2.1. Dust polarisation observations: a probe of magnetic fields in star-forming clouds

2.2. Insights from Herschel and Planck: a filamentary paradigm for star formation?

The Herschel mission has led to spectacular advances in our knowledge of the texture of the cold ISM and its link with star formation. While interstellar clouds have been known to be filamentary for a long time (e.g., Schneider & Elmegreen Reference Schneider and Elmegreen1979; Bally et al. Reference Bally, Langer, Stark and Wilson1987; Myers Reference Myers2009, and references therein), Herschel imaging surveys have established the ubiquity of filaments on almost all length scales (approximately $0.5\,$–$100\,$pc) in the MCs of the Galaxy and shown that this filamentary structure likely plays a key role in the star formation process (e.g., André et al. Reference André2010; Henning et al. Reference Henning, Linz, Krause, Ragan, Beuther, Launhardt, Nielbock and Vasyunina2010; Molinari et al. Reference Molinari2010; Hill et al. Reference Hill2011; Schisano et al. Reference Schisano2014; Wang et al. Reference Wang, Testi, Ginsburg, Walmsley, Molinari and Schisano2015).

The interstellar filamentary structures detected with Herschel span broad ranges in length, central column density, and mass per unit length (e.g., Schisano et al. Reference Schisano2014; Arzoumanian et al. Reference Arzoumanian2019). In contrast, detailed analysis of the radial column-density profiles indicates that, at least in the nearby MCs of the Gould Belt, Herschel filaments are characterised by a narrow distribution of inner widths with a typical value of ${\sim} 0.1$ pc and a dispersion of less than a factor of 2, when the data are averaged over the filament crests (Arzoumanian et al. Reference Arzoumanian2011, Reference Arzoumanian2019). Independent studies of filament widths in nearby clouds have generally confirmed this result when using submillimeter continuum data (e.g., Koch &Rosolowsky Reference Koch and Rosolowsky2015; Salji et al. Reference Salji2015; Rivera-Ingraham et al. Reference Rivera-Ingraham2016), even if factor of ${\sim}$2–4 variations around the mean inner width of $\sim 0.1\,$pc has been found along the main axis of a given filament (e.g., Juvela et al. Reference Juvela2012; Ysard et al. Reference Ysard2013). Measurements of filament widths obtained in molecular line tracers (e.g., Pineda et al. Reference Pineda, Goodman, Arce, Caselli, Longmore and Corder2011; Fernández-López et al. Reference Fernández-López2014; Panopoulou et al. Reference Panopoulou, Tassis, Goldsmith and Heyer2014; Hacar et al. Reference Hacar, Tafalla, Forbrich, Alves, Meingast, Grossschedl and Teixeira2018) have been less consistent with the Herschel dust continuum results of Arzoumanian et al. (Reference Arzoumanian2011, Reference Arzoumanian2019), but this can be attributed to the lower dynamic range achieved by observations in any given molecular line tracer. Panopoulou et al. (Reference Panopoulou, Psaradaki, Skalidis, Tassis and Andrews2017) pointed out an apparent contradiction between the existence of a characteristic filament width and the essentially scale-free nature of the power spectrum of interstellar cloud images (well described by a single power law from ${\sim} 0.01$ to ${\sim} 50\,$pc—Miville-Deschênes et al. Reference Miville-Deschênes2010, Reference Miville-Deschênes, Duc, Marleau, Cuillandre, Didelon, Gwyn and Karabal2016), but Roy et al. (Reference Roy2019) showed that there is no contradiction given the only modest area filling factors ($ \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} 10{\mkern 1mu} $) and column-density contrasts (${\leq} 100 $ in most cases) derived by Arzoumanian et al. (Reference Arzoumanian2019) for the filaments seen in Herschel images. While further high-resolution submillimeter continuum studies would be required to investigate whether the same result holds beyond the Gould Belt, the median inner width of ${\sim} 0.1\,$pc measured with Herschel appears to reflect the presence of a true common scale in the filamentary structure of nearby interstellar clouds. If confirmed, this result may have far-reaching consequences as it introduces a characteristic scale in a system generally thought to be chaotic and turbulent (i.e., largely scale-free—cf. Guszejnov, Hopkins, & Grudić Reference Guszejnov, Hopkins and Grudić2018). It may thus present a severe challenge in any attempt to interpret all ISM observations in terms of scale-free processes.

Another major result from Herschel studies of nearby clouds is that most (${>}75 $) prestellar cores and protostars are found to lie in dense, ‘supercritical’ filaments above a critical threshold $\sim 16\, {\rm M}_\odot $/pc in mass per unit length, equivalent to a critical threshold $\sim 160\, {\rm M}_\odot $/pc$^2$ ($A_V \sim 8)$ in column density or $n_{{\rm H}_2} \sim 2 \times 10^4\, {\rm cm}^{-3} $ in volume density (André et al. Reference André2010; Könyves et al. Reference Könyves2015; Marsh et al. Reference Marsh2016). A similar column-density threshold for the formation of prestellar cores (at $A_V \sim \, $5–10) had been suggested earlier based on ground-based millimeter and submillimeter studies (e.g., Onishi et al. Reference Onishi, Mizuno, Kawamura, Ogawa and Fukui1998; Johnstone, Di Francesco, & Kirk Reference Johnstone, Di Francesco and Kirk2004; Kirk, Johnstone, & Di Francesco Reference Kirk, Johnstone and Di Francesco2006), but without clear connection to filaments. Interestingly, a comparable threshold in extinction (at $A_V \sim \, $8) has also been observed in the spatial distribution of young stellar objects (YSOs) with Spitzer (e.g., Heiderman et al. Reference Heiderman, Evans, Allen, Huard and Heyer2010; Lada, Lombardi, & Alves Reference Lada, Lombardi and Alves2010; Evans, Heiderman, & Vutisalchavakul Reference Evans, Heiderman and Vutisalchavakul2014).

Overall, the Herschel results support a filamentary paradigm for star formation in two main steps (e.g., André et al. Reference André, Di Francesco, Ward-Thompson, Inutsuka, Pudritz, Pineda and Beuther2014; Inutsuka et al. Reference Inutsuka, Inoue, Iwasaki and Hosokawa2015): First, multiple large-scale compressions of interstellar material in supersonic turbulent MHD flows generate a cobweb of ${\sim} 0.1$ pc-wide filaments in the cold ISM; second, the densest filaments fragment into prestellar cores (and subsequently protostars) by gravitational instability above the critical mass per unit length $ M_{\rm line,crit} = 2\, c_s^2/G$ of nearly isothermal, cylinder-like filaments (see Figure 1), where $c_s$ is the sound speed and G the gravitational constant. This paradigm differs from the classical gravo-turbulent picture in that it relies on the unique features of filamentary geometry, such as the existence of a critical line mass for nearly isothermal filaments (e.g., Inutsuka & Miyama Reference Inutsuka and Miyama1997, and references therein). The validity and details of the filamentary paradigm are strongly debated, however, and many issues remain open. For instance, according to some numerical simulations, the above two steps may not occur consecutively but simultaneously, in the sense that both filamentary structures and dense cores may grow in mass at the same time (e.g., Gómez & Vázquez-Semadeni Reference Gómez and Vázquez-Semadeni2014; Chen & Ostriker Reference Chen and Ostriker2015). The physical origin of the typical ${\sim} 0.1\,$pc inner width of molecular filaments is also poorly understood and remains a challenge for numerical models (e.g., Padoan et al. Reference Padoan, Juvela, Goodman and Nordlund2001; Hennebelle Reference Hennebelle2013; Smith, Glover, & Klessen Reference Smith, Glover and Klessen2014; Federrath Reference Federrath2016; Ntormousi et al. Reference Ntormousi, Hennebelle, André and Masson2016). Auddy et al. (Reference Auddy, Basu and Kudoh2016) point out that magnetised filaments may actually be ribbon-like and quasi-equilibrium structures supported by the magnetic field, and therefore, not have cylindrical symmetry. Regardless of any particular scenario, there is nevertheless little doubt after Herschel results that dense molecular filaments represent an integral part of the initial conditions of the bulk of star formation in our Galaxy.

As molecular filaments are known to be present in the Large Magellanic Cloud (LMC—Fukui et al. Reference Fukui2015), the proposed filamentary paradigm may have implications on galaxy-wide scales. Assuming that all filaments have similar inner widths, it has been argued that they may help to regulate the star formation efficiency in dense molecular gas (André et al. Reference André, Di Francesco, Ward-Thompson, Inutsuka, Pudritz, Pineda and Beuther2014), and that they may be responsible for a quasi-universal star formation law in the dense molecular ISM of galaxies (cf. Lada et al. Reference Lada, Forbrich, Lombardi and Alves2012; Shimajiri et al. Reference Shimajiri2017), with possible variations in extreme environments such as the CMZ (Longmore et al. Reference Longmore2013; Federrath et al. Reference Federrath2016).

In parallel, the Planck mission has led to major advances in our knowledge of the geometry of the magnetic field on large scales in the Galactic ISM. The first all-sky maps of dust polarisation provided by Planck at 850 $\, \mu$m have revealed a very organised magnetic-field structure on $ \mathbin{\lower.3ex\hbox{$\buildrel>\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} $1–10 pc scales in Galactic interstellar clouds (Planck int. res. XXXV 2016, see Figure 1a). The large-scale magnetic field tends to be aligned with low-density filamentary structures with subcritical line masses such as striations (see Figure 1b) and perpendicular to dense star-forming filaments with supercritical line masses (Planck int. res. XXXII 2016; Planck int. res. XXXV 2016, see Figure 1b and c), a trend also seen in optical and near-IR polarisation observations (Chapman et al. Reference Chapman, Goldsmith, Pineda, Clemens, Li and Krcčo2011; Palmeirim et al. Reference Palmeirim2013; Panopoulou, Psaradaki, & Tassis Reference Panopoulou, Psaradaki and Tassis2016; Soler et al. Reference Soler2016). There is also a hint from Planck polarisation observations of the nearest clouds that the direction of the magnetic field may change within dense filaments from nearly perpendicular in the ambient cloud to more parallel in the filament interior (cf. Planck int. res. XXXIII 2016). These findings suggest that magnetic fields are dynamically important and play a key role in the formation and evolution of filamentary structures in interstellar clouds, supporting the view that dense molecular filaments form by accumulation of interstellar matter along field lines.

The low resolution of Planck polarisation data (10 arcmin at best or 0.4 pc in nearby clouds) is, however, insufficient to probe the organisation of field lines in the ${\sim} 0.1\,$pc interior of filaments, corresponding both to the characteristic transverse scale of filaments (Arzoumanian et al. Reference Andersson, Pintado, Potter, Straižys and Charcos-Llorens2011, Reference Arzoumanian2019) and to the scale at which fragmentation into prestellar cores occurs (cf. Tafalla & Hacar Reference Tafalla and Hacar2015). Consequently, the geometry of the magnetic field within interstellar filaments and its effects on fragmentation and star formation are essentially unknown today.

2.3. Investigating the role of magnetic fields in the formation and evolution of molecular filaments with B-BOP

Improving our understanding of the physics and detailed properties of molecular filaments is of paramount importance as the latter are representative of the initial conditions of star formation in MCs and GMCsFootnote ^e (see Section 2.2 above). In particular, investigating how dense, ‘supercritical’ molecular filaments can maintain a roughly constant $\sim$0.1$\,$pc inner width and fragment into prestellar cores instead of collapsing radially to spindles is crucial to understanding star formation. The topology of magnetic-field lines may be one of the key elements here. For instance, a longitudinal magnetic field can support a filament against radial collapse but not against fragmentation along its main axis, while a perpendicular magnetic field works against fragmentation and increases the critical mass per unit length but cannot prevent the radial collapse of a supercritical filament (e.g., Tomisaka Reference Tomisaka2014; Hanawa, Kudoh, & Tomisaka Reference Hanawa, Kudoh and Tomisaka2017). The actual topology of the field within molecular filaments is likely more complex and may be a combination of these two extreme configurations.

One plausible evolutionary scenario, consistent with existing observations, is that star-forming filaments accrete ambient cloud material along field lines through a network of magnetically dominated striations (e.g., Palmeirim et al. Reference Palmeirim2013; Cox et al. Reference Cox2016; Shimajiri et al. Reference Shimajiri, André, Palmeirim, Arzoumanian, Bracco, Könyves, Ntormousi and Ladjelate2019, see also Figures 1b and 2a). Accretion-driven MHD waves may then generate a system of velocity-coherent fibres within dense filaments (Hacar et al. Reference Hacar, Tafalla, Kauffmann and Kovács2013, Reference Hacar, Tafalla, Forbrich, Alves, Meingast, Grossschedl and Teixeira2018; Arzoumanian et al. Reference Arzoumanian, André, Peretto and Könyves2013; Hennebelle & André Reference Hennebelle and André2013, cf. Figure 2) and the corresponding organisation of magnetic-field lines may play a central role in accounting for the roughly constant ${\sim} 0.1\,$pc inner width of star-forming filaments as measured in Herschel observations (cf. Section 2.2). Constraining this process further is key to understanding star formation itself, since filaments with supercritical masses per unit length would otherwise undergo rapid radial contraction with time, effectively preventing fragmentation into prestellar cores and the formation of protostars (e.g., Inutsuka & Miyama Reference Inutsuka and Miyama1997). Information on the geometry of magnetic-field lines within star-forming filaments at $A_V > 8$ is thus crucially needed, and can be obtained through 200–350 $\mu$m dust polarimetric imaging at high angular resolution with B-BOP. Large area coverage and both high angular resolution and high spatial dynamic range are needed to resolve the 0.1 pc scale by a factor ${\sim}$3–10 on one hand and to probe spatial scales from ${>} 10\,$pc in the low-density striations of the ambient cloud (see Figure 1), down to $\sim$0.01–0.03 pc for the fibres of dense filaments (see Figure 2). In nearby Galactic regions (at $d \sim \, $150–500 pc), this corresponds to angular scales from ${>} 5^\circ$ or more down to ${\sim}$20 arcsec or less.

Figure 2. (a) Fine (column) density structure of the B211/B213 filament based on a filtered version of the Herschel 250 $\mu$m image of Palmeirim et al. (Reference Palmeirim2013) using the algorithm getfilaments (Men'shchikov Reference Men’shchikov2013). In this view, all transverse angular scales larger than 72 arcsec (or $\sim 0.05$ pc) were filtered out to enhance the contrast of the small-scale structure. The colour scale is in MJy sr$^{-1}$ at 250 $\mu$m. The coloured curves display the velocity-coherent fibres independently identified by Hacar et al. (Reference Hacar, Tafalla, Kauffmann and Kovács2013) using N$_2\textit{H}^+$/C$^{18}$O observations. (b) MHD simulation of a collapsing/accreting filament performed by E. Ntormousi & P. Hennebelle with the adaptive mesh refinement (AMR) code RAMSES. Line-of-sight velocities (in km/s) after one free-fall time ($\sim 0.9$ Myr) are coded by colours. For clarity, only the dense gas with $10^4\, {\rm cm}^{-3} < {n_{\rm H_2}} \lt 10^5\, {\rm cm}^{-3} $ is shown. Note the braid-like velocity structure and the morphological similarity with the fibre-like pattern seen in the B211/B213 observations on the left. Thanks to its high resolution and dynamic range, B-BOP can probe, for the first time, the geometry of the magnetic field within the dense system of fibres and the connection with the low-density striations in the ambient cloud.

Low-density striations are remarkably ordered structures in an otherwise chaotic-looking turbulent medium. While the exact physical origin of both low-density striations (Heyer et al. Reference Heyer, Goldsmith, Yıldız, Snell, Falgarone and Pineda2016; Tritsis & Tassis Reference Tritsis and Tassis2016, Reference Tritsis and Tassis2018; Chen et al. Reference Chen, Li, King and Fissel2017) and high-density fibres (e.g., Clarke et al. Reference Clarke, Whitworth, Duarte-Cabral and Hubber2017; Zamora-Avilés, Ballesteros-Paredes, & Hartmann Reference Zamora-Avilés, Ballesteros-Paredes and Hartmann2017) is not well understood and remains highly debated in the literature, there is little doubt that magnetic fields are involved. For instance, Tritsis and Tassis (Reference Tritsis and Tassis2016) modelled striations as density fluctuations associated with magnetosonic waves in the linear regime (the column-density contrast of observed striations does not exceed 25%). These waves are excited as a result of the passage of Alfvén waves, which couple to other MHD modes through phase mixing (see Figure 3, right panel). In contrast, Chen et al. (Reference Chen, Li, King and Fissel2017) proposed that striations do not represent real density fluctuations, but are rather a line-of-sight column-density effect in a corrugated layer forming in the dense post-shock region of an oblique MHD shock. High-resolution polarimetric imaging data would be of great interest to set direct observational constraints and discriminate between these possible models. Specifically, the magnetosonic wave model predicts that a zoo of MHD wave effects should be observable in these regions. One of them, that linear waves in an isolated cloud should establish standing waves (normal modes) imprinted in the striations pattern, has recently been confirmed in the case of the Musca cloud (Tritsis & Tassis Reference Tritsis and Tassis2018). Other such effects include the ‘sausage’ and ‘kink’ modes (see Figure 3, left panel), which are studied extensively in the context of heliophysics (e.g., Nakariakov et al. Reference Nakariakov2016), and which could open a new window to probe the local conditions in MCs (Tritsis et al. Reference Tritsis, Federrath, Schneider and Tassis2018).

Figure 3. Simulated striations (from Tritsis & Tassis Reference Tritsis and Tassis2016). Right panel: volume density image from the simulations. Left panel: zoomed-in column-density view of a single striation, showing the ‘sausage’ instability setting in, with characteristic imprints in both the magnetic-field and the column-density distribution. In both panels, the drapery pattern traces the magnetic-field lines and the mean direction of the magnetic field is indicated by a black arrow. The passage of Alfvén waves excites magnetosonic modes that create compressions and rarefactions (colourbar) along field lines, giving rise to striations. The simulated data in both panels have been convolved to an effective spatial resolution of 0.012 pc, corresponding to the 18 arcsec HPBW of B-BOP at $200\, \mu$m.

A first specific objective of B-BOP observations will be to test the hypothesis, tentatively suggested by Planck polarisation results (cf. Planck int. res. XXXIII 2016) that the magnetic field may become nearly parallel to the long axis of star-forming filaments in their dense interiors at scales ${\lt} 0.1$ pc, due to, e.g., gravitational or turbulent compression (see Figure 4) and/or reorientation of oblique shocks in magnetised colliding flows (Fogerty et al. Reference Fogerty, Carroll-Nellenback, Frank, Heitsch and Pon2017). A change of field orientation inside dense star-forming filaments is also predicted by numerical MHD simulations in which gravity dominates and the magnetic field is dragged by gas flowing along the filament axis (Gómez, Vézquez-Semadeni, & Zamora-Avilés Reference Gómez, Vázquez-Semadeni and Zamora-Avilés2018; Li, Klein, & McKee Reference Li, Klein and McKee2018), as observed in the velocity field of some massive infrared dark filaments (Peretto et al. Reference Peretto2014). An alternative topology for the field lines within dense molecular filaments often advocated in the literature is that of helical magnetic fields wrapping around the filament axis (e.g., Fiege & Pudritz Reference Fiege and Pudritz2000; Stutz & Gould Reference Stutz and Gould2016; Schleicher & Stutz Reference Schleicher and Stutz2018; Tahani et al. Reference Tahani, Plume, Brown and Kainulainen2018). As significant degeneracies exist between different models because only the plane-of-sky magnetic field is directly accessible to dust polarimetry (cf. Reissl et al. Reference Reissl, Stutz, Brauer, Pellegrini, Schleicher and Klessen2018; Tomisaka Reference Tomisaka2015), discriminating between these various magnetic topologies will require sensitive imaging observations of large samples of molecular filaments for which the distribution of viewing angles may be assumed to be essentially random. One advantage of the model of oblique MHD shocks (e.g., Chen & Ostriker Reference Chen and Ostriker2014; Inoue et al. Reference Inoue, Hennebelle, Fukui, Matsumoto, Iwasaki and Inutsuka2018; Lehmann & Wardle Reference Lehmann and Wardle2016) is that it could potentially explain both how dense filaments maintain a roughly constant ${\sim} 0.1\,$pc width while evolving (cf. Seifried & Walch Reference Seifried and Walch2015) and why the observed spacing of prestellar cores along the filaments is significantly shorter than the characteristic fragmentation scale of 4$\, \times$ the filament diameter expected in the case of non-magnetised nearly isothermal gas cylinders (e.g., Inutsuka & Miyama Reference Inutsuka and Miyama1992; Nakamura, Hanawa, & Nakano Reference Nakamura, Hanawa and Nakano1993; Kainulainen et al. Reference Kainulainen, Stutz, Stanke, Abreu-Vicente, Beuther, Henning, Johnston and Megeath2017).

Figure 4. (a) 3D view of a model filament system similar to Taurus B211/3 and associated magnetic-field lines (in blue), with a cylindrical filament (red lines) embedded in a sheet-like background cloud (in light green). In this model, the magnetic field in the ambient cloud is nearly (but not exactly) perpendicular to the filament axis and the axial component is amplified by (gravitational or turbulent) compression in the filament interior. (b) Synthetic polarisation map expected at the ${\sim}$20 arcsec resolution of B-BOP at 200 $\mu$m for the model filament system shown in (a). SPICA will follow the magnetic field all the way from the background cloud to the central filament. (c) Synthetic polarisation map of the same model filament system at the Planck resolution. Note how Planck data cannot constrain the geometry of the field lines within the central filament.

A second specific objective of B-BOP observations will be to better characterise the transition column density at which a switch occurs between filamentary structures primarily parallel to the magnetic field (at low $N_{{\rm H}_2}$) and filamentary structures preferentially perpendicular to the magnetic field (at high $N_{{\rm H}_2}$) (see Planck int. res. XXXV 2016, and Section 2.2 above). Based on a detailed analysis of numerical MHD simulations, Soler & Hennebelle (Reference Soler and Hennebelle2017) postulated that this transition column density depends primarily on the strength of the magnetic field in the parent MC, and therefore, constitutes a key observable piece of information. Moreover, Chen, King, and Li (Reference Chen, King and Li2016) showed that, in their colliding flow MHD simulations, the transition occurs where the ambient gas is accelerated gravitationally from sub-Alfvénic to super-Alfvénic speeds. They also concluded that the nature of the transition and the 3D magnetic-field morphology in the super-Alfvénic region can be constrained from the observed polarisation fraction and dispersion of polarisation angles in the plane of the sky, which provides information on the tangledness of the field.

As a practical illustration of what could be achieved with B-BOP, a reference polarimetric imaging survey would map, in Stokes I, Q, U at $100, 200, 350\, \mu$m, the same ${\sim} 500\,$deg$^2$ area in nearby interstellar clouds imaged by Herschel in Stokes I at 70–500 $\, \mu$m as part of the Gould Belt, HOBYS, and Hi-GAL surveys (André et al. Reference André2010; Motte et al. Reference Motte2010; Molinari et al. Reference Molinari2010). To first order, the gain in sensitivity of B-BOP over SPIRE and PACS on Herschel would compensate for the low degree of polarisation (only a few %) and make it possible to obtain Q and U maps of polarised dust emission with a signal-to-noise ratio similar to the Herschel images in Stokes I. Assuming the B-BOP performance parameters given in Table 1 (see also Table 4 of Roelfsema et al. Reference Roelfsema2018 and Table 1 of Rodriguez et al. Reference Rodriguez, Poglitsch and Aliane2018) and an integration time of ${\sim} 2\,$h per square degree, such a survey would reach a signal-to-noise ratio of 7 in Q, U intensity at both 200 and 350$\, \mu$m in low column-density areas with $A_V \sim 0.2$ (corresponding to the diffuse, cold ISM), for a typical polarisation fraction of 5% and a typical dust temperature of $T_d \sim 15\,$K. The same survey would reach a signal-to-noise ratio of 5 in Q, U at 100$\, \mu$m down to $A_V \sim 1$. The entire survey of ${\sim} 500\,$deg$^2$ would require ${\sim} 1\,500\,$h of telescope time, including overheads. It would provide key information on the magnetic-field geometry for thousands of filamentary structures spanning ${\sim} 3$ orders of magnitude in column density from low-density subcritical filaments in the atomic (HI) medium at $A_V \lt 0.5$ to star-forming supercritical filaments in the dense inner parts of MCs at $A_V > 100$.

Table 1 B-BOP performance parameters

^a Surface brightness level in I to map Q, U at 5$\sigma$ over 1 deg$^2$ in 10 h assuming 5% fractional polarisation.

^b Assuming ${\geq} 1$ fractional polarisation.

^c The first band of B-BOP has recently been shifted from 100 $\mu$m to 70 $\mu$m.

2.4. Key advantages of B-BOP over other polarimetric facilities

Far-IR/submillimeter polarimetric imaging from space with B-BOP will have unique advantages, especially in terms of spatial dynamic range and surface brightness dynamic range. Studying the multi-scale physics of star formation within molecular filaments requires a spatial dynamic range of ${\sim} 1\,000$ or more to simultaneously probe scales ${>} 10\,$pc in the parent clouds down to ${\sim} 0.01\,$pc in the interior of star-forming filaments (corresponding to angular scales from ${\sim} 18$ arcsec $\,$to ${>} 5 \,^\circ$ in the nearest MCs—see Figure 1). Such a high spatial dynamic range was routinely achieved with Herschel in non-polarised imaging, but has never been obtained in ground-based submillimeter continuum observations. It will be achieved for the first time with B-BOP in polarised far-IR imaging.

The angular resolution and surface brightness dynamic range of B-BOP will make it possible to resolve 0.1$\,$pc-wide filaments out to 350 pc and to image a few % polarised dust emission through the entire extent of nearby cloud complexes (cf. Figure 1), from the low-density outer parts of MCs (${A_V} \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} 0.5$) all the way to the densest filaments and cores ($A_V > 100$). In comparison, Planck had far too low resolution (10 arcmin at best in polarisation) to probe the magnetic field within dense 0.1 pc-wide filaments or detect faint 0.1 pc-wide striations. Near-IR polarimetry cannot penetrate the dense inner parts of star-forming filaments, and ground-based or air-borne millimeter/submillimeter polarimetric instruments, such as SCUBA2-POL (the polarimeter for the Sub-millimetre Common-User Bolometer Array 2—Friberg et al. Reference Friberg, Bastien, Berry, Savini, Graves and Pattle2016), NIKA2-POL (the polarisation channel for the New IRAM KID Arrays 2—cf. Adam et al. Reference Adam2018), HAWC$+$ (the High-resolution Airborne Wideband Camera-Plus for SOFIA, the Stratospheric Observatory for Infrared Astronomy—Harper et al. Reference Harper2018), or BLAST-TNG (the next generation Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry—Galitzki et al. Reference Galitzki2014), will lack the required sensitivity and dynamic range in both spatial scales and intensity.

More specifically, BLAST-Pol, the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry operating at 250, 350, and 500 $\mu$m (Fissel et al. Reference Fissel2010, Reference Fissel2016), has only modest resolution (30 arcsec–1 arcmin), sensitivity, and dynamic range. HAWC$+$, the far-infrared camera and polarimeter for SOFIA (Dowell et al. Reference Dowell2010) and BLAST-TNG (cf. Dober et al. Reference Dober2014), both benefit from a larger 2.5-m primary mirror equivalent to that of SPICA, and thus, have comparable angular resolution, but are not cooled, and therefore, are 2–3 orders of magnitude less sensitive (Noise Equivalent Power ${\rm NEP} > 10^{-16}\, {\rm W\, Hz}^{-1/2}$) than B-BOP. Stated another way, the mapping speedFootnote ^f of B-BOP will be 4–5 orders of magnitude higher than that of HAWC$+$ or BLAST-TNG. Future ground-based submillimeter telescopes on high, dry sites such as CCAT-p (the Cerro Chajnantor Atacama Telescope, prime) and CSST (the Chajnantor Submillimeter Survey Telescope) will benefit from larger aperture sizes (6 and 30 m, respectively) and will thus achieve higher angular resolution than SPICA at 350 $\, \mu$m, but will be limited in sensitivity by the atmospheric background load on the detectors and in spatial dynamic range by the need to remove atmospheric fluctuations. The performance and advantage of B-BOP over other instruments for wide-field dust polarimetric imaging are illustrated in Figure 5.

Figure 5. Surface-brightness sensitivity of B-BOP for wide-field polarimetric imaging compared to other existing or planned polarimetric facilities. The total surface-brightness level required to detect polarisation (i.e., Stokes parameters Q, U) with a signal-to-noise ratio of 7 per resolution element (e.g., 9 arcsec pixel at $200\,\mu $m for B-BOP) when mapping 1 deg$^2$ in 2 h assuming 5% fractional polarisation is plotted as a function of wavelength for each instrument (SOFIA-HAWC$+$, B-BOP, BLAST-TNG, CCAT-p, SCUBA2-POL, CSST, NIKA2-POL). For comparison, the typical surface-brightness level expected in total intensity from the diffuse outer parts of MCs ($A_V = 1$) is shown for two representative dust temperatures ($T_d = 10\,$K and $T_d = 14\,$K, assuming simple modified black-body emission with a dust emissivity index $\beta = 2$), as well as the SED of the halo of the nearby galaxy M82 (cf. Galliano, Dwek, & Chanial Reference Galliano, Dwek and Chanial2008; Roussel et al. Reference Roussel2010).

Dust polarimetric imaging with ALMA at $\lambda \sim \,$0.8–3$\,$mm will provide excellent sensitivity and resolution, but only on small angular scales (from ${\sim}$0.02 arcsec $\,$ to ${\sim} 20$ arcsec ). Indeed, even with additional observations with ACA (the ALMA Compact Array), the maximum angular scale recoverable by the ALMA interferometer remains smaller than ${\sim}$1 arcmin in total intensity and ${\sim} 20$ arcsec in polarised emission (see ALMA Technical Handbook).Footnote ^g This implies that ALMA polarimetry is intrinsically insensitive to all angular scales ${>} 20$ arcsec, corresponding to structures larger than 0.015–0.05$\,$pc in nearby clouds. Using multi-configuration imaging, ALMA can achieve a spatial dynamic range of ${\sim} 1\,000$, comparable to that of Herschel or B-BOP, but only for relatively high surface brightness emission. Because ALMA can only image the sky at high resolution, it is indeed ${\sim}$2–3 orders of magnitude less sensitive to low surface brightness emission than a cooled single-dish space telescope such as SPICA. Expressed in terms of column density, this means that ALMA can only produce polarised dust continuum images of compact objects with ${N_{{{\rm{H}}_2}}} \mathbin{\lower.3ex\hbox{$\buildrel>\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} {10^{23}}{\mkern 1mu} {\rm{c}}{{\rm{m}}^{ - 2}}$ (such as sub-structure in distant, massive supercritical filaments—see Beuther et al. Reference Beuther2018) at significantly higher resolution (${\sim} 1$ arcsec $\,$ or better) than SPICA, while polarimetric imaging of extended, low column-density structures down to ${N_{{{\rm{H}}_2}}} \mathbin{\lower.3ex\hbox{$\buildrel>\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} 5 \times {10^{20}}{\mkern 1mu} {\rm{c}}{{\rm{m}}^{ - 2}}$ (such as subcritical filaments and striations) will be possible with B-BOP. Furthermore, the small size of the primary beam (${\sim}$0.3–1 arcmin at 0.8–3$\,$mm) makes mosaicing of wide (${>} 1\, {\rm deg}^2$) fields impractical and prohibitive with ALMA. In practice, ALMA polarimetric studies of star-forming MCs will provide invaluable insight into the role of magnetic fields within individual protostellar cores/disks and will be very complementary to, but will not compete with, the B-BOP observations discussed here which target the role of magnetic fields in the formation and evolution of filaments on larger scales.

Figure 6. These simulations resolve the dissipation scales of turbulence; they characterise the morphology of magnetic structures formed in magnetised turbulence. For parameters typical of diffuse MCs, the box size is ${\approx}$1 pc. Left: projections of the vorticity (the modulus in colour) and of the magnetic field (arrows) on the plane of the sky. Right: small-scale increments of the orientation of the plane-of-the-sky component of the magnetic field, a proxy for the dust polarisation angle gradient. Source: Figure adapted from Falgarone, Momferratos, and Lesaffre (Reference Falgarone, Momferratos, Lesaffre, Lazarian, de Gouveia Dal Pino and Melioli2015).

3.1. Interstellar magnetic fields

Magnetic fields pervade the multi-phase ISM of galaxies. In the Milky Way, and more generally in local universe galaxies, the ordered (mean) and turbulent (random) components of interstellar magnetic fields are comparable and in near equipartition with turbulent kinetic energy (Heiles & Troland Reference Heiles and Troland2005; Beck Reference Beck2015). The galactic dynamo amplification is saturated, but exchanges between gas kinetic and magnetic energy still occur and are of major importance to gas dynamics. Magnetic fields are involved in the driving of turbulence and in the turbulent energy cascade (Subramanian Reference Subramanian2007). The two facets of interstellar turbulence, gas kinematics and magnetic fields, are dynamically so intertwined that they may not be studied independently of each other.

The multiphase magnetised ISM is far too complex to be described by an analytic theory. Our understanding in this research field follows from observations, MHD simulations and phenomenological models. MHD simulations allow us to quantify the non-linear ISM physics but within numerical constraints that limit their scope. They may guide the interpretation observations but alone they do not provide conclusive answers because they are very far from reproducing the high Reynolds ($R_e$) and magnetic Prandtl numbers ($P_m$)Footnote ^h of interstellar turbulence (Kritsuk et al. Reference Kritsuk2011). The fluctuation dynamo and shock waves contribute to produce highly intermittent magnetic fields where the field strength is enhanced in localised magnetic structures. The volume filling factor of these structures decreases for increasing values of the magnetic Reynolds number $R_m = R_e\times P_m$ (Schekochihin et al. Reference Schekochihin, Maron, Cowley and McWilliams2002; Brandenburg & Subramanian Reference Brandenburg and Subramanian2005). The inhomegeneity in the degree of magnetisation of matter associated with intermittency is an essential facet of interstellar turbulence (Falgarone et al. Reference Falgarone, Momferratos, Lesaffre, Lazarian, de Gouveia Dal Pino and Melioli2015; Nixon & Pringle Reference Nixon and Pringle2019), which simulations miss because they are far from reproducing the interstellar values of $R_m$. In this context, to make headway, we must follow an empirical approach where a statistical model of interstellar turbulence is inferred from observations.

3.2. The promise of B-BOP

B-BOP will image dust polarisation with an unprecedented combination of sensitivity and angular resolution, providing a unique data set (Section 2.4) to characterise the magnetic facet of interstellar turbulence. This leap forward will open an immense discovery space, which will revolutionise our understanding of interstellar magnetic fields, and their correlation with matter and gas kinematics.

At $200\,\mu$m, for the SED of the diffuse ISM(Planck int. res. XVII 2014), the surface brightness sensitivity of B-BOP is 3 orders of magnitude greater than that of the Planck $353\,$ GHz all-sky map for deep imaging (10 h per square degree) and a few 100 times better for faster mapping (2 h per square degree). The analysis of dust polarisation at high Galactic latitude with the Planck data is limited by sensitivity to an effective angular resolution of ${\sim}1^\circ$ in the diffuse ISM and 10 arcmin in MCs where the column density is larger than $10^{22}\,$H cm$^{-2}$ (Planck 2018 res. XII 2019), while B-BOP will map dust polarisation with a factor $\sim $20–70 better resolution at 100–350$\, \mu$m.

Dust polarisation probes the magnetic-field orientation in dust-containing regions, i.e., mostly in the cold and warm phases of the ISM, which account for the bulk of the gas mass, and hence of the dust mass. These ISM phases comprise the diffuse ISM and star-forming MCs. They account for most of the gas turbulent kinetic energy in galaxies (Hennebelle & Falgarone Reference Hennebelle and Falgarone2012). Thus, among the various means available to map the structure of interstellar magnetic fields, dust polarisation is best suited to trace the dynamical coupling between magnetic fields, turbulence, and gravity in the ISM. This interplay is pivotal to ISM physics and star formation. It is also central to cosmic magnetism because it underlies dynamo processes (Subramanian Reference Subramanian2007).

Observations have so far taught us that magnetic fields are correlated with the structure of matter in both the diffuse ISM and in MCs (Clark et al. Reference Clark, Peek and Putman2014; Planck int. res. XXXII 2016; Planck int. res. XXXV 2016) but this correlation does not fully describe interstellar magnetism. Data must also be used to characterise the intermittent nature of interstellar magnetic fields.

The magnetic structures identified in MHD simulations (Figure 6) may be described as filaments, ribbons or sheets with at least one dimension commensurate with dissipation scales of turbulent and magnetic energy in shocks, current sheets or through ambipolar diffusion (Momferratos et al. Reference Momferratos, Lesaffre, Falgarone and Pineau des Forêts2014; Falgarone et al. Reference Falgarone, Momferratos, Lesaffre, Lazarian, de Gouveia Dal Pino and Melioli2015). While the viscous and Ohmic dissipation scales of turbulence are too small to be resolved by B-BOP, turbulence dissipation due to ion-neutral friction is expected to occur on typical scales between ${\sim} 0.03$ and ${\sim} 0.3\,$pc (cf. Momferratos et al. Reference Momferratos, Lesaffre, Falgarone and Pineau des Forêts2014), which is well within the reach of B-BOP for matter in the local ISM.

Although dust polarisation does not measure the field strength, the polarisation angle may be used to map these magnetic structures, as illustrated in Figure 6. The figure shows that the largest values of the increment of the polarisation angle, $\Delta \Phi$, delineate structures that tend to follow those of intense dissipation of turbulent energy. B-BOP will allow us to identify magnetic structures, such as those in Figure 6, even if their transverse size is unresolved because (i) they are highly elongated and (ii) their spatial distribution in the ISM is fractal.

Regions of intermittency in interstellar turbulence correspond to rare events. Their finding requires obtaining large data sets combining brightness sensitivity and angular resolution, as illustrated by the CO observations with the Institut de Radioastronomie Millimétrique (IRAM) 30-m telescope analysed by Hily-Blant, Falgarone, and Pety (Reference Hily-Blant, Falgarone and Pety2008) and Hily-Blant and Falgarone (Reference Hily-Blant and Falgarone2009). B-BOP has the unique capability to extend these pioneering studies of the intermittency of gas kinematics to dust polarisation observations, tracing the structure of magnetic fields (Section 2.1.2), with a comparable angular resolution. B-BOP will also greatly strengthen their statistical significance by covering a total sky area more than 2 orders of magnitude larger.

B-BOP holds promises to reveal a rich array of magnetic structures, characterising the intermittency of interstellar magnetic fields. Planck data, at a much coarser scale, gives a first insight at the expected outcome of the observations illustrated in Figure 7. Magnetic structures will be identified in the data as locations where the probability distributions of the increments of the polarisation angle, and of the Stokes Q/I and U/I ratios, depart from Gaussian distributions. Compared to Planck, B-BOP will only map a small fraction of the sky (${\sim} 1$ for nearby MCs and diffuse ISM observed away from the Galactic plane), but it will probe the field structure on much smaller scales (by a factor 30 or more) where the surface density of magnetic structures is expected to be much larger.

Figure 7. Non-Gaussianity of the magnetic-field structure in the Planck dust polarisation data. This all-sky image, in Galactic coordinates centered on the Galactic center, presents the modulus of the angular polarisation gradient, $|\nabla{\psi}|$, built from the Planck data at 353 GHz smoothed to 160 arcmin resolution. Source: Figure adapted from Appendix D of Planck 2018 res. XII (2019).

3.3. Observing strategy

B-BOP will considerably expand our ability to map the structure of interstellar magnetic fields. These data will be complementary to a diverse array of polarisation observations of the Galaxy.

Stellar polarisation surveys will be combined with Gaia astrometry (e.g., Tassis et al. Reference Tassis2018) to build 3D maps of the magnetic fields in the Galaxy but with a rather coarse resolution, comparable to that of the density structure of the local ISM in Lallement et al. (Reference Lallement2018).

Synchrotron observations at radio wavelengths with the Square Kilometer Array (SKA) and its precursors will probe the structure of magnetic fields (Dickinson et al. Reference Dickinson2015; Haverkorn et al. Reference Haverkorn2015), in particular, in ionised phases through Faraday rotation (Gaensler et al. Reference Gaensler2011; Zaroubi et al. Reference Zaroubi2015). SKA will also provide Faraday rotation measurements towards ${\sim} 10^7$ extragalactic sources (Johnston-Hollitt et al. Reference Johnston-Hollitt2015), which will be available for comparison with B-BOP dust polarisation data as illustrated in the pioneering study of Tahani et al. (Reference Tahani, Plume, Brown and Kainulainen2018).

B-BOP will allow us to study interstellar turbulence over an impressive range of physical scales and astrophysical environments from the warm ISM phases to MCs. Observations of nearby galaxies are best suited to probe the driving of turbulence in relation to galaxy dynamics (spiral structure, bars, galaxy interaction, outflows) and stellar feedback as discussed in Section 6. Galactic observations will probe the inertial range of turbulence over 4–5 orders of magnitude from the injection scales (${\sim} 100\,$pc–$1\,$kpc) down to $0.01\,$pc. The smallest physical scales will be reached by observing interstellar matter nearest the Sun, away from the Galactic plane: the diffuse ISM at high Galactic latitudes and star-forming MCs in the Gould Belt. These sky regions are best suited for the study of turbulence because the overlap of structures along the line of sight is minimised. The Gould Belt clouds are already part of the filament science case in Section 2. This survey will include star-forming clouds and diffuse clouds representative of the cold neutral medium. Deeper polarimetric imaging of high Galactic latitude fields (10 h per deg$^2$), sampling regions of low gas column density ($ A_V \sim 0.1$–0.3), will allow us to probe turbulence in the warm ISM phases. These deep imaging observations could potentially share the same fields as those used to carry out a SPICA-SMI cosmological survey. The size of the area that may be mapped to that depth (of order ${\sim} 100\,$deg$^2$) will be optimised with the needs of this survey. Altogether, we estimate that B-BOP will cover a total area of about 500 deg$^2$ away from the Galactic Plane including diffuse ISM fields at high Galactic latitudes, which will be available to study turbulence in diverse interstellar environments. At the angular resolution of B-BOP at $200\,\mu$m, these data correspond to a total of $2 \times 10^7$ polarisation measurements. This number is 20 times larger than the statistics offered by the Planck polarisation data. The gain in angular resolution and sensitivity is so large, that B-BOP will supersede Planck in terms of data statistics, even if the maps used cover only ${\sim} 1$ of the sky.

A wealth of spectroscopic observations of HI and molecular gas species, tracing the gas density, column density and kinematics, will become available before the launch of B-BOP with SKA and its precursors (McClure-Griffiths et al. Reference McClure-Griffiths2015), and the advent of powerful heterodyne arrays on millimeter ground-based telescopes, e.g., the Large Millimeter Telescope and the IRAM 30-m telescope. Furthermore, we will be able to investigate the link between coherent magnetic structures and turbulent energy dissipation observing main ISM cooling lines from H$_2$, C _II, and O _I with the SPICA mid and far-IR spectrometers SMI and SAFARI. These complementary data from SPICA and ground-based observatories will be combined to characterise the turbulent magnetised ISM statistically. The data analysis will rely on on-going progress in the development of statistical methods (e.g., Makarenko et al. Reference Makarenko, Shukurov, Henderson, Rodrigues, Bushby and Fletcher2018; Allys et al. Reference Allys, Levrier, Zhang, Colling, Regaldo-Saint Blancard, Boulanger, Hennebelle and Mallat2019), which we will use to characterise the structure of interstellar magnetic fields and their correlation with gas density and velocity. This process will converge towards an empirical model of interstellar turbulence, which will be related to ISM physics comparing data and MHD simulations.

4.1. Current state of the art

In MCs, protostellar dense cores are the ‘seeds’ where the gravitational force proceeds to form stars. Class 0 objects are the youngest known accreting protostars: most of their mass is still in the form of a dense core/envelope ($M_{\rm env} \gg M_\star $) and this phase is characterised by high accretion rates of gas from the dense core onto the central stellar object, accompanied by ejection of powerful highly collimated flows (André, Ward-Thompson, & Barsony Reference André, Ward-Thompson, Barsony and Mannings2000; Dunham et al. Reference Dunham and Beuther2014).

How many stars can be formed out of a typical MC depends not only on the physical conditions in filamentary structures, but also on the detailed manner the gravitational collapse proceeds within individual protostellar cores (i.e., would it form a single/binary stellar system, one or several low-mass stars or high-mass stars?).

By the end of the protostellar phase, the star has gained most of its final mass: understanding the role of magnetic fields during the protostellar stage is therefore crucial to clarify how they affect some of the most remarkable features of the star formation process, such as the distribution of stellar masses, the stellar multiplicity, or the ability to host planet-forming disks (McKee & Ostriker Reference McKee and Ostriker2007; Li et al. Reference Li, Banerjee, Pudritz, Jørgensen, Shang, Krasnopolsky, Maury and Beuther2014).

The development of numerical MHD models describing the collapse of protostellar cores and the formation of low-mass stars has opened new ways to explore in more details the physical processes responsible for the formation of solar-type stars. MHD models suggest that protostellar collapse proceeding with initially strong and well-aligned magnetic field produces significantly different outcomes than hydrodynamic or weakly magnetised models (Fiedler & Mouschovias Reference Fiedler and Mouschovias1993; Hennebelle & Fromang Reference Hennebelle and Fromang2008; Masson et al. Reference Masson, Chabrier, Hennebelle, Vaytet and Commerçon2016). For example, if the field is strong enough and well coupled to the core material, magnetic braking will regulate the formation of disks and multiple systems during the Class 0 phase. This has been the focus of recent studies (Hennebelle et al. Reference Hennebelle, Commerçon, Chabrier and Marchand2016; Krasnopolsky, Li, & Shang Reference Krasnopolsky, Li and Shang2011; Machida, Inutsuka, & Matsumoto Reference Machida, Inutsuka and Matsumoto2011), because it could potentially explain the low end of the size distribution of protostellar disks (e.g., Maury et al. Reference Maury2010; Segura-Cox et al. Reference Segura-Cox2018; Maury et al. Reference Maury2019).

All protostellar cores are magnetised to some level and current observations suggest that at least in some cases the magnetic field at core scale is remarkably well organised, pointing towards scenarii with strong field even at the high column densities typical of protostellar cores (e.g., IRAS 4A, G31.41, G240.31, NGC 6334, L1157, B335: Girart, Rao, & Marrone Reference Girart, Rao and Marrone2006; Girart et al. Reference Girart, Beltrán, Zhang, Rao and Estalella2009; Qiu et al. Reference Qiu, Zhang, Menten, Liu, Tang and Girart2014; Li et al. Reference Li2015; Stephens et al. Reference Stephens2013; Galametz et al. Reference Galametz2018; Maury et al. Reference Maury2018), while in other cases (e.g., Girart et al. Reference Girart, Frau, Zhang, Koch, Qiu, Tang, Lai and Ho2013; Hull et al. Reference Hull2017; Ching et al. Reference Ching, Lai, Zhang, Girart, Qiu and Liu2017, and Figure 8 for an example in the G14 massive star forming region) the core-scale magnetic field shows very complex morphology. In Figure 8, for instance, it is noteworthy that the northern hub of the G14 region, with a more uniform magnetic field, has a lower level of fragmentation than the southern hub (that shows a more perturbed magnetic field). These observations suggest the field may remain organised at scales where collapse occurs in most solar-type progenitors, and also at least some of the massive cores (Zhang et al. Reference Zhang2014; Beuther et al. Reference Beuther2018). Current results may be biased, however, because present single-dish facilities selectively trace magnetic fields from the brightest regions within star-forming cores (dust polarisation is only detected at the highest column densities, see Figure 8).

Figure 8. Composite images of the G14.225-0.506 massive star forming region (Busquet et al. Reference Busquet2013, Reference Busquet2016; Santos et al. Reference Santos, Busquet, Franco, Girart and Zhang2016). Top left panel: R band optical polarisation vectors (red segments) overlaid on Herschel 250 $\mu$m image overlapped (from Santos et al. Reference Santos, Busquet, Franco, Girart and Zhang2016). Central panels: SOFIA/HAWC+ 200 $\mu$m images (beam 14 arcsec) of the Northern (top) and Southern (bottom) hubs, with black segments showing the magnetic-field direction (F. Santos, private communication). Right panels: Submillimeter Array (SMA) images of the 1.2 mm emission towards the center of the Northern (top) and Southern (bottom) hubs (Busquet et al. Reference Busquet2016), with orange segments showing the magnetic-field direction (N. Añez-López, private communication).

4.2. Role of magnetic fields in controlling the typical outcome of protostellar collapse

B-BOP can perform statistical studies in unprecedentedly large samples of protostellar cores, testing for example whether the magnetic field in cores is directly inherited from their environment (if the magnetic field in low-density filamentary structures, see Section 2.3, connects to the magnetic field in high-density cores, which is expected in the strong field case), or if the field in cores is disconnected from the local field in the progenitor cloud (weak field case). While the ALMA interferometer can only provide constraints on the magnetic-field topology at the smallest scales (approximately 0.02–20 arcsec, i.e., ${\lt}5\,000$ au in Gould Belt clouds), the polarisation capabilities of other facilities probing larger spatial scales (SMA, NIKA2, and HAWC+) are severely sensitivity limited. Accordingly, studies linking cores and filaments can currently be carried out in bright, massive star-forming regions mostly (see Figure 8), and only in a handful of nearby solar-type protostellar cores.

Some indications have been found, in small samples (${\lt}20$ objects), that the topology of the magnetic field at core scales may be linked to the distribution of angular momentum in solar-type cores, and hence that the magnetic field may be of paramount importance to set the initial conditions for the formation of protoplanetary disks and multiple systems (see Figure 9 and Galametz et al. Reference Galametz2018; Segura-Cox et al. Reference Segura-Cox2018). An example of the type of studies that B-BOP could extend to the full mass function of protostellar cores in a statistical fashion is shown in Figures 8 and 9: these two figures illustrate the tentative link between the magnetic-field topology at core scale and the disks and multiplicity fraction found within protostellar cores at smaller scale. The magnetic-field properties found with B-BOP at dense core scales can be compared with the protostellar properties observed with interferometers at smaller scales to build correlation diagrams similar to the one shown in Figure 9. In this way, B-BOP observations can test the hypothesis, tentatively suggested by current studies of the brightest protostars, that magnetic fields regulate the formation of disks and multiple systems during the main accretion phase. Observations of large samples of protostars could be carried out thanks to the sensitivity and spatial resolution of B-BOP, which is crucially needed not only to populate diagrams such as Figure 9, but also because only statistics will allow us to solve the degeneracy induced by projection effects intrinsically linked to dust polarisation (tracing only the magnetic-field component in the plane of the sky). Moreover, B-BOP will provide information on the geometry of magnetic-field lines across the full protostellar core mass distribution, probing different behaviours in different mass regimes, and potentially as a function of environment in different star-forming regions.

Figure 9. Potential role of the magnetic-field topology at core scales in the formation of disks and multiple systems. Top: magnetic field (red/orange line segments, from dust polarisation observations with the SMA at 850$\,\mu$m) in two solar-type Class 0 protostellar cores (Galametz et al. Reference Galametz2018). The blue arrows indicate the jet/rotation axis of these cores, aligned with the core-scale magnetic field in L1157 (left), and mostly orthogonal to it in L1448N (right). Bottom: level of core rotation (from kinematic observations at core scales, Yen et al. Reference Yen, Koch, Takakuwa, Ho, Ohashi and Tang2015 and Gaudel et al. Reference Gaudel, Maury and Belloche2019) as a function of the misalignment between the rotation/outflow axis and the magnetic field (observed at core scale with the SMA—Galametz et al. Reference Galametz2018) in a sample of nearby Class 0 sources. There is a hint that large misalignments of the magnetic field at core scales lead to sources with large rotational gradients and multiple systems at smaller scales (red symbols).

The angular resolution and surface brightness dynamic range of B-BOP will make it possible to resolve most ${\sim}$2 000–20 000 au protostellar cores in nearby star-forming regions out to 250 pc. A wide-field B-BOP survey of all nearby clouds as envisaged in Section 2.3 (${\sim} 2\,$h per square degree) will map dust polarisation (fraction $>1\%$) at core scales with signal-to-noise ratio $>7$, in complete populations of $ \mathbin{\lower.3ex\hbox{$\buildrel>\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} $1 000 protostars (Class 0 and Class I) and their parent cloud/environment, from massive protostellar cores down to the low-mass progenitors of solar-type stars. In contrast, current millimeter/submillimeter polarimetric instruments, such as SCUBA2-POL, NIKA2-POL, SOFIA/HAWC$+$, or BLAST-TNG (cf. Section 2.4) are limited to the subset of the $\sim$50–100 brightest cores, and without the important context provided by the magnetic-field information in the parental clouds.

6.1. Current observational status

Significant progress has been made in recent decades to characterise the interstellar magnetic fields of external galaxies, with measurements of the magnetic-field strength and orientation obtained for about 100 nearby galaxies (see the Appendix of Beck & Wielebinski Reference Beck and Wielebinski2013).Footnote ^k This effort has established a broadly consistent picture of the large-scale (${>}1$ kpc) properties of galactic magnetic fields. As in the Milky Way, the interstellar magnetic field in external galaxies can be described as a combination of large-scale regular fields and small-scale turbulent fields. Observations of face-on spiral galaxies demonstrate that galaxies typically host spiral fields in the disk, with the observed large-scale magnetic-field orientations appearing similar to the material spiral arms. The vertical structure of the field is more easily probed via observations of edge-on systems, which typically show an X-shaped structure such that the field tends to become more inclined (and eventually perpendicular) with increasing distance from the midplane. Field strengths vary, but are usually in the range of several to tens of $\mu$G, with roughly similar contributions from ordered and random field components (Beck & Wielebinski Reference Beck and Wielebinski2013).

To date, magnetic-field properties in external galaxies have mostly been investigated via observations of synchrotron emission at GHz frequencies (for a review, see Beck & Wielebinski Reference Beck and Wielebinski2013; Beck Reference Beck2015). At the same frequencies, Faraday rotation of background radio sources provides an alternative, direct determination of the direction and strength of magnetic field within galaxies. This technique has been used for detailed studies of the Milky Way’s magnetic field (e.g., Terral & Ferrière Reference Terral and Ferrière2017; Mao et al. Reference Mao, Gaensler, Haverkorn, Zweibel, Madsen, McClure-Griffiths, Shukurov and Kronberg2010), but its application to external galaxies has thus far been limited to the most nearby galaxies (which have a large angular size and thus a sufficient number of bright background sources, e.g., M31, LMC, Han, Beck, & Berkhuijsen Reference Han, Beck and Berkhuijsen1998; Gaensler et al. Reference Gaensler, Haverkorn, Staveley-Smith, Dickey, McClure-Griffiths, Dickel and Wolleben2005). Faraday rotation measurements for a much larger sample of nearby galaxies is an important science driver for SKA (see, e.g., Beck et al. Reference Beck2015).

At other wavelengths, the magnetic-field structure of a much smaller number of external galaxies has been surveyed using optical polarisation, e.g., the Magellanic Clouds (LMC and SMC; Mathewson & Ford Reference Mathewson and Ford1970), NGC1068, and M51 (Scarrott, Ward-Thompson, & Warren-Smith Reference Scarrott, Ward-Thompson and Warren-Smith1987). Wide-field imaging of polarised extinction at near-IR wavelengths is a newer capability that has been used to probe the magnetic-field structure in nearby edge-on galaxies, with results that are generally in good agreement with radio observations (e.g., Clemens, Pavel, & Cashman Reference Clemens, Pavel and Cashman2013; Montgomery & Clemens Reference Montgomery and Clemens2014). The near-IR extinction technique is less suited to observations of face-on galaxies, due to the relatively short path length that can produce internal extinction (see, e.g., Pavel & Clemens Reference Pavel and Clemens2012, for the case of M51).

B-BOP will probe the magnetic-field structure via observations of dust polarisation in far-IR emission. An important advantage of this technique compared to radio synchrotron observations is that it traces the magnetic-field structure in the cold gas where star formation occurs, with minimal contamination from the warm ionised gas in the halo (e.g., Mao et al. Reference Mao, Zweibel, Fletcher, Ott and Tabatabaei2015). Studies in nearby galaxies further suggest that the magnetic field is coupled to the interstellar gas independently of the star formation rate (e.g., Schinnerer et al. Reference Schinnerer2013; Tabatabaei et al. Reference Tabatabaei, Minguez, Prieto and Fernández-Ontiveros2018), highlighting the importance of tracing the field in the neutral ISM. The SCUBA-POL camera on the James Clerk Maxwell Telescope (JCMT), operating at 850 $\mu$m, obtained the first such dust polarisation observations of external galaxies (e.g., Matthews et al. Reference Matthews, McPhee, Fissel and Curran2009), but was only able to access extremely bright extragalactic regions, such as the centre of the nearby starburst system M82 (e.g., Greaves et al. Reference Greaves, Holland, Jenness and Hawarden2000). The Planck mission has recently provided all-sky measurements of the polarised submillimeter dust emission, but with an angular resolution (${\sim}$10 arcmin at 353 GHz) sufficient to resolve sub-kiloparsec scales only in the closest Local Group galaxies (${\lt}1$ Mpc). With $\sim$arcsecond resolution, a key opportunity for ALMA will be targeted imaging of the detailed magnetic-field structure in extragalactic MCs, but wide-field polarisation surveys of nearby galaxies will remain impractical, due to prohibitive integration times for fields larger than a few square arcminutes.

6.2. Key opportunities for B-BOP on nearby galaxies

Mapping the structure of interstellar magnetic fields in the cold ISM of nearby galaxies is crucial to understand how magnetic fields influence gas dynamics in galaxies, and in particular the role of the field in regulating star formation, driving galactic outflows, and fuelling galactic nuclei. Observational studies of these processes in nearby galaxies complement Milky Way studies, which typically have superior spatial resolution, but may be limited by distance ambiguity and line-of-sight confusion. Among current and near-future facilities, only B-BOP will be able to make these measurements across a representative sample of external galaxies, probing a much wider range of ISM conditions than those encountered in the Milky Way, and to conduct spatially complete mapping of the field structure in Local Group targets.

To highlight B-BOP’s unique capabilities for such an effort, Figure 10 shows the estimated signal-to-noise ratio in polarised intensity for several iconic nearby galaxies at $100\,\mu$m (top row) and $200\,\mu$m (bottom row) after 2 h on-source integration with B-BOP. These maps are constructed assuming the performance parameters given in Table 1 and a conservative polarisation fraction of 1%. At the intrinsic resolution of the 100 $\mu$m band, the sensitivity is sufficient for tracing the detailed polarisation structure of bright features such as spiral arms, bar dust lanes, and galaxy centers. For the galaxies in Figure 10, several 100 independent 100 $\mu$m polarisation vectors would be obtained. Measurements in the more sensitive 200 and 350 $\mu$m bands would essentially cover the entire galactic disk within $0.6\,R_{25}$ (where $R_{25}$ is the optical radius). The excellent signal-to-noise ratio that can be achieved with a modest integration time per galaxy means that B-BOP could conduct the first systematic survey of the polarised far-IR dust emission—and hence magnetic-field structure—in ${\sim}100$ nearby galaxies. This is slightly larger than the combined sample of galaxies targeted by the VNGS and KINGFISH Herschel nearby galaxy projects, and would require only 200 h of on-source observing time. In the remainder of this section, we highlight some of the potential science drivers for such a B-BOP nearby galaxy survey.

Figure 10. Expected signal-to-noise in 100 $\mu$m (top row) and 200 $\mu$m (bottom row) polarised intensity after 2 h on-source integration with B-BOP for four nearby ($d\lt10$ Mpc) galaxies. The maps are constructed using Herschel data at 70 and 250 $\mu$m as input. We assume the B-BOP performance parameters given in Table 1, a dust spectral index of $\beta=1.9$, and a conservative polarisation fraction of 1%. The colour scale, which runs between a signal-to-noise ratio of 1 and 100 (top row) or 1 and 1 000 (bottom row), uses a logarithmic stretch, with green indicating a signal-to-noise of 10.

6.2.4. The Magellanic Clouds

The Large and the Small Magellanic Clouds (LMC, SMC) are the closest gas-rich galaxies to the Milky Way. A B-BOP survey of the Magellanic Clouds would for the first time probe the magnetic-field structure in the cold ISM across all spatial scales between the clumpy sub-structure within GMCs (${\sim}2$ pc) and the galactic disk (several kpc). Observations across such a large range of spatial scales are needed to decipher the dynamical importance of the magnetic field for the inherently hierarchical process of star formation, i.e., from the formation of GMCs out of the diffuse ISM, down to the formation of individual stars. Spatially complete surveys of dust emission in the Magellanic Clouds with ALMA are unfeasible due to their large angular size (${\sim}50$ and ${\sim}10$ deg$^2$ for the LMC and SMC, respectively).

As an example of what could be achieved with B-BOP, Figure 11 shows the estimated signal-to-noise ratio for a 50-h polarimetric imaging survey of the LMC at 100, 200, and $350\, \mu$m. This hypothetical survey would achieve a signal-to-noise ratio of 3 for the polarised intensity at 100$\,\mu$m for interstellar gas with H column densities above ${\sim}2.5 \times 10^{21}$ cm$^{-2}$ (equivalent to $A_{V}\sim0.4$ in the LMC—Weingartner & Draine Reference Weingartner and Draine2001). This sensitivity would yield $\sim$0.5 million independent measurements of the magnetic-field orientation in the interstellar gas on spatial scales of 2 pc, including in the column-density regime of the atomic-to-molecular phase transition. At 200 and 350 $\mu$m, a similar number of significant detections of the magnetic-field orientation would be achieved in even more diffuse gas (${\sim}1 \times 10^{21}$ cm$^{-2} \approx 0.15$ mag). This represents $\sim$2 orders of magnitude increase in detail over measurements with Planck’s 353 GHz channel in the Magellanic Clouds, and would provide the first spatially complete view of the parsec-scale magnetic-field structure in the molecular gas reservoir of any galaxy.

Figure 11. Expected signal-to-noise in polarised intensity for B-BOP observations of the LMC after 50 h on-source integration. The maps are constructed using Herschel data at 100 and 250 $\mu$m as input (Meixner et al. Reference Meixner2013). We assume the B-BOP performance parameters given in Table 1, a dust spectral index of $\beta=1.9$, and a conservative polarisation fraction of 1%. The colour scale, which runs between a signal-to-noise ratio of 1 and 100, uses a logarithmic stretch, with green indicating a signal-to-noise of 10.

6.3. Distant galaxies and the potential detection of the Cosmic Infrared Background polarisation

The build-up of coherent magnetic fields in galaxies and their persistence along cosmic evolution is being investigated with analytical models of the galactic dynamo (e.g., Rodrigues et al. Reference Rodrigues, Chamandy, Shukurov, Baugh and Taylor2019) and numerical simulations of galaxy formation (e.g., Martin-Alvarez et al. Reference Martin-Alvarez, Devriendt, Slyz and Teyssier2018). These studies suggest that the mean-field dynamo is effective early in the evolution of galaxies but, today, polarisation data available to trace the redshift evolution of galactic magnetic fields are very scarce (Mao et al. Reference Mao2017). While SKA holds exciting promises to extend observations of cosmic magnetism to the distant universe (e.g., Basu et al. Reference Basu, Mao, Fletcher, Kanekar, Shukurov, Schnitzeler, Vacca and Junklewitz2018; Mao Reference Mao2018), we argue here that B-BOP can also uniquely contribute providing the first polarimetric extragalactic survey at far-IR wavelengths.

To quantify what could be achieved with B-BOP, we consider the point source sensitivity of a polarimetric extragalactic survey for an integration time of 10 h per deg$^2$ (Table 1). At the detection limit of Herschel imaging surveys in total intensity, the signal-to-noise ratio of B-BOP in Stokes Q and U is ${\sim} 200$ at $200\, \mu$m and ${\sim} 100$ at 100 and $350\, \mu$m. This sensitivity needs to be compared to the few existing values of the far-IR polarisation fraction for galaxies as a whole.

The net polarisation fraction resulting from the integrated emission of galaxies depends on the existence of a coherent mean magnetic field and on viewing angle. In disk galaxies, the polarisation angle is aligned with the projection of the galaxy angular momentum vector on the plane of the sky, and the polarisation fraction increases from a face-on to an edge-on view. Integrating the Planck dust polarisation maps at 353 GHz over a $20^\circ$ wide band centered on the Galactic plane, De Zotti et al. (Reference De Zotti2018) found a polarisation fraction $p= 2.7$%. Within a simple model, p is expected to scale as sin$\,i$, where i is the inclination angle of the galaxy axis to the line of sight. For this scaling, the mean p fraction averaged over inclinations is $1.4$. This may be taken as a reference value for spiral galaxies like the Milky Way, but p is likely to be on average lower for distant infrared galaxies. Indeed, SOFIA polarisation imaging of the two template starburst galaxies, M82 and NGC253, revealed regions with different polarisation orientations, which tend to average out when computing the integrated polarised emission yielding an overall mean $p \sim 0.1$% (Jones et al. Reference Jones2019).

Even if B-BOP only detects polarised emission from only a small fraction of Herschel galaxies, the number of detections will be significant given the present dearth of such measurements. If the detections are numerous, the emission from galaxies could even limit the polarisation sensitivity of B-BOP deep surveys. This is a possibility that needs to be assessed. Beyond the study of individual galaxies, we anticipate that the main outcome of a deep polarimetric extragalactic survey with B-BOP could follow from a statistical analysis of the data.

Statistical analysis is the reference in cosmology and much can be learned without detecting sources individually. In particular, the cross-correlation of surveys across the electromagnetic spectrum is a powerful means commonly used. In the far-IR, this is illustrated by the results obtained stacking Herschel data on positions of extragalactic sources in the near- and mid-IR. This approach has been successfully used to statistically identify sources accounting for the bulk of the Cosmic Infrared Background (CIB), although they were too faint to be detected individually (Béthermin et al. Reference Béthermin2012; Viero et al. Reference Viero2013). B-BOP, which will extend these studies to polarisation, is uniquely suited to detect—or set tight constraints on—the CIB polarisation. We note that the analysis of point sources circumvents the difficulty of separating the CIB from the foreground polarised emission of the diffuse Galactic ISM.

For polarisation, data stacking needs to be oriented to align polarisation vectors. This can be achieved by using, e.g., galaxy shapes measured from near-IR surveys at the appropriate angular resolution. Another interesting path will be the study of correlations between B-BOP extragalactic survey data and maps of the cosmic web inferred from weak-lensing surveys. The angular momenta of galaxies are not randomly oriented on the sky. The cosmic web environment has a strong influence on galaxy formation and evolution, and tidal gravitational fields tend to locally align the spins of dark-matter halos and galaxies. Such alignments, observed in dark-matter simulations, bear information on galaxy formation and evolution, as well as on the growth of structure in the Universe (Kirk et al. Reference Kirk2015). In this picture, low-mass haloes tend to acquire a spin parallel to cosmic web filaments, while the most massive haloes, which are typically the products of later mergers, have a spin perpendicular to filaments (e.g., Codis et al. Reference Codis, Pichon, Devriendt, Slyz, Pogosyan, Dubois and Sousbie2012; Dubois et al. Reference Dubois2014). Quasar observations provide observational evidence of a correlation between the polarisation orientation of galaxies and the large-scale structure of the Universe (Hutsemékers et al. Reference Hutsemékers, Braibant, Pelgrims and Sluse2014), but only for a small number of sources. B-BOP can uniquely contribute to characterising this correlation for infrared-luminous galaxies.

The scientific goals outlined here are new and promising but still qualitative. Modelling is required to assess the scientific outcome of a deep polarimetric extragalactic survey with B-BOP and decide on the best observing strategy in terms of survey depth and sky coverage.

7.1. Probing the grain alignment mechanism

Grain alignment is subordinate to various processes. First, grains must rotate supra-thermallyFootnote l to be well aligned. Radiative torques, or chemical torques resulting from the formation of H$_2$ molecules on the surface of grains, are good candidates for grain spin-up. Second, alignment torques of magnetic, radiative, or mechanical origin (Hoang & Lazarian Reference Hoang and Lazarian2016) are needed to align the supra-thermally rotating dust grains. Compared to the time evolution of MCs and cores, the alignment of grains along magnetic-field lines by radiative torques is a fast process, with a timescale on the order of $10^3$–$10^4\,$ yr (Hoang & Lazarian Reference Hoang and Lazarian2014),Footnote m so that situations where grain alignment would be out-of-equilibrium can be safely ignored.

While the mechanisms of dust grain alignment are still debated (see, e.g., Section 2.1.1), polarisation measurements at UV to optical wavelengths imply that the alignment efficiency of dust grains is sensitive to grain size. Such a behaviour, well observed in the Mie regime where absorption and scattering are size-dependent (Bohren & Huffman Reference Bohren and Huffman1983), is however more difficult to extract from the polarised thermal SED because the dust temperature and dust spectral index depend more on the grain shape, internal structure, and composition (through its emissivity) than on the exact grain size.

As already mentioned in Section 2.1.1, the leading grain alignment theory is RATs (e.g., Lazarian & Hoang Reference Lazarian and Hoang2007, and references therein). The RATs alignment mechanism, if present, will lead to characteristic signatures in observations. For instance, in this theory, the alignment efficiency is directly dependent on the angle between the incident radiation field and the magnetic-field direction ($\psi$). When dust is heated by a single nearby star or in starless dense cores where the field is strongly attenuated and anisotropic, the incident radiation field direction is well characterised. Since the magnetic-field orientation projected on the plane of the sky can be determined from the polarised signal, mapping dust polarisation in such regions can in principle be used to test alignment by RATs. This is illustrated in Figure 12 which sketches the relative geometry of the radiation field and magnetic field in a region of the ISM where the radiation field is dominated by a single star. In such regions, the RATs alignment theory predicts a stronger alignment, and therefore, a higher polarisation fraction where $\psi$ is close to $0^\circ$.

Figure 12. Sketch of the geometry around a single star dominating the heating of the local ISM. The magnetic-field direction is represented by the horizontal dashed lines. The aligned dust grains are sketched as prolate rotating parallelograms. If RATs dominate, dust alignment will be more efficient in regions with low values of $\psi$, the angle between the stellar radiation and magnetic-field directions. Source: Figure adapted from Potter (Reference Andersson and Potter2010) and Andersson et al. (Reference Andersson, Pintado, Potter, Straižys and Charcos-Llorens2011).

Despite an expected clear signature, direct observational evidence of this angular effect has been scarce. The only positive detection reported in emission is by Vaillancourt and Andersson (Reference Vaillancourt and Andersson2015) who detected a periodic modulation of the dust polarisation fraction around the Becklin–Neugebauer Kleinmann–Low (BN-KL) object in Orion OMC-1. Some authors also claim to have evidenced a correlation between dust temperature and polarisation fraction, as expected for dust grains aligned through the RATs mechanism (Andersson et al. Reference Andersson, Pintado, Potter, Straižys and Charcos-Llorens2011; Matsumura et al. Reference Matsumura, Kameura, Kawabata, Akitaya, Isogai and Seki2011). There are also a few reports that indicate a possible influence of H$_2$ formation (e.g., Andersson et al. Reference Andersson2013, in IC63). In any case, only a handful of cases have been investigated so far and there is certainly a bias in the literature for publishing detections rather than non-detections. Given the intrinsically tangled nature of magnetic-field geometry, chance coincidences are very difficult or even impossible to exclude for these few isolated studies and a statistically representative study is clearly needed.

Such a study has not been carried out so far using Planck all-sky data, essentially because the number of interstellar regions where dust is directly and predominantly heated by a single star is very low at the Planck angular resolution. Attempts to unambiguously detect a statistical increase of the polarisation fraction with dust temperature in the Planck data, which would also be attributable to radiation-enhanced spin-up and alignment of dust grains, have not led to a strong conclusion. Planck 2018 res. XII (2019) showed that it is possible to disentangle, statistically, between what can be attributed to variations in grain alignment efficiency or grain properties, and what is due to line of sight and beam averaging of magnetic-field structures. This study demonstrated that there is no strong variations in grain alignment efficiency in the diffuse ISM (up to a column density, $N_{\rm H} \sim 2\times10^{22}$ cm$^{-2}$), but, due to the low angular resolution of the Planck data, could not conclude in the case of the high-density ISM. Planck 2018 res. XII (2019) did not find any correlation either between dust temperature and polarisation fraction in the diffuse ISM. In conclusion, the analysis of the Planck all-sky data have so far not allowed to strongly confirm or rule out any specific grain alignment theory, but have provided an upper limit to the drop of alignement in the diffuse ISM.

Owing to its much higher angular resolution and sensitivity, B-BOP will allow us to systematically map the polarisation of dust emission around thousands of individual stars heating the nearby ISM locally. The good coverage of the polarised SED will allow us to measure the temperature of aligned dust grains responsible for the polarised emission. Analysis of the polarisation fraction as a function of the angle between the known radiation field and the magnetic-field direction derived from polarisation will allow us to test, for the first time, the RATs alignment theory with statistical significance, in a way that is not affected by local variations and the complexity of individual objects. At the same time, we will be able to detect, if present, the polarised emission resulting from the small temperature difference between grains heated face-on and edge-on immersed in an anisotropic radiation field (Onaka Reference Onaka1995). This process, which is only efficient at short wavelength ($\lambda \le 100\,\mu$m, Onaka Reference Onaka2000), would appear in B-BOP data as a characteristic difference between the polarisation fraction and angle measured at $100\,\mu$m and the ones measured by unaffected channels at longer wavelengths.

Altogether, the high resolution, sensitivity, and spectral coverage of B-BOP will set unprecedented, probably unexpected constraints on the physics of grain alignment in star-forming regions, a topic which Planck observations could hardly address.

7.2. Dust polarisation as a proxy for dust evolution

The wavelength range covered by B-BOP will allow us to disentangle between various dust models. The Wien part of the polarised dust emission is currently not constrained. It is in this wavelength range that dust models present the strongest differences in spectral variations of $P/I$ (Figure 13), in particular, between those where carbon grains are aligned and those where they are not (Draine &Hensley Reference Draine and Hensley2013; Guillet et al. Reference Guillet2018). Moreover, as dust models now predict both emission and absorption properties of dust grain populations in polarisation (Siebenmorgen, Voshchinnikov, & Bagnulo Reference Siebenmorgen, Voshchinnikov and Bagnulo2014; Draine & Hensley Reference Draine and Hensley2017; Guillet et al. Reference Guillet2018), joint observations of common targets with B-BOP and survey experiments targeting extinction polarisation of background stars, such as PASIPHAE (Tassis et al. Reference Tassis2018), can be used to further test such models.

Figure 13. Polarisation fraction as a function of wavelength predicted using the DustEM (http://www.ias.u-psud.fr/DUSTEM) numerical tool (Compiègne et al. Reference Compiègne2011; Guillet et al. Reference Guillet2018). The vertical bands show the B-BOP photometric channels. The dashed band shows a suggested shifted location for the short-wavelength band of B-BOP at $70\,\mu$m, which would better cover the Wien part of the polarised dust SED. In model A, only silicate grains are aligned, while carbon grains are randomly aligned. In model D, both silicate and carbon are aligned, with carbon inclusions incorporated in the silicate matrix (6% in volume). Source: Figure adapted from Guillet et al. (Reference Guillet2018).

High-resolution polarisation observations with B-BOP will allow us to probe dust properties in dense environments and to further characterise dust evolution between diffuse and dense media (e.g., Köhler, Ysard, & Jones Reference Köhler, Ysard and Jones2015). Observationally, a number of studies based on emission and extinction data have provided evidence of grain growth within dense clouds. One of the main results is an increase of the far-IR/submillimeter emissivity by a typical factor of 2–3 compared to standard grains in the diffuse medium (cf. Stepnik et al. Reference Stepnik2003; Planck early res. XXV 2011; Ysard et al. Reference Ysard2013; Roy et al. Reference Roy2013; Juvela et al. Reference Juvela2015), as predicted by calculations of aggregate optical properties (Ossenkopf & Henning Reference Ossenkopf and Henning1994; Köhler et al. Reference Köhler, Stepnik, Jones, Guillet, Abergel, Ristorcelli and Bernard2012, Reference Köhler, Ysard and Jones2015). Another striking result is the so-called coreshine effect, i.e., enhanced mid-IR light scattering detected with Spitzer towards a number of dense cores (Pagani et al. Reference Pagani, Steinacker, Bacmann, Stutz and Henning2010; Steinacker et al. Reference Pagani, Steinacker, Bacmann, Stutz and Henning2010), implying the presence of larger (Steinacker et al. Reference Steinacker2015) or, taking into account the change in dust optical properties, only moderately larger (Ysard et al. Reference Ysard, Köhler, Jones, Dartois, Godard and Gavilan2016) dust grains.

Stochastic emission by very small grains ($a\ll 10$ nm) is known to contribute significantly to the 60 and 100 $\mu$m emission bands. This contribution is estimated to be on the order of 13% at 100 $\mu$m and 45% at 60 $\mu$m (e.g., Jones et al. Reference Jones, Fanciullo, Köhler, Verstraete, Guillet, Bocchio and Ysard2013). When the 100 $\mu$m band is used to derive the dust temperature, this contamination affects the accuracy of mass determinations using dust continuum measurementsFootnote ⁿ. The formation of dust aggregates first removes the very small grains from the gas phase, as suggested by observations showing a significant decrease in the 60 $\mu$m emission (Laureijs, Clark, & Prusti Reference Laureijs, Clark and Prusti1991; Bernard et al. Reference Bernard1999; Stepnik et al. Reference Stepnik2003; Ysard et al. Reference Ysard2013) and as predicted by dust evolution models (Ossenkopf & Henning Reference Ossenkopf and Henning1994; Köhler et al. Reference Köhler, Ysard and Jones2015). Because small grains are not aligned with the magnetic field, such contamination is absent from the polarised thermal emission SED.Footnote ^o As a consequence, the dust temperature derivedFootnote ^p from the polarised dust SED that B-BOP can observe will only reflect the temperature of large aligned dust grains in the transition from the diffuse to the dense ISM, a constraint that will be used in addition to that inferred from the total intensity SED to study dust evolution processes.

Just like unpolarised emission, polarised dust emission will also probe variations in dust emissivity as expected from dust evolution in dense clouds. Dense environments could not be properly characterised in polarisation at the low resolution of the Planck data. Unlike unpolarised emission, the anisotropic nature of polarised emission makes it sensitive to the grain shape. The formation of dust aggregates by grain–grain coagulation must have its counterpart in polarisation, and B-BOP will detect signatures which will have to be analysed through detailed modelling of the coagulation process. Here again, the combination of B-BOP data with the increasing amount of high-resolution polarisation observations in the optical and the near-IR will provide strong constraints on dust evolution (Planck int. res. XXI 2015; Planck 2018 res. XII 2019).

Observations of total dust emission intensity at far-IR and submillimeter wavelengths with Planck and Herschel have also brought surprises. One of them is evidence that the logarithmic slope of the dust emission SED at long wavelengths, often referred to as the dust emissivity index, $\beta$, exhibits significant variations at large scales across the Galaxy. The Planck all-sky data clearly show variations of $\beta$ along the Galactic plane, from very steep SEDs towards inner regions of the Milky Way to much flatter SEDs ($\beta \simeq1.5$) towards the Milky Way anticenter (Planck 2013 res. XI 2014). This has also been confirmed in the far-IR by the analysis of Hi-GAL data (Paradis et al. Reference Paradis2012). Even larger variations have been found in observations of external galaxies, with the SMC and LMC having $\beta\simeq1.3$ and $\beta\simeq1.0$, respectively (Planck early res. XVII 2011). Such variations are observed in the Herschel data within individual nearby galaxies such as M31 (Smith et al. Reference Smith2012) and M33 (Tabatabaei et al. Reference Tabatabaei2014). The origin of these variations is currently unclear and three main classes of dust models have been proposed to explain them. The first type involves the mixing of different materials during the dust life-cycle (Köhler et al. Reference Köhler, Ysard and Jones2015; Ysard et al. Reference Ysard, Köhler, Jones, Miville-Deschênes, Abergel and Fanciullo2015). The second type of models invokes Two-Level-System (TLS) low-energy transitions in the amorphous material composing dust grains (Meny et al. Reference Meny, Gromov, Boudet, Bernard, Paradis and Nayral2007) as the cause for the flattening of the SED. The third type of models proposes that magnetic inclusions in dust grains (Draine & Hensley Reference Draine and Hensley2013) could produce the observed variations (Draine & Hensley Reference Draine and Hensley2012). Determining the origin of these variations is critical in many respects, not only to understand the dust cycle in the ISM, but also for accurate mass determinations from dust continuum measurements (which require good knowledge of the dust emissivity, its wavelength dependence, and its spatial variations).

In this domain again, extensive polarimetric imaging at far-IR wavelengths is likely to play a critical role in the future. Dust models based on dust evolution have not yet presented their predictions in polarisation, but the other two classes of models mentioned above predict significantly different behaviours for the polarisation fraction as a function of wavelength. TLS-based models essentially predict a flat spectrum for the polarisation fraction, a prediction compatible with Planck observations. In contrast, metallic-inclusion models predict variations of the polarisation fraction in the submillimeter (Draine & Hensley Reference Draine and Hensley2013), which are not observed. It will be possible to evidence those distortions of the polarisation SED by comparing far-IR B-BOP observations with existing submillimeter Planck data for the Magellanic Clouds and polarisation data obtained with new ground-based polarimetric facilities such as NIKA2-POL and SCUBA2-POL for Milky Way regions/sources and nearby galaxies. Correlating changes in the polarised SED with variations of $\beta$ will allow us to constrain models of the submillimeter dust emissivity in a very unique way.

7.3. Towards a tentative detection of polarisation by dust self-scattering in the densest cores

In the past decade, interesting constraints on grain sizes in dense clouds have come from the detection of the ‘coreshine’ effect (Pagani et al. Reference Pagani, Steinacker, Bacmann, Stutz and Henning2010), which results from scattering of near-IR stellar photons by dust grains present in the cloud. This has been interpreted as evidence of grain growth ($a=1\, \mu$m, Steinacker et al. Reference Steinacker, Pagani, Bacmann and Guieu2010) or grain compositional and structural evolution with a modest size increase ($a\lt0.5\, \mu$m, Ysard et al. Reference Ysard, Köhler, Jones, Dartois, Godard and Gavilan2016). More recently, it has been demonstrated that very large ($a \gt 10\, \mu$m) dust grains are able to produce polarisation by scattering thermal dust emission, a process that is called ‘self-scattering’. This was first predicted to be observable in protoplanetary disks (Kataoka et al. Reference Kataoka2015) and then confirmed by numerous ALMA observations (Kataoka et al. Reference Kataoka, Muto, Momose, Tsukagoshi and Dullemond2016; Yang et al. Reference Yang, Li, Looney, Girart and Stephens2017; Girart et al. Reference Girart2018).

B-BOP, with its 100 $\mu$m polarised channel, would be able to detect and characterise the spectral dependence of polarisation by scattering due to ${\sim} 15$ $\mu$m dust grains (Kataoka et al. Reference Kataoka2015), if present. For the effect to be observable, the thermal emission of dust must first present a quadrupolar anisotropy: scattering grains must receive more far-IR irradiation along one direction in the plane of the sky than along the perpendicular direction. Such a condition is naturally met in a dense protostellar core or in the presence of density gradients. Second, high local densities (${>}10^6\, {\rm cm}^{-3}$) must be present along the line of sight so that dust grains can have grown to the very large sizes ($a \sim \lambda/2\pi$) needed for scattering to occur in the far-IR. Observing such a high-density medium should be feasible at $100\,\mu$m at the resolution of SPICA, but simulations of grain growth and polarisation by scattering are needed to confirm this idea.

Polarisation by self-scattering at $100\,\mu$m with B-BOP will most likely concern only a few lines of sight through the densest cores. Because polarisation due to scattering sharply declines at wavelengths larger than the grain size, it will not alter the polarised emission from aligned dust grains at 200 and $350\,\mu$m used to trace the local magnetic-field orientation in MCs (Sections 2–5).