The Ophiuchus stream progenitor: a new type of globular cluster and its possible Sagittarius connection
James M. M. Lane, Julio F. Navarro, Azadeh Fattahi, Kyle A. Oman, Jo Bovy
MMNRAS , 1–11 (2019) Preprint 31 May 2019 Compiled using MNRAS L A TEX style file v3.0
The Ophiuchus stream progenitor: a new type of globularcluster and its possible Sagittarius connection
James M. M. Lane , (cid:63) , Julio F. Navarro , Azadeh Fattahi , , Kyle A. Oman , ,Jo Bovy Department of Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4, Canada Department of Physics & Astronomy, University of Victoria, 3800 Finnerty Road, Victoria, BC V8P 5C2, Canada Institute for Computational Cosmology, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK Kapteyn Astronomical Institute, University of Groningen, Postbus 800, NL-9700 AV Groningen, The Netherlands
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
The Ophiuchus stream is a short arc-like stellar feature of uncertain origin located ∼ kpc North of the Galactic centre. New proper motions from the second Gaia data release reconcile the direction of motion of stream members with the stream arc,resolving a puzzling mismatch reported in earlier work. We use N-body simulationsto show that the stream is likely only on its second pericentric passage, and thus wasformed recently. The simulations suggest that the entire disrupted progenitor is visiblein the observed stream today, and that little further tidal debris lies beyond the endsof the stream. The luminosity, length, width, and velocity dispersion of the streamsuggest a globular cluster (GC) progenitor substantially fainter and of lower surfacebrightness than estimated in previous work, and unlike any other known globulars inthe Galaxy. This result suggests the existence of clusters that would extend the knownGC population to fainter and more weakly bound systems than hitherto known. Howsuch a weakly-bound cluster of old stars survived until it was disrupted so recently,however, remains a mystery. Integrating backwards in time, we find that the orbitsof Sagittarius and Ophiuchus passed within ∼ kpc of each other about ∼ Myrsago, an interaction that might help resolve this puzzle.
Key words: globular clusters: general – Galaxy: evolution – Galaxy: kinematics anddynamics – Galaxy: structure – Galaxy: halo – galaxies: dwarf
Recent wide-field imaging campaigns have revealed numer-ous examples of stellar streams in the halo of the MilkyWay (MW) that span a wide range of scales, from the wideremains of the Sagittarius dwarf spheroidal (dSph), whichwraps more than once around the sky (Majewski et al.2003; Belokurov et al. 2006), to relatively short, thin tailsthat emerge from globular clusters (GCs) such as Palomar5 (Odenkirchen et al. 2001).Kinematically cold, thin streams are particularly inter-esting, since they place the tightest contraints on the MWgravitational potential (e.g. Bovy et al. 2016). Their mor-phology may also provide clues to the existence of low-massdark matter sub-haloes which, although invisible, may in- (cid:63)
E-mail: [email protected] duce stream ‘gaps’ through gravitational interaction (Ibataet al. 2002; Johnston et al. 2002; Bovy et al. 2017).The Ophiuchus stream is a short, thin overdensity ofstars discovered by Bernard et al. (2014, hereafter B14)in the Pan-STARRS1 3 π survey (Kaiser et al. 2010). Thestream is located at ( l , b ) ≈ ( . ◦ , + ◦ ) , and subtends ∼ . degrees in length and ∼ arcmin in width. The mainsequence is clearly identifiable in deep color-magnitude dia-grams of the region, although the sparsely populated redgiant branch is barely discernible amid the stellar fore-ground/background. B14 found that the stream’s colour-magnitude profile was well approximated by the isochroneof an old metal-poor globular cluster (namely NGC 5904)at a distance of ∼ . kpc from the Sun, suggesting a tidallydisrupted globular cluster.Sesar et al. (2015, hereafter S15) obtained spectra for ∼ potential stream stars, out of which 14 were identifiedas stream members based on their radial velocities. Theseauthors concurred that the stream likely originated from a c (cid:13) a r X i v : . [ a s t r o - ph . GA ] M a y J. M. M. Lane et al. metal-poor globular cluster with an age and [ Fe/H ] of aboutand 11.7 Gyr and -1.95, respectively. They concluded thatthe stream, which lies almost directly north of the Galac-tic centre, is highly forshortened in projection, with a truelength of about 1.5 kpc. Using radial velocities and propermotions, they integrated an orbit for the stream in a MilkyWay-like potential and inferred that it must have disruptedaround 240 Myr ago.Such recent disruption is difficult to reconcile with theold ages of Ophiuchus’ constituent stars. No bound core hasbeen identified within its extent or near its orbital path, sug-gesting that the stream is highly evolved and has completeda number of orbits around the Galaxy. In contrast, the shortdeprojected length of the stream suggests the opposite; i.e.,that the stream is dynamically young, and has completedvery few orbits. This paradox has motivated a number ofpossible scenarios.One is that the stream has been shortened by the grav-itational influence of the Galactic bar. Indeed, Sesar et al.