ASTR 1120: Spring 2006Measuring the mass of galaxiesMeasuring the mass of galaxiesLuminous matter in a galaxy:• stars (of different masses)• gas (mostly hydrogen)Can detect these directly using optical and radio telescopes - get an estimateof how much mass they containBUT… also non-luminous matter which we can’tsee directly. Example that we know exists - black holes that formed from stellar collapse.ASTR 1120: Spring 2006How can we measure mass we canHow can we measure mass we can’’t see?t see?If we know the mass M of a body, can work outhow fast we need to go to orbit at distance r:velocity vradiusof orbit rFor a circular orbit:† v2=GMr…where G is called thegravitational constant.Numerically:† G = 6.67 ¥10-11 m3/(kg ¥ s2)Recall: used this formula (lecture #13) to findmass of black hole at Galactic CenterASTR 1120: Spring 2006Measuring the mass of the Milky WayMeasuring the mass of the Milky WayMeasure the velocity v of a star orbiting on a circular orbit at distance r from the center of the Milky Way. Same formula:† M =rv2G…gives the mass M interiorinterior to the orbit of the starWhy only the interior mass? Gravitational forcesfrom mass outside cancel out (exactly if the massdistribution is spherically symmetric).ASTR 1120: Spring 2006e.g. the Sun orbits aroundthe Galactic center at:r = 2.6 x 1020 mv = 220 km / sMass inside the orbit of the Sun is:† M =2.6 ¥1020 m ¥ 2.2 ¥105 m/s( )26.67 ¥10-11 m3/ kg s2( )= 2 ¥1041 kg…which is about 100 billion Solar masses. Thisnumber is not unreasonable given the masses ofknown stars and gas in the inner regions of theMilky Way.Rotation curve for gravity• Example: SolarSystem• Almost ALL the massis in the center (Sun)• Gravity is weakerfarther out• Rotation curve fallsASTR 1120: Spring 2006A flat rotation curveA flat rotation curveSuppose we measure the velocities of stars at different radii from the center of the GalaxyEach star allows us to calculate the mass interiorto the orbit of that particularstarIf we observe many stars (orgas clouds), can map out therotation curverotation curve of the galaxyMeasures the massMeasures the massdistribution of thedistribution of theMilky WayMilky WayASTR 1120: Spring 2006What do we expect?What do we expect?distance from center rvelocity vInner galaxyInner galaxy: enclosed massrises, so does the velocityBeyond the optical edge ofBeyond the optical edge ofthe galaxythe galaxy: no stars, so no more mass, velocity fallsExpected rotation curveof a galaxy if all the massis due to observed starsand gasASTR 1120: Spring 2006Rotation curve of the Milky WayRotation curve of the Milky Wayvelocity ofstars and gasin orbit aroundthe centerof the MilkyWaydistance from the centerInstead, observe a Instead, observe a flat rotation curveflat rotation curve - - velocity stays the velocity stays the same as we move same as we move furtherfurther away from the center! away from the center!ASTR 1120: Spring 2006What does a flat rotation curve imply? Go backto the formula:† M =rv2GIf the velocity is constant with increasing radius,then the mass is proportional to radius:massinsideradius rradius rMore and more massas we go to larger and larger distancesfrom the centerASTR 1120: Spring 2006Dark matterDark matterFlat rotation curve showsthere is more matter outbeyond the apparent edgeof spiral galaxiesFor the Milky Way, the total mass exceeds thevisible mass (stars + gas) by about a factor of 10`Extra’ mass is called DARK MATTERDARK MATTER:• infer existence from gravitational effect onordinary stars and gas• cannot be luminous or we would see itASTR 1120: Spring 2006Rotation curves of other spiral galaxiesRotation curves of other spiral galaxiesCan also measure the rotation curve of otherspiral galaxiesUse the Doppler shift of spectral lines emitted by hydrogen gas to infer velocity of rotation - same idea as for measuring redshiftsASTR 1120: Spring 2006ASTR 1120: Spring 2006Dark matter ismore extendedthan the luminousmatterPicture of the Galaxy - verylarge massive halohalo of dark matterRelatively insignificantsprinkling of ordinary stars and gas in the middleASTR 1120: Spring 2006Does dark matter really exist?Does dark matter really exist?Flat rotation curves could be explained by:• existence of dark matter• perhaps gravity does not behave in thesame way as in the Solar System onvery large scales?Many independent ways to test how gravity behaves… so most astronomers confident darkmatter exists even though we don’t see itdirectlyASTR 1120: Spring 2006Nature of dark matter is one of the most importantmysteries in astronomy. Many candidates:1)1)Very low mass starsVery low mass starsVery low mass starsor brown dwarfs emitvery little light for theirmassPopulation of stars thatonly contained low massstars would be hard toseeDim, red stars and browndwarfs (failed stars)ASTR 1120: Spring 20062) Very cold clouds of hydrogen gas2) Very cold clouds of hydrogen gasCold clouds (~10K) of hydrogen molecules emitvery little radiation - would be hard to detect unless they formed stars3) White dwarfs or neutron stars3) White dwarfs or neutron starsPerhaps the first stars in the Galaxy were allmassive - they died long ago leaving only stellarremnants which are now cool and hard to see?All examples of BARYONIC DARK MATTER:All examples of BARYONIC DARK MATTER:dark matter made of the same stuff (neutronsdark matter made of the same stuff (neutronsand protons) as ordinary gas and starsand protons) as ordinary gas and starsASTR 1120: Spring 2006There are also more exotic possibilities:4) Black holes4) Black holes - either formed from the collapseof very massive stars, or primordial (formed in the early Universe)5) Unknown elementary particles5) Unknown elementary particles - stable particleswhich have not yet been discovered in lab experiments on Earth (e.g. because they are too massive)Called NON-BARYONIC DARK MATTERCalled NON-BARYONIC DARK MATTERMost astronomers reckon unknown particlesmake up most of the dark matterASTR 1120: Spring 2006Dark matter on Earth?Dark matter on Earth?In the Solar System, the density of ordinary matter vastly exceeds that of dark matter.BUT, dark matter particles should be present, passfreely through the Earth, Sun, us…Very rarely, thedark matter mightcollide with ordinarynuclei - this might be detectableASTR 1120: Spring 2006Dark matter on Earth?Dark matter on Earth?Not seen, yetNumerous experiments in deep mines underway,Numerous experiments in deep