The James Clerk Maxwell Telescope Legacy Survey of Nearby Star-forming Regions in the Gould Belt

Understanding star formation is a crucial goal of astronomy. Star formation plays a pivotal role in most aspects of astronomy from the formation and evolution of galaxies to the origins of extra-solar planets and the potential for life elsewhere in our Galaxy. Our knowledge of the star-formation process has increased dramatically due to the advent of sensitive far-infrared and submillimetre detectors but has suffered from the piece-meal fashion in which such observations have been undertaken to date. We describe here a project that aims to produce a large and unbiased sample of star-forming molecular material in the solar vicinity at relatively high resolution (8–14 arcsec).

To understand star formation, we need to probe the physical conditions of molecular clouds before and during the star formation process. Although near-IR images can tell us a great deal about the results of star formation, the objects visible are too old to assess the crucial conditions in which star formation originates. We need to illuminate the earliest conditions in order to understand the formation process (e.g. Di Francesco et al., 2007; Ward-Thompson et al., 2007).

Submillimetre continuum imaging selects the very earliest stages of star formation because it traces the high column densities of dust, even when that dust is at low temperatures, within star-forming cores and allows important physical parameters such as density to be traced in detail. From its earliest days the James Clerk Maxwell Telescope (JCMT) has been mapping submillimetre continuum emission from star-forming regions (e.g. Ward-Thompson et al., 1989; 1995). The JCMT identified first the youngest known protostars (Class 0 objects; André et al. 1993) and molecular cloud cores on the verge of collapse to form protostars (prestellar cores; Ward-Thompson et al. 1994).

The JCMT also helped determine that the prestellar core mass function mimics the IMF, indicating that it may be determined at the very beginning of the star formation process – this was the first observational breakthrough in understanding its origin in nearly 50 years (Johnstone et al. 2000; Motte et al. 2001; Nutter & Ward-Thompson 2007). Many large area continuum mapping surveys have also been carried out with the Submillimetre Common-User Bolometer Array (SCUBA) on JCMT of star-forming regions (e.g. Johnstone & Bally 1999; Pierce-Price et al., 2000; Johnstone et al., 2000; 2001; 2006; Hatchell et al., 2005; 2007; Nutter et al., 2005; 2006; Nutter & Ward-Thompson 2007; J. Kirk et al., 2005; Moriarty-Schieven et al., 2006). Many of these regions lie in a ring around the sky, coincident with the Gould Belt.

The Gould Belt is a ring of nearby O-type stars inclined at about 20^∘ to the Galactic Plane. It was first discovered in the southern hemisphere in fact by John Herschel (1847), who noted that many of the brightest stars in the southern sky lie in a band that is inclined to the plane of the Galaxy. Subsequently, Gould (1879) traced the northern part of the band, thereby completing the ring.

The Gould Belt is centred on a point $\sim 200\,$pc from the Sun and is about 350 pc in radius (e.g. Clube 1967; Stothers & Frogel 1974; Comeron et al. 1992; de Zeeuw et al., 1999; Pöppel 2001). Figure 1 shows a schematic of the Gould Belt, and Figure 2 shows its projection onto the plane of the sky, showing the inclination to the Galactic Plane.

The formation mechanism of the Belt remains something of a mystery. One hypothesis is that it may be the result of a high velocity cloud impacting the Galactic Plane (Comeron & Torra, 1992; 1994; Guillout et al., 1998). An alternative possibility is a local massive supernova remnant or stellar wind interacting with a large molecular cloud (Blaauw 1991).

Whatever the cause, the Gould Belt is a highly active ring of nearby star formation, and most of the local star-forming molecular clouds are associated with it, including Taurus, Auriga, Orion, Lupus, Ophiuchus, Scorpius, Serpens and Perseus. Study of the star formation within the Gould Belt sheds light on the process of star formation within these respective clouds. Moreover, it may also help to shed light on the whole of the Gould Belt itself. For example, accurate dating of the bursts of star formation around the Belt may be able to test the various formation mechanisms of the Gould Belt.