(2016) identified 4 blue horizontal branch stars projectednear the end of the stream that have radial velocities dis-tinct from the stream, but still unusual for halo stars atthat location ( v los > km s − ). These authors interpretedthose stars as stream members that may have ‘fanned out’through non-linear interactions with the bar. Stream ‘fan-ning’ may be enough to disperse the stream ends below de-tectability, causing the stream to appear shorter than it trulyis. Price-Whelan et al. (2016) reached similar conclusions af-ter exploring the effects of bar-induced chaotic orbits on theproperties of a stream like Ophiuchus. Finally, Hattori et al.(2016) argued that the bar may have a ‘shepherding’ effecton the Ophiuchus stream, allowing it to remain at a fixedlength for 1 Gyr or more, which is many times longer thanthe disruption time predicted by S15.While these studies suggest that the Galactic bar mayhave played an important role on the evolution of the Ophi-uchus stream, their results are highly sensitive to the massof the bar and its exact pattern speed, as well as to the dy-namical age and previous evolution of the stream, none ofwhich are known well enough to reach definitive and reliableconclusions.A simpler alternative is that the progenitor was origi-nally so weakly bound that it completely disrupted in justa few orbits, leaving behind a short tidal tail and no boundcore. This is indeed the scenario explored by S15, who es-timated for the progenitor a stellar mass of ∼ × M (cid:12) ,and a velocity dispersion of ∼ . km s − . These propertiesimply a rather large size, unusual for a typical GC. Anotherdifficulty is that a system so weakly bound cannot have or-bited the Galaxy in its present orbit more than a few times,raising questions about its origin. Presumably the progen-itor formed in a very different orbit and has only recently,perhaps as a result of interactions with a Galactic satellite,reached its present-day orbit.The work presented here examines these issues furtherby carefully analyzing the tidal remnants of a large numberof possible progenitors, spanning a large range in GC stel-lar mass and size/velocity dispersion. Detailed comparisonwith observations allows us to revise earlier constraints onthese parameters, suggesting that the most likely progeni-tor GC was even more unusual in its properties, deepeningthe mystery of its origin. Although we do not consider the L o g ( R / / p c ) C o n s t a n t L / R (M prog / M ) L o g ( l o s / k m s ) MWMW no M31S15S15-NB M V [mag] L o g ( l o s R / / k m s p c ) Figure 1.
The globular clusters of the Milky Way (circles, fromHarris 1996), M31 (crosses, from Huxor et al. 2014; Peacock et al.2010), and the S15 and S15-NB progenitors shown in three param-eter spaces as functions of their absolute magnitude. Clusters withblue symbols have line-of-sight velocity dispersion measurements.
Top: projected half-light radius as a function of the absolute mag-nitude. The grey dashed lines show constant surface brightness.The grey outline shows the range of progenitor properties studiedin this work.
Middle:
Velocity dispersion as a function of the ab-solute magnitude for those clusters which have velocity dispersionmeasurements.
Bottom:
Dynamical mass as a function of the ab-solute magnitude for those clusters which have velocity dispersionmeasurements. The cluster mass shown on the top axis is calcu-lated assuming a mass-to-light ratio of 1.45. In all three panelsthe grey shaded box shows the range of magnitudes excluded bythe observed luminosity of the stream. effects of the Galactic bar in this work, we do explore thepossibility that Ophiuchus may have interacted in the recentpast with the Sagittarius dwarf, offering a possible clue tothe resolution of this puzzle in future work.The paper is arranged as follows: in Section 2 we de-scribe our simulations and models for both the cluster andthe Milky Way potential. Section 3 describes the streamanalysis procedure, while Section 4 explains how the proper-ties of simulated streams are derived. Section 4.2, in partic-
MNRAS , 1–11 (2019) he Ophiuchus stream progenitor Y [ k p c ] Present DayApocenterPericenterAp2Ap3Ap4SunGalactic Center
10 0 10X [kpc]10010 Z [ k p c ]
10 0 10Y [kpc]
Figure 2.
Orbit of the Ophiuchus stream over the last
Myr ingalactocentric Cartesian coordinates. Squares and triangles markapocentric and pericentric passages, respectively. The colouredsquares are the apocentres where we begin simulations. The solid,dashed, and dotted lines cumulatively show the orbit startingfrom the second, third and fourth most recent apocentric pas-sages. The black circle marks the present-day location of thestream. The black cross and orange dot mark the positions of theSun at ( − . , , ) , and the Galactic centre at ( , , ) , respectively. ular, explores the possibility that Ophiuchus has interactedwith the Sagittarius dwarf spheroidal (dSph). We summarizeour findings in Section 5. We model each globular cluster progenitor as a particlerealization of a Plummer (1911) model with density profile, ρ ( r ) = ρ P / ( + r / r ) / , where ρ P = M / ( π r ) . The N-bodyinitial conditions are realized using the Zeno toolkit . Weassume that the GC contains only stars, which implies thatits physical properties are set by the mass, M , and scaleradius, r P , of our model, from which the velocity dispersionfollows. We set the gravitational softening to . times thePlummer scale radius, and allow the N-body system to relaxin isolation for many cluster crossing times before evolvingit in the Galactic potential. We begin by considering the progenitor models presentedin S15. These authors consider two different models, whoseproperties are listed in Table 1 and are shown, by the redsquare and triangle, in Figure 1. Masses in Figure 1 refer https://github.com/joshuabarnes/zeno Table 1.
