text: 10 Metzger & Pejcha ∼ − − from M 11 to 14. These so-called SPRITES (eSPecially codes due to long timescales involved, (potentially) insuﬃcient res- V Red Intermediate-luminosity Transient Events) are characterized olution near the stellar surface, and possible radiative/thermal pro- by a wide range of photometric evolution rates, corresponding to cesses that control the runaway of the binary (which are not typ- timescales as short as months or as long as several years. Our re- ically modeled). Sustained pre-dynamical mass loss furthermore sults suggest that stellar mergers of giant stars, with particularly implies that initial conditions for the dynamical phase are likely − long pre-dynamical mass loss phases (trun ∼> 10 100torb), repre- to be substantially diﬀerent than currently assumed, due to changes sent an attractive explanation for the SPRITE phenomenon. These in the envelope of the stars caused by the preceding phase of grad- events may have been optically-bright brieﬂy near the point of the ual mass loss. All of these aspects informing the appropriate “ini- dynamical merger, but their time interval as unobscured optical tial conditions” for numerical studies can be constrained by devel- transients could be very short compared to the bulk of the latter oping more sophisticated models for shock-powered emission in shock-powered, infrared-bright phase. Potentially supporting pic- LRN. These will more tightly constrain M , M , and their rela- ej w ture is the discovery of shock-excited molecular hydrogen emis- tive velocity from the timing and luminosity of the secondary light sion from SPIRITS 14ajc, which Kasliwal et al. (2017) propose curve peak, combined with constraints on the ejecta velocity struc- could have resulted from the merger of a proto-stellar binary. The ture from spectroscopy. object OGLE2002-BLG-360 (Tylenda et al. 2013) might represent MacLeod et al. (2017) interpret the ﬁrst peak of M31 LRN ∼ − a low-mass counterpart to SPRITES. 2015 as being due to cooling envelope emission of 10 2M(cid:12) of 5 DISCUSSION AND CONCLUSION fast ejecta driven at the onset, and they interpret the later plateau- shaped emission as being powered by hydrogen recombination of a Previous work has interpreted the late phase of LRN emis- ∼ larger ejecta mass 0.3M(cid:12) to power the later recombination-driven sion as being powered by hydrogen recombination (Ivanova et al. plateau. In our picture, both components of emission result from a 2013; MacLeod et al. 2017). However, the required ejecta masses singular mass ejection event created during the dynamical phase in some cases are quite large: MacLeod et al. (2017) estimate that − of the merger. The low inferred mass of the “fast” ejecta, which the 100 200 day emission of M101 OT2015-1 requires an ejecta − contributes to the earliest emission phase, is a simple byproduct of mass of 1 10M(cid:12), close to the entire mass of the binary. In our the typical density proﬁle of an dynamical explosion (eq. 3), which shock-powered scenario, the same luminosity can be powered by a places only a small fraction of the total mass at high velocities (as much lower ejecta ∼mass ∼< M(cid:12) since the energ∼y per gram of shock- commonly inferred also in Type IIP supernovae). Supporting our powered emission v2 greatly exceeds the 1 Rydberg per par- interpretation of this event is pre-outburst photometry showing ev- esc ticle supplied by hydrogen recombination. idence for pre-dynamical mass loss (Dong et al. 2015). Ultimately, If the optical LRN can be explained by the ejection of rela- the luminosity and duration of the ﬁrst light curve peak constrains ∼ tively small amount of mass Mej 0.1M then this would imply the initial thermal energy and quantity of the fastestest expanding that most of the current sample are likely to be bona ﬁde stellar dynamically-ejected matter. mergers, in which most of the envelope is retained. Furthermore, We have discussed scenarios for producing the second light the progenitors of LRN are consistent with being relatively com- curve peaks, which are commonly but not ubiquitously observed pact stars near the main sequence and not red (super)giants. Merg- in LRN (Fig. 1). LRN without second peaks include V1309 Sco § ers of the latter, more evolved stars are likely to appear signiﬁcantly and M31 LRN 2015. In we described how a second plateau could redder, dustier, and longer in duration, consistent with the observed possibly be avoided if the shocks are insuﬃcient to keep the ejecta properties of SPRITEs (Kasliwal et al. 2017). Given the limited hot enough to stay ionized until the nominal Arnett peak timescale information available on the ﬁnal outcome of LRN, it is unclear (eq. 21). In this case the resulting drop in opacity results in rapid whether these events completely eject their envelope, leaving be- cooling of the ejecta and dust formation, precluding a true optical hind a tight binary pair. Direct detection of the surviving binary - peak (though the plateau-shaped emission prior to this point may or even a single merger remnant - is challenging due to lingering still be shock-powered, and a secondary peak may still occur in the presence (and perhaps continual production) of dust. The prolonged infrared). Another possible explanation for lack of a plateau is due 3.6 and 4.5µm emission from M101 OT2015-1 and NGC 4490-OT to the inﬂuence of viewing angle. V1309 Sco was likely observed (Blagorodnova et al. 2017; Smith et al. 2016) hints that a continuum near the binary equatorial plane (Tylenda et al. 2011), in which of transient properties may exist between SPRITES and LRN. case equatorially-concentrated dust formation in the pre-dynamical § In order to reproduce the light curves of LRN, we require that mass loss or shock-compressed gas ( ) could result in obscuration the total amount of mass loss from the binary during the dynam- of the shock-powered emission peak (which diﬀuses out through ∼ ical and pre-dynamical phases are roughly comparable, i.e. M the lower density polar regions; Fig. 2). In the latter case the dense ∼ ej Mw 0.1M. Such a substantial amount of pre-dynamical mass shell would need to reside near or above the optical photosphere of loss is potentially surprising within the current “common enve- the fast ejecta; future work should address possible emission line lope” paradigm, which dictates that the most important phases of signatures of these exposed shocks. the merger process occurs only once the binary loses co-rotation From the sample of LRN light curves in Figure 1, an apparent with - and begins to feel hydrodynamical drag on - the envelope. correlation exists between the shock-powered emission peak and Indeed, the pre-dynamical mass loss required by our models would the time interval between the peaks. Comparing equation (21) and ∝ alone be suﬃcient to carry away the angular momentum required (23), for shock-powered emission we predict t M1/4a1/4 and ∝ − pk to merge the binary, if this matter leaves the binary with the same L M5/2a 5/2. A positive correlation between t and L would pk pk pk speciﬁc angular momentum of the L2 point. therefore suggest that binary mass instead of semi-major axis is a Our results also have implications for the ability of numeri- primary candidate for the variable driving this relationship. How- cal simulation to address the stellar merger problem. The accumu- ever, this apparent correlation could also be shaped by selection lation of slowly-expanding or quasi-stationary circumbinary wind eﬀects: mergers of wide (large a) binaries may suﬀer early dust material, released over many orbital periods, would be very chal- formation, making them observable only as SPRITES instead of lenging to study using typical common envelope hydrodynamical optically-luminous LRN (Fig. 6). (cid:13) c 2017 RAS, MNRAS 000, 1–12

