Inferring the Galac/c gravita/onal poten/al with chemodynamics
Robyn Sanderson
NSF Postdoctoral Fellow
Columbia University/NYU
The accreted stellar halo is clumpy in ac/on space
View in Galac/c coordinates
6
Jr �kpc2 Myr�1�
5
View in ac)on space (using input poten)al)
n��497198
M�2.7x1012 M�
b�8 kpc
4
3
2
1
0
R.E. Sanderson • 21 July 2015
�5
Lz �kpc Myr �
0
2
�1
5
Review of ac/on-­‐angle variables
R.E. Sanderson • 21 July 2015
Ac/ons are most clustered in the correct poten/al
� Potential parameters
�
1�
GM
−
L + L2 + 4GM b Observations
Jr = √
2
−2E
Both
Mtrue=2.7x1012 M⊙
R.E. Sanderson • 21 July 2015
The Kullback-­‐Leibler divergence measures clustering
DKL (p||q) =
Clumpier distribution =
larger relative entropy
DKL = 1.1
R.E. Sanderson • 21 July 2015
�
ln
�
p(x)
q(x)
�
p(x)dx
Smoother distribution =
smaller relative entropy
DKL = 0.4
Errors blur, but do not destroy the informa/on
Without errors
With Gaia (pre-launch) errors
Sanderson, Helmi, & Hogg, 2015
R.E. Sanderson • 21 July 2015
Results of tests with a mock isochrone halo
Sanderson, Helmi, & Hogg, 2015
Log10 conditional probability
Without errors
With pre-­‐launch Gaia errors
67, 95, 99% confidence equivalents
dGC<20 kpc
R.E. Sanderson • 21 July 2015
Simulated stellar halo in cosmological poten/al
15 thin streams chosen by hand from tagged Aquarius halo Aq-­‐A
(Cooper+2010, Helmi+2011)
Sanderson, Hartke, & Helmi, in prep
R.E. Sanderson • 21 July 2015
Best-­‐fit halo matches present-­‐day mass profile
Model: smooth, spherical NFW
*Membership info not used in fit*
Sanderson, Hartke, & Helmi, in prep
R.E. Sanderson • 21 July 2015
Synergy in observa/ons
RVs
• Northern Hemisphere: WEAVE on William Herschel Telescope (INT/IAC, La Palma, Canary Islands); DESI at KPNO
• Southern Hemisphere: 4MOST on VISTA telescope in Chile (ESO, Cerro Paranal, Chile)
• 4m telescope with mul)ple-­‐fiber instrument
• ~10 halo stars (per survey)
• RV errors <2 km s to V=20-­‐22
• Adds RVs to stars with Gaia proper mo)ons
20% photometric distances
•
RR Lyrae
• Distances to 2%, RV errors 5-­‐10 km s
6
-­‐1
-­‐1
R.E. Sanderson • 21 July 2015
Improved distances increase informa/on, but decrease sampling
KIII giants, Gaia parallaxes
R.E. Sanderson • 21 July 2015
RRLe distances
Observa/ons with larger average dGC do beYer
Sanderson, in prep
R.E. Sanderson • 21 July 2015
R.E. Sanderson • 21 July 2015
Chemical dimensions
Bullock & Johnston Halo 2 + Galaxia (S. Sharma), single stellar popula9ons
-­‐> M Giants (mag & color selected)
error models: Gaia + RVs + some kind of abundance error (wild guesses)
cut error-­‐convolved sample in es9mated energy (~40,000 stars)
view here is without observa9onal errors for stars selected as above
bad poten9al model: spherical NFW for bulge/disk/halo system!
R.E. Sanderson • 21 July 2015
Chemical dimensions
Same as before, but now with observa9onal errors
error models: Gaia parallaxes/pms,
2 km/s RVs,
abundances to 0.1 dex
bad poten9al model: spherical NFW for bulge/disk/halo system!
R.E. Sanderson • 21 July 2015
Chemical dimensions
Same as before, but now with observa9onal errors
error models: Gaia parallaxes/pms,
2 km/s RVs,
abundances to 0.05 dex
bad poten9al model: spherical NFW for bulge/disk/halo system!
R.E. Sanderson • 21 July 2015
Chemical dimensions
Same as before, but now with observa9onal errors
error models: Gaia parallaxes/pms,
2 km/s RVs,
abundances to 0.01 dex
bad poten9al model: spherical NFW for bulge/disk/halo system!
R.E. Sanderson • 21 July 2015
Phase space only (3 dimensions)
Without obsv. errors
R.E. Sanderson • 21 July 2015
With obsv. errors Adding [Fe/H] (4 dimensions)
Without obsv. errors
R.E. Sanderson • 21 July 2015
With obsv. errors ([α/Fe] to 0.1 dex) Adding [Fe/H] and [α/Fe] (5 dimensions)
Without obsv. errors
R.E. Sanderson • 21 July 2015
With obsv. errors ([α/Fe] to 0.1 dex) Adding [Fe/H] and [α/Fe] (5 dimensions)
Without obsv. errors
R.E. Sanderson • 21 July 2015
With obsv. errors ([α/Fe] to 0.05 dex) Adding [Fe/H] and [α/Fe] (5 dimensions)
Without obsv. errors
R.E. Sanderson • 21 July 2015
With obsv. errors ([α/Fe] to 0.01 dex) Finding streams in ac/on space
Using EnLink (Sharma & Johnston 2009)
1 group found
512/41,028 stars classified
did not fine-­‐tune parameters of group finder
R.E. Sanderson • 21 July 2015
Finding streams in 5D chemodynamical space
abundances to 0.05 dex 5 groups found
1,120/41,028 stars classified
R.E. Sanderson • 21 July 2015
Finding streams in chemodynamical space
abundances to 0.01 dex (yeah)
10 groups found
5,427/41,028 stars classified
R.E. Sanderson • 21 July 2015
Finding streams in chemodynamical space
R.E. Sanderson • 21 July 2015
For discussion
• BeIer choice of stellar popula9on?
• BeYer poten/al model?
• Other things I am doing wrong with abundances?
R.E. Sanderson • 21 July 2015
Advantages
• No need to assign membership of stars in streams (membership probability is an output)
• Robust to adiaba/c /me-­‐evolu/on of host, substructure, some chao/c diffusion
• Can use any informa/ve parameter (i.e. abundances)
Disadvantages
• Needs 6D phase space info (plus whatever else)
• Not a forward model (no way to treat uncertain/es)
• Derailed by large (>50%) smooth component
• Limited to integrable poten/als
R.E. Sanderson • 21 July 2015
The takeaway
• Tidal streams are sensi)ve to the poten)al of the Galac)c dark mager halo
• Streams form clumps in ac)on space that s)ll look clumpy at Gaia precision (δπ/π < 0.2) • Maximizing D
KL of ac)on distribu)on iden9fies the poten9al parameters
• Rela)on between D
KL and posterior probability lets us set confidence intervals
• Expected number of MW streams is enough
• Stream membership info not required R.E. Sanderson • 21 July 2015