Properties of the progenitor globular clusters from S15.Progenitor Name Mass (M (cid:12) ) r / (pc) σ vlos (km s − )S15 ×
90 0.40S15–NB ×
29 0.50 to the total stellar mass of the cluster ( M V is the absolutemagnitude assuming a mass-to-light ratio of . M (cid:12) L (cid:12)− ),R / is the 2D projected half-mass radius (calculated as 3/4times the 3D half-mass radius), and σ los is the line-of-sightvelocity dispersion.The properties of the progenitor labelled ‘S15’ are takenfrom table 1 of S15. The half-mass radius is derived follow-ing equation (2) of Wolf et al. (2010) for the relationshipbetween mass, radius and velocity dispersion in spherical,dispersion-supported systems. Model S15-NB is a King pro-file of mass of M (cid:12) , tidal radius of 94 pc, and ratio ofcentral potential to velocity dispersion squared of 2.0. Theseproperties imply a concentration parameter of 0.5 (see fig-ure 4.9 in Binney & Tremaine 2008) and therefore a half-mass radius of approximately 29 pc. Using the mass-radius-velocity dispersion relations of Wolf et al. (2010) this impliesa velocity dispersion of 0.5 km s − . In addition to S15 and S15-NB, we explore a grid of GCmodels in the space of total mass and half-mass radius.More specifically, we consider Plummer models with half-mass radii between pc and pc, and masses between × M (cid:12) and × M (cid:12) . We sample this range of param-eters, shown in Figure 1, in 0.2 dex intervals. In addition,for clusters less massive than × M (cid:12) we also examineradii up to 250 pc, for a total of candidate progenitors.The lower mass boundary is motivated by the totalluminosity of the stream, which according to B14, is ∼ . ± . × L (cid:12) . At a mass of × M (cid:12) the selectedrange of half-mass radii correspond to a range of line-of-sight velocity dispersions between 0.37 and 1.2 km s − , andat × M (cid:12) the range of dispersions is between 0.11 and0.37 km s − . This range comfortably spans the 68 per centconfidence interval derived by S15 for the velocity dispersionof the progenitor. To model of the Galactic potential we follow S15 and use the3-component Milky Way potential
MWPotential2014 fromthe galactic dynamics package galpy (Bovy 2015). Thispotential consists of a Miyamoto & Nagai (1975) disc, anexponentially truncated power law density profile for thebulge, and an NFW halo (Navarro et al. 1997). For a fulllist of the physical parameters that describe this model werefer the reader to section 3.5 and table 1 of Bovy (2015).S15 report that the stream traces an orbit in this poten-tial, with consistent radial velocities. They also estimatedproper motions using 2MASS and archival photographic https://github.com/jobovy/galpy MNRAS , 1–11 (2019)
J. M. M. Lane et al. b [ d e g ] M2E3-R63-Ap2270280290300310 v l o s [ k m s − ] Stream membersFanned stream members l [deg] . . . . . D i s t a n ce [ k p c ] − − − − Surface density [ N MSTO /arcsec ] Figure 3.
Kinematics of the M2E3-R63-Ap2 progenitor streamas a function of Galactic longitude. The top, middle and bottompanels show the Galactic latitude, heliocentric radial velocity, anddistance. The colour scale in the top panel shows number surfacedensity of N-body particles expressed as
MSTO stars, while in thebottom two panels the particles are individually shown as blackdots. The red circles are the confirmed stream members from S15.The thick black line in the top panel is the best-fitting quadraticto the stream extent. The red crosses show the candidate fannedstream members from Sesar et al. (2016), which do not have mea-sured distances. Arrows mark fanned stream candidates that lieoutside of the plotting window. Our simulated streams match theobservations well in all of the observed coordinates. plate observations and reported that, for the inferred dis-tance of the stream, the resulting 3D velocities were mis-aligned with the stream, suggesting an inconsistency be-tween the stream and the Galactic model. However, accurateproper motions for the stream stars have recently becomeavailable from the
Gaia second data release (DR2 Gaia Col-laboration et al. 2018a). We have obtained proper motions
Table 2.
Present-day kinematics of the Ophiuchus stream fromS15. Parameter Value l ◦ b ◦ d (cid:12) v los − µ l -7.7 mas yr − µ b − for the 14 stream members from the Gaia
DR2 archive andfound them to be consistent with the orbit of S15, neatlyresolving this tension. For more information about streammember kinematics from Gaia
DR2 see Appendix A. Theorbital parameter values are summarized in Table 2; we referthe reader to S15 for a full discussion of their derivation andthe associated uncertainties.
To simulate the disruption of the progenitors of the Ophi-uchus stream we use the
Gadget-2 code (Springel 2005),after including a static
MWPotential2014 potential. The ini-tial conditions for the simulations were derived using thepresent-day orbit discussed above, after evolving it back-wards in time for 4 full radial periods. (The radial period ofthe orbit is 240 Myr.)Figure 2 shows the orbital path over the last
Myr.We ran each of our GC models three times, starting at thesecond, third, or fourth most recent apocentric passage, de-noted as Ap2, Ap3 and Ap4, respectively. The locations oftheir starting points are marked with the coloured squares inFigure 2. The duration of the simulations are t = , ,and Myr for Ap2, Ap3 and Ap4, respectively. Theseintegrations are short enough that our use of a static Galac-tic potential is a reasonable approximation to the MilkyWay potential over time. Each simulation is halted when thestream reaches its present day position for comparison withthe observed stream. Throughout the remainder of the pa-per our naming convention is such that, for example, M2E3-R63-Ap2 refers to a progenitor mass of × M (cid:12) , halfmass radius of 63 pc, evolved from the second most recentapocentre. We mock-observe our simulated streams by converting themto Galactic coordinates and observing them from the Sun’slocation. Particles in the simulation are used to render ac-tual stars using a Chabrier IMF and a sampling proceduredescribed in detail in Appendix B. This procedure allows usto associate total stellar mass at some sky location with adirect observable, such as the total number of main sequenceturnoff (MSTO) stars. In Appendix B1 we assess the poten-tial impact of the flattening of the stellar mass function due https://gea.esac.esa.int/archive/ MNRAS , 1–11 (2019) he Ophiuchus stream progenitor − −
15 0 15 30 B [arcmin]050100150200 N M S T O S15S15-NBM2E3-R63-Ap2B14 − − N M S T O Figure 4.
Histograms of MSTO star counts along the length and width of the simulated streams. The dark red dashed and dottedhistograms show the S15 and S15-NB models, respectively. The black shaded histogram shows the observations from B14. For comparisonthe stream M2E3-R63-Ap2 is shown in blue, which is clearly a better match to the data than the S15 or S15-NB models. to the impact of tides and the internal dynamical evolutionof the cluster.Figure 3 illustrates the mock observation procedure forone particular stream, M2E3-R63-Ap2. This figure shows,as a function of Galactic longitude, l , the Galactic latitude, b , the heliocentric line-of-sight velocity V los , and the helio-centric distance of stream stars. Confirmed stream membersfrom S15 are shown as red circles.It is clear that our simulated streams match the overallmorphology of the observed stream quite well. The radialvelocities of member stars appear to have greater scatterthan the simulated stream, but this is due mainly to obser-vational uncertainties, which are of order ∼ km s − rms.The red crosses in this figure show, for completeness, the‘fanned’ stream candidates from Sesar et al. (2016) (threeof which have velocities outside the plot limits). We do notexpect our models to match the kinematics of these stars. Each of the simulated stream profiles in projection may beapproximated by a quadratic polynomial, as shown by thesolid line in the top panel of Figure 3. When fitting thepolynomial to the ensemble of N-body particles we weightthe fit by the inverse of the projected surface density. Oncethe polynomial is fit we can rectify the stream to a referencesystem where parameters like the length and width of thestream can be meaningfully measured and compared withobservations. In this new coordinate system the ‘latitude’ B measures the minimum distance from each star to the fit andthe longitude coordinate Λ measures the arc length along the quadratic polynomial from a reference position, chosenas the median Galactic longitude of all stream particles.Using these new coordinates, and the conversion be-tween N-body particle mass and MSTO stars detailed inAppendix B, we calculate below the length and width of oursimulated streams following the approach of B14 (see theirfigure 3). The stream length and width are estimated from histogramsof the number of MSTO stars along both the Λ and B di-rections (Figure 4). For the histogram, all particles between − ◦ < Λ < ◦ are used. Similarly, for Λ all particles between − < B < are used. The gray histogram in eachplot is observational data from B14.A stellar background has been added to each of thesimulated streams in order to mimic foreground and back-ground stars in the observations of B14. The purpose of thebackground is to ensure that our determination of streamparameters is as faithful to those of B14 as possible. Thebackground noise is assumed Gaussian with a mean of N and standard deviation of √ N , where N is estimated fromfigure 3 in B14. For the figure showing B , we use a meanof N = and for Λ we use a mean that decreases linearlyfrom N = at Λ = to N = at Λ = − to account for thelatitude dependence of foreground stars.To determine the width of the stream we follow B14and fit a Gaussian to the B histogram using a least-squaresmethod, and take the FWHM (approximately 2.355 times MNRAS , 1–11 (2019)
J. M. M. Lane et al. the standard deviation). The length is estimated by startingat the peak of the Λ histogram and moving towards bothhigher and lower values of Λ until a bin with a value be-low the local noise is reached (without considering the back-ground) on each side of the peak. The length is taken as thedifference between these two stream–noise limits.The number of MSTO stars in the stream, S MSTO , isestimated by summing both the B and Λ histograms be-tween the stream–noise limits (also calculated for the B his-togram but not related to the reported width), after cor-recting for the expected number of background stars. Inpractice, the correction involves drawing repeated samplesof the foreground and background stars, and averaging thefinal results. The uncertainty in the resulting mean S MSTO is much smaller than the observational uncertainty, ensuringthat any difference between observed and simulated streamparameters is not due to the artificial background.The line-of-sight velocity dispersion is determined foreach simulated stream by measuring the radial velocity dis-persion of the particles in individual × binsprojected on the sky (the same bins shown in the top panel ofFigure 3). These individual measurements are then weightedby the particle surface density in the bin and averaged toproduce a velocity gradient-independent measurement of theline-of-sight velocity dispersion for the whole stream. Thisis similar to the manner in which S15 measured the intrinsicvelocity dispersion of the observed stream.We note that the only uncertainties involved in our anal-ysis arise from the uncertainty in the fit to the B histogramand the determination of the velocity dispersion. The un-certainty in the width arises from the least-squares fit, andfor most streams is of order . The uncertainty in thevelocity dispersion is the standard deviation of the individ-ual velocity dispersion samples, and ranges from less than0.1 km s − for lower mass progenitors to about 0.5 km s − for higher mass progenitors. By design of the backgroundsubtraction scheme the length measurements carry no un-certainties and mean S MSTO measurements carry uncertain-ties which are less than 10 per cent of their observationalcounterparts.
