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# Detection of the Milky Way reflex motion due to the Large Magellanic Cloud infall

## Abstract

The Large Magellanic Cloud is the most massive satellite galaxy of the Milky Way, with an estimated mass exceeding a tenth of the mass of the Milky Way1,2,3,4,5. Just past its closest approach of about 50 kpc, and flying past the Milky Way at an astonishing speed of 327 km s−1 (ref. 6), the Large Magellanic Cloud can affect our Galaxy in a number of ways, including dislodging the Milky Way disk from the Galactic centre of mass7,8,9. Here, we report evidence that the Milky Way disk is moving with respect to stellar tracers in the outer halo in a direction that points at an earlier location on the Large Magellanic Cloud trajectory. The resulting reflex motion is detected in the kinematics of outer halo stars and Milky Way satellite galaxies with accurate distances, proper motions and line-of-sight velocities. Our results indicate that dynamical models of our Galaxy cannot neglect gravitational perturbations induced by the Large Magellanic Cloud infall, nor can observations of the stellar halo be treated in a reference frame that does not correct for disk reflex motion. Future spectroscopic surveys of the stellar halo combined with Gaia astrometry will allow for sophisticated modelling of the Large Magellanic Cloud trajectory across the Milky Way, constraining the dark matter distribution in both galaxies with unprecedented detail.

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## Data availability

All data used in this study is publicly available. This work made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). The data that support the plots within this paper and other findings of this study are available from https://github.com/michael-petersen/ReflexMotion or from the corresponding author upon reasonable request.

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## Acknowledgements

M.S.P. acknowledges funding from the UK Science and Technology Facilities Council (STFC) Consolidated Grant and support from M. Weinberg for use of the exp code. Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

## Author information

Authors

### Contributions

Both authors assisted in the interpretation of the results and writing of the paper.

### Corresponding author

Correspondence to Michael S. Petersen.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

Peer review information Nature Astronomy thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Tracer population properties as a function of distance.

a, Logarithm of number of sources larger than some Galactocentric radius, r, as a function of Galactocentric radius r in kiloparsecs. We show the three datasets analysed in this paper in colour (red: K Giants, blue: Blue Horizontal Branch, orange: satellites). We show two explored, but unused, datasets in grey (solid grey: globular clusters, dashed gray: RR Lyrae stars). b, The mean proper motion error in milliarcseconds per year for the stellar sources (K Giants, Blue Horizontal Branch, RR Lyrae), as a function of Galactocentric radius. As the brightest sample, K Giants have the smallest uncertainty. We mark 100, 200, and 300 km s−1, the approximate range of halo velocities, as a dotted black curves.

### Extended Data Fig. 2 Angular momentum components of halo stars at Galactocentric distances r > 20 kpc.

Blue and red dots denote BHB and K giant stars, respectively. The angular momentum of the Sagittarius dwarf is marked with a black dot at $${{\bf{L}}}_{{\rm{sgr}}} \,\,(\ {\rm{in}}\, {\rm{units}}\, {\rm{of}}\, {\rm{kpc}}\ {\rm{km}}\ {{\rm{s}}}^{-1})=(605,-4,515,-1,267)$$. For reference, circles mark angular momentum difference $$| {\bf{L}}-{{\bf{L}}}_{{\rm{sgr}}}| =3,000\ \ {\rm{kpc}}\ {\rm{km}}\ {{\rm{s}}}^{-1}$$. Panels ac and panels df correspond to stars at Bsgr < 20 and Bsgr > 20 off the orbtital plane of the Sagittarius stream, respectively. We show the mean 1σ error bar at r > 40 kpc in the lower left of the centre column.

### Extended Data Fig. 3 Corner plot of covariance in the nine fitting parameters for the Blue Horizontal Branch (blue), K Giant (red), satellite (orange) and combined K Giant+Blue Horizontal Branch samples (silver).

The fit parameters are disk velocity, vtravel; Galactocentric longitude apex apex; Galactocentric latitude apex bapex; the mean velocity of halo stars in spherical coordinates 〈vr〉, 〈vϕ〉 and 〈vθ〉; the three hyperparameters σh,los, σh, and σh,b. A full description of the model may be found in the Supplementary Information.

### Extended Data Fig. 4 Corner plot for mock datasets of K Giant stars at r > 40 kpc drawn from live n-body simulations of the MW where the LMC falls in with a mass MLMC/(1011M⊙) = 1, 2 and 3.

Posteriors from the fits for the three models are shown in greyscale from dark to light to indicate increasing mass: 1 × 1011M (black), 2 × 1011M (dark grey), 3 × 1011M (light grey). See Supplementary Information for mock data details. All parameters are well constrained and show a relatively minor covariance. Note that the bounds on the apex direction and the magnitude of the reflex motion improve in proportion to the LMC mass. Values derived directly from the simulation are shown as dashed vertical lines (on histograms), or coloured ‘x’ markers on contour plots: light red (1 × 1011M), red (2 × 1011M), dark red (3 × 1011M).

### Extended Data Fig. 5 Apex direction measured from mock samples of K Giant stars located at r > 40 kpc in the SDSS footprint.

We use live Galaxy models that experience the infall of LMC-like galaxies with masses MLMC/1011M = 1, 2 and 3 (panels a, b and c respectively). Solid lines denote the infall trajectory of the LMC derived from backwards orbit integration of HST proper motions, while dashed lines show models where the LMC trajectory has been flipped. Red (blue) symbols denote the measurement for mock samples with an LMC-like (flipped) trajectory. Uncertainties are the standard deviation derived from the posteriors of the fit locations. Open circles show the point on the trajectory where the LMC crossed the virial radius of the Galaxy. Note that within statistical uncertainties the apex direction derived from the kinematics of distant stellar halo particles points towards the direction where the MW disk is currently moving (crossed circles). The disk component is currently travelling to an earlier point on the LMC trajectory.

### Extended Data Fig. 6 Velocity of the Galactic disk (vtravel) inferred from the kinematics of stellar tracers located at r > 40 kpc as a function of LMC mass.

The solid (dashed) lines show the true speed of the disk barycentre relative to dark matter particles within a radial range 40 < r < 150 on the infall (flipped) trajectories in the mock LMC models, where radius r is in kiloparsecs. The blue (red) symbols show the value of vtravel measured from the mock models in the infall (flipped) trajectory case.

### Extended Data Fig. 7 Dynamical time of particles in the model MW-LMC systems as a function of Galactocentric radius.

For ease of reference, horizontal dashed lines show the lookback time for the onset of disk motion. Halo particles with a dynamical time above the horizontal lines react impulsively to the LMC infall. At a fixed radius, radial and circular orbits provide the shortest and longest periods, respectively. As a function of radius, a star’s period will fall in the grey-shaded region.

### Extended Data Fig. 8 Comparison of the appearance of reflex motion versus rotation.

ac, Our reflex motion model, projected onto the (, b) plane in vlos, v, vb. Velocities in each panel have been normalized to units of vtravel. df, A rotation model, with magnitude vϕ, projected onto the (, b) plane in vlos, v, vb where velocities in each panel have been normalized to units of vrotation. The smoothed SEGUE footprint is outlined in black. Comparing the upper and lower rows shows that the line-of-sight and b velocities are similar, supporting the need for 6-dimensional data and all-sky coverage.

## Supplementary information

### Supplementary Information

Supplementary Discussion, including Supplementary Table 1.

## Rights and permissions

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Petersen, M.S., Peñarrubia, J. Detection of the Milky Way reflex motion due to the Large Magellanic Cloud infall. Nat Astron 5, 251–255 (2021). https://doi.org/10.1038/s41550-020-01254-3

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41550-020-01254-3

• ### All-sky dynamical response of the Galactic halo to the Large Magellanic Cloud

• Charlie Conroy
• Rohan P. Naidu
• Benjamin D. Johnson

Nature (2021)