The JCMT is currently undergoing a complete overhaul of its instrumentation, including a new bolometer array camera, the Submillimetre Common-User Bolometer Array 2 (SCUBA-2; Holland et al., 2006), with an imaging polarimeter, the SCUBA-2 Polarimeter (POL-2; Bastien et al., 2005), and a heterodyne array receiver, the Heterodyne Array Receiver Programme for B-band (HARP; Smith et al., 2003). The combination of SCUBA-2, HARP, and POL-2 are a powerful tool set with which to study star formation.

SCUBA-2 is an innovative 10,000 pixel submillimetre camera due to be delivered shortly to the JCMT. The camera is expected to revolutionize submillimetre astronomy in terms of its ability to carry out wide-field surveys to unprecedented depths. SCUBA-2 uses Transition Edge Super-conducting (TES) bolometer arrays, which come complete with in-focal-plane Superconducting Quantum Interference Device (SQUID) amplifiers and multiplexed readouts, and are cooled to 100mK by a liquid cryogen-free dilution refrigerator. SCUBA-2 will observe simultaneously at 850 and 450 microns, with angular resolutions of 14 and 8 arcsec respectively (Holland et al., 2006).

The polarimeter POL-2 will have an achromatic continuously rotating half-wave plate in order to modulate the signal at a rate faster than atmospheric transparency fluctuations. Such a modulation should improve significantly the reliability and accuracy of submillimetre polarimetric measurements. The signal will be analyzed by a wire-grid polarizer. For calibration, a removable polarizer will also be available. The components, in the order that the radiation will encounter them, are the calibration polarizer, the rotating wave plate, and the polarizer. The components will be mounted in a box fixed permanently in front of the entrance window of the main cryostat of SCUBA-2. All components will be mounted so that they can be taken in and out of the beam remotely, making it very easy and fast to start polarimetry at the telescope (Bastien et al., 2005).

HARP is a 350GHz, 4$\times$4 element, heterodyne focal plane array, using SIS detectors, recently commissioned on the JCMT. Working in conjunction with the backend Auto-Correlation and Spectral-line Imaging System (ACSIS; Hovey et al., 2000), HARP provides 3-dimensional imaging capability with high sensitivity at 325 to 375GHz. This is the first submillimetre spectral imaging system on JCMT, affording significantly improved productivity in terms of speed of mapping. The core specification for the array is that the combination of the receiver noise temperature and beam efficiency, weighted optimally across the array is $<$330K single side-band (SSB) for the central 20GHz of the tuning range (Smith et al., 2003). The 16 pixels have receiver temperatures of 94–165 K. The angular resolution of HARP is 14 arcsec, matching the 850-$\mu$m resolution of SCUBA-2.

ACSIS has 16 inputs (actually 32, paired up), with a maximum bandwidth per channel of approximately 2GHz in a 2$\times$1 GHz configuration. It has a minimum sample time of 50ms and a maximum output map size of 16 Gbytes. It has a number of spectral bandwidths and resolutions that can be selected by the user: 250MHz bandwidth with 30kHz resolution; 500MHz bandwidth with 61kHz resolution (multi-subsystem mode); 1GHz bandwidth with 500kHz resolution; and 2GHz bandwidth with 1000kHz resolution (merged). In practise, the usable bandwidth will be about 10% less than this, because of the filter roll-off.

ACSIS and HARP together have a number of observing modes, including raster mapping with position switching for mapping large areas, chopped jiggle mapping for fully sampled mapping of areas comparable to the HARP focal plane area, and jiggle mapping with fast frequency switching for fully sampled mapping of compact areas where no nearby off-source reference position is available.

During the planning phase of observations with the new JCMT instrumentation, numerous ideas were put forward for science questions that could be addressed (e.g. Ward-Thompson 2004). From these plans a number of proposals emerged. One such proposal, described herein, was to map local star-forming regions with SCUBA-2, HARP and POL-2. This was one of seven proposals accepted as part of the JCMT Legacy Programme.

With the increased mapping speed of SCUBA-2, one can cover essentially all of the star-forming regions within 0.5 kpc in a reasonable amount of time, detecting all of the protostars and prestellar cores. SCUBA-2 is designed to have increased sensitivity in each pixel, but also has two orders of magnitude more pixels than SCUBA, giving it about a 1000-fold increase in mapping speed. The increased mapping speed of SCUBA-2 can be illustrated by comparison with the large-scale mapping survey carried out by SCUBA of the Galactic Centre (Pierce-Price et al., 2000), which took $\sim$50 hours of telescope time and covered only 1.4 square degrees. By contrast this survey with SCUBA-2 will cover roughly 700 square degrees to a greater depth in $\sim$120 hours.

