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Stellar objects

Stellar objects. By the end of this topic you should be able to : -describe the method of parallax , the method of spectroscopic parallax and the Cepheid method for determining distances in astronomy ; -define the parsec;

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Stellar objects

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  1. Stellarobjects Bytheend of thistopicyoushouldbeableto: -describe themethod of parallax, themethod of spectroscopicparallax and theCepheidmethodfordeterminingdistances in astronomy; -define the parsec; -statethedefinitions of absolute and apparentmagnitude.

  2. Parallaxmethod Theparallaxmethodtakesadvantage of thefactthat, whenanobjectisviewedfromtwodifferent positions, itappears displaced, relativeto a fixedbackground of stars, because of thefactthat in theintervening time theEarth has moved in itsorbitaroundtheSun. Sincetheparallaxangleisverysmall, tan p ≈ p

  3. Parallaxmethod Theparallaxangleistheangle at the position of thestarthatsubtends a distanceequaltotheradius of theEarth’sorbitaroundtheSun, a distanceknown as oneastronomicalunit, 1 AU = 1.5 x 1011 m. Parallaxes are measured quite accuratelyprovidedthey are nottoosmall. Forexample, parallaxesdownto 1 arcsecond (1/3600 of a degree) are easilymeasured. Ifthestaristoofaraway, theparallaxistoosmall and themethodfails. Typically, measurementsfromobservatoriesonEarthallowdistances up to 300 lytobedeterminedwiththeparallaxmethod. UsingmeasurementsfromsatellitesabovetheEarth’satmosphere, largerdistances can bedetermined.

  4. Parsec Theparallaxmethod can beusedto define a commonunit of distance in astronomy, the parsec. One parsec isthedistanceto a starwhoseparallaxis 1 arcsecond. 1 pc = 3.09 x 1016 m = 3.26 ly Thismeansthatiftheparallax of a starisknowntobeparcsecond, thedistanceis1/p parsecs

  5. Absolute and apparent magnitudes Themodernmagnitudescaleisdefined as follows: Given a star of apparentbrightness b, weassigntothatstaranapparentmagnitude m definedby b/b0 = 100-m/5 = 2.512-m (Thevalue b0 = 2.52 x 10-8 W/m2istaken as thereferencevalueforapparentbrightness). Takinglogarithms (to base 10) givestheequivalentform m = -5/2 log(b/b0) Theancientastronomersdevised a relativesystem of classifyingstarsaccordingtohowbrighttheappearedtoanobserveronEarth. Eachstarwasgiven a numbercalledtheapparentmagnitudem-thehighertheapparentmagnitude, thedimmerthestar. In thissystemsixclasses of brightnessweredefined, and assignednumbersfrom 1 to 6. A magnitude 6 starwassupposedtobe 100 times dimmerthan a magnitude 1 star.

  6. Absolute and apparent magnitudes Thehumaneye can detect a star of apparentmagnitudenotlongerthanabout 6. With simple binocularsthelimitisraisedtostars of magnitude 9. Thelargesttelescopes can record images of objects of apparentmagnitude as faint as 27.

  7. Absolute and apparent magnitudes Twostarsthathavethesameapparentmagnitude are notnecessarilyequallybrightintrinsically, sincetheymaybe at differentedistances. Toestablish a system of absolute magnitudes thatwilltellusifonestarisintrinsicallybrighterthananother, we imagine thatallstars are positioned at thesamedistancefromEarth. Theapparentmagnitude a starwouldhaveif placed at a distance of 10 pcfromEarthiscalledtheabsolutemagnitudeM of thestar. Thus, it can beprovedthat:

  8. Absolute and apparent magnitudes

  9. Examplequestions Calculatetheabsolutemagnitude of a starwhosedistanceis 25 ly and whoseapparentmagnitudeis 3.45 Calculatethedistanceto Sirius usingthat m = -1.43 and M = 1.4

  10. Spectroscopicparallax Thetermspectroscopicparallaxrefersto a method of findingthedistancetoanstargiventhestar’sluminosity and apparentbrightness. Thetermismisleading in that no use of parallaxisbeingmade. λ0T = 2.9 x 10-3 Km Thequestionisthenhowto determine theluminosity of thestar. Thisis done byexaminingitsspectrum, fromwhichthetemperature can bededuced. Knowingthetemperature and usingthe HR diagramallowusto determine theluminosity as well.

  11. Examplequestion A mainsequencestaremitsmost of itsenergy at a wavelength of 2.4 x 10-7 m. Itsapparentbrightnessismeasuredtobe 4.3 x 10-9 Wm-2. Howfaristhestar?

  12. TheCepheids Cepheid variable stars are starswhoseluminosityisnotconstant in time butvariesfrom a minimumto a maximumperiodically, theperiodsbeingtypicallyfrom a 1 to 70 days. Thebrightness of thestarincreasessharply and thenfades off more gradually. Thereasonfortheperiodicbehaviour of thebrightness of Cepheidstars has to do withtheinteraction of radiationwithmatter in theatmosphere of thestar. Thisinteraction causes theouterlayesrs of thestartoundergoperiodicexpansions and contractions. Thestaris at itsbrightestwhenthesurface of thestarexpandsoutward at highvelocity. Itis at itsdimmestwhenthesurfacemovesinward.

  13. TheCepheids HenriettaLeavittdiscovered a remarkablerelationshipbetweenthepeakluminosity of Cepheids and theirperiod. Thelongertheperiod, thelargertheluminosity. Observing a Cepheid and findingitsperiodallowsthedetermination of itsluminosity. This, in turn, allowsthedetermination of itsdistance.

  14. Range of efectivenessforeachmethod Theordinaryparallaxmethodallowsthedetermination of distances up toabout 100 pc. Thespectroscopicparallaxmethodextendsdistancemeasurementstoabout 10000 pc. TheCepheid variable starmethodextendsthescalefurtherto 15 Mpc.

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