The observational value of S MSTO is estimated using a pro-cedure similar to that described above, using figures 3 and 4of B14. In practice, we add up stars in their figure 3a between − (cid:48) ≤ B ≤ + (cid:48) , and then subtract a constant background of35 stars per bin. We also add up stars from their figure 3bbetween − ◦ ≤ Λ ≤ . ◦ and subtract a noise profile thatvaries linearly from 60 at Λ = ◦ to 40 at Λ = − ◦ . We thenaverage the two values to obtain S MSTO = ± for theobserved stream.For the observed length and width we adopt . ◦ and . ± . (Gaussian FWHM), respectively, as reportedby B14. We adopt an uncertainty in length of . ◦ whichcorresponds to half the width of one bin in figure 3b of B14.Finally, we use the measured value of σ vlos from S15,which is . + . − . ; the uncertainty is the central 68 per centconfidence interval of the posterior probability distribution.We note that this is not the inferred velocity dispersion ofthe stream progenitor, but rather the intrinsic velocity dis- persion of the stream, comparable to the measurement per-formed on the simulated streams as described above. We assess the viability of different stream progenitors bycomparing the integrated number of MSTO stars, S MSTO ,the length, width, and the line-of-sight velocity dispersion, σ vlos of simulated streams with those of Ophiuchus. Ourmain results are summarized in Figure 5, where we reporthow well each of the GC candidates in our model grid is ableto match the observed properties of the stream. The compar-ison is made at second (Ap2, left panel) or third (Ap3, rightpanel) pericentric passage. We do not discuss Ap4 models aswe find that none of the Ap4 streams provide a convincingmatch to the Ophiuchus stream.The coloured grids in each of the four panels showeach one of the measured properties of the resulting stream.The colour bar indicates the value of the parameter for thestream generated by each progenitor, where white has beenset to the observed stream parameters. Red or blue thus in-dicate deviations from observations where the parameter issmaller or larger than observed, respectively. Dark grey in-dicate progenitors whose streams can be excluded becauseof obvious morphological considerations, such as cases wherethe progenitor has not disrupted, or an obvious bound coreremains.To make a quantitative statement about how well oursimulated progenitors match the observed stream we needto consider the uncertainties in the measured properties ofboth simulated and observed streams. We generate a com-bined uncertainty, defined as the combination in quadratureof both the uncertainties which arise from our analysis (com-puted as described in Section 3.2.1), and observational un-certainties taken from the literature. For S MSTO we make theapproximation that σ Log ( S MSTO ) ≈ σ S MSTO / ( S MSTO ln10 ) .In order to visualize our results we highlight in boldprogenitors in Figure 5 for which the measurement of therespective parameter differs from the observed value by lessthan two combined standard deviations. The progenitors forwhich all four parameters match observations in this mannerare outlined in green instead.Figure 5 shows that the most discriminating parametersare the length of the stream and S MSTO , with the width alsoexcluding mainly high-mass progenitors. The line of sight ve-locity dispersion, on the other hand, is a weak discriminantbetween progenitors, mainly because the observational un-certainties are larger for these progenitors, which have fewMSTO stars, therefore inflating the standard deviation.There are three progenitors which match all four mea-sured parameters within the uncertainties. Two of theseare very similar Ap2 progenitors, with masses of order × M (cid:12) and half-mass radii between ∼ and pc.The third is an Ap3 model of similar mass but with half-mass radius of ∼ pc. These progenitors have total lumi-nosity consistent with the luminosity of the stream reportedby B14, implying that most of the progenitor is visible inthe stream. In contrast, both the S15 and S15-NB modelsdo not match well any of the observed parameters, with theexception of the line-of-sight velocity dispersion. MNRAS , 1–11 (2019) he Ophiuchus stream progenitor L o g ( R / / p c ) Log (M prog / M ) Log (M prog / M ) M V (mag) L o g ( R / / p c ) M V (mag) Log ( S MSTO ) Length (deg)
Width (arcmin) los (km s ) L o g ( R / / p c ) Log (M prog / M ) Log (M prog / M ) M V (mag) L o g ( R / / p c ) M V (mag) Log ( S MSTO ) Length (deg)
Width (arcmin) los (km s ) Figure 5.
Comparing simulated streams to observations. The values of each derived parameter for our simulated streams for Ap2 (left)and Ap3 (right) models are shown overlaid on a plot of globular cluster total magnitude against logarithmic projected half-light radius.The colouring of the grid in each panel shows one of the derived parameters: logarithmic number of MSTO stars, length, width, andline-of-sight velocity dispersion. The boxes forming the grids are centred on the value of the total magnitude and 2-D half-mass radiusof that progenitor. Dark grey cells represent progenitors that can be excluded on morphological grounds. Bolded cells are those in whichthe parameter value matches the observed value within − σ . Green-bordered cells are those in which all four parameters match within − σ . The top axis shows progenitor mass assuming a mass-to-light ratio of . . The black circles and crosses are Milky Way (Harris1996) and M31 (Huxor et al. 2014; Peacock et al. 2010) globular clusters, respectively. The S15 and S15-NB progenitors are marked usingred triangles and squares, respectively. This demonstrates that progenitors best-matched to observations have masses of × M (cid:12) , buta range of potential sizes. In Appendix B1 we demonstrate that if the Ophi-uchus progenitor has undergone any mass function flatten-ing, whether due to internal dynamical evolution or externaltidal effects, the result will be that we overestimate the in-ferred mass of the progenitor. We can therefore confidentlysay that our progenitor mass determination of × M (cid:12) represents an upper bound. We do not find that progenitorsize estimates are affected by mass function flattening, withAp2 models continuing to favour half-mass radii between and pc, and Ap3 models favouring even smaller radii.Note that there are no known GCs in the Local Groupas faint and as weakly-bound as the progenitors that ouranalysis favours. The only known clusters with similar stel-lar mass/luminosity have half-mass radii about an order ofmagnitude smaller than expected for the Ophiuchus pro-genitor. This is an intriguing finding, as it suggests that theGC population may span a larger range of radii and surfacebrightness than hitherto known. A progenitor like the onefavoured by our modeling would be rather difficult to find,given its vanishingly small surface brightness, but we seeno a priori reason to exclude their presence in the Galactichalo, even in large numbers. Taken at face value, our resultssuggest that our understanding of the faint GC populationmay be rather incomplete. The above analysis demonstrates that a very low mass,weakly-bound GC is a viable progenitor for the Ophiuchusstream, but it does not address the question of its origin.Given the age of its stars and the short time it takes to dis-rupt, it is clear that the Ophiuchus progenitor could not have formed in its present orbit. One possibility is that the Ophi-uchus progenitor cluster was brought into the inner MilkyWay by one of its satellite galaxies, or that its original orbitwas perturbed following some dynamical interaction withone or several of them.The orbit of the Ophiuchus stream is mostly containedin the Galactocentric X–Z plane (the plane containing theSun, the Galactic centre, and the MW rotation axis), andhas an apocentric distance of about 15 kpc. The SagittariusdSph (Sgr) is a conspicuous candidate for interaction, sinceit orbits the Galaxy primarily in the same X–Z plane and hasa pericentric distance that coincides with that of Ophiuchus’apocentre (Gaia Collaboration et al. 2018b).These may be just coincidences, but they are intriguingenough to warrant further exploration. A full study of allpossible GC orbits around Sgr or the Milky Way that maylead to Ophiuchus is beyond the scope of the present work,but we can at least verify the viability of this scenario byassessing whether the presently available data allows for anear passage between Sgr and Ophiuchus in the recent past.This seems like a minimum requirement to argue for a directconnection between Sgr and Ophiuchus.To investigate this we adopt the kinematics for Sgr fromGaia Collaboration et al. (2018b) and sample 1000 sets ofphase space coordinates for both Sgr and Ophiuchus, assum-ing Gaussian uncertainties. We integrate these orbits back-wards in
MWPotential2014 for 500 Myr. We determine atwhich point Sgr and Ophiuchus come closest to one anotherand record the time, separation and relative velocity of theencounter. We find that Sgr and Ophiuchus came to within . ± . kpc of one another about ± Myr ago, which cor-responds to roughly the last apocentric passage of the Ophi-uchus stream. At closest approach, Sgr and Ophiuchus had
MNRAS , 1–11 (2019)
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X [kpc] Y [ k p c ] SgrOphPresent LocationClosest Approach
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X [kpc] Z [ k p c ]
20 0 20
Y [kpc] Z [ k p c ] Time [Gyr] S e p a r a t i o n [ k p c ] Figure 6.
Kinematics of 25 pairs of past orbits of the Ophiuchusprogenitor and the Sagittarius dSph (Sgr). The top left and bot-tom two panels show three orthogonal projections. The Sun isat ( − . , , ) , and the Galactic centre at ( , , ) , respectively, inthese projections. The top right panel shows the separation be-tween the two bodies as a function of time. The bolded orbitsare those corresponding to the unsampled (i.e. not sampled fromthe error distribution) kinematics of Sgr and Ophiuchus. Theseintegrations suggest a close passage between Sgr and Ophiuchusabout Myrs ago, at about the time of the last Ophiuchusapocentric passage. a large relative velocity, of order ± km s − . Figure 6shows the past orbital trace of Sgr (in red) and Ophiuchus(in blue) for 25 example orbits, and highlights the likelihoodof a past close encounter.These findings suggest that while Ophiuchus was likelynot originally bound to Sgr due to their large relative veloc-ity, the massive dwarf definitely played a role in shaping thepresent-day orbit of the stream. It is therefore worthwhileto include Sgr as a gravitating body during future efforts tomodel Ophiuchus’ orbit, especially when the long-term be-haviour of the system is under investigation. The scenariosproposed by Price-Whelan et al. (2018) and Hattori et al.(2016) are both sensitive to the alignment of Ophiuchus’orbit with the galactic bar, suggesting that the interactionwith Sgr may require re-assessment of these theories. Includ-ing an analytic prescription for Sgr in N-body realizationsof Ophiuchus will also highlight any tidal impact Sgr mayhave had on Ophiuchus during one of their close passages,which could alter the manner in which Ophiuchus disrupts.We plan to pursue this in future work.We note that our finding that Sgr may have influencedthe orbit of Ophiuchus within the time period over which ourorbits are integrated should not invalidate our results. Theonly parameter which we find to be sensitive to the time ofdisruption is the half-mass radius of the progenitor cluster,which for Ap3 models may be reduced to as low as 10 pc.We therefore propose that if Sgr were to modify the orbit of the progenitor beyond the last 100 Myr, then the effectwould likely be to change the inferred size of the progenitorin accordance with the changing tidal field of the resultingorbit. The Ophiuchus stream is an interesting dynamical puzzle.The observed length of the stream is short, suggesting arecent disruption of the progenitor. On the other hand thereis no observed bound core and the stellar population is thatof an old metal-poor cluster, suggesting that the stream ismuch older. One possible resolution to this discrepancy isthat the progenitor of this stream is an extremely weaklybound globular cluster, the likes of which are not observedin the Milky Way today.We have performed a grid search over the possible