Astronomy Detailed Lecture Notes Feb. 17 & 19
Astronomy Detailed Lecture Notes Feb. 17 & 19
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Date Created: 02/20/15
217 Luminosity and Apparent Brightness Luminosity absolute brightness measure of the total energy radiated by a star 0 Units energy per second Apparent brightness how bright a star appears when viewed from earth Depends on luminosity and distance to the star The farther away you are from a light source the dimmer it looks How does light spread outThe Inverse Square Law of Radiation The amount of light received gets diluted by the square of the distance from the source The same amount of energy is spread out over a larger and larger sphere as light travels away from a star 0 The area of a sphere is 47TI39A2 Apparent brightness b intrinsic brightness 47tDA2 L 47tDA2 D distance between star and observer L luminosity intrinsic brightness energy radiated per second b apparentobserved brightness If we know a star s apparent brightness and its distance we can calculate its luminosity Brighter doesn t always mean more luminous Two stars that appear equally bright to us might be a closer dimmer star and a farther brighter one greater distance can counteract greater luminosity Star Colors and Temperature Red stars are cooler blue stars are hotter A star s color depends on its surface temperature The intensity of light from relatively cool objects peaks at long wavelengths making the star look red A hot star s intensity curve peaks at short wavelengths making it look blue Classifying Stars Spectral Classes The atmospheres of stars produce absorption line spectra depending on the presence of different elements These spectra are diverse allowing us to classify stars into spectral classes 0 OBAFGKM 0 Oh Be A Fine Guy Kiss Me Spectral types reveal temperatures Based on the structure of atoms we understand that OBAFGKM spectral sequence is actually a sequence in temperature The hottest stars are 0 stars their absorption lines can occur only if these stars have surface temperatures above 25000 K The coolest stars are M stars the spectral features of M stars are consistent with stellar surface temperatures of about 3000 K In other words the sequence OBAFGKM is also a temperature sequence from hottest to coldest Surface temperature affects stellar spectra For hydrogen lines to be prominent in a star s spectrum the star must be hot enough to excite the electrons out of the ground state but not so hot that all the hydrogen atoms become ionized A stellar surface temperature of about 9000 K produces the strongest hydrogen lines this is the case with A0 and A5 stars Every other type of atom or molecule also has a characteristic temperature range in which it produces prominent absorption lines in the observable part of the spectrum Spectral Classes for Brown Dwarfs Brown dwarfs too small to sustain thermonuclear reactions but too big to be considered planets Observing in the infrared 2 new spectral classes are added for brown dwarfs L and T o The modern classes are OBAFGKMLT Concept Check 1 What quantity dictates what spectra class you give to a star Temperature 2 Is a spectral class F2 star more similar to an Aspectral class star or a Gspectral class star 0 A 3 As spectral type numbers increase within the Gspectral class of star do the larger numbers represent higher temperature stars 4 If hydrogen is the most abundant atom in a star why do the spectra of hot stars show no prominent hydrogen lines 5 Which brown dwarf is hotter an L or a T 0 L Stellar Sizes Some stars are close enough and big enough that we can directly measure their sizes For example Betelgeuse is hundreds of times larger than the sun Stellar radii vary widely Relationship between a star s luminosity radius and surface temperature L 4nrA2 6TA4 L star s luminosity Watts R star s radius meters 6 StefanBoltzmann constant T star s surface temperature K StefanBoltzmann s Law energy radiated sec per mquot2 E oTA4 If the distance is known then the intrinsic luminosity is also known Inverse Square Law of Radiation The radius size of the star can then be calculated If R radius of star then total surface area of star 47TRA2 o L 47TRA26TA4 energy radiated per sec J oules s T can be determined from the spectrum of the star This method is an indirect determination or R If 2 stars have the same luminosity but A has a twice the surface temperature A s radius is 1A as large as B What does this mean A cool star can be bright