A Field Guide to Stars

Red Giants and White Dwarfs

The Solar Neighborhood

Milky Way Galaxy

100 billion stars

Volume of nearly 100,000 light years across

Orbits Galactic Center- 25,000 light years from Earth

Stellar Parallax

Parallax decreases as distance increasesDistance (in parsecs)= 1 parallax (in arc

seconds)Parallax=0.5”

1/0.5= 2pcParallax=0.1” 1/0.1=10pc

One Parsec≈3.3 Light years

Measuring Parsecs

Our Neighbors

Proxima Centauri

Alpha Centauri Complex

0.77” parallax

270,000 AU

4.3 Light years

Interstellar Void

Luminosity and apparent brightnessLuminosity is intrinsic also called the absolute brightness

We see apparent brightness

Another Inverse Square LawLeaving a star, light travels through imaginary spheres of increasing radius surrounding the source.

Doubling the distance from a star makes it appear 22, or 4 times dimmer.Tripling makes it look 32, or 9 times more dim.

Luminosity also affects brightness.Doubling the luminosity also doubles the

energy crossing any spherical shell surrounding the star.

This doubles the apparent brightness.The apparent brightness of a star is directly

proportional to the star’s luminosity and inversely proportional to the square of its distance.

Inverse Square

Apparent brightness (energy flux)∞ luminosity

distance2

Okay…WHAT?

Two things are neededDetermine apparent brightnessStar’s distance Magnitude ScaleSecond century Greek astronomer

HipparchusClassified into six groups

Determining Luminosity

The use of telescopes that could measure energy shows two important facts

The 1-6 magnitude range spans a magnitude of 100 in apparent brightness

Hipparchus used his eyes

The Magnitude Scale

Define a change of 5 in magnitude to correspond to exactly a factor of 100

1-6 or 7-2..Numbers in Hipparchus’s ranking are

apparent magnitudesScale is no longer limited to whole numbersMagnitudes outside of the 1-6 range are

allowed

Modern Magnitude Scale

Apparent Magnitude

Ranges from the Sun (-26.7) to the Hubble/Keck limit

≈5x1022

Measures apparent brightness when the star is seen at its actual distance from the sun

Absolute magnitude is apparent magnitude from 10 parsecs from the observer

Inverse Square (again)Star @ 100pc “moved” to 10pcDistance decreases by a factor of 10Apparent brightness increases 102 or 100

timesIts apparent magnitude would decrease by 5

Absolute Magnitude

Sun’s absolute magnitude is 4.83Since an increase in brightness by a factor of

100 corresponds to a reduction in a star’s magnitude by 5 units, a star with a luminosity 100 times that of the Sun has an absolute magnitude of4.83-5=-0.17

A star with .01 Solar luminosity has an absolute magnitude of4.83+5=9.83

More on the Magnitude Scale

We can fill in the gaps if we realize 1 magnitude corresponds to a factor of 1001/5≈2.512, 2 magnitudes to 1002/5≈6.310 and so on.

A factor of 10 in brightness corresponds to 2.5 magnitudes.

More on the Magnitude Scale

Luminosity Conversion ChartCalculate the luminosity (in solar units) of a star having absolute magnitude of M. The star’s absolute magnitude differs from the Sun by (M-4.83) magnitudes, So the luminosity, L, differs from the solar luminosity by a factor of:

100 -(M-4.83)/5 or

L(solar units)= 10–((M-4.83)/2.5)

From appendix 3:

MSun=4.83, has L=100=1

Sirius A with M=1.45, has L=101.35=22 Solar Units

Barnard’s Star with M=13.24, has L=10-3.5 = 4.3x10-4 Solar Units.

Betelgeuse has M= -5.14 and L=9,700 suns…

More on the Magnitude Scale

Invert the previous formulaM=4.83-2.5 log10L

Vega: L=50M=4.83-2.5 log(50)

M=0.58Eridani: M=0.3M=4.83-2.5 log(0.3)

M=6.2

Converting Luminosity to Absolute Magnitude

m=M+5 log (D/10pc)OrD= 10pc X 10((m-M)/5)

Knowing the difference m-M between apparent and absolute magnitudes is equivalent to the objects distance from us.

