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Red Giants and White Dwarfs. A Field Guide to Stars. 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. Measuring Parsecs. Parallax decreases as distance increases

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red giants and white dwarfs

Red Giants and White Dwarfs

A Field Guide to Stars

the solar neighborhood
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

measuring parsecs
Measuring Parsecs
  • Parallax decreases as distance increases
  • Distance (in parsecs)= 1

parallax (in arc seconds)

Parallax=0.5”

1/0.5= 2pc

Parallax=0.1” 1/0.1=10pc

One Parsec≈3.3 Light years

our neighbors
Our Neighbors

Proxima Centauri

Alpha Centauri Complex

0.77” parallax

270,000 AU

4.3 Light years

luminosity and apparent brightness
Luminosity and apparent brightness

Luminosity is intrinsic also called the absolute brightness

We see apparent brightness

another inverse square law
Another Inverse Square Law

Leaving a star, light travels through imaginary spheres of increasing radius surrounding the source.

inverse square
Inverse Square
  • 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.
okay what
Okay…WHAT?

Apparent brightness (energy flux)∞ luminosity

distance2

determining luminosity
Determining Luminosity
  • Two things are needed
  • Determine apparent brightness
  • Star’s distance
  • Magnitude Scale
  • Second century Greek astronomer Hipparchus
  • Classified into six groups
the magnitude scale
The Magnitude Scale
  • 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
modern magnitude scale
Modern 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 magnitudes
  • Scale is no longer limited to whole numbers
  • Magnitudes outside of the 1-6 range are allowed
apparent magnitude
Apparent Magnitude

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

≈5x1022

absolute magnitude
Absolute Magnitude
  • 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 10pc
  • Distance decreases by a factor of 10
  • Apparent brightness increases 102 or 100 times
  • Its apparent magnitude would decrease by 5
more on the magnitude scale
More on the Magnitude Scale
  • Sun’s absolute magnitude is 4.83
  • Since 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 of
    • 4.83-5=-0.17
  • A star with .01 Solar luminosity has an absolute magnitude of
    • 4.83+5=9.83
more on the magnitude scale1
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.
luminosity conversion chart
Luminosity Conversion Chart

Calculate 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

more on the magnitude scale2
More on the Magnitude Scale
  • 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…
converting luminosity to absolute magnitude
Converting Luminosity to Absolute Magnitude
  • Invert the previous formula
  • M=4.83-2.5 log10L
    • Vega: L=50
    • M=4.83-2.5 log(50)
      • M=0.58
    • Eridani: M=0.3
    • M=4.83-2.5 log(0.3)
      • M=6.2
apparent luminosity absolute magnitude and distance
Apparent Luminosity, Absolute Magnitude, and Distance
  • m=M+5 log (D/10pc)
  • Or
  • D= 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 distance1
Apparent Luminosity, Absolute Magnitude, and Distance
  • The star Rigel:
    • m=0.18
    • D=240 pc
    • M= 0.18-5log(24)=-6.7
stellar temperatures
Stellar Temperatures
  • Color and the Blackbody Curve
  • Measure the apparent brightness at several different frequencies
  • Match observations to appropriate blackbody curve
blackbody curves
Blackbody Curves

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

spectral classification
Spectral Classification
  • 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 classification1
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: A0
    • Barnard’s Star: M5
    • Betelgeuse: M2
direct and indirect measurements
Direct and Indirect Measurements
  • 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
radiation laws
Radiation Laws
  • Stefan Boltzmann Law
  • Energy 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 temperature
    • Luminosity 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
estimating stellar radii
Estimating Stellar Radii
  • Stefan Boltzmann law: F=σT4
  • Area of a sphere: A=4πR2
    • Luminosity α radius2 X temperature4
    • So
      • Luminosity= 4π σ R2 T4
    • Or
      • Luminosityα radius2 X temperature4
estimating stellar radii1
Estimating Stellar Radii
  • Use solar units
    • L (in solar luminosities)= 3.9x1026W
    • R (in solar radii)= 696,000 Km
    • T (solar temperature)= 5800K
  • We can eliminate the constant 4π σ and rewrite the equation as
    • L (in solar units)= R2 (in solar radii) x T4 (in units of 5,800K)
estimating stellar radii2
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 to
    • R=√L/T2
      • Aldebaran
      • Surface Temperature: 4000K
      • Luminosity: 1.3x1023W
  • So the luminosity is 330 times the Sun and temperature is 4,000/5,800= 0.69
    • R=√330/0.69
    • R=18/0.48
    • R=39 solar radii
estimating stellar radii3
Estimating Stellar Radii
  • Canopus, the second brightest star in the southern sky
    • Apparent magnitude of -0.62
    • Parallax of 0.0104”
  • Distance (pc)= 1/ parallax
    • 1/0.0104= 96pc
  • M=m-5log(dist/10pc)
    • M=-0.62-5log(9.6)
    • M=-5.5
estimating stellar radii4
Estimating Stellar Radii
  • M=-5.5
  • L= 10 –(M-4.83)/2.5
    • L= 10-(-5.5-4.83)/2.5
    • L=10 -(-4.132)
    • L≈ 14,000
  • Canopus spectral type is an F0: implying a surface temperature of 7,400 K or 1.3 solar temperature
  • L=R2xT4
  • R=√L/T2
    • R=√14,000/1.69
    • R≈70 solar Radii
giants and dwarfs
Giants and Dwarfs
  • 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 dwarfs1
Giants and Dwarfs
  • Sirius B
    • T= 27,000 K (4.5)
    • L= 1025W (0.025)
  • R=√0.025/4.52
    • R=0.007 solar radii
  • A 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.
hertzsprung russell diagram
Hertzsprung-Russell Diagram

Relationship exists between stellar temperature and luminosity