text: Metzger

text: Pejcha

text: from

text: M

text: to

text: These

text: so-called

text: SPRITES

text: (eSPecially

text: codes

text: due

text: to

text: long

text: timescales

text: involved,

text: (potentially)

text: insuﬃcient

text: res-

text: V

text: Red

text: Intermediate-luminosity

text: Transient

text: Events)

text: are

text: characterized

text: olution

text: near

text: the

text: stellar

text: surface,

text: and

text: possible

text: radiative/thermal

text: pro-

text: by

text: a

text: wide

text: range

text: of

text: photometric

text: evolution

text: rates,

text: corresponding

text: to

text: cesses

text: that

text: control

text: the

text: runaway

text: of

text: the

text: binary

text: (which

text: are

text: not

text: typ-

text: timescales

text: as

text: short

text: as

text: months

text: or

text: as

text: long

text: as

text: several

text: years.

text: Our

text: re-

text: ically

text: modeled).

text: Sustained

text: pre-dynamical

text: mass

text: loss

text: furthermore

text: sults

text: suggest

text: that

text: stellar

text: mergers

text: of

text: giant

text: stars,

text: with

text: particularly

text: implies

text: that

text: initial

text: conditions

text: for

text: the

text: dynamical

text: phase

text: are

text: likely

text: long

text: pre-dynamical

text: mass

text: loss

text: phases

text: (trun

text: repre-

text: to

text: be

text: substantially

text: diﬀerent

text: than

text: currently

text: assumed,

text: due

text: to

text: changes

text: sent

text: an

text: attractive

text: explanation

text: for

text: the

text: SPRITE

text: phenomenon.

text: These

text: in

text: the

text: envelope

text: of

text: the

text: stars

text: caused

text: by

text: the

text: preceding

text: phase

text: of

text: grad-

text: events

text: may

text: have

text: been

text: optically-bright

text: brieﬂy

text: near

text: the

text: point

text: of

text: the

text: ual

text: mass

text: loss.

text: All

text: of

text: these

text: aspects

text: informing

text: the

text: appropriate

text: “ini-

text: dynamical

text: merger,

text: but

text: their

text: time

text: interval

text: as

text: unobscured

text: optical

text: tial

text: conditions”

text: for

text: numerical

text: studies

text: can

text: be

text: constrained

text: by

text: devel-

text: transients

text: could

text: be

text: very

text: short

text: compared

text: to

text: the

text: bulk

text: of

text: the

text: latter

text: oping

text: more

text: sophisticated

text: models

text: for

text: shock-powered

text: emission

text: in

text: shock-powered,

text: infrared-bright

text: phase.

text: Potentially

text: supporting

text: pic-

text: LRN.