Apparent Luminosity, Absolute Magnitude, and Distance

The star Rigel:m=0.18D=240 pcM= 0.18-5log(24)=-6.7

Apparent Luminosity, Absolute Magnitude, and Distance

Color and the Blackbody CurveMeasure the apparent brightness at several

different frequenciesMatch observations to appropriate blackbody

curve

Stellar Temperatures

Blackbody Curves

B and V filters admit different amounts of light for objects of different temperatures.

Between 1880 and 1920 stellar spectra was collected

No firm theories on how the lines were produced

Stars were classified by their hydrogen-line intensities

Now are classified as O, B, A, F, G, K, and M.

Spectral Classification

Astronomers further divided each letter into 10 subdivisions Our sun is a G2 (cooler than a G1, but hotter

than a G3)Vega: A0Barnard’s Star: M5Betelgeuse: M2

Spectral Classification

With distance known and angular diameter measured, we can calculate actual radius.130pc and angular diameter of up to 0.045”Betelgeuse’s maximum radius is 630 times that

of the Sun. (Betelgeuse is a variable star).Most stars are too distant or too small to be

measured directly

Direct and Indirect Measurements

Stefan Boltzmann LawEnergy emitted per unit area per unit time

increases as the fourth power of the star’s surface temperature.

Large bodies radiate more energy than do small bodies at the same temperatureLuminosity α radius2 X temperature4

Radius-Luminosity-Temperature relationship:Knowledge of a star’s luminosity and

temperature can yield an estimate of the star’s radius

Radiation Laws

Stefan Boltzmann law: F=σT4

Area of a sphere: A=4πR2

Luminosity α radius2 X temperature4

SoLuminosity= 4π σ R2 T4

OrLuminosityα radius2 X temperature4

Estimating Stellar Radii

Use solar unitsL (in solar luminosities)= 3.9x1026WR (in solar radii)= 696,000 KmT (solar temperature)= 5800K

We can eliminate the constant 4π σ and rewrite the equation asL (in solar units)= R2 (in solar radii) x T4 (in

units of 5,800K)

Estimating Stellar Radii

L (in solar units)= R2 (in solar radii) x T4 (in units of 5,800K)

To compute the radius, we change the formula toR=√L/T2

AldebaranSurface Temperature: 4000KLuminosity: 1.3x1023W

So the luminosity is 330 times the Sun and temperature is 4,000/5,800= 0.69R=√330/0.69R=18/0.48R=39 solar radii

Estimating Stellar Radii

Canopus, the second brightest star in the southern skyApparent magnitude of -0.62Parallax of 0.0104”

Distance (pc)= 1/ parallax1/0.0104= 96pc

M=m-5log(dist/10pc)M=-0.62-5log(9.6)M=-5.5

Estimating Stellar Radii

M=-5.5L= 10 –(M-4.83)/2.5

L= 10-(-5.5-4.83)/2.5

L=10 -(-4.132)

L≈ 14,000Canopus spectral type is an F0: implying a

surface temperature of 7,400 K or 1.3 solar temperature

L=R2xT4

R=√L/T2

R=√14,000/1.69R≈70 solar Radii

Estimating Stellar Radii

Giants are any star whose radii are between 10 and 100 solar radii.

Aldebaran is red in color, so it is classified as a Red Giant.

Stars ranging up to 1000 solar radii are known as supergiant

Betelgeuse is a supergiant

Giants and Dwarfs

Sirius BT= 27,000 K (4.5)L= 1025W (0.025)

R=√0.025/4.52

R=0.007 solar radiiA dwarf is any star whose radius is

comparable to or smaller than the Sun (including the Sun)

Because any 27,000 K object glows blue-white, Sirius B is a white dwarf.

Giants and Dwarfs

Hertzsprung-Russell Diagram

Relationship exists between stellar temperature and luminosity