Lecture 6: distribution of stars in. elliptical galaxies

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1 Lecture 6: distribution of stars in topics: elliptical galaxies examples of elliptical galaxies different classes of ellipticals equation for distribution of light actual distributions and more complex shapes later lecture: dynamics of elliptical galaxies that produce the stellar distribution Galaxies AS

2 M32 local ellipticals E2 at 750 kpc, satellite of M31 spiral NGC 205, 147, 185 de s at kpc Sagittarius, Sculptor, Fornax etc. dsph at 25 kpc these are part of the Local Group of galaxies Milky Way is a major member of this Galaxies AS

3 NGC 185 Phoenix dwarf And VI dwarf images from seds.org Galaxies AS

4 Galaxies AS image from anzwers.org

5 local dwarfs and spheroidals none of the ellipticals in the Local Group is very impressive dwarf spheroidals were discovered between 1938 and ~1998 faint excess of stars in one region of sky hardest to spot behind Galactic Plane (e.g. Sgr dsph) these are old galaxies low metallicity, [Fe/H] of -1.3 or less some have RR Lyrae stars that take 8 Gyr to evolve large M/L ratios, ~ 5-75 stars are small addition to the dark matter! Galaxies AS

6 star formation history stars are very distributed in a colourmagnitude diagram plotting isochrones for main sequence stars demonstrates a large range of ages e.g Gyr in Leo I cf. a globular cluster has ~one birth age Caputo et al. (1999) N. Drakos Galaxies AS

7 ellipticals in clusters more massive ellipticals are found in other galaxy clusters, beyond the Local Group. a typical cluster might have: > 50 galaxies cluster-core radius ~ 300 kpc but median radius ~ 3 Mpc Local Group has ~1/10 th the galaxy density of a rich cluster mass-to-light ratio ~ 200 cluster-core regions are elliptical rich: proportions 10 / 40 / 50 in spirals / ellipticals / lenticulars but in outer regions of a cluster, 80 / 10 / 10 in spirals / ellipticals /lenticulars Galaxies AS

8 luminosity classes ellipticals have a very wide range of luminosities, and for convenience are divided into luminosity sub-classes: dwarf: L < 3 x 10 9 L solar locally, from M32: 3 x 10 8 L solar down to Draco dsph: 2 x 10 5 L solar! de are diffuse, with dsph having even lower surface brightness and luminosity (only detectable nearby) midsized : L 3 x 10 9 L solar,, or M B -18 luminous: L ~ 2 x L solar or M B ~ -20 supergiant or cd: a few times more luminous still D refers to the diffuse outer envelope can be nearly 1 Mpc across! Galaxies AS

9 possibly cd s form by swallowing up other galaxies in a cluster: A1060 galaxy cluster A3827 (M. West) false colour brings out galaxy nuclei Galaxies AS

10 ε describing the structure although featureless we need ways to describe the structure of elliptical galaxies light is concentrated towards the centre most luminous (e.g. cd s) have an extended outer halo overall shape is defined by the ellipticity parameter = 1 b/a this is basically the ellipticity sub-class En where n = 10 (1 b/a) more complex examples have three symmetry axes. and/or change of shape with radius Galaxies AS

11 Σ characterising properties for typical mid-sized and luminous ellipticals, a greater luminosity is closely related to a lower surface brightness (and to a larger core region) B per arcsec E globulars S de M B Galaxies AS

12 Σ Σ Σ Σ Σ surface brightness equation we already defined surface brightness, as flux density per unit solid angle. or in magnitudes per arcsec 2 : = -2.5 log 10 + constant NB more luminous ellipticals have lower a larger number (fainter) and so describe the surface brightness by an empirical formula, (NB sometimes see I instead of ) (R) = (R e ) exp { -b [ (R/R e ) 1/n -1 ] } b is just a constant chosen so that half the light of the galaxy comes from within the effective radius R e n is the exponent describing how the light decreases with radius is Galaxies AS

13 Σ elliptical light profiles the exponent ¼ fits the rise in central light (the galaxy core) as well as the slow outer decline cd s have a diffuse outer halo which adds extra light (R) n=4 n=1 E cd R (arcsec) Galaxies AS