struc-tural properties of a globular cluster progenitor of the Ophi-uchus stream. We evolve these progenitors using N-bodysimulations to disrupt them along the same orbit as theOphiuchus stream, and then perform detailed comparisonsof the resulting streams to observations.We find that previously proposed progenitors are toomassive to account for the observed properties of the stream.Instead, we find that the width, length, and the number ofstars in simulated streams from progenitors with masses of ∼ × M (cid:12) half-mass radii in the range – pc, whichbegan disrupting about 360 Myr ago yield the best match toobservations. There are no known GCs in the Galaxy withthese properties, and we speculate that Ophiuchus highlightsthe presence of yet undiscovered globular clusters in theMilky Way at the faint, low surface brightness end of theGC population.The Ophiuchus stream may not be unique in this sense.The Phlegethon stream (Ibata et al. 2018) is a stellar streamrecently found in the Gaia
DR2 release, and is thought tohave a mass around . × M (cid:12) . It may once have beena globular cluster with similar properties to the progen-itor of the Ophiuchus stream. The now highly dispersedPhlegethon has an extremely low surface brightness of about . mag arcsec − in Gaia G -band. It was only discoveredthrough the use of a dedicated structure-finding algorithmthat leverages the full
Gaia astrometric data set. Thesetypes of highly dispersed streams originating from weaklybound globular clusters may be common throughout theMilky Way and remain invisible to us due to their extremelylow surface brightnesses.A cluster as weakly bound as the proposed Ophiuchusprogenitor cannot have formed on its current orbit, or any-where in the inner galaxy for that matter, since it wouldbe susceptible to tidal disruption by the disk and bulge (e.g.see figure 21 in Gnedin & Ostriker 1997). For the Ophiuchusprogenitor to survive to the present day it would have there-fore needed to orbit in the outer galaxy, on a low-eccentricitytrajectory, for the majority of its ∼ Gyr life.If this interpretation is correct, a major question re-mains: how did Ophiuchus come to orbit where it does to-day? An interaction with a massive Galactic satellite couldprovide a possible explanation. We therefore briefly exploredthe possibility of an interaction between Sgr and the Ophi-uchus progenitor, and found that the two passed very close
MNRAS , 1–11 (2019) he Ophiuchus stream progenitor to each other during Ophiuchus last apocentric passage. Itis clear that this interaction could have had a substantialeffect on Ophiuchus, and that future work will need to con-sider carefully how the interaction with Sagittarius may havehelped to shape the stream properties.To summarize: we have shown that the progenitor ofthe Ophiuchus stream likely had a mass of × M (cid:12) orless and half-mass radius in the range - pc. We find adegeneracy between the size and disruption time of the sys-tem, with models with half-mass radii of 60–100 pc whichdisrupted 360 Myr ago, and denser models with half-massradii around 10 pc which disrupted 600 Myr ago both pro-viding convincing matches to observations. We obtain ourresults by analyzing the properties of our simulated streamsin a manner consistent with how the real stream was stud-ied. We also perform a basic investigation into the possibilitythat Ophiuchus has interacted with the Sgr dwarf galaxy inits recent past, and find that the two came to ∼ kpc fromeach other about Myrs ago. It is still unclear what rolethe bar has played in the evolution of this tidal feature, orhow this ∼ Gyr old progenitor came to be on its presentorbit. Answers to these questions will require a more detailedmodeling of the Galactic potential to include a realistic barmodel, as well as a framework to include the influence ofSagittarius on the stream properties.
ACKNOWLEDGEMENTS
The authors would like to thank Jeremy Webb and Ed-uardo Balbinot for helpful comments which greatly im-proved the results in this paper. KO received supportfrom VICI grant 016.130.338 of the Netherlands Founda-tion for Scientific Research (NWO). This project makesuse of open source software including galpy (Bovy 2015),
Gadget-2 (Springel 2005),
Matplotlib (Hunter 2007),and
Astropy (Price-Whelan et al. 2018). This research hasmade use of NASA’s Astrophysics Data System. This workhas made use of data from the European Space Agency(ESA) mission
Gaia ( ),processed by the Gaia
Data Processing and Analysis Con-sortium (DPAC, ). Funding for the DPAC has been pro-vided by national institutions, in particular the institutionsparticipating in the
Gaia
Multilateral Agreement.
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APPENDIX A:
GAIA
DR2 KINEMATICS
Measurements for the fourteen stars studied by S15 are in-cluded in the
Gaia
Data Release 2 (Gaia Collaboration et al.2018a). On-sky positions, parallaxes, proper motions, uncer-tainties on these quantities, and the proper motion correla-tion coefficients were obtained from the
Gaia
DR2 archive.Figure A1 shows the proper motions of these objects inGalactic coordinates as a function of Galactic longitude. Thestraight lines show the best fit to the data from S15 (dashedgrey) and their best orbital fit (blue).These new proper motions seem consistent with the S15orbital fit, and in tension with the old proper motion data.As a simple way to confirm this we calculate the reducedChi-square statistic between the new data and both the orbitand old data linear fits. The results are shown in Figure A1.The old proper motion data are difficult to reconcile withany reasonable orbit, including one in a non-axisymmetricpotential, lending even more weight to the
Gaia measure-ments.
MNRAS , 1–11 (2019) J. M. M. Lane et al. − . − . − . − . . µ l ( m a s / y r ) data χ red = χ red = . . . . . . l (deg) − µ b ( m a s / y r ) data χ red = χ red = Figure A1.
Gaia
DR2 proper motions as functions of Galacticlongitude for stars from S15. The dashed grey and blue lines showthe best fit to their data and their best orbital fit, respectively.The
Gaia
DR2 measurements agree very well with the propermotions predicted by the orbit fit in S15.