text: These

text: will

text: more

text: tightly

text: constrain

text: M

text: M

text: and

text: their

text: rela-

text: ej

text: w

text: ture

text: is

text: the

text: discovery

text: of

text: shock-excited

text: molecular

text: hydrogen

text: emis-

text: tive

text: velocity

text: from

text: the

text: timing

text: and

text: luminosity

text: of

text: the

text: secondary

text: light

text: sion

text: from

text: SPIRITS

text: which

text: Kasliwal

text: et

text: al.

text: propose

text: curve

text: peak,

text: combined

text: with

text: constraints

text: on

text: the

text: ejecta

text: velocity

text: struc-

text: could

text: have

text: resulted

text: from

text: the

text: merger

text: of

text: a

text: proto-stellar

text: binary.

text: The

text: ture

text: from

text: spectroscopy.

text: object

text: (Tylenda

text: et

text: al.

text: might

text: represent

text: MacLeod

text: et

text: al.

text: interpret

text: the

text: ﬁrst

text: peak

text: of

text: LRN

text: a

text: low-mass

text: counterpart

text: to

text: SPRITES.

text: as

text: being

text: due

text: to

text: cooling

text: envelope

text: emission

text: of

text: of

text: DISCUSSION

text: AND

text: CONCLUSION

text: fast

text: ejecta

text: driven

text: at

text: the

text: onset,

text: and

text: they

text: interpret

text: the

text: later

text: plateau-

text: shaped

text: emission

text: as

text: being

text: powered

text: by

text: hydrogen

text: recombination

text: of

text: a

text: Previous

text: work

text: has

text: interpreted

text: the

text: late

text: phase

text: of

text: LRN

text: emis-

text: larger

text: ejecta

text: mass

text: to

text: power

text: the

text: later

text: recombination-driven

text: sion

text: as

text: being

text: powered

text: by

text: hydrogen

text: recombination

text: (Ivanova

text: et

text: al.

text: plateau.

text: In

text: our

text: picture,

text: both

text: components

text: of

text: emission

text: result

text: from

text: a

text: MacLeod

text: et

text: al.

text: However,

text: the

text: required

text: ejecta

text: masses

text: singular

text: mass

text: ejection

text: event

text: created

text: during

text: the

text: dynamical

text: phase

text: in

text: some

text: cases

text: are

text: quite

text: large:

text: MacLeod

text: et

text: al.

text: estimate

text: that

text: of

text: the

text: merger.

text: The

text: low

text: inferred

text: mass

text: of

text: the

text: “fast”

text: ejecta,

text: which

text: the

text: day

text: emission

text: of

text: requires

text: an

text: ejecta

text: contributes

text: to

text: the

text: earliest

text: emission

text: phase,

text: is

text: a

text: simple

text: byproduct

text: of

text: mass

text: of

text: close

text: to

text: the

text: entire

text: mass

text: of

text: the

text: binary.

text: In

text: our

text: the

text: typical

text: density

text: proﬁle

text: of

text: an

text: dynamical

text: explosion

text: (eq.

text: which

text: shock-powered

text: scenario,

text: the

text: same

text: luminosity

text: can

text: be

text: powered

text: by

text: a

text: places

text: only

text: a

text: small

text: fraction

text: of

text: the

text: total

text: mass

text: at

text: high

text: velocities

text: (as

text: much

text: lower

text: ejecta

text: ∼mass

text: since

text: the

text: energ∼y

text: per

text: gram

text: of

text: shock-

text: commonly

text: inferred

text: also

text: in

text: Type

text: IIP

text: supernovae).

text: Supporting

text: our

text: powered

text: emission

text: greatly

text: exceeds

text: the

text: Rydberg

text: per

text: par-

text: interpretation

text: of

text: this

text: event

text: is

text: pre-outburst

text: photometry

text: showing

text: ev-

text: esc

text: ticle

text: supplied

text: by

text: hydrogen

text: recombination.

text: idence

text: for

text: pre-dynamical

text: mass

text: loss

text: (Dong

text: et

text: al.

text: Ultimately,

text: If

text: the

text: optical

text: LRN

text: can

text: be

text: explained

text: by

text: the

text: ejection

text: of

text: rela-

text: the

text: luminosity

text: and

text: duration

text: of

text: the

text: ﬁrst

text: light

text: curve

text: peak

text: constrains

text: tively

text: small

text: amount

text: of

text: mass

text: Mej

text: then

text: this

text: would

text: imply

text: the

text: initial

text: thermal

text: energy

text: and

text: quantity

text: of

text: the

text: fastestest

text: expanding

text: that

text: most

text: of

text: the

text: current

text: sample

text: are

text: likely

text: to

text: be

text: bona

text: ﬁde

text: stellar

text: dynamically-ejected

text: matter.

text: mergers,

text: in

text: which

text: most

text: of

text: the

text: envelope

text: is

text: retained.

text: Furthermore,

text: We

text: have

text: discussed

text: scenarios

text: for

text: producing

text: the

text: second

text: light

text: the

text: progenitors

text: of

text: LRN

text: are

text: consistent

text: with

text: being

text: relatively

text: com-

text: curve

text: peaks,

text: which

text: are

text: commonly

text: but

text: not

text: ubiquitously

text: observed

text: pact

text: stars

text: near

text: the

text: main

text: sequence

text: and

text: not

text: red

text: (super)giants.

text: Merg-

text: in

text: LRN

text: (Fig.

text: LRN

text: without

text: second

text: peaks

text: include

text: Sco

text: ers

text: of

text: the

text: latter,

text: more

text: evolved

text: stars

text: are

text: likely

text: to

text: appear

text: signiﬁcantly

text: and

text: LRN

text: In

text: we

text: described

text: how

text: a

text: second

text: plateau

text: could

text: redder,

text: dustier,

text: and

text: longer

text: in

text: duration,

text: consistent

text: with

text: the

text: observed

text: possibly

text: be

text: avoided

text: if

text: the

text: shocks

text: are

text: insuﬃcient

text: to

text: keep

text: the

text: ejecta

text: properties

text: of

text: SPRITEs

text: (Kasliwal

text: et

text: al.

text: Given

text: the

text: limited

text: hot

text: enough

text: to

text: stay

text: ionized

text: until

text: the

text: nominal

text: Arnett

text: peak

text: timescale

text: information

text: available

text: on

text: the

text: ﬁnal

text: outcome

text: of

text: LRN,

text: it

text: is

text: unclear

text: (eq.

text: In

text: this

text: case

text: the

text: resulting

text: drop

text: in

text: opacity

text: results

text: in

text: rapid

text: whether

text: these

text: events

text: completely

text: eject

text: their

text: envelope,

text: leaving

text: be-

text: cooling

text: of

text: the

text: ejecta

text: and

text: dust

text: formation,

text: precluding

text: a

text: true

text: optical

text: hind

text: a

text: tight

text: binary

text: pair.

text: Direct

text: detection

text: of

text: the

text: surviving

text: binary

text: peak

text: (though

text: the

text: plateau-shaped

text: emission

text: prior

text: to

text: this

text: point

text: may

text: or

text: even

text: a

text: single

text: merger

text: remnant

text: is

text: challenging

text: due

text: to

text: lingering

text: still

text: be

text: shock-powered,

text: and

text: a

text: secondary

text: peak

text: may

text: still

text: occur

text: in

text: the

text: presence

text: (and

text: perhaps

text: continual

text: production)

text: of

text: dust.

text: The

text: prolonged

text: infrared).

text: Another

text: possible

text: explanation

text: for

text: lack

text: of

text: a

text: plateau

text: is

text: due

text: and

text: emission

text: from

text: and

text: NGC

text: to

text: the

text: inﬂuence

text: of

text: viewing

text: angle.

text: Sco

text: was

text: likely

text: observed

text: (Blagorodnova

text: et

text: al.

text: Smith

text: et

text: al.

text: hints

text: that

text: a

text: continuum

text: near

text: the

text: binary

text: equatorial

text: plane

text: (Tylenda

text: et

text: al.

text: in

text: which

text: of

text: transient

text: properties

text: may

text: exist

text: between

text: SPRITES

text: and

text: LRN.

text: case

text: equatorially-concentrated

text: dust

text: formation

text: in

text: the

text: pre-dynamical

text: In

text: order

text: to

text: reproduce

text: the

text: light

text: curves

text: of

text: LRN,

text: we

text: require

text: that

text: mass

text: loss

text: or

text: shock-compressed

text: gas

text: could

text: result

text: in

text: obscuration

text: the

text: total

text: amount

text: of

text: mass

text: loss

text: from

text: the

text: binary

text: during

text: the

text: dynam-

text: of

text: the

text: shock-powered

text: emission

text: peak

text: (which

text: diﬀuses

text: out

text: through

text: ical

text: and

text: pre-dynamical

text: phases

text: are

text: roughly

text: comparable,

text: i.e.

text: M

text: the

text: lower

text: density

text: polar

text: regions;

text: Fig.

text: In

text: the

text: latter

text: case

text: the

text: dense

text: ej

text: Mw

text: Such

text: a

text: substantial

text: amount

text: of

text: pre-dynamical

text: mass

text: shell

text: would

text: need

text: to

text: reside

text: near

text: or

text: above

text: the

text: optical

text: photosphere

text: of

text: loss

text: is

text: potentially

text: surprising

text: within

text: the

text: current

text: “common

text: enve-

text: the

text: fast

text: ejecta;

text: future

text: work

text: should

text: address

text: possible

text: emission

text: line

text: lope”

text: paradigm,

text: which

text: dictates

text: that

text: the

text: most

text: important

text: phases

text: of

text: signatures

text: of

text: these

text: exposed

text: shocks.