if it has a very large radius A very hot star can be dim if it has a very small radius Binary Stars Orbit Each Other A seesaw balances if the fulcrum is at the center of mass of the 2 children The members of a binary star system orbit around the center of mass of the 2 stars Although their elliptical orbits cross each other the 2 stars are always on opposite side of the center of mass and thus never collide The Concept of Center of Mass 0 M1R1 M2R2 R1 distance of mass Ml from center of mass R2 distance of mass M2 from center of mass Binary Stars The middle star of the handle is binary Most stars are members of multiple star systems the majority of stars are found in binary pairs Visual binaries can be measured directly Ex Mizar A Kruger 60 Sirius is a binary o Sirius A has a smaller orbit but is larger 0 Sirius B has a larger orbit but is smaller and further away from center of mass The more massive object makes a smaller circle and vice versa Eclipsing binary star one star comes in front of the other 0 Can be used to measure size 0 If we know how far away the stars are we can calculate how big they are 0 Shape and timing of eclipse gives sizes of stars Binary stars are very useful for determining the masses of stars Orbital parameters such as period and size of the orbit and velocities of the 2 stars can sometimes be observed We can then use Newton s theory of gravity to calculate stellar masses F Gmlm2 rA2 Binary Star Systems Reveal the Masses of Stars There s no practical direct way to measure the mass of an isolated star Binary star binaries are pairs of stars that orbit each other Their mutual gravitational attraction causes their orbital motions Newton s law of gravity can be used to get 0 M1 M2 masses of2 stars o a semimajor axis in AU 0 P orbital period in years 0 Kepler s Third Law of Planetary Motion I M1M2aA3PA2 Spectroscopic binaries can be measured using their Doppler shifts Motion away from observer causes redshift Motion toward observer causes blueshift The HertzsprungRussell HR Diagram This is a plot of stellar luminosity vs surface temperature Some wellknown stars are plotted here Temperature changes from low to high 3000 K to 30000 K Each star is represented by a dot The position of each dot corresponds to its luminosity and temperature The vertical position represents the star s luminosity The horizontal position represents the star s surface temperature Once many stars are plotted on an HR Diagram a pattern begins to form 9 Diagram of closest 80 stars Dark curve on the graph is called the main sequence where most stars are located The white dwarf region is where very hot stars are located but they aren t very luminous since they re small 9 Diagram of 100 brightest stars All more luminous than the sun Two new categories appear red giants and blue giants The brightest stars in the sky appear bright because of their enormous luminosities not their proximity 9 Diagram of 20000 stars Main sequence and red giant region are clear About 90 of stars lie on main sequence 9 re red giants and 1 are white dwarfs Stellar Masses Mass is the main determinant of where a star will be on the Main Sequence This pie chart shows the distribution of stellar masses The more massive stars are much rarer than the least massive Mass is correlated with radius and is very strongly correlated with luminosity for stars that lie on the Main Sequence The MassLuminosity Relation The greater the mass of a mainsequence star the greater its luminosity its surface temperature and its radius A main sequence star of mass 10 M has roughly 3000 times the Sun s luminosity 3 000L one with 01 M has a luminosity of only about 0001 L Mass is also related to stellar lifetime The more mass the shorter its lifetime Stellar lifetime l stellar mass3 So the most massive stars have the shortest lifetimes they have a lot of fuel but burn it at a very rapid pace On the other hand small red dwarfs burn their fuel extremely slowly and can have lifetimes of a trillion years or more Chapter 11 The Interstellar Medium Dust clouds dark regions in the Milky Way that block light from the stars beyond M8 The Lagoon Nebula M20 The Trifid Nebula M17 The Omega Nebula M16 The Eagle Nebula Nebula general term for fuzzy objects in the sky 0 Dark Nebula dust cloud 0 Emission Nebula glows due to hot stars near them 0 Reflection Nebula blue due to light scattering by dust I Lower concentrations of dust than dark nebulae
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