

2 2.5122 = 6.31:1

3 2.5123 = 15.85:1

4 2.5124 = 39.81:1

5 2.5125 = 100:1

10 2.51210 = 104:1

20 2.51220 = 108:1

Photons in Stellar Atmospheres:

Absorption spectra provides, a “fingerprint” for the star’s composition. The strength of this spectra is determined by the star’s temperature.

Stellar Surface Temperatures

• The peak wavelength emitted by a star shifts with the star’s surface temperature:– Hotter stars look blue– Cooler stars look red

• We can use the star’s color to estimate its surface temperature:– If a star emits stronger at a particular wavelength (nm),

then its surface temperature (T) is often given by Wien’s Law:

λnmK102.9T

6

Wien’s Law: Hotter bodies emit more strongly at shorter wavelengths. When decreases, T increases.

Measuring the Temperatures of Astronomical Objects

Wien’s Law:

To estimate the temperature T in degrees Kelvin (K) of stars:• We just need to measure the

wavelength (max) at which the star emits the most photons.

• Solving for T:

If the wavelength of maximum emission (max) for the spectral distribution of the blackbody curve is plotted versus 1/T, a straight line is obtained.

maxλnmK 109.2T

6

Measuring Temperature T using Wien’s Law

λnmK6109.2T

Measure a star’s brightness at several wavelengths () and then plot the brightness versus wavelength.

The total emitted radiant energy is proportional to the 4th power of the temperature T (K): K4

• If we know an object’s temperature (T), then we can calculate how much energy is being emitted by the object, using the Stefan-Boltzmann law:

• The power P is in Watts, area A is in square meters and the Stefan-Boltzmann constant:

= 5.6710-8 Watts/m2K4

4σTAP

Stefan-Boltzmann LawLuminosity increases rapidly with temperature

The Stefan-Boltzmann Law

A star’s luminosity is related to both a star’s size and temperature: (a) Hotter stars emit more. (b) Larger stars emit more.

Each square meter of the star’s surface emits T4 watts.

The total energy radiated per second is the Luminosity L:

A spherical star of radius R, has a surface area S = 4pR2

42 σTRπ4L

Spectral Classification

• Spectral classification system: By temperatureHotter stars are O typeCooler stars are M type

• New Types: L and T– Cooler than M

• From hottest to coldest, they are: O-B-A-F-G-K-M

– Mnemonics: “Oh, Be A Fine Girl/Guy, Kiss Me

– Or: Only Bad Astronomers Forget Generally Known Mnemonics

Spectral Classification

• Application of Wien’s law and theoretical calculations show that temperatures range from more than 30,000 K for O stars to less than 3500 K for M stars.

• Because a star’s spectral type is set by its temperature, its type also indicates its color; ranging from violet-blue colors for O and B stars, to reddish colors for K and M stars.

• To distinguish still smaller gradations in temperature, astronomers subdivide each type by adding a numerical suffix—for example, B0, B1, B2,..., B9—with the smaller numbers indicating progressively higher temperatures.

Summary of Spectral TypesSpectral Type Temperature Range (K) Features

O Hotter than 30,000 Ionized helium, weak hydrogen.

B 10,000-30,000 Neutral helium, hydrogen stronger.

A 7500-10,000 Hydrogen very strong.

F 6000-7500 Hydrogen weaker, metals—especially ionized Ca—moderate.

G 5000-6000 Ionized Ca strong, hydrogen weak.

K 3500-5000 Metals strong, CH and CN molecules appearing.

M 2000-3500 Molecules strong: especially TiO and water.

L 1300-2000 TiO disappears. Strong lines of metal hydrides, water and reactive metals such as potassium and cesium.

T 900?-1300? Strong lines of water and methane.

23

O-B-A-F-G-K-M SchemeStellar Spectral Classes

A convenient tool for organizing stars

• A star’s luminosity depends on its temperature and diameter. A Hertzsprung-Russell diagram is used to find trends in this relationship.

