# Scale height and Luminosity

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1 The Milky Way I suggest to consult the excellent lectures held at Saas-Fee by Gilmore, King and van der Kruit in the Book The Milky Way as a Galaxy edited by Buser & King and published by the University Science Books. Indeed these lectures on the Milky Way are simply introductory and for a deepest understanding I suggest reading the book that is indeed a good book to keep in your own libray. I use these lectures as an introduction to the dynamics of galaxies, a subject a will deal with next. 1

2 Scale height and Luminosity By counting stars as a function of the distance from the Sun I can measure various quantities, some of these are: D(r) The density of stars of any spectral type. D S (r) The density of stars for a given spectral type. The above are generally defined respect the density of stars near the sun. We can also define a scale height counting stars perpendicular to the galactic plane. Obviously the density distribution perpendicular to the galactic plane will also depend from the the distance on the plane from the galactic center. For a model see for instance Kent, Dame and Fazio The scale height, α S is defined for the spectral type S by the following equation: D S (z)=d S (0) e -( z /α S ) Keeping in mind that about the plane the plane the cusp must be modified by a Gaussian. The step is accounted for by the life time of main sequence stars, the age Of the disk etc. 2

3 Scale Height of the Disk Scale Height for various objects Cp = Classical Cepheids O_Cl= Open Clustres PN = Planetary nebulae Nae = Novae Scale Heigt (pc) O Cp B O_Cl D_G A F PN gk Nae dg dk dm gg Object 3

4 Scale Height above the disk Old Galactic Objects 3500 WD = White Dwarfs V5_8 = Long Period Variables M5 M8 V0_4 = Long Period Variables M0 M4 RRL< = RRLyrae P<0.5 days RRL> = RRLyrae P<0.5 days WV = W Virginis Variable SD = Subdwarfs GCl = Globular Clusters Scale Heught (pc) dk dm gg WD V5_8 RRL< V0_4 RRL> WV SD GCl Object 4

5 The z density distribution of K-dwarfs 5

6 The Nuclear Region The radial velocities are from Genzel and Townes Note that the region shown here is of about 4.8 pc. It seems we are looking at a spiral arm structure. Obviously the peculiar structure we see must also be inclined to the plane otherwise we would not be able to see the pseudo arms. Compare next with the velocity curve and with the HI map. It seems clear we are witnessing organized motion. 6

7 The HI distribution At the center a schematic representation of the expanding 3 kpc arm (Rougoor and Oort). That is almost 1000 larger than the size of the previous structure. 7

8 Mean velocities of stars near the Galactic Center Referred to the position of IR16 8

9 Velocity Dispersion The student estimate the Mass as a function of the distance from the center. We will do it also later on in the course when we study the dynamics of Galaxies. Look also at the rotational velocity. Black Hole or Stellar Cluster? 9

10 Velocity of OH/IR stars Galactic Longitude 10

11 Molecules, Radio continuum and much more The center of our galaxy is very much revealing about the activity observed in other pseudo normal galaxies and in active galaxies. As we know the Center is very much obscured by dust, Indeed a concentration of stars at the very center can be observed only if we use the K band at 2.2 microns. We have in the innermost 2 pc region the emission of ionized gas and molecules. But we also receive Gamma rays from sources emitting at.511 MeV - positorn electron annihilation and Gamma ray continuum. But we also receive in line radiation, 1.8 MeV, due to the decay of Al 26 (lifetime about 10 6 years). The nuclear region is rich of on going phenomena and may make us understand details on the physics of external galaxies. 11

12 And now? The frame covers about 50 x 50 parsecs and South is to the right. These radio emission carried out at 20 cm maps a very particular structure since the emission come from parallel wisps and bend of about 90 degrees. In addition it has been observed the presence of strong polarization. Quite likely the structure observed is due to a strong magnetic field of about 10-2 Gauss (the mean field of a Galaxy is generally 10-5 Gauss). 12

13 The spiral arms Open Clusters Young Clusters and Stellar Associations 13

14 Now let s see further away from the Center We use of the Globular Clusters as a probe of the old population distribution. In the Figure I show the H R plot of a Globular Cluster. HB = Horizontal Branch AGB = Asymptotic Giant Branch RGB = Red Giant branch SGB = Sub Giant branch MS = Main Sequence TO = Turn Off Point BS = Blue Strugglers 14

15 A Younger Cluster M92 Globular clusters are fundamental in the determination of the Age of the Universe being among the oldest objects we know. Thanks to the theoretical knowledge we have on the stellar evolution we can estimate the age of these objects quite accurately. In this Clusters we have a very well defined main sequence turning off at a magnitude of about V=18.5. Here we begin to burn hydrogen in a thick shell which will narrow in the course of its evolution. More massive stars are already forming the gian sequence. 15

