Orbital  properties  of  the  M31  satellitesLaura  Watkins  (MPIA),  Wyn  Evans  (Cambridge),  Glenn  van  de  Ven  (MPIA)

why?

watkins@mpia.de      ✦      http://mpia.de/~watkins      ✦      arXiv:1211.2638

✦ And XII and And XIV have higher line-of-sight velocities than expected for satellites at similar distances from M31, so they are thought to be on their first infall into the M31 system. We want to look at their orbits and see if this is true.

✦ Hierarchical structure formation predicts that dark matter clumps together into filaments. Subhalos fall in along filaments so we should expect to see satellites falling in together (Li & Helmi 2008). We want to look for infalling groups.

✦ We use distance probability profiles from Conn et al. (2012), and line-of-sight velocities from Tollerud et al. (2012) and Collins et al. (2013).

100 200 300 400a [kpc]

0.00

0.01

0.02

0.03

0.04

0.05

f(a

)

� = 1� = 2� = 3� = 4� = 5

0.0 0.2 0.4 0.6 0.8 1.0e

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

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f(e

)

m = 0m = 3m = 6m = 9m = 12

2

51020

m

M32 NGC 205 And I And XVII And III And XXV And V

2

51020

m

NGC 147 And XXIII And XXI And XX And X And XIX And XI

2

51020

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And XII And IX And XXIV And XIV And XV NGC 185 Cass II

2

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And II M33 And VII And XIII And XXII And XXVI IC 10

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2

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Pisces

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And VI

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And XVI

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And XXVII

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And XVIII

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Pegasus

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IC 1613

0.2

0.4

0.6

0.8

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1.2

1.4

1.6

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5

0 100 200 300 400 500 600

rsep [kpc]

�400

�200

0

200

400

v los[k

m/s

]

Norb = 5000Npos = 10

� = 2.3m = 6.9

And XII

And XIVAnd XXVII

M32

30

60

90

120

150

180

210

240

270

Nnei

ghbours

1 2 3 4solution

0

100

200

300

400

500

600

700

d[k

pc]

apocentresemi-major axispericentre

2.02.22.42.62.83.03.23.4

M[⇥

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n]

468

101214

T[G

yr]

1 2 3 4solution

0.86

0.87

0.88

0.89

e

1 2 3 4solution

0

100

200

300

400

d[k

pc]

apocentresemi-major axispericentre

1.11.21.31.41.51.61.71.8

M[⇥

1012

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n]

468

101214

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1 2 3 4solution

0.200.250.300.350.400.450.50

e

how?

to  find  first-­‐infall  satellites  and  infalling  groups

timing  argument  and  phase  space  distribution  functions  to  overcome  lack  of  proper  motions

first  infall? minimum  mass  solutions

infalling  groups?

And  XII  &  And  XIV  are  not  well  fit  by  our  models  ➙  suggests  they  are  on  their  first  infall

✦ 𝚲CDM predicts that satellites orbit in groups. We use the models to calculate mean orbital properties for the satellites, using their probabilities as weights, and then searched for satellites that were spatially within 100 kpc and had consistent orbital properties. We found 4 candidate groups:✦ NGC 185 & Cass II (And XXX).✦ And IX & And X.✦ And I & And XVII.✦ NGC 147, And V & And XXV.

three  pairs  and  one  triple  group

Figure 1: Distribution functions for semi-major axis a (left) and eccentricity e (right) for different values of

the model parameters 𝛾 and m.

references

✦ We have only positions, distances and line-of-sight velocities for the satellites, no proper motions, so we cannot get the orbital properties directly.

✦ Instead we draw orbits from distribution functions: f(a) ∝ a𝛾, f(e) ∝ (1-e2)m (see Figure 1).

✦ This assumes that the satellites are a well-mixed population.

✦ We use the timing argument (eg. van der Marel & Guhathakurta 2008) to run these orbits for a Hubble time to get their present-day separations from the host. We “observe” the model satellites from a random viewing direction to get their line-of-sight velocities (see Figure 2).

✦ This assumes that the other satellites and the Milky Way have a negligible effect on the orbit of an individual satellite: Li & White (2008) showed that this is a reasonable assumption.

Collins et al. 2013, ApJ, submitted ✦ Conn et al. 2012, ApJ, 758, 11 ✦ Li & White 2008, MNRAS, 384, 1459 ✦ Li & Helmi 2008, MNRAS, 385, 1365 ✦ Tollerud et al. 2012, ApJ 752, 45 ✦ van der Marel & Guhathakurta 2008, ApJ, 678, 187 ✦ Watkins, Evans, An 2010, MNRAS, 406, 264 ✦ Watkins, Evans, van de Ven 2013, MNRAS, accepted (arXiv:1211.2638)

Figure 2: Distribution of separations and line-of-sight velocities from a model with 𝛾=2.3 and m=6.9. The colours indicate the number of orbits in each pixel. The black crosses show the observed M31 satellites.

✦ We calculate the likelihood of observing each satellite given a particular model over a grid of (𝛾,m) models (see Figure 3).

✦ Seven satellites are not well fit by the models:✦ M32: is very close to M31 and very few of the model orbits probe in so near.✦ And XXVII: its distance uncertainty is very large (see Figure 2).✦ And XVIII, Pegasus and IC 1613: these have large separations so the

assumption that the orbits are unperturbed might well break down.✦ And XII and And XIV: as satellites at similar distances are well described by

the models, it is the assumption of belonging to a well-mixed population that must be in error, indicating that these two are on their first infall into M31.

Figure 3: Probabilities of observing each satellite for a grid of (𝛾,m) models. The colours are consistent across all panels. Red-yellow-green satellites are well-fit by the models; blue

satellites are unlikely. The satellites are shown in order of their separation from M31.

relax  assumptions  for  And  XII  &  And  XIV➙  results  consistent  with  first  infall  into  M31

Figure 4: The first four minimum-mass solutions for And XII (top) and And XIV (bottom). Left

panels show semi-major axis, apocentre and pericentre. Right panels show (from top to

bottom) mass, period and eccentricity.

✦ Given the lack of proper motion measurements, we search over all possible proper motion values and adopt the solution that gives the minimum mass.

✦ The equations are multi-valued: the n-th solution assumes that the satellite is on its n-th orbit. We obtain a set of orbital parameters for each solution.

✦ For And XII:✦ multiple-orbit solutions are

disfavoured as they predict small pericentres; such close encounters with M31 would leave behind tidal debris that we do not detect.

✦ multiple-orbit solutions also predict masses higher than previously estimated (e.g. M=1.5±0.4 M⦿ by Watkins et al. (2010)).

✦ the first-orbit solution is highly eccentric, as expected for a satellite on its first infall.

✦ For And XIV:✦ we cannot rule out multiple-

orbit solutions as all predicted masses are consistent with previous estimates. The predicted orbits are of moderate eccentricity.

✦ the first solution predicts that And XIV is very near pericentre, which would explain its high velocity.

✦ We relax the assumption that And XII and And XIV belong to a smooth, well-mixed population and re-analyse their orbits.