AST 301Introduction to AstronomyJohn LacyRLM [email protected] LiRLM [email protected] JeonRLM [email protected] site: www.as.utexas.eduGo to Department of Astronomy courses,AST 301 (Lacy), course websiteTopics for this weekDescribe the reactions in the proton-proton chain.How does Einstein’s equation, E = m c2, help explain hownuclear reactions generate energy?Describe how neutrinos allow us to observe the interior ofthe Sun, and say what was found.Describe the ideas of thermal and hydrostatic equilibriumfor a star.How are flux (or apparent brightness), luminosity, anddistance of a star related?How do we measure flux and distance of a star?How do we measure temperatures and masses of stars?How do we use the Hertzsprung-Russell diagram to makesense of the temperatures and luminosities of stars?Equilibriums in starsThe idea of thermal equilibrium said that the Earth mustradiate as much energy into space as it absorbs insunlight. Otherwise it would change temperature.For a star to be in thermal equilibrium, it must radiate asmuch energy into space as it is generating by nuclearfusion.Stars are also in hydrostatic equilibrium.For a star to be in hydrostatic equilibrium, the pressure atany point in the star must be right to support the weightof what’s above that point.Pressure is the force per unit area that a gas exerts on itssurroundings.Gas propertiesTemperature is a measure of how much energy of motiongas atoms have (how fast they move).Pressure is the force the gas atoms exert on theirsurrounding as they bounce off of the walls.Pressure is proportional to the number of atoms in the box(actually the density, or number of atoms per unit volume).Pressure is also proportional to the temperature of the gas(because fast moving atoms hit the walls harder and moreoften).Squeezing a gas increases both its density and itstemperature.Gravity makes the gas settle toward the bottom of the box,so the pressure is higher toward the bottom.This is an example of hydrostatic equilibrium.More on hydrostatic equilibriumWe usually describe hydrostatic equilibrium by saying thatthe pressure at any point in a star must be right tosupport the weight of what’s above that point.What if the pressure was too high inside a star?The star will expand, which decreases the pressure, untilpressure is right to support the weight.This happens quickly, in about an hour.More on thermal equilibriumWhen a star is in thermal equilibrium, the rate of energygeneration by fusion equals the rate of energy loss byradiation from the surface of the star.The rate of fusion depends strongly on temperature,because the protons must be moving fast to get closeenough together so they can be attracted by the strongforce before their electrical repulsion pushes them apart.If the center of a star is too hot, fusion will run faster thanenergy is being radiated from the surface.But the high temperature will cause high pressure, which willcause the star to expand. And since the star is a gas,when it expands it cools.So fusion slows down.Until its rate is right to generate the energy lost by radiation.Measuring properties of starsWhat properties of stars can we measure?Flux or apparent brightness (Watts/m2)Distance (km or parsecs)Luminosity or absolute brightness (Watts)Mass (kg or solar masses)(surface) Temperature (K)CompositionWhat else?Flux or Apparent BrightnessThe flux of a star is the power in the light from that star thatwould hit a 1 m2 area facing the star.To measure a star’s flux, we use a telescope to collect lightfrom the star, measure the power in the light we collect,and the divide the power by the collecting area of thetelescope. (A bigger telescope will collect more light.We don’t want the flux to depend on what telescope weuse to measure it.)The flux of a star depends on how much light it emits andon how far we are from that star.We’ve defined flux so it doesn’t depend on what telescopewe use, but it does depend on where the telescope is.Parallax and DistanceYou judge the distance to objects (depth perception) fromthe fact that your two eyes view an object from twodifferent locations, so have to look in different directionsto look at an object.The different direction to an object from different positionsis called parallax.Astronomers use the change in the direction to a starduring a year, as the Earth orbits around the Sun, tojudge the distance to the star.Nearer stars have bigger parallaxes, orparallax α 1 / distanceStellar parallaxAstronomers use a unit for distance called the parsec(abbreviated pc) so that a star at a distance of 1 pchas a parallax of 1 arcsecond (1/60 of 1/60 of 1o).1 pc is approximately 3 light-years or 200,000 AUWhat is the parallax of a star with a distance of 2 pc?A. ½ arcsecondB. 2 arcsecondsC. 102 arcsecondsD. 10-2 arcsecondsStellar parallaxWhat is the parallax of a star with a distance of 2 pc?A. ½ arcsecondB. 2 arcsecondsC. 102 arcsecondsD. 10-2 arcsecondsparallax α 1/distance, so if you increase the distance from1 pc to 2 pc, the parallax decreases by a factor of 2, from1 arcsecond to ½ arcsecond.p = 1/d if you measure p in arcseconds and d in parsecs.Another questionWhat is the distance to a star with a parallax of 0.1arcseconds?A. 0.1 pcB. 1 pcC. 10 pcApparent brightnessHow bright a star appears is determined by how much lightfrom that star enters your eye.That is given by the product of the area of your pupil andthe light power per unit area reaching you from the star.We refer to the power per unit area as the flux or apparentbrightness of the star.Flux = Power / AreaYou can calculate the flux of light from a star by dividing thepower emitted by the star by the area it has spread overby the time it gets to you.Because all areas vary as the square of the size of theobject, the area the light has spread over varies as thesquare of the distance it has traveled.Flux or Apparent BrightnessIn traveling a distance of 1 pc from a star, light spreads outover some area.When the light has traveled a distance of 2 pc from thestar, it has spread out over 4 times as much area.Since the flux of starlight is the power emitted divided bythe area it has spread over, the flux is 4 times smaller2 pc from the star than it is at 1 pc.The formula is: Flux α 1 / distance2Or if the stars we are comparing have different luminosities(power emitted), the formula becomes:Flux α Luminosity /
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