APPENDIX B: CONVERTING PARTICLEMASS TO STAR COUNTS
In order to facilitate a comparison between simulated andobserved streams we must define a correspondence betweensimulation particles and stream stars. This is achieved byusing an isochrone and luminosity function (LF) that matchthe stellar population of the stream progenitor. The proper-ties of that population – metallicity, alpha-abundance, age,and the mass-loss parameter – are all determined by S15and presented in their table 1. We generate an isochroneand LF from the PARSEC v1.2S grid (the same grid usedby S15; Bressan et al. 2012; Chen et al. 2014, 2015; Tanget al. 2014) assuming these parameters. The LF is calcu-lated using a Chabrier log-normal initial mass function.To minimize contamination from non-stream stars intheir analysis, B14 isolate a subset of stars near the mainsequence turnoff (MSTO) of the overdensity they detect incolour-magnitude space. Their MSTO selection box lies be-tween PS1 i -band magnitudes 20.5 to 18, and spans approx-imately 0.2 magnitudes in PS1 g − i . Using this magnitudeinformation, and the isochrone and LF offset by the meandistance modulus of Ophiuchus, we derive a conversion be-tween particle mass to number of MSTO stars in the follow-ing way. The number of MSTO stars in the progenitor sys-tem is proportional to the luminosity function, Φ , integratedfrom 18 to 20.5 magnitudes (about 0.1 M (cid:12) < M < (cid:12) for our isochrone). The mass of the entire globular cluster isthe luminosity function times the mass for the correspond-ing magnitude (inferred from the isochrone), integrated overall magnitudes. The conversion factor can therefore be ex-pressed as the ratio of the above quantities, and we derivethis factor to be 0.23 MSTO stars per solar mass. N MSTO M (cid:12) = (cid:82) . Φ ( i ) d i (cid:82) all Φ ( i ) M ( i ) d i = .
23 M − (cid:12) (B1)In making this conversion we make a number of assump-tions. First, that each simulated particle is representativeof the entire stellar population. Second, that the mass of the GC is entirely contained in stars that appear in theisochrone, specifically that that there is no dark matter inthe globular cluster, that the mass fraction of stars moreevolved than the red-giant phase is negligible. We check theresiliency of this conversion to a change in the isochrone andLF grid by performing the same calculation using isochronesand LFs with similar input properties from the DartmouthStellar Evolution Database (DSED, Dotter et al. 2008). Thechange in the conversion factor is less than 1 per cent. Ourresulting conversion factor agrees heuristically with the re-sults of B14. They find the luminosity of the stream is ∼ . × L (cid:12) , and that there are between 300 and 700 starsin the stream above PS1 g -band magnitude of 21 (most ofwhich will be in the MSTO selection box, see B14 figure 2c).Assuming our mass-to-light ratio of about 1.45 this equatesto about ∼ × M (cid:12) and 500 MSTO stars, implying a ratioof 0.25 MSTO stars per M (cid:12) . B1 The impact of tidal evolution on the massfunction
A major systematic uncertainty that we must address is howthe mass function of a globular cluster evolves in a strongtidal field. It has been well established that the mass functionof a globular cluster undergoing tidal stripping is flattened(Vesperini & Heggie 1997; Kruijssen 2009; Webb & Leigh2015), decreasing the perceived mass-to-light ratio (Anderset al. 2009; Kruijssen & Mieske 2009) and altering its in-ferred properties (e.g. Balbinot & Gieles 2018). Given thatthe Ophiuchus stream progenitor is thought to be ∼ . Gyrold, and its history is poorly understood beyond about ahundred Myr ago, little can be known about the tidal envi-ronment in which this cluster has been evolving. If the clus-ter has been disrupting in place for many Gyr, either being‘shepherded’ or ‘fanned’ by the bar, it will have been subjectto a strong tidal field for the majority of its existence. Con-versely, if the system moved onto its present orbit from theouter galaxy, it may have spent most of its life in a weak tidalfield. Therefore the exact shape of Ophiuchus mass functionis difficult to predict, and is of key importance to inferringthe properties of the progenitor.Here we attempt to estimate the impact of a flat-tened mass function on the properties of our simulatedstreams. First, we investigate the effect of flattening onthe N MSTO / M (cid:12) conversion factor. We generate a series ofisochrone-LF pairs from the DSED database with the sameinput parameters as presented above, except we now choosea power law initial mass function and vary the power lawindex between α = − . (Salpeter) and α = (constantnumber with mass). We compute the conversion factor foreach isochrone-LF pair, and find that it varies linearly from0.12 at α = − . to 0.49 at α = . Recall that the value de-rived above used a Chabrier log-normal initial mass function,which explains why the bottom-heavy Salpeter α = − . initial mass function returns such a low conversion factor.Very few globular clusters in the Milky Way have α > ,and those few that do have extreme perigalacticon distancesof around 1 kpc (e.g. see table 3 of Webb & Leigh 2015,and references therein). We can therefore be confident thatthe effect of mass function flattening on the conversion fromparticle mass to N MSTO will be at most an increase by abouta factor of 2, from 0.23 to 0.49. We also calculate the V-band
MNRAS , 1–11 (2019) he Ophiuchus stream progenitor mass to light ratio using the same isochrone-LF pairs, andfind that it varies from 2.97 for α = − . down to 0.61 for α = . Using similar reasoning as above, we can posit thatthe effect of mass function flattening on the mass to light ra-tio would be at most a decrease by a factor of about 2.5, from1.45 to 0.61. We also note that the mass function would notbe expected to evolve over the course of our short ( < § α = , and represent ex-treme flattening of the mass function. We find that the threematching progenitors now have masses of about × M (cid:12) ,which matches our predictions made above, which were thatthe inferred mass would be decreased by about a factor of 2.Otherwise the results are nearly identical to those presentedin Figure 5, with measured widths, lengths, and velocitydispersions being unchanged, except for the near constantoffset in mass. × M (cid:12) is therefore an upper bound onthe progenitor mass. For the Ap3 models, when mass func-tion flattening is taken into account, the favoured half-massradius increases slightly to between 16 and 25 pc, and mod-els with masses lower than × M (cid:12) (but the same half-mass radius) also match within the uncertainties. Given that × M (cid:12) is already an upper limit for the mass of the pro-genitor we do not consider these extra models further. This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS000