COSMICCOSMIC DISTANCEDISTANCE SCALESCALE

HowHow WeWe KnowKnow thethe DistancesDistances toto Stars,Stars, Clusters,Clusters, andand GalaxiesGalaxies DistanceDistance DeterminationDetermination ToolsTools

ParallaxParallax –– actualactual distancedistance measuremeasure

MovingMoving ClusterCluster ParallaxParallax

StandardStandard CandlesCandles – Cepheid variables – Type 1a Supernovae

OtherOther MethodsMethods DistanceDistance LadderLadder

Parallax DistanceDistance LadderLadder

ThereThere areare severalseveral veryvery importantimportant ““rungsrungs ”” inin thethe distancedistance ladder,ladder, wherewhere overlappingoverlapping techniquestechniques areare testedtested – The Hyades cluster in our galaxy – The Magellanic clouds (dwarf companion galaxies to ours) – The Local Group (Andromeda M31 and Pinwheel M33) – The Virgo Cluster – The Coma Cluster ParallaxParallax

Ground observation accuracy ± .025” (40 parsecs) Space observation (Hipparcos) accuracy ± .0025” (400 parsecs) MovingMoving ClusterCluster ParallaxParallax

The total space velocity of a star, V, can be broken into the ra dial velocity ( vr) and the tangential velocity ( vt)
The radial velocity we get via its Doppler shift (spectroscopic observation)
To get the tangential velocity we need its proper motion ( µ) and distance (d):
Hence if we know radial velocity and tangential velocity, we ca n calculate the distance MovingMoving ClusterCluster ParallaxParallax

Think of a cluster of stars moving through space. Their proper m otion will appear to converge towards a certain point in space called the convergent point MovingMoving ClusterCluster ParallaxParallax

So if we measure the proper motion, radial velocity, and converg ent point angular distance, we get the parallax – that is the distance -- to the cluster.
Parallax = proper motion / radial velocity x tangent (angle to convergent point): π = /( vr tan θ)

Example: Hyades Cluster

Mean proper motion 0.12 “/year Mean radial velocity 40 km/sec Main core of cluster 33 o from convergent point

Distance 50 parsec StandardStandard CandlesCandles

Assume some type of star or other celestial object is of known brightness
Measure the apparent brightness, and calculate the distance based on the ”known ” brightness
There are two problems – Finding a reliable set of known -brightness objects – Determining the interstellar absorption in the measure of apparent brightness CepheidCepheid VariablesVariables

Cepheid variables are pulsating stars, named for the prototype Delta Cephei
Cepheids were determined to have a period - luminosity relationship
Hence it was presumed if you measured the period of pulsation, you could determine the absolute magnitude, and thus calculate the distance
Cepheids are a critical tool in the distance ladder
Cepheids were the initial clue that spiral nebulae were, in fact, distant galaxies CepheidCepheid VariablesVariables

Delta Cephei CepheidCepheid VariablesVariables

The Cepheid period -luminosity (PL) relationship was first determined in 1912 from measurements in the Magellanic clouds
Over time, however, it became obvious that the PL relationship was not so simple
It was discovered there were more than one type of “Cepheid ”: – Classical Cepheids – recently evolved stars – W Virginis Variables – old metal -poor Cepheids – RR Lyrae Variables – fainter old metal -poor stars CepheidCepheid VariablesVariables

Period -Luminosity Relationships CepheidCepheid VariablesVariables

TheThe nearestnearest Cepheid,Cepheid, Polaris,Polaris, isis notnot ““normalnormal ”” (how(how manymany othersothers areare alsoalso notnot normal?)normal?)

TheThe nearestnearest ““normalnormal ”” Cepheid,Cepheid, DeltaDelta CepheiCephei isis 250250 parsecparsec away,away, beyondbeyond thethe rangerange ofof accurateaccurate directdirect parallaxparallax measuremeasure (until(until HipparcosHipparcos ))

AccurateAccurate CepheidCepheid distancedistance determinationdetermination remainsremains elusiveelusive CepheidCepheid VariablesVariables

InitialInitial distancedistance determinationdetermination mademade byby – Assuming Cepheids moving randomly through space (with respect to Sun)

– Thus the vt is the same as the vr (which can be measured)

– If we know vt, then from the proper motion we can calculate the distance CepheidCepheid VariablesVariables

OneOne methodmethod ofof CepheidCepheid distancedistance measurementmeasurement isis thethe BaadeBaade --WesselinkWesselink method:method: combinescombines – Radial velocity measures of pulsation (as star surface moves toward and away from us) – Color (hence temperature) at different phases – Measure of change in diameter
By modeling via above parameters
By direct VLBI measures of diameter StandardStandard CandlesCandles

TheThe brightnessbrightness ofof CepheidsCepheids limitslimits theirtheir usefulnessusefulness forfor distancedistance determinationdetermination toto aboutabout 1010 MpcMpc

TheThe nextnext importantimportant standardstandard candlecandle isis thethe TypeType 1a1a supernovasupernova – 13 magnitudes brighter than a Cepheid – Much more rare than the occurrence of Cepheids TypeType 1a1a SupernovaeSupernovae

TheThe catastrophiccatastrophic explosionexplosion ofof aa whitewhite dwarf,dwarf, inin aa binarybinary starstar system,system, wherewhere thethe companioncompanion giantgiant starstar isis beenbeen rainingraining mattermatter downdown onon thethe whitewhite dwarfdwarf TypeType 1a1a SupernovaeSupernovae

ProfessorProfessor ChandasekharChandasekhar determineddetermined theoreticallytheoretically thatthat thethe upperupper limitlimit ofof aa whitewhite dwarfdwarf massmass isis 1.41.4 solarsolar masses.masses.

ThusThus whenwhen thethe mattermatter rainedrained downdown pushespushes thethe starstar pastpast 1.41.4 solarsolar masses,masses, itit createscreates aa typetype 1a1a supernova.supernova. TypeType 1a1a SupernovaeSupernovae

TypeType 1a1a supernovaesupernovae cancan bebe identifiedidentified byby thethe naturenature ofof theirtheir spectrumspectrum

TheThe evidenceevidence isis thatthat allall typetype 1a1a supernovaesupernovae reachreach thethe samesame absoluteabsolute magnitudemagnitude ofof --1919

ThusThus thethe distancedistance measurementmeasurement rangerange isis extendedextended toto aboutabout 50005000 MpcMpc TypeType 1a1a SupernovaeSupernovae

RecentlyRecently aa ““TypeType 1a1a ”” supernovasupernova waswas foundfound toto containcontain 2.52.5 solarsolar masses,masses, thethe resultresult ofof twotwo mergingmerging whitewhite dwarfs.dwarfs. ItIt waswas muchmuch brighterbrighter thanthan aa normalnormal TypeType 1a.1a.

ThusThus ourour presumptionpresumption ofof thethe TypeType 1a1a supernovasupernova asas aa standardstandard candlecandle isis questionable.questionable. DistanceDistance DeterminationDetermination ToolsTools OtherOther MethodsMethods

WithinWithin ourour galaxygalaxy – Secular parallax – Statistical parallax – Main sequence curve fitting – Expansion parallax – Spectroscopic visual or eclipsing binaries – Spectroscopic parallax – RR Lyrae stars SecularSecular andand StatisticalStatistical ParallaxParallax

SecularSecular ParallaxParallax – Uses the fact that the sun is moving through space at 20 km/sec, providing an extended baseline for parallax of groups of stars

StatisticalStatistical ParallaxParallax – Uses the scatter in radial velocities to determine the scatter in proper motions for a group of stars assumed to have zero net motion MainMain SequenceSequence CurveCurve FittingFitting

If one plots stars on a graph of absolute brightness versus temp erature (color), most stars fall on the “main sequence ” of the HR ( Herzsprung - Russell) diagram.

Thus color gives absolute magnitude and yields distance ExpansionExpansion parallaxparallax UsingUsing SpectroscopicSpectroscopic DataData

SpectroscopicSpectroscopic observationsobservations ofof visualvisual binariesbinaries – The true size of the orbit and the angular size of the orbit giv e us the distance

SpectroscopicSpectroscopic observationsobservations ofof eclipsingeclipsing binariesbinaries – The surface brightness and size of the stars can be determined, and the distance calculated

SpectroscopicSpectroscopic observationsobservations ofof singlesingle starsstars – The estimates of temperature and luminosity class allow estimate of distance (related to use of HR diagram) RRRR LyraeLyrae StarsStars

RRRR LyraeLyrae starsstars obeyobey aa periodperiod --luminosityluminosity lawlaw

SinceSince thesethese starsstars areare fainterfainter thanthan CepheidsCepheids ,, theirtheir useuse isis limitedlimited toto ourour galaxygalaxy

ImportantImportant rolerole inin determiningdetermining distancesdistances toto globularglobular clustersclusters DistanceDistance DeterminationDetermination ToolsTools OtherOther MethodsMethods

Beyond our galaxy – Tully -Fisher relationship
The rotational velocity of a spiral galaxy is proportional to its mass, and hence its luminosity – Faber -Jackson relationship
For an elliptical galaxy, the velocity dispersion is proportional to its mass, and hence its luminosity – Globular Cluster Luminosity Function
Using globular clusters as “standard candles ” – Hubble Law
Doppler red shift due to expansion of the Universe DistanceDistance DeterminationDetermination ToolsTools OtherOther MethodsMethods

TheseThese methodsmethods areare complicatedcomplicated byby twotwo issuesissues – The possible impact of dark matter on these mass -luminosity relationships (TF and FJ) – Calibration of these methods depends on the use of Type 1a supernovae as standard candles SummarySummary

TheThe cosmiccosmic distancedistance scalescale isis aa ladder,ladder, builtbuilt upup oneone rungrung atat aa timetime

TheThe onlyonly ““truetrue ”” distancedistance measurementmeasurement isis parallaxparallax (at(at best,best, goodgood toto aa fewfew hundredhundred parsecs)parsecs)

AllAll thethe restrest ofof thethe rungsrungs dependdepend uponupon statisticalstatistical methodsmethods oror ““standardstandard candlescandles ””

StandardStandard candlescandles areare problematicproblematic