The formation of the Local Group ASTC22. Lecture L14 The formation of the Local Group Jacobi radius in flat-Vc galaxies Chemical evolution models G-dwarf problem

Computation of Roche lobe in R3B (Restricted 3 Body) equations of motion ( , a = semi-major axis of the binary) Point masses only! L

Jacobi radius rJ We consider one large and one small, massive stellar systems, circling each other. The larger one might represent the Milky Way, the small either a globular cluster, or a dwarf galaxy merging with the Galaxy. The derivation of tidal radius proceeds along the lines of the Roche lobe size derivation in R3B (see Lecture 11). One difference is that force of the Galaxy is not ~1/r^2. Three forces acting on a test particle placed at the Lagrange point L1 are summed up and equated with zero: two gravitational pulls toward the two massive bodies, plus the centrifugal force. Let’s denote as r_J the Jacobi or tidal radius (m2-L1 distance), and as r_0 the distance between bodies 1 and 2; point L1 is then at r = r_0 - r_J (we count the r from body m1). (1) force from body 1 = -G M(r_0 - r_J) /(r_0 - r_J)^2 ~ -GM(r_0)/r_0^2 *(1 + r_J/r_0) where we took into account M(r_0-r_J) = M(r_0) *(1 - r_J/r_0) in a flat-Vc galaxy. (2) force from body 2 = +Gm/ r_J^2 (3) centrifugal force = v_c^2 /(r0-r_J) ~ +GM(r_0)/r_0^2 *(1 - r_J/r_0) because this force is a constant rotation speed Omega^2 times the distance r, so it’s linearly scaling with r, thus being (1- r_J/r_0) times smaller at L1 than at r=r_0. Dividing by the unit force (acceleration) GM(r_0)/r_0^2 we obtain, equating the sum of the three terms to zero, and denoting x=r_J/r_0, and M_0=M(r_0), we obtain: -(1 + x) + (m/M_0)/x^2 + (1 - x) = 0, therefore 2x = (m/M_0)/x^2, or r_J/r_0 = [m/(2M_0)]^(1/3) Example: globular cluster mass = 1e6 M_sun, Galactic bulge mass 1e10 M_sun ==> r_J = r_0 (50^0.333)*1e-2 ~ 0.04. Stars beyond 0.04r_0 from the globular cluster are ‘evaporating’.

M31 = Andromeda galaxy

Local Group = Only 3 spirals Only 1 elliptical (!) Lots of dwarf, irregular galaxies How did they form?

Z = 1000 = epoch of recombination = beginning of structure/galaxy/clusters formation At t~0.3 Myr after Big Bang, the electron opacity of plasma drops a lot, because of recombination of p and e into H. The universe becomes transparent, loses radiation pressure support. Z = 6….5 = epoch of first star formation

Metallicity - age relation for F-stars in the solar neighborhood: heavy element enrichment with time, but also a great scatter above the lower envelope...

Closed-box model of heavy element enrichment of ISM/stars definitions

Def.!

Consider some gas turned into stars, and at the same time enriched in heavy elements by dying stars chain differentiation rule change = input - output of Mh

Like in a closed-box model, metallicity Z is lower in regions where gas content is lower (LMC, dwarf Irr, or outer radii of M33)

So far so good...

(observations give ~10 times fewer low-Z stars) …but let’s compute in our closed-box the mass of stars with metallicity less than a given value Z (observations give ~10 times fewer low-Z stars)

LMC = Large Magellanic Cloud, a neighbor bound to the Milky Way Rotation speed ~80 km/s SMC = Small Magellanic Cloud No rotation

Fornax dwarf spheroidal galaxy Foreground MW star Know the differences between: dwarf ellipticals, dwarf spheroidals, and dwarf irregulars (read Ch.4 of textbook)!