ASTR 1120 February 6

Transcription

1 ASTR 1120 February 6. First Exam: Thursday, February 20 Recitations will be held Duane G131, Mondays 5-5:50 Website Third Homework Posted to Web Due 2/11 Next Observatory Opportunity Mon Feb 10, 7pm

2 The Doppler Shift Another Powerful Tool Frequency of light changes depending on velocity of source. Similar to sound wave effect Higher pitch when vehicle approaches Lower when it recedes.

3 Spectral Shifts Spectrum is identifiable as known element, but lines appear shifted. Measure the shift, and we get velocity information! Shift to blueward implies approach Shift to redward implies departure

4 The Doppler Shift vt ct Observer D During t seconds, source emits n waves of wavelength λ. They move ct during that time. But source also moves vt during that time. So the n waves are scrunched into ct-vt instead of the usual ct ct vt c v ( ) Thus the wavelength is reduced from λ to λ = λ = λ 1 v ct c c

5 The Doppler Formula v λ = λ 1 0 c δλ λ0 λ = = λ 0 λ0 V c v is positive if coming toward us Wavelength λ decreases from lab value δν ν 0 = v v v 0 0 = V c Frequency shifts up as source approaches

6 Doppler Examples I run toward you with laser at 3m/s c = 3x10 8 m/s, λ = 6328Å v/c = 10-8 So δλ = λ x v/c = 6328 x 10-8 = 6.3x10-5 λ = Å ---- That s why we can t sense a change Shuttle orbits at 6km/s v/c = 6/300,000 = 2x MHz becomes 100MHz x 2x10-5 = 100,002,000Hz if coming at you.

7 Another Doppler Example Star has known hydrogen line at 6563Å Detect line at 6963Å δλ = 400Å v δλ = c = λ 0 300, = 18,284km / s Star is receding at 18,000km/s!! In some cases astronomers can detect shifts as small as one part in a million. That implies detection of motion as small as 300m/s.

8 What about that radar gun? Cop uses radar which typically operates near λ = 1cm If you are going 65mph = 65 mi/hr x 1600m/mi / (3600 s/hr) = 30m/s This creates a shift of δλ = 30/3x10 8 = 10-7 in the wavelength 1cm shifts to cm. Not much. To say you were 5mph over the limit needs to measure one part in 100million!

9 Example of How Its Used in Astronomy Stellar lines are broadened by star s rotation.

10 Stellar Classification Full range of surface temperatures from 2000 to 40,000K Spectral Classification is Based on Surface Temperature Hottest O B A F G K M { Girl Oh Be A Fine } Kiss Me Guy Coolest Each Letter has ten subdivisions from 0 to 9 0 is hottest, 9 is coolest

11 The Spectral Types O Stars of Orion's Belt >30,000 K Lines of ionized helium, weak hydrogen lines <97 nm (ultraviolet)* B Rigel 30,000 K- 10,000 K Lines of neutral helium, moderate hydrogen lines nm (ultraviolet)* A Sirius 10,000 K-7,500 K Very strong hydrogen lines nm (violet)* F Polaris 7,500 K- 6,000 K Moderate hydrogen lines, moderate lines of ionized calcium nm (blue)* G Sun, Alpha Centauri A 6,000 K- 5,000 K Weak hydrogen lines, strong lines of ionized calcium nm (yellow) K Arcturus 5,000 K- 3,500 K Lines of neutral and singly ionized metals, some molecules nm (red) M Betelgeuse, Proxima Centauri <3,500 K Molecular lines strong >830 nm (infrared) *All stars above 6,000 K look more or less white to the human eye because they emit plenty of radiation at all visible wavelengths.

12 Stellar Luminosity By 1915 had lots of spectra and classifications Had a few distances from parallax Once distance was available, luminosity and Absolute Magnitude could be calculated. Herzsprung and Russel, working independently both plotted absolute magnitude (luminosity) vs classification (temperature)

13 The H-R Diagram Plot of Brightness vs Temperature -5 0 Rigel Capella Giants Brightness +5 Sirius Procyon Sun Main Sequence α Cen B +10 White Dwarfs Sirius B +15 O B A F G K Prox Cen M Spectral Type

14 The H-R Diagram

15 The Main Sequence Stars Differ By: Mass Age Composition Nothing else! And composition doesn t vary Age and Mass only. Those on main sequence are all burning H so age drops out. MS is function of MASS only!!!

16 Full, Artistic H-R As mass of MS star increases, both R and T increase increasing size σat 4 T constant on any vertical line

17 Newly Formed Star -5 M Rigel Sirius White Dwarfs Sirius B Procyon Capella Giants Protostar Sun Main Sequence α Cen B Large, Low T. Settles down to MS Then sits while burning H +15 O B A F G K Prox Cen M Spectral Type

18 MS Lifetime What determines amount of time a star stays on Main Sequence? Just like a kerosene heater: Amount of fuel and rate of burn. More Mass = More Fuel More Luminosity = Greater Burn Rate We can scale from the Sun: M = 1M L = 1L Sun lasts years MSLife 10 =10 M L M in solar masses L in solar luminosities

19 Some Lifetimes Mass Luminosity Lifetime in Billion Years Sun Sirius Prox Cen Rigel 8 10, Dinky little stars like Prox Cen will last trillions of years Huge stars like Rigel are gone in a few million There aren t many large stars out there, because they don t last. 10,000 O stars of the 100,000,000,000 Milky Way stars

20 Chemical Energy for Sun? Chemical Energy Generates 2eV per atom in forming molecule (burning) 2eV = 3x10-19 Joules Number of Atoms in Sun: N M 2x10 30 = = 27 mp 1.6x10 kg kg = Available Energy E = 3 x10 x10 = 3x10 38 J Time it can run: 38 E 3x10 J 11 t = = = 7x10 s = 20, 000years 26 L 4x10 W

21 Gravitational Energy? Available Gravity Energy: E = GM R 2 = 6x10 11 x 7x ( 2x10 ) 24x10 41 = = 3x10 J 8 7x10 8 Time it can run: t = E L = 3x10 3x = s = 3x10 7 years Sun can only run 30million years on gravity. It does this during formation Best understanding of Sun until Einstein.

22 Nuclear Energy for Sun? Nuclear Energy Generates 2MeV per atom in forming molecule (burning) 2MeV = 3x10-13 Joules Number of Atoms in Sun: N M 2x10 30 = = 27 mp 1.6x10 kg kg = Available Energy E = 3 x10 x10 = 3x10 44 J Time it can run: 44 E 3x10 J 17 t = = = 7x10 s = 20,000,000, 000years 26 L 4x10 W Sun can run 20 Billion years on nuclear energy Which is what it does.