Survey of Astronomy
Survey of Astronomy ASTR 1050
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Date Created: 10/27/15
During a supernova explosion about 10quot44 Joules of energy is released This is more energy than the Sun produces in its 10 billion year lifetime and the supernova is brighter than the entire galaxy that houses it for a brief time Using Einstein s famous equation calculate the amount of mass in solar masses required to obtain 10quot44 Joules Note The majority of energy in a supernova actually comes from the conversion of gravitational potential energy to kinetic moving energy E m c2 1044 Joules m x 3 x108 mIs2 10449x1o16m m11x1027 kg m 55 x 10394 solar masses The spectrum of the excited nebula below would be an example of which of Kirchhoff s laws assuming you are observing the nebula itself and not a star within the nebula l A solid liquid or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum II A lowdensity gas excited to emit light will do so at specific wavelengths and thus produce an emission spectrum lf light comprising a continuous spectrum passes through a cool low density gas the res twill be an absorption spectrum The Fox Fur Nebula gt The Trigonometric Parallax Example Nearest star or Centauri has a parallax of p 076 are seconds cl 1p 1O76 13 pc 43 LY With groundbased telescopes we can measure parallaxes p 2 002 are sec gtds50pc This method does not work for stars farther away than 50 pc If starA is three times farther away than star B star A s parallax is A Three times larger C Three times smaller E Nine time larger D Nine times smaller Intrinsic Brightness Absolute Visual Magnitude The more distant a light source is the fainter it appears The same amount of light falls onto a smaller area at distance 1 than at distance 2 gt smaller apparent brightness a m Area increases as square of distance gt apparent brightness decreases as inverse of distance squared If a source is 2x farther away it is 4x fainter 3x farther away means 9x fainter Distance and Intrinsic Brightness Exangm Recaw Magn Diff Intensity Ratio 1 2512 2 25122512 25122 631 5 25125 100 For a magnitude difference of 041 014 027 we find an intensity ratio of 2512 27 128 Distance and Intrinsic Brightness Rigel appears 128 times brighter than Betelgeuse But Rigel is 16 times further away than Betelgeuse Thus Rigel is actually intrinsically 1281ES2 33 times brighter than Betelgeuse Absolute Visual Magnitude To characterize a star s intrinsic brightness define absolute visual magnitude MV Apparent visual magnitude that a star would have if it were at a distance of 10 pc Absolute Visual Magnitudell Back to our example of Betelgeuse and Rigel Betelgeuse Rigel mV 041 014 MV 55 68 d 152 pc 244 pc Difference in absolute magnitudes 68 55 13 gt Luminosity ratio 251213 33 The Distance Modulus If we know a star s absolute magnitude we can infer its distance by comparing absolute and apparent magnitudes Distance Modulus mv Mv 395 5 I091od 90 Distance in units of parsec Equivalent Example of Distance from Absolute magnitudes Suppose we see a star like our sun a G2 star with absolute visual magnitude MV483 have an apparent visual magnitude of 110 How far away is it MV 55 Example of Absolute magnitudes from Distance Suppose we see a star like our sun a G2 star with absolute visual magnitude MV483 1000 pc away What is its apparent visual magnitude mV MV 510gdPC 5 mV MV 510gdpc 5 148 The Size Radius of a Star We already know flux increases with surface temperature T4 hotter stars are brighter But brightness also increases with size Star B will be brighter than star A Absolute brightness is proportional to radius squared L R2 Quantitatively L 4 n R2 0 T4 F39JLI Surface flux clue to a Surface area of the star blackbody spectrum Example If starA and star B have the same temperature but starA is twice as large as star B what is the luminosity of starA compared to star B L 4nR20T4 LA 475RAZOTA4 LA R 2T 4 2214 4 L 4L LB 415123207134 LB RBZTB4 1214 A B If starA has 2 times the temperature of star B but star B is three times as large as star A what is the luminosity of starA compared to star B 2 4 LA RATA 12241618 L18L T o I LB RB TB 3 1 9 A B Organizing the Family of Stars The HertzsprungRussell Diagram We know Stars have different temperatures different luminosities and different sizes To bring some order into that zoo of different types of stars organize them in a diagram of Luminosity versus Temperature or spectral type HertzsprungRussell Diagram Absolute mag or Luminosity Temperature Spectral type O B A F G K M The Hertzsprung Russell Diagram More luminous slats are ploned luward the top of an HE diagram Supergianls Homestas are blue and lie lo the laquot Most stars are found along the main sequence Fainter stars are planed as points near lhe bonom Nole Star slzes are ml to scale anon 2mm a me ammcm Tnnmsnn Radii of Stars in the HertzsprungRussell Diagram 4 En am a m ms 100 times smaller than the sun Luminosity Classes ilb Supergiants IV Subgiants V MainSequence Stars Luminosity effects on the width of spectral lines Luminosity effects on the widths of spectral lines imaglanr Same spectral type but different glam luminosity Mairreenuence star Lower gravity near the surfaces of giants 2 smaller pressure 2 smaller effect of pressure broadening 2 narrower lines Examples Our Sun G2 star on the main sequence G2V Polaris G2 star with supergiant luminosity G2b You have two stars A and B StarA is 25 times the temperature of Star B but Star B is 4 times the radius of Star A How much brighter is A than B L 4nR20T4 LA 4nRjaTA4 LB 4nR aTg LA Rin g LA Rj25TB4 254 2M LB 4RA2TB4 42 What if StarA suddenly ballooned to twice it s original radius How would that affect the previous answer L 4nR20T4 LA 4nRjaTA4 LB 4nR aTg LA Rin L3 RET LA 2RA225TB4 22254 0 61 LB 4RA2TB4 42 39 MT299 is an 07V star in Cygnus with an apparent magnitude of 644 1084 mag minus 44 mag due to dust in the way It s a member of a large group of massive hot stars known as the Cygnus 0B2 Association As an 07V star it has a predicted absolute magnitude of 463 Using spectroscopic parallax determine the distance to the Cygnus 0B2 Association d 10mV Mv55 d 1011o55 pc d 1585 pc Real distance 17 kpc Where does the error come from Binary Stars More than 50 or all stars in our Milky Way are not single stars but belong to binaries Pairs or multiple systems of stars which orbit their common center of mass If we can measure and understand their orbital motion we can estimate the stellar masses a me BrooksCal gtThnm3nn gamer Qf magg E ba amca pmm Qf Em Sygtem Qijtemfmass BO39CEh masgeg equa 2gt center Qf magg g m the m dd e FA 2 KB The mme umequa the maggeg are the mare it gh s iczgward the mare magg ve star Examples a Binary system with period of P 32 years and separation of a 16AU 33 MA MB PT 3 MA MB 32 2 4 solar masses b Any binary system with a combination of period P and separation a that obeys Kepler s 3 Law must have a total mass of 1 solar mass For example let the sun s mass be MA 1 solar mass and Venus s mass be 24x10396 solar masses If Venus is 072 AU from the sun it s period is a3 072 P2 MA MB 124x10 6 037yr2 P P2 O61yr Estimating Stellar Masses Recall Kepler s 3rd Law Py2 aAU3 Valid for solar system star with 1 solar mass in the center 1 Py2 aAU3 We find almost the same law for binary stars with masses MA and ME different from 1 solar mass aAU3 MAMBT y MA and MB in units of solar masses Example Find the combined mass of 2 stars which are separated by 5 AU and have a period of 2 years Enter an answer in solar masses Visual Binaries The ideal case Both stars can be seen directly and their separation and relative motion can be followed directly 2ims smaxycme Thurman Spectroscopic Binaries Usually binary separation a can not be measured directly because the stars are too close to each other A limit on the separation and thus the masses can be inferred in the most common case Spectroscopic Binaries Radial Velocity km s 50 IV II 1 moss I P 48527 i 00002 d e 01l i 004 Spectroscopic Binaries II The approaching star produces blueshifted lines the receding star produces redshifted lines in the spectrum quot Doppler shift gt Measurement of radial velocities gt Estimate of separation a SWWSW m n gt Estimate of masses piwi Example StarA in a binary system shows only half The Doppler shift of star B StarA must b A Half as massive as star B a i B Twice as massive as star B massesmmuiar C Fourtimes as massive as Star B D 14 as massive as star B gamma 9 A Redshi T 2005 BrooksEula mmun Spectroscopic Binaries III Typical sequence of spectra from a spectroscopic binary system Helalivsinnensity 851 0 655 0 Wavelength urn E 2006 BrueksiCole Thomson ewu Relative intensity Hydrogen and He absorption lines i i i 1 5434180 20 5434272 54324183 5434476 4 5434679 5434884 VOW l l l 4000 2000 0 2000 4000 7i Rodiol Velocity km s Relative intensity OW l l 1000 500 i500 O Rodiol Velocity km 5quot Radial Velocity km squot ilOO 200 Radial velocity versus time curve Schulte 3 P 47464 1 00002 d e 0070 1 0009 Eclipsing Binaries Usually inclination angle of binary systems is Tipped 45 unknown 9 uncertainty in mass estimates Special case Eclipsing Binaries Here we know that we are looking at the Edge system edge on l ECI i 38 i ng Binaries Peculiar doubledip light curve In Computed gm curve without spots E m c E E mums 14 n m Jeplh a 39he 9c p522 depwm nr v as IEMDEVEKUV 01012 ms Evnamcnxa mamquot Example VW Cephei 3 2006 Eraoksfco e Thomson Eclipsing Binaries Ill Example Cooler star parlia n Algolinthe K i constellation of 39 39y 4 Perseus 0 Size olsun The eclipsing binary Algal lS in the constellation Perseus From the light curve of Algol we can infer that the system contains two stars of very different surface temperature orbiting in a slightly inclined plane Masses of Stars in the Hertzsprung Russell Diagram The higher a star s mass the more luminous brighter it is L M35 Highmass stars have much shorter lives than lowmass stars t VI25 39 helpwer mainsequencered life dwarfs are me lowestmass stars Sun yr Nntezslarsizesarenollo seal 44 quotL ar 10 MW 30 million y 3mm 2 min anon anon Msun N 3 yr39mD ErnuksEaleThnmun The MassLuminosity Relation More massive stars are more luminous LLQ Example If you double the mass of a star its luminosity becomes A 2X greater B 4x greater C 8X greater D 113X greater E 231x greater aaaaaaaaaaaaaaaaaa rm