The origin of the steep vertical stellar distribution in the Galactic disc

The origin of the steep vertical stellar distribution in the Galactic disc Arunima Banerjee Department of Physics Indian Institute of Science Bangalore 560012 India Email: arunima_banerjee@physics.iisc.ernet.in Observatoire de Paris, Meudon 1

Plan of the talk A brief review of disc galaxies The observed steep stellar distribution in the galaxies Our model solution Results Comparison with observations Alternative solutions Summary Observatoire de Paris, Meudon 2

NGC 891 A spiral galaxy, seen edge-on NGC 628 - a typical spiral galaxy, seen face-on Observatoire de Paris, Meudon 3

A brief review of disc galaxies The observed steep stellar distribution in the galaxies Observational evidences Our proposition Our model & solution Alternative solutions Summary Observatoire de Paris, Meudon 4

A brief review of disc galaxies A spiral galaxy consists of a disc of stars and gas [visible] embedded in a gigantic envelope of the dark matter halo [invisible] Disc Stars constitute 90% whereas gas 10% of the total mass of the disc. The stellar disc scale length (R D ) is of the order of a few kpc. HI disc is extended beyond a few times R D. H 2 is confined to the inner galaxy only. Stars have an order of magnitude higher velocity dispersion (18 km/s) compared to gas (5-8 km/s). Observatoire de Paris, Meudon 5

HI Gas [Mg = 0.1 Ms] Stars[Ms = 0.1 M G ] Bulge 250 pc 350 pc 1 kpc σ s = 18 kms -1 R D σ g = 8 kms -1 Dark Matter 3-4 R D Observatoire de Paris, Meudon 6

A brief review of disc galaxies The observed steep stellar distribution in the galaxies Our model solution Results Comparison with observations Alternative solutions Summary Observatoire de Paris, Meudon 7

The observed steep vertical stellar distribution in galaxies Spitzer(1942) theoretically showed that a self-gravitating, isothermal stellar disk obeys a Sech 2 like vertical density profile. But observations show that it is better-approximated by an Exponential or Sech function close to the galactic mid-plane, i.e the observed profiles are found to be steeper than the Sech 2 profile We address this problem theoretically for our Galaxy. Observatoire de Paris, Meudon 8

The Galaxy Observational evidences Kent, Dame & Fazio (1991): From a 2.4 μm map of the northern Galactic plane, the vertical distribution of light was found to follow the law exp (- z /h z ) more closely than a canonical Sech 2 profile Gould, Bahcall & Flynn (1996): Study of 257 Galactic M Dwarfs from HST images showed that v( z) 0.80Sech 2 ( z / 323pc) + 0.20 exp( z / 656 pc) Observatoire de Paris, Meudon 9

External galaxies Tsikoudi (1979): Surface photometry study of edge-on lenticular NGC 3115 showed that the light profiles were fitted by a Gaussian distribution perpendicular to the galactic plane. Wainscoat et al (1989): Optical and near-infrared imaging of the edgeon galaxy IC 2531 shows an excess of light at small z over the isothermal model of an old disk and seems to be better fitted by an exponential. Observatoire de Paris, Meudon 10

van Dokkum et al (1994): The vertical stellar distribution of the edgeon spiral galaxy NGC 6504 is well approximated by an exponential distribution in the inner parts and a Sech function at large R. Rice et al (1996): Analysis of near-infrared J, H & K band images of edge-on spiral NGC 4565 gives a Sech fit to the light profile in the z direction. Observatoire de Paris, Meudon 11

A brief review of disc galaxies The observed steep stellar distribution in the galaxies Our model solution Results Comparison with observations Alternative solutions Summary Observatoire de Paris, Meudon 12

Our model solution A balance between the upward kinetic pressure, and the downward gravitational pull decides the vertical density distribution of the stars In the past, gas gravity was ignored, even when studying the density distribution of the gas. Observatoire de Paris, Meudon 13

We show that although gas is 10% by mass, it is closer to the mid plane (low dispersion). So it significantly affects the dynamics of both stars and gas. stars Gas Z=0 Thus stars and gas have to be treated jointly to get the correct vertical distribution Main new feature of our work. Observatoire de Paris, Meudon 14

3-component, gravitationally-coupled, Galactic disc model Stars, atomic (HI) and molecular hydrogen (H 2 ) treated as three thin, axisymmetric and coplanar disks embedded into each other. Symmetry of the system reduces it to a one-dimensional problem in the z direction. Also, the joint Poisson equation for a thin axisymmetric disk is 2 d ψ s 2 dz + 2 d ψ 2 dz HI + d ψ 2 dz H 2 2 = 4πG ( ρ + ρ + ρ ) s HI H 2 Observatoire de Paris, Meudon 15

The equation for pressure equilibrium normal to the plane is given by i 2 i < ( v z ) > dρ i ρ dz = ( K z ) s + ( K z ) HI + ( K z ) H 2 + ( K z ) DM i = 1 (stars), 2 (HI), 3 (H 2 ), DM ( dark matter halo) dψ = - (force per unit mass along z) K z ψ i ( v ) 2 z i dz is the corresponding potential is the random velocity dispersion along z Observatoire de Paris, Meudon 16

