Measuring Stars What We Want to Know l
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Measuring Stars What We Want to Know •Brightness •Temperature Easy •Composition •Distance Hard •Luminosity •Size (Radius) •Mass Binary Stars lpeak T = 2900 Km •Spectrum tells you composition (M+m)P2 = a3 •Spectrum also tells you much more Luminosity and Brightness •The Luminosity L is how much power something is putting out •The Brightness B is how bright something appears •They are related: L = 4d2B •The brightness is always easy to determine •If we can get one of the distance or the luminosity, we can get the other. Sphere: A = 4d2 d Star A and star B are equally bright, but star A is farther away. Which one is actually more luminous? A) Star A B) Star B C) They are equally luminous D) There is insufficient information Finding the Distance •If we can get the distance, we can get the luminosity too •We will use a new unit for measuring distance, the light year •The distance light goes in a year ly = 9.46 1015 m = 63,240 AU •Real astronomers use parsecs •But we won’t •Brightness •Temperature Easy •Composition •Distance Hard •Luminosity •Size (Radius) •Mass Methods for Finding Distance •Radar •Solar System Only •Excellent accuracy •Parallax •Nearby Stars (< 300 ly) •Moderate accuracy •Spectroscopic Parallax •Main Sequence Stars only •Poor accuracy Radar Distance Earth Venus d 2d = ct, solve for d •We know what an AU is •Effectively no error Methods for Finding Distance •Radar •Solar System Only •Excellent accuracy •Parallax •Nearby Stars (< 300 ly) •Moderate accuracy •Spectroscopic Parallax •Main Sequence Stars only •Poor accuracy Parallax •The distance to an object can be judged if you view it from two angles •The difference in the angle you see it from is called parallax •The more distant, the smaller the parallax Parallax •The farther apart you put your “two eyes”, the better you can judge distance 3.26 ly •The smaller p is, the farther away the star is. d d p p p •p in arcseconds (The distance 3.26 ly is also known as a parallax second) parsec nearest stars several ly away Centauri C = Proxima Centauri : 4.2 ly Sirius: 9 ly Spectral Type The following are all equivalent information: Why I hate •The surface temperature of a star astronomers •The color of the star •The spectral type of the star •From hottest to coldest, OBAFGKM “Oh Be A Fine •Subdivided 0-9, with 0 the hottest Girl, Kiss Me.” •Sun is a G2 star •The spectral type is easy to determine Which star is hottest? A) G2 B) G4 C) F3 D) F7 Spectral Type Spectra and Motion – Doppler Effect Spectra and Motion – Doppler Effect Star A Spectrum Hydrogen Spectrum Star A is A) Made of a hydrogen variant B) Moving towards us C) Moving away from us D) Rotating Announcements Date Read Today Sec. 11.1, 11.2 Wednesday Sec. 12.1, 12.2 Thursday Sec. 12.3 Posted Now: •Test 2 questions •Test 2 solutions •Midterm grades Lab Tonight •Out-4, Out-6, In-4 6/14 Spectra and Motion – Doppler Effect Star B Spectrum •Binary stars are two stars that are orbiting each other •A spectroscopic binary are two stars that look like one but their binary nature can be deduced from their spectrum Hydrogen Spectrum Star B is A) Made of two kinds of hydrogen B) Moving away from us AND moving towards us C) Actually two stars moving at different speeds Spectra and Motion – Doppler Effect Star C Spectrum – Day 200 0 50 100 150 •Other object could be smaller in mass •This is the Doppler method whereby we discover planets around other stars Hydrogen Spectrum Star C is A) In orbit around an invisible companion B) Alternately expanding and contracting C) Alternately heating and cooling D) Rotating Summary – What Spectra Tell Us •Temperature •From the peak of the spectrum •Composition •From wavelengths and strength of dark lines •Motion •From the Doppler shift •Multiplicity •From the number of sets of spectral lines •Orbit and masses •From the changing Doppler shift •Pressure and rotation •From width of lines Luminosity, Temperature, and Radius •The spectrum of a star is pretty much a black body distribution •How bright each point on the surface is depends only on temperature F = T4 •Multiply by the area to get the Luminosity 4 2 L = AF = 4R2T4 L T R Star X is the same temp. as the L T R Sun, but it is 4 times more 2 luminous. How large is it? R 4 R 4 4 1 A) 2 times the Sun R R B) 4 times the Sun C) 16 times the Sun R 2 R D) 44 = 256 times the Sun Intrinsic Properties of Stars •To describe stars, we want to talk about intrinsic properties •Luminosity •Radius •Composition •Mass •Temperature •Composition is almost always the same •Mass is difficult to measure •Radius can be deduced from Luminosity and Temperature Temperature and Luminosity The Hertzsprung-Russell Diagram •A plot of temperature vs. luminosity •Hot on left, cold on right •Luminous at top, dim at bottom •Stars fall into categories: •The Main Sequence contains about 90% of the bright stars •The Giants are rare but very bright •The Supergiants are very rare but extremely bright •The White Dwarfs are not uncommon but very dim Main Sequence Stars •Main Sequence stars have different sizes, masses, and luminosities •But spectral class determines everything else •This diagram shows correct relative sizes and approximate colors of stars •But not correct relative luminosities Luminosity from Spectral Class Suppose you have a G2 star. What is its luminosity? •90% of all stars are main sequence G2: L L B5: L 800 L K5: L 0.1L •For main sequence stars, the spectral type tells you the luminosity •Together with brightness, this tells you the distance •Spectroscopic parallax Spectroscopic Parallax •Another distance method •Has nothing to do with parallax •Works only on main sequence stars How it works: •Observe the star – determine it’s brightness B •Measure its spectral type from spectrum •Deduce its luminosity from the HertzsprungRussell Diagram •Find its distance from: L = 4d2B Stellar Masses •Only some stars can have their masses measured •They need to be in binary systems •The masses of main sequence stars depends pretty much only on their spectral type T O5 B0 B5 A0 A5 M 60 18 5.9 2.9 2.0 T F0 F5 G0 G5 K0 M 1.6 1.3 1.05 .92 .85 T K5 M0 M5 M8 M .74 .51 .21 .06 The Main Sequence •The mass of a main sequence star affects everything 60M •Temperature •More massive is hotter •Luminosity •More massive is much 1M more luminous •Radius •More massive is bigger 0.1M
