2.  SIM-Lite: 6 m baseline optical interferometer in space for precision/deep astrometry.  Pointing mode not survey (spinning).  SIM concept is finishing up phase B.  Goal: 4 μas absolute positions, 1 μas relative positions, M V = - 4 th to 20 th mag. Factor of 1000 better astrometry than current state of art.  Was 10m, but lab tests showed design beat goals, so redesign to 6m and trade guide star interferometer for telescope.  Result in large decrease in mass and size of launch vehicle.  Themes – Find earths around neighbor stars, reveal distribution of dark matter at r =10 kpc – 10 Mpc, fundamental physics of stars.  Pathfinder for optical interferometry.

3. V = √ GM/r, If V = constant then M α r

4. . v  = 4.7 [θ/( μas/y)][d/Mpc] km/s  SIM can obtain proper motions (3 μas/y) for a sample of 27 nearby (<5 Mpc) galaxies.  These measurements complete our knowledge of the 6-dimensional position and velocity vector for each galaxy.  In conjunction with advanced gravitational flow models, the result will be true total mass measurements of individual galaxies and a few groups.

5.  Observe 5-20 stars per galaxy to beat down scatter from internal motions and measurement error.  Use brightest stars: supergiants. Can not get proper motion of E and S0 galaxies. This project is brightness limited.  Stellar crowding requires range of spectral channels to increase u-v plane coverage plus more then 2 baseline orientations.

6. Peculiar velocity, u, depends linearly on g today. Can transform from u field to density distribution. Dekel & Bertschinger

7.  M(<R)/R max ³ = π² /(8G t²) assuming spherical collapse Karachentsev and Makarov A&A 2001

8. TRGB

11.  Cen A Group › Distance = 3.76 ±.05 Mpc › σ v = 145 km/s › R = 187 kpc › Virial Mass of (7.5-8.9) X 10 12 M sun  M83 Group › Distance = 4.79 ±.1 Mpc › σ v = 61 km/s › R = 89 kpc › Virial Mass of (0.8 – 0.9) X 10 12 M sun

12.  M turnaround = π² R³ /(8Gt²) in spherical collapse › R turnaround (CenA) = 1.4 Mpc › M(r < R) = 7.1±1 x 10 12 M sun › Implies no mass between M83 and CenA › M/L B = 118 › M/L K = 49.

13. The Action Integral is the integral of Lagrangian along the path over time with constraints at the endpoints. Physical solutions are paths with extrema of the Action Integral. In comoving coordinates, the cosmological formula is:

16.  Start with M/L constant.  Input distances, LA outputs cz and v . Make small changes to distance to improve χ 2. χ 2 = ∑{ [(cz o - cz m ) / σ cz ] 2 + [(v  o - v  )/σ v ] 2 }  χ 2 ~3 because M/L is not constant.  Use multidimensional minimization to solve for M/L per object and new orbits.  Can also use constrained N-body calculations. ( Yepes, G.; Martinez-Vaquero, L.; Hoffman, Y.; Gottlöber, S.; Klypin, A. ) Yepes, G.Martinez-Vaquero, L.Hoffman, Y. Gottlöber, S.Klypin, A.

17.  Warm dark matter escapes galaxies more than clusters so look for differential dark matter-baryon ratio in clusters and galaxies.  1% hot dark matter was 10% at z~10, changes orbits and proper motions. Also LA sensitive to total Ω m at 2% level.  Proper Motions are key to deciding among multiple solutions in Least Action and allowing solutions for masses of individual galaxies and groups. This mass distribution, at the 1- 5 Mpc region, is critical scale for DM character.  PM put constraints on tidal fields from Virgo Cluster, Great Attractor, Pisces-Perseus, and Local Void.  by careful study of the motions of nearby galaxies.  Proper Motions can provide understanding of the state of groups and how they formed.  Required: a few μarcsec/year absolute at V>18mag - only SIM can do this.

18.  Added smooth density component. Motivated by N-body simulation: ~ 30% of dark matter particles are not in galaxies or even groups (orphans).  Allow for a galaxy mass to be very extended at early times by introducing an accretion sphere (V = Mgal/ ) which transfers mass to the halo according to linear growth theory.  Input both d and cz and solve for the best χ 2 = ∑[(µ o - µ m ) 2 / σ µ + (cz o - cz m ) 2 / σ cz ].  Restart program with earlier solution.  Slow down adjustments in individual orbits that have good distances.  Code to wiggle individual masses of objects to improve fit.