text: the

text: merger

text: process

text: occurs

text: only

text: once

text: the

text: binary

text: loses

text: co-rotation

text: From

text: the

text: sample

text: of

text: LRN

text: light

text: curves

text: in

text: Figure

text: an

text: apparent

text: with

text: and

text: begins

text: to

text: feel

text: hydrodynamical

text: drag

text: on

text: the

text: envelope.

text: correlation

text: exists

text: between

text: the

text: shock-powered

text: emission

text: peak

text: and

text: Indeed,

text: the

text: pre-dynamical

text: mass

text: loss

text: required

text: by

text: our

text: models

text: would

text: the

text: time

text: interval

text: between

text: the

text: peaks.

text: Comparing

text: equation

text: and

text: alone

text: be

text: suﬃcient

text: to

text: carry

text: away

text: the

text: angular

text: momentum

text: required

text: for

text: shock-powered

text: emission

text: we

text: predict

text: t

text: and

text: pk

text: to

text: merge

text: the

text: binary,

text: if

text: this

text: matter

text: leaves

text: the

text: binary

text: with

text: the

text: same

text: L

text: A

text: positive

text: correlation

text: between

text: t

text: and

text: L

text: would

text: pk

text: pk

text: pk

text: speciﬁc

text: angular

text: momentum

text: of

text: the

text: point.

text: therefore

text: suggest

text: that

text: binary

text: mass

text: instead

text: of

text: semi-major

text: axis

text: is

text: a

text: Our

text: results

text: also

text: have

text: implications

text: for

text: the

text: ability

text: of

text: numeri-

text: primary

text: candidate

text: for

text: the

text: variable

text: driving

text: this

text: relationship.

text: How-

text: cal

text: simulation

text: to

text: address

text: the

text: stellar

text: merger

text: problem.

text: The

text: accumu-

text: ever,

text: this

text: apparent

text: correlation

text: could

text: also

text: be

text: shaped

text: by

text: selection

text: lation

text: of

text: slowly-expanding

text: or

text: quasi-stationary

text: circumbinary

text: wind

text: eﬀects:

text: mergers

text: of

text: wide

text: (large

text: a)

text: binaries

text: may

text: suﬀer

text: early

text: dust

text: material,

text: released

text: over

text: many

text: orbital

text: periods,

text: would

text: be

text: very

text: chal-

text: formation,

text: making

text: them

text: observable

text: only

text: as

text: SPRITES

text: instead

text: of

text: lenging

text: to

text: study

text: using

text: typical

text: common

text: envelope

text: hydrodynamical

text: optically-luminous

text: LRN

text: (Fig.

