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A star’s color, temperature, size, brightness and distance are all related!






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Ohio University - Lancaster Campus slide 1 of 47 Spring 2009 PSC 100. A star’s color, temperature, size, brightness and distance are all related!. Ohio University - Lancaster Campus slide 2 of 47 Spring 2009 PSC 100. The Beginnings.
A star’s color, temperature, size, brightness and distance are all related!

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Slide 1

Ohio University - Lancaster Campus slide 1 of 47Spring 2009 PSC 100

A star’s color, temperature, size, brightness and distance are all related!

Slide 2

Ohio University - Lancaster Campus slide 2 of 47Spring 2009 PSC 100

The Beginnings

  • Late 1800’s, early 1900’s – how light is produced by atoms is being intensely studied by…

    • Gustav Kirchoff & Robert Bunsen

    • Max Planck…Josef Stefan...

    • Ludwig Boltzmann…Albert Einstein

Slide 3

Ohio University - Lancaster Campus slide 3 of 47Spring 2009 PSC 100

Black Bodies

  • In 1862, Kirchoff coins the phrase “black body” to describe an imaginary object that would perfectly absorb any light (of any wavelength) that hit it.

    • No light transmitted through, no light reflected off, just totally absorbed.

Slide 4

Ohio University - Lancaster Campus slide 4 of 47Spring 2009 PSC 100

  • a perfect absorber of light would also be a perfect emitter

  • amount of light energy given off each second (its brightness or luminosity) and the color of its light are related to the object’s temperature.

Slide 5

Ohio University - Lancaster Campus slide 5 of 47Spring 2009 PSC 100

  • Molten lava and hot iron are two good examples of black bodies, but…

  • a star is an excellent black body emitter.

Slide 6

Ohio University - Lancaster Campus slide 6 of 47Spring 2009 PSC 100

  • Max Planck, a German physicist, was able to make theoretical predictions of how much light of each color or wavelength would be given off by a perfect black body at any given temperature.

  • These predictions or models are today called Planck Curves.

Slide 7

Ohio University - Lancaster CampusSpring 2009 PSC 100 slide 7 of 47

Slide 8

Ohio University - Lancaster Campus slide 8 of 47Spring 2009 PSC 100

  • What 2 characteristics of the curves change as the temperature increases?

  • The size of the curve increases.

(2) The peak of the curves shift to theleft, to shorter wavelengths & higher

energies.

Slide 9

Ohio University - Lancaster Campus slide 9 of 47Spring 2009 PSC 100

Can we draw some conclusions?

  • Hotter stars should be brighter than cooler stars.

  • Hotter stars should emit more of their light at shorter wavelengths (bluer light)

  • Cooler stars should emit more of their light at longer wavelengths (redder light).

  • All stars emit some energy at all wavelengths!

Slide 10

Ohio University - Lancaster Campus slide 10 of 47Spring 2009 PSC 100

  • In 1879, Josef Stefan discovered that the luminosity of a star was proportional to the temperature raised to the 4th power.

  • In 1884, Stefan’s observations were confirmed when Ludwig Boltzmann derived Stefan’s equation from simpler thermodynamic equations.

Slide 11

Ohio University - Lancaster Campus slide 11 of 47Spring 2009 PSC 100

Stefan-Boltzmann Law

  • Today, we honor both scientists by naming the equation after them…the Stefan-Boltzmann Law:

  • At the surface of the star, the energy that’s given off per square meter (Watts / m2) called the luminous flux is...

    W / m2 = 5.67 x 10-8 T4

Slide 12

Ohio University - Lancaster Campus slide 12 of 47Spring 2009 PSC 100

  • At 100 K (cold enough to freeze you solid in just seconds), a black body would emit only 5.67 W/m2.

  • At 10x hotter, 1000 K, the same black body would emit 104 times as much light energy, or 56,700 W/m2.

Slide 13

Ohio University - Lancaster Campus slide 13 of 47Spring 2009 PSC 100

  • If the temperature of a star were to suddenly double, how much brighter would the star become?

  • If the temperature of a star somehow fell to 1/3 of what it was, how much fainter would the star become?

24 = 16 times brighter(1/3)4 = 1/81, or 81 times dimmer

Slide 14

Ohio University - Lancaster Campus slide 14 of 47Spring 2009 PSC 100

  • In 1893, Wilhelm Wien (pronounce “vine”) discovered by experiment the relationship between the “main” color of light given off by a hot object and its temperature.

  • This “main” color is the peak wavelength, called λmax , at the top of the Planck Curve.

Slide 15

For each curve, the

top of the curve is the

peak wavelength.

Slide 16

Ohio University - Lancaster Campus slide 16 of 47Spring 2009 PSC 100

Wien’s Law

  • Wien’s Law says that the peak wavelength is proportional to the inverse of the temperature:

    λmax = 2.9 x 106 T = 2.9 x 106

    T λmax

  • T must be in Kelvin, and λmax in nanometers.

Slide 17

Ohio University - Lancaster Campus slide 17 of 47Spring 2009 PSC 100

  • What is the peak wavelength of our sun, with a T = 5750 K?

  • What is the peak wavelength of a star with a surface temperature of 3500 K?

2.9 x 106 = 504 nm (yellowish-green)

5750 K

2.9 x 106 = 829 nm (this star emits the

3500 K majority of its light as

infrared, IR).

Slide 18

Ohio University - Lancaster Campus slide 18 of 47Spring 2009 PSC 100

  • A reddish star has a peak wavelength of 650 nm. What is the star’s temperature?

    A star has a peak wavelength in the ultra-violet of 300 nm. What is the star’s temperature?

2.9 x 106 = 4462 K (cooler than the sun)

650 nm

2.9 x 106 = 9667 K

300 nm

Slide 19

Ohio University - Lancaster Campus slide 19 of 47Spring 2009 PSC 100

  • We now have a “color thermometer” that we can use to determine the temperature of any astronomical object, just by examining the light the object gives off.

  • We know that different classes of objects are at different temperatures and give off different peak wavelengths.

Slide 20

Clouds of cold hydrogen gas (nebulae) emit radio waves

What kinds of objects?

http://www.narrowbandimaging.com/images/vdb142_small.jpg

Slide 21

Warmer clouds of molecules where stars form emit microwaves and IR.

Slide 22

Protostars emit IR.

http://www.antonine-education.co.uk/Physics_GCSE/Unit_3/Topic_10/protostar.jpg

Slide 23

Sun-like stars emit mostly visible light, while hotter stars peak in the UV.

http://www.nasa.gov/images/content/138952main_whywe16full.jpg

Slide 24

Neutron stars and black holes peak in the X-ray.

Slide 25

Star cores emit gamma rays.

http://aspire.cosmic-ray.org/labs/star_life/images/star_pic.jpg

Slide 26

Ohio University - Lancaster Campus slide 26 of 47Spring 2009 PSC 100

  • Where would the peak wavelength be for

    • your body

    • a lightning bolt

    • the coals from a campfire

Slide 27

Ohio University - Lancaster Campus slide 27 of 47Spring 2009 PSC 100

  • A star’s spectrum is also influenced by

  • its temperature.

  • In 1872, Henry Draper obtained the first

  • spectrum of a star, Vega, in the

  • constellation Lyra.

photojournal.jpl.nasa.gov/jpeg/PIA04204.jpg

Credit: Lick Observatory Archives

Slide 28

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  • In 1885, Edward Pickering began a project at Harvard University to determine the

  • spectra of many stars. Draper’s widow

  • funded the work.

  • The first 10,000 spectra obtained were

  • classified by Williamnia Fleming, using the

  • letters A through Q.

Slide 29

Ohio University - Lancaster Campus slide 29 of 47Spring 2009 PSC 100

  • From 1901 to 1919, Pickering & his assistant

  • Annie Jump Cannon classified and published

  • the spectra of 225,000 stars (at the rate of

  • about 5000 per month!)

  • When Pickering died in 1919, Cannon

  • continued the work, eventually classifying

  • and publishing the spectra of 275,000 stars.

Credit: amazing-space.stsci.edu

Slide 30

Ohio University - Lancaster Campus slide 30 of 47Spring 2009 PSC 100

Hotter stars have

simpler spectra.

Cooler stars have

more complex

spectra, since most

atoms are not ionized.

Slide 31

Ohio University - Lancaster Campus slide 31 of 47Spring 2009 PSC 100

  • Class O >30,000 K bluish

  • He lines in spectrum.

  • (These stars are so hot that H is mostly ionized & doesn’t shows lines.) Pleiades

    • Class B 11,000-30,000 K bluish

    • He lines, weaker H lines

  • Rigel, Regulus, Spica

    • Class A 8,000-11,000 K blue-white H lines (Balmer Series)

  • Sirius, Vega

  • Slide 32

    Ohio University - Lancaster Campus slide 32 of 47Spring 2009 PSC 100

    • Class F 6,000-8,000 K white

    • H, Ca lines, weaker H lines Procyon

    • Class G 5,000-6,000 K yellow

    • Ca, Na lines, + other metals

  • Sun, Capella, -Centauri

    • Class K 3,500-5,000 K orange

    • Ca & other metals

  • Arcturus, Aldebaran

  • Slide 33

    Ohio University - Lancaster Campus slide 33 of 47Spring 2009 PSC 100

    • Class M <3,500 K red

    • metal oxides (TiO2), molecules

  • Betelgeuse, Antares

    • Oh, Be AFine Girl, Kiss Me!

  • Slide 34

    Ohio University - Lancaster Campus slide 34 of 47Spring 2009 PSC 100

    The stellar classes (OBAFGKM) are further

    subdivided with a number 0 to 9 following the

    letter.

    Our sun, a G2 star, is slightly cooler than the

    F range. A G9 star would be just a bit warmer

    than the K range.

    Slide 35

    Ohio University - Lancaster Campus slide 35 of 47Spring 2009 PSC 100

    • 1910-1913, Henry Russell, a professor at

    • Princeton, and Ejnar Hertzsprung, an

    • astronomer at Leiden Observatory in the

    • Netherlands, used the data from the Draper

    • catalog to plot the temperature of the stars

    • vs. their brightness or luminosity.

    • What kind of result would you expect, a

    • random scatter, or a pattern?

    Slide 36

    universe-review.ca/I08-01-HRdiagram.jpg

    Slide 37

    Ohio University - Lancaster Campus slide 37 of 47Spring 2009 PSC 100

    Betelgeuse and Antares show on the diagram

    as being red stars, and red stars should be

    faint.

    Both stars are also hundreds of light

    years distant, so why do they appear so

    bright in our sky?

    Slide 38

    Ohio University - Lancaster Campus slide 38 of 47Spring 2009 PSC 100

    Slide 39

    Ohio University - Lancaster Campus slide 39 of 47Spring 2009 PSC 100

    Slide 40

    Ohio University - Lancaster Campus slide 40 of 47Spring 2009 PSC 100

    Slide 41

    ‘Red’

    ‘Red’

    Red Dwarfs

    Slide 42

    Ohio University - Lancaster Campus slide 42 of 47Spring 2009 PSC 100

    The H-R Diagram makes a lot more

    sense when you realize that the

    different regions don’t show different

    kinds of stars…

    …but stars at different stages

    of their lives.

    Slide 43

    Ohio University - Lancaster Campus slide 43 of 47Spring 2009 PSC 100

    • Determining distance using the HR Diagram

    • From a star’s color-temperature, determine

    • its absolute magnitude (M).

    • Observe the star’s apparent magnitude (m)

    • through a telescope.

    • Use the distance modulus equation to

    • calculate the distance.

    Slide 44

    Ohio University - Lancaster Campus slide 44 of 47Spring 2009 PSC 100

    How far away is an F1 star that has a surface

    temperature of 8000 K, if its apparent

    magnitude is +9.6?

    Slide 46

    Ohio University - Lancaster Campus slide 46 of 47Spring 2009 PSC 100

    distance in parsecs =

    10^[(9.6 - 3.0 +5)  5] =

    10^[11.6  5] =

    10^2.32 =

    209 parsecs (or 681 light years)

    Slide 47

    Where might this method run into trouble?

    Red & Orange star come in 2 varieties:

    giants & dwarfs.

    The spectrum of the star must be used to

    determine if the star is large or small.

    The presence of what element(s) in higher

    than normal percentages might indicate

    that the star is a giant, not a dwarf?


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