Mon. Not. R. Astron. Soc. 000, 1–18 (2017) Printed 30 March 2020 (MN LATEX style file v2.2)

A closer look at the spur, blob, wiggle, and gaps in GD-1

T.J.L. de Boer1,2?, D. Erkal2 and M. Gieles2,3,41 Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA2 Department of Physics, University of Surrey, Guildford, GU2 7XH, UK3 Institut de Ciencies del Cosmos (ICCUB-IEEC), Universitat de Barcelona, Martı i Franques 1, 08028 Barcelona, Spain4 ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain.

Received ...; accepted ...

ABSTRACTThe GD-1 stream is one of the longest and coldest stellar streams discovered to date, and oneof the best objects for constraining the dark matter properties of the Milky Way. Using datafrom Gaia DR2 we study the proper motions, distance, morphology and density of the streamto uncover small scale perturbations. The proper motion cleaned data shows a clear distancegradient across the stream, ranging from 7 to 12 kpc. However, unlike earlier studies thatfound a continuous gradient, we uncover a distance minimum at ϕ1 ≈-40 deg, after which thedistance increases again. We can reliably trace the stream between -85< ϕ1 <15 deg, show-ing an even further extent to GD-1 beyond the earlier extension of Price-Whelan & Bonaca(2018). We constrain the stream track and density using a Boolean matched filter approachand find three large under densities and significant residuals in the stream track lining up withthese gaps. The gaps are located at ϕ1=-36, -20 and -3 deg, with the gap at -3 deg being sur-rounded by a clear sinusoidal wiggle. We argue that this wiggle is due to a perturbation sinceit has the wrong orientation to come from a progenitor. We compute a total initial stellar massof the stream segment of 1.58±0.07×104 M�. With the extended view of the spur in this work,we argue that the spur may be unrelated to the adjacent gap in the stream. Finally, we showthat an interaction with the Sagittarius dwarf can create features similar to the spur.

Key words: Galaxy: structure – Galaxy: fundamental parameters — Stars: C-M diagrams —Galaxy: halo — Galaxy: kinematics and dynamics

1 INTRODUCTION

Stellar streams are rivers of stars formed from the disruption ofstellar systems within a larger host galaxy due to the effects of thehost gravitational field. Their location and appearance is uniquelygoverned by the host’s gravitational field, which makes them one ofthe best tracers for measuring its properties. In general, the meantrack and phase-space density of the streams encode informationabout the underlying unseen distribution of mass on galactic scales(e.g., Johnston et al. 1999). However, for systems with a suitablysmall initial phase-space volume (such as globular clusters), thestellar streams can also retain imprints from encounters with otherperturbers, such as small-scale dark matter (DM) subhaloes (e.g.Johnston, Spergel & Haydn 2002; Ibata et al. 2002; Carlberg 2009;Yoon, Johnston & Hogg 2011; Erkal et al. 2016; Sanders, Bovy& Erkal 2016; Bovy, Erkal & Sanders 2017). Therefore, stellarstreams provide not just dramatic confirmation of the hierarchicalgalaxy formation scenario, but can also be directly used to quantifythe properties of the (unseen) matter distribution (Lynden-Bell &

? E-mail: tdeboer@hawaii.edu

Lynden-Bell 1995; Ibata et al. 2002; Johnston, Spergel & Haydn2002).

Although initially rare, the gallery of stellar streams has ex-panded greatly during the last two decades with the availabilityof large scale, homogeneous sky surveys. Discoveries of streamshave been made in all the large surveys such as SDSS, 2MASS,Pan-STARRS, ATLAS, and DES (Skrutskie et al. 2006; Ahn et al.2014; Shanks et al. 2015; Chambers et al. 2016), after applyingphotometric selection methods specifically designed to find streams(Grillmair & Carlin 2016). Gaia has provided exquisite data whichhas been used to discover a wealth of streams (e.g. Malhan, Ibata &Martin 2018; Ibata et al. 2018; Ibata, Malhan & Martin 2019). Atpresent, more than 60 streams have been found in the Milky Way(MW) alone, with wildly different morphologies ranging from mul-tiple wraps (Sagittarius) to the very short (Ophiuchus) and anythingin between (Belokurov et al. 2006; Bernard et al. 2014).

Since the initial survey finds, individual streams have beenused to place constraints on the mass distribution of the MW halo,confirming they are a powerful tool for probing the unseen MWcomponents (e.g., Koposov, Rix & Hogg 2010; Law & Majewski2010; Gibbons, Belokurov & Evans 2014; Bowden, Belokurov &Evans 2015; Kupper et al. 2015; Bovy et al. 2016). Furthermore,

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Figure 1. Distance determination for GD-1 as a function of ϕ1, showing thecolumn normalised density of stars in bins of distance modulus. The blueline shows literature distances from Koposov, Rix & Hogg (2010). The redpoints indicate the best-fit Gaussian distance peak to each bin of ϕ1. Thedotted red line shows a best fit second order polynomial to the distance, asdescribed by f (ϕ1) = 15.001 + 2.421 × 10−2ϕ1 + 2.410 × 10−4ϕ2

1.

in recent years detailed stream morphology has been modelled toprobe for the existence of dark matter (DM) subhalos (e.g. Carlberg2009; Yoon, Johnston & Hogg 2011; Carlberg 2012; Erkal & Be-lokurov 2015a), which are not observable by conventional methods(Ikeuchi 1986; Rees 1986). Indeed, tentative evidence for a distur-bance by low mass subhaloes has been found in the Pal 5 stream(Bovy, Erkal & Sanders 2017; Erkal, Koposov & Belokurov 2017).

One of the difficulties in uncovering the origin of details inthe stream morphology is related to the uniqueness of the signatureleft by an encounter with a dark subhalo (Yoon, Johnston & Hogg2011; Carlberg 2012; Erkal & Belokurov 2015a; Sanders, Bovy &Erkal 2016). For some streams (including Pal 5), interaction with agiant molecular cloud, the MW bar, or spiral arms (Amorisco et al.2016; Erkal, Koposov & Belokurov 2017; Pearson, Price-Whelan& Johnston 2017; Banik & Bovy 2019) can result in similar signa-tures as those left by a close subhalo passage. This complicates theotherwise straightforward interpretation of stream features, and hasled to the search for a suitable stream in which the other explana-tions are excluded or unlikely due to their distance or orbit.

The GD-1 stream is one of the most promising streams forthe study of DM on small scales, given its morphology and orbit.When first discovered in SDSS, it was found as a 63 degree long,very thin stream with a width of only 0.2 deg (Grillmair & Dionatos2006). This means it has a small initial phase-space volume, whichallows us to more easily distinguish velocity kicks induced by darksubstructures from the secular dynamics of the progenitor. Further-more, the GD-1 stream is moving in a retrograde sense with respectto the disk, which means interactions with MW disk sub-strucureare less effective in creating stream features (Koposov, Rix & Hogg2010; Bowden, Belokurov & Evans 2015). The orbit of the stream(with a perigalacticon of 14 kpc and apogalacticon of 26-29 kpc) issuch that interactions with giant molecular clouds or the MW barare also unlikely. Finally, the stream is on a retrograde orbit mak-ing such interactions negligible (e.g. Amorisco et al. 2016; Hattori,Erkal & Sanders 2016), making GD-1 an ideal candidate for thestudy of gaps induced by dark subhaloes.

Several previous studies of GD-1 have revealed that it displaysa complex morphology, despite its initial simple appearance. Using

SDSS data, Carlberg & Grillmair (2013) found a large number ofgaps in GD-1. A study of deep photometric data from the Canada-France-Hawaii-Telescope (CFHT) by de Boer et al. (2018) showedthat there are at least two clear gaps where the density is consis-tent with zero given the uncertainties, and the stream track showsdeviations that could be due to interactions. Earlier this year, datafrom the recently released Gaia DR2 was used to identify streammembers with much greater accuracy, enabling the discovery of astream extension (the total length is now in excess of 90 degrees)and two associated but separate stream structure, dubbed the spurand the blob (Price-Whelan & Bonaca 2018). The connection be-tween the spur feature and the main stream (in a location wherea stream gap was found) is a prime candidate for DM interac-tion, as recently modelled by Bonaca et al. (2019). Independently,Webb & Bovy (2019) also found that the GD-1 stream extends from−90 < ϕ1 < 10 degrees, which makes it even longer than the Price-Whelan & Bonaca (2018) detection, and measure the track and den-sity. However, there are no obvious differences between both worksin terms of data sample selection, indicating that the outer extent ofthe stream (and its length) is subject to small scale selection differ-ences.

In this work, we will revisit the investigation of GD-1 usingGaia DR2 data, and employ a more sophisticated data filtering us-ing a matched filter approach (Rockosi et al. 2002; de Boer et al.2018). The aim of the present work is to extract the maximum ofinformation from the Gaia DR2 data and search for small scalevariations in the stream track. By definition, the matched filter tech-nique selects the best possible (highest S/N) selection box that canbe used, with size/width driven completely by the data quality. Thisin turn gives a greater capability of tracing the stream in the faceof contamination than can be done with a simple colour-magnitudeselection box, and potentially trace GD-1 beyond its current foot-print. We will constrain the distance to the stream across (and be-yond) it current length and fit the proper motion signal as a functionof stream angle. The evolution of the stream centroid of the sky willbe constrained, which will yield wiggles and gaps, all of which areindicative of perturbations due to tidal encounters (Carlberg 2012;Erkal & Belokurov 2015a,b). We will also study the stream densityprofile and determine the total stellar mass encompassed by GD-1. This data will be used in two companion papers (Banik et al.(2019), Banik et al. in prep b) to explore the dark matter substruc-ture in the Milky Way and place a lower bound on mass of the darkmatter particle.

This paper is organised as follows: in Section 2 we discussthe data used, followed by the determination of the distance to GD-1 in Section 2.1. Section 2.2 then discusses the PM signal of thestream and how this was fit, with the determination of the streamtrack locus in Section 3. The density and mass of GD-1 is subse-quently determined in Section 4, and the residuals in location andPMs is discussed in Section 5. In Section 6 we fit this data with anorbit, explore how well the velocities of GD-1 are aligned with thestream, show that an interaction with Sagittarius can create featuressimilar to the spur, and discuss the morphology of features in GD-1.Finally, Section 7 discusses the results and their implications.

2 DATA

To investigate the GD-1 stream, we make use of data from the Gaiamission (Gaia Collaboration et al. 2016a,b; Lindegren et al. 2018),which contains proper motion (PM) measurements for ≈1.6 billionsources covering the full sky. The astrometry of Gaia are excel-

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lent, but the spectro-photometric colours suffer from systematicsin crowded regions. Therefore, we will instead use the crossmatchtable between Gaia DR2 and Pan-STARRS DR1 (Chambers et al.2016) produced by the Gaia collaboration, and released as one ofthe external tables along with the nominal DR2 catalog. The pho-tometry of Pan-STARRS is corrected for extinction using dust mapsfrom Schlegel, Finkbeiner & Davis (1998) with coefficients fromSchlafly & Finkbeiner (2011), on a star by star basis.

