text: Draft version May 31, 2020 Preprint typeset using LATEX style emulateapj v. 01/23/15 THE PROPER MOTION FIELD OF THE SMALL MAGELLANIC CLOUD: KINEMATIC EVIDENCE FOR ITS TIDAL DISRUPTION Paul Zivick 1, Nitya Kallivayalil1, Roeland P. van der Marel2,3, Gurtina Besla4, Sean T. Linden1, Szymon Kozłowski5, Tobias K. Fritz 1,6,7, C. S. Kochanek8,9, J. Anderson2, Sangmo Tony Sohn2, Marla C. Geha10, Charles R. Alcock11 0 1Department of Astronomy, University of Virginia, 530 McCormick Road, Charlottesville, VA 22904, USA; email: pjz2cf@virginia.edu 2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 3 Center for Astrophysical Sciences, Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA 4 Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA 5 Warsaw University Observatory Al. Ujazdowskie 400–478 Warszawa, Poland 6 Instituto de Astroﬁsica de Canarias, calle Via Lactea s/n, E-38205 La Laguna, Tenerife, Spain 7 Universidad de La Laguna, Dpto. Astroﬁsica, E-38206 La Laguna, Tenerife, Spain 8 Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA 9 Center for Cosmology and AstroParticle Physics, The Ohio State University, 191 W. Woodruﬀ Ave., Columbus, OH 43210, USA 10 Department of Astronomy, Yale University, New Haven, CT 06520, USA 11 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA Draft version May 31, 2020 ABSTRACT We present a new measurement of the systemic proper motion of the Small Magellanic Cloud (SMC), based on ∼ an expanded set of 30 ﬁelds containing background quasars and spanning a 3 year baseline, using the Hubble Space Telescope Wide Field Camera 3 (HST WFC3). Combining this data with our previous 5 HST ﬁelds, and an additional 8 measurements from the Gaia-Tycho Astrometric Solution Catalog, brings us to a total of 43 SMC ﬁelds. We measure − ± ± − − ± a systemic motion of µ = 0.82 0.02 (random) 0.10 (systematic) mas yr 1 and µ = 1.21 0.01 (random) ± W − N 0.03 (systematic) mas yr 1. After subtraction of the systemic motion, we ﬁnd little evidence for rotation, but ﬁnd an ordered mean motion radially away from the SMC in the outer regions of the galaxy, indicating that the SMC is in the process of tidal disruption. We model the past interactions of the Clouds with each other based on the measured ± − present-day relative velocity between them of 103 26 km s 1. We ﬁnd that in 97% of our considered cases, the Clouds ± ± experienced a direct collision 147 33 Myr ago, with a mean impact parameter of 7.5 2.5 kpc. Keywords: Galaxies: Kinematics and Dynamics, Galaxies: Magellanic Clouds 1. INTRODUCTION that the LMC is a relatively well-behaved system. The structure and dynamics of the SMC has not proved Our understanding of the Small and Large Magellanic to be as easy to understand. NK13 had results for only Clouds (SMC and LMC) has evolved greatly in the age 5 ﬁelds, enough to attempt a measurement of the COM of space-based proper motion (PM) measurements. The PM, but not enough to describe the internal kinematics. HST PM measurements by Kallivayalil et al. (2006) were vdMS16 analyzed PMs for eight individual stars in the used to demonstrate that the Clouds had not orbited the SMC from the TGAS Catalog (Lindegren et al. 2016), Milky Way (MW) multiple times as expected but instead but the resulting residual motions were not indicative of were likely on their ﬁrst infall into the MW (Besla et al. any coherent motion. A third COM PM was measured 2007). With the supporting results from Piatek et al. by Cioni et al. (2016) as a by-product of their work on (2008), this view of the Clouds became the new paradigm 47 Tuc did not provide any additional insight into the and has driven our understanding of their evolution. internal workings of the SMC. Since then, the evolution of the LMC has proved more Line of sight (LOS) motion studies have attempted to tractable to understanding. Using a longer baseline and ﬁll this gap. Stanimirović et al. (2004) found a rota- the then new Wide Field Camera 3 (WFC3), Kallivayalil et al. (2013, hereafter NK13) signiﬁcantly improved the tion signature in the HI gas in the SMC with the line of nodes, deﬁned as the line joining the points of maximum PM errors for 26 LMC ﬁelds. Using the decreased uncer- and minimum relative velocity, parallel to the visible ma- tainties, van der Marel & Kallivayalil (2014) were able to jor axis of the SMC and a dynamical center located in make a direct measurement of the PM rotation curve of the northeastern section of the SMC. A study of the red the LMC in the plane of the sky. A follow-up examina- giants in the SMC by Harris & Zaritsky (2006) suggested tion of the center of mass (COM) PM of the LMC and that the older population was dynamically separate from its rotation curve using PMs from the Tycho-Gaia Astro- the neutral gas, having a very weak rotation signature metric Solution (TGAS) Catalog (Lindegren et al. 2016), and a much more signiﬁcant velocity dispersion, suggest- which combines Gaia Data Release 1 (Gaia Collabora- ing a spheroidal rather than disk structure for the SMC. tion et al. 2016a,b) with the Hipparcos Tycho-2 Cata- However, Dobbie et al. (2014) conducted a broader in- logue (Høg et al. 2000), supported this ﬁnding (van der vestigation of the red giant population, extending beyond Marel & Sahlmann 2016; hereafter vdMS16), suggesting the central area considered by Harris & Zaritsky (2006),

text: Draft

text: version

text: May

text: Preprint

text: typeset

text: using

text: LATEX

text: style

text: emulateapj

text: v.

text: THE

text: PROPER

text: MOTION

text: FIELD

text: OF

text: THE

text: SMALL

text: MAGELLANIC

text: CLOUD:

text: KINEMATIC

text: EVIDENCE

text: FOR

text: ITS

text: TIDAL

text: DISRUPTION

text: Paul

label: author

text: Zivick

text: Nitya

text: Roeland

text: P.

text: van

text: der

text: Gurtina

text: Sean

text: T.

text: Szymon

text: Tobias

text: K.

text: Fritz

text: C.

text: S.

text: J.

text: Sangmo

text: Tony

text: Marla

text: C.

text: Charles

text: R.

text: of

text: Astronomy,

text: University

text: of

text: Virginia,

text: McCormick

text: Road,

text: Charlottesville,

text: VA

text: USA;

text: email:

text: Space

text: Telescope

text: Science

text: Institute,

text: San

text: Martin

text: Drive,

text: Baltimore,

text: MD

text: USA

text: Center

text: for

text: Astrophysical

text: Sciences,

text: Department

text: of

text: Physics

text: Astronomy,

text: Johns

text: Hopkins

text: University,

text: Baltimore,

text: MD

text: USA

text: Steward

text: Observatory,

text: University

text: of

text: Arizona,

text: North

text: Cherry

text: Avenue,

text: Tucson,

text: AZ

text: USA

text: Warsaw

text: University

text: Observatory

text: Al.

text: Ujazdowskie

text: Warszawa,

text: Poland

text: Instituto

text: de

text: Astroﬁsica

text: de

text: Canarias,

text: calle

text: Via

text: Lactea

text: s/n,

text: La

text: Laguna,

text: Tenerife,

text: Spain

text: Universidad

text: de

text: La

text: Laguna,

text: Dpto.

text: Astroﬁsica,

text: La

text: Laguna,

text: Tenerife,

text: Spain

text: Department

text: of

text: Astronomy,

text: The

text: Ohio

text: State

text: University,

text: West

text: Avenue,

text: Columbus,

text: OH

text: USA

text: Center

text: for

text: Cosmology

text: and

text: AstroParticle

text: Physics,

text: The

text: Ohio

text: State

text: University,

text: W.

text: Woodruﬀ

text: Ave.,

text: Columbus,

text: OH

text: USA

text: Department

text: of

text: Astronomy,

text: Yale

text: University,

text: New

text: Haven,

text: CT

text: USA

text: Harvard-Smithsonian

text: Center

text: for

text: Astrophysics,

text: Garden

text: Street,

text: Cambridge,

text: MA

text: USA

text: Draft

text: version

text: May

text: ABSTRACT

text: We

text: present

text: a

text: new

text: measurement

text: of

text: the

text: systemic

text: proper

text: motion

text: of

text: the

text: Small

text: Magellanic

text: Cloud

text: (SMC),

text: based

text: on

text: an

text: expanded

text: set

text: of

text: ﬁelds

text: containing

text: background

text: quasars

text: and

text: spanning

text: a

text: year

text: baseline,

text: using

text: the

text: Hubble

text: Space

text: Telescope

text: Wide

text: Field

text: Camera

text: (HST

text: Combining

text: this

text: data

text: with

text: our

text: previous

text: HST

text: ﬁelds,

text: and

text: an

text: additional

text: measurements

text: from

text: the

text: Gaia-Tycho

text: Astrometric

text: Solution

text: Catalog,

text: brings

text: us

text: to

text: a

text: total

text: of

text: SMC

text: ﬁelds.

text: We

text: measure

text: a

text: systemic

text: motion

text: of

text: µ

text: (random)

text: (systematic)

text: mas

text: yr

text: and

text: µ

text: (random)

text: W

text: N

text: (systematic)

text: mas

text: yr

text: After

text: subtraction

text: of

text: the

text: systemic

text: motion,

text: we

text: ﬁnd

text: little

text: evidence

text: for

text: rotation,

text: but

text: ﬁnd

text: an

text: ordered

text: mean

text: motion

text: radially

text: away

text: from

text: the

text: SMC

text: in

text: the

text: outer

text: regions

text: of

text: the

text: galaxy,

text: indicating

text: that

text: the

text: SMC

text: is

text: in

text: the

text: process

text: of

text: tidal

text: disruption.

text: We

text: model

text: the

text: past

text: interactions

text: of

text: the

text: Clouds

text: with

text: each

text: other

text: based

text: on

text: the

text: measured

text: present-day

text: relative

text: velocity

text: between

text: them

text: of

text: km

text: s

text: We

text: ﬁnd

text: that

text: in

text: of

text: our

text: considered

text: cases,

text: the

text: Clouds

text: experienced

text: a

text: direct

text: collision

text: Myr

text: ago,

text: with

text: a

text: mean

text: impact

text: parameter

text: of

text: kpc.

text: Keywords:

text: Galaxies:

text: Kinematics

text: and

text: Dynamics,

text: Galaxies:

text: Magellanic

text: Clouds

text: INTRODUCTION

text: that

text: the

text: LMC

text: is

text: a

text: relatively

text: well-behaved

text: system.

text: The

text: structure

text: and

text: dynamics

text: of

text: the

text: SMC

text: has

text: not

text: proved

text: Our

text: understanding

text: of

text: the

text: Small

text: and

text: Large

text: Magellanic

text: to

text: be

text: as

text: easy

text: to

text: understand.

text: had

text: results

text: for

text: only

text: Clouds

text: (SMC

text: and

text: LMC)

text: has

text: evolved

text: greatly

text: in

text: the

text: age

text: ﬁelds,

text: enough

text: to

text: attempt

text: a

text: measurement

text: of

text: the

text: COM

text: of

text: space-based

text: proper

text: motion

text: (PM)

text: measurements.

text: The

text: PM,

text: but

text: not

text: enough

text: to

text: describe

text: the

text: internal

text: kinematics.

text: HST

text: PM

text: measurements

text: by

text: Kallivayalil

text: et

text: al.

text: were

text: analyzed

text: PMs

text: for

text: eight

text: individual

text: stars

text: in

text: the

text: used

text: to

text: demonstrate

text: that

text: the

text: Clouds

text: had

text: not

text: orbited

text: the

text: SMC

text: from

text: the

text: TGAS

text: Catalog

text: (Lindegren

text: et

text: al.

text: Milky

text: Way

text: (MW)

text: multiple

text: times

text: as

text: expected

text: but

text: instead

text: but

text: the

text: resulting

text: residual

text: motions

text: were

text: not

text: indicative

text: of

text: were

text: likely

text: on

text: their

text: ﬁrst

text: infall

text: into

text: the

text: MW

text: (Besla

text: et

text: al.

text: any

text: coherent

text: motion.

text: A

text: third

text: COM

text: PM

text: was

text: measured

text: With

text: the

text: supporting

text: results

text: from

text: Piatek

text: et

text: al.

text: by

text: Cioni

text: et

text: al.

text: as

text: a

text: by-product

text: of

text: their

text: work

text: on

text: this

text: view

text: of

text: the

text: Clouds

text: became

text: the

text: new

text: paradigm

text: Tuc

text: did

text: not

text: provide

text: any

text: additional

text: insight

text: into

text: the

text: and

text: has

text: driven

text: our

text: understanding

text: of

text: their

text: evolution.

text: internal

text: workings

text: of

text: the

text: SMC.

text: Since

text: then,

text: the

text: evolution

text: of

text: the

text: LMC

text: has

text: proved

text: more

text: Line

text: of

text: sight

text: (LOS)

text: motion

text: studies

text: have

text: attempted

text: to

text: tractable

text: to

text: understanding.

text: Using

text: a

text: longer

text: baseline

text: and

text: ﬁll

text: this

text: gap.

text: Stanimirović

text: et

text: al.

text: found

text: a

text: rota-

text: the

text: then

text: new

text: Wide

text: Field

text: Camera

text: Kallivayalil

text: et

text: al.

text: hereafter

text: signiﬁcantly

text: improved

text: the

text: tion

text: signature

text: in

text: the

text: HI

text: gas

text: in

text: the

text: SMC

text: with

text: the

text: line

text: of

text: nodes,

text: deﬁned

text: as

text: the

text: line

text: joining

text: the

text: points

text: of

text: maximum

text: PM

text: errors

text: for

text: LMC

text: ﬁelds.

text: Using

text: the

text: decreased

text: uncer-

text: and

text: minimum

text: relative

text: velocity,

text: parallel

text: to

text: the

text: visible

text: ma-

text: tainties,

text: van

text: der

text: Marel

text: Kallivayalil

text: were

text: able

text: to

text: jor

text: axis

text: of

text: the

text: SMC

text: and

text: a

text: dynamical

text: center

text: located

text: in

text: make

text: a

text: direct

text: measurement

text: of

text: the

text: PM

text: rotation

text: curve

text: of

text: the

text: northeastern

text: section

text: of

text: the

text: SMC.

text: A

text: study

text: of

text: the

text: red

text: the

text: LMC

text: in

text: the

text: plane

text: of

text: the

text: sky.

text: A

text: follow-up

text: examina-

text: giants

text: in

text: the

text: SMC

text: by

text: Harris

text: Zaritsky

text: suggested

text: tion

text: of

text: the

text: center

text: of

text: mass

text: (COM)

text: PM

text: of

text: the

text: LMC

text: and

text: that

text: the

text: older

text: population

text: was

text: dynamically

text: separate

text: from

text: its

text: rotation

text: curve

text: using

text: PMs

text: from

text: the

text: Tycho-Gaia

text: Astro-

text: the

text: neutral

text: gas,

text: having

text: a

text: very

text: weak

text: rotation

text: signature

text: metric

text: Solution

text: (TGAS)

text: Catalog

text: (Lindegren

text: et

text: al.

text: and

text: a

text: much

text: more

text: signiﬁcant

text: velocity

text: dispersion,

text: suggest-

text: which

text: combines

text: Gaia

text: Data

text: Release

text: (Gaia

text: Collabora-

text: ing

text: a

text: spheroidal

text: rather

text: than

text: disk

text: structure

text: for

text: the

text: SMC.

text: tion

text: et

text: al.

text: with

text: the

text: Hipparcos

text: Cata-

text: However,

text: Dobbie

text: et

text: al.

text: conducted

text: a

text: broader

text: in-

text: logue

text: (Høg

text: et

text: al.

text: supported

text: this

text: ﬁnding

text: (van

text: der

text: vestigation

text: of

text: the

text: red

text: giant

text: population,

text: extending

text: beyond

text: Marel

text: Sahlmann

text: hereafter

text: suggesting

text: the

text: central

text: area

text: considered

text: by

text: Harris

text: Zaritsky


text: − and found instead a rotation signature of 20–40 km s 1 nature (Besla et al. 2012). A comprehensive study of the − kpc 1, although their line of nodes did not agree with classical Cepheids in the SMC (Ripepi et al. 2017) found that found by Stanimirović et al. (2004). To complicate a complex geometric structure, with the near side form- the picture further, Evans & Howarth (2008) found a ing a rough spheroidal shape before gradually shifting similar rotation curve to Dobbie et al. (2014) but in the into a more linear shape, adding more detail to the SMC young, massive star population (O, B, and A stars). A but presenting yet another potentially conﬂicting stellar slight velocity gradient was also found for the OB stars structure. from Lamb et al. (2016). While one could argue that In order to address the still sparse PM-coverage of the red giant population could be dynamically decoupled the SMC, we obtained two epochs of HST data with from the underlying neutral gas, one would not expect WFC3/UVIS for 30 ﬁelds in the SMC, focusing on ob- the same to have happened for the young stars. Dobbie taining data in the outer regions. Combined with the et al. (2014) proposed an inclined disk to help explain data already available from NK13 and vdMS16 for the the diﬀerences, but further kinematic evidence is needed interior of the SMC, this provides a broader kinematic to fully evaluate this possibility. view of the SMC. In this paper, we present the results Because of the interest in the nature of the past mu- from this combined dataset, and their implications for tual interactions of the Clouds, many photometric stud- the orbital history of the SMC. ies have searched for tidal debris at large radii from the The paper is organized as follows. In Section we dis- Clouds, or evidence for SMC stars in the stream of HI gas cuss the quality of the data, our process for creating an linking the LMC and SMC, referred to as the Magellanic astrometric reference frame, and how we quantify the Bridge. There is evidence for both young stars, presum- uncertainties in the PMs for each ﬁeld. We use these ably formed in situ (Harris 2007), and intermediate-age motions in Section , in conjunction with a dynamical stars in the Bridge (Nidever et al. 2013; Bagheri et al. model similar to the one in van der Marel et al. (2002), 2013; Skowron et al. 2014; Noël et al. 2015). Even old to analyze the measured PMs under various model as- stellar populations have been detected in the vicinity of, sumptions. This produces a set of best ﬁt parameters, but not aligned with, the gaseous Bridge (Belokurov & including measurements of the overall COM PM for the Koposov 2016; Deason et al. 2016; Belokurov et al. 2017; SMC and a measurement of the rotational velocity. In Carrera et al. 2017), adding support to the idea that the Section , we subtract the best-ﬁt COM motion to study SMC is being tidally stripped by the LMC. the internal motions of the SMC, both for all stars and Dias et al. (2016) studied the ages of star clusters by stellar type. We use the newly determined COM PM throughout the SMC, ﬁnding clear age and metallicity to constrain the SMC’s past orbit, and examine its inter- gradients consistent with tidal interactions between the actions with the LMC and MW in Section . Finally, we LMC and SMC. These results are supported by numeri- discuss the overall ramiﬁcations of the new SMC data for cal models of the Magellanic system which predict that our understanding of the Magellanic system and where Draft version May 31, 2020 the SMC should be constantly churning and only at large future studies will allow for further improvements in Sec- Preprint typeset using LATEX style emulateapj v. 01/23/15 radii would there potentially be a coherent rotation sig- tion . THE PROPER MOTION FIELD OF THE SMALL MAGELLANIC CLOUD: KINEMATIC EVIDENCE FOR ITS TIDAL DISRUPTION Paul Zivick 1, Nitya Kallivayalil1, Roeland P. van der Marel2,3, Gurtina Besla4, Sean T. Linden1, Szymon Kozłowski5, Tobias K. Fritz 1,6,7, C. S. Kochanek8,9, J. Anderson2, Sangmo Tony Sohn2, Marla C. Geha10, Charles R. Alcock11 0 1Department of Astronomy, University of Virginia, 530 McCormick Road, Charlottesville, VA 22904, USA; email: pjz2cf@virginia.edu 2 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA 3 Center for Astrophysical Sciences, Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA 4 Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA 5 Warsaw University Observatory Al. Ujazdowskie 400–478 Warszawa, Poland 6 Instituto de Astroﬁsica de Canarias, calle Via Lactea s/n, E-38205 La Laguna, Tenerife, Spain 7 Universidad de La Laguna, Dpto. Astroﬁsica, E-38206 La Laguna, Tenerife, Spain 8 Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA 9 Center for Cosmology and AstroParticle Physics, The Ohio State University, 191 W. Woodruﬀ Ave., Columbus, OH 43210, USA 10 Department of Astronomy, Yale University, New Haven, CT 06520, USA 11 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA Keywords: Galaxies: Kinematics and Dynamics, Galaxies: Magellanic Clouds 2. DATA & ANALYSIS presence of nearly 200 QSOs behind the SMC. From this set of QSOs, we selected 30 of the brightest QSOs (17.7 2.1. Description of Observations ≤ ≤ V 20.1 mag) to provide an inertial reference frame Kozłowski et al. (2013) spectroscopically conﬁrmed the across the two epochs of observations. The QSOs were also selected to provide roughly uniform coverage of the

label: paragraph

text: and

text: found

text: instead

text: a

text: rotation

text: signature

text: of

text: km

text: s

text: nature

text: (Besla

text: et

text: al.

text: A

text: comprehensive

text: study

text: of

text: the

text: kpc

text: although

text: their

text: line

text: of

text: nodes

text: did

text: not

text: agree

text: with

text: classical

text: Cepheids

text: in

text: the

text: SMC

text: (Ripepi

text: et

text: al.

text: found

text: that

text: found

text: by

text: Stanimirović

text: et

text: al.

text: To

text: complicate

text: a

text: complex

text: geometric

text: structure,

text: with

text: the

text: near

text: side

text: form-

text: the

text: picture

text: further,

text: Evans

text: Howarth

text: found

text: a

text: ing

text: a

text: rough

text: spheroidal

text: shape

text: before

text: gradually

text: shifting

text: similar

text: rotation

text: curve

text: to

text: Dobbie

text: et

text: al.

text: but

text: in

text: the

text: into

text: a

text: more

text: linear

text: shape,

text: adding

text: more

text: detail

text: to

text: the

text: SMC

text: young,

text: massive

text: star

text: population

text: (O,

text: B,

text: and

text: A

text: stars).

text: A

text: but

text: presenting

text: yet

text: another

text: potentially

text: conﬂicting

text: stellar

text: slight

text: velocity

text: gradient

text: was

text: also

text: found

text: for

text: the

text: OB

text: stars

text: structure.

text: from

text: Lamb

text: et

text: al.

text: While

text: one

text: could

text: argue

text: that

text: In

text: order

text: to

text: address

text: the

text: still

text: sparse

text: PM-coverage

text: of

text: the

text: red

text: giant

text: population

text: could

text: be

text: dynamically

text: decoupled

text: the

text: SMC,

text: we

text: obtained

text: two

text: epochs

text: of

text: HST

text: data

text: with

text: from

text: the

text: underlying

text: neutral

text: gas,

text: one

text: would

text: not

text: expect

text: for

text: ﬁelds

text: in

text: the

text: SMC,

text: focusing

text: on

text: ob-

text: the

text: same

text: to

text: have

text: happened

text: for

text: the

text: young

text: stars.

text: Dobbie

text: taining

text: data

text: in

text: the

text: outer

text: regions.

text: Combined

text: with

text: the

text: et

text: al.

text: proposed

text: an

text: inclined

text: disk

text: to

text: help

text: explain

text: data

text: already

text: available

text: from

text: and

text: for

text: the

text: the

text: diﬀerences,

text: but

text: further

text: kinematic

text: evidence

text: is

text: needed

text: interior

text: of

text: the

text: SMC,

text: this

text: provides

text: a

text: broader

text: kinematic

text: to

text: fully

text: evaluate

text: this

text: possibility.

text: view

text: of

text: the

text: SMC.

text: In

text: this

text: paper,

text: we

text: present

text: the

text: results

text: Because

text: of

text: the

text: interest

text: in

text: the

text: nature

text: of

text: the

text: past

text: mu-

text: from

text: this

text: combined

text: dataset,

text: and

text: their

text: implications

text: for

text: tual

text: interactions

text: of

text: the

text: Clouds,

text: many

text: photometric

text: stud-

text: the

text: orbital

text: history

text: of

text: the

text: SMC.

text: ies

text: have

text: searched

text: for

text: tidal

text: debris

text: at

text: large

text: radii

text: from

text: the

text: The

text: paper

text: is

text: organized

text: as

text: follows.

text: In

text: Section

text: we

text: dis-

text: Clouds,

text: or

text: evidence

text: for

text: SMC

text: stars

text: in

text: the

text: stream

text: of

text: HI

text: gas

text: cuss

text: the

text: quality

text: of

text: the

text: data,

text: our

text: process

text: for

text: creating

text: an

text: linking

text: the

text: LMC

text: and

text: SMC,

text: referred

text: to

text: as

text: the

text: Magellanic

text: astrometric

text: reference

text: frame,

text: and

text: how

text: we

text: quantify

text: the

text: Bridge.

text: There

text: is

text: evidence

text: for

text: both

text: young

text: stars,

text: presum-

text: uncertainties

text: in

text: the

text: PMs

text: for

text: each

text: ﬁeld.

text: We

text: use

text: these

text: ably

text: formed

text: in

text: situ

text: (Harris

text: and

text: intermediate-age

text: motions

text: in

text: Section

text: in

text: conjunction

text: with

text: a

text: dynamical

text: stars

text: in

text: the

text: Bridge

text: (Nidever

text: et

text: al.

text: Bagheri

text: et

text: al.

text: model

text: similar

text: to

text: the

text: one

text: in

text: van

text: der

text: Marel

text: et

text: al.

text: Skowron

text: et

text: al.

text: Noël

text: et

text: al.

text: Even

text: old

text: to

text: analyze

text: the

text: measured

text: PMs

text: under

text: various

text: model

text: as-

text: stellar

text: populations

text: have

text: been

text: detected

text: in

text: the

text: vicinity

text: of,

text: sumptions.

text: This

text: produces

text: a

text: set

text: of

text: best

text: ﬁt

text: parameters,

text: but

text: not

text: aligned

text: with,

text: the

text: gaseous

text: Bridge

text: (Belokurov

text: including

text: measurements

text: of

text: the

text: overall

text: COM

text: PM

text: for

text: the

text: Koposov

text: Deason

text: et

text: al.

text: Belokurov

text: et

text: al.

text: SMC

text: and

text: a

text: measurement

text: of

text: the

text: rotational

text: velocity.

text: In

text: Carrera

text: et

text: al.

text: adding

text: support

text: to

text: the

text: idea

text: that

text: the

text: Section

text: we

text: subtract

text: the

text: best-ﬁt

text: COM

text: motion

text: to

text: study

text: SMC

text: is

text: being

text: tidally

text: stripped

text: by

text: the

text: LMC.

text: the

text: internal

text: motions

text: of

text: the

text: SMC,

text: both

text: for

text: all

text: stars

text: and

text: Dias

text: et

text: al.

text: studied

text: the

text: ages

text: of

text: star

text: clusters

text: by

text: stellar

text: type.

text: We

text: use

text: the

text: newly

text: determined

text: COM

text: PM

text: throughout

text: the

text: SMC,

text: ﬁnding

text: clear

text: age

text: and

text: metallicity

text: to

text: constrain

text: the

text: SMC’s

text: past

text: orbit,

text: and

text: examine

text: its

text: inter-

text: gradients

text: consistent

text: with

text: tidal

text: interactions

text: between

text: the

text: actions

text: with

text: the

text: LMC

text: and

text: MW

text: in

text: Section

text: Finally,

text: we

text: LMC

text: and

text: SMC.

text: These

text: results

text: are

text: supported

text: by

text: numeri-

text: discuss

text: the

text: overall

text: ramiﬁcations

text: of

text: the

text: new

text: SMC

text: data

text: for

text: cal

text: models

text: of

text: the

text: Magellanic

text: system

text: which

text: predict

text: that

text: our

text: understanding

text: of

text: the

text: Magellanic

text: system

text: and

text: where

text: Draft

text: version

text: May

text: the

text: SMC

text: should

text: be

text: constantly

text: churning

text: and

text: only

text: at

text: large

text: future

text: studies

text: will

text: allow

text: for

text: further

text: improvements

text: in

text: Sec-

text: Preprint

text: typeset

text: using

text: LATEX

text: style

text: emulateapj

text: v.

text: radii

text: would

text: there

text: potentially

text: be

text: a

text: coherent

text: rotation

text: sig-

text: tion

text: THE

text: PROPER

text: MOTION

text: FIELD

text: OF

text: THE

text: SMALL

text: MAGELLANIC

text: CLOUD:

text: KINEMATIC

text: EVIDENCE

text: FOR

text: ITS

text: TIDAL

text: DISRUPTION

text: Paul

text: Zivick

text: Nitya

text: Roeland

text: P.

text: van

text: der

text: Gurtina

text: Sean

text: T.

text: Szymon

text: Tobias

text: K.

text: Fritz

text: C.

text: S.

text: J.

text: Sangmo

text: Tony

text: Marla

text: C.

text: Charles

text: R.

text: of

text: Astronomy,

text: University

text: of

text: Virginia,

text: McCormick

text: Road,

text: Charlottesville,

text: VA

text: USA;

text: email:

text: Space

text: Telescope

text: Science

text: Institute,

text: San

text: Martin

text: Drive,

text: Baltimore,

text: MD

text: USA

text: Center

text: for

text: Astrophysical

text: Sciences,

text: Department

text: of

text: Physics

text: Astronomy,

text: Johns

text: Hopkins

text: University,

text: Baltimore,

text: MD

text: USA

text: Steward

text: Observatory,

text: University

text: of

text: Arizona,

text: North

text: Cherry

text: Avenue,

text: Tucson,

text: AZ

text: USA

text: Warsaw

text: University

text: Observatory

text: Al.

text: Ujazdowskie

text: Warszawa,

text: Poland

text: Instituto

text: de

text: Astroﬁsica

text: de

text: Canarias,

text: calle

text: Via

text: Lactea

text: s/n,

text: La

text: Laguna,

text: Tenerife,

text: Spain

text: Universidad

text: de

text: La

text: Laguna,

text: Dpto.

text: Astroﬁsica,

text: La

text: Laguna,

text: Tenerife,

text: Spain

text: Department

text: of

text: Astronomy,

text: The

text: Ohio

text: State

text: University,

text: West

text: Avenue,

text: Columbus,

text: OH

text: USA

text: Center

text: for

text: Cosmology

text: and

text: AstroParticle

text: Physics,

text: The

text: Ohio

text: State

text: University,

text: W.

text: Woodruﬀ

text: Ave.,

text: Columbus,

text: OH

text: USA

text: Department

text: of

text: Astronomy,

text: Yale

text: University,

text: New

text: Haven,

text: CT

text: USA

text: Harvard-Smithsonian

text: Center

text: for

text: Astrophysics,

text: Garden

text: Street,

text: Cambridge,

text: MA

text: USA

text: Keywords:

text: Galaxies:

text: Kinematics

text: and

text: Dynamics,

text: Galaxies:

text: Magellanic

text: Clouds

text: DATA

text: ANALYSIS

text: presence

text: of

text: nearly

text: QSOs

text: behind

text: the

text: SMC.

text: From

text: this

text: set

text: of

text: QSOs,

text: we

text: selected

text: of

text: the

text: brightest

text: QSOs

text: Description

text: of

text: Observations

text: V

text: mag)

text: to

text: provide

text: an

text: inertial

text: reference

text: frame

text: Kozłowski

text: et

text: al.

text: spectroscopically

text: conﬁrmed

text: the

text: across

text: the

text: two

text: epochs

text: of

text: observations.

text: The

text: QSOs

text: were

text: also

text: selected

text: to

text: provide

text: roughly

text: uniform

text: coverage

text: of

text: the


text: SMC Kinematics 7 3. PROPER MOTION RESULTS −0.8 3.1. Model Design & Analysis This Work −0.9 Including the PM measurements from NK13 and NK13 vdMS16 with our new sample, we have a total of 41 −1.0 vdMS16 data points for describing the motion of the SMC. This aﬀords us the opportunity to consider the complicating −1.1 factor of motions internal to the SMC when attempting to determine the COM motion. As can be seen from −1.2 Figure 7, residual motions are present and signiﬁcant. −1.3 We ﬁx the radial velocity of the SMC at v = 145.6 ± − sys 0.6 km s 1 (Harris & Zaritsky 2006) and the distance −1.4 − ± modulus at m M = 18.99 0.1 (Cioni et al. 2000). We −1.5 additionally consider the impact of viewing perspective (projection eﬀects of the 3D COM motion) in the same −1.6 manner as van der Marel et al. (2002). While the SMC −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 only subtends ∼5 degrees on the sky, this eﬀect can con- µW (mas yr−1) ≤ − tribute up to 0.16 mas yr 1, a non-negligible fraction of the measured PMs. Figure 6. The measured proper motions for each ﬁeld (green), along with the earlier measurements by NK13 (cyan) and vdMS16 For the SMC center, we test two diﬀerent positions: ◦ ◦ (magenta). the HI kinematical center at (α,δ) = (16.25 , -72.42 ) (Stanimirović et al. 2004) and the center determined by are used to create mock data, using a Monte Carlo ap- the structure of the Cepheid population of the SMC at ◦ ◦ proach. As in NK13, these mock data are used to es- (α,δ) = (12.54 , -73.11 ) (Ripepi et al. 2017). With the timate the uncertainties in the best-ﬁt parameters for growing body of work suggesting a disconnect between the model. Each set of mock data are given uncertain- the stellar motions and the underlying HI gas, we felt ties, drawn from the the observational uncertainties but it prudent to examine the new stellar geometric center iTnhaedldocitaitoinontsootfhbeomthoroef tthraedseitcioenntaelrHs aIrdeysnhaomwincainl cFeingtuerre. sacnayleudn−bdyeraestfaimctaotre ooff(tχh2meinu/nNcdeorft)a1i/n2titeos,cwomhepreensNadteof fo=r 9. For the centers, we use a ﬁxed uncertainty of 0◦.2 for Nstadattisatic fNorpatrhame m+oNdeﬁlx.eWd, eagnedneχr2matine aisndthﬁet mmiunlitmipulemseﬁtst the position. of mock data, and then we use the dispersion in the pa- As discussed in Section , multiple LOS studies have rameters found as an estimate of the random uncertainty. found evidence for rotation in the SMC. To address this 3.2. Center of Mass Results possibility, we test for two diﬀerent rotation scenarios in our model. For one, we constrain the rotation velocity, The ﬁnal best ﬁt parameters for each of the four mod- ± − V = 0 40 km s 1, and for the second option, we els are listed in Table 2. We see that the choice of the rot allow V to be a free parameter. For both, we treat dynamical center does have an eﬀect on the estimated rot ∼ ∼ the rotation as rising out to a radius of 0.6 kpc and then COM PMs, diﬀering by 3σ in µ and by 2σ in µ . W N be constant after that. As a ﬁfth case, we also test for To reﬂect this uncertainty in the COM motion, we add allowing both V and the center position to be free a systematic error term to our ﬁnal PM measurement, rot parameters ﬁt. However, we ﬁnd that the data are un- which we deﬁne as the diﬀerence between the best ﬁt PM able to provide a useful constraint on the center position, values for the V free cases (see the discussion below). rot − − converging to a center close to the HI center but with an For µ this is 0.1 mas yr 1, and for µ is 0.03 mas yr 1. W N uncertainty of 4 degrees. Additionally, the choice of the center seems to aﬀect the Most of these LOS studies focused on the innermost likelihood of a detection of a rotation signature when two degrees of the SMC, an area that we do not sample V is allowed to be free. The HI center converges on rot ± − well. Instead, most of our statistical leverage comes from V = 12 4 km s 1, while the geometrically-determined rot ± − the outer regions of the SMC. As we are limited in our center is consistent with no rotation, V = 0 4 km s 1. rot sampling density, we opt to keep the inclination of the While the model using the H I center and allowing V ◦ rot model near 0 . In total, we have four cases to test, two to be free does formally produce the best ﬁt, the diﬀer- choices of the SMC center and two options for its internal ences are not signiﬁcant (see Table 2). This underscores rotation about each center. the diﬃculty of using a simple model to describe the po- For the COM PM itself, we leave it as a free parameter, tentially complex nature of the SMC internal kinematics. optimized by minimizing the model’s χ2 with respect to We choose the V free, H I center model for our ﬁnal rot the data. The ﬁt statistic is the same as used by van der estimate and comparison with previous studies (seen in Marel & Kallivayalil (2014), Table 3) because it formally has the smallest χ2 /N (cid:88) and most previous works have adopted the H Imdiynnamdoif- cal center1. All four of our new COM motion estimates ≡ M − are statistically consistent with the prior values found for χ2 [(µ µ )/∆µ ]2 PM W,obs,i W,mod,i W,obs,i (1) the SMC given the uncertainties. These is a slight oﬀ- i=1 set between our work and vdMS16 as compared to NK13 − +[(µ µ )/∆µ ]2, N,obs,i N,mod,i N,obs,i 1 We do examine the impact of this choice of dynamical center The resulting parameters for the minimized χ2 model on our subsequent orbital modeling. )1−ry sam( Nµ ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: SMC

text: Kinematics

label: section

text: PROPER

text: MOTION

text: RESULTS

font: default

text: Model

text: Design

text: Analysis

text: This

text: Work

text: Including

text: the

text: PM

text: measurements

text: from

text: and

text: with

text: our

text: new

text: sample,

text: we

text: have

text: a

text: total

text: of

text: data

text: points

text: for

text: describing

text: the

text: motion

text: of

text: the

text: SMC.

text: This

text: aﬀords

text: us

text: the

text: opportunity

text: to

text: consider

text: the

text: complicating

text: factor

text: of

text: motions

text: internal

text: to

text: the

text: SMC

text: when

text: attempting

text: to

text: determine

text: the

text: COM

text: motion.

text: As

text: can

text: be

text: seen

text: from

text: Figure

text: residual

text: motions

text: are

text: present

text: and

text: signiﬁcant.

text: We

text: ﬁx

text: the

text: radial

text: velocity

text: of

text: the

text: SMC

text: at

text: v

text: sys

text: km

text: s

text: (Harris

text: Zaritsky

text: and

text: the

text: distance

text: modulus

text: at

text: m

text: M

text: (Cioni

text: et

text: al.

text: We

text: additionally

text: consider

text: the

text: impact

text: of

text: viewing

text: perspective

text: (projection

text: eﬀects

text: of

text: the

text: COM

text: motion)

text: in

text: the

text: same

text: manner

text: as

text: van

text: der

text: Marel

text: et

text: al.

text: While

text: the

text: SMC

text: only

text: subtends

text: ∼5

text: degrees

text: on

text: the

text: sky,

text: this

text: eﬀect

text: can

text: con-

text: µW

text: (mas

text: tribute

text: up

text: to

text: mas

text: yr

text: a

text: non-negligible

text: fraction

text: of

text: the

text: measured

text: PMs.

text: Figure

text: The

text: measured

text: proper

text: motions

text: for

text: each

text: ﬁeld

text: (green),

text: along

text: with

text: the

text: earlier

text: measurements

text: by

text: (cyan)

text: and

text: For

text: the

text: SMC

text: center,

text: we

text: test

text: two

text: diﬀerent

text: positions:

text: (magenta).

text: the

text: HI

text: kinematical

text: center

text: at

text: (α,δ)

text: (Stanimirović

text: et

text: al.

text: and

text: the

text: center

text: determined

text: by

text: are

text: used

text: to

text: create

text: mock

text: data,

text: using

text: a

text: Monte

text: Carlo

text: ap-

text: the

text: structure

text: of

text: the

text: Cepheid

text: population

text: of

text: the

text: SMC

text: at

text: proach.

text: As

text: in

text: these

text: mock

text: data

text: are

text: used

text: to

text: es-

text: (α,δ)

text: (Ripepi

text: et

text: al.

text: With

text: the

text: timate

text: the

text: uncertainties

text: in

text: the

text: best-ﬁt

text: parameters

text: for

text: growing

text: body

text: of

text: work

text: suggesting

text: a

text: disconnect

text: between

text: the

text: model.

text: Each

text: set

text: of

text: mock

text: data

text: are

text: given

text: uncertain-

text: the

text: stellar

text: motions

text: and

text: the

text: underlying

text: HI

text: gas,

text: we

text: felt

text: ties,

text: drawn

text: from

text: the

text: the

text: observational

text: uncertainties

text: but

text: it

text: prudent

text: to

text: examine

text: the

text: new

text: stellar

text: geometric

text: center

text: iTnhaedldocitaitoinontsootfhbeomthoroef

text: tthraedseitcioenntaelrHs

text: aIrdeysnhaomwincainl

text: cFeingtuerre.

text: sacnayleudn−bdyeraestfaimctaotre

text: fo=r

text: For

text: the

text: centers,

text: we

text: use

text: a

text: ﬁxed

text: uncertainty

text: of

text: for

text: Nstadattisatic

text: fNorpatrhame

text: m+oNdeﬁlx.eWd,

text: aisndthﬁet

text: mmiunlitmipulemseﬁtst

text: the

text: position.

text: of

text: mock

text: data,

text: and

text: then

text: we

text: use

text: the

text: dispersion

text: in

text: the

text: pa-

text: As

text: discussed

text: in

text: Section

text: multiple

text: LOS

text: studies

text: have

text: rameters

text: found

text: as

text: an

text: estimate

text: of

text: the

text: random

text: uncertainty.

text: found

text: evidence

text: for

text: rotation

text: in

text: the

text: SMC.

text: To

text: address

text: this

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text: II. PROPOSED SYSTEM DESCRIPTION X=194.0 Y=-114.0 X=125.0 Y=19.0 X=64.0 Y=-97.0 With the use of mmWaves on MIMO systems, the resulting 0 0 0 >-50dBm multipath propagation is deﬁned by the used BF and the 10 10 10 existing obstacles. For 5G BSs, which are expected to be 20 20 20 located in elevated positions of urban scenarios, most of the 30 30 30 obstacles are static for a signiﬁcant amount of time, as they are -100dBm predominantly buildings. Therefore, successive measurements 40 40 40 of the received radiation pattern at a given position are 50 50 50 expected to remain comparable until a signiﬁcant change in 60 60 60 the surrounding area occurs. -150dBm 70 70 70 In order to infer the position from the hypothetical infor- 80 80 80 no_data mation contained in the received radiation, two requirements 0 20 0 20 0 20 have to be respected: i) the adopted transmitter BFs must Beamforming Index Beamforming Index Beamforming Index be constant, to culminate in an equivalent set of transmitted Fig. 2. Noiseless data samples from the experimental simulations, before radiation patterns, and ii) the target devices must be able removing low-power entries due to the detection threshold. Adjacent beam- to detect the transmitted radiation with the same detection forming patterns have a high probability of having similar patterns. scheme, to gather the required information. To comply with both requirements, the system depicted in Fig. 1 is proposed. It contains four distinct phases, as − labeled in the diagram, whose details are described bellow. d [n] = max y (nT), n = 0, 1, . . . , N 1, (2) b i Phase A will broadcast pulse waveforms using constant set i=1,...,BRx of radiation patterns, while phase B focuses on measuring the where T is the sampling period and N is the number of resulting radiation at the target device. After all the required samples to gather per BF. To be effective, T (and the pulse measurements are performed and transmitted to the BS, phase duration) must be smaller than 100 ns, as it will examined C infers the device’s position, which will be relayed back to in the following section. Nowadays smartphones can connect the device in phase D. to LTE networks with bandwidths exceeding 10 MHz, so, Phase A: Since mmWave transmissions must employ direc- in order to use the proposed system, no additional hardware tive (and therefore, narrow) beam patterns, a ﬁxed codebook should be required at a device with mmWave capabilities. with BTx BFs is proposed, so as to fully cover all possible Phases C and D: Upon obtaining the required data from all angles of transmission. Assuming a BS with N antennas, the S the BFs in the codebook (d), performing inference on a trained frequency-domain signal at the N mobile devices antennas ∈ R × R CNN will result in a position estimation. The proposed system y NR 1 can be written as can thus be considered ﬁngerprint-based, since the CNN must be trained with data from the possible positions. The inference y = Hfx + z, (1) can either be performed on the device, or at the base station (after transmitting the required data from the device, and where H ∈ CNR×NS is the channel matrix, f ∈ CNS×1 then reporting the result back to it). However, performing the denotes the currently selected beamforming, x ∈ C is the inference at the device has its limitations, since a CNN can waveform to be detected, and z ∈ CNR×1 is the noise. easily have millions of weights. In that case, the device would In order to avoid losing information due to destructive have to download (and store) all those weights each time it interference, the transmissions using those codebook entries connects to a new BS, or when a network is retrained. For should have a minor time interval between them (T ), to those reasons, we propose to perform the inference at the BS, guard account for longer paths with multiple reﬂections. as depicted in Fig. 1 Phase B: To capture the detail inherent to the radiation III. DATA ANALYSIS power over time patterns, the system must be able to measure The accuracy resulting from the proposed system ultimately the transmitted pulses at a high rate. As the data patterns must depends on the learning capabilities of the inference block. be consistent regardless of the target device, the sampling rate The system performance is thus determined by two factors: must be equal for all the receivers, and those receivers must be the data obtained in phase B and the learning method used in synchronized with the BS. Furthermore, if BF at the receiver phase C. is also included in the system, a speciﬁc array gain must also As mentioned in section II, the used pulse duration in be set for all receivers (to ensure consistency). In that case, the phase A and the measurement mechanism selected for phase receiver would also have to deﬁne a BF codebook to search B should be able to provide a temporal resolution exceeding over all AoAs with similar gain, containing B entries, and 100 ns. In such conditions, the received radiations will arrive Rx it would have to sample the original transmission B times, in clusters with voids large enough to be reliably detected Rx storing the maximum measured value for each data point. The [11], and the resulting data will be sparse (as it is observable acquired data from transmit BF b, d , can thus be written as in Fig. 2). The ability to distinguish these voids provides b rebmuN elpmaS rebmuN elpmaS rebmuN elpmaS ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

text: II.

text: PROPOSED

text: SYSTEM

text: DESCRIPTION

text: With

text: the

text: use

text: of

text: mmWaves

text: on

text: MIMO

text: systems,

text: the

text: resulting

text: multipath

text: propagation

text: is

text: deﬁned

text: by

text: the

text: used

text: BF

text: and

text: the

text: existing

text: obstacles.

text: For

text: BSs,

text: which

text: are

text: expected

text: to

text: be

text: located

text: in

text: elevated

text: positions

text: of

text: urban

text: scenarios,

text: most

text: of

text: the

text: obstacles

text: are

text: static

text: for

text: a

text: signiﬁcant

text: amount

text: of

text: time,

text: as

text: they

text: are

text: predominantly

text: buildings.

text: Therefore,

text: successive

text: measurements

text: of

text: the

text: received

text: radiation

text: pattern

text: at

text: a

text: given

text: position

text: are

text: expected

text: to

text: remain

text: comparable

text: until

text: a

text: signiﬁcant

text: change

text: in

text: the

text: surrounding

text: area

text: occurs.

text: In

text: order

text: to

text: infer

text: the

text: position

text: from

text: the

text: hypothetical

text: infor-

text: mation

text: contained

text: in

text: the

text: received

text: radiation,

text: two

text: requirements

text: have

text: to

text: be

text: respected:

text: i)

text: the

text: adopted

text: transmitter

text: BFs

text: must

text: Beamforming

text: Index

text: Beamforming

text: Index

text: Beamforming

text: Index

text: be

text: constant,

text: to

text: culminate

text: in

text: an

text: equivalent

text: set

text: of

text: transmitted

text: Fig.

text: Noiseless

text: data

text: samples

text: from

text: the

text: experimental

text: simulations,

text: before

text: radiation

text: patterns,

text: and

text: ii)

text: the

text: target

text: devices

text: must

text: be

text: able

text: removing

text: low-power

text: entries

text: due

text: to

text: the

text: detection

text: threshold.

text: Adjacent

text: beam-

text: to

text: detect

text: the

text: transmitted

text: radiation

text: with

text: the

text: same

text: detection

text: forming

text: patterns

text: have

text: a

text: high

text: probability

text: of

text: having

text: similar

text: patterns.

text: scheme,

text: to

text: gather

text: the

text: required

text: information.

text: To

text: comply

text: with

text: both

text: requirements,

text: the

text: system

text: depicted

text: in

text: Fig.

text: is

text: proposed.

text: It

text: contains

text: four

text: distinct

text: phases,

text: as

text: labeled

text: in

text: the

text: diagram,

text: whose

text: details

text: are

text: described

text: bellow.

text: d

text: [n]

text: max

text: y

text: (nT),

text: n

text: N

text: b

text: i

text: Phase

text: A

text: will

text: broadcast

text: pulse

text: waveforms

text: using

text: constant

text: set

text: of

text: radiation

text: patterns,

text: while

text: phase

text: B

text: focuses

text: on

text: measuring

text: the

text: where

text: T

text: is

text: the

text: sampling

text: period

text: and

text: N

text: is

text: the

text: number

text: of

text: resulting

text: radiation

text: at

text: the

text: target

text: device.

text: After

text: all

text: the

text: required

text: samples

text: to

text: gather

text: per

text: BF.

text: To

text: be

text: effective,

text: T

text: (and

text: the

text: pulse

text: measurements

text: are

text: performed

text: and

text: transmitted

text: to

text: the

text: BS,

text: phase

text: duration)

text: must

text: be

text: smaller

text: than

text: ns,

text: as

text: it

text: will

text: examined

text: C

text: infers

text: the

text: device’s

text: position,

text: which

text: will

text: be

text: relayed

text: back

text: to

text: in

text: the

text: following

text: section.

text: Nowadays

text: smartphones

text: can

text: connect

text: the

text: device

text: in

text: phase

text: D.

text: to

text: LTE

text: networks

text: with

text: bandwidths

text: exceeding

text: MHz,

text: so,

text: Phase

text: A:

text: Since

text: mmWave

text: transmissions

text: must

text: employ

text: direc-

text: in

text: order

text: to

text: use

text: the

text: proposed

text: system,

text: no

text: additional

text: hardware

text: tive

text: (and

text: therefore,

text: narrow)

text: beam

text: patterns,

text: a

text: ﬁxed

text: codebook

text: should

text: be

text: required

text: at

text: a

text: device

text: with

text: mmWave

text: capabilities.

text: with

text: BTx

text: BFs

text: is

text: proposed,

text: so

text: as

text: to

text: fully

text: cover

text: all

text: possible

text: Phases

text: C

text: and

text: D:

text: Upon

text: obtaining

text: the

text: required

text: data

text: from

text: all

text: angles

text: of

text: transmission.

text: Assuming

text: a

text: BS

text: with

text: N

text: antennas,

text: the

text: S

text: the

text: BFs

text: in

text: the

text: codebook

text: (d),

text: performing

text: inference

text: on

text: a

text: trained

text: frequency-domain

text: signal

text: at

text: the

text: N

text: mobile

text: devices

text: antennas

text: R

text: R

text: CNN

text: will

text: result

text: in

text: a

text: position

text: estimation.

text: The

text: proposed

text: system

text: y

text: NR

text: can

text: be

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text: 45 45 1.0 Binary Data 40 Floating-Point Data 40 0.8 35 35 30 30 Zoomed CDF, excluding the last 10% 0.6 0.8 25 25 20 20 0.6 0.4 15 15 0.4 Median: 10 10 0.2 0.2 6.07665 95th percentile: 5 5 31.6179 0.0 0 5 10 15 0 0 0.0 0 2 4 6 8 10 0 50 100 150 200 Noise (dB) Error (m) Fig. 4. Average and 95th percentile prediction errors for the proposed Fig. 5. CDF of the prediction errors, considering binary data samples and a system, for multiple log-normal modeled noise levels, depicted by its standard noise σ of 6 dB. The least accurate predictions are very inaccurate, and thus deviation (σ). For larger noise values, using binary data resulted in improved the average error is larger than the median error. performance. of said radiation could help to pinpoint the receiver. In Fig. in Fig. 2. Regarding the BF at the receiver, a 10 dBi gain 4, the proposed system accuracy is plotted against multiple was considered, akin to the mmWave mobile device tested in noise levels, for the original (ﬂoating-point) simulation data [15], which is able to cover most of the receive directions and for a binary version of the same data. For the assessed employing a codebook with 16 elements. The resulting data was labeled with the corresponding bidimensional position, in binary dataset, the average error rages from 6.2 m (noiseless a area centered at the base station. data) to 12.1 m (σ = 10 dB), with a 95th percentile error When noise is considered in the proposed system, it is never exceeding 35.3 m. As for the ﬂoating-point dataset, the added to the ray-tracing data following a log-normal distri- average error rages from 4.3 m to 13.6 m, with a maximum bution. This happens before discarding any data entry below 95th percentile error of 40.4 m. Therefore, from the obtained − results, it is possible to conclude that using binary data is the detection threshold of 100 dBm (selected due to the actually helpful for the CNN at higher noise regimes. thermal noise for the considered bandwidth). If the simulated system considers a binary detection of the received signal, In Fig. 5, the cumulative distribution function (CDF) for the the simulation data is transformed after adding the noise and binary dataset with moderate noise (σ = 6 dB) is shown. From passing through the detection threshold. This data is then the CDF, its is observable that the least accurate predictions are sampled for each position that contains at least one non-zero very inaccurate, explaining the signiﬁcant difference between entry, so as to create a training set (for each CNN training the median and the average errors (6.1 m and 10.6 m, respec- epoch, a new training set is generated). Since the system is tively). For this conﬁguration, the predictions have a RMSE of expected to be used to predict positions for which it already 22.1 m, which denotes superior performance when compared has samples, the test set is generated as the training set. When to the RMSE of 35 m obtained in [9] (which also considers evaluating the average results, a total of 10 test sets are used. a lower noise, with σ = 5 dB). However, it is important to The selected CNN follows a traditional architecture, whose point out that the numerical simulations performed in [9] do hyperparameters were selected after empirical tests, also taking not contain NLOS positions. in account the total execution time (the training takes less than To explain the inaccurate predictions, Fig. 6 plots the error 8 hours in a Nvidia GTX 780 Ti, using Google’s TensorFlow against the number of detected (non-zero) entries per sample, framework). The system can thus be summarized as depicted for the aforementioned dataset and noise parameters. The in table II1. general trend is a lower average error with an increasing V. SIMULATION RESULTS number of detected entries per sample. Furthermore, it is important to notice that when a sample contains fewer than When working with the proposed system, the data for- 10 non-zero entries, the average prediction error soars due mat must be carefully selected, since it manages a trade-off to the lack of information in the received data, explain- between achievable performance and hardware requirements. ing the last percentiles of the CDF. Therefore, due to the While employing a binary detection of the received radiation mmWave propagation characteristics, the presence of multiple is far simpler, obtaining the information regarding the power paths between the transmitter and the receiver enhances the information perceived by the proposed system, resulting in 1The simulation code and used data are available on https://github.com/gante/mmWave-localization-learning improved predictions. 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text: Binary

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text: last

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text: percentile:

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text: Error

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text: Fig.

text: Average

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text: proposed

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text: CDF

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