This week at Astro 3303 Lecture 06, Sep 13, 2017 Pick up PE#6 Please turn in HW#2 HW#3 is posted Today: Introduction to galaxy photometry Quantitative morphology Elliptical galaxies Reading: Continue reading Chapter 3, in particular 3.3-3.7 Wed Sep 27: 30-minute test
The Hubble Tuning Fork Diagram Image from Galaxy Zoo Why do galaxies look the way they do?
Quantitative morphology Levels of symmetry: 1. spherical: glob. clusters, E0 galaxies (some round by projection) 2. axial: natural result of rotation => disk - basic shape for most galaxies 3. triaxial: (less recognized); results in strongly anisotropic velocity distributions. Fundamental planes of galaxy properties (are there more?) 1. Form: morphology, color, star formation rate, specific angular momentum 2. Scale: luminosity, linear size, mass Question: Is the shape of a galaxy, in the absence of active perturbations, dominated by: 1. present equilibrium conditions? 2. initial (or early) conditions?
Surface brightness I(x) = F/a 2 = L/(4pd 2 )*(d/d) 2 = L/(4pD 2 ) Units: L /pc 2 Nearby, surface brightness is independent of distance d! Often, use magnitudes to denote flux at given point in image µ l (x) = -2.5 log 10 I l (x) + const l Units are [mag/arcsec2 ]
Galaxy photometry Fitting isophotes: in practice Fix center Allow smooth variation in position angle (of major axis), ellipticity Where does the image above come from? Surface brightness profile => I(r) in L pc -2 µ(r) in mag arcsec -2
SDSS Sky Server
Photometric Properties of Galaxies Surface brightness µ(r) measured in mag/arcsec 2 (µ I, µ B, µ R, etc. in I,B,R band) is independent of distance since light falls as 1/d 2, but the area subtended by 1 sq arcsec increases as 1/d 2. however, cosmological dimming of 1/(1+z) 4 causes higher z galaxies to have lower surface brightnesses 15 20 µ B 25 30 Night sky at 22.7 radius Much of the galaxy structure is fainter than the sky which must be accurately subtracted. SB profiles are produced by azimuthally averaging around the galaxy along isophotes of constant brightness. Must understand viewing geometry. Seeing effects on SB profiles - unresolved points spread out due to effects of our atmosphere, etc. makes central part of profile flatter makes isophote rounder
Elliptical isophotes Ellipticity e = 1 (b/a) where a,b are the major,minor axes. PA q = position angle = angle (measured from north towards east) of the major axis Surface brightness = µ(r) = azimuthally averaged brightness in mag/arcsec 2 along the major axis
Quantitative Morphology Sérsic profile: I(r) = I(0) exp (-k r 1/n ) = I e exp { -b n [(r/r e ) 1/n 1]} where b n must be determined numerically from the condition r e 0 r I n (r) dr = ½ 0 r I n (r) dr de Vaucouleurs profile : I(r)= I(r e ) exp[-(r/r e ) ¼ ] where r e is the effective radius and L(<r e )=½ L total Works for ellipticals and for bulges exponential profile : I(r)= I(0) exp[-r/r d ] where r d is the exponential scale length or disk scale length Spiral: I(r) = I bulge (r) + I disk (r) [+ I bar (r)] Works for spiral disks
The R 1/4 Law µ(r) = I e exp { -7.67 [(R/R e ) 1/4 1]} Fits many E s Van Albada (1992) showed that dissipationless collapse (gravitating particles without losing energy by heating or turbulence) can lead to the R 1/4 shape. R e = effective radius = radius encompassing half the light I e = I(R e ) Note that the SB falls > 10 magnitudes from center to outskirts
Elliptical galaxies display a variety of sizes and masses Giant elliptical galaxies can be 20 times larger than the Milky Way Dwarf elliptical galaxies are extremely common and can contain as few as a million stars
Properties of elliptical galaxies S0-type E s central cluster E s normal E s dwarf E s dwarf spheroidals blue compact dwarfs sizes up to ~1Mpc! faint, studies typ. restricted to local group abs.mag mass size mass-to-light ratio excess in cds -> environment Most E s: Read and dead (except BCDs)
APOD credit J. Bers Dwarf elliptical galaxies Credit A. Block/NOAO High surface brightness APOD credit J. Schedler Sculptor dsph Credit: ROE/AAO Low surface brightness
let s understand isophotes! PE#6
let s understand isophotes! PE#6
Elliptical Galaxies Morphology-density relation => found in regions of high galaxy density M87 jet Often show hints of interactions/merger Offset M87 field: Point sources are globular clusters CenA
Ellipticals are not so simple ATLAS3D/P-A. Duc
Elliptical galaxies not all that simple Elliptical galaxies constitute the brightest and faintest galaxies known This statement lumps the des and dsphs; tbd later. Apparent simple structure roundish appearance Light is smoothly distributed Lack star formation patches Lack strong internal obscuration by dust. Many fit by R 1/4 law: I(R) = I e exp{-7.67[(r/r e ) 1/4-1]} where L(R<R e )=½L tot and I e = I(R e ) Actual complexity Shapes (from oblate to triaxial) Large range of L and light concentration Fast and slow rotation; even counter-rotation Cuspy and cored
Photometry and the structure of galaxies What can we infer about the 3-D luminosity density j(r) in a transparent galaxy from its projected surface-brightness distribution µ(r) If µ(r) is circularly symmetric, j(r) may be spherically symmetric: µ(r)
Shapes of E gals What can we learn from the distribution of observed apparent ellipticities about the true (intrinsic) distribution of axial ratios? The contours of constant density are ellipsoids of m 2 = const. a ¹ g ¹ b : triaxial a = g < b: prolate (cigar-shaped) a = g > b: oblate (rugby-ball) Assume E s are oblate spheroids with q = b/a Along the z-axis: see E0 Viewed at angles => q o = b/a How is q o related to a, b? on average, ellipticals are observed to be modestly triaxial ~ 1:0.95:0.7
Isophotes Isophote: contour of equal apparent, projected surface brightness In general: not perfect ellipses If intrinsic shape of a galaxy is triaxial, the orientation of the projected ellipses depends on 1. The inclination of the body 2. The body s tri axial ratio Twisted isophotes Since e changes with r, even if the major axes of all ellipses have the same orientation, they appear as if rotated in the projected image. It is not possible to tell whether a set of twisted isophotes arises from a real twist or triaxiality.
Twisted isophotes in M32
Fine structure in E s We will learn later that mergers, tidal encounters and other interactions are important in galaxy evolution. Probably result from accretion/merger of a small galaxy on a very elongated (radial) orbit Quinn (1984)
Exceptions: cd galaxies cd galaxies - extended power-law envelopes seen predominantly in dominant cluster galaxies cd = cluster diffuse Found in regions of local high galaxy number density, often at center of potential (low relative velocity) - clusters, compact groups SB excess at large R caused by remnants of captured galaxies? OR Envelope belongs to the cluster of galaxies (not just central galaxy) -- ellipticity of envelope follows curves of constant # density of gals Multiple nuclei common galactic cannibalism? dynamical friction? later
Ellipticity and flattening Ellipticity 1 - / => Classication En where n = 10(1-b/a) If the galaxy is an ideal, oblate rotator with an isotropic stellar velocity dispersion, then we can show that: Hence, if the observed ellipticity of 0.4 is due purely to rotation, then V rot / should be 0.8 We define the rotation parameter (V/ ) as (V/ ) (V rot / ) observed (V rot / ) isotopic Although it is somewhat arbitrary, a galaxy is considered to be primarily rotationally supported if (V/ ) > 0.7.
Rotation vs. flattening of ellipticals i.e., why are E s not round? Open circles: lower L galaxies; filled circles: brighter galaxies rotation: (v rot /s v ) iso ~ (e/1-e) 1/2 Dashed line shows fastest rotation expected for a given flattening. but find: v rot << s v faint bright Massive ellipticals are not rotationally supported Low mass ellipticals and bulges (crosses) are rotationally supported Þ Massive E s are self-gravitating equilibrium systems of random orbits around grav. potential
Deviations from ellipses Often, isophotes are not perfect ellipses disky : excess of light on the major axis boxy : excess of light on the minor axis Bender et al., 1988, A&AS, 74, 385 Disky isophotes can be explained by a superposition of an elliptical bulge and a faint edge-on disk. Isophotal analysis is perhaps the only way to detect weak disks in Ells. It is likely that disky Ells are an intermediate class between boxy Ell s and S0 s
Disky vs Boxy => Embedded disk
Power-law Cusp vs Flat Cores The central regions of elliptical galaxies include two types of profiles: flat and power-law centers. Characterize the profile by its central slope and break radius r b : Flat core flattening of profile towards center Power-law cusp: increases to high value at center Common usage today defines a flat core galaxy as one with a flat inner profile, such than < 0.3 and a power-law galaxy has > 0.5 From R. Bender
Boxy vs disky; core vs cusp Faint ellipticals (and bulges) are rotationally flattened; bright ellipticals are often anisotropic Strong correlation between rotational properties and the shape of the isophotes and core properties: - Boxy isophotes, flat (core) centers: anisotropic, peculiar velocity fields (high L) - Disky isophotes, powerlaw (steep/cusp) centers: usually rotationally flattened (low L)
Elliptical galaxies: Summary Faint ellipticals (and bulges) are rotationally flattened; bright ellipticals are often anisotropic Strong correlation between rotational properties and the shape of the isophotes and core properties: - Boxy isophotes, core centers: anisotropic, peculiar velocity fields (high L) - Disky isophotes, power-law centers: usually rotationally flattened (low L) Counter-rotating nuclei show that ellipticals cannot be formed by simple collapse of uniformly rotating gas spheres => formed via merger processes (more later on this ) High rotation velocities and velocity dispersions in core regions => SMBH (more later on this )
Core galaxies are boxy and slow rotators Cusp (power-law) galaxies are disky and fast rotators Revised tuning fork Kormendy & Bender 1996, ApJL 464, L119