16 Turnoffs and Main Sequence for GCl. 16

17 Stella evolution tracks allow the estimate of the age of Globular clusters. Uncertainties are however present both because we do not know accurately the metal abundances and because we have observational uncertainties on the distance, photometry and other parameters. The reference age is in the range of Gyr with an uncertainty of 2 3 Gyr. From theoretical studies and evolutionary tracks we can derive an equation relating the Luminosity of the turn off point to the age of the cluster. This is equation (1). The time spent on the main sequence, the core hydrogen burning phase, depends on the the amount of hydrogen available for burning and on the Luminosity of the star. Assuming that the fraction of stellar mass which takes part to the hydrogen burning (very dubious assumption see also Christensen - Dalsgaard) and the efficiency by which H is transformed into He is not a function of the stellar mass we derive for the duration of the Main sequence phase equation (2). The age TO 2 ( 1) log ( log Z ) log Z Y log ( t ) ( ) MS L L ( ν ) ( ) log Z 0.272log Z 1.073Y 1 7 MS ( ) 2 t M 3 ν 5 M = 15M t 10 TBC 9 17

18 Distribution and Abundance Given the distribution of Globular Clusters it is fairly easy to estimate the centroid of the distribution and assume that coincide with the Center of the Galaxy. By definition then we have the distance of the Sun from the Center of the Galaxy. The observations could be RA and D with the determination of the distance via the RR Lyrae stars (or better Main Sequence fitting), estimate of the interstellar absorption and transformation of coordinates in order to have (x,y,z) with the x axis pointing to the Galactic Center and the y in the direction rotation (l = 90, b = 0). The North Galactic pole is the direction of z (b = 90). The values <x> <y> <z> give the distance from the Galactic Plane and from the Sun (a lower limit since, due to obscuration, we can not observe very many distant clusters. From the List of Clusters give in Cox Astrophysical Quantities the students estimate these parameters. z l b x y 18

19 Z Globular Clusters respect to the Sun Y X

20 Plane Y_Z Globular Clusters Z Y 20

21 GCl Plane X_Z Z 0-20 Distance of the Solar System From the Center of the Galaxy ~ 8.8 kpc X 21

22 Distribution of Clusters Globular Clusters are the brightest objects located in the halo of a galaxy. They seem to cover a region of about kpc delimiting in this way the Halo of the Galaxy ( see Zinn, 1985, Ap.J. 293, 424). Those clusters that are more thn 40 kpc above the galactic plane may not belong to the Galaxy. Many are located near the galactic plane and the metal abundance, [Fe/H], is much smaller than solar. A fact that is relevant when considering the formation of the Galaxy. 22

23 Number Density of Globular Clusters Number of Clusters per kpc 3 Distance from the Galactic Center 23

24 Abundances The estimate of the abundances of the heavy elements is of fundamental importance because it reflects the result of previous evolution of the stellar content. The determination of the abundances is accurate for those elements for which it is possible to observe many spectroscopic lines and when the physical parameters of the emitting regions, Temperature and Pressure, are accurately known. The metals are more abundant near the Galactic Center. 24

25 Abundances in Astronomy W = N * m grams N Number of Avogadro; m mass of nucleus i i A i A i W = ; ρ = N ( Number density )* m He m i i i 12 ( C) W C Atomic weight W ( C) = A( C) = 12 Unit of A = = 12 N 12 N m B j m j( A,Z ) = Z jmh + ( Aj Z j) m n 2 ; mh = mp + m e; B j = nuclear binding ener c gy Z Ch arg e Number; A Mass Number ρ W = ;W = H N*W i i i i i i i i m = N i* m i = ~ ρ = ; Nucleon Fraction X i = i NA NA ρ NA i i j j i = = i j = = = i ρ A j ρ A n N*A N*A X N Nucleon of species j X 1;Y N A N Total # Nucleons A A N*A 25

26 Continue Convention j j n = N j j Aj Total Number of Nucleons; Y j j = 1 generally in Astronomy By definition the# of Hydrogen atoms equals10 log y = log f + log Y or j H j N N = j i i j log log log ( Ni ) ( N ) ( Ni ) j ( N j ) A Half solar Abundance of ratio A i ito Aj = log ( 0.5) = 0.3 A j n N N N i j 12 26

27 They coexist 27

28 Distribution of Dark nebulae 28

29 HI and Absorption Lines, NaI & CaII 29

30 Some details The observations have been carried out in the I Persei association. The * marks the radial velocity of the Stars. The 21 cm profiles have been obtained at separation of about 1 degree in order to scan a reasonable region of the sky in that direction. There is strong coincidence in velocity of the two components HD l=135.0 b=-3.3 with two well marked maxima in the 21 cm profile l=135.2 b=-3.6 Same for HD l=134.6 b=-3.7 with 21 cm l=134.2 b=

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