On the relation between the column density structures and the magnetic field orientation in the Vela C molecular complex
Key Words.:ISM: general, dust, magnetic fields, clouds – Infrared: ISM – Submillimetre: ISM
We statistically evaluate the relative orientation between gas column density structures, inferred from Herschel submillimetre observations, and the magnetic field projected on the plane of sky, inferred from polarized thermal emission of Galactic dust observed by the Balloon-borne Large-Aperture Submillimetre Telescope for Polarimetry (BLASTPol) at 250, 350, and 500 m, towards the Vela C molecular complex. First, we find very good agreement between the polarization orientations in the three wavelength-bands, suggesting that, at the considered common angular resolution of 3.0 that corresponds to a physical scale of approximately 0.61 pc, the inferred magnetic field orientation is not significantly affected by temperature or dust grain alignment effects. Second, we find that the relative orientation between gas column density structures and the magnetic field changes progressively with increasing gas column density, from mostly parallel or having no preferred orientation at low column densities to mostly perpendicular at the highest column densities. This observation is in agreement with previous studies by the Planck collaboration towards more nearby molecular clouds. Finally, we find a correspondence between (a) the trends in relative orientation between the column density structures and the projected magnetic field, and (b) the shape of the column density probability distribution functions (PDFs). In the sub-regions of Vela C dominated by one clear filamentary structure, or “ridges”, where the high-column density tails of the PDFs are flatter, we find a sharp transition from preferentially parallel or having no preferred relative orientation at low column densities to preferentially perpendicular at highest column densities. In the sub-regions of Vela C dominated by several filamentary structures with multiple orientations, or “nests”, where the maximum values of the column density are smaller than in the ridge-like sub-regions and the high-column density tails of the PDFs are steeper, such a transition is also present, but it is clearly less sharp than in the ridge-like sub-regions. Both of these results suggest that the magnetic field is dynamically important for the formation of density structures in this region.
Magnetic fields are believed to play an important role in the formation of density structures in molecular clouds (MCs), from filaments to cores and eventually to stars (crutcher2012; heiles2012). However, their particular role in the general picture of MC dynamics is still controversial, mostly due to the lack of direct observations.
A crucial tool for the \colorblackstudy of the interstellar magnetic field is the observation of aligned dust grains, either \colorblackvia the polarization of background stars seen through MCs, or \colorblackvia maps of the polarization of the far-infrared or submillimetre emission from dust in the cloud (hiltner1949; hildebrand1988; planck2014-XIX). Aspherical spinning dust particles preferentially align their rotation axis with the local direction of the magnetic field, producing linearly polarized emission that is perpendicular to the magnetic field (davis1951; lazarian2000; andersson2015). Thus, observations of the linear polarization provide an estimate of the magnetic field orientation projected on the plane of the sky and integrated along the line of sight, .
Recent observations by the Planck satellite (planck2014-a01) have produced the first all-sky map of the polarized emission from dust at submillimetre wavelengths, providing an unprecedented data set in terms of sensitivity, sky coverage, and statistical significance for the study of . Over most of the sky, planck2014-XXXII analysed the relative orientation between column density structures and , inferred from the Planck 353-GHz (850\colorblack-m) polarization observations at 15′ resolution, revealing that most of the elongated structures (filaments or ridges) are predominantly parallel to the \colorblackorientation measured on the structures. This statistical trend becomes less striking for increasing column density.
Within ten nearby ( pc) Gould Belt MCs, planck2015-XXXV measured the relative orientation between the total column density structures, inferred from the Planck dust emission observations, and , inferred from the Planck 353-GHz (850\colorblack-m) polarization observations at 10′ resolution. They showed that the relative orientation between and changes progressively with increasing , from preferentially parallel or having no preferred orientation \colorblackat low to preferentially perpendicular \colorblackat the highest .
The results presented in planck2015-XXXV correspond to a systematic \colorblackanalysis of the trends described in previous studies of the relative orientation between structures and inferred from starlight polarization (palmeirim2013; li2013; sugitani2011), as confirmed by the close agreement between the orientations inferred from the Planck 353 GHz polarization and starlight polarization observations presented in soler2016. Subsequent studies of the relative orientation between structures and have identified similar trends to those described in planck2015-XXXV, using structures derived from Herschel observations at 20″ resolution and inferred from the Planck 353 GHz polarization observations towards the high-latitude cloud L1642 (malinen2016) \colorblackas well as using structures derived from Herschel observations \colorblacktogether with starlight polarization (cox2016).
The physical conditions responsible for the observed change in relative orientation between structures and \colorblackare related to the degree of magnetization of the cloud (hennebelle2013a; soler2013). soler2013 identified similar trends in relative orientation in simulations of molecular clouds where the magnetic field is at least in equipartition with turbulence, i.e., trans- or sub-Alfvénic turbulence. This numerical interpretation, which has been further studied in chen2016, is in agreement with the classical picture of MC formation, where the molecular cloud \colorblackforms following compression of background gas, by the passage of the \colorblackGalactic spiral shock or by an expanding supernova shell, and the compressed gas cools and so flows down the magnetic field lines to form a self-gravitating mass (mestel1965; mestel1984).
In this paper, we extend the study of the relative orientation between structures and by using observations of the Vela C molecular complex obtained during the 2012 flight of the Balloon-borne Large-Aperture Submillimetre Telescope for Polarimetry, BLASTPol (pascale2012; galitzki2014). Towards Vela C, BLASTPol provides unprecedented observations of the dust polarized emission in three different wavelength-bands \colorblack(namely, 250, 350, and 500 m\colorblack) at 2.5 resolution, thus sampling spatial scales comparable to those considered in planck2015-XXXV, but for a more distant, more massive, and more active MC.
Previous studies by the BLASTPol collaboration include \colorblackan investigation of the relation between the total gas column density , the fractional polarization , and the dispersion of orientation angles observed at 500 m towards the Vela C molecular complex\colorblack, presented in fissel2016. Also using the BLASTPol data, gandilo2016 present\colorblacked a study of the variation of in the three observed wavelength-bands towards the Vela C region, concluding that the polarization spectrum is relatively flat and does not exhibit a pronounced minimum at m, as suggested by previous measurements towards other MCs. \colorblackAdditionally, santos2016 present\colorblacked a quantitive comparison between the near-infrared (near-IR) polarization data from background starlight and the BLASTPol observations towards Vela C. \colorblackIn this new paper, we consider for the first time the analysis of the orientations derived from the BLASTPol observations towards Vela C.
This paper is organized as follows. In Section 2, we present the previously observed characteristics of Vela C. In Section 3, we introduce the BLASTPol polarization observations and the Herschel-based estimates of total gas column density. In Section 4, we introduce \colorblackthe method of using the histogram of relative orientations for quantifying the \colorblackrelation between structures and . In Section 5, we discuss the results of our analysis. Section LABEL:section:conclusions gives our conclusions and anticipates future work. \colorblackWe reserve some additional analyses to three appendices. Appendix LABEL:appendix:HROI presents the HRO analysis of Vela C based only on the BLASTPol observations. Appendix LABEL:appendix:refRegions \colorblackpresents a study of the results of the HRO analysis in the BLASTPol maps obtained with the different diffuse emission subtraction methods introduced in fissel2016. Finally, Appendix LABEL:appendix:AquilaRegion presents the HRO analysis of a portion of the Aquila rift based on the \colorblackvalues estimated from the Herschel observations and estimated from the Planck\colorblack-353 GHz polarization observations.
2 The Vela C region\color
blackFigure 1 shows dust column density and magnetic field observations toward the Vela Molecular Ridge (VMR), a collection of molecular clouds lying in the Galactic plane at distances ranging from approximately 700 pc to 2 kpc (murphy1991; liseau1992). The total molecular mass of the VMR, including four distinct cloud components labeled as Vela A, B, C, and D, amounts to about M of gas (may1988; yamaguchi1999). netterfield2009 presented observations of Vela C in dust emission at 250, 350, and 500 microns, obtained using the Balloon-borne Large Aperture Submillimetre Telescope (BLAST, pascale2008). That work confirmed that there are large numbers of objects in the early stages of star formation scattered throughout Vela C, along with a well-known bright compact H II region, RCW 36 (baba2004). hill2011 mapped the dust emission from Vela C using multiple Herschel wavelength bands, and identified five sub-regions with distinct characteristics which they named as North, Centre-Ridge, Centre-Nest, South-Ridge, and South-Nest. The last four of these were observed by BLAST-Pol and are indicated in Fig. 1 and Fig. 2.
blackVela C has long been suspected to be a rare example of a nearby ( pc; liseau1992) and massive ( M; yamaguchi1999) molecular cloud at an early evolutionary stage. This conclusion stems from the observation that despite its relatively high mass, Vela C is characterized by extended regions of low temperature (netterfield2009) and has produced only one or two late-type O-stars (in RCW 36; baba2004).
In the present analysis we use two data sets. First, the Stokes , , and observations obtained during the 2012 flight of BLASTPol. Second, the total column density maps derived from the Herschel satellite \colorblackdust continuum observations.
3.1 BLASTPol observations
The balloon-borne submillimetre polarimeter BLASTPol and its Antarctic flights in 2010 and 2012, have been described by pascale2012, galitzki2014, matthews2014, and fissel2016. BLASTPol used a 1.8 m primary mirror to collect submillimetre radiation, splitting it into three wide wavelength bands () centred at 250, 350, and 500 m. While the telescope scanned back and forth across the target cloud, the three wavelength bands were observed simultaneously by three detector arrays operating at 300 mK. The receiver optics included polarizing grids as well as an achromatic half-wave plate. The Vela C observations presented here were obtained \colorblackas part of the 2012 Antarctic flight, during which the cloud was observed for 54 hours. The Stokes , , and maps \colorblackhave already been presented by fissel2016 and gandilo2016.
fissel2016 employed three methods for subtracting the contribution that the diffuse Galactic emission makes to the measured , , and maps for Vela C; \colorblackwhich referred to respectively as the “aggressive”, “conservative”, and “intermediate” methods. The aggressive method uses two reference regions located very close to the Vela C cloud (one on either side of it) to estimate the levels of polarized and unpolarized emission contributed by foreground and/or background dust unassociated with the cloud. \colorblackThese contributions \colorblackare then removed from the measured , , and maps. Because the reference regions are so close to the cloud, it is likely that they include some flux from material associated with Vela C. Thus, this method may over-correct, hence the name “aggressive.” By contrast, the single reference region that is employed when the conservative method is used is more \colorblackwidely separated from Vela C, lying at a significantly higher Galactic latitude. This method may \colorblacktherefore under-correct. Finally, the intermediate diffuse emission subtraction method of fissel2016 is the mean of the other two methods and was judged to be the most appropriate \colorblackapproach.
Naturally, the use of background subtraction imposes restrictions on the sky areas that may be expected to contain valid data following diffuse emission subtraction. fissel2016 define a validity region outside of which the subtraction is shown to be invalid. With the exception of North and a very small portion of South-Ridge, all of the hill2011 sub-regions are included in the validity region. Unless otherwise specified, we employed the intermediate diffuse emission subtraction \colorblackapproach. In Appendix LABEL:appendix:refRegions, we use the aggressive and conservative methods to quantify the extent to which uncertainties associated with diffuse emission subtraction affect our main results.
As noted by fissel2016, the point spread function obtained by BLASTPol during our 2012 flight was several times larger than the prediction of our optics model. Furthermore, the beam was elongated. To obtain an approximately round beam, fissel2016 smoothed their 500\colorblack-m data to 2.5 FWHM resolution. gandilo2016 \colorblackalternatively smoothed all three bands to approximately 5.0 resolution in order to compare with Planck results for Vela C. For the purposes of this work, we require similarly shaped and nearly round beams at all three wavelengths, but \colorblackwe also do not want to sacrifice resolution. We were able to achieve these goals by smoothing all three bands to a resolution of 3.0 FHWM.
3.2 Column density maps
The column density maps of Vela C were derived from the publicly available Herschel SPIRE and PACS data. SPIRE uses nearly identical filters to BLASTPol, but has higher spatial resolution (FWHM of 17.6, 23.9, and 35.2 for the 250-, 350-, and 500\colorblack-m bands, respectively). Data taken with the PACS instrument in a band centred at 160 m (FWHM of 13.6) were used to provide additional sensitivity to warm dust. These Herschel-based maps were generated using Scanamorphos (roussel2013) and additional reduction and \colorblackