Today in Astronomy 14: te Milky Way Te sape of te Galaxy Stellar populations and motions Stars as a gas: Scale eigt, velocities and te mass per area of te disk Missing mass in te Solar neigborood Wide-angle poto and overlay key of te Sagittarius region of te Milky Way. Te very center of te Milky Way lies beind particularly eavy dust obscuration. (By Bill Keel, U. Alabama.) 19 Marc 013 Astronomy 14, Spring 013 1 Te number of stars brigter tan f 0 Suppose stars are uniformly distributed in space, wit number density n, and ave typical luminosity L. How many are brigter (tat is, ave flux greater) tan some value f 0? Presuming tat tere is no extinction: to te flux f 0 corresponds a distance r 0. f0 L 4r0 r0 L 4 f0 3/ 4 3 f 0 N f f r0n log N 0 3 3 4 n L 3 f0 3 4 f log f 0 0 19 Marc 013 Astronomy 14, Spring 013 Wat is te sape of te Milky Way? Herscel (1785), and later Kapteyn (19), used tis fact to caracterize te sape of te Milky Way. Teir idea was tat if te Milky Way as edges, tere would be points past wic N would decrease 3/ faster tan f 0. And indeed actual star counts at low fluxes are less tan predicted by tis relationsip, and te numbers at larger fluxes. log N f f0 3/ f 0 log f 0 Star counts in directions of te Milky Way disk (blue), and in te perpendicular directions (red). 19 Marc 013 Astronomy 14, Spring 013 3 (c) University of Rocester 1
Herscel s Milky Way Section of our sidereal system (Herscel 1785). Te long axis of te figure runs rougly from 0 m, +35 in Cygnus (left) to 8 0 m, -35 in Puppis (rigt); te sort axis points toward 1 4 m,+58 (Ursa Major). Sun Te Great Rift in te summer Milky Way, interpreted as a deart of stars referred to as an opening in te eavens, since e was writing in Englis tis time. 19 Marc 013 Astronomy 14, Spring 013 4 Kapteyn s universe Kapteyn (19) knew te distances to many nearby stars, and could terefore calibrate te star counts in terms of te stellar density n, and a sape of te stellar assemblage in terms of ydrostatic structure. Tis enabled im to and-wave a position for te Sun based upon te stellar density in te Solar neigborood: r = 650 parsecs, z = 38 parsecs. Sun 19 Marc 013 Astronomy 14, Spring 013 5 Sapley and Galactocentric distance Harlow Sapley tougt tat globular clusters, massive as tey are, would indicate Galactic structure better tan stars. He was also armed wit Henrietta Leavitt s discovery of te Cepeid period-luminosity relation (6 April 013), wic e applied to te RR Lyr stars. Tis led to a Solar distance from te center of te cluster distribution of 100 parsecs (Sapley 1918). Dots: cluster positions projected onto te plane of te Milky Way. Circles: radii in integer multiples of 10 kpc. From Sapley 1919. 9 Marc 011 Astronomy 14, Spring 011 6 (c) University of Rocester
Te Milky Way as an island universe All tese metods got te sape, and te Sun s distance witin from te center, quite wrong. As we ave seen, interstellar extinction is substantial in te plane of te Milky Way, and obscures most of te distant starligt. Bot Herscel and Kapteyn were terefore seeing only to te edge of te extinction, not to te edge of te stars. By Kapteyn s time many astronomers were on te rigt track by analogy: tat te Milky Way is like te spiral nebulae, and we live well off te center, as Sapley found. But not nearly as far: modern measurements of parallax of water-vapor masers in molecular clouds near te Galactic center give 8.4 kpc for our Galactocentric radius. (Reid et al. 009). 19 Marc 013 Astronomy 14, Spring 013 7 Halo, bulge and disk Te globular clusters seem to trace a sperical alo around te galaxy, in wic we are immersed ourselves. One can see non-cluster stars out tere too, if one looks ard enoug. Once we know were to look for te Galactic center, we notice a couple of oter features: te bulge, a ticker, brigter concentration of stars surrounding te center Bruno Gilli/ESO 19 Marc 013 Astronomy 14, Spring 013 8 Halo, bulge and disk and te disk, a belt of stars and extinction tat passes troug te center tis is te Milky Way proper. Since te belt seems not to ave ends, we are also immersed witin it. Distribution of stars ticker tan tat of dust everywere along te belt: tere is a tick disk and a tin disk. Muc like many oter galaxies. Bruno Gilli/ESO 19 Marc 013 Astronomy 14, Spring 013 9 (c) University of Rocester 3
Te Milky Way s central regions, in starligt (nearinfrared), from te NASA COBE DIRBE experiment. NGC 891, also in starligt (nearinfrared), from te MASS survey (U. Mass./NASA). 19 Marc 013 Astronomy 14, Spring 013 10 Scematic structure of te Milky Way Figure: Caisson and McMi illan, Astronomy Today 19 Marc 013 Astronomy 14, Spring 013 11 Halo, bulge and disk (continued) As we will be seeing tis week and next, te different components of te Galaxy owe teir distributions to differences in motion. Te disk is dominated by rotation. Objects wic belong to te disk ave randomly-directed and rotational components of motion, but te rotational components are muc larger. Te bulge and alo are dominated by random motion, wit little to no trace of rotation. Toug our immersion witin two of te components makes tings complicated, we can use te motions to weig te various components, and te Galaxy itself. 19 Marc 013 Astronomy 14, Spring 013 1 (c) University of Rocester 4
Halo, bulge and disk (continued) Te visible mass of te galactic alo is small compared to tat of te disk and bulge. As we will see, tere are strong reasons to tink tat te true mass of te alo is similar to te oters, leading to ypoteses of dark matter. Dynamics and composition of stars are correlated: Population I: small dispersion of velocities (i.e. small random velocities), absorption lines of eavy metals, confined to a very tin plane. Relatively young. Population II: large dispersion of velocities, can lie furter from te Galactic plane. Population I lies predominantly in te disk, less in te bulge, not in te alo. Population II can be found in all tree components. 19 Marc 013 Astronomy 14, Spring 013 13 Motions of stars in te Galaxy, and teir use in determining its mass distribution How muc does te Galaxy weig? Stars move about in response to te gravitational potential of te rest of te stars in te galaxy, so teir systematic motions (rotation) can be used wit Newton s Laws to measure masses witin te Galaxy. Tis works even btt better wit it interstellar tll gas tan wit stars. Stars are too massive to be influenced by te pressure of te interstellar medium, but tey collide inelastically very rarely, so teir random motions can be used wit termodynamics to measure masses witin te Galaxy - te stars in tis sense can be tougt of as particles in a gas. 19 Marc 013 Astronomy 14, Spring 013 14 Sun s neigborood Te radial structure of te disk is determined in te usual manner from centrifugal support: balancing te force on a test particle at radius r from te mass M(r) contained in interior orbits, wit centrifugal force. Just like a protoplanetary disk, or any oter astro-disk. mv r V GM rm r 19 Marc 013 Astronomy 14, Spring 013 15 (c) University of Rocester 5
Te vertical structure is determined by ydrostatic equilibrium, as usual, but tere are two main differences from protoplanetary disks: muc of a galactic disk is self gravitating: te weigt is from te disk itself, not from a star in te middle. te pressure is tat t of te stars motions. Guess: PstarsA kinetic energy 1 Pstars starsvrandom volume V ma disk 19 Marc 013 Astronomy 14, Spring 013 16 Weigt. If te disk is tin and self gravitating, we can regard it locally as an infinite plane, and work out te weigt of stars above and below te plane accordingly. m df r dr Gmrdr df r r Mass per unit disk area, not to be confused wit mean particle mass in a gas. 19 Marc 013 Astronomy 14, Spring 013 17 m df r dr rdr du F Gm Gm 3/ 0 3/ r u 1/ u 1 Gm Gm Gm 1/ 19 Marc 013 Astronomy 14, Spring 013 18 (c) University of Rocester 6
Pressure. Recall formula for pressure in terms of particle number density, speed and momentum (1 February): F 1 dp 1 na z P pz A A dt A t nvz pz vz Number of particles tat it wall Typical momentum per particle Time interval in wic tey it Consider a certain class of stars to be gas particles, and consider te component of teir motion perpendicular to te Galactic plane. Suppose te distribution of tese stars extends above and below te plane by some scale eigt H/. Consider stars lying on te ends of a cylinder of Galactic matter tat extends one scale eigt above and below te plane. 19 Marc 013 Astronomy 14, Spring 013 19 Weigt of te cylinder, approximately: da dw gzdm w gzh da da dw If stellar pressure balances gravity, ten H/ v z gg zh, or g z v z H. From above, for self gravitating disk: F Gmmgz gz G vz GH. All terms on te rigt are observable! dw 19 Marc 013 Astronomy 14, Spring 013 0 Sun s neigborood (concluded) Putting te numbers in, for te solar neigborood: 3-1.510 gm cm Star counts in te solar neigborood enable us to estimate te luminosity per unit area L (also called te surface brigtness) of te disk locally. Tis leads to te mass to ligt ratio: 1 5 ML. L Tus te solar neigborood on average emits ligt less efficiently tan te Sun does consistent wit tere being more lower-mass stars tan iger-mass stars. 19 Marc 013 Astronomy 14, Spring 013 1 (c) University of Rocester 7
Dark matter I: te Galactic disk in te solar neigborood Wen tis procedure was first applied to observations by Oort in te late 1940s, te resulting value of was greater tan tat of visible stars and interstellar gas in te Solar neigborood by a factor of about. Missing mass, or dark matter: mass tat emits no ligt but can be detected by its gravity? Since ten, Better (less biased) samples of stars ave led to smaller estimates of te total. Te discovery of neutral atomic and molecular gas in te ISM as increased te luminous mass a bit. Now te luminous and gravitating matc precisely: tis form of dark matter as vanised (e.g. Kuijken and Gilmore 1991). 19 Marc 013 Astronomy 14, Spring 013 (c) University of Rocester 8