We will use SCUBA-2 to map the submillimetre continuum emission from as many clouds within 0.5 kpc as are visible from the JCMT, including several well known Gould Belt clouds such as Orion, Taurus, Perseus, and Ophiuchus. Several objects outside of the Gould Belt, including nearby Bok Globules, will also be mapped (c.f. Launhardt et al., 1997). We estimate that the source catalogue that we will produce will contain over five thousand sources. Such large samples of protostars and starless cores are required to provide robust statistics on objects over a range of evolutionary stages. With SCUBA-2’s predicted improvement in per-pixel sensitivity over SCUBA, we will measure the prestellar clump mass functions down to substellar masses.

HARP increases the heterodyne mapping speed of the JCMT by over an order of magnitude. We will use this increased mapping speed to map a significant fraction of the SCUBA-2 sources in isotopologues of CO. The combination of dust continuum maps from SCUBA-2 plus spectral line data cubes from the heterodyne array at matched resolution will be extremely powerful. Since molecular clouds are highly turbulent, and star formation generates infall, outflow, and rotational motions, velocity measurements are critical in understanding the mass-assembly process, feedback, and star-formation efficiency (e.g. Goodwin et al., 2004a & b; Vazquez-Semadeni et al., 2005). In addition, another use of the HARP data will be a determination of the amount of line contamination in the SCUBA data. Johnstone et al. (2003) considered this problem in Orion and argued that it was not significant except for faint sources. With the increased sensitivity of SCUBA2 such contamination may be important.

POL-2 will be able to make polarization maps of both high and low density material in molecular clouds. We will use it to map one hundred bright sources found in the SCUBA-2 survey. At present there is a debate over the relative importance of magnetic fields and turbulence in regulating the star formation process (e.g. Mouschovias 1991; Padoan & Nordlund 2002). Combined with kinematics from HARP, the POL-2 observations will allow for an investigation into the balance between gravity, turbulent support, and magnetic fields over a statistically meaningful number of star-forming cores. Previously only a few cores have been mapped (e.g., Holland et al., 1999; Ward-Thompson et al., 2000; Matthews & Wilson 2002; Crutcher et al., 2004; J. Kirk et al., 2006).

The goal of this paper is to outline the aims of the Gould Belt Survey and to describe the observations that will be carried out. In total this programme will take roughly 1000 hours of observing time on the JCMT, 500 of which have been allocated over the first two years between 2007/8 and 2009/10. Section 2 details the SCUBA-2 aspects of the survey, section 3 discusses the HARP survey, section 4 describes the survey to be carried out with POL-2, section 5 outlines some surveys at far-infrared wavelengths being carried out in parallel with this survey, and section 6 provides a brief summary of the paper.

For the shallow survey, we will map areas with $A_{V}>$ 1 at 850 $\mu$m to a depth of 1 $\sigma$ = 10 mJy beam^-1. Within the Gould Belt, this comprises an area of $\sim$400 square degrees. In addition, we will map 120 square degrees outside of the major star-forming complexes, but positionally associated with the Gould Belt. This will cover nearby small clouds and isolated star formation regions selected from dark cloud catalogues (e.g. Lynds 1962; Cambresy 1999; Dobashi et al., 2005) and previous catalogues (e.g. Clemens & Barvainis 1988; Jijina et al. 1999; Lee & Myers 1999; Visser et al. 2002).

Finally, we will map $\sim$10 square degrees of blank sky (i.e. $A_{V}$ $<$ 1) split into several fields near the Gould Belt to the same depth. This will act as a control sample to see if we have missed significant numbers of objects by using $A_{V}$ to select our target regions. The data from the shallow survey will be sensitive at 3 $\sigma$ to masses down to the sub-stellar mass limit of 0.08 M_⊙ per beam for objects at 0.5 kpc that have T_d $\geq$ 20 K, which is typical of the low extinction parts of molecular clouds.

