This week at Astro 3303

Transcription

1 This week at Astro 3303 Pick up PE#9 I am handing back HW#3 Please turn in HW#4 Usual collaboration rules apply Today: Introduction to galaxy photometry Quantitative morphology Elliptical galaxies Reading: For Thursday, see the ALFALFA website See links on the schedule page. Tues Feb 28: 30-minute test; it will cover material through today Future events: Remote Observing with Arecibo Sunday March 9pm AST Launch of NuSTAR from Kwajalein Atoll (Marshall Islands)

2 30 minute test: next Tues <=10 multiple choice questions <=10 short answer questions (including definitions) Emphasis: Main concepts, simple laws/formulae; general relationships needed for interpretation of observational data. Review: text (emphasis on material covered in class; no gravitational lensing yet), homeworks, portfolio. Examples: (1) The distance modulus of a galaxy is What is its distance? A. 10 Mpc B. 1 Mpc C. 100 Mpc D. 50 Mpc (2) Define the color excess of a star.

3 HW#3: Kinematic distances If we know the galactic rotation law, then we can place limits on the distance to an object of observed V rad along a line of sight towards the inner Galaxy. The problem is that (a) we don t know the law very well (it s one of the things we want to know); (b) it only works for Pop I objects in the place; (c) there can be ambiguities. But: kinematic distances can be useful when no other means of determining the distance is available (e.g. HI clouds)

4 HW#3

5 Galactic rotation

6 Galactic rotation

7 Radial velocities

8 HW#3 Remember: what we measure is the RADIAL VELOCITY A cloud/star at 0 km/s is not moving with respect to us! Watch out: Oorts constants only apply in the Solar neighborhood where R - R ʘ << R ʘ ; see section of the textbook.

9 Morphological Classification

10 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?

11 Surface brightness I(x) = F/ 2 = L/(4 d 2 ) (d/d) 2 = L/(4 D 2 ) Units: L /pc 2 Nearby, S.B. is independent of D Often, use magnitudes to denote flux at given point in image (x) = -2.5 log 10 I (x) + const Units are [mag/arcsec 2 ]

12 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 (r) in mag arcsec -2

13 B Photometric Properties of Galaxies Surface brightness measured in mag/arcsec 2 ( I, B, R, etc.) 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 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

14 Elliptical isophotes Ellipticity = 1 (b/a) where a,b are the major,minor axes. PA = 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 PE#9: let s understand isophotes!

15 PE#9

16 The R 1/4 Law µ(r) = I e exp { [(r/r e ) 1/4 1]} Fits many Es 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

17 SDSS Sky Server

18 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

19 Quantitative Morphology Photometric surface brightness profile 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. Works for spiral disks

20 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

21 Properties of elliptical galaxies

22 Elliptical galaxies overview 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 counterrotation Cuspy and cored

23 n=1 exponential Sérsic + Exponential profiles I(R) = I(R e ) exp {-b[ (R/R e ) 1/n 1]} n=4 devauc

24 Surface brightness profiles While many Es are well fit by a R 1/4 law, not all are. Sérsic law: 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 R I n (R) dr Nuker law : include possibility of a central core 0 For r>>r b, I(r) ~ r -, matching the outer power law. For r<< r b, I(r) ~ r -, describing the central cusp. The break r b corresponds to the point at which the slope is the mean of and and the radius of min. curvature in log. coords; I(r b ) = break brightness controls the sharpness of the transition bet. cusp and outer Tremaine et al 1994, AJ 107, 634 Lauer et al. 1995, AJ 110, 2622

25 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 try axial ratio Twisted isophotes Since 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.

26 Twisted isophotes in M32

27 Fine structure in Es We will learn later that mergers, tidal encounters and other interactions are important in evolution. Probably result from accretion/merger of a small galaxy on a very elongated (radial) orbit Quinn (1984)

28 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. : triaxial = < : prolate (cigar-shaped) = > : oblate (rugby-ball) Assume Es are oblate spheroids with q = / Along the z-axis: see EO Viewed an an angles => q o = b/a How is q o related to,?

29 Flattening of ellipticals Open circles: lower L galaxies; filled circles: brighter galaxies Dashed line shows fastest rotation expected for a given flattening. Massive ellipticals are not rotationally supported Low mass ellipticals and bulges (crosses) are rotationally supported

30 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

31 Disky vs Boxy => Embedded disk

32 Anisotropy and shape Core galaxies are boxy and slow rotators Cusp (power-law) galaxies are disky and fast rotators

33 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

34 The Milky Way has a SuperMassive Black Hole (SMBH) of about 4 million solar masses at its center. M32 also has a SMBH at its center of 3 x 10 6 solar masses Joseph et al 2001 Astrophys J 500, 668 M32 and its SMBH

35 M32 and its SMBH The Supermassive Black Hole in M32 Measure the dynamical mass by measuring the motions of stars in the vicinity of the SMBH

36 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, cuspy 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 )

37 Elliptical galaxy spectra

38 Got this far