We adopt the stream-aligned coordinate scheme of Koposov,Rix & Hogg (2010), converting ra,dec into ϕ1, ϕ2 representingalong and perpendicular to the stream respectively. Furthermore,the Gaia PMs µra, µdec are converted to µϕ1 , µϕ2 representing thePM in the stream-aligned frame.

We stress that the same combination of Gaia DR2 and Pan-STARRS DR1 data has been adopted previously by Price-Whelan& Bonaca (2018) when studying the GD-1 stream. The aim of thiswork is simply to employ a different technique of selecting GD-1stars using the same dataset and study the resulting stream featuresin greater detail.

2.1 Distance to the stream

A crucial step in extracting the best sample of stream stars is de-termining an accurate distance to the individual parts of the stream.The distance to GD-1 has been determined using deep CFHT datafor a small portion of the stream (de Boer et al. 2018) and for alonger stretch of stream from SDSS CMDs (Koposov, Rix & Hogg2010). Across the range of ϕ1 for which distances could be derivedby SDSS data (−55 < ϕ1 < 0 deg) GD-1 displays a linear distancevariation between 7.5 and 10 kpc.

To investigate the distances beyond the range probed bySDSS, we compare the observed magnitude of main sequence starsto those of a reference isochrone with [Fe/H]=-1.9, age=12 Gyrfrom the Padova library (Marigo et al. 2017), as queried fromhttp://stev.oapd.inaf.it/cmd. To select GD-1 stars,we apply rough cuts in PM (less than 2 mas/yr from the simu-lation shown in Fig 2) and consider only stars within 2 degreesof the stream track based on results from Price-Whelan & Bonaca(2018). We then sample small bins of distance modulus and sum upthe number of stars consistent with the reference isochrone withintwice the photometric errors. To bring out the signal of the GD-1stream, we correct for the effects of MW contamination by per-forming the same analysis for stars located between 2-4 degreesaway from the track on either side, and subtracting those.

Figure 1 shows the density of stars in bins of distance modu-lus, as a function of ϕ1. The red points indicate the best-fit distancefrom a Gaussian fit to each bin of ϕ1. For reference, the distancecomputed by Koposov, Rix & Hogg (2010) are shown as the blueline. It is apparent that the recovered distance trend is not linearlyvarying in the Gaia data, but instead recedes to larger distancesbeyond the ϕ1 range sampled by SDSS. This can have importantimplications for the orbit of the stream, and the number of interac-tions with subhaloes at smaller distances. Interestingly, the locationof the distance minimum based on our fit is close to ϕ1 ≈-40 de-grees, which corresponds very well to the predicted minimum offrom the dynamical model of GD-1 by Bovy et al. (2016).

2.2 GD-1 proper motions

With distances to the stream in place, we now revisit the PM selec-tion for GD-1 stars. We once again select the sample of probable

GD-1 stars consistent with the reference isochrone within twice thephotometric errors, but also apply a distance cut in each bin of ϕ1

as given by Figure 1. The PM distribution of the resulting sampleis then fit in µϕ1 , µϕ2 using a Gaussian mixture model consisting ofone Gaussian for the stream distribution and another for the MilkyWay foreground distribution. Distributions are fit using the emceepython MCMC package for each bin of ϕ1 (Foreman-Mackey et al.2013).

Figure 2 shows the extracted samples of GD-1 stars, with µϕ1

in the top panel and µϕ2 in the bottom. For reference, the PMs froma simulation aimed to reproduce the observed properties of GD-1 are shown as the blue line, showing good agreement (see Sec-tion 6.3 for more details). The stream signal is visible in µϕ1 , as a se-quence separated from the main locus of MW PMs for -90< ϕ1 <0deg. Beyond ϕ1=0 deg, the stream PMs become similar to thoseof the MW, leading to increased contamination of the stream sam-ple. The stream PMs in ϕ2 are separated as much from those of theMW as for µϕ1 . Therefore, in the bottom panel of Figure 2, we onlyshow stars with µϕ1 consistent with our best-fit within 2.5 mas/yr tobetter bring out the stream signal. The GD-1 stars are visibly over-dense in µϕ2 but not as distinct from the MW distribution as in ϕ1

coordinates. Solid red lines in Figure 2 shows the best-fit solutionas function of ϕ1, with dashed lines indicating the uncertainties ineach PM component from the Gaussian mixture model. The best-fitPM values of GD-1 are also shown in table 1.

3 FITTING THE STREAM TRACK OF GD-1

Next up, we will constrain the stream track of GD-1 on the sky, bycombining PM selections (although as function of ϕ1 as opposedto what was done by Price-Whelan & Bonaca 2018) with CMDmatched filtering. In this way, we will extract the optimum infor-mation from the combined Gaia DR2 and Pan-STARRS dataset.Matched filtering relies on selecting an appropriate signal filter Pstr

for the population of interest (the stream), and comparing that toa suitable background population filter PBG to find which pixels ofa CMD provide the optimum signal-to-noise of the signal popula-tion (see e.g. Rockosi et al. 2002). In our case, we use the referencePadova isochrone with [Fe/H]=-1.9, age=12 Gyr as our stream pop-ulation template, and generate a synthetic CMD by drawing starsfrom the isochrone with masses following a Kroupa IMF (Kroupa2001). The colours and magnitudes of the synthetic stars are shiftedto the appropriate distance for each ϕ1 considered (using the func-tion determined in Section 2.1) and convolved with photometricerrors for that spatial bin to create a signal filter consistent with theobservational conditions of the observed stars. To avoid a filter thatis arbitrarily thin at the bright end (where photometric errors aresmall), a minimum filter magnitude width of 0.05 is adopted.

The background filter is constructed by selecting observedstars far enough away from the track locus defined by (Price-Whelan & Bonaca 2018) to be free of stream stars. We includeonly stars with ϕ2 greater than 1.5 and less than 3 degrees awayfrom the track locus on each side, and apply a PM cut to within 2mas/yr of the stream motions following Section 2.2. To ensure ourbackground filter samples the same mix of MW populations as thesignal filter, we select only stars with Galactic latitudes consistentwith the mean latitude of the signal filter pixel, to within 5 degrees.The resulting background sample is converted into a Hess and fur-ther convolved using a 2x2 pixel kernel to smoothen the MW popu-lations and avoid spurious hot pixels in the signal-to-noise filteringdue to low number sampling. To exclude selecting other known

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r]Figure 2. Proper motion of GD-1 stars in stream-aligned coordinates ϕ1, ϕ2 adopting the distances shown in Figure 1. To better bring out the stream sample inµϕ2 , the bottom panel shows only for stars with |µϕ1 − µϕ1 ,track | 62.5 mas/yr, where µϕ1 ,track is the red line in the top panel. Panels on the left show the sampleas is, while panels on the right also show overlaid fits to the PMs. The solid red line shows the best-fit PM solution as function of ϕ1 for µϕ1 in the top paneland µϕ2 in the bottom, with dashed lines indicating the uncertainties in each PM component from the Gaussian mixture model. The blue line shows the PMtrends from a simulation aimed to reproduce the observed properties of GD-1 (Erkal et al., in prep).

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Figure 3. Matched filter map in GD-1 centric coordinates after applying the distance and PM relations shown in Figures 1 and 2, using spatial bins of 2×0.1deg bins. The top panel shows a convolved matched filter density map, while the bottom panel shows a column normalised version of the convolved map toincrease the stream track contrast. The maps have been convolved using a Gaussian kernel of 1x1 pixel to smooth over stochastic noise. The black lines showthe fitted stream track (and widths), while the red lines show the fit to the spur track.

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Table 1. Distance modulus, heliocentric distance and PMs (along with Gaussian widths) of the GD-1 stream from Gaia DR2.

ϕ1 m-M distance µϕ1 µϕ2 σµϕ1σµϕ2

[deg] [mag] [kpc] [mas/yr] [mas/yr] [mas/yr] [mas/yr]

-85 14.73±0.02 8.84±0.07 -9.66±0.28 -3.29±0.26 0.89±0.31 0.62±0.21-75 14.66±0.03 8.57±0.12 -10.90±0.15 -3.65±0.15 0.40±0.11 0.63±0.16-65 14.27±0.05 7.14±0.16 -11.89±0.34 -4.05±0.33 1.22±0.37 0.93±0.28-55 14.41±0.02 7.63±0.07 -13.25±0.06 -3.49±0.09 0.51±0.05 0.82±0.08-45 14.39±0.02 7.55±0.05 -13.35±0.04 -3.38±0.09 0.34±0.03 0.82±0.07-35 14.33±0.02 7.34±0.06 -13.05±0.06 -3.15±0.08 0.33±0.04 0.64±0.08-25 14.49±0.02 7.90±0.06 -12.35±0.06 -2.80±0.07 0.44±0.05 0.59±0.07-15 14.68±0.03 8.63±0.11 -10.63±0.12 -2.58±0.07 0.87±0.11 0.49±0.06-5 14.80±0.03 9.10±0.11 -9.38±0.19 -2.16±0.11 1.06±0.17 0.56±0.105 15.22±0.02 11.07±0.08 -7.66±0.25 -1.82±0.21 1.37±0.23 0.98±0.18

15 15.41±0.01 12.06±0.08 -6.33±0.40 -1.77±0.40 1.44±0.33 1.58±0.3625 15.98±0.01 15.73±0.05 -4.64±0.35 -1.66±0.36 1.31±0.29 1.46±0.31

streams that cross the same area of sky, we also include an ex-tra background filter during the matched filter process, based onthe stellar populations (and distance) of the Orphan and Sagittariusstreams. This ensures that CMD bins coincident with these streamsare rejected in the filtering, thereby avoiding contamination fromother streams.

Both of the filters are then normalised and the fraction Pstr(g-r,r)/PBG(g-r,r) is used to determine the filter that provide the op-timum stream detection signal-to-noise. In our case, we adopt aboolean matched filter procedure instead of a CMD pixel weight-ing procedure, since that will preserve the Poisson distribution forthe data and allow for realistic error determination. We simply as-sign a weight of zero to values of Pstr(g-r,r)/PBG(g-r,r) lower thanthe adopted threshold and a weight of 1 for value higher than thethreshold. The optimum threshold is chosen for each spatial pixelby looping through the possible values and finding the one whichmaximises the total signal-to-noise in the CMD.

