Extra Gal 9: Photometry & Dynamics

Transcription

1 Extra Gal 9: Photometry & Dynamics Two books, among many others, that can be used by the studenys for extensive references and details are: Binney and Merrifield: Galactic Astronomy Binney and Tremaine : Galactic Dynamics Here we begin discussing very simple matters and computations since I often find out students do not know how to carry out simple computations. 1

2 Preliminaries Assume a distribution of stars with a mean density equal to the mean density of the Milky Way. Is the luminosity of the stars occulted by other stars so that I may have to take that into account? The student answer by doing a computation and estimate the length of the path needed to have a star occulted by an other star. Now let s make a rather simple exercise: We relate the luminosity of a surface S to the absolute magnitude to the Surface brightness observed in magnitudes. L = Luminosity Solar Units S = Area Ω = Solid Angle [1 arcsec ] I = Intensity µ = SB in mag arcsec - I 0 = Intensity in the Central region of our Galaxy DM = Distance Modulus = m-m π = = = L I S I d Ω I d L= I d M =.5 Log L+ M 11 = M.5 Log LogI 5Logd + M m µ = M + DM = ( 1arcsec ) V 0,V = LogI + M 5 = LogI + M ; M = 4.87,V for I = 150 L / pc µ = 1.0 mag arc sec

3 Complications by Dust ed DUST Blue White Observer Observer Observer 3

4 And the Abel Integral I() Circular Symmetry J(r) Circular Symmetry Hypothesis z r ( ) ( ) I = dz j r = ( ) j r 1 di d = π r d r ( ) j r r dr r r z Column Density 4

5 The Night Sky µ U =.0 Sun 5.61 µ B = µ V = µ = µ I = That is the Sky should be subtracted and may have an important effect especially on the faint outskirt of galaxies. How faint can we observe the Surface Brightness profile of external galaxies? The effect of seeing is also important since the change in resolution may bias the profile (especially in the central regions) and the color if images are obtained in different seeing conditions. The student should look into the concept of convolution and eventually discuss how to account for the seeing. The student could, as a report at the end of the course, try to explain the luminosity of the sky and its color. For elliptical galaxies the most common fitting is the De Vaucouleurs profile. See however more general fittings of which the GV profile is a particular case and the King s approximation. From the observations (see next Image) we derive : B µ 4 B 0.4 y I and GV wrote ( ) e 1 4 µ = x y which means e I = I 10 = 1 4 IeExp e 5

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7 Effective adius and I e If we assume the distribution of light is approximated by regular ellipses of different SB and summed up, then we can define the effective radius e = (a * b) 1/ where a and b are the semi_major and semi_minor axes. The value 3.33 is chosen so that ½ of the total light of the Galaxy is within e. I e is the Surface Brightness at = e. The Central Brightness I 0 = I e ~ 000 I e. Observations show that the profile of the elliptical galaxies is fairly constant for all galaxies. However differences that may be significant and often dependent on the environment exist. A very significant case is that of the cd galaxies. For the Integral below, the student try to solve it, see dissertation by Manoussoyanaki. e π r d I = π r d I = 7.π I 0 0 ( ) ( ) e e 7

8 Disk Galaxies The disk galaxies show a composite profile which is the sum of a GV profile due to the central bulge (spheroids) and to the disk. The distribution of light in the disk follows the exponential law as: I() = I d e -/d. The following relations therefore apply: d ( ) = I e d Lum = d I e = I 1 1+ e 0 π I d d d Tot π 0 d π d d d L = d I e = I Bu lg e : LB = 7. π I d π Tot e e d d d Σd 0.8 e e e Σe D π I = = B 7.π I B I = Total I 0.8I e e e e + d d d 8

9 9 Table Sc 598_M Sb 4_M S S S S S S D/B Be/SD e/kpc Bd/SB d/kpc MB Type NGC

10 Example NGC 470 D 3.1 = B ( ) 10

11 Profiles {Sandage s argument} 11

12 Statistical Distribution of q=b/a - TBD 1

13 otation - Observations Pos Neg Km/s Line of sight Folding adio & 1 cm 13

14 otation Curves & Folding 14

15 Back to Dynamics GM 4 G Central Force r po int mass r φ = π ρ φ = Vc dφ GM ω r = = Vc = r dr r ( ) ( ) Disk Vc( ) = π G h σ0 I0 K0 I1 K1 h h h h h Scale length 1 σ = σ 0 e -/h Surface Density Bulge Halo Disk 15

16 In a more general way TBC & ef. The distribution of mass could be suggested by the distribution of light under the assumption (we know it is wrong at least in the Halo because of the need of Dark Matter) that the distribution of matter is proportional to the distribution of light. That is σ(r) = µ(r) M/L. Bu lg e & Ellipsoids = ρ0 + c Add in quadrature π G 4G Vc ( ) = r ( r) dr arcsin r ( r) dr σ + σ 0 r r c Vc ( ) = 4πGρ0c 1 ( ) ρ a a da Vc ( ) = 4π G 1 e 0 a e Halo Isothermal King' s approximation ρ( ) 1 1 ArcTan Flat with asymptotic value 4πGρ c 0 c 16

17 How to compute it 17