Combining them, the density distribution of a component at radius R is given by 2 d ρi = 2 dz < 2 ρi d( Kz) DM 1 dρi 4 ( ) + 2 2 ( ) πg ρs + ρhi + ρh + v > dz z i ρi dz This represents a set of three coupled, second order ordinary differential equations Observatoire de Paris, Meudon 17

Each equation is solved numerically by the Fourth-order Runge Kutta Method in an iterative fashion which gives (z) as a function of z. ρ i For each component, following two initial conditions are required at the mid-plane ( z = 0 ) ( ρ 0 ) i Solution of equations d ρ dz ρ i = ( ρ 0 ) i i = 0 for each component is not known a priori, but obtained indirectly by trial and error method from i (R) (given by twice the area under the curve of ρ i (z) vs z) which is known observationally. Observatoire de Paris, Meudon 18

A brief review of disc galaxies The observed steep stellar distribution in the galaxies Our model solution Results Comparison with observations Alternative solutions Summary Observatoire de Paris, Meudon 19

Results 0.16 0.14 Stars ( in coupled system ) R=6 kpc rho_z [M sun pc -3 ] 0.12 0.10 0.08 0.06 0.04 Stars ( alone ) 0.02 0.00 0 200 400 600 800 1000 Vertical distance (pc) Effect of gas gravity Observatoire de Paris, Meudon 20

0 R=6 kpc Stars H2-1 HI Log K z -2-3 -4-5 0 20 40 60 80 100 120 140 160 180 200 Vertical distance (pc) Vertical constraining force Observatoire de Paris, Meudon 21

A brief review of disc galaxies The observed steep stellar distribution in the galaxies Our model solution Results Comparison with observations Alternative solutions Summary Observatoire de Paris, Meudon 22

Comparison with observations Numerical solution for ρ (z) was fitted to the family of curves suggested van der Kruit (1988) ρ ( z ) = 2 2 / n characterized by three free parameters, namely ρ the extrapolated outer mass density, ze e ρ the vertical scale-parameter, n is the steepness index. n = 1 (Sech 2 ) n = 2 (Sech) n = infinity (Exponential) e Sech 2 / n ( nz / 2 z e ) Observatoire de Paris, Meudon 23

0.0 exp R = 6 kpc -0.5 Sech log(rho) -1.0 Sech 2-1.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 z/z e Model profile compared with the prototypes Observatoire de Paris, Meudon 24

Radius Σ HI Σ H2 (Σ HI +Σ H2 ) ------------ Σ stars n 2/n 2 1.8 4.0 0.02 3.33 0.60 4 4.6 13.1 0.10 7.32 0.27 5 4.6 14.2 0.14 7.91 0.25 6 4.6 10.8 0.16 6.89 0.29 Molecular 7 Ring 4.7 4.9 0.13 4.86 0.41 8.5 5.6 2.1 0.17 4.26 0.47 10 5.6 0.8 0.23 2.93 0.68 12 5.6 0.4 0.40 2.83 0.71 Observatoire de Paris, Meudon 25

0.8 0.7 0.6 2/n 0.5 0.4 0.3 0.2 Molecular Ring 2 4 6 8 10 12 Radius(kpc) Radial variation of n Observatoire de Paris, Meudon 26

A brief review of disc galaxies The observed steep stellar distribution in the galaxies Our model solution Results Comparison with observations Alternative solutions Summary Observatoire de Paris, Meudon 27

Alternative solutions Multi-component Stellar Disc We analyzed a 3 component system of G-K-M dwarfs, and two separate giant populations. Dwarfs: Main mass fraction of the disc Giants: Main contributor to disc luminosity Components G-K-M dwarfs Surface Density (M sun /pc 2 ) 13.5 18 Giants 1 0.046 28 Giants 2 0.154 14 Dispersion velocity (km/s) Observatoire de Paris, Meudon 28

The resulting stellar distributions from our model are then fitted with the van der Kruit (1988) function. Results Components Best fit n G-K-M dwarfs 1.01 Giants 1 + Giants 2 1.01 The net luminosity profile of the giants will be Sech 2 (isothermal)0 Observatoire de Paris, Meudon 29

Conclusions A multi component stellar disk with observed parameters for the dwarfs and the giants cannot explain the steep light distribution in the galaxies. It also confirms that our assumption of a single component stellar disk is valid for dynamical study ( as the dwarfs do not affect the dynamics of the dwarfs ) Observatoire de Paris, Meudon 30

Burkert & Yoshii (1996) Vertical exponential profile for stellar luminosity is the direct outcome of gaseous proto discs settling into isothermal equilibrium prior to star formation This is followed by cooling which causes the gravitational contraction of the gas towards the mid plane with a stellar exponential z profile. The final stellar scale height depends on the initial gas temperature and the local surface density. Observatoire de Paris, Meudon 31

Summary The steepening of the stellar vertical density distribution near the Galactic midplane can be explained even for an isothermal population of stars if the gravitaional force due to the gas is considered. Due to the low velocity dispersion of the gas, it is confined to a thin layer near the midplane, and effectively regulates the dynamics there even though it is a less massive component of the disc. Observatoire de Paris, Meudon 32

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