ALIGNMENT BETWEEN PROTOSTELLAR OUTFLOWS and FILAMENTARY STRUCTURE Ian W

Home , Bipolar outflow, Perseus molecular cloud

Draft version July 27, 2017 Preprint typeset using LATEX style emulateapj v. 01/23/15

ALIGNMENT BETWEEN PROTOSTELLAR OUTFLOWS AND FILAMENTARY STRUCTURE Ian W. Stephens1, Michael M. Dunham2,1, Philip C. Myers1, Riwaj Pokhrel1,3, Sarah I. Sadavoy1, Eduard I. Vorobyov4,5,6, John J. Tobin7,8, Jaime E. Pineda9, Stella S. R. Offner3, Katherine I. Lee1, Lars E. Kristensen10, Jes K. Jørgensen11, Alyssa A. Goodman1, Tyler L. Bourke12,Hector´ G. Arce13, Adele L. Plunkett14 Draft version July 27, 2017

ABSTRACT We present new Submillimeter Array (SMA) observations of CO(2–1) outflows toward young, embedded protostars in the Perseus molecular cloud as part of the Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES) survey. For 57 Perseus protostars, we characterize the orientation of the outflow angles and compare them with the orientation of the local filaments as derived from Herschel observations. We find that the relative angles between outflows and filaments are inconsistent with purely parallel or purely perpendicular distributions. Instead, the observed distribution of outflow-filament angles are more consistent with either randomly aligned angles or a mix of projected parallel and perpendicular angles. A mix of parallel and perpendicular angles requires perpendicular alignment to be more common by a factor of ∼3. Our results show that the observed distributions probably hold regardless of the protostar’s multiplicity, age, or the host core’s opacity. These observations indicate that the angular momentum axis of a protostar may be independent of the large-scale structure. We discuss the significance of independent protostellar rotation axes in the general picture of filament-based star formation. Keywords: stars: formation – galaxies: star formation – stars: protostars – ISM: jets and outflows – ISM: clouds – ISM: structure

1. INTRODUCTION be hierarchically transferred from molecular clouds to Many stars form in filamentary structures with widths cores to protostars (e.g., Bodenheimer 1995). For a star- of order 0.1 pc (e.g., Arzoumanian et al. 2011). While forming filament, large-scale flows are probably either the exact shape of filaments is debated, e.g., cylinders onto the short axes of the filament from its cloud (either versus ribbons (Auddy et al. 2016), filaments are de- via accretion from the cloud or accretion via a collision) fined by a long axis and two much shorter axes. Dense or along the long filamentary axis. In a simplistic, non- cores (∼0.1 pc scale) either form within the filaments or turbulent scenario where one of the flows about the three form simultaneously with the filaments (Chen & Ostriker filamentary axes dominates, a core will likely rotate pri- 2015). Inhomogeneous flow or shear from colliding flows marily parallel or perpendicular to the parent filament. can torque cores (e.g., Fogerty et al. 2016; Clarke et al. If the angular momentum direction at the protostellar 2017). Classically, angular momentum is expected to scale is inherited from this core scale, the rotation axes of newly formed protostars will also be preferentially par- 1 Harvard-Smithsonian Center for Astrophysics, 60 Garden allel or perpendicular to the filaments. Street, Cambridge, MA, USA [email protected] One way to empirically test the alignment between a 2 Department of Physics, State University of New York at Fre- protostar’s spin and its filamentary structure is to ob- donia, 280 Central Ave, Fredonia, NY 14063, USA 3 Department of Astronomy, University of Massachusetts, serve a protostar’s outflow direction and compare it to Amherst, MA 01003, USA the filamentary structure as probed by dust emission. 4 Institute of Fluid Mechanics and Heat Transfer, TU Wien, Vi- By using this method across five nearby star-forming re- enna, 1060, Austria gions, Anathpindika & Whitworth(2008) found sugges- 5 Research Institute of Physics, Southern Federal University, Stachki Ave. 194, Rostov-on-Don, 344090, Russia tive evidence that outflows (as traced by scattered light) 6 University of Vienna, Department of Astrophysics, Vienna, tend to be preferentially perpendicular to filaments. On 1180, Austria the other hand, Davis et al.(2009) found that in Orion, arXiv:1707.08122v1 [astro-ph.GA] 25 Jul 2017 7 Homer L. Dodge Department of Physics and Astronomy, Uni- the orientation between outflows (as traced by H ) and versity of Oklahoma, 440 W. Brooks Street, Norman, OK 73019, 2 USA filaments appear random. A well-focused study that an- 8 Leiden Observatory, Leiden University, P.O. Box 9513, 2300- alyzes the outflow-filament angles is needed to reconcile RA Leiden, The Netherlands this disagreement. 9 Max-Planck-Institut für extraterrestrische Physik, D-85748 The rotation axis of a protostar, or even the parent Garching, Germany 10 Centre for Star and Planet Formation, Niels Bohr Institute protostellar core, could also be independent of its na- and Natural History Museum of Denmark, University of Copen- tal filamentary structure. Some observations have shown hagen, Øster Voldgade 5-7, DK-1350 Copenhagen K, Denmark that the angular momentum vectors of cores themselves 11 Niels Bohr Institute and Center for Star and Planet Forma- may be randomly distributed about the sky, regardless tion, Copenhagen University, DK-1350 Copenhagen K., Denmark 12 SKA Organization, Jodrell Bank Observatory, Lower With- of the cloud, core, or filamentary structure (Heyer 1988; ington, Macclesfield, Cheshire SK11 9DL, UK Myers et al. 1991; Goodman et al. 1993; Tatematsu et al. 13 Department of Astronomy, Yale University, New Haven, CT 2016). Multiplicity could also affect rotation axes. In the 06520, USA 14 European Southern Observatory, Av. Alonso de Cordova Submillimeter Array (SMA, Ho et al. 2004) large project 3107, Vitacura, Santiago de Chile, Chile called the Mass Assembly of Stellar Systems and their 2

Evolution with the SMA (MASSES; co-PIs: Michael data published in Lee et al. 2015, 2016) since these ob- Dunham and Ian Stephens), Lee et al.(2016) found that servations were either better quality and/or at higher outflows of wide-binary pairs (i.e., binary pairs sepa- resolution. These published PAs each came from obser- rated by 1000 AU and 10,000 AU) are typically randomly vations of one of three different J rotational transitions aligned or perpendicular (but not parallel) to each other. of CO: CO(1–0), CO(2–1), and CO(3–2). The rest fre- Radiation-magnetohydrodynamic simulations by Offner quencies for these three spectral lines are 115.27120 GHz, et al.(2016) of slightly magnetically-supercritical turbu- 230.53796 GHz, and 345.79599 GHz, respectively. lent cores found the same results for wide-binary pairs. 2.2. Herschel-derived Optical Depth Maps These simulations suggest that the direction of the protostellar spin axis can evolve significantly during formation, Herschel is well-suited for finding filaments in Perseus indicating that, at least for wide-binaries, the rotation given its resolution and wavelength range. The resolu- axes are independent of the large-scale structure. tion at the longest Herschel wavelength (500 µm) is 3600 In this paper, we aim to observationally test whether or ∼0.04 pc at the distance of Perseus (235 pc, Hirota or not a preferential alignment exists between the local et al. 2008). Star-forming filaments have temperatures filamentary elongation and the angular momentum axis of ∼10 to 20 K, and thus the dust continuum will peak as traced by outflows. To test such alignment, we use within the Herschel bands (70 µm to 500 µm). These new CO observations from the MASSES survey to trace wavebands can be used to approximate the optical depth the molecular outflows in the Perseus molecular cloud. and the column density of Perseus filaments. Indeed, Along with ancillary data, we determine accurate pro- several studies have already created optical depth or col- jected outflow position angles (PAs) for 57 Class 0 and I umn density maps of the Perseus molecular cloud using protostars. The MASSES survey provides uniform spa- Herschel observations, including Sadavoy et al.(2014), tial coverage of the same molecular line tracers in a single Zari et al.(2016), and Abreu-Vicente et al.(2016). All cloud, and only focuses on young sources – Class 0 and I three of the aforementioned studies assumed a modified protostars. Since these protostars are young, their par- blackbody with a specific intensity of ent filamentary structure has had less time to change in I = B (T )(1 − e−τν ) ≈ B (T )τ , (1) morphology since the birth of the stars. These outflow ν ν ν ν observations can then be compared to the filamentary where Bν is the blackbody function at temperature T structure as observed by the Herschel Gould Belt sur- and τν is the optical depth. τν is assumed to follow a β vey (e.g., Andréet al. 2010). power-law function of the form τν ∝ ν , where β is the We describe the observations used in Section2 and the dust emissivity index. The dust column density, Ndust, outflow/filament PA extraction techniques in Section3. can be calculated assuming τν = Ndustκν , where κν is We present the results in Section4 and discuss their pos- the dust opacity. Each study assumed τν and T to be sible implications in Section5. Finally, we summarize the free parameters. main results in Section6. While these studies varied slightly, e.g., on their as- sumption for β, the resulting maps are very similar. We choose to use the 353 GHz optical depth (τ353 GHz) map 2. OBSERVATIONS from Zari et al.(2016) since this map has been made 2.1. Outflow and Continuum Data publicly available. Zari et al.(2016) assumed a value For the Perseus protostellar outflows studied in this pa- of β = 2, and they did not convert the τ353 GHz maps per, we introduce new, unpublished MASSES CO(2–1) to column density. The τ353 GHz maps were made using data. The SMA observations were calibrated using the only the Herschel 160, 250, 350, and 500 µm maps. Each MIR software package15 and imaged using the MIRIAD Herschel map was zero-point corrected with P lanck and smoothed to the coarsest resolution (500 µm), resulting software package (Sault et al. 1995). More details of the 00 data reduction process for the MASSES survey are pre- in an τ353 GHz map at 36 resolution. The final τ353 GHz map has the pixels regridded to equatorial coordinates sented in Lee et al.(2015). The new MASSES data all 00 00 come from the SMA’s subcompact configuration, which with pixel sizes of 18 × 18 . This τ353 GHz map also typically has baselines between 3 kλ and 54 kλ, resulting includes coarse resolution P lanck τ353 GHz maps in the in an average synthesized beam size of ∼300. 8. The ve- field external to the Herschel observations. locity resolution of the observations is 0.26 km s−1, and Figure1 shows the Zari et al.(2016) τ353 GHz map of the data were smoothed to 0.5 km s−1 in this study. The Perseus. For simplicity, we masked out the P lanck-only typical 1σ rms in a 0.5 km s−1 channel is 0.15 K. regions of the map which extend beyond the Herschel Along with the new MASSES CO(2–1) data, we also observations. The resolution of these P lanck-only re- used new MASSES 1.3 mm continuum data to locate the gions are too coarse to resolve the filaments and none of centroid of the bipolar outflow, which is used to help our MASSES targets are located within them. measure the outflow PAs (see Section 3.1). A more de- 3. DATA ANALYSIS TECHNIQUES tailed analysis of the continuum data will be discussed in In this section, we summarize how we measure PAs a forthcoming paper (R. Pokhrel et al. in preparation). for both outflows and filaments from observations. All The SMA data will become publicly available with the angles are measured counterclockwise from the north ce- MASSES data release paper (I. Stephens et al. in prepa- lestial pole. These PAs are used to calculate the main ration). parameter of interest, γ, which is the projected angle dif- In some cases, we use already published CO PAs (pri- ference between the outflows and filaments. Specifically, marily from Plunkett et al. 2013 and from other MASSES γ is given by

15 ◦ https://www.cfa.harvard.edu/~cqi/mircook.html γ = MIN |PAOut −PAFil|, 180 −|PAOut −PAFil| , (2) 3

0.00050 0.00045 0.00040 +33° B5 0.00035 0.00030 0.00025 IC348 +32° 0.00020

NGC1333 τ 3 5

B1 0.00015 3 G H z +31° L1448 0.00010 Dec (J2000) B1E

0.00005

+30° L1451 L1455

1◦ = 3.3 pc

48m 42m 36m 30m 3h24m RA (J2000)

Figure 1. τ353 GHz map of the Perseus molecular cloud (Zari et al. 2016), with magenta lines showing the directions of the outﬂows measured in this study. The size of the lines only represents the direction of the outﬂow and not the angular extent. Thin blue contours are shown for τ353 GHz = 0.0002. These contours roughly show the boundaries of each labeled clump and correspond to a column density 21 −2 of N(H2) ≈ 5 ×10 cm (Sadavoy et al. 2014).

where PAOut and PAFil are the PAs of the outflow and line emission obviously traces the outflow cavity walls filament, respectively. MIN indicates that we are inter- rather than the outflow centroid, we connect the contin- ested in the minimum of the two values in the brackets. uum peak to a local CO maximum near the continuum Table3 lists the measured PAs for all outflows and fila- rather than the absolute maximum. In cases where there ments in this study. are no clear local outflow maxima for one lobe, we use the PA measured by the other lobe. If no local maxima 3.1. Outflow Position Angles exists for both lobes and the CO only traces cavity walls, We present the outflow PAs in Table3. We indepen- we manually measure the PA by eye. We indicate in the dently measure the outflow PAs for both the blue- and “Ref/Info” column of Table3 which outflow measuring red-shifted outflows (henceforth, called the blue and red method we used. For the angles measured in this paper, lobes). The range of the PA measurements are from a crude approximation of the uncertainty can be found –180◦ to +180◦; both positive and negative values allow by subtracting the blue outflow PA from the red outflow one to assign the appropriate quadrant for the outflow. PA. With such an approximation, the uncertainty in the outflow PA is typically less than 10◦. We also provide the combined PA, PAOut, which is simply the average of the two outflows after adding 180◦ to Frequently, the observed field about a MASSES tar- the lobe with the negative PA. Some entries only pro- get overlaps with other protostellar sources, which can vide measurements for one lobe because the other lobe cause significant confusion in assigning which emission was undetected. comes from which protostar. To disentangle which emis- In many cases (about half of the sources) we used out- sion belongs to which source, we used SAOImage DS9 to flow PAs from other CO line studies in place of MASSES overlay all CO emission detected with MASSES on top observations since these studies had data that are better of Spitzer IRAC emission (not shown). In particular, quality and/or at higher resolution. We indicate which both the 3.6 and 4.5 µm Spitzer bands trace the outflow study provided the outflow direction for each protostar cavities in scattered light and/or knots of H2 emission in the “Ref/Info” column of Table3. For the majority of that are most prominent in the 4.5 µm channel. We also the measured outflow PAs in this study, we made mea- use the catalog of Perseus protostars from Young et al. surements using a methodology very similar to that used (2015) to locate other nearby T Tauri stars that may be in Hull et al.(2013). We connect the peak intensity of contributing to the CO emission observed by the SMA. the SMA 1.3 mm continuum observations with the peak Together, we are able to disentangle which outflow em- of the integrated intensity maps for both the blue and anates from which source. In this paper, we only present red outflow lobes. Based on visual inspection, if the CO the outflow PAs that we believe we were confidently able 4

0.0020 30" 0.0018 Per-emb 1 [3.0, 5.0] -13.5 to 6.5 km s−1 10' 10' [6.6, 10.0] 10.5 to 48.5 km s−1 0.0016 [0.013, 0.02] 0.0014 15" 0.0012 0.0010 05' 05' 0.0008 01'00" τ

0.0006 GHz 353 +32°00' +32°00' 0.0004 45" Dec (J2000)Dec 0.0002 55' 55' 30"

+31°50' +31°50' +32°00'15"

40s 20s 44m00s 40s 20s 3h43m00s 40s 20s 44m00s 40s 20s 3h43m00s 59s 58s 57s 56s 55s 3h43m54s RA (J2000) RA (J2000) RA (J2000)

0.0020 0.0018 Per-emb 22 [8.0, 5.0] -32.9 to -0.9 km s−1 55' 55' −1 0.0016 45" [4.1, 5.0] 8.1 to 23.6 km s [0.016, 0.02] 0.0014 0.0012 0.0010 50' 50' 30" 0.0008 τ

0.0006 GHz 353 15" 45' 45' 0.0004 Dec (J2000)Dec 45'00" 0.0002 40' 40'

+30°44'45"

+30°35' +30°35'

20s 26m00s 40s 20s 25m00s 3h24m40s 20s 26m00s 40s 20s 25m00s 3h24m40s 25s 24s 23s 22s 21s 3h25m20s RA (J2000) RA (J2000) RA (J2000)

0.0020 15" 0.0018 25' Per-emb 27 25' [5.4, 5.4] -19.5 to 1.5 km s−1 [6.0, 6.0] 11.5 to 22.5 km s−1 0.0016 [0.03, 0.05] 0.0014 15'00" 0.0012 20' 20' 0.0010

0.0008 45" O2 τ 0.0006 GHz 353 15' 15' 0.0004 30" Dec (J2000)Dec

10' 10' O1 0.0002 15"

+31°05' +31°05' +31°14'00"

40s 20s 29m00s 40s 20s 3h28m00s 40s 20s 29m00s 40s 20s 3h28m00s 58s 57s 56s 55s 54s 3h28m53s RA (J2000) RA (J2000) RA (J2000)

Figure 2. Figures demonstrating the FILFINDER algorithm for Per-emb 1 (top 3 panels), Per-emb 22 (middle 3 panels), and Per-emb 27 (bottom 3 panels); other Perseus protostars can be found in the eletronic version of this paper. The left and middle panels show the τ353 GHz maps (Zari et al. 2016) and the fitted filament skeletons from FILFINDER (Koch & Rosolowsky 2015), respectively. The red line in the middle panel shows the fitted PAFil,F for the protostar. The yellow squares in these two panels show the area we zoom-in for the right panels. The right panels show the τ353 GHz overlaid with SMA red and blue CO(2–1) integrated intensity contours of the red and blue lobes, respectively. The white contours show the SMA 1.3 mm continuum. The color-coded bracketed numbers in the top left give the first contour level followed by the contour level increment for each subsequent contour. The CO(2–1) contour levels and increments are in units of Jy beam−1 km s−1 while the continuum contour levels and increments are in units of Jy beam−1. The red and blue velocity interval for CO(2–1) intensity integration are shown next to their corresponding contour levels. The small green circles show the location of the protostellar sources as determined at high resolution by the VLA (Tobin et al. 2016). The measured PAOut is shown as a line under the contours, and the line is yellow if PAOut comes from this study, and magenta if PAOut comes from other studies (as indicated in Table 3). The white circle shows the 4800 diameter (FWHM) primary beam of the SMA. to determine. Protostars surveyed by MASSES that are 3.2. Filament Direction not presented in this paper were either not yet imaged We present the filament PAs in Table3. We deter- or had confusing CO emission that did not allow for a mine the filament directions based on Herschel-derived reliable measurement of PAOut. In total, we have PAOut τ353 GHz maps (see Section 2.2). Since extracting fila- measurements for 57 protostellar outflows. In Figure1 ments directions can sometimes depend on the method we overlay each PAOut measurement on the Herschel- used, we use two different techniques. One technique is derived τ353 GHz map. The SMA CO(2–1) integrated in- based on FILFINDER and the other is based on SExtrac- tensity maps for two protostars are shown in the right tor. For both techniques, we also investigate how the panels of Figure2; other sources can be found in the elec- filament directions depend on both small and large scale tronic version of the paper. The average spectra within optical depth characteristics. the vicinity of the protostar (i.e., within a radius of 800) is shown in Figure3. 3.2.1. Using FILFINDER for Filament Position Angles 5

Per-emb-1 Per-emb-2 Per-emb-3 Per-emb-5 Per-emb-6 Per-emb-8 Per-emb-9 2 2 8 4 1 6 0.5 1 2 1 1 4 2 0 0 0 0 0 0 0.0 0 20 40 0 10 20 0 10 20 0 20 0 10 20 0 10 20 0 10 -emb-10 -emb-11,O1 -emb-11,O2 -emb-12 Per-emb-13,O1 Per-emb-13,O2 -emb-15 3 2 1 1 0 0 0 20 0 20 Per-emb-16 Per-emb-17 -emb-18 Per-emb-19 -emb-20 -emb-21 -emb-22 3 4 2 0.5 2 1 0 0 0.0 ) 0 10 20 0 10 0 10 1

− Per-emb-23 Per-emb-24 Per-emb-25 -emb-26 -emb-27,O1 -emb-27,O2 Per-emb-28 2 3 2 1 0.5 2 1 1 0 0 0.0 0 0 10 0 10 20 0 10 0 10 20 Per-emb-29 -emb-33,O1 -emb-33,O2 -emb-33,O3 Per-emb-35,O1 Per-emb-35,O2 Per-emb-36 3 4 4 3 3 2 2 2 2 1 1 1 0 0 0 0 0 20 0 10 20 0 10 20 0 20 Per-emb-37 -emb-40 Per-emb-41 -emb-42 Per-emb-46 -emb-49 Per-emb-50

Intensity (Jy beam 4 1 2 1 3 1 2 0 1 0 0 0 0 10 0 10 0 10 0 10 20 -emb-53 Per-emb-55 Per-emb-56 Per-emb-57 Per-emb-58 Per-emb-61 Per-emb-62 1 9 0.5 3 6 1 1 2 3 1 0 0.0 0 0 0 0 0 10 20 0 10 20 0 10 0 10 0 10 0 10 20 B1-bN B1-bS L1448IRS2E L1451-MMS Per-bolo-58 6 0.3 3 0.3 2 2 4 1 2 1 0.0 0 0 0 0.0 0 10 0 10 0 10 20 30 0 10 0 10 Velocity (km s−1 )

Figure 3. Average CO(2–1) spectra within a radius of 800 from each protostar, where the protostar’s position is given in Table3. The velocity resolution is 0.5 km s−1. The vertical dashed lines show the interval ranges used to produce the integrated intensity maps in the right panels of Figure2. The two blue and two red lines show the integrated intervals for the blue- and red-shifted emission, respectively. These integrated intensity ranges were manually adjusted to produce the best visualization of the outflows for each source. In some cases, no outflows were found for a particular lobe, or the lobe emission was difficult to extract from the large-scale CO(2–1) emission. Note that for Per-emb-57, the dominant outflow emission is toward the southeast, more than 800 from the source’s center, and thus the spectrum poorly represents the outflow emission. The first method extracts the filamentary structure us- FILFINDER determines the filament direction via the ing the FILFINDER algorithm (Koch & Rosolowsky 2015) Rolling Hough Transform (Clark et al. 2014). Unfor- as implemented in PYTHON. FILFINDER is unique in that tunately, the Rolling Hough Transform often performs it can find filaments with relatively low surface bright- poorly in the Perseus molecular cloud since FILFINDER ness compared to the main filaments, which is achieved sometimes combines distinct molecular clumps as a sin- by using an arctangent transform on the image. This gle filamentary structure. For example, FILFINDER com- algorithm first isolates the filamentary structure across bines NGC 1333 and L1455 into a single filamentary the entire map. Then, each filament within the filamen- network and measures the direction of the combined tary structure is made into a one-pixel-wide skeleton via structure. We find that in most of these instances, the Medial Axis Transform (Blum 1967). We use the the Rolling Hough Transform poorly estimates both the default implemented parameters in the FILFINDER algo- small and large scale filamentary direction. Instead of rithm, with the exception of the parameters size thresh this transform, we approximate the filamentary direc- and skel thresh, which were altered to provide the best tion by fitting a line to the filamentary skeleton output visual fit to the actual Perseus data. Specifically, for from FILFINDER. To do this, we first find the closest these parameters we used the values size thresh = 300 FILFINDER skeleton pixel to the position of the proto- and skel thresh = 100. The resolution of the obser- star given by Tobin et al.(2016). We then extract a vations (3600) and the distance to the Perseus molecular square skeleton map of 11×11 pixels (19800 × 19800 or cloud (235 pc) were also provided to the FILFINDER al- ∼0.2 pc × 0.2 pc) centered on this closest skeleton pixel gorithm. and fit an ordinary least squares bisector line (Isobe et al. 6

20' B5 IC348 B1 40' NGC1333NGC1333 0.0020 +33°00' 0.0018 10' 10' 54' 30' 0.0016 +31°00' 0.0014 48' +32°00' 20' 50' 0.0012 42' 50' 10' 0.0010 Dec (J2000) +32°36' +30°40' +31°00' 0.0008

+31°40' τ 3

48m 47m 3h46m 45m 44m 3h43m 34m 33m 32m 3h31m 31m 30m 29m 28m 3h27m 0.0006 5 3

+31°00' RA (J2000) G L1455 L1448 36' L1451 H 24' 0.0004 z 54' 18' 30' 48' 0.0002 12' 24' 42' 06' 18' Dec (J2000) +30°00' 36' +30°12' +29°54' +30°30' 29m 28m 3h27m 26m 3h25m 26m 25m 3h24m RA (J2000) RA (J2000) RA (J2000)

Figure 4. τ353 GHz maps (Zari et al. 2016) of clumps within the Perseus molecular cloud. Yellow dots show the locations of protostars with measured outflow PAs. The closest blue and red line-centers to each yellow dot represent the small and large scale direction of the filament, respectively, based on fits using SExtractor (essentially a by eye fit; see Section 3.2). Lines are centered based on the centroid of the SExtractor fit. For both the blue and red lines, the length of the lines are the same angular size in each panel. 1990; Feigelson & Babu 1992) to the scatter plot of the the Graphical Astronomy and Image Analysis (GAIA) skeleton pixels. The slope of this fitted line is then con- Tool16. SExtractor works by fitting ellipses to the emis- verted to a PA. We use an extraction of an 11×11 pixel sion data. We then adopt the position angle of the fitted square because we find it large enough to fit the elonga- ellipses as the filament PA. To measure both the large tion of the filament, but small enough that the filament’s scale and small scale filamentary structure, we extract direction is not strongly influenced by other nearby fila- two different filament directions for each protostar. For mentary structures. We have also ran the same algorithm the large scale structure, we fit a single filamentary direc- for extracting squares of skeleton pixels that are up to ∼3 tion to the clump (i.e., the pc-scale cloud structure), and times larger or smaller than 11×11 pixels, and the results for the small scale, we fit the most localized elongated in our paper are qualitatively the same. The 11×11 pixel structure for the protostar. For both scales, the param- extraction provides the best visual fits to the filaments eters Detection threshold, Analysis threshold, and across all sources. Contrast parameter were adjusted for each source so Figure2 shows examples of this fitting process for two that the fitted ellipse best matches the elongation as sources; other sources can be found in the electronic ver- judged by the human eye. We find that no single set sion of this paper. Note that the measured PA (red line of values for these three parameters can fit all filaments in middle panels of Figure2) are slightly off as one may in the Perseus cloud that is agreeable with the human measure by eye simply because nearby filament branches eye, and thus the parameters were adjusted filament-by- in the 11×11 pixel cutout of the skeleton map affects filament. Therefore, this method is primarily a “by eye” the bisector fit. In the rest of the paper, we will re- determination of the filament direction with the aid of fer to this method for extracting filament directions as software. This method of determining the filament PA the “FILFINDER algorithm.” In Table3, we provide these is very similar to the method used in Anathpindika & filament angles, PAFil,F, along with their corresponding Whitworth(2008). We note that even at the small scale, projected outflow-filament angle, γF . the best SExtractor fit for a local filament may be the Angular momentum of a protostar could possibly be same for multiple protostars. inherited from filamentary structures larger than the fil- Figure4 shows both the small and large scale filament aments measured with 3600 resolution. Therefore, we also PAs determined for each protostar using this method. make a comparison to larger scales by Gaussian smooth- The final projected outflow-filament angles using this ing the Zari et al.(2016) τ353 GHz maps and rerunning method for both the small scale (γse,S) and large scale the FILFINDER algorithm discussed above. Specifically, (γ ) are given in Table3. The measured filament we smooth the data to resolutions of 10, 20, 30, 40, 50, and se,L 60, where 10 is 0.068 pc, assuming a distance of 235 pc to PAs for both of these methods can be derived from γse,S Perseus. FILFINDER progressively finds fewer branches and γse,L by using Equation3 and the individual PA Out in the Perseus filaments when we smooth τ353 GHz maps measurements. to these coarser resolutions. The measured projected outflow-filament angles for these resolutions are shown 3.2.3. Comparison of the FILFINDER and SExtractor 0 0 in Table3 as γX , where X is the smoothed resolution in Techniques arcminutes. Both the FILFINDER and SExtractor filament-finding 3.2.2. Using SExtractor for Filament Position Angles methods have their advantages and disadvantages. For example, the first method is completely automated, and The second method fits ellipses to the filaments via SExtractor (Bertin & Arnouts 1996), as implemented in 16 http://star-www.dur.ac.uk/~pdraper/gaia/gaia.html 7

18 IC348 14 Outflows from All Protostars 16 B1 NGC1333 12 14 L1448 L1451 10 12 L1455 B5 10 8

8 6

6 4 Number of Outflow PAs Outflow of Number 4

Number of Angle Differences Angle of Number 2 2

0 0 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50 60 70 80 Outflow Position Angle |γ−γ|

Figure 6. Stacked histogram (with 20◦ bins) of outflow PAs in Figure 5. Histogram showing the magnitude of the difference in the Perseus molecular cloud. Colors correspond to the clump that the projected outflow-filament angles measured by the two methods PAOut belongs to. used to find the filament orientation. γ values for the FILFINDER algorithm and the small scale SExtractor fits are indicated by γF and γ , respectively. se,S IC348 14 Outflows from Single Systems if there are multiple filamentary branches in the field, the B1 NGC1333 algorithm attempts to find the best filamentary direction 12 in a fixed area of ∼0.2 pc × 0.2 pc. However, filamentary L1448 L1451 branches may be considered as a contaminate, in which 10 case the second method (the SExtractor by eye measure- L1455 B5 ment) may more accurately determine the filamentary 8 direction. When comparing the two methods, the filament di- 6 rection found with the FILFINDER algorithm are most comparable to those found at small scale with SExtrac- 4 tor since these both measure filaments at approximately PAs Outflow of Number the same size scales. Figure5 shows the absolute value 2 of the difference in the measured angles γF and γse,S for each protostar. Since PA for each protostar is mea- Out 0 sured the same regardless of the method used to measure 0 20 40 60 80 100 120 140 160 180 Outflow Position Angle the filament orientation, γF – γse,S is equivalent to the difference in the measured filament directions for each technique. This histogram shows that the measured fil- Figure 7. Same as Figure6 but now only considering protostars ament position angles mostly agree, but in some cases, that were not identified as multiples in the VANDAM survey (To- the measured filament angles for each technique vary sig- bin et al. 2016). nificantly. Therefore in the following section, we present statistical comparisons to the outflows for both filament- p-values near 0 imply that they are unlikely drawn from finding techniques. the same distribution.

4. RESULTS 4.1. Outﬂow Directions in Perseus

In this section, we analyze the distributions of PAOut Figure6 shows a stacked histogram of PA Out, where and γ. We note that, when we compare our empirical the color of each stacked bar indicates the protostar’s distributions of angles PAOut and γ to simulated data, parental clump. As with Figure1, this figure does not we favor the Anderson–Darling (AD) test (e.g., Stephens show any obvious relationship between PAOut and the 1974) over the Kolmogorov–Smirnov test. The AD test protostar’s parental clump. Since a stellar companion tends to be more powerful in detecting differences in dis- could possibly affect the spin axis of a protostar (e.g., tributions than the Kolmogorov–Smirnov test, particu- Offner et al. 2016; Lee et al. 2017), we also show a stacked larly at the tail ends of the distributions (e.g., Hou et al. histogram of the “single” systems identified in the VAN- 2009; Engmann & Cousineau 2011; Razali & Wah 2011). DAM survey (Tobin et al. 2016) in Figure7. This sur- While the p-values differ for these two tests, the overall vey used multi-wavelength data with resolutions as high statistical significance does not change dramatically and as 15 AU, and defined a system as a “single” system if our conclusions remain unchanged. For the two-sample it has no detected companions within 10,000 AU. Again, AD test, p-values near 1 imply that the two distribu- the distribution is mostly random. We compare the “all” tions are likely drawn from the same distribution, while and “single system” data to a random distribution, and 8 the AD test gives p-values of 0.65 and 0.62, respectively. IC348 16 This signifies that we cannot distinguish the PAOut his- B1 tograms in Figures6 and7 from a random distribution NGC1333 14 of angles. L1448 12 L1451 1.0 L1455

◦ B5 0−20 Angles 10 γ 0.8 8

0.6 of Number 4

Random 2 0.4 70−90 ◦ 0 0 10 20 30 40 50 60 70 80 90 γ 0.2

Cumulative Distribution Function Distribution Cumulative Observations MASSES Outflows, Herschel Filaments Figure 9. Same as Figure6, but now the stacked histogram is ◦ 0.0 shown for γF . The histogram bin size is 10 . 0 15 30 45 60 75 90 Projected angle between outflow and filament, γ (deg) over 99% confidence (AD test gives a p-value = 0.0045). However, we cannot significantly distinguish the γ dis- Figure 8. Cumulative distribution function of the projected an- F gles between outflows and filaments, γ. The red step function shows tribution from a distribution of randomly aligned outflows and filaments (p-value = 0.20). Table1 summarizes γF for this study, which measures the angle between MASSES outflows and fitted Herschel filaments directions using the FILFINDER the statistical tests conducted on all the γ measurements algorithm discussed in Section 3.2. The three blue lines show discussed in Section3. In Figure9, we show the dis- Monte Carlo simulations of the expected projected γ for outflows and filaments that are 3-dimensionally only parallel (actual tribution of γF as a stacked histogram, with colors rep- outflow-filament angle that is between 0 and 20◦), only perpendic- resenting the parental clump. No obvious non-random ular (70–90◦), or completely random (0–90◦). relationship is found, regardless of the protostar’s clump location.

4.2. Cumulative Distribution Functions using 1.0 FILFINDER Filament Angles While the first visual and clump regional tests did not % Parallel 100 show any obvious relationship between clump structure 0.8 and protostellar outflow directions, clumps are pc-sized while filaments are about 0.1 pc in diameter (e.g., Ar- zoumanian et al. 2011). As discussed in Section 3.2, we 0.6 use FILFINDER to extract filament directions at the 3600 50% Parallel, 50% Perpendicular (0.04 pc) scale. These filament directions, PAFil,F, are then compared to PAOut to determine the projected out- 0.4

flow and filament angular difference, γF . We plot the cumulative distribution function (CDF) of the observed 100% Perpendicular

γF in Figure8. To investigate whether the distribution 0.2 Observations of γ reflects outflows and filaments that are primarily Function Distribution Cumulative F Best Fit Bimodal Distribution aligned parallel, perpendicular, or at random, we per- Simulated Random Distribution form 3-D Monte Carlo simulations that we project onto 0.0 2-D. Specifically, we simulate the CDF of the expected 0 15 30 45 60 75 90 projected angles in the sky for outflow-filament angles Projected angle between outflow and filament, γ (deg) that are 3-dimensionally “only parallel” (defined as actual outflow-filament angles that are distributed between ◦ ◦ Figure 10. Cumulative distribution function of the projected an- 0 and 20 ), “only perpendicular” (actual angles between gles between outflows and filaments, γ, with the red step curve ◦ ◦ 70 and 90 ), or completely random (actual angles be- showing the empirical distribution, γF . Black dashed lines show tween 0◦ and 90◦). The expected observed (i.e., pro- different mixes of projected outflow-filament angles that are 3- dimensionally parallel and perpendicular in increments of 10% (i.e., jected) γ for these three Monte Carlo instances are also the top line is 100% parallel and 0% perpendicular, the next line shown in Figure8. Detailed information on the Monte is 90% parallel and 10% perpendicular, and so on). Parallel angles Carlo simulations is presented in AppendixA. are defined as 3-dimensional angles drawn from a distribution be- Immediately evident from Figure8 is that the distribu- tween 0◦ and 20◦, while perpendicular angles are defined as angles drawn from a distribution between 70◦ and 90◦ (see AppendixA tion of γF is inconsistent with outflows and filaments that for details). The blue line shows a random distribution of projected are preferentially parallel. The projected angles are also angles, while the magenta line shows the best bimodal fit to the inconsistent with a purely perpendicular alignment with data of 22% parallel and 78% perpendicular. 9

So far, we produced simple models of γ from outflow- filament angles that are only parallel, only perpendicu- Table 1 lar, or aligned at random. As mentioned in Section1, Anderson–Darling Test p-values outflow orientation may be determined by the dominant Empirical γ p-value, compared p-value, compared flow direction about the filament. Therefore, a bimodal Distribution with Random with Perpendicular distribution of γ is possible, e.g., a mix of both parallel γF 0.20 0.0045 and perpendicular orientations. γ 0.33 0.00085 10 We test different 3-dimenisonal combinations of purely γ 0.40 0.0011 ◦ 20 parallel (again, where angles are distributed between 0 γ 0.42 0.0029 30 ◦ ◦ γ 0.49 0.00024 and 20 ) and purely perpendicular (angles between 70 40 ◦ γ 0.24 0.023 and 90 ) outflow-filament angles via Monte Carlo sim- 50 γ 0.59 0.00069 ulations. We consider 101 bimodal cases in increments 60 of 1% (i.e., 100% parallel, 99% parallel and 1% perpen- γse,S 0.74 0.00014 dicular, 98% parallel and 2% perpendicular, ..., 100% γse,L 0.64 0.0021 Anathpindika & Whitworth 0.017 0.16 perpendicular). Figure 10 shows the CDFs of several of γ , Single Protostars 0.60 0.18 these bimodal distributions projected into 2 dimensions. F γF , Multiple Protostars 0.20 0.011 We find that, when comparing to the observed distribu- γF , with Tbol < 50 0.53 0.021 γF , with Tbol > 50 0.18 0.075 tion γF , the simulated γ that is a mix of 22% parallel γF , with τ353 GHz < 0.016 0.15 0.20 and 78% perpendicular maximizes the p-values for the γ , with τ > 0.016 0.27 0.0050 AD test (as well as the Kolmogorov–Smirnov test). The F 353 GHz Note.— p-values are not shown for empirical γ distributions compared with parallel p-value for this case is 0.55, signifying a slightly more γ distributions because they are all extremely low in value (less than 10−9). consistent distribution with the observed γF distribution than a random distribution. As discussed in Section 3.2, we also determine filament This bimodal test can also constrain which mixes of angles by running the FILFINDER algorithm on Perseus parallel and perpendicular are unlikely. According to τ353 GHz maps that have been smoothed to coarser resolution. The resulting CDFs for γ at these resolutions are the AD test, we find that at 95% confidence, γF probably does not come from a bimodal distribution that is more shown in Figure 11. We find that the CDFs at all res- than 39% parallel or more than 94% perpendicular. At olutions are similar with each other, with the AD test 85% confidence, we find that the γ distribution does not p-value 0.45 or greater when comparing any two dis- F tributions. We also find consistent results between the come from a bimodal distribution that is more than 33% 00 parallel or more than 90% perpendicular. smoothed and the non-smoothed (36 ) resolution γ an- Other mixes of γ distributions are also possible, such gles. Specifically, as shown in Table1, none of the γ as mixes of a random distribution with perpendicular distributions extracted from the smoothed τ353 GHz maps and/or parallel distributions. We do not test other dis- can be statistically distinguished from a random distribu- tribution mixes in this paper since we mainly want to tion, but all are inconsistent with projected angles from show that perpendicular outflows and filaments are much an only perpendicular and only parallel distributions. more likely than parallel. Filaments Directions Using SExtractor Fitting 1.0 Filament Directions Using Different Resolutions 1.0 0−20 ◦

◦ 0−20 0.8

0.8

Random 0.6

0.6 Random

Distribution Function Distribution 0.4 70−90 ◦

0.4 70−90 ◦

0.2 36" resolution 1' resolution Cumulative SExtractor, small scale 0.2 2' resolution SExtractor, large scale

Cumulative Distribution Function Distribution Cumulative 3' resolution Anathpindika & Whitworth 4' resolution 0.0 5' resolution 6' resolution 0 15 30 45 60 75 90 0.0 Projected angle between outflow and filament, γ (deg) 0 15 30 45 60 75 90 Projected angle between outflow and filament, γ (deg) Figure 12. Figure caption is the same as Figure8, except now the step functions show the SExtractor fitting of filament direc- Figure 11. Figure caption is the same as Figure8, except with tions (which is essentially a “by eye” fit) at both small and large additional step curves showing the effects of smoothing the Perseus scales, as described in Section 3.2. The results from Anathpindika τ353 GHz map before running the FILFINDER algorithm described in & Whitworth(2008) are also shown, but we caution any interpre- Section 3.2. The colors indicate which resolution the τ353 GHz map tation of this curve due to shortcomings of the study discussed in was smoothed to in creating the empirical γ CDF. AppendixB. 10

4.3. Cumulative Distribution Functions using gorithm, the results would be qualitatively the same if we SExtractor Filament Angles used the filament fits from SExtractor. In Figure 12, we show the CDFs when using the SEx- We also find that the empirical CDFs in each panel tractor filament direction fits, which is essentially a fit by are not inconsistent with each other. Specifically, the p- eye (see Section 3.2). We find similar results for both the value between singles and multiples is 0.80, between the small-scale (i.e., fitting the closest elongated feature to two Tbol bins is 0.56, and between the two τ353 GHz bins is each protostar) and large-scale (i.e., fitting the main part 0.24. The latter shows that τ353 GHz could possibly be the of the clump containing each group of protostars) SEx- best discriminator between two populations of γ. This tractor fitting as with the FILFINDER algorithm. That would imply that protostars that are less embedded (and is, the SExtractor fits are not inconsistent with a ran- likely older) have outflows perpendicular to their natal dom distribution and are significantly inconsistent with filaments. Indeed, this idea is supported by the fact that both parallel and perpendicular angle distributions (see higher Tbol (i.e., older protostars) are closer to the per- Table1). Also shown in this figure are the results from pendicular curve (albeit, very slightly) than sources with Anathpindika & Whitworth(2008), which uses a simi- lower Tbol. However, we stress that this trend is only lar filament fitting algorithm. Unlike our results, their tentative, as it is far from being statistically significant distribution for γ is more consistent with perpendicular to draw firm conclusions. A much larger sample of proto- (p-value of 0.17) than random (p-value of 0.017). How- stars would allow for a better understanding of whether ever, we caution an interpretation of the Anathpindika or not individual protostellar characteristics affect the & Whitworth(2008) γ distribution due to several short- observed γ distribution. comings in their study, which are discussed in detail in 5. DISCUSSION AppendixB. We do not show the results from Davis et al. (2009) because they do not supply any information on γ We find that the observed distribution of the projected or the filament PAs. angle between outflow and filaments, γ, is significantly As in Section 4.2, we also test which bimodal distribu- inconsistent with projected “only parallel” (angles between 0◦ and 20◦) and “only perpendicular” (angles be- tion of parallel and perpendicular projected orientations ◦ ◦ matches the observations using SExtractor filament fits. tween 70 and 90 ) angle distributions. The observed γ The results are similar as those found with FILFINDER. distribution instead appears more consistent with a random distribution and for certain bimodal distributions of parallel and perpendicular angles. The best match for 4.4. Cumulative Distribution Functions Based on the bimodal distribution are angles that are only paral- Protostellar Characteristics lel 22% of the time and only perpendicular 78% of the Here we investigate whether or not individual charac- time. These results are at apparent disagreement with teristics of the protostars themselves or their surround- Anathpindika & Whitworth(2008), but that study has a ing environment affect the underlying γ distribution. We number of caveats, as explained in AppendixB. There- consider the protostar’s multiplicity, the protostar’s bolo- fore, we believe that, at least in Perseus, our results are metric temperature (Tbol), and the Zari et al.(2016) a better representation of the actual γ distribution. τ353 GHz pixel value at the protostar. Both the proto- Davis et al.(2009) also found an apparently random stellar multiplicity and Tbol were taken from Tobin et al. alignment when comparing molecular hydrogen outflows (2016) and references therein. For multiples that were to the filament/core directions in Orion, but they did resolved with the VLA but not with Spitzer, we assign not test the idea of a mixed distribution of only parallel the same Tbol for all multiples within the Spitzer-defined and only perpendicular angles. Such random alignment source. The left panel of Figure 13 shows two CDFs: one is supported by Tatematsu et al.(2016), who found that for systems that have only one known protostar within the angular momentum axes of cores in the Orion A fil- 10,000 AU and another for systems with more than one ament are random with respect to the filamentary struc- known protostar within 10,000 AU. The middle panel ture. Our study and these studies show that protostellar shows two CDFs based for protostars with Tbol above outflows in both low- and high-mass star-forming regions and below 50 K, where lower Tbol indicates younger pro- show no preferred orientation relative to their local fil- tostars. The right panel shows two CDFs based on the ament. In a study that does not compare outflows an- τ353 GHz pixel value at the Tobin et al.(2016) protostellar gles to filaments, Ioannidis & Froebrich(2012) investi- location for τ353 GHz above and below 0.016. Protostars gated whether outflows are perpendicular to the Galac- at locations of higher τ353 GHz are more likely to be in tic plane. Specifically, they observed molecular hydrogen their natal star-forming filament. We select delimitations outflows within part of the Galactic plane (18◦ < l < 30◦; ◦ ◦ of Tbol = 50 K and τ353 GHz = 0.016 so that roughly half −1.5 < b < +1.5 ), and they also found a somewhat of the sample is in each CDF. We note that Tbol = 70 K is random distribution of outflow PAs, with a marginal typically used to separate Class 0 and Class I protostars preference for outflows to be aligned perpendicular to (Chen et al. 1995; Enoch et al. 2009). the Galactic plane.

Since the distribution of γF angles is separated into two Theoretical models and simulations at parsec-scales CDFs for each panel in Figure 13, statistically differen- have shown that filaments can be the result of colliding tiating the distributions from random and perpendicular clouds or flows, and the initial orientation of the angu- Monte Carlo simulations is more difficult. Table1 shows lar momentum in these systems can dictate how angular that none of these CDFs can be distinguished from a momentum is transported to smaller scales. Theoretical random distribution, and several CDFs are statistically expectations of γ vary significantly and can often depend inconsistent with perpendicular. While we only show the on the initial conditions set in the simulation. Hydro- corresponding p-value results if we use the FILFINDER al- dynamic turbulent simulations of collapsing clouds by 11

Multiplicity bol 345 GHz 1.0 1.0 1.0

0−20 ◦ 0−20 ◦ 0−20 ◦

0.8 0.8 0.8

0.6 0.6 0.6

Random Random Random

Distribution Function Distribution 0.4 70−90 ◦ Function Distribution 0.4 70−90 ◦ Function Distribution 0.4 70−90 ◦

0.2 0.2 0.2 Cumulative Cumulative Cumulative Single Protostar bol < 50 K 345 GHz < 0.016 Multiple Protostars bol > 50 K 345 GHz > 0.016 0.0 0.0 0.0 0 15 30 45 60 75 90 0 15 30 45 60 75 90 0 15 30 45 60 75 90 Projected angle between outflow and filament, γ (deg) Projected angle between outflow and filament, γ (deg) Projected angle between outflow and filament, γ (deg)

Figure 13. CDFs of γ, binning data based on multiplicity (left), bolometric temperature (middle, an indicator of age), and optical depth (right). All CDFs use filament measurements from the FILFINDER algorithm. Tilley & Pudritz(2004) show that cores within filaments tions of 3-dimensionally random and mostly perpendic- can form at oblique shocks, and these shocks can impart ular distributions look quite similar, making it difficult angular momentum to the core. Simulations by Clarke for even large samples to distinguish between the two. et al.(2017) show that filaments accreting from a tur- Moreover, the fact that the angles between outflows and bulent medium have a vorticity (and hence, angular mo- filaments are neither purely parallel nor purely perpen- mentum) that is typically parallel to filaments, which is dicular may reflect how material is funneled toward the primarily derived from radial inhomogeneous accretion. protostars at both the large and small scales. On large Chen & Ostriker(2014, 2015) included magnetohydrody- scales, Chen & Ostriker(2014) suggested that material namics in their simulations and found that for filaments flows along magnetic field lines, which could be mainly forming due to converging flows, mass flows along mag- perpendicular to the filament along its exterior and par- netic field lines to both the filaments and cores (which allel within the interior. This mix of flows could induce form simultaneously). For dense filaments of size-scales a more random-like vorticity to the parental cores of the on order of 0.1 pc, some observations have suggested that protostars. magnetic field lines are perpendicular to the filament’s Higher resolution simulations have explored angular elongation (e.g., Matthews & Wilson 2000; Pereyra & momentum transfer within cores (i.e., scales .0.1 pc). Magalhães 2004; Santos et al. 2016). If such fields help Walch et al.(2010) used smoothed particle hydrody- drive gas perpendicular to the filaments, the results from namic simulations of a low-mass, transonically turbu- Clarke et al.(2017) suggest that this could induce a vor- lent core, and found that the rotation axes of protostars ticity parallel to the filaments. The ability for such vor- tend to be perpendicular to “small” filaments (diam- ticity to be transferred to angular momentum at the core eters ∼0.01 pc) within cores. However, the Herschel- 00 scale or smaller is unclear, and this was not investigated derived τ353 GHz maps (36 = 0.04 pc resolution) do not by Clarke et al.(2017). However, if angular momentum resolve these small filaments. Observations of molecu- is inherited by the protostar in the same direction of the lar line (Hacar et al. 2013, e.g.,) or continuum tracers vorticity, we would expect the rotation of the protostar (e.g., Pineda et al. 2011a) suggest that filaments break to be parallel with the filament. Indeed, simulations by into smaller substructures, and therefore the initial con- Tilley & Pudritz(2004) and Banerjee et al.(2006) show ditions for protostellar rotation and collapse may be set that for filaments forming due to colliding flows, oblique by these smaller structures. These substructures some- shocks can impart net rotation parallel to the filament, times have similar elongation as their parent filaments which in turn can produce parallel filaments and proto- (Pineda et al. 2011a; Hacar et al. 2013), but not always stellar rotation axes. However, numerical simulations by (e.g., Pineda et al. 2010, 2015). At scales of ∼10,000 AU, Whitworth et al.(1995) suggest that filaments can form elongated, flattened envelopes are observed to be perpen- via two colliding clumps, and the initial net angular mo- dicular to their outflows (e.g., Looney et al. 2007). The mentum of the system will typically be perpendicular to typical size of these flattened structures and their univer- the filaments that form. The protostar can inherent this sality remains unclear. Observational surveys that probe angular momentum, and thus its rotation axis will tend dense structures at scales between ∼0.01 to 0.1 pc can un- to be perpendicular to the filament. Theoretical predic- cover whether and at what scale an elongated structure tions of rotation axes either parallel or perpendicular to is perpendicular with a protostar’s angular momentum the filament axes are at odds with observations at both axis. the core (Tatematsu et al. 2016) and protostellar scales Regardless of the initial conditions that create fila- (this study). ments, the actual spin of a protostar may be independent Since filaments may be created through a variety of of the filamentary structure. The local vorticity of turbu- mechanisms, a combination of these mechanisms could lence may determine the spin of the parent core (McKee cause outflow-filament alignment to appear more ran- & Ostriker 2007). Even within the core, the rotation axes domly aligned. Assuming the alignment is not purely of protostars may change. Offner et al.(2016) and Lee random, our observations suggest that outflows are more et al.(2017) found that both turbulent accretion onto a likely to form perpendicular than parallel to the filamen- protostar and interaction with companions can cause a tary elongation. Unfortunately, two-dimensional projec- significant evolution in a protostar’s spin. Essentially, at 12 small scales it is feasible that the underlying structure, ∼0.01 to 0.1 pc are needed to reveal whether and how a turbulence, and/or multiplicity could significantly alter protostar’s angular momentum axis may be related to its the initial rotation axes. While random alignment is fa- natal structure. vored in some models of turbulent accretion, even models with strong magnetic fields could result in random alignment. Mouschovias & Morton(1985) suggested that for We thank an anonymous referee for thorough and help- fragments linked by strong magnetic fields, the angular ful reviews. I.W.S. acknowledges support from NASA momentum orientation of the fragments depends solely grant NNX14AG96G. E.I.V. acknowledges support form on the shape of the magnetic flux tubes, which can have the Russian Ministry of Education and Science grant quite irregular shapes. If fragments in filaments are in- 3.5602.2017. J.J.T. acknowledges support from the Uni- deed magnetically linked, our study suggests that the versity of Oklahoma, the Homer L. Dodge endowed chair, flux tubes connecting them are indeed irregular. The- and grant 639.041.439 from the Netherlands Organisa- oretical simulations have begun to incorporate gravity, tion for Scientific Research (NWO). J.E.P. acknowledges turbulence, magnetic fields, and outflows to study the the financial support of the European Research Coun- formation of filamentary complexes (e.g., Myers et al. cil (ERC; project PALs 320620). The authors thank the 2014; Federrath 2016). Such simulations can supply a SMA staff for executing these observations as part of the more robust expectation of the observed distribution of queue schedule, Charlie Qi and Mark Gurwell for their γ for a large sample of outflows and filaments. technical assistance with the SMA data, and Eric Keto for his guidance with SMA large-scale projects. The Sub- 6. SUMMARY millimeter Array is a joint project between the Smithso- The MASSES survey observed CO(2–1) in all the nian Astrophysical Observatory and the Academia Sinica known Class 0/I protostars in the Perseus molecular Institute of Astronomy and Astrophysics and is funded cloud. With these data, along with ancillary observations by the Smithsonian Institution and the Academia Sinica. of CO rotational transitions, we were able to determine This research has made use of the VizieR catalogue ac- the outflow PAs for each protostar. We compare these cess tool and the SIMBAD database operated at CDS, angles to the filament directions based on optical depth Strasbourg, France. This research made use of APLpy, maps derived from Herschel (Zari et al. 2016). We find an open-source plotting package for Python (Robitaille that: & Bressert 2012). 1. The outflow directions are randomly distributed in the Perseus molecular cloud. This random distri- APPENDIX bution appears to hold regardless of parental clump A. MONTE CARLO SIMULATIONS of a protostar. Many studies have used Monte Carlo simulations to 2. The projected angle between the outflow and fila- show the expected observed distribution of angles of two ment, γ, is significantly inconsistent with a “purely vectors projected into three dimensions. Several of these parallel” and a “purely perpendicular” distribution studies (Hull et al. 2013, 2014; Lee et al. 2016; Offner of projected angles. et al. 2016) were specifically interested in the same projected distributions we are interested in this study, i.e., 3. The observed γ distribution cannot be distin- the projection of angles that are 3-dimensionally purely guished from a random distribution. parallel (between 0 and 20◦), purely perpendicular (70– 90◦), or completely random (0–90◦). These studies do 4. We also consider bimodal distributions, and find not discuss the exact details of the Monte Carlo simula- a slightly more consistent distribution to the ob- tions. Here we discuss our Monte Carlo method, and the served gamma distribution when 22% of the pro- results are consistent with the aforementioned studies. jected angles are parallel and 78% are perpendicu- For our methodology, we generated N pairs of 3- lar. Our observations are unlikely to come from dimensional vectors with each vector random about the bimodal distributions that are more than ∼33% sky. To generate a random vector, we chose a random parallel or more than ∼90% perpendicular. point on the surface of a unit sphere and then connected the sphere’s origin to this point. For the purposes of 5. Regardless of the multiplicity, Tbol (age), or opacity of the individual protostars, the observed γ dis- Monte Carlo simulations, sampling a random point from tribution cannot be distinguished from a random a unit sphere that avoids biases has been well-studied distribution. However, to better test how these (e.g., Marsaglia 1972). We outline one such way to se- different parameters of the protostars affect the γ lect random points on a unit sphere below, which is based distribution, a larger sample is needed. on Weisstein(2017). We first selected a random angle θ between 0 and 2π and a random number u that’s between We discuss the implications of the fact that outflows –1 and 1. From random variables θ and u, we then se- and filaments are neither purely perpendicular or purely lected a random point on a unit sphere at position x, y, parallel. We suggest that this feature could reflect the and z where physical conditions at large or small scale. At large scale, p a dominant flow direction toward cores may not exist. At x = 1 − u2 cos θ (A1) small scale, the underlying structure, turbulence, and/or multiplicity could affect the angular momentum axes. p Observational surveys of dust emission at scales between y = 1 − u2 sin θ (A2) 13

sphere (Figure 14). Our tests show that the curve of z = u. (A3) the CDF of the Monte Carlo simulation (e.g., Figure8) is very smooth as long as the sample size is larger than A unit vector between the sphere’s origin and this point ∼20,000 projections. is: " # x B. DISCREPANCY WITH ANATHPINDIKA & ~v = y (A4) WHITWORTH z As seen in Table1 and Figure 12, Anathpindika & Whitworth(2008, henceforth in this appendix, AW08) 18000 found a distribution of projected outflow-filament angles, γ, that favors outflows and filaments that are generally 16000 perpendicular rather than random. When comparing a

14000 random distribution to the AW08 distribution of γ, the AD test p-value is 0.017, indicating a significantly non- 12000 random distribution. AW08 also found that, if they assumed γ follows a tapered Gaussian (i.e., between 0◦ and 10000 90◦) centered at perpendicular, 72% of the time the out- ◦ 8000 flow is within 45 of being perpendicular to the filament. To identify the PA of the outflow, AW08 connected 6000 a line between a near-IR identified YSO and the cor- Number of Angles of Number responding Herbig Haro Object from Reipurth(1999). 4000 The PA of the filaments are determined from flux maps of 2000 various submillimeter surveys using SExtractor in STAR- LINK (with a visual confirmation of the PA). AW08 ac- 0 0 10 20 30 40 50 60 70 80 90 knowledged a few selection effects that may bias their results. Specifically, they assumed that all objects have γ3 (deg) random inclinations, although adjacent sources may have correlated inclinations. Our study also suffers from this Figure 14. Histogram of γ3D for a Monte Carlo simulation of N = bias. AW08 also suggested that they are inherently more 106 vector pairs. Histogram bin widths are 1◦. This histogram likely to find perpendicular outflows since Herbig Haro shows the approximate shape of the distribution of all possible angles between two vectors in a unit sphere. objects are more likely to be extincted if they are coinci- dent with the filament. For these reasons, they call their To randomly sample from all angles within a unit conclusion not statistically robust. sphere, we generated two random unit vectors, ~v and AW08 also have some other disadvantages with their 1 dataset. Their measured outflow angles rely primarily on ~v2 and measure the angle between the vectors. The angle is simply published catalogs rather than the physical images. For about half of their sources, they interpreted multiple Her- γ = arccos( ~v · ~v ). (A5) big Haro objects emitting from a young stellar object as 3D 1 2 independent outflows. However, upon further analysis, Since we are interested in the smallest angle created we find this interpretation is not always accurate. As an by the two intersecting vectors, we constrained γ3D to example, Figure 15 shows a 3-color Spitzer image of the ◦ ◦ ◦ be between 0 and 90 , e.g., if γ3D is larger than 90 , outflow emanating from the SVS 13 protostellar region. ◦ we subtracted γ3D from 180 . We generated N pairs The Spitzer image shows only one obvious bipolar out- of vectors to produce N angles of γ3D. For the Monte flow from the protostar (greenish 4.5 µm color), and the Carlo simulations in this paper, we chose N = 106. We molecular CO(1–0) line observations confirm this is a sin- 6 show the distribution of γ3D for N = 10 via the his- gle outflow (contours in Figure 15; Plunkett et al. 2013). togram in Figure 14. We then mapped each γ3D angle However, AW08 declared that the five HH objects asso- to a projected angle in 2D, γ, by setting one axis for the ciated with this outflow are five separate outflows, and vector pair to 0 (the x-value of the vector in our code) each of these had a measurement of γ above 45◦. There- and calculating the new angle between the vectors. fore, AW08 sometimes have multiple measurements for γ From this mapping, we can extract a range of angles for a single outflow, which will significantly bias their re- from the distribution of γ3D and plot its corresponding γ sults toward a non-random distribution. Moreover, Fig- distribution. For this study, we were primarily inter- ure 15 shows that significantly different measurements ested in projections for 3-dimensional angles that are for PAOut can be made for each Herbig Haro object for purely parallel (between 0 and 20◦), purely perpendic- the same outflow. The dispersion of HH objects about ular (70–90◦), or completely random (0–90◦). For the the outflow lobe may occur due to a precessing outflow Monte Carlo sample size of N = 106 (equivalent to the coupled with episodic ejections (e.g., Arce & Goodman number for the completely random sample size), we ex- 2001; Arce et al. 2010) and/or due to the structure (e.g., tracted from the γ3D distribution ∼60,000 projections for clumpiness) of the ambient cloud. Therefore, measur- a purely parallel sample and ∼340,000 for a purely per- ing PAOut from Herbig Haro objects alone can result in pendicular sample. The reason why the sample size for large PAOut measurement errors. AW08 also rely on pre- purely perpendicular is much larger than purely parallel vious published protostellar positions based on near-IR is simply due to the fact that perpendicular-like angles observations, and these objects sometimes are not the are much more likely for two random vectors in a unit 14

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16 ◦ se,L γ )( ◦ se,S γ )( 0 6 ◦ γ )( 0 5 ◦ γ )( 0 4 ◦ γ )( 0 3 ◦ γ )( 0 2 ◦ γ )( 0 1 ◦ γ )( F ◦ γ F , )( ◦ Fil Ref/Info PA )( Out ◦ )( ◦ )( ◦ Blue PA Red PA PA Table 2 )( 3 10 × 353 GHz τ bol T Source Information and Measured Position Angles Y 28 7.9 -90 90 90 (3) 130 40 40 41 44 49 64 45 43 70 Multiple c 0 Other Names b DEC b (J2000) (J2000) (Y/N) (K) ( a Source RA Name Per-emb-15Per-emb-16Per-emb-17 03:29:04.055Per-emb-18 03:43:50.978 +31:14:46.237Per-emb-19 03:27:39.104 +32:03:24.101 RNO15-FIRPer-emb-20 03:29:11.258 +30:13:03.078 ...Per-emb-21 03:29:23.498 +31:18:31.073 ...Per-emb-22 03:27:43.276 +31:33:29.173 NGCPer-emb-23 1333 IRAS7 03:29:10.668 +30:12:28.781 ...Per-emb-24 03:25:22.410 +31:18:20.191 L1455-IRS4Per-emb-25 03:29:17.211 +30:45:13.254 ...Per-emb-26 03:28:45.297 +31:27:46.302 L1448-IRS2Per-emb-27,O1 N 03:26:37.511 +31:05:41.693 ASRPer-emb-27,O2 30 03:28:55.569 03:25:38.875 +30:15:27.813 Y ...Per-emb-28 03:28:55.563 +31:14:37.022 +30:44:05.283 ...Per-emb-29 36 +31:14:36.408 NGC L1448C, 1333Per-emb-33,O1 L1448-mm IRAS2A 03:43:51.008 NGC Y 59 1333Per-emb-33,O2 IRAS2A 03:25:36.380 N 03:33:17.877 +32:03:08.042 YPer-emb-33,O3 3.1 03:25:36.499 +30:45:14.723 +31:09:31.817 ...Per-emb-35,O1 03:25:35.669 Y +30:45:21.880 L1448IRS3B, 1.3 N B1-c 39 L1448NPer-emb-35,O2 03:28:37.091 +30:45:34.110 65 L1448IRS3B, Y 59 L1448N YPer-emb-36 03:28:37.219 145 +31:13:30.788 L1448IRS3B, Y L1448N Y NPer-emb-37 +31:13:31.751 43 NGC 1.6 60 1333 -30Per-emb-40 IRAS1 1.6 03:28:57.374 NGC 0.5 Y 1333 47 69Per-emb-41 IRAS1 -35 03:29:18.965 +31:14:15.765 N Y 45 69Per-emb-42 42 1.1 03:33:16.669 +31:23:14.304 1.0 N Y NGC 150Per-emb-44 14 1333 IRAS2B 03:33:20.341 -61 +31:07:54.902 1.8 -127 1.7 ... 145 57Per-emb-46 03:25:39.135 +31:07:21.355 1.6 1.7 B1-a 67 57 1.0Per-emb-49 150 Y 03:29:03.766 -62 +30:43:57.909 B1-b 61 57 -32 -173Per-emb-50 112 03:28:00.415 Y 60 +31:16:03.810 Y (2) 4.7 N L1448C-S -156 -21Per-emb-53 03:29:12.953 +30:08:01.013 0.9 4.8 SVS13APer-emb-55 -125 48 -77 Y (3) 103 118 03:29:07.768 +31:18:14.289 11 0.4 4.3 ... 148 115Per-emb-56 103 03:47:41.591 +31:21:57.128 57 ... 45 165 42 48 4Per-emb-57 -58 03:44:43.298 +32:51:43.672 -103 ... 61 0.6 -132 105 118Per-emb-58 106 38 148 03:47:05.450 20 +32:01:31.223 (1) B5-IRS1 (1) -78 0.6Per-emb-61 -52 77 03:29:03.331 162 +32:43:08.240 1.8 (1) 2.7 IRAS 122Per-emb-62 03415+3152 14 (1),(8) 03:28:58.422 104 (1),(8) 93 +31:23:14.573 48 1.6 IRAS 50 77 58SVS13B -142 03439+3233 -57 03:44:21.357 +31:22:17.481 Y Y ... 107 77 128 YSVS13C 58 169 (1) 03:44:12.977 73 122 82 +31:59:32.514 146 Y 61 ... 112 133B1-bN 27 (2) (2) Y +32:01:35.419 85 (3) 38 -156 ... (1)B1-bS 123 87 3 67 104 58 128 03:29:03.078 (3),(4) 132 ... 22 89 163 -11 57 Y 130 59 03:29:01.970 157 -68 +31:15:51.740 -50 82 4 18 (3),(4) N 125 7 125 90 188 (1) N (3),(4) ... 123 43 +31:15:38.053 20 138 ... 127 57 03:33:21.209 (1) 2.0 N 85 1.9 32 0.8 15 Y 169 61 ... 81 75 309 4.1 03:33:21.355 37 +31:07:43.665 112 69 127 132 21 N 77 (1),(8) 3.0 130 84 39 312 79 26 28 14 5 +31:07:26.372 ... 221 82 24 74 54 (1),(8) 37 80 10 287 17 61 101 239 89 79 -139 36 ... 17 0.5 15 27 43 (3) 12 86 -150 (1) 12 66 2 32 37 128 84 0.4 17 6 (2),(7) 0.8 72 31 120 75 35 17 35 32 29 N 43 83 0.8 9 2.3 37 79 19 63 -79 34 24 56 N -137 11 29 75 89 78 39 45 115 25 28 0.7 30 31 77 134 83 N 7 36 46 19 12 43 145 -40 42 44 27 68 72 -49 33 51 43 313 N 73 3 101 45 6 -153 52 22 22 23 65 43 13 38 322 70 26 -65 35 68 26 73 71 55 39 46 30 55 -83 371 64 130 -35 Y 4 27 27 24 66 0.4 (1),(9) 85 9 131 378 3 63 23 86 69 32 90 85 Y 58 29 70 27 1.2 -114 47 53 (3) 115 (1) 48 21 22 85 57 10 0.7 (3) 56 86 74 112 Y 145 57 33 (2) 6 56 44 48 131 20 0.4 49 19 73 145 89 Y 15 59 59 89 21 30 27 62 54 (3) -13 10 7 130 5 30 84 46 104 38 (10) 57 14.7 125 36 7 85 (10) 15 48 2.7 13 33 28 147 -155 33 17.7 84 39 51 0 87 33 2.5 (1) (3) 9 80 7 85 67 39 65 ... 4.9 (1) 54 64 63 80 54 67 -165 10 4 43 146 5.8 85 76 24 7 ... 7 78 72 -172 83 50 54 26 20 167 21 89 84 32 (1),(11) 120 59 67 15 90 22 20 70 84 53 51 112 81 24 83 -20 28 33 62 (1),(7) 12 8 135 16 7 65 80 53 51 (1),(9) 4 88 78 84 30 64 ... 16 4 21 85 52 35 16 34 -68 135 170 (1) 11 15 80 13 21 134 19 76 8 80 55 15 8 26 7 82 82 32 (3),(7) 43 24 90 120 16 56 61 3 132 4 49 86 8 11 29 34 45 20 57 62 (2) 50 61 14 (3),(7) 18 81 34 32 72 (3) 3 46 46 15 20 66 66 14 17 8 76 75 54 66 42 128 24 20 67 14 75 71 17 125 9 63 73 58 32 74 38 38 76 83 48 16 79 68 55 30 6 6 5 37 86 18 75 54 84 46 14 6 38 84 5 78 7 22 14 30 39 41 54 6 84 36 28 38 34 41 7 62 76 39 43 18 37 6 38 52 61 10 45 31 55 7 76 13 15 46 Per-emb-1Per-emb-2Per-emb-3 03:43:56.806Per-emb-5 03:32:17.932Per-emb-6 +32:00:50.202 03:29:00.575Per-emb-8 +30:49:47.705 HH211-MMS 03:31:20.942Per-emb-9 +31:12:00.204 IRAS 03292+3039 03:33:14.404Per-emb-10 +30:45:30.263 ... 03:44:43.982Per-emb-11,O1 +31:07:10.715 IRAS 03282+3035 03:29:51.832Per-emb-11,O2 +32:01:35.210 03:43:57.065 ... 03:33:16.424Per-emb-12 +31:39:05.905 03:43:57.688 ... +32:03:04.788 +31:06:52.063Per-emb-13,O1 IRAS +32:03:09.975 03267+3128, IC348MMS Y Perseus5 ...Per-emb-13,O2 03:29:12.016 N 03:29:10.537 IC348MMS 03:29:12.842 N +31:13:08.031 +31:13:30.925 Y +31:13:06.893 NGC 27 NGC 1333 1333 IRAS4B IRAS4A 27 NGC 1333 IRAS4B 36 32 2.4 N 2.2 Y 0.8 1.2 Y N Y Y 129 Y 32 114 30 63 N 126 28 52 29 30 -50 1.1 43 -61 1.6 -125 -56 7.1 30 2.9 4.6 1.9 129 116 0.7 -82 59 125 -17 3.8 180 -145 (1) 50 36 (1) 95 15 (1) (1) 161 -134 35 132 0 -109 ... 40 -165 97 162 39 54 57 3 60 35 180 76 36 15 (2) 4 (1) 86 82 5 52 (1) (2) (2) (3),(7) 75 77 35 (3) 2 10 134 80 83 25 (1) 134 128 1 130 48 73 85 24 27 87 65 82 1 80 87 87 50 19 27 87 12 48 81 50 87 84 86 50 21 3 38 14 82 88 47 85 4 80 48 40 75 11 75 77 79 86 47 85 46 38 73 5 11 73 14 85 88 39 48 35 0 37 11 64 2 27 81 89 45 26 61 38 9 9 2 7 50 39 45 78 47 11 80 50 2 48 47 15 82 85 77 88 1 41 21 16 15 3 62 24 8 17 ) ◦ se,L γ )( ◦ se,S γ )( 0 6 ◦ γ )( 0 5 ◦ γ )( 0 4 ◦ γ )( 0 3 ◦ γ )( 0 2 ◦ γ )( 0 1 ◦ γ )( F ◦ γ F , )( ◦ Fil Ref/Info PA )( Out ◦ )( ◦ )( Table 2 ◦ Blue PA Red PA PA )( 3 10 × 353 GHz τ bol 15 0.9 87 -93 87 (1) 56 32 40 41 65 67 72 52 41 67 T Source Information and Measured Position Angles d Multiple c Other Names b DEC b (J2000) (J2000) (Y/N) (K) ( a . — (1) Our study; measured by connecting outflows to continuum peaks, (2) Plunkett et), al. ( 2013 (3) Lee et al. ( 2016 ), (4) Lee et al. ( 2015 ), (5) Chen et),( 2010 al. measured manually by our study, (6) Source RA Name RA and DEC positions are from Tobin etThis al. ( 2016 ). sources was In not the detected case in whereTobin a et close al. ( 2016 ). binary is unresolved by the SMA, we pick the brightest Tobin et al. ( 2016 ) protostar for the source of the emission. Names including O1, O2, and O3 are sources with multiple outflows. Note Alternate names are taken from Tobin et al. ( 2016 ). L1448IRS2EL1451-MMS 03:25:25.660Per-bolo-58 03:25:10.245 +30:44:56.695 03:29:25.464 +30:23:55.059 ... +31:28:14.880 ...... N N N 15 15 2.6 0.9 ... 11 165 -169 165 11 (5),(7) (6) 62 123 77 87 68 87 71 86 37 83 71 84 60 81 61 73 34 54 76 53 Pineda et al. ( 2011b ),manually; measured (11) manually red by and oura study, blue (7) lobe only are oneb both outflow in lobe same detectedc quadrant; in we the consider cited this study,d (8) as outflow a PA single fit outflow only that using may blue be lobe, in (9) the outflow PA plane fit of only the using sky. red lobe, (10) our study; PA measured