Table of Content Wavelengths 4 Galaxy Masses Radio Infrared - PDF document

The Milky Way at Different Table of Content Wavelengths � 4 – Galaxy Masses Radio Infrared Visible Structure of our Galaxy � Rotation and Mass of the Milky Way � Mass of Spiral Galaxies � � Long-slit vs IFU Rotation curves � � HSB vs LSB Mass modeling � � Baryonic vs Dark Matter Cores vs cusps � Rotation and velocity dispersion � X-rays Gamma Rays Jeans Equation � � We now have a wealth � Binney diagram: oblate vs prolate rotators of data on our own � Non-circular velocities; asymmetric drift Galaxy, as these images Mass of Elliptical Galaxies � show. � Virial estimator Lensing studies � � It’s clear that the Milky Mass of Galaxy Clusters � Stellar Masses Way is a far more � � SEDs vs colours complex system than once thought. Lecture 4 Padova Lecture Series 2007 2 Lecture 4 Padova Lecture Series 2007 4 The Modern View of the Milky Way Scale heights and velocity dispersions � By the time of Shapley and Plaskett, astronomers had realized that our home galaxy has the following appearance (imagine that we can view it from outside!) Lecture 4 Padova Lecture Series 2007 5 Lecture 4 Padova Lecture Series 2007 6 Anatomy of the Milky Way Does the Milky Way Have Spiral Arms? � Our Galaxy is classified a spiral � Because we are in the plane of the Galaxy, we see all of the because of its prominent Galaxy’s structure projected onto a thin band across the sky luminous spiral arms. The high luminosity of the arms is due to (the Milky Way). the very bright O and B stars which are often located in open � Furthermore, dust limits our clusters and surrounded by very view at optical wavelengths luminous regions of ionized hydrogen (H II regions) � : the to only ~1 to 2 kiloparsecs. bright objects that delineate the This is a small fraction of spiral arms are called tracers . the Galaxy. NGC 1232 (D=22 Mpc) � Is there reason to believe the Galaxy may have spiral arms? M39: Open Cluster in Cygnus Lecture 4 Padova Lecture Series 2007 8 Lecture 4 Padova Lecture Series 2007 9

Three Spiral Arms Near the Sun Spiral Arms in the Galaxy M83 � If we want to map out the orbital motions of stars in the Galactic disk, � Assume a planet is we need to do three things: located here in M83, a galaxy 1. Find the OB that is similar to OB Associations the Milky Way. associations. � If we can find Perseus Arm 2. Measure their radial the bright OB velocities using spectra Sun associations , ~ 1 Kpc and the Doppler Shift. and measure their distances, we can Orion Arm map the arms. 3. Measure the distances by using their H-R diagrams. Sagittarius Arm To the Galactic Center Lecture 4 Padova Lecture Series 2007 10 Lecture 4 Padova Lecture Series 2007 11 HI Map of the Galaxy Radio Maps of Other Galaxies Show That Spiral Arms are Traced by H I � In practice, astronomers usually use radio observations of neutral hydrogen (H I ) to map out the orbital motions within the disk of the Milky Way. � Measuring the Doppler Shift of the neutral hydrogen clouds in the disk, astronomers can: 1. map out the rotation in the disk; and 2. measure the mass of the Galaxy! The Milky Way as seen Optical Image 21 cm Radio Image from above, in HI. Lecture 4 Padova Lecture Series 2007 12 Lecture 4 Padova Lecture Series 2007 13 H I in the Galaxy: Sizing out the Milky Way The maximum velocity along the line of Doppler Shift by sight occurs at the tangent point; knowing D center , we can calculate r and l. Differential Rotation Position 4 has near zero velocity wrt the sun, and is at a distance 2l from Sun l the sun. r D center 4 2 3 Velocity This method of mapping HI works, provided the H I orbits the galaxy with circular velocity. Lecture 4 Padova Lecture Series 2007 14 Lecture 4 Padova Lecture Series 2007 15

