Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.stsci.edu/~lwatkins/pubs/2013-01_aas.pdf Дата изменения: Tue Sep 17 04:02:41 2013 Дата индексирования: Fri Feb 28 19:06:25 2014 Кодировка: Поисковые слова: earth orbit

Orbital properties of the M31 satellites
Laura Watkins (MPIA), Wyn Evans (Cambridge), Glenn van de Ven (MPIA)
watkins@mpia.de http://mpia.de/~watkins arXiv:1211.2638

why?
to find first-
infall satellites and infalling groups
And XII and And XIV have higher line-of-sight velocities than expected for

first infall?
And XII & And XIV are not well fit by our models suggests they are on their first infall
We calculate the likelihood of observing each satellite given a particular model

minimum mass solutions
relax assumptions for And XII & And XIV
results consistent with first infall into M31
We relax the assumption that And XII and And XIV belong to a smooth, well

how?
timing argument and phase space distribution functions to overcome lack of proper motions
We have only positions,
0.05 0.04 = = = = = 1 2 3 4 5 4 3 3 2 2 1 1 0 0 . . . . . . . . . 0 5 0 5 0 5 0 5 0 0 .0 0 .2 0 .4 0 m m m m m = = = = = 0 3 6 9 12

20 10 5 2 20 10 5 2 20 10 5 2 20 10 5 2 1
Pisces And VI And XVI And XXVII And XVIII Pegasus IC 1613 And II M33 And VII And XIII And XXII And XXVI IC 10 And XII And IX And XXIV And XIV And XV NGC 185 Cass II NGC 147 And XXIII And XXI And XX And X And XIX And XI

m

1 .4 1 .2 1 .0 0 .8 0 .6 0 .4 0 .2


5

m

P

sat

10



0.02 0.01 0.00 100 200 300

400

a [kpc]

e

.6 0 .8 1 .0

Figure 1: Distribution functions for semi-major axis a (left) and eccentricity e (right) for different values of the model parameters and m.
We use the timing argument

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

(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.

270 400

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.



N

orb

200

0

150 120

los

N

neighb ours

[km/s]

M32

= 5000 Npos = 10 = 2.3 m = 6.9

240 210 180

infalling groups?
three pairs and one triple group
CDM predicts that satellites orbit in groups. We use the models to calculate

v

200

And XIV And XXVII And XII

90 60 30

400 0 100 200 300 400 500 600

r

sep

[kpc]

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

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 .

references
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)

e

T [Gyr]

d [kpc]

M [10

0.03

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) a, f(e) (1-e2)m (see Figure 1). This assumes that the satellites are a well-mixed population.

m

m

f ( a)

f ( e)

Figure 3: Probabilities of observing each satellite for a grid of (,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.

12

M

2

3

41

2

3

41

2

3

41

2

3

41

2

3

41

2

3

41

2

3

4

sun

]

e

T [Gyr]

d [kpc]

M [10

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 for mation 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).

over a grid of (,m) models (see Figure 3).
20 10 5 2
M32 NGC 205 And I And XVII And III And XXV And V

1 .8 1 .6

mixed population and re-analyse their orbits. Given the lack of proper motion measurements, we search over all 3 .4 apocentre 3 .2 700 possible proper motion values semi-major axis 3 .0 2 .8 pericentre and adopt the solution that gives 2 .6 600 2 .4 the minimum mass. 2 .2 2 .0 500 The equations are multi-valued: 14 12 the n-th solution assumes that the 10 400 satellite is on its n-th orbit. We 8 6 obtain a set of orbital parameters 300 4 for each solution. 0.89 200 For And XII: 0.88 multiple-orbit solutions are 100 0.87 disfavoured as they predict 0.86 0 small pericentres; such close 1 2 3 4 1234 encounters with M31 would solution solution leave behind tidal debris that we do not detect. 1 .8 apocentre 1 .7 multiple-orbit solutions also 1 .6 semi-major axis 1 .5 400 pericentre 1 .4 predict masses higher than 1 .3 1 .2 previously estimated (e.g. 1 .1 M=1.5±0.4 M by Watkins et 14 300 12 al. (2010)). 10 the first-orbit solution is highly 8 6 200 eccentric, as expected for a 4 0.50 satellite on its first infall. 0.45 For And XIV: 0.40 100 0.35 we cannot rule out multiple0.30 0.25 orbit solutions as all predicted 0.20 0 masses are consistent with 1 2 3 4 1234 solution solution previous estimates. The predicted orbits are of Figure 4: The first four minimum-mass solutions moderate eccentricity. for And XII (top) and And XIV (bottom). Left the first solution predicts that panels show semi-major axis, apocentre and And XIV is very near pericentre. Right panels show (from top to pericentre, which would bottom) mass, period and eccentricity. explain its high velocity.
12

m

M

sun

]