Temperatures vary within molecular clouds and the inner regions are colder (T_d $\sim$ 10 K) than the outer regions (T_d $\sim$ 20 K) due to increased shielding from the interstellar UV field. For the deep survey we will map regions with $A_{V}$ $>$ 3 to a depth of 1 $\sigma$ = 3 mJy beam^-1 at 850 $\mu$m to ensure a complete census of star-forming cores. These regions comprise an area of $\sim$64 square degrees. These data will also reach the sub-stellar mass limit of 0.08 M_⊙ per beam at 3 $\sigma$ for objects at 0.5 kpc at T_d = 10 K.

Furthermore, these observations will simultaneously provide maps at 450 $\mu$m with a mean 1 $\sigma$ rms of 12 mJy per 450 $\mu$m beam (i.e. equal to 6 mJy per 850 $\mu$m beam after smoothing). This is because this aspect of the survey will be carried out in ‘Grade 1’ weather conditions ($\tau_{\rm 225GHZ}\leq$ 0.05). The 450 $\mu$m and 850 $\mu$m data together will provide spectral index information, where it is essential to have comparable resolution, to constrain the dust opacity indices and thus the masses of the objects.

The total star formation rate for clouds within 0.5 kpc is $\sim$6 $\times$ 10${}^{-3}\$M_⊙ yr^-1 (e.g. McKee & Williams 1997). Using the measured IMF (e.g. Kroupa 2001), the total stellar production rate within this distance is therefore $\sim$0.02 stars yr^-1. The best current estimates of the timescales for prestellar cores and Class 0 protostars are $\sim$3 $\times$ 10⁵ yr and $\sim$3 $\times$ 10⁴ yr respectively (e.g. André et al., 2000). Thus, we expect $\sim$6000 prestellar cores and $\sim$600 Class 0 protostars to be found in our wide survey. Even allowing for possible uncertainties in these by factors of $\sim$2, we would still expect thousands of objects in total, with hundreds at low mass (M $<0.5$ M_⊙) and tens at high-mass (M $>8$ M_⊙).

These objects will fill in the under-populated extremes of currently measured mass functions. Note that only tens of Class 0 protostars and hundreds of prestellar cores in total are currently known (André et al., 2000). Finally, the expected numbers of objects at the mass function peak (M $\approx 0.5$ M_⊙) will be large enough ($\sim$20-50 in each cloud) to reveal statistically if differences in characteristic stellar masses that exist between clouds are caused by local environmental influences on core formation such as cloud density and sound speed.

The census of prestellar cores and protostars from the continuum mapping will allow us to calculate the relative duration of these stages. Since half of the envelope mass is accreted during the Class 0 stage and the rest during the Class I stage (André et al., 1993), the duration of each stage tells us about the protostellar accretion rate. For instance, if they are roughly equal then the accretion rate is probably constant, as in the Shu collapse model (Shu 1977).

Alternatively, if the Class 0 duration is only one-tenth the Class I duration, as is currently suspected (André et al., 2000), then accretion must start very rapidly and decrease over time (e.g. Whitworth & Ward-Thompson 2001), implying a very different collapse scenario. In addition, if much of the envelope mass is ejected (e.g. Matzner & McKee 2000), then the fractions accreted will sum to less than 1. Current observations are limited by small-number statistics (e.g. Visser et al. 2002) but the wide survey will provide a sufficiently large sample to answer this question.

Furthermore, the relative quantities of prestellar cores at varying degrees of central condensation (given by continuum radial profiles) will inform models that predict the onset of protostellar collapse (e.g. turbulent dissipation vs. magnetic regulation).

With the census of nearby prestellar cores provided by the continuum mapping, we will be able to plot a very well-populated mass spectrum of these objects over a very wide range of masses. This will allow us to confirm or refute the claim that this mass function (e.g. Motte et al. 2001; Johnstone et al., 2006; Nutter & Ward-Thompson 2007) mimics the stellar IMF (Salpeter 1955). Recent observations appear to show that the prestellar core mass function follows the same form as the IMF down to very low masses – see Figure 13 (Nutter & Ward-Thompson 2007).

Such a steep mass function implies that low-mass cores dominate (both by number and by mass). This is in contrast to the cloud mass function where most of the mass resides in the largest structures (e.g. Williams et al., 1994), implying that a different physical mechanism is responsible for the cores. Two other obvious differences between the cloud and core mass function also exist. First, while the cloud mass function includes all the mass in the cloud (by definition), the core mass function generally only adds up to a few percent of the mass of the parent cloud (Johnstone et al., 2004; H. Kirk et al., 2006). Second, the mass-radius relation for clouds implies non-thermal motions for the largest structures whereas the cores reveal mostly thermal motions.

If the link between the core mass function and the IMF is confirmed, this will provide very strong evidence that the IMF is determined at the prestellar core stage of star formation – i.e. the physics behind core formation is also the cause of the IMF. The two currently competing theories of core formation invoke either magnetic fields or turbulence (e.g. Mouschovias 1991; Ballesteros-Paredes et al., 2003). Of particular note will be the detection of numerous objects with masses below the substellar limit (0.08 M_⊙), allowing for the first time a comparison between the mass functions of very low mass molecular cloud cores with the brown dwarf IMF. Some detections have already been made of sub-stellar mass cores (e.g. Greaves et al., 2003), but the numbers are very limited so far. Similarities between these mass functions would imply a similar formation process for brown dwarfs and stars. A statistically significant deviation, however, would imply differing origins – for example, brown dwarfs may form out of protostellar disks (for a review, see: Whitworth et al., 2007).

Additional important questions for these very low-mass cores include: whether they resemble the solar mass cores, or exist only inside a collapsing region; whether they also resemble Bonnor-Ebert spheres, and if so, what provides the confining pressure; or alternatively, whether they only form within protostellar disks (e.g. Matzner & Levin 2005). Thus the survey has a capacity to constrain brown dwarf formation directly, as well as through IMF/CMF comparisons.

With a distance limit of 0.5 kpc, the linear resolution of the continuum mapping at 850 $\mu$m will be 0.03 pc (7000 AU) or better. This scale is well matched for probing the structures of the detected prestellar and protostellar envelopes, as well as their surrounding environments. For example, the radial density profiles of prestellar cores show a flat inner region and steep outer region with the turnover at $\sim$0.03 pc (Ward-Thompson et al., 1994; J. Kirk et al., 2005).

Some have claimed that the observed radial density profiles indicate cores are pressure-supported Bonnor-Ebert spheres (e.g. Alves et al., 2001), while others have argued that such configurations result naturally from dynamic evolution of gas on large scales and do not indicate equilibrium (Ballesteros-Paredes et al., 2003). The differences between the model predictions centre around the velocity profiles of the cores. The larger sample of cores revealed by the continuum mapping, and followed up by CO spectroscopy with HARP (see section 3 below), will provide enough examples of both velocity structure and detailed morphology to settle this debate. On slightly larger scales, the continuum mapping will have the sensitivity to probe the lower-density surroundings of these cores, allowing insights into core formation. For instance, if one assumes that the continuum maps trace the mass, then one could use them to assess the importance of gravitational torques on assembling disks (Jappsen & Klessen 2004).

Previously, these surroundings could be probed only by lower density tracers such as CO (in regions where it is not depleted and its lines are optically thin), but with continuum mapping it will be possible to link the structures of cores with their environments using the same tracer. On even larger scales, the continuum mapping (especially that of the deep survey) will reveal the structure of extended filaments within clouds (c.f. Johnstone & Bally 1999; Fiege et al. 2004; Hatchell et al. 2005).

Molecular clouds exhibit filamentary structures, which are often the locus of star formation along their length. Although turbulence and magnetic fields have been suggested to explain the filamentary structures in molecular clouds, few detailed studies have been made due to limitations in mapping both the velocity fields and the polarized light which traces the magnetic field. Coupled with the dynamical information obtained with HARP and the magnetic field geometry obtained with POL-2, the morphologies and structures of filaments revealed by the continuum mapping will provide clues both to the origins and evolution of molecular clouds (c.f. Khalil et al., 2004).

HARP is a much faster mapping instrument than previous single-pixel receivers. However, it is still not possible to map all of the regions covered by the SCUBA-2 survey. Hence we will select a typical sample of cores and cloud regions from the SCUBA-2 survey, and observe these with HARP.

The proposed molecular line observations consist of two sets of targets. We will make single fully-sampled footprint images ($\sim$4 square arcmin) of a set of 1000 cores, and larger (0.08 degree²) maps of 10 cloud regions containing filaments and clustered star formation. For the well-studied clouds, many of the target regions are already known from previous SCUBA surveys. The cores, selected from the SCUBA-2 catalogue, will consist of a flux-limited sample plus a representative selection covering the full range of conditions and clouds.

In order to meet the science goals outlined above, we will map all of the cloud regions and 300 of the cores in the ¹²CO, C¹⁸O and ¹³CO J = 3–2 lines – the latter two lines can be obtained simultaneously within the ACSIS bandwidth. A further 700 cores will be mapped in the ¹²CO 3–2 line only. Most of the core maps will be a single fully-sampled HARP footprint, but for clustered cores we will combine footprints to map contiguous areas.

As summarised in Table 2, the ¹²CO maps will be made with a channel width of 1.0 km/s. The target root-mean-square (rms) 1-$\sigma$ noise level will be 0.3 K in each channel. The ¹³CO and C¹⁸O maps will both have a channel width of 0.1 km/s, and the target rms 1-$\sigma$ noise level in each channel will be 0.25 and 0.3 K respectively. The slightly poorer predicted rms in C¹⁸O is due to its location near the edge of an atmospheric band. The equivalent H₂ column density sensitivities are noted in Table 2.

The first observation targeting cores will be in the ¹²CO J = $3-2$ line, to search for and image any high velocity gas – see Figure 14. The presence of a high velocity molecular outflow is a standard way to differentiate between prestellar and protostellar cores (e.g. Bontemps et al., 1996b; Wolf-Chase et al., 1998; Visser et al., 2002; Hatchell et al., 2007). For compact submillimetre objects with no IR detection, outflows are a critical discriminant between prestellar and protostellar cores. Where outflows are detected, we will estimate outflow momentum flux (e.g., Bontemps et al., 1996a) in this large homogeneous sample, allowing us to put on a firm statistical footing the proposed correlations with bolometric luminosity and envelope mass.

The envelope mass-luminosity-momentum flux relationships test models of mass accretion and outflow ejection, and therefore how much of the envelope mass is ultimately converted into stars (Matzner & McKee 2000). Reasonable estimates of momentum flux can be made without mapping the whole outflow, as most of the momentum flux is seen close to the star (Fuller & Ladd 2002).

In the larger cloud regions, mapping the outflows of a large number of protostellar objects will make it possible to determine their energy input to the cloud (e.g. Norman & Silk 1980; Li & Nakamura 2006; Matzner 2007). The magnitudes of these energies will allow a determination of the roles of outflows in stimulating turbulent motions or parent cloud dispersal (e.g. Silk 1995).

We note that all molecular tracers are affected by chemistry and depletion onto dust grains. CO is no exception, depleting in the densest regions of molecular cores (e.g. Caselli et al., 1999; Redman et al., 2002). We will use these observations to investigate CO depletion.

Prestellar cores are known to be heavily affected, with CO depletion factors reaching 10 or more (e.g. Crapsi et al., 2005). A limited study suggests that Class 0 sources are also centrally depleted by factors of 5, but by the time the Class I phase is reached, CO abundances have returned to the canonical value of $10^{-4}$ (Jorgensen et al., 2002).

Typical size scales for depletion are $\sim$6000 AU (Caselli et al., 1999), which corresponds to $12^{\prime\prime}$ at 500 pc or $40^{\prime\prime}$ at 150 pc. Outside the density peaks, CO abundance should be stable (e.g. van Dishoeck 2006; Di Francesco et al., 2007).

This survey will produce simultaneous dust and CO isotopologue images of hundreds of cloud cores classified on the basis of infrared counterparts or molecular outflows. We can use this sample to statistically investigate the levels and size scales for CO depletion as a function of core properties such as mass and evolution.

Two independent measurements of the envelope gas mass, to compare with the dust mass, can be derived from C¹⁸O. Firstly, the C¹⁸O integrated line strength, assuming optically thin emission, will yield a gas mass. Although this will be a lower limit due to depletion it is still valuable as it relies on a different set of assumptions (CO abundance, gas excitation) to mass estimates from dust, where the dust opacity and dust temperature are subject to their own uncertainties. Secondly, the velocity dispersion and size provide a virial mass estimate largely unaffected by depletion as linewidths fall towards cloud cores (e.g. Goodman et al. 1998a & b).

In total, the CO observations are vital to deriving reliable core parameters in order to understand how clusters form and how the initial mass function is determined. Combining the HARP data with existing lower-$J$ maps of these clouds (e.g. Ridge et al., 2006) will allow us to estimate temperature and density using multi-transition multi-isotopologue radiative transfer methods.

Measurement of the detailed kinematic and density properties of the cores will be carried out using the C¹⁸O and ¹³CO lines, observable simultaneously – see Figure 14. In nearly all cores, we expect the C¹⁸O line to be optically thin. Hence, we will be able to measure the thermal and non-thermal contributions to the line width, enabling a study of core support mechanisms and their evolution (e.g. Jessop & Ward-Thompson 2001).

The combination of a high-density tracer such as the J=3–2 transition, with lower-density tracers (e.g. lower-J CO lines) allows an investigation of the dynamical motion of cores through their parent cloud (e.g. Walsh et al., 2004; 2006; Ayliffe et al., 2007).

Where cores are clustered, we will also compare the velocity dispersion between cores, a simple quantity to measure which can be compared both with star formation simulations and with young clusters of pre-main-sequence stars (e.g. Belloche et al., 2001).

These quantities may potentially discriminate between competitive accretion/core mergers (e.g. Bate et al., 2003) and the alternative where one submillimetre core results in one star system (e.g. Goodwin et al., 2004a,b).

In addition, the distribution of C¹⁸O line velocities of cores observed with HARP in individual molecular clouds will probe theories of cloud turbulence. Such cores may act as test particles within the larger-scale turbulent motions within such clouds. Similar smaller-scale studies have recently been carried out in, for example, Perseus (H. Kirk et al., 2007).

We will also produce large maps of 10 filamentary or clustered star formation regions. Many of these will be well-studied regions (e.g. the Orion filament and the $\rho$ Ophiuchi cluster), but not all of them have pre-existing submillimetre maps (e.g. the Pipe Nebula and L1506 in Taurus). These regions will be mapped in ¹²CO, C¹⁸O and ¹³CO lines to the spectral resolutions summarized in Table 2. These maps will cover regions of order 300 square arcminutes (0.08 deg²) in size.

The key goal here will be to compare the observations to gas dynamic and MHD turbulence simulations (e.g. Balsara et al., 2001; Padoan & Nordlund 2002; Bate et al. 2003; Vazquez-Semadeni et al. 2005). These models make strong predictions on the expected clump mass spectrum, the spatial and velocity structure, the shapes of the cores and filaments, and the star formation efficiency.

Comparisons can be made by analysing cloud spatial and velocity structure using techniques such as clumping analyses (Williams et al., 1994), axial ratios (e.g. Kerton et al., 2003), delta variance (Stutzki et al. 1998; Bensch et al. 2001), principal component analysis (e.g. Heyer & Schloerb 1997), structure function (e.g. Brunt et al., 2003), and spectral correlation function (Rosolowsky 1999).

Mapping the J = 3–2 transitions, which trace reasonably high densities, at an angular resolution typically less than a thermal Jeans length (for an H₂ number density of $10^{5}\,$cm^-3), reveals the kinematics over the critical transition to gravitational dominance (Ossenkopf 2002), whereas existing low J CO maps (e.g. Dame et al., 2001; Wilson et al., 2005) trace only the lower density large-scale molecular cloud structure and kinematics. We note that lower J (usually J=1–0) maps exist for many of our clouds and can be analysed in conjunction with the HARP data (e.g. Ridge et al., 2006).

In total, the CO observations are vital in deriving reliable core parameters in order to understand how clusters form and how the initial mass function is determined. When combined with the SCUBA-2 data, the HARP data will provide a powerful way to explore the detailed dynamics and density structure in star-forming clouds, presenting rigorous tests of the details of the theoretical models.

From the SCUBA-2 850 $\mu$m continuum survey we expect to detect at least 100 cores of sufficient brightness ($>$250 mJy beam^-1 peak 850 $\mu$m flux) for observation with POL-2 in single SCUBA-2 footprints. These polarimetry targets will be located in different star-forming regions and be of various classes (starless, prestellar, Class 0, Class I).

To probe the initial field conditions for core formation, maps of $\sim$0.08 deg² in extent will be made of 10 cloud regions containing filaments and clustered star formation in synergy with the HARP large-scale mapping to measure the gas dynamics and characterize the turbulence.

Candidate types of regions would include a starless fragment of a filamentary cloud, such as a portion of the Pipe Nebula (see Figure 9). In addition we will map filamentary clouds for which absorption polarimetry exists, such as the L1506 filament in Taurus. We will use these data to compare directly the magnetic field directions yielded by emission and absorption polarimetry at the same locations, allowing these methods to be directly compared for the first time. We will also map regions around clusters exhibiting different rates of star formation.

According to one paradigm of low-mass star formation, collapse is guided by magnetic fields, producing flattened cores and disks (e.g. Mouschovias 1991). Outflows are then generated orthogonal to the disk, producing outflows aligned with the nascent field direction. Greaves et al. (1997) tested this correlation for five sources, finding the alignment of field and outflow appeared to be correlated to the angle of the outflow to the line of sight (see also Matthews et al. 2007).

With $\sim$ 70 sources with outflows (Class 0 and Class I), we will be able to establish statistically whether outflows are preferentially oriented with respect to the field direction. Using the SCUBA-2 data, we will also determine whether the field direction is related to the core morphology. Many cores for which polarization maps exist are too distant to compare field geometry to core morphology, since the cores are poorly resolved. A sizeable fraction of the objects mapped are also embedded in filaments, making measurements of core axis ratios particularly challenging.

Models predict different relations between core morphology and polarization position angle depending on field geometry (straight or helical) and core morphology (oblate, prolate or triaxial). Since the outflow, core and field orientations are all measured in 2D projection, statistical corrections can be made for an ensemble of cores which are not applicable to individual objects.

Polarized dust emission yields only the 2D field geometry projected onto the plane of the sky. Utilizing all three components from the survey (continuum, line and dust polarimetry), we will generate a set of analytic models of the three dimensional field geometry of all 100 cores as well as extended coherent structures such as filaments. This will be practical utilizing a new generalized modelling code (Fiege 2005), which has already been applied to the case of a filamentary cloud (Fiege et al., 2004).

The most general question to be addressed is whether there are any quasi-static magnetic models of cores that can explain the polarization and continuum maps for a statistically significant number of sources, as some theoretical models predict (e.g. Mouschovias 1976; Tomisaka et al. 1988).

If all quasi-static models fail to provide adequate fits to the data, then the data could only be explained by MHD turbulence. Regardless of the outcome, the polarization dataset will settle this important question in star formation theory. It will also provide a polarization catalogue of legacy value, which can be used as a definitive test for future models and simulations, and a powerful tool for their refinement.

The resulting modelling database will provide the theoretical counterpart to the observational dataset, which would be augmented as new and improved models are developed. In principle, one could search for regions in parameter space where the allowed solution sets intersect for multiple cores. This would provide a way to search for preferred ranges of parameters, which would help to refine future models.

The fractional polarization from dust yields no direct estimate of the magnetic field strength, since it is dependent on several additional unknowns (e.g. degree of grain alignment, grain shape and composition). The field strength will be derived from the commonly-used Chandrasekhar-Fermi (CF) method (Chandrasekhar & Fermi 1953) utilizing dispersion in polarization vectors (where high dispersion indicates a highly turbulent field and a weak mean field component), the line widths estimated from the HARP C¹⁸O/¹³CO data, and the density from the SCUBA-2 fluxes (c.f. Crutcher et al., 2004; J. Kirk et al., 2006).

Simulations show that this estimate can be corrected for a statistical ensemble of objects to yield realistic estimates of the field strength (Ostriker et al., 2001; Heitsch et al. 2001). Due to measurements of line widths and dispersion estimates, we will be able to test effectively whether the cores with broader line widths show more dispersion, thereby determining the applicability of the CF method in molecular clouds.

The same extended regions will be mapped with POL-2 and HARP. The relation between the core field geometry and that of the larger-scale structure in clustered and filamentary regions will be observed and modelled. Polarization maps can reveal abrupt changes in polarization direction (see Figure 15), which indicate underlying changes in the magnetic field direction.

The gas dynamics from HARP C¹⁸O/¹³CO observations will be used with the polarization maps to test predictions of magnetized simulations of turbulence (e.g., Heitsch et al. 2001; Ostriker et al. 2001; Padoan & Nordland 2002). Such large-scale maps are the key to unraveling the overall geometry of the magnetic field.