Constructing Hertzsprung-Russell

(H-R) Diagrams

The H-R Diagram• A star’s location on the H-R diagram is given by: temperature (x-axis) and luminosity (y-axis).

• Many stars are located on a diagonal line running from cool, dim stars to hot bright stars: The Main Sequence

• Other stars are cooler and more luminous than main sequence stars:

Have large diameters (Red and Blue) Giant stars

• Some stars are hotter, yet less luminous than main sequence stars:

Have small diameters White Dwarf stars

H-R Diagram

• Most stars are found on the main sequence.

• Giants

• Supergiants

• White dwarfs

Main Sequence

White Dwarfs

Giants

Super Giants

Temperature (K)

Lum

inos

itySpectral Type

27

Lines of constant Radius in the H-R diagram

Main sequence• B stars: R ~ 10 RSun

• M stars: R ~ 0.1 RSun

Betelgeuse: R ~ 1,000 Rsun

(Larger than 1 AU)

White dwarfs: R ~ 0.01 Rsun

(A few Earth radii)

l

A Family of Stars

Stars of all sizes

The Mass-Luminosity Relation• When we look for trends in stellar masses, we notice something interesting:

Low mass main sequence stars tend to be cooler and dimmer.

High mass main sequence stars tend to be hotter and brighter.

• Mass-Luminosity Relation:

Massive stars burn brighter.

5.3ML

31

Mass-Luminosity Plot

L = M3.5

Stellar Luminosity Classes

Class Description Example

Ia Bright supergiants

Betelgeuse, Rigel (brightest stars in Orion)

Ib Supergiants Antares (brightest star in Scorpius)

II Bright giants Polaris (the North Star)

III Ordinary giants Arcturus (brightest star in northern constellation Boötes)

IV Subgiants Procyon A (brightest star in Canis Minor)

V Main sequence The Sun, Sirius A (brightest star in sky, in Canis Majoris)

Luminosity Classes

Ia Bright supergiant

Ib Supergiant

II Bright giant

III Giant

IV Subgiant

V Main sequence

Sun: G2 VRigel: B8 IaBetelgeuse: M2 Iab

Measuring Star Diametersby employing

Interferometric Techniques

• Stars are simply too far away to easily measure their diameters.

• Atmospheric blurring and telescope effects smear out the light.

• Interestingly, we can combine the light from multiple telescopes in a process called astronomical interferometry:

Two telescopes separated by a distance of 300 meters have nearly the same resolution as a single telescope with a diameter of 300 meters.

The diameter of the red giant Betelgeuse was determined using this technique.

Speckle interferometry, which employs Fourier analysis, uses multiple images from the same telescope to increase resolution.

Using eclipsing binary systems to measure stellar diameters

Types of Binary Stars• Stars found orbiting other stars are called binary stars.

Three types are known:

1. Visual Binary - If we can see from photos taken over time that the stars are orbiting each other, the system is a visual binary.

2. Spectroscopic Binary - If the stars are so close together that their spectra blur together, the system is called a spectroscopic binary.

3. Eclipsing Binary - If the stars are oriented edge-on to the Sun, one star will periodically eclipse the other star in the system. These are known as eclipsing binaries.

Using the Doppler Shift to detect binary systems

• As a star in a binary system moves away from us, its spectrum is shifted towards red wavelengths. As it moves toward us again, the spectrum is shifted toward blue wavelengths.

• This Doppler Shifting allows us to detect some binaries.

Measuring Stellar Masses with Binary StarsThis technique gives us the combined mass of the two stars.

The Center of Mass COM: (1) calculate the combined mass, (2) using the distance from the center of mass COM, we can calculate each star’s mass.

• In a binary system, the two stars orbit a common COM.

• The masses and distances from the COM are related through:

MA × aA = MB × aB

• If the stars are of equal mass, the COM is directly between them.

• If the stars are of unequal mass, the COM is closer to the more massive star.