The resulting matched filter map of the GD-1 stream is shownin Figure 3. The map is convolved using a Gaussian kernel of 1x1pixels to smooth over stochastic noise and bring out low contraststream features in more detail. The top panel shows the convolvedmap, with pixel colours indicating the number of stream stars, whilethe bottom panel shows a column normalised version of the mapaimed at highlighting the stream track locus. The stream is readilyvisible, as in Price-Whelan & Bonaca (2018), and spans a signif-icant range in ϕ1, extending well beyond the footprint shown inSDSS data (Grillmair & Dionatos 2006). The stream can be reli-ably traced between -85< ϕ1 <+15 deg before being swamped bycontamination. This is due in part to the increase in MW disk den-sity on the left side of the coverage as the stream approaches theMW mid plane, and the . However, another reason for losing thestream signal is due to the increasing distance on either end of thestream coverage (see Figure 1). For distances greater than 10 kpc,there are not enough stars above the Gaia brightness limit to tracethe stream confidently. Therefore, it might be possible to trace theGD-1 stream further by obtaining deeper data. While deeper PMdata is ideal, suitably deep photometry would be sufficient to al-low for good separation between the stream signal and backgroundMW populations, as shown in de Boer et al. (2018).

To extract the GD-1 stream track, we fit a Gaussian densitymodel and background to each column of ϕ1 data. The recoveredstream track locus is shown as the solid black line in Figure 3, withthe recovered stream width indicated by dashed lines. The values

for the track centre and width are also listed in Table 2. The streamtrack shows noticeable wiggles and changes in the width are alsoreadily apparent in Figure 3, most notably the increasing width to-ward lower ϕ1. The recovered track is mostly consistent with thetrack determined from deep photometric data in de Boer et al.(2018), given the uncertainties. The difference in the track locationis most pronounced in the region covering −45 < ϕ1 < −36 deg,and likely influenced by the spur feature (Price-Whelan & Bonaca2018) connecting on to the main stream track.

Given the relevance of the spur feature for the formation of thestream, we also constrain the track of the spur itself, by repeatingthe fitting in the spatial region showing the spur (−40 < ϕ1 < −15deg) using a double Gaussian fit. The recovered parameters for thespur track are shown in Table 3. We stress that the fitting of twosimultaneous Gaussian profile does not lead to changes in the nom-inal stream track, which is well separated from the spur in the re-gions studied. The spur track is shown in Figure 3 as a red linealong with dashed lines indicating the recovered width.

To discuss the stream morphology in more detail, Figure 4shows a zoom of the convolved density map highlighting some ofthe more interesting regions of the stream. Once again, the streamclearly shows wiggles, similar to those found in de Boer et al.(2018). Three clear underdense regions can be identified, at ϕ1 ≈-36,-20 and -3 deg respectively. The stellar spur coming off thestream is clearly visible and seen to extend slightly further and far-ther out than found in Price-Whelan & Bonaca (2018). The featurealso appears to arc back toward the stream track at ϕ1 ≈-20 deg.However, it is hard to determine the significance of this given thesmall sample sizes involved. Deep follow-up observations of thisregion are needed to unambiguously nail down the track of the spurfeature.

Our fit of the spur track shows that the spur feature is stillwell separated from the main stream (>0.8 deg) at ϕ1=-38 deg andtherefore does not connect to the higher ϕ1 gap edge as suggestedby (Bonaca et al. 2019). While we cannot conclude that the spurconnects to the other side of the gap due to insufficient data quality,it is interesting that the spur across most of the nearby gap. Thisis also consistent with the deep photometric study performed in deBoer et al. (2018) as visible in their Figure 8. We will discuss theinterpretation of this in more detail in Section 6.6.

The blob feature from Price-Whelan & Bonaca (2018) is alsovisible in Figure 4 at [ϕ1, ϕ2] ≈ [−14.7, 1.0] deg ([RA,Dec] ≈[176.3,52.7]), composed of ≈70 stars. The feature covers roughly

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8 deg along the stream and cannot be connected to the stream withthe present data. Finally, we find an underdense feature at ϕ1 ≈ −3deg, which was neither seen in data from de Boer et al. (2018) norPrice-Whelan & Bonaca (2018) but was detected in Malhan et al.(2019). This feature is especially intriguing given the distinct sinu-soidal wiggles in the stream track on each side of the under density.We argue that this feature is likely a perturbation to the stream inSection 6.7.

4 STREAM DENSITY AND TOTAL MASS

Following the stream track determination, we will now constrainthe surface brightness and density of the GD-1 stream. This will re-veal the location and depth of the under densities shown in Figure 3as well as the overall density evolution of the stream. To determinethe stream densities, we construct another matched filter map ofGD-1 using a finer binning in a transformed coordinates ϕ1,ϕ2, inwhich ϕ2 = ϕ2 − ϕ2,0 and ϕ2,0 being the stream track location foreach star interpolated using the values given in Table 2. The result-ing number densities are then fit using a Gaussian profile plus a firstorder polynomial for the residual background contamination. Thefits allow us to determine the surface brightness I(ϕ1) of the GD-1stream as a function of angle along the stream as well as the lineardensity λ(ϕ1), calculated as λ(ϕ1) =

√2πI(ϕ1)σϕ2 . The resulting

values are shown in Figure 5, along with the stream track locationϕ2,track and stream width σϕ2 . We note that the recovered distance,track location and proper motions are in very good agreement withthe dynamical model of GD-1 by Bovy et al. (2016), even outsidethe range of ϕ1 probed in the SDSS data modelled there, makingit the model in the literature that best reproduces the behaviour ofthe stream track. The surface brightness and linear density of thespur are also computed using the same procedure, given the trackdetermined in Section 3, and shown in Table 3.

Given the variation of stream distance as a function of ϕ1 asdetermined in Section 2.1, the range of masses sampled is not equalacross the covered footprint. To correct for this potential biasingfactor in the densities, we compute the total mass sampled abovethe Gaia DR2 brightness limit, in each bin of ϕ1. The masses ofthe synthetic GD-1 stars used to construct the signal filter (see Sec-tion 3) are combined with the optimised matched filter to find the

Table 2. The track centre ϕ2, width σϕ2 , surface brightness I, linear densityλ and mass sampling fraction (samp of the GD-1 stream as a function of ϕ1.

ϕ1 ϕ2,track σϕ2 I λ fsamp[deg] [deg] [deg] [deg−2] [deg−1]

-88 -3.74±0.16 0.08±0.02 7.28±1.51 0.77±0.20 0.83-86 -3.47±0.19 0.11±0.03 5.73±1.14 0.78±0.25 0.86-84 -3.43±0.68 0.26±0.12 2.76±0.86 0.88±0.41 0.88-82 -2.46±0.71 0.33±0.17 2.22±0.66 0.93±0.43 0.89-80 -1.80±0.23 0.09±0.02 8.09±1.73 0.90±0.25 0.91-78 -1.73±0.10 0.13±0.03 6.92±1.30 1.12±0.29 0.92-76 -1.72±0.08 0.13±0.04 5.80±1.25 0.94±0.28 0.94-74 -1.62±0.08 0.20±0.09 3.74±0.87 0.94±0.37 0.95-72 -1.51±0.07 0.06±0.05 3.68±1.91 0.28±0.22 0.96-70 -1.45±0.06 0.07±0.03 5.58±1.90 0.48±0.23 0.96-68 -1.38±0.07 0.10±0.04 4.91±1.46 0.65±0.27 0.98-66 -1.22±0.14 0.26±0.08 4.75±0.74 1.56±0.41 0.98-64 -0.69±0.07 0.22±0.07 4.77±0.91 1.29±0.39 0.99-62 -0.65±0.05 0.20±0.05 5.79±1.07 1.48±0.40 0.99-60 -0.61±0.05 0.23±0.05 7.92±1.10 2.31±0.51 1.00-58 -0.47±0.05 0.25±0.04 11.46±1.22 3.54±0.61 1.00-56 -0.34±0.05 0.29±0.04 14.83±1.16 5.33±0.70 1.00-54 -0.19±0.03 0.29±0.03 18.55±1.17 6.64±0.69 1.01-52 -0.12±0.02 0.24±0.02 23.71±1.51 7.22±0.64 1.01-50 -0.07±0.02 0.24±0.01 27.83±1.66 8.28±0.69 1.01-48 -0.02±0.02 0.24±0.02 29.30±1.70 8.77±0.73 1.00-46 0.04±0.03 0.24±0.02 27.23±1.64 8.15±0.71 1.01-44 0.10±0.03 0.24±0.02 22.33±1.50 6.73±0.66 1.01-42 0.20±0.03 0.25±0.03 16.99±1.32 5.38±0.65 1.01-40 0.22±0.04 0.24±0.03 13.78±1.29 4.20±0.61 1.01-38 0.20±0.04 0.18±0.03 13.59±1.54 3.12±0.50 1.00-36 0.14±0.03 0.14±0.02 16.41±1.93 2.87±0.46 1.00-34 0.13±0.02 0.12±0.01 20.58±2.39 3.02±0.47 0.99-32 0.12±0.02 0.11±0.01 25.88±2.74 3.53±0.49 0.98-30 0.13±0.02 0.11±0.01 30.54±2.85 4.30±0.52 0.98-28 0.13±0.02 0.11±0.01 35.13±2.99 4.87±0.53 0.97-26 0.14±0.02 0.11±0.01 36.05±3.03 4.90±0.52 0.96-24 0.13±0.02 0.11±0.01 29.82±2.78 4.20±0.50 0.95-22 0.10±0.03 0.12±0.01 20.71±2.31 3.17±0.47 0.94-20 0.03±0.03 0.13±0.02 15.94±2.01 2.54±0.44 0.93-18 -0.02±0.03 0.12±0.01 18.45±2.24 2.79±0.46 0.92-16 -0.03±0.02 0.11±0.01 28.42±2.91 3.80±0.52 0.90-14 -0.05±0.02 0.10±0.01 38.30±3.42 4.92±0.58 0.89-12 -0.09±0.02 0.11±0.01 40.02±3.36 5.59±0.62 0.87-10 -0.16±0.02 0.13±0.01 35.80±2.97 5.63±0.63 0.85-8 -0.27±0.03 0.13±0.01 29.76±2.60 5.01±0.59 0.83-6 -0.42±0.05 0.14±0.01 23.57±2.38 4.06±0.56 0.81-4 -0.70±0.06 0.14±0.02 20.18±2.35 3.42±0.56 0.79-2 -0.93±0.05 0.14±0.02 21.50±2.47 3.68±0.60 0.770 -1.09±0.04 0.15±0.02 24.40±2.54 4.45±0.67 0.752 -1.24±0.04 0.15±0.02 24.59±2.59 4.53±0.69 0.734 -1.37±0.05 0.14±0.02 21.34±2.65 3.71±0.67 0.716 -1.55±0.05 0.13±0.03 16.64±2.70 2.64±0.63 0.698 -1.64±0.04 0.11±0.04 12.57±2.78 1.79±0.60 0.67

10 -1.66±0.05 0.13±0.06 13.27±3.40 2.19±0.97 0.6312 -1.73±0.05 0.10±0.05 9.48±3.22 1.16±0.62 0.6014 -1.76±0.07 0.07±0.04 12.08±4.12 1.07±0.56 0.5916 -2.35±0.18 0.06±0.03 12.40±4.48 0.94±0.51 0.5518 -2.59±0.07 0.06±0.04 10.51±4.25 0.82±0.51 0.5320 -2.62±0.06 0.04±0.62 8.06±5.22 0.35±0.47 0.5122 -4.58±0.07 0.14±0.31 5.03±7.45 0.89±0.71 0.4824 -4.55±0.09 0.03±0.04 8.74±6.67 0.33±0.40 0.4626 -4.73±0.27 0.06±0.06 11.70±6.85 0.89±0.82 0.4328 -5.14±0.20 0.05±0.04 13.67±6.84 0.79±0.65 0.4130 -5.31±0.21 0.03±0.03 11.38±7.83 0.41±0.42 0.39

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Spur, blob, wiggle, and gaps in GD-1 7

Table 3. The track centre ϕ2, width σϕ2 , surface brightness I, linear densityλ of the stream spur as a function of ϕ1.

