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The Mass-Luminosity Relationship and Stellar Lifetimes Measuring the Masses of Stars

Ohio University - Lancaster Campus slide 1 of 41 Spring 2009 PSC 100. The Mass-Luminosity Relationship and Stellar Lifetimes Measuring the Masses of Stars. Ohio University - Lancaster Campus slide 2 of 41 Spring 2009 PSC 100. Masses of Stars.

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The Mass-Luminosity Relationship and Stellar Lifetimes Measuring the Masses of Stars

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  1. Ohio University - Lancaster Campus slide 1 of 41Spring 2009 PSC 100 The Mass-Luminosity Relationshipand Stellar LifetimesMeasuring the Masses of Stars

  2. Ohio University - Lancaster Campus slide 2 of 41Spring 2009 PSC 100 Masses of Stars • Previously, we plotted color-temperature against luminosity…(the HR diagram!) • If the mass of the stars is plotted against their luminosities, the graph reveals another relationship.

  3. Red line - higher mass stars Green line - low mass stars Luminosity - Solar Luminosities astronomynotes.com

  4. Ohio University - Lancaster Campus slide 4 of 41Spring 2009 PSC 100 • A star has a luminosity that is proportional to its mass ^ 4th power. In other words, the brightness of a star increases much faster than its mass does. • In equation form, the mass-luminosity relationship is… Lstar / Lsun = (Mstar / Msun)4

  5. Ohio University - Lancaster Campus slide 5 of 41Spring 2009 PSC 100 • The equation is only true for stars that are more massive than 0.43 Msun. • If the star is very low mass, smaller than 0.43 Msun, then the equation is modified: Lstar / Lsun = (Mstar / Msun)2.3 Slight change

  6. Ohio University - Lancaster Campus slide 6 of 41Spring 2009 PSC 100 • Intuition would seem to say that since big stars have more fuel to consume, they should last longer than smaller stars. • However, if the luminosity of a star increases with the 4th power of the mass, that means that the star is producing energy and using its fuel at the same faster rate.

  7. Ohio University - Lancaster Campus slide 7 of 41Spring 2009 PSC 100 • A star of 2 solar masses has twice the H fuel available, but uses it 24 or 16 times faster. • Mathematically, 21/24 = 1/23 = 1/8. A star of 2 solar masses would last only 1/8th as long as a 1 solar mass star. • This is like a bonfire burning all its fuel and being out in an hour, where a small campfire still has hot embers the next morning!

  8. Burns out quickly! Still burning slowly the next morning…

  9. How Long Do Stars Last? • A 1 Msun star (like our sun) will spend about 10 billion or 1 x 1010 years on the main sequence • Larger stars will live (1 / Mstar)3 x 1010 years • This equation is used for stars 0.43 Msun and above.

  10. Ohio University - Lancaster Campus slide 10 of 41Spring 2009 PSC 100 • For small stars, their lifetimes are given by (1 / Mstar)1.3 x 1010 years

  11. Ohio University - Lancaster Campus slide 11 of 41Spring 2009 PSC 100 • How long would a 10-solar-mass star live? (1 / 10)3 x 1010 = 1/1000 x 1010 = 1 x 107 or 10 million years.

  12. The smallest stars have about 0.08 solar masses. How long would a star like this live? (1 / 0.08)1.3 x 1010 = 26.7 x 1010 = 267 billion years • The universe isn’t yet old enough for small red dwarf stars to have begun dying. Some red dwarfs may have been around since the universe began!

  13. The largest “typical” star can be about 100 solar masses. • How luminous would a star like this be? Lstar = 1004 = 100 million Lsun • How long would a star this size live? (1/100)3 x 1010 = 10,000 years • Huge stars are actually visible longer than this, but spend about 10,000 years on the main sequence.

  14. Ohio University - Lancaster Campus slide 14 of 41Spring 2009 PSC 100 Measuring the Masses ofStarsBinary Star Systems

  15. How Can the Mass of a Star be Measured? • Knowing the mass of a star is important to astronomers. It’s the star’s mass that controls all the other characteristics of the star: it’s luminosity, temperature, color, size, lifetime. • BUT…it’s not possible to directly measure the mass of a single, isolated star. So what can we do?

  16. Binary Star Systems • If something, like a planet or a 2nd star, is in orbit around the star whose mass we wish to know…we can use Newton’s form of Kepler’s 3rd Law to find the total mass of the system: (MassStar A + MassStar B) = 4π2a3 G p2 (a is the distance between the stars in meters, and p is the period of revolution of the stars in seconds.)

  17. Ohio University - Lancaster Campus slide 17 of 41Spring 2009 PSC 100 • The good thing is that 50% to 75% of all stars are found in binary or multiple star systems. • If we can watch 2 stars orbit each other and determine the period of revolution and the distance between the stars, we can calculate the total mass of the system and maybe even the individual masses of the two stars.

  18. Ohio University - Lancaster Campus slide 18 of 41Spring 2009 PSC 100 Extending to single stars • Once we know the masses of many stars in binary star systems, we can infer the masses of single, isolated stars by comparing them to similar stars with known masses.

  19. Ohio University - Lancaster Campus slide 19 of 41Spring 2009 PSC 100 • False Binaries • Visual Binaries • Spectroscopic Binaries • Astrometric Binaries • Eclipsing Binaries

  20. Ohio University - Lancaster Campus slide 20 of 41Spring 2009 PSC 100 • Warning - not all stars that look like they orbit one another actually do. • Mizar and Alcor are a prime example.

  21. Alcor is81 LY away Mizar is78 LY away. Mizar and Alcor do not orbit each other. http://jumk.de/astronomie/special-stars/mizar-alcor.shtml

  22. Ohio University - Lancaster Campus slide 22 of 41Spring 2009 PSC 100 Visual Binary Stars • 2 stars actually orbit a common center of mass. • Both stars are visible either to the naked eye or through a telescope. • We call the brighter star the primary, and the fainter star the secondary.

  23. Albireo is the beak of Cygnus the Swan. domeofthesky.com/clicks/images/albireo.gif http://www.astro.princeton.edu/~esirko/sky/pix/albireo.jpg Ohio University slide 23 of 42Spring 2009 PSC 100

  24. Procyon, in the winter triangle is a class F subgiant with a white dwarf, 11 LY from us. http://www.synapses.co.uk/astro/procyon.gif http://www.glyphweb.com/esky/_images/illustrations/procyon.gif

  25. Sirius A is an A-typestar 25 times brighter than our sun, with a tiny white dwarf companion, Sirius B. Ohio University slide 25 of 42Spring 2009 PSC 100 http://www.space.com/images/sirius_a_b_photo_030715_03.jpg

  26. Spectroscopic Binary Stars • In a spectroscopic binary system, one of the two stars can’t be seen in a telescope. • The system may be too distant to resolve the two stars. • One of the stars may be too faint to see (a red dwarf). • The two stars may be very close to one another. • How do we even know 2 stars are there?

  27. Ohio University - Lancaster Campus slide 27 of 41Spring 2009 PSC 100 • If the orbits of the two stars are edge-on to us, then one of the stars is moving towards us, while the other star is moving away. • The light from the star moving towards us is blueshifted, while the light from the star moving away is redshifted. (Doppler shift)

  28. Ohio University - Lancaster Campus slide 28 of 41Spring 2009 PSC 100 • As we observe the spectrum of light from the stars, over time we see each spectral line split into two lines, then come back together. • We can get the stars’ orbital period from how long it takes the lines to split, come back, split, and come back together again.

  29. Ohio University - Lancaster Campus slide 29 of 41Spring 2009 PSC 100 Animation of Spectral Lines Splitting On your own computer, view this website: http://www.astronomy.ohio-state.edu/ ~pogge/Ast162/Movies/spbin.mov

  30. Dubhe, in Ursa Major, about 124 LY away, is a spectroscopic binary system, as is Capella in Auriga, 40 LY away. http://pioneer.utah.gov/utah_on_the_web/images/dubhe1.gif http://www.carbonar.es/s33/Auriga/Capella.jpg

  31. The “star” that we call Castor, in Gemini, is actually 3 pairs of stars. Each pair is a spectroscopic binary pair. Pairs A & B orbit each other every 400 years. Pair C orbits A & B with a period of about 10,000 years. http://www.jb.man.ac.uk/public/AList/Gemini.jpg

  32. Mizar in Ursa Major is also a spectroscopic binary star. In fact, it was the first one ever discovered, in 1889. Recent work has been able to resolve the two stars. http://paginas.terra.com.br/arte/astrophotography/double/Mizar_19-04-2004_hi.jpg

  33. Astrometric Binary Stars • An astrometric binary system is a spectroscopic binary where we can actually observe the primary star “wobble” as it moves across the sky (proper motion.) • The star’s “wobble” lets us know that something massive, but unseen, is in orbit with the primary star.

  34. Above is the proper motion of Sirius A (orange) as it moves across the sky. At right are the orbits of the two stars. http://linus.highpoint.edu/~atitus/ast121/Chapter_11/binary_stars/sirius-path.jpg http://linus.highpoint.edu/~atitus/ast121/Chapter_11/binary_stars/sirius-orbit.jpg

  35. Eclipsing Binary Stars • An eclipsing binary system is a special type of spectroscopic binary, where the orbit of the two stars is edge-on to our line of sight. • We periodically see one star pass in front of or eclipse the other star. When this happens the total amount of light that we receive from the pair dims for a few hours.

  36. http://outreach. atnf.csiro.au/ education/senior/astrophysics/ images/binvar/svcamweba.jpg

  37. Ohio University - Lancaster Campus slide 37 of 41Spring 2009 PSC 100 • Eclipsing binaries give us some very special information. If you plot the light curve of the stars, the total amount of light received over time, you can actually measure the diameters of the two stars. • The plot on the previous page was a light curve.

  38. Ohio University - Lancaster Campus slide 38 of 41Spring 2009 PSC 100 Click here for an animation of an eclipsing binary system. Scroll down to the bottom of the web page. Click here for a good illustration of a light curve.

  39. Ohio University - Lancaster Campus slide 39 of 41Spring 2009 PSC 100 Algol • The first eclipsing binary system studied was the “winking demon star” Algol, the knee of Perseus. • Algol has a period of 2.87 days and is easily noticeable to the naked eye.

  40. Ohio University - Lancaster Campus slide 40 of 41Spring 2009 PSC 100 • The Algol system is about 96 LY away. • The primary is a massive blue-white B8 star with 3.5 Msun and 100 Lsun. • The secondary is an orange K2 subgiant star with 0.8 Msun and 3 Lsun. Click here for an animation of Algol.

  41. Algol’s Light Curve

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