Radial Velocity � Taking material a distance R from the galactic centre, moving in a circular orbit with speed v ( R ) � Radial velocity v v ( R ) cos( 90 o ) v cos( 90 o ) = � � � � l r 0 v R ( R ) sin R sin l = � � � � r 0 0 � From the figure, we can see � Eliminate � using the sin( 180 o ) / R sin / R l � � = the distance of the subcentral 0 sine law, and simplify point to the galactic centre, sin / R sin / R l � = R min R R sin l 0 = min 0 � v max is the maximum radial � Substitute back into [ ] R 0 sin l v r = � ( R ) � � 0 velocity along a given line of previous equation and ( R sin ) ( v / R sin ) l l � = + � sight, we have the angular 0 max 0 0 factor speed � ( R min ) Lecture 4 Padova Lecture Series 2007 16 Lecture 4 Padova Lecture Series 2007 17 Transverse Velocity Rotation Curve of the Galaxy � We measure v r from Doppler shifts and the longitude l l v T R ( R ) cos R cos l = � � � 0 � � Relative velocity for any object and we determine the angular speed � 0 � From the figure we can R cos d R cos ( v r / R sin ) derive this relationship l = + � l � = + � 0 0 0 R cos R cos d l � = � 0 � Substituting back into previous equation [ ] R 0 cos l � � ( R ) d v T = � ( R ) � � 0 Lecture 4 Padova Lecture Series 2007 18 Lecture 4 Padova Lecture Series 2007 19 Rotation in the Galactic Disk Rotation in the Galactic Disk � We find that the disk rotates in two different ways, depending on the distance from the Galactic center: Rotation Speed Differential Rotation (km/s) 1. Inner Parts: Solid-Body Rotation Solid-Body speed rises with radius. Rotation � SUN orbital period is roughly constant. � 2. Outer Parts: Differential Rotation speed is about constant with radius. � Radius from the Center (kpc) orbital period increases with radius. � Lecture 4 Padova Lecture Series 2007 20 Lecture 4 Padova Lecture Series 2007 21

The Galaxy’s Rotation vs . Radius The Galaxy’s Rotation vs . Radius Rotation Curves and Dark Matter : v rot 2 = GM(R)/R M(R) = V 2 R/G The rising rotation curve beyond the luminous “edge” of the galaxy shows that the majority of the galaxy’s mass is “dark matter”. Put another way, � V 2 circ = V 2 + V 2 disk + V 2 bulge halo Mass/Light increases with distance. V circ is observed; V disk is inferred from the light profile, L(R), and assuming a constant mass-to-light ratio, M/L . V halo is then deduced by subtracting the different component velocities in quadrature. Flat rotation curves � Dark matter ! V circ = C ste implies that M(R) � R and � DM (R) � R -2 Lecture 4 Padova Lecture Series 2007 22 Lecture 4 Padova Lecture Series 2007 24 Halo Density First evidence for Dark Matter (1933) � We use the rotation curve to give 2 rv ( r ) Coma cluster : “contains 20x more mass M ( r ) the mass distribution in the halo = G than is visible in the form of galaxies” 2 dM ( r ) v � We take v ( r ) = v o as constant and 0 = differentiate with respect to r dr G GM G ( M / L ) L V tot = = R R Zwicky at Palomar 2 � We relate M ( r ) to the density dM / dr 4 r ( r ) = � � distribution � ( r ) 1 dM ( r ) � � � � ( r ) � = � � � � 2 4 r dr � � � � � v 2 � Substitute back into the previous ( r ) 0 � = equation 2 4 Gr � Isothermal profile Lecture 4 Padova Lecture Series 2007 25 Lecture 4 Padova Lecture Series 2007 26 The History of Dark Virial theorem Matter � In internal motions, the virial mass is 2 Fritz Zwicky (1898-1974) 5 v R � Pioneer of modern jet engine M = � Predicted neutron stars (1934) 3 G and origin of cosmic rays � Discovered 120 supernovae � In Doppler shifts, the virial mass is � Mapped out clusters of galaxies; - First evidence of dark matter 2 5 v R in galaxies (1933) r - Proposed gravitational lensing M = from clusters (1937) G Lecture 4 Padova Lecture Series 2007 27 Lecture 4 Padova Lecture Series 2007 28