ϕ1 ϕ2,track σϕ2 I λ

[deg] [deg] [deg] [deg−2] [deg−1]

-38 1.07±0.20 0.23±0.14 5.24±1.41 1.53±0.79-36 1.16±0.07 0.26±0.10 6.34±1.19 2.04±0.69-34 1.22±0.07 0.26±0.10 7.22±1.23 2.40±0.78-32 1.30±0.05 0.22±0.07 8.03±1.44 2.18±0.61-30 1.34±0.05 0.20±0.06 7.66±1.46 1.89±0.52-28 1.37±0.06 0.18±0.06 6.09±1.37 1.41±0.46-26 1.41±0.08 0.17±0.08 4.24±1.31 0.91±0.42-24 1.50±0.08 0.11±0.08 3.22±1.62 0.45±0.33-22 1.54±0.09 0.07±0.09 2.44±2.02 0.22±0.26-20 1.54±0.12 0.07±0.12 1.80±1.87 0.17±0.26-18 1.53±0.12 0.16±0.21 1.83±1.64 0.37±0.48-16 1.41±0.18 0.18±0.35 3.46±2.38 1.22±1.35

total stellar mass sampled at each ϕ1 given the distance and photo-metric errors (controlling the filter width). Following this, we de-rive the relative mass sampling fraction fsamp in each ϕ1 bin relativeto the bin at ϕ1=-40 deg. The resulting mass sampling fractions aregiven in table 2 and shown in Figure 5. We stress that the sam-pling fraction is only dependent on the adopted stellar population,distance and colour-magnitude selection, and independent of dataquality and selection functions (outside of the selection of the filteritself). Over most of the extent of the GD-1 stream probed here,fsamp is consistent to within 20%, showing only a limited effect onthe density determination. However, for ϕ1 >-10 deg the Gaia DR2data probes less and less of the stream as the distance increases (seeFigure 1), culminating in a 40% sampling at ϕ1=30 deg. In Figure 5,we have corrected the surface brightness Iϕ1 and linear density λϕ1

for the relative effects of mass sampling shown in the top panel.The surface brightness and linear density displayed in Figure 5

make it clear that the GD-1 stream has experienced significant den-sity fluctuations across the extent studied here. There are four cleardensity peaks separated by three under densities of varying depth.Besides the peaks, the more negative ϕ1 side of GD-1 shows a de-creasing density accompanied by increasing stream width until thestream signal is lost. On the positive ϕ1 side the linear density alsodecreases, which is partially driven by a narrowing of the streaminstead of a lower surface brightness. Given that is the most dis-tant part of the stream sampled, the uncertainties on the density arehighest here.

The morphology of GD-1 complicates determining which ofthe under densities is most significant, since there is no clear streamcontinuum level and no progenitor. Nonetheless, we can concludethat the highest density part of the GD-1 stream is centered aroundϕ1=-48 deg, close to the location of the spur feature and a possibleplace where it attaches to the main stream track. The three otherpeaks at ϕ1 ≈-27,-10 and +2 deg are lower by nearly a factor two.The three under densities are located at roughly ϕ1 ≈-36,-20 and-3 deg, with the one at most negative ϕ1 showing a different loca-tion (ϕ1 ≈-38 deg) in surface brightness compared to linear density.This might be related to the spur feature, which is expected to in-fluence the stream width in this region. The least pronounced underdensity at ϕ1 ≈-3 deg is flanked by similar density peaks acrossan ≈20 degrees stretch of stream, shown to display a sinusoidalwiggle in the track in Figure 3. While this wiggle looks similar tocharacteristic “S”-shape of stars coming off the stream’s progeni-tor (as in Pal 5, Odenkirchen et al. 2001), this wiggle has the wrong

orientation given the orbit of GD-1 (e.g. Fig. 12 of de Boer et al.2018). If this larger scale structure is indeed related to the gap inits centre, it is likely the feature comes from a perturbation to thestream. Since GD-1 is on a retrograde orbit, the effect of baryonicperturbers in the disk should be minimal (Amorisco et al. 2016;Price-Whelan et al. 2016; Erkal, Koposov & Belokurov 2017; Pear-son, Price-Whelan & Johnston 2017) and thus this is a promisingcandidate for a subhalo interaction. Note however, that the streammorphology does appear to be somewhat affected by the presenceof baryons (Banik et al. 2019). Deeper data is needed to unambigu-ously determine the stream density here and to confirm the wigglein the stream. We discuss this feature in more detail in Section 6.7.Besides determining the mass sampling fraction in each ϕ1 bin, wecan also use the synthetic CMDs to determine the total mass andnumber of stars in the sampled region of the stream. Similar to themethod described above, we can determine what fraction of the to-tal mass is sampled within the optimised matched filter. Therefore,we can convert the observed densities to the total initial number andmass of the stream.

We start of with a fully sampled population of stars within amass range of 0.1-120 M�, under the assumption of a Kroupa IMF(Kroupa 2001). We then use an isochrone with the appropriate ageand metallicity to generate the number/masses of stars that are stillalive at the present day. These synthetic stars are then convolvedwith observational effects and the optimised matched filter to getthe filtered, current day density of stars that this population corre-sponds to. This number can be directly compared to the observeddensities to scale the initial mass of the population up or down, anddetermine the initial mass and initial number of stars of the streamsegment. The obtained number is computed under the assumptionof a mass range of 0.1-120 M� and Kroupa IMF, and will be differ-ent if there are changes in some of the more uncertain evolutionaryfactors such as mass loss or unusual stellar evolution processes.Given these restrictions, we determine that the visible stretch ofGD-1 corresponds to a total of 2.6 ± 0.09 × 104 initial stars, with atotal initial stellar mass of 1.80 ± 0.13 × 104 M�.

We also determine the total initial stellar mass containedwithin the spur feature within the spatial region over which we candetermine its track (see Section 3). Given these considerations, wefind that the spur should contain a total of 1.17±0.15×103 stars,with a total stellar mass of 0.81±0.22×103 M�.

Comparing the initial stellar mass of the visible stretch of GD-1 to the initial masses of Galactic GCs as computed by (Balbinot& Gieles 2018), we find that the mass of GD-1 corresponds to thevery lowest end of the mass spectrum of surviving MW GCs (whichhave a mean mass of 5.4×105 M�). Although the GCs we are com-paring to are the surviving ones (and therefore a sample biased to-wards larger masses), the GD-1 stream could contain several timesmore mass than probed here and still be lighter than the lowest massGC in the sample (Whiting1 with M=6±1×103 M�).

Compared to other stellar streams, such as those found in theDES survey, GD-1 has an intermediate total stellar mass (Shippet al. 2018). However, the GD-1 stream is much longer than thestreams found in the DES survey, while also being narrower acrossthat length. Therefore, GD-1 is a very low density stream spanninga wide range across the sky, making it a very interesting object totry to reproduce in simulations. In particular, it would be extremelyvaluable to determine the formation timescale of a stream like GD-1, and the survival chances of low mass globular clusters in the MWacross that timescale.

We can compare these numbers to the lifetimes of dissolvingGCs from Baumgardt & Makino (2003), who ran numerical simu-

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8 T.J.L. de Boer et al.

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Figure 5. Overview of the best-fit parameters of the GD-1 stream, showing the mass sampling fraction (fsamp), track position ϕ2,track (with stream widthshown as dashed lines), stream width (σϕ2 ), surface brightness I(ϕ1) and linear density λ(ϕ1). Parameters have been determined by fitting a Gaussian plus 1storder polynomial background to the data shown in Figure 3. The surface brightness and linear density shown here have been corrected for the effects of masssampling given in the top panel.

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Spur, blob, wiggle, and gaps in GD-1 9

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Figure 6. Residuals of the extracted member stars of the GD-1 stream, in position (top panel) with zoom-in (second panel) and PM space (bottom twopanels). Black points indicate the overall stream sample, while red (blue) points show the spatially selected spur (blob) stars, given the rough positions fromPrice-Whelan & Bonaca (2018) The lines show straight line fits to the proper motions of the spur and underlying stream stars.

lations of dissolving GCs in realistic tidal fields. Using their equa-tions 7 and 8, with a GD-1 apocentre distance of 28 kpc (Willettet al. 2009), we find that a GC with an initial number of 1.3×104

stars has a dissolution time of roughly 12 Gyr, being the upper limitof GD-1 dissolution. This corresponds to an initial mass of roughly0.88×104 M� and about half that at the present day after mass lossdriven by stellar evolution (i.e. ∼ 4.4 × 103 M�). The difference inmass is roughly a factor 4, with the stream having too much massat the present day to be produced by the full dissolution of a GCwithin the appropriate time interval. This indicates that either theprogenitor of the GD-1 stream has not (fully) dissolved, or there issome missing physics in the Baumgardt & Makino (2003) simula-tions. This discrepancy would be exacerbated if we consider thatwe are not probing the full length of the stream within the GaiaDR2 data. To produce higher dissolved stream masses, cases thatboost the stellar escape rate need to be considered, such as start-ing with low density progenitors or retaining black holes within theparent GC (Giersz et al. 2019, Erkal, Gieles, & de Boer in prep).

It would be beneficial for the study of GD-1 to obtain an es-timate of the age of the stream. This will likely require greatermapping of the stream extent to find its true length, as well asa more extensive campaign of spectroscopic follow-up to obtain

the full kinematic profile. It is interesting to note that Banik et al.(2019) find good stream fits for simulations with young ages (≈5Gyr) and Webb & Bovy (2019) infer a (dynamical) stream age of3.4Gyr. This would imply the progenitor of the stream should stillbe around and potentially traceable with adequate data.

5 STREAM RESIDUALS

Besides the stream density and widths, we also look at the track andPM residuals along the stream, to search for hints of small scalewiggles and deviations. To facilitate this, we first extract the sam-ple of stream stars from the data, given the parameters determinedabove. For each ϕ1 bin, we extract all the stars contained withinthe maximum signal-to-noise matched filter and satisfying cuts inspatial position and PM around the best-fit tracks shown in Fig-ures 2 and 3. The sample of best-fit member stars is available onhttps://github.com/tdboer/GD1_members. Figure 6shows the residuals in both spatial coordinates ϕ2 = ϕ2-ϕ2,0 andPMs µϕ1 − µϕ1,0 ,µϕ2 − µϕ2,0 for the extracted sample of GD-1 stars,as a function of ϕ1. The second panel shows a zoom-in of the streamtrack to bring out small offsets in ϕ2 around the stream track.

c© 2017 RAS, MNRAS 000, 1–18

10 T.J.L. de Boer et al.

The stream is readily apparent as an over-density aroundthe fitted tracks, although background contamination is also stillvisible. We have not attempted to quantify the stream member-ship probability here, since part of our goal is to investigate thebehaviour of the features described in Price-Whelan & Bonaca(2018), which would be excluded on the basis of spatial member-ship probability. Figure 6 makes it clear our fitted tracks well repro-duce the large scale behaviour of GD-1 as function of ϕ1. However,there are also signs of small scale wiggles in the stream track oforder 0.2 deg, as already seen in de Boer et al. (2018). In particular,there is a small scale wiggle corresponding to the sinusoidal trackshape shown in Figure 4, which does not appear to correspond toany clear changes in the PMs in the bottom two panels.

Besides the main GD-1 stream stars, in Figure 6 we have alsohighlighted the stars belonging to the spur and blob discovered byPrice-Whelan & Bonaca (2018). The selections of both features arebased solely on the spatial positions, without considering selectionin PM apart from the rough cuts around the track. The extractedstars are consistent with the stream PMs, showing unequivocallythat these features are not due to background contamination. Thewidth in PM space for both features appears slightly larger thanfor the underlying stream stars at similar ϕ1. To study this in moredetail, we determine the mean PM residuals and widths of bothsamples from the highlighted samples in Figure 6.

For the spur stars, the mean PM residuals are (µϕ1 , µϕ2 ) =

(0.038, 0.177) mas/yr along with standard deviation widths of(σµϕ1

, σµϕ2) = (0.882, 0.927) mas/yr. This can be compared to

the residuals for stars within the main stream (with |ϕ2| < 0.75deg), covering the same range of ϕ1, which are (µϕ1 , µϕ2 ) =

(−0.021,−0.004) mas/yr and widths (σµϕ1, σµϕ2

) = (0.620, 0.802)mas/yr. Therefore, the spur stars are slightly offset from the streamand have a larger width in both µϕ1 and µϕ2 . Notable, the propermotions of the spur stars point away from the stream in µϕ2 . How-ever, the sample sizes are small and the errors are large enough(the error on the mean is (0.096, 0.101) mas/yr for spur stars and(0.037,0.048) mas/yr for stream stars) that the differences are notsignificant enough to conclude unambiguously that the two samplesshow different PMs.

To investigate the proper motions of the spur in more detail,we divide the sample using a cut at ϕ1 = −30 degrees to select thespur closer to and further away from the possible connection point.For the spur below ϕ1 = −30 degrees, the mean PM residuals are(µϕ1 , µϕ2 ) = (−0.064, 0.225) mas/yr along with standard deviationwidths of (σµϕ1

,σµϕ2) = (0.895, 0.842) mas/yr. The error on the

mean is (0.138,0.130) mas/yr. In comparison the stream stars cover-ing the same spatial range show (µϕ1 , µϕ2 ) = (−0.090, 0.022) mas/yrand widths (σµϕ1

, σµϕ2) = (0.649, 0.774) mas/yr and an error on the

mean of (0.069,0.082) mas/yr. Clearly, the proper motions are morelike the stream closer to the connection point, and agree withinroughly one sigma. However, for the spur above ϕ1 = −30 degreesthings look slightly different. The mean PM residuals of spur starsare (µϕ1 , µϕ2 ) = (0.162, 0.335) mas/yr along with standard devia-tion widths of (σµϕ1

, σµϕ2) = (0.853, 1.018) mas/yr, with an error on

the mean of (0.174,0.208) mas/yr. In comparison the stream starscovering the same spatial range show (µϕ1 , µϕ2 ) = (0.064, 0.051)mas/yr and widths (σµϕ1

, σµϕ2) = (0.557, 0.792) mas/yr and an er-

ror on the mean of (0.055,0.079) mas/yr. In this case, the propermotions are significantly higher in the spur than in the accompany-ing stream, and even higher than the proper motion in the streamat the connecting point around ϕ1 = −45 degrees. This implies thatthe spur stars likely received a noticeable velocity kick away fromthe main stream due to the interaction with an external source.

Finally, we consider the case of a gradient in proper mo-tions across the spur region. To that end, we fit the data usinga straight line ( f (x) = A(x + 45) + B) in the region −45 <

ϕ1 < −20 degrees, which is well populated. This results in so-lutions (A, B) = (−0.010 ± 0.011, 0.121 ± 0.164) for µϕ1 and(A, B) = (0.010 ± 0.010, 0.090 ± 0.165) for µϕ2 . For compari-son, we also fit the same line to the main stream, resulting in(A, B) = (0.006 ± 0.006,−0.167 ± 0.088) for µϕ1 and (A, B) =

(−0.010 ± 0.006, 0.108 ± 0.089) for µϕ2 . The stream stars are con-sistent with a flat slope within 2 sigma in µϕ1 , for both spur andstream stars. However, the proper motion gradient in µϕ2 is morepronounced and is pointing in the direction away from the streamfor the spur stars. Considering Figure 6 it becomes clear the num-ber of stars populating the furthest part of the spur is small, mean-ing these gradient are subject to small number statistics and shouldbe followed up with additional observations, most notably radialvelocity measurements.

In the case of the blob feature, the PM residuals have(µϕ1 , µϕ2 ) = (0.058, 0.067) mas/yr with widths (σµϕ1

, σµϕ2) =

(0.892, 0.769) mas/yr and the associated stream stars at similar ϕ1

have (µϕ1 , µϕ2 ) = (0.184, 0.002) mas/yr with width (σµϕ1, σµϕ2

) =

(0.993, 0.735) mas/yr. While slightly larger, the PM differences arestill not significant enough (the error on the mean is (0.078,0.067)mas/yr for the blob and (0.161,0.119) mas/yr for the stream) to con-clude they follow different orbits.

6 DISCUSSION

6.1 Data quality and selection functions

To assess the robustness of the GD-1 densities and features pre-sented in this work, it is relevant to consider the effects of selectionfunctions and systematics on the recovered stream sample.

The selection functions used to extract the stream sample aremostly simple cuts in quantities, such as for the proper motions asdiscussed in section 2.2 of the data section. This is similar to whatwas done by Price-Whelan & Bonaca (2018), although our selec-tion are allowed to vary with angle along the stream. The morecomplicated selection function is that of colour and magnitude,which is slightly different from the simple colour-magnitude boxadopted by Price-Whelan & Bonaca (2018). In practice, our selec-tion function is also a colour-magnitude box, but it is allowed tovary in shape both due to differing distance as well differing dataquality and back/foreground contamination, as a function of streamangle. While more complicated, the adoption of the mass samplingcorrection ensures that the densities recovered from this more com-plicated colour-magnitude box are corrected for GD-1 stars not in-cluded within that selection (be that by not being observed or bynot being included in the final sample due to selection functions).Therefore, the use of the matched filtering approach does not leadto systematics in the recovered densities.

The completeness of the Gaia data varies across the sky dueto the current coverage in DR2, with reported completeness in G inbetween 19th and 22th mag. The spatial region covered in this studyis complete down to 21th mag according to the completeness plotsproduced by the Gaia collaboration (Arenou et al. 2018), and sincewe are restricting ourselves to G=20 data for astrometry, we arelimiting ourselves to a sample that is complete, at least in terms ofstars having measurements from Gaia. To asses whether these mea-surements are robust or not, we have investigated the particulars ofthe sample in more detail. The sample of stream stars selected by

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Figure 7. Comparison between the surface brightness profile of deep CFHTdata from de Boer et al. (2018) and from Gaia. The Gaia profile has beenscaled up to account for the differing depth between both datasets.

our filtering contains only 5 stars that do not satisfy the selection onthe unit weight error for robust astrometry provided by Lindegrenet al. (2018) (their Equation C.1) none of which is located near thestream track, spur or blob features. Furthermore, our best selectedsample has only 13 stars for which less than 8 visibilityperiods wereused, out of which only 5 are actually on the stream, in the well-populated region around ϕ1=−50 deg. Therefore, the vast majorityof the sample satisfies the criteria for possessing a robust astromet-ric solution. Therefore, the quantities that are used to characterisethe stream are all well measured.

Nonetheless, we cannot rule out effects of the Gaia scanninglaw on e.g. the low-density features, as already mentioned by Price-Whelan & Bonaca (2018). However, the typical spatial scale ofscanning law effects implies that they do not influence the largerscale trends observed in the GD-1 stream track. To investigate thisin more detail, we have made a comparison between our Gaia mea-surements and those obtained from a completely different dataset.Figure 7 compares the (appropriately scaled) surface brightness(density) profile of the Gaia data to the one obtained from the verydeep CFHT data shown in de Boer et al. (2018). The comparisonshows that the peaks/gaps are largely consistent, barring some dis-agreement at the edge of the CFHT footprint (below ϕ1=−45 deg),mainly due to a difference in the stream track/width used with theCFHT data. All the major gaps and peaks are found in the samelocations, showing that the Gaia data results in robust measure-ments of the GD-1 density profile. Comparison between the streammorphology in the overlapping parts of the two datasets also showsgood agreement in the recovered tack and width. This indicates thatthe GD-1 densities and features extracted from the Gaia data arenot sensitive to the selection functions and scanning law patternwhere they are well sampled. Nonetheless, we avoid making def-inite statements regarding the exact depth, shape or centre of anyfeatures found in poorly sampled regions of the dataset, until theycan be followed up with deeper data.

6.2 Alignment of GD-1

Recently, Carlberg (2019) argued that in ΛCDM, tidal streamsshould have velocities misaligned with the stream orientation due tolate-time accretion events and the subsequent damped oscillationsin the host galaxy’s dark matter halo. They predict that the veloc-

ity perpendicular to the stream will in general be non-zero and thatit should follow an exponential distribution with a scale velocityof ∼ 10 − 20 km/s. Using the technique suggested in Erkal et al.(2019), we can compare the orientation of GD-1 on the sky with itsproper motions to determine whether stars move along the stream.Similarly, we can compare the distance gradient along the streamwith its radial velocity.

We show this alignment in Figure 8. In the top left panel wecompare the slope of the stream on the sky, dϕ2/dϕ1, with the ra-tio of reflex corrected proper motions, µϕ2/µϕ1, as was done in Fig.1 of Erkal et al. (2019). We stress that this µϕ1 does not have thetypical cosϕ2 factor. The close alignment shows that the streamstars are moving along the stream on the sky. Interestingly, we alsosee that the stream slope shows some rapid changes, i.e. wiggles inthe stream track, which are aligned with the underdensities in thestream (shown with vertical black dashed lines). These correlatedsignals between the density and stream track are expected fromsubhalo impacts (e.g. Erkal & Belokurov 2015b). Furthermore, theproper motions also appear to show the same rapid changes (e.g.around -5 deg and -45 deg), however this is not statistically sig-nificant. Improved data with Gaia DR3 will allow us to determinewhether these associated proper motion signals are real.

In the bottom left panel of Figure 8 we present an alternativeway of looking at the stream alignment on the sky. We define theperpendicular velocity, v⊥, as the velocity perpendicular to the localstream track. This is defined as

v⊥ =kr

(−µ∗ϕ1

dϕ2dϕ1

1cosϕ2

+ µϕ2

)(1 +

(dϕ2dϕ1

1cosϕ2

)2)1/2 , (1)

where k = 4.74047 km s−1 kpc−1 mas−1 and r is the distance to eachstar. These velocities are small and consistent with zero althoughwe note that the error bars are still quite significant.

As with the proper motion on the sky, we can also compare theradial velocity, proper motion, and distance gradient. If the streamis an orbit these will be related, namely dr/dϕ1 = vr/µϕ1. We com-pare these two quantities in the top right panel of Figure 8 and wesee that they match over the range where we have radial velocities.This shows that the stream is aligned in the radial direction andalong the line of sight. Finally, we can use this gradient to deter-mine the excess radial velocity along the line of sight, i.e.

∆vr = vr −dr

dϕ1µϕ1. (2)

This quantity is shown in the bottom right panel of Figure 8 andshows a scatter consistent with zero although the error bars arequite large.

Given the substantial time needed to form a stream as longas GD-1 (∼ 5 Gyr, see Sec. 6.5), this alignment suggests that theobserved portion of GD-1 has not been significantly affected byaccretion events. We estimate the closest approach between GD-1 and the Large Magellanic Cloud (LMC) using the simulationsin Section 6.5 and find the observed part of GD-1 has a closestapproach of ∼ 45 kpc at φ1 ∼ −90◦. This is substantially largerthan the closest approach of ∼20 kpc between Orphan and the LMC(Erkal et al. 2019). Furthermore, we note that simulations of theLMC’s effect on the Milky Way’s stellar halo show that its effectis small within ∼ 30 kpc due to the short orbital period of thesestars compared to the LMC’s infall timescale (Garavito-Camargoet al. 2019; Petersen & Penarrubia 2020; Erkal, Belokurov & Parkin2020). Thus, the alignment of GD-1 is not inconsistent with thepicture of Carlberg (2019) but shows that streams in the inner part

c© 2017 RAS, MNRAS 000, 1–18

12 T.J.L. de Boer et al.

of the Galaxy may be less sensitive to the halo’s time-dependencethan those in the outskirts.

Improved measurements of the proper motions with Gaia DR3will allow us to better measure these perpendicular velocities forGD-1 and other streams and thus more precisely measure the time-dependence of the Milky Way halo as suggested in Carlberg (2019).

6.3 Orbit fits

In order to further highlight how perturbed GD-1 is, we performorbit fits in the Milky Way potential from McMillan (2017) usingGALPOT (Dehnen & Binney 1998). We choose to restrict the fit towhere GD-1 has a significant density, −60 < ϕ1 < 10 deg andto fix the potential to that of McMillan (2017). We integrate theorbit forwards and backwards from ϕ1 = −45 deg. For orbit fitswe note that this choice is arbitrary and will give an identical fitfor any choice of ϕ1. While the potential is fixed, we vary the other5 parameters describing the orbit: radial velocity, proper motions,distance, and ϕ2. The orbit is integrated forwards and backwardsfor 150 Myr which produces a stream substantially longer than theobserved region of GD-1 and is thus sufficient to compare withthe data. Given the orbit, we compute a combined likelihood usingall observables (track on sky, distance, radial velocity, and propermotions). We use EMCEE to explore the likelihood space with 100walkers and 1000 steps.

The best fit stream is shown in the left panel of Figure 9. Thestream matches all observables well, although the track deviatesfrom the orbit outside of the range we fit. The right panel of Figure9 shows the residuals of this best fit and the data. Interestingly, thereare significant residuals in the stream track. These residuals arecorrelated with the underdensities in the stream (vertical dashed-black lines), especially the gap at ϕ1 = −4 deg. These wiggles inthe residual show that the stream track has significant small scalestructure in it. This will not be ameliorated by changing the globalMilky Way potential which will instead make large scale changesto the stream.

These correlated signals are essential for determining theproperties of the perturbers which created these features. Indeed,Erkal & Belokurov (2015b) showed that 3 observables are neededto fully fit the stream gap down to a 1d degeneracy between theperturber’s mass and relative velocity. It is not clear if more ex-tended substructure like the bar or spiral (e.g. Hattori, Erkal &Sanders 2016; Price-Whelan et al. 2016; Erkal, Koposov & Be-lokurov 2017; Pearson, Price-Whelan & Johnston 2017; Banik &Bovy 2019) can produce identical features or whether the featuresproduced can be used to measure the properties of the bar or spiralarms. For GD-1, there are now several features for which we havetwo observables (track on sky and density). Thus, radial velocityfollow-up of these features is essential for completing the fits.

6.4 Connection of the spur with other nearby structures

In addition to the spur near GD-1 discovered by Price-Whelan &Bonaca (2018), there are a number of other stream-like featuresnear GD-1. In particular there is the Gaia-5 stream discovered byMalhan, Ibata & Martin (2018) which is seemingly coincident withthe spur. There is also the PS1-E stream discovered by Bernardet al. (2016) which also looks like an extension of GD-1 (see e.g.Fig. 1 of Malhan et al. 2019). In Figure 10 we show both of thesestreams in addition to our measured track for GD-1 and the spur.Note that in this figure, the track for PS1-E is taken from GAL-STREAMS (Mateu, Read & Kawata 2018). The points for Gaia-5

from Malhan, Ibata & Martin (2018) and for the spur as used inBonaca et al. (2019) are extracted from those papers. Althoughthese streams are coincident on the sky, they are likely unrelatedto GD-1 or the spur. Gaia-5 has a distance (18.5-20.5 kpc) which ismuch larger than GD-1 and a proper motion which is much smaller(Malhan, Ibata & Martin 2018). Similarly, although PS1-E has adistance of ∼ 12.6 kpc which is similar to GD-1 and the spur, theextended view of the spur in this work shows that the orientationof PS1-E is quite different in the region on the sky where they areco-located.

6.5 Effect of the classical dwarfs on GD-1

Now we turn to the classical dwarfs to determine whether they canhave an effect on GD-1. We use proper motions from Gaia Collab-oration et al. (2018) and radial velocities and distances from Mc-Connachie (2012). We model each dwarf (except the LMC) as aHernquist profile (Hernquist 1990) with a mass of 109 M� and ascale radius of 1 kpc. Since the LMC can affect the orbits of eachsatellite (Erkal & Belokurov 2019), we must include the effect ofthe LMC. We model the LMC as a Hernquist profile with a massof 1.5 × 1011 M� and a scale radius of 17.14 kpc, consistent withthe measurement in Erkal et al. (2019). We include the dynamicalfriction on the LMC from the Milky Way using the prescription ofJethwa, Erkal & Belokurov (2016). We choose to model the MilkyWay using the MWPotential2014 from Bovy (2015) since itis computationally cheaper than the potential in McMillan (2017).Since we are using a different potential and since we include theLMC, we first re-fit GD-1 including the LMC. This cannot be donewith orbits since different parts of the stream are affected differ-ently by the LMC.

Instead, we fit GD-1 using the stream generation techniquefrom Erkal et al. (2019) which is based on the modified LagrangeCloud Stripping technique from Gibbons, Belokurov & Evans(2014). This technique is able to reproduce the full 6d shape ofstreams (e.g. Gibbons, Belokurov & Evans 2014; Erkal et al. 2019)but is not designed to match the density along the stream since thisdepends on how much stripping occurs along the orbit. We choseto place the progenitor of GD-1 at ϕ1 = −45◦. This location waschosen since it roughly lines up with an overdensity in GD-1 atϕ1 = −48◦ (see Fig. 5). We note this choice is also consistent withpredicted progenitor location from Webb & Bovy (2019). Sincethere is no obvious progenitor over the observed extent of GD-1,we linearly interpolate the mass from an original value of 2×104 M�5 Gyr ago to zero at the present. The disruption time of 5 Gyr wasneeded to produce a stream matching the observed length of GD-1.We fit for its position on the sky, ϕ2, distance, radial velocity, andproper motions. As in Section 6.3, we define the likelihood usingall of the observables and perform the fit using EMCEE (Foreman-Mackey et al. 2013). This gives a good fit for GD-1 and althoughwe have included the LMC, these best-fits do not show any appre-ciable difference from the best-fit we show in Figure 9.

For each classical dwarf (except the LMC), we make 100 real-izations of its present-day phase-space position. Using the best-fitstream parameters, the progenitor for GD-1 is then rewound for 5Gyr in the combined presence of the dwarf, the LMC, and the MilkyWay. Note that we account for the force of each of these compo-nents (i.e. GD-1 progenitor, dwarf, LMC, and Milky Way) on eachother during this process. Thus, we also account for the reflex mo-tion in the Milky Way from the LMC. Following this, the progen-itor is then disrupted using the stream generation technique from

c© 2017 RAS, MNRAS 000, 1–18

Spur, blob, wiggle, and gaps in GD-1 13

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Figure 8. Alignment of the GD-1 streams’s kinematics and 3d structure. Top left: Comparison of the slope of the stream on the sky, dϕ2dϕ1

(blue error bars), with

the ratio of its reflex corrected proper motions,µϕ2µϕ1

(red error bars). These are well matched across the entire range. Interestingly, stream track shows somesharp features which correspond to the location of the gaps in density (shown with vertical black dashed lines). Bottom left: On-sky velocity perpendicular tothe stream track. This shows that the velocity perpendicular to the stream track is small and consistent with zero, i.e. that the stars are moving along the streamon the sky. Top right: Comparison of the slope of the stream in distance, dr

dϕ1, with the slope corresponding to its reflex corrected radial velocity and proper

motions, vrµϕ1

. The close match shows that the stream’s velocity in the radial direction is pointed along the stream. The radial velocities used in this figure fromcome Koposov, Rix & Hogg (2010). Bottom right: Difference between the stream’s radial velocity and that expected from its proper motion and distancegradient. This difference is consistent with zero showing that the stream does not have a measurable velocity perpendicular to its track.

Erkal et al. (2019) which is based on the modified Lagrange CloudStripping technique from Gibbons, Belokurov & Evans (2014).

Amongst the classical satellites, we find that only Sagittariuscan have an appreciable effect on GD-1 based on visual inspectionof mock observations of each stream. In particular, we searched forstreams with particles with angular offsets similar to the spur andthe blob. We chose to do this by eye to see if there was any signif-icant variation in morphology. The fact that only Sgr has an affectmakes sense since the pericenter of Sagittarius is ∼ 15 kpc (e.g.Gaia Collaboration et al. 2018) and it is the only classical dwarfwhich passes within the extent of GD-1’s orbit. Since only Sagittar-ius can pass close to GD-1, this null-result for the other dwarfs doesnot depend strongly on the mass and scale radius we chose for thedwarfs. We note that the chosen mass and scale radius match whatwas needed to fit the Sagittarius stream (Law & Majewski 2010)thus our results should be robust for Sagittarius. Out of the 100realizations, 4 show spur-like features with a low-density streamnearly parallel to the main stream with a similar angular offset tothe spur. Each of these has a close (. 3 kpc) approach with Sagit-tarius during its previous pericenter (∼ 3 Gyr ago).

In order to study the effect of Sagittarius more closely, we per-

form an additional 900 realizations with positions and velocitiessimilar to the most promising 4 of the initial 100 realizations. Wedo this by sampling the observables (i.e. distance, radial velocity,and proper motions) about the values of this realization with 1% ofthe observed errors. 356 of these realizations produce a spur-likefeature which overlaps with the observed spur in GD-1 and 445have features in the location of the blob. We show five of these re-alizations in Figure 11. These features are due to a close encounter(∼0.5-3 kpc) with Sagittarius approximately 3 Gyr ago. We stressthat these five examples were chosen to have features like the spurand thus this is not a generic prediction of the effect of Sagittariusbut rather a possibility given uncertainties on its present-day phase-space position. In order to better assess whether the spur is due tothe effect of Sagittarius or a substructure as modelled in Bonacaet al. (2019), we will need to compare the detailed morphologyof the spur and better understand the past orbit of Sagittarius bygetting a faithful fit to its stream. We note that we have ignored thedisrupted dark matter halo of Sagittarius in this exploration and thiscould have a significant effect (e.g. Bovy 2016).

We note that the perturbations from Sagittarius shown in Fig-ure 11 feature a spur which extends much further to the left than

c© 2017 RAS, MNRAS 000, 1–18

14 T.J.L. de Boer et al.

420

2 (de

g)

101418

r (kp

c)

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0

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v r (k

m/s

)

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12840

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as/y

r)

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g)

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c)

250

2550

v r (k

m/s

)

60 50 40 30 20 10 0 101 (deg)

1

0

1

PM (m

as/y

r)Figure 9. Best fit orbit in the Milky Way potential from McMillan (2017). The fit is restricted to the region where the stream has a significant density, i.e.−60 < ϕ1 < 10 deg. The left panel shows the best-fit against the observables while the right panel shows the residuals for each observable. Interestingly, thereare significant residuals in the stream track (top right panel) on small scales. These small scale residuals cannot be ameliorated by changing the Milky Waypotential which will change the stream on larger scales. These residuals line up with the underdensities in the stream (vertical dashed-black lines) suggestingthat they are connected. Such correlated signals are expected from perturbations by baryonic and dark substructure (e.g. dark subhaloes, satellites, globularclusters, giant molecular clouds, Erkal & Belokurov 2015b).

60 50 40 30 20 10 01 [deg]

2

1

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1

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4

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2 [de

g]

PS1-EGaia-5Bonaca+19

GD-1Spur

Figure 10. Comparison of the results of this work with previously knownfeatures near GD-1. The black points show the spur from Bonaca et al.(2019). The blue points show the stream, Gaia-5, found by Malhan, Ibata &Martin (2018). Although Gaia-5 looks like a continuation of the spur, it hasa significantly different distance and proper motion than GD-1. The greyband shows the stream PS1-E discovered in Bernard et al. (2016). Althoughthis stream has a similar distance to GD-1, it has a different orientation tothe spur when they overlap. Thus, although there appears to be a wealth ofstructure near GD-1, most of this is unrelated to the stream. We note that thelast two green datapoints suffer from low significance due to a low numberof stars in the sample.

the known spur. Interestingly, the observed width of GD-1 roughlydoubles to the left of ϕ1 ∼ −38◦ which is close to where the ob-served spur terminates (see middle panel of Fig. 5). Thus, it is pos-sible that the spur is much longer than currently observed but istoo close to GD-1 to distinguish it with current data. Deeper pho-tometry in this region is needed to better understand how the spurconnects onto GD-1 and how far it extends.

Recently, Bonaca et al. (2020) measured the radial velocitiesof stars in the spur and main stream of GD-1 and have made these

2.5

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Figure 11. Effect of the Sagittarius dwarf on the GD-1 stream. The panelsshow five different realizations of the present-day phase-space of Sagittar-ius. These were selected since they exhibited features similar to the spur. Ineach panel, the red error bars show the observed stream track and the greenerror bars show the observed track of the spur. In some of the realizations(i.e. lowest two panels) the interaction with Sagittarius can also create afeature below GD-1 in a similar location to where the blob.

publicly available. In Figure 12 we compare these with our modelsof perturbations by the Sagittarius dwarf. To make this comparison,we compute the radial velocity offsets of our stream models froma linear fit to the radial velocity over the range −50◦ < ϕ1 < −25◦.We separate our simulated stream particles into particles withinthe main stream (< 0.4◦ from the simulated stream track) and off-stream (> 0.4◦ from the simulated stream track). We compare theradial velocity offsets of these particles with the measurements ofBonaca et al. (2020), in particular with their radial velocity offsetsfrom their best fit orbit. We choose to compare offsets instead of ve-locities because our GD-1 models have been fit to the radial veloc-

c© 2017 RAS, MNRAS 000, 1–18

Spur, blob, wiggle, and gaps in GD-1 15

505

v r(k

m/s

)

Main streamOff-stream

Bonaca+2020, streamBonaca+2020, spur

505

v r(k

m/s

)

505

v r(k

m/s

)

505

v r(k

m/s

)

50 45 40 35 30 251 (deg)

505

v r(k

m/s

)

Figure 12. Effect of the Sagittarius dwarf on the radial velocity of the GD-1stream. Each panel corresponds to the panels in Fig. 11. In each panel, theblue points show the radial velocity offset of the main stream and the redpoints show the radial velocity offset of stars off the stream (> 0.4 deg fromthe stream track). These radial velocity offsets are computed by subtractinga linear fit to the radial velocity. The blue (red) points with error bars showthe radial velocity offsets from Bonaca et al. (2020) in the main stream(spur). In all cases we find that the mean radial velocity of the spur starsare within 1 km/s of the main stream, consistent with the results of Bonacaet al. (2020). Note that the x-axis has a reduced range compared to Fig. 11.

ities from Koposov, Rix & Hogg (2010) which have an offset fromthose in Bonaca et al. (2020). Over the range −34◦ < ϕ1 < −29.5◦

where Bonaca et al. (2020) have radial velocity measurements ofboth the main stream and spur stars, we find that the mean veloc-ity of the main stream and off-stream stars are within 1 km/s ofeach other, consistent with their measurements. Interestingly, wefind that the off-stream stars have a slightly larger dispersion, up to∼ 1.8 km/s in the 5 cases considered here, compared to the mainstream which has a dispersion of ∼ 0.6 km/s. In order to comparethis with the measurements of Bonaca et al. (2020), we fit a Gaus-sian to the radial velocity offsets of their spur stars and found adispersion of 2.1 ± 0.4 km/s, consistent with our slightly increaseddispersion.

6.6 Morphology of the spur

In general, features like the spur, highlighted in Figure 4, can nat-urally arise from a subhalo interaction. As a subhalo passes nearthe stream, it kicks stars and changes their orbits (e.g. Carlberg2012; Erkal & Belokurov 2015a). The kicks along the stream di-rection change the orbital period of stars, causing them to subse-quently move along the stream, while kicks perpendicular to thestream lead to oscillations about the stream. Generically, the per-turbed streams will have wiggles in them. However, at late times,the perturbed stars overtake (or undertake) the unperturbed starssince they have different orbital periods and the stream folds on it-self, giving the “caustic” phase of gap growth identified in Erkal& Belokurov (2015a). In such a case, the stream folds on both theleading and trailing side of the gap. Indeed, Bonaca et al. (2019)has provided the first fits to the spur where it arises from such aperturbation.

Interestingly, the extended view of the spur shown in this workis difficult to reconcile with the adjacent gap at ϕ1 ∼ −36 deg. This

2

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Figure 13. Example of a spur created from a recent subhalo impact. The toppanel shows the stream on the sky where blue points are the model and redand green error bars show the observed stream track and spur respectively.The bottom panel shows the stream density. The red histogram shows theobserved density and the blue line shows the density of the model stream.The vertical black dashed lines show the location of the peaks in the streamdensity. Crucially, in the model the connection of the spur and the streamalways lines up with the density peak in the stream. This is in contrast wherethe spur extends across most of the gap.

is because although features like the spur are generically expected,they also come with a precise relation between the stream track andthe density. In particular, the peak in the density corresponds to thelocation where the spur attaches onto the stream. To demonstratethis point, in Figure 13 we show an example of a spur created fromthe impact of a stream with a subhalo. To do this, we start with thebest-fit orbit from Section 6.3, we then rewind the orbit for 1 Gyrand initialize a train of 1000 particles at 1 Gyr in the past using aspacing of 0.025 Myr. This train is then evolved to the present inthe presence of the Milky Way potential and a subhalo modelledas a Hernquist profile. For the example shown in Figure 13, weused a subhalo with a mass of 107 M� and a scale radius of 0.25kpc. The closest approach with the stream (i.e. the particle train)occurs 400 Myr ago and gives rise to the spur feature. We notethat this is not meant to be a fit to the stream but rather to highlighthow the spur and density are connected. This also follows from theanalytical results in Erkal & Belokurov (2015b). This connectionbetween the spur connection and density is also apparent in themodels of Bonaca et al. (2019) (e.g. their Fig. 3).

Unlike the model, however, the observed spur extends acrossmuch of the gap (e.g. Fig. 13). Thus, despite the close proximityof the spur and the gap, they may be unrelated. Indeed, Webb &Bovy (2019) have recently suggested that the gap at ∼ −35◦ maybe due to the disruption of the progenitor. Instead, the spur couldbe explained by the model of Sagittarius we presented in Section6.5 or by a subhalo impact further to the left of the spur. Carlberg(2018) has also argued that the original host dwarf galaxy whichGD-1 was accreted with could significantly perturb the stream andMalhan et al. (2019) found debris around GD-1 which they arguedwas consistent with this picture.

6.7 Mechanism for gap and wiggle at -3 deg

One other feature which stands out in the maps of GD-1 (e.g. seeFig. 4) is the under-density at ϕ ∼ −3◦. Although the significanceof the under density itself is the lowest out of all the gaps detected

c© 2017 RAS, MNRAS 000, 1–18

16 T.J.L. de Boer et al.

in GD-1, the wiggle of the stream track surrounding it is of specialrelevance when considering the progenitor location of the stream.This feature was also found by Malhan et al. (2019). They inter-preted this feature as the location of the possible progenitor of GD-1. However, while the progenitor would be expected to be asso-ciated with a wiggle in the stream track (see e.g. Fig. 12 in deBoer et al. 2018), this wiggle has the wrong orientation. The wig-gle from a progenitor should be below and then above the averagestream track as ϕ1 decreases. This is the opposite to what is seen atϕ1 ∼ −3◦. Thus, it appears that this wiggle and associated under-density is likely a perturbation to the stream from substructure inthe Milky Way. Such a feature is generically expected from a sub-halo perturbation (e.g. Erkal & Belokurov 2015b). Future fits to thisfeature will allow us to determine whether it is due to a baryonicsubstructure or a dark matter subhalo.

6.8 Association with globular clusters

Using the orbits from Section 6.3, we now compare the energy andactions of GD-1 with the population of GCs to look for possibleassociations. These quantities are computed in the Milky Way po-tential from McMillan (2017) using AGAMA (Vasiliev 2019a). Theglobular cluster properties come from Vasiliev (2019b). To get thedifferences in energy and actions, we sample the chains from ourfit to GD-1 in Section 6.3 and sample the observables for each GCfrom their errors. For the difference in actions, we add the differ-ences of each action in quadrature, i.e. ∆J =

√∆J2

z + ∆J2φ + ∆J2

r .The difference in energy and action is shown in Figure 14

which shows that both NGC 3201 and NGC 6101 are the closestto GD-1 in phase space. Although neither of these is on a simi-lar enough orbit to be the progenitor of GD-1, this is particularlyinteresting since both of these are believed to have been accretedwith the Gaia-Sequoia event (Myeong et al. 2019). We note thatMyeong et al. (2019) also point out the similarity in action betweenthe Gaia-Sequoia clusters and GD-1. This suggests that GD-1 couldbe exposed to a higher background of dark matter subhaloes than astream on a random orbit since the subhaloes of the Gaia-Sequoiagalaxy will be on similar orbits to GD-1. Furthermore, these sub-haloes will have smaller relative velocities to GD-1, allowing themto impart larger velocity kicks and thus perturb GD-1 more thannaively expected.

7 CONCLUSIONS

In this work, we have utilised data from Gaia DR2 to study the dis-tance, morphology and density of stars in the GD-1 stream. Similarto other works, we stress that the precise PMs delivered by the Gaiamission were instrumental in selecting a high probability sample ofmembers, which can hopefully be reproduced in other streams.

Our analysis of the distance to GD-1 in Section 2.1 resultsin values consistent with previous works across the often limitedspatial range sampled (Koposov, Rix & Hogg 2010; de Boer et al.2018). However, the increased confidence of stream member selec-tion using PMs from Gaia DR2 uncovers that the distance does notmonotonically decrease across the leading tail (negative ϕ1), butinstead shows a minimum of ≈7 kpc around ϕ1 ≈ −50 degrees fol-lowed by an increasing distance to ≈15 kpc. This has consequencesfor the possible orbits inhabited by GD-1 and will serve as a valu-able constraint on models reproducing the GD-1 morphology.

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0.5

1.0

EE G

D1

NGC3201NGC6101

Figure 14. Difference in energy and actions between GD-1 and the MilkyWay globular clusters. Note that we have normalized the energy differencesand action differences by the mean action and mean energy for our fits toGD-1. NGC 6101 and NGC 3201 both stand out as having the closest as-sociation in energy and action space. Both of these globular clusters havebeen associated with the Sequoia merger (Myeong et al. 2019), suggestingthat the remnants of this merger will be on similar orbits to GD-1 and canthus have a substantial effect on the stream.

Furthermore, the increasing distance on both ends of the sam-pled stream footprint implies that GD-1 might still extend out fur-ther than currently determined. At current, stars at these distancesdo not have accurate PMs from the Gaia satellite, nor will they havegood photometry in the relatively shallow wide-fill surveys such asSDSS and 2MASS. The most straightforward path to uncoveringthe continuation of the stream is by obtaining even deeper photo-metric data on either end, in order to probe the faint main sequenceof the stream population. This will allow us to obtain a robust sam-ple of high likelihood member stars and uncover the true extent ofGD-1.

The PMs of GD-1 were studied in Section 2.2, and probe to beinstrumental in decoupling the stream motion from that of the MWforeground. Figure 2 shows that the GD-1 stars stand out clearlyin µϕ1 across most of the stream angle probed here. Separation inµϕ2 is less pronounced due to the relatively small sample size aboveg=20, but the stream over density is visible and consistent modelsof GD-1 (Erkal et al., in prep). We stress that the stars belongingto the spur and blob features show PMs very close to those of themain stream, and are therefore decoupled from the MW at high sig-nificance. The likelihood of these stars being drawn from the con-taminating MW populations are very low, and any chance overlapwith another retrograde stream is unlikely. Therefore, we concludethat these features are genuinely associated to the GD-1 stream andmust be taken into account in a full modelling of the stream.

The stream track of GD-1 was studied in Section 3 after ap-plying a Boolean matched filter procedure taking into account thedistance and the PM cuts. The recovered track in Figure 3 showssmall scale wiggles around the large scale stream track, along withseveral under dense gaps. The gaps and wiggles largely line up withrecent works by de Boer et al. (2018); Price-Whelan & Bonaca(2018) and confirm that GD-1 a long, narrow stream with signifi-cant disturbances. Notably, we uncover a striking sinusoidal wigglein the stream track at high ϕ1 straddling a gap feature at ϕ1 ≈ −3 de-grees. While this wiggle looks similar to characteristic “S”-shape ofstars coming off the stream’s progenitor (as in Pal 5, Odenkirchenet al. 2001), this wiggle has the wrong orientation given the orbit

c© 2017 RAS, MNRAS 000, 1–18

Spur, blob, wiggle, and gaps in GD-1 17

of GD-1 (e.g. Fig. 12 of de Boer et al. 2018). Thus, this featuremust instead come from a perturbation to the stream. Since GD-1is on a retrograde orbit, the effect of baryonic substructure in thedisk is expected to be small (Amorisco et al. 2016) and thus this isa promising candidate for a subhalo interaction.

The mass sampling corrected 1D density histograms of GD-1(see Figure 5) show clear density variations across the ≈100 de-grees of stream sampled here. Three significant under densities arevisible at ϕ1 = −36,−20 and -3 deg, along with over dense peaksin between. This shows that GD-1 is likely to have experiencedmultiple disturbances and/or stripping episodes during the forma-tion of its stream. Unfortunately, the location of the progenitor stillremains a mystery, despite several promising candidate locations(e.g., Webb & Bovy 2019). The total initial stellar mass of GD-1 isconstrained from the matched filter procedure to be 1.58±0.07×104

M�, which is in line with expectations for a globular cluster origin.The stream mass is not unusually low compared to others (Shippet al. 2018), but GD-1 is much longer and narrowed than otherstreams of comparable mass.

The track and PM stream residuals from extracted streammembers in Figure 6 show that the stars spatially belonging to theblob and spur are not significantly different from those of the mainstream at similar ϕ1. Given the absolute PMs at these locations, thismakes it highly likely that both features are associated to GD-1 andmust be taken into account when fully modelling the stream for-mation. Although small offsets in PM space are present, the PMaccuracy and small sample size prevent us from seeing if the fea-tures are moving on different orbits than the main stream, at thispoint.

With the data in hand, we then fit the stream with an orbit andfound a good match. Most interestingly, the stream has significantresiduals in the stream track which line up with the location of thegaps in the density. These correlated signals will be crucial for fit-ting the perturbations to the stream, both by fitting each feature assuggested by Erkal & Belokurov (2015b) and for fitting the per-turbations statistically while taking these correlations into accountas suggested by Bovy, Erkal & Sanders (2017). Equipped with thisdata set, we also showed that the stars in GD-1 are moving alongthe stream and do not have a significant velocity perpendicular tothe stream. This is in contrast to the Orphan stream which shows asignificant offset due to the effect of the LMC (Erkal et al. 2019;Koposov et al. 2019).

Finally, we showed that an interaction with Sagittarius couldcreate features similar to the spur. In these models, the spur shouldbe significantly longer than currently detected so this can be testedwith future, deeper photometric data which shows how the spurconnects onto the stream. We also argued that the spur is unlikelyto be connected to the gap which is next to it since the observedspur extends across at least half of the gap instead of lining up withthe edge of the gap as models predict.

The continuing investigation of the GD-1 stream reveals thatit is highly complex with large and small scale variations and asso-ciated tidal debris. All of these will provide vital clues to the originand evolution of the stream, which is a puzzle waiting to be unrav-eled.

ACKNOWLEDGEMENTS

T.d.B. and M.G. acknowledge support from the European ResearchCouncil (ERC StG-335936). The authors also thank the Interna-tional Space Science Institute (ISSI, Bern, CH) for welcoming the

activities of Team 407 “Globular Clusters in the Gaia Era”. Theauthors also thank Adrian Price-Whlen and Vasily Belokurov fordiscussions on Sagittarius and Jo Bovy and Jeremy Webb for use-ful comments on an early version of the manuscript.

This work presents results from the European Space Agency(ESA) space mission Gaia. Gaia data are being processed by theGaia Data Processing and Analysis Consortium (DPAC). Fund-ing for the DPAC is provided by national institutions, in partic-ular the institutions participating in the Gaia MultiLateral Agree-ment (MLA). The Gaia mission website is https://www.cosmos.esa.int/gaia. The Gaia archive website is https://archives.esac.esa.int/gaia.

This paper made used of the Whole Sky Database (wsdb) cre-ated by Sergey Koposov and maintained at the Institute of Astron-omy, Cambridge by Sergey Koposov, Vasily Belokurov and WynEvans with financial support from the Science & Technology Facil-ities Council (STFC) and the European Research Council (ERC).

The Pan-STARRS1 Surveys (PS1) and the PS1 public sci-ence archive have been made possible through contributions bythe Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participat-ing institutes, the Max Planck Institute for Astronomy, Heidelbergand the Max Planck Institute for Extraterrestrial Physics, Garch-ing, The Johns Hopkins University, Durham University, the Uni-versity of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observa-tory Global Telescope Network Incorporated, the National Cen-tral University of Taiwan, the Space Telescope Science Institute,the National Aeronautics and Space Administration under GrantNo. NNX08AR22G issued through the Planetary Science Divisionof the NASA Science Mission Directorate, the National ScienceFoundation Grant No. AST-1238877, the University of Maryland,Eotvos Lorand University (ELTE), the Los Alamos National Labo-ratory, and the Gordon and Betty Moore Foundation.

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