14 defining the edge of a galaxy we use R e because it s hard to define the true outer edge of a galaxy (the last star ) outer regions may be well below the night sky brightness!... only the isophote shows there are stars there some catalogues use e.g. D 25, where is magnitude 25 per arcsec 2 but this is really just a telescope limit de Vaucouleurs proposed an R 1/4 law fitting elliptical light profiles in this is the basis of the exponent law the half-light enclose radius idea is more useful, if all ellipticals have about this same light profile we always comparing a region with half the galaxy s stars Galaxies AS

15 Σ actual light profiles NB, (R) actually comes from an azimuthal average, i.e of the light between isophotes of the same shape as the galaxy NB we do not always see the steep rise in the core if a galaxy has a small core, the atmospheric seeing may blur it out to an apparent size equal to the seeing (e.g. 1 arcsec) hence smaller galaxies such as de may seem to have smaller n exponents azimuthal angle φ Galaxies AS

16 Σ πσφ πσ from surface brightness to luminosity luminosity is the surface brightness integrated over radius and azimuthal angle to start we have to go back a bit and define a simpler expression for the surface brightness (R) = 0 exp [ -(R/R s )1/n ] where R S is a scale length similar to that defined before for stars in spirals then integrate to get the luminosity L = 0 2 (R) R d dr, i.e. L = R exp [ -(R/R s ) 1/n ] dr Galaxies AS

17 πσ Γ πσγ πσ πσ to make this workable, substitute x = (R/R s ) 1/n i.e. R = R S x n, from which dr = n R S x (n-1) dx so now we have L = 2 0 R S 2 n 0 x (2n-1) e -x dx which can be looked up in tables of integrals the Gamma (or factorial) function is (z) = 0 t (z-1) e -t dt = (z-1)! (for integers) so using this, L = 2 0 R S 2 n (2n) or L = 0 R S 2 2n (2n-1)! but 2n (2n-1)! = 2n!, so we finally get: L = (2n)! 0 R S 2 Galaxies AS

18 πσ Σ πσ Σ however, the scale height turns out to be rather small for ellipticals because n is large this is why the half-light radius is used instead we equate: 2 0 Re 2 R (R) dr = 0 2 from which it turns out that (R) = R (R) dr (R e ) exp { -b [ (R/R e ) 1/n -1 ] } where b = 7.67 for n = 4, for ellipticals integrating to get the luminosity, as before L = [ 8! exp(7.67) / ] { R e 2 and the central surface brightness is (R e ) } 0 ~ 2000 e Galaxies AS

19 true shapes the value of b/a for a galaxy depends somewhat on what direction we see it from consider an oblate spheroid (a sphere flattened down one axis) looks round if we look down this axis looks as flat as it is if we look perpendicular to this can show that q obs2 = (b/a) 2 = (B/A) 2 sin 2 i + cos 2 i where B and A are the real axis sizes and i is the inclination of the axis to our line of sight note that it can t look flatter than it really is elliptical galaxy courtesy of cherryblossomgardens.com Galaxies AS

20 we could calculate the fraction we expect to see with any value of q, assuming only that i is random (galaxies don t know about us ) for mid-sized ellipticals q is ~ 0.75 and we deduce that the B/A range is commonly 0.55 to 0.7 (not very flat) smaller ellipticals appear more elongated but with a lot of variation so shape and dynamics not strongly related to size? luminous ellipticals have q ~ 0.85 but very few look actually circular which is unexpected break-down of simple model: these may have three symmetry axes Galaxies AS

21 isophote shapes triaxiality reflects complicated orbits of stars in ellipticals axis ratio of galaxy may be changing with radius, and this also affects the orientations of the isophotes we see long axis seems to twist Galaxies AS

22 disky, boxy, indecribable some ellipticals contain non-elliptical isophotes disky ones suggest some orbits in a disk plane boxy ones suggest some orbits that pass through the galaxy centre dynamics; next lecture lastly, NB, encounters between galaxies can distort their shapes Naab et al J. Dunlop Galaxies AS

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