text: c

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text: A&A proofs: manuscript no. Calissendorﬀ_J1036 (Hormuth et al. 2008) on the 2.2m telescope at Calar Alto in by vibrational motions of the telescope, which causes the com- Spain, along with the AstraLux Sur camera (Hippler et al. 2009) ponents to appear stretched out. In order to obtain good enough on the ESO/NTT 3.5m telescope at La Silla in Chile. We ob- astrometric measurements we apply the primary component A tain one of the epochs in this study from Daemgen et al. (2007)2, as a reference PSF. This works, since A is suﬃciently separated where the Gemini North/Altair natural guide star adaptive optics from the BC pair so that the PSFs are isolated, and we assume the was used. A more detailed description of the individual astrom- stretching of the image to behave similarly for all three compo- etry measurements is presented in Table 1. nents. This technique provides us with smaller residuals by typ- AstraLux multiplicity observations employ the same proce- ically one third compared to convolving a single star PSF with dures as described by Daemgen et al. (2009); Bergfors et al. a stretched out Gaussian or earlier PSF ﬁtting by Janson et al. (2013) where a total integration time of 300 s is obtained by (2012). adding up short individual readouts, typically of 15-30 ms. Sub- Calibration of the astrometric measurements is done by com- array readouts are often utilised in order to minimise readout paring AstraLux and Hubble Space Telescope (HST) observa- times and obtain the short integrations, which number range be- tions of the Orion Trapezium Cluster and M15 from McCaugh- tween 10 000 to 20 000. The full frame ﬁeld of view under nor- rean & Stauﬀer (1994); van der Marel et al. (2002) as refer- ≈ (cid:48)(cid:48) × (cid:48)(cid:48) mal circumstances for AstraLux Norte is 24 24 , and for ence astrometry. The astrometric measurements are shown in ≈ (cid:48)(cid:48) × (cid:48)(cid:48) AstraLux Sur 15.7 15.7 . The AstraLux observations are Table 1 together with the angle of true North and the pixel scale (cid:48) mainly performed in the SDSS z -band but in some cases also for the AstraLux observations. Astrometric errors listed are de- (cid:48) (cid:48) in the i -band. We primarily use the z -band images for the as- termined from standard mean deviations of statistical measure- trometric analysis here because they are of higher quality and ments added quadratically with the calibration uncertainties pre- (cid:48) aﬀected by less atmospheric refraction in comparison to the i - sented in the same table. band (Bergfors et al. 2010). Data reduction for AstraLux is formed with the pipeline that 2.1. Age, distance and group membership is described by Hormuth et al. (2008), identical to previous As- traLux surveys (e.g. Bergfors et al. 2010; Janson et al. 2012, Knowing the age of the stellar components is imperative 2014, 2016). Several Lucky Imaging outputs are produced by when placing young stars in a mass-luminosity diagram, espe- the reduction pipeline and we select 10% of the frames which cially at very young ages when the characteristics of the star has the best seeing for further analyses, which provides a good changes drastically (Baraﬀe et al. 1998, 2015). Previous stud- trade-oﬀ between resolution and sensitivity. ies of J1036 assumes an age between 35 – 300 Myr, based on young moving group association and stellar evolutionary mod- els (Daemgen et al. 2007; Shkolnik et al. 2009, 2012). Shkolnik et al. (2012) place J1036 in the Ursa Major Moving Group (UMa MG) with a 42% membership probability with the velocity space − ± parameters UVWJ1036 = (15.1, 2.4, 7.4) (1.2, 1.0, 0.7) km/s. Klutsch et al. (2014) obtain a higher membership probability of 94% by using a more rigorous statistical approach and dif- ferent UVW for the UMa MG. The discrepancy in member- A ship probability is likely to originate from the diﬀerent kinemat- ics for the UMa MG. Comparing with the nucleus of the UMa MG estimated by Mamajek et al. (2010) as UVW = − ± UManucleus (15.0, 2.8, 8.1) (0.4, 0.7, 1.0) km/s suggests that the system is 1'' a bona ﬁde member. The estimated parallax distance to J1036 of ± C 20.1 2.0 is also≈consistent with the distance to the nucleus of the UMa MG of 25 pc. X-ray luminosities can also be used as an indicator for youth B among stellar populations, where young, low-mass stars that have yet to move onto the main sequence usually exhibit more X-ray emission than their older counterparts (Stahler & Palla 2005). Using the X-ray luminosity from the ROSAT catalogues (Voges et al. 1999, 2000), Shkolnik et al. (2009) set an upper (cid:48) ∼ Fig. 1. Reduced z -ﬁlter image of 2MASS J10364483+1521394 ob- limit for the age of J1036 as 300 Myr. This upper age limit is tained with AstraLux Norte at Calar Alto, Spain, in November 2008. consistent with earlier estimates of the age of the UMa MG of The separation between A and B is roughly 1”, and the separation be- ∼ 300 Myr by Soderblom & Mayor (1993). However, the age of tween B and C is 150 mas (cf. Table 1). The orientation in the image the moving group has since been discussed and revised several is North up and East to the left. times and the now more accepted age is 500 Myr (e.g. King et (cid:48)(cid:48) al. 2003; King & Schuler 2005; Brandt & Huang 2015). Jones As the system is quite compact (separations of (cid:46) 1 ), we et al. (2015) use interferometric measurements and modelling of use Point Spread Function (PSF) ﬁtting to determine the relative A type stars in Ursa Major to determine a more precise and con- astrometric positions and angles between the components. Nor- ± sistent age of 414 23 Myr. Nevertheless, the X-ray and UV mally, we would use a single star as a reference PSF to iteratively emissions from J1036 imply signs of youth by showing simi- produce binary conﬁgurations that minimise the squared residu- lar trends as other low-mass stars of comparable spectral type in als of the ﬁt. However, the later three observed epochs taken be- the UMa MG (e.g. 2MASS J11240434+3808108). Furthermore, tween 2015 and 2016 with the AstraLux Sur camera are aﬀected the X-ray emission exhibited by J1036 is also similar to that of 2 The position angle is shifted exactly 360 ◦ compared to the literature systems associated with other young moving groups of diﬀer- value (see Table 2 in Daemgen et al. 2007). ent ages ranging between 25 and 600 Myr, for example 2MASS Article number, page 2 of 9 ##LTFigure## ##LTFigure## ##LTLine## ##LTLine##

