1. GALAXIA – synthetic Galaxy model and its application to Kepler
Joss Bland-Hawthorn
Sanjib Sharma
KASC 6 Meeting
Sydney, June 2013
We have been charged with writing 2014 ARAA on fundamental constants of the Galaxy….
Notes for Sanjib: surveys more specific than realizations
A great deal of work that builds on machinery started by Sharma & Steinmetz; Sharma & Johnston
A publicly available fast code:

2. Context
Far-field cosmologists have a "concordance model" for cleaning and comparing redshift surveys (W(α,δ); completeness; sampling; bias…)
In the near field, we are far from a chemically and dynamically consistent Galactic model. But a framework for comparing surveys, analytic and N-body models is essential.
To test a hypothesis, we must understand:
Our selection function
Consequences of our selection function
Uncertainties from statistical realizations
In surveys, the selection function is the science, like a boundary condition sets the solutions to a DE
Spergel WMAP figure; 60,000 citations to all WMAP papers….(2013)
This awaits much work from Binney's group, future Nbody codes and sims; these must converge.
Besancon is very useful but very limited.
Roskar+ (2010); W(a,d) = redshift survey window function

3. M. Ireland Friday talk Majewski 2010 conf proc: now out of date
4MOST, TESS, Taipan
M. Ireland
Friday talk

4. A publicly available fast code: http://galaxia.sourceforge.net

5. In the good old days, it was easy to present complex codes

7. Besancon: has Gaussian velocity dispersion (DF), q gradient parameters, asymm drift
Neither they nor us have dispersion tilts…
How do we sample f…. This is how….

8. Sampling Analytical Model (Von Neumann rejection sampling)
How to sample points for this function?
Too many wasted. So use adaptive binning.
Next slide is 3D analogue…

9. Adaptive Mesh (Barnes Hut Tree)
A paradigm shift over small FOV (LOS) codes like Besancon and TRILEGAL
The 1D analogy of vN rejection taken to N dimensions
Galaxia is efficient over
arbitrarily large solid angles

10. Once you know inputs from user, can determine minimum mass in cells
At any r, theta, phi in mesh. Very efficient. This takes most of the computational time.

11. Galaxia summary Analytical model for disc system + bulge + warp
Robin et al 2003 (Besancon model)
Stellar halo simulated using N-body simulations
Bullock & Johnston 2005
Padova Isochrones
m >0.15 , Marigo et al 2008, Bertilli et al 1994
0.07<m<0.15 Chabrier et al 2000
3D extinction model
double exponential disc with warp and flare, hR=4.4 kpc, hz=0.088 kpc
E(B-V) at infinity match Schlegel et al 1998 or
0.54 mag/kpc in solar neighborhood
Can actually tune the extinction with an arbitrary function (this is a prior)
We modified extinction fn to get RAVE selection fn right near Gal Plane.

12. Hipparcos V<8, r<100 pc
Difference in total number of stars, due to binarity (27%)
Binary flag set, star removed from Hipparcos set, hence fewer than Galaxia

13. MCMC fitting Now we want extract new insight from a given survey.
Given a model (e.g. Galaxia), we can fit a large set of fundamental parameters to explain the observations.
We need new optimized MCMC methods to fit N model parameters with M missing data variables (marginalization) to 250,000 RAVE and 5000 GCS stars.
In the example that follows, we want to fine tune Galaxy kinematic parameters and test Gaussian DF vs. more theoretically sound DFs (e.g. Shu 1969).
Marginalization is hard. So at each point, want to determine likelihood. If analytic, compute; if nonanalytic, for each star need to integrate over several missing dimensions, say ages, v_l, v_b which we don’t know, even Fe/H.
You are integrating over the likelihood in the missing DATA dimensions… e.g. P(l,b,v_l,v_b,v_r, r | model set)
We know l,bv_r, but not v_l,v_b; we don’t know r; but given model, we could marginalize over v_l,v_b,r given
Input definition of catalogue.
SS’s new hierarchical MCMC allows us to bring r over to model set.
Kepler analysis in next talk…. SS
SB^2 = Sellwood-Binney, Schonrich-Binney
Supplied N-body output assumes input consistent with Galaxy model if only subset given, say
Does Besancon allow error convolution?
When comparing to redshift surveys, we need to invent galaxies to compare to real data.

14. Disk
Dust
epsilon = vertical to radial axis ratios, change with time
Dust model: want to project to Schlegel, Finkbeiner, Davis
Disk warp

15. DF & asymmetric drift Shu 1969
Shu solves Boltzmann's eqn: as A. Just says, no need for third integral.
Just construct from energy and angular momentum (see Shu 1969)
Comment from O. Bienyame that Shu'69 is not consistent, since different scale length; JJB to look at

16. Quick summary of the previous slide

17. These have been explored to

19. GCS-SHU
First audience to see these… No v_circ since only a very local volume
GCS Gauss and Shu both good.

20. RAVE-SHU
RAVE Shu better than RAVE Gauss

21. G. Ricker, Friday talk: FGK dwarfs: V=4.5-13.5 M dwarfs: I < 13
All sky: 2,500,000 targets
Launch: 2018
VERY complementary with (RAVE) HERMES
Lunch with him on Thursday?

22. Galaxia A consistent framework is essential to progress
Results for the Kepler sample in the next talk
Powerful N-body phase space sampling and comparison not shown. In an era of Gaia, we can start to separate Galactic stars from “extragalactic stars.”
Every time you see this symbol, it means WE NEED A FRAMEWORK