galaxies (Sales et al., 2007, Figures 3 and 6). The issue therefore arises on
a much larger scale than that addressed in previous works regarding the
anisotropic distribution of the MW and M31 satellite systems (e.g. Pawlowski
et al., 2014). In a $\Lambda$CDM context, baryonic physics does not seem to
have a major effect on the expected anisotropy of these systems (Pawlowski et
al., 2015, Figure 3). Thus, it seems unlikely that it would affect our results
on a still larger scale.

In this contribution, we assess the feasibility of a scenario involving a past
close flyby of the MW and M31, whose once fast relative motion could have
flung out these HVGs via gravitational slingshot encounters. To help constrain
the orientation of the MW-M31 orbital plane, we develop a toy model of their
flyby forming the recently discovered planes of satellites around the MW
(Pawlowski & Kroupa, 2013) and M31 (Ibata et al., 2013). A past close MW-M31
encounter seems able to form correctly oriented satellite planes only for a
particular MW-M31 orbital pole (Section 2.2).

Using this information, we constructed a MOND-based dynamical model of the LG
to investigate the effect of a past MW-M31 flyby on it (Section 3). We tracked
the evolution of a spherical cloud of several hundred thousand LG test
particles initially on the Hubble flow, leaving a gap around the MW and M31
(Equation 27). Although our results are somewhat dependent on details of how
MOND works in a cosmological context, it is clear that a small fraction of
these particles end up with a large radial velocity away from the LG after
closely interacting with the MW or M31 around the time of their encounter
(Figure 5). Such slingshot interactions are expected to be most efficient for
particles flung out almost parallel to the motion of the perturbing body. This
probably explains why simulated particles flung out to the greatest distances
from the LG preferentially lie close to the MW-M31 orbital plane (Figure 9).

To see if such a pattern is evident in the real LG, we made several
improvements to our $\Lambda$CDM modelling of the LG (Section 4.1) and
developed a method for selecting HVGs (Section 4.2) so that we could quantify
their spatial anisotropy (Section 5). The HVGs we identified are indeed mostly
located close to a plane (Figure 11) oriented similarly to our expectation for
the MW-M31 orbital plane based on the flyby scenario (Figure 15). The galaxies
in our sample which are not HVGs (the vast majority) do not preferentially lie
close to the HVG plane. Importantly, the MW and M31 lie near this plane
(barycentre $\,{\sim}\,70$ kpc off it), suggesting that it has dynamical
significance.

These characteristics of the observed HVG plane are natural outcomes of our
MOND simulation of the LG (Section 3). To quantify how likely it is that a
random distribution of HVGs shares these properties, we conducted Monte Carlo
(MC) trials where the directions to the HVGs were randomised and their
distances selected from a Gaussian distribution corresponding to observations
(Section 6).181818We converted negative mock distances to 0.

Based on the criteria in Table 5, there is a ${<0.01}$ probability of
obtaining a situation analogous to that observed, mainly because it is very
unusual for all but one of the HVGs (listed in Table 3) to so nearly lie
within a common plane. Our result holds even if we vary certain assumptions,
with the nominal choices leading to a still smaller value of only ${1.5\pm
0.1\text{\textperthousand}}$ (Table 7). As the observed HVG plane has an
aspect ratio of 0.08 (Table 4), our results are not consistent with a mildly
flattened prior distribution for the HVGs (Section 6.6). More extreme
flattening could lead to consistency and may well be realistic as our entire
sample of LG galaxies does indeed exhibit a moderate flattening. However, the
preferred flattening axis is misaligned by ${25^{\circ}}$ 191919${35^{\circ}}$
when excluding HVGs to the HVG plane normal. Thus, the flattened distribution
of the HVGs is very likely related to their anomalous radial velocities and
not merely a consequence of the entire LG being moderately anisotropic about a
different axis.

As well as more detailed modelling, our ideas regarding the LG may be tested
using a more accurate distance to HIZSS 3 to see if it really should be
treated as a HVG. Better observations of Antlia could help clarify whether it
is a satellite of NGC 3109 or an independent galaxy. In the long run, it is
important to try and discover more HVGs to see if they mostly remain close to
a plane.202020Observers do not search for HVGs per se but instead for LG dwarf
galaxies which may turn out to be HVGs when their kinematics are analysed
using a $\Lambda$CDM-based dynamical model. If so, it will be interesting to
know whether its orientation is altered much compared to our determination.
Considering the effect of Antlia on this, adjustments of up to
$\,{\sim}\,5^{\circ}$ could well be in store (Table 4).

Our work suggests a particular great circle on the sky in which observers
would be more likely to discover HVGs. However, it is important to search
other directions too as only then is it possible to determine just how
anisotropic the distribution of HVGs is. Fortunately, the plane we identified
is inclined by a large angle to the MW disk and to the Ecliptic, which should
help minimise observational biases. Moreover, there are unlikely to be any
strong selection effects based on the radial velocity.

Both 2D and 3D $\Lambda$CDM-based dynamical models of the LG face difficulties
in explaining the observed kinematics of its non-satellite galaxies (Banik &
Zhao, 2016, 2017a). In particular, the existence of 7 galaxies with
anomalously high radial velocities but only 1 with anomalously low radial
velocity (Figure 10) suggests that the central region of the LG has been much
more efficient at scattering dwarf galaxies than these models allow. This is
problematic given that even LG galaxies as massive as the MW and M31 appear
incapable of scattering dwarfs as far out as the HVGs, not only in our
simulations but also when considered in full cosmological simulations of
$\Lambda$CDM (Sales et al., 2007). This may hint that the MW and M31 were once
moving much faster than at present, pointing towards a past close MW-M31
flyby. If such an event occurred, it would provide a natural explanation for
several aspects of the spatial distribution of the HVGs, especially their
tendency to lie close to a plane (Figures 9 and 11). A past flyby interaction
of such massive galaxies only makes sense in the context of certain modified
gravity theories where galaxies lack massive dark matter halos and their
associated dynamical friction in close encounters, which would otherwise cause
a merger.

##  9 Acknowledgements

The authors are grateful to Marcel Pawlowski for suggesting the idea behind
this contribution. IB is supported by Science and Technology Facilities
Council studentship 1506672. This work was partly supported by a Scottish
Universities Physics Alliance travel award hosted by Nima Arkani-Hamed at the
Institute for Advanced Studies. The algorithms were set up using
matlab${}^{\text{\textregistered}}$.

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