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text: A&A proofs: manuscript no. Calissendorﬀ_J1036 0.20 3000 No constraints 2008.88 2016.38 2500 DPhyontaommiecatrli cm masasss 0.15 2008.03 2015.90 2015.16 B+C CM A 2009.13 2006.38 2000 0.10 1500 1000 0.05 500 0.00 0 500 0.05 Periastron 1000 2011 Jul 13 0.10 1500 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 2000 1500 1000 500 0 500 1000 1500 Offset in R.A. [mas] Offset in R.A. [mas] Fig. 2. Best-ﬁt orbit of C around B in the rest frame of B. The ascending and descending nodes are marked by the dash-dotted line and the peri- 500 astron by the dashed line. The ellipses mark the errors of the observed positions, with red lines connecting the observed positions with the cal- culated orbit. The orbital motions is counter-clockwise, as depicted by 600 the arrow. Table 2. Best orbital solution parameters for B–C 700 800 Orbital Element Value Periastron date T0 2455756 +−326 900 (2011 Jul 13) PSeermioi-dmPaj(oyreaaxrsi)s a (mas) 81.6411 +−+−002..0042 1000 OBCrbit of CM 2 Distance to CM Semi-major axis a (AU) 3.2 +−0.3 1100 0.3 0 100 200 300 400 500 600 700 Eccentricity e 0.460 +−0.005 Offset in R.A. [mas] ◦ 0.007 Argument of periastron ω (◦ ) 68 +−32 Fig. 3. Motion of J1036 B and C centre of mass in the reference frame P.A. of ascending node Ω ( ) 90.0 +−0.4 of J1036 A. Upper plot shows the full estimated period of the centre of ◦ 0.3 mass between B and C around A for our ﬁt using no mass constraints Inclination i ( ) 45.4 +−30..89 (dashed), our dynamical mass of the system as Mest,dyn = 1.0 ± 0.3 M(cid:12) SDyissttaenmcemearsrsorM(MB+(cid:12)C)(mas3/year2) 59330±+−22000.0010044 (0s.o6l5id±)0a.2ndMth(cid:12)e. Tphheotloomweertrpiclomt daespsiecststitmheatseamofetahsethsyesatebmoveasbuMt ezsot,pohmote=d in on the observed data points where the ellipsis depicts the errors of the System mass MB+C (M(cid:12)) 0.482 +−00..114455 B (green) and C (blue) component positions. Th≈e bro◦wn lines connect reduced χ2 1.0 B and C to the computed centre of mass. Only 35 of the full orbit has been covered and thus may not be well represented here. make our prediction of the orbit with an already predetermined suggest that near-equal mass companions are common3, but this mass. This procedure does not provide us with any new informa- may be one of the few cases where the precision of the ratio is tion of the mass, as what we put in is the value that will come out so close to unity. of the ﬁt. The orbital ﬁtting procedure is the same as described The orbit of the BC pair around A is onl≈y partially covered above with an additional(cid:32)term to the co(cid:33)mputation of the χ2 of the and a naive best-ﬁt orbit yields a period of 100 years, shown form by the dashed line in the upper plot of Figure 3. The correspond- − ing system mass exceeds 2 M(cid:12), which seems too high and very M M 2 mod est unlikely in comparison to the dynamical mass estimate of the 0.3 M(cid:12) other components B and C and their relative measured bright- ness. Nevertheless, following the same approach as Köhler et al. where the orbit model system mass is Mmod and the esti- (2013) we can constrain the estimated mass of the orbital ﬁt, and mate of the mass we plug in is Mest. We run the orbital ﬁt for 3 scenarios: without any mass constraint, with the dynamical 3 In their paper, Daemgen et al. (2007) count J1036 twice; ﬁrst as the mass estimate as a constraint, and with a photometric mass es- A-BC pair, then also the B–C pair. timate as a constraint. 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text: a single pair of lensed images. With deeper, higher- resolution imaging data, we would detect more strongly- lensed systems and achieve constraints similar to the CLASH or the HFF analyses (?), where many more lensed systems have been identiﬁed from HST imag- ing. Yet, even with a single lensed image pair, we add meaningful constraints to the properties of the main J0850 cluster, a result with implications for the lensing ﬁelds identiﬁed in wide-area photometric surveys such as the Large Synoptic Survey Telescope (LSST). Follow-up space-based observations of large numbers of clusters will be prohibitively expensive, and it may be neces- sary to rely on a limited number of constraints from ground-based data alone, as we have done here. Figure ?? is a magniﬁcation map of the J0850 ﬁeld for a source redshift of z = 5.03 using the best model from − S Fig. 11.— Mvir cvir relation for massive clusters. The main our combined strong and weak lensing analysis. This J0850 cluster (blue star) is plotted in comparison to the CLASH best model shows characteristics similar to that of the sample of X-ray-selected clusters (black points; ?). Also shown ensemble distribution, such as a large ellipticity and a is the relation determined from simulations (red line; ?, assuming the Planck cosmology). The comparison samples are at similar position angle slightly East of North. The small inﬂu- masses and redshifts. The cluster has a concentration consistent ence of the foreground halo can be seen in the southeast- with both the CLASH and simulation results. The uncertainties ern part of the magniﬁcation map, but it does not aﬀect for the CLASH clusters are slightly larger than ours due to the the majority of the high-magniﬁcation region. The large inclusion of systematic errors arising from diﬀerent model param- eterizations. area of intermediate-to-high magniﬁcation further sug- gests that this ﬁeld is an excellent candidate to search factor of two (cvir = 3.46+−00..7509). Past results from sim- for highly-magniﬁed high-redshift galaxies. ulations and observations have shown that dark matter To give a sense of the uncertainty in the magniﬁcation halos parameterized as NFW proﬁles show a negative maps, we show similar maps for several other successful correlation between halo mass and concentration (e.g, models in our sample in Figure ??. Despite the diversity, ??????) as a consequence of hierarchical structure for- the successful models have the same general shape and a mation. It is also known that lensing-selected clusters large area of intermediate-to-high magniﬁcation. can show a bias toward higher concentrations at a given 4.3. Highly-magniﬁed Fold Arc mass due to their triaxial shapes and projection eﬀects As noted in Section ??, the majority of our successful (e.g., ??????). In Figure ??, we show the virial mass and strong lens models have the northern image of the lensed concentration of the main J0850 cluster in comparison to ≈ z 5.03 background galaxy lying across a lensing caus- theoretical and observational results from the literature tic (Figure ??). This conﬁguration is quite diﬀerent from for comparable mass and redshift ranges. The cluster the typical method of producing a close pair of lensed im- has a concentration consistent with those of the CLASH ages in which the source lies near but not across a lensing X-ray-selected clusters (?) and derived from simulations caustic and each image is of the entire source. The part (?) assuming the Planck cosmology28. This ﬁeld was se- of the source that lies inside the lensing caustic has an lected by LRG luminosity density rather than by lensing, extremely large magniﬁcation: the overall magniﬁcation so the cluster should not suﬀer from an overconcentration for the northern arc is µ = 118 for our best model, and bias due to projection eﬀects, Thus, it is not surprising the factor is even higher (µ > 1000) for portions of the to ﬁnd a relatively typical concentration for its mass. image close to the critical curve. Past observations of The addition of the strong lensing constraint shifts the ∼ (cid:48)(cid:48) cluster lenses have revealed arcs with extreme magniﬁ- cluster centroid 17 in the direction of the ? cen- cations near the critical curves, but these have almost troid, which was determined from the average position always been at lower redshifts since higher redshift ob- of the spectroscopically conﬁrmed cluster members. The jects are often intrinsically smaller. Our model predicts likely explanation is that the weak lensing alone pro- that J0850 is a unique ﬁeld in which a source is both at vides a noisy centroid measurement, as the central re- high redshift and is highly magniﬁed, which is very rare. gions of the cluster are ignored (Section ??). The ad- ∼ (cid:48)(cid:48) Our model indicates that the small ( 0. 1) region of dition of the strong lensing constraint adds information the source that lies within the caustic is elongated into from these central regions, allowing a more accurate mea- ∼ (cid:48)(cid:48) a 1. 75 image, potentially allowing us to study fea- sure of the mass centroid, as can be seen in the smaller tures at physical scales of < 30 pc with suﬃciently high- uncertainty. It is likely that constraints from additional resolution observations. Thus, this unique conﬁguration multiply-imaged systems, particularly those at diﬀerent could provide new insights into resolved star formation ≈ locations along the tangential critical curve, will greatly and stellar populations at z 5. imDprraovfte vtheresicoenntMroaiyd3d0e, t2e0r2m0ination. The additional constraints provided by the strong lensing information in this analysis are coming from just 28 Our assumed cosmology is slightly diﬀerent from the Planck cosmology, but this diﬀerence has a negligible eﬀect on the mass- concentration relation in Figure ??. ##LTFigure## ##LTFigure##

text: a

text: single

text: pair

text: of

text: lensed

text: images.

text: With

text: deeper,

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text: cluster,

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text: identiﬁed

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text: Follow-up

text: space-based

text: observations

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text: large

text: numbers

text: of

text: clusters

text: will

text: be

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text: it

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text: limited

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text: data

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text: here.

text: Figure

text: is

text: a

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text: map

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text: the

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text: redshift

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text: z

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text: Fig.

text: Mvir

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text: relation

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text: massive

text: clusters.

text: The

text: main

text: our

text: combined

text: strong

text: and

text: weak

text: lensing

text: analysis.

text: This

text: cluster

text: (blue

text: star)

text: is

text: plotted

text: in

text: comparison

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text: the

text: CLASH

text: best

text: model

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text: characteristics

text: similar

text: to

text: that

text: of

text: the

text: sample

text: of

text: X-ray-selected

text: clusters

text: (black

text: points;

text: Also

text: shown

text: ensemble

text: distribution,

text: such

text: as

text: a

text: large

text: ellipticity

text: and

text: a

text: is

text: the

text: relation

text: determined

text: from

text: simulations

text: (red

text: line;

text: assuming

text: the

text: Planck

text: cosmology).

text: The

text: comparison

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text: position

text: angle

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text: North.

text: The

text: small

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text: masses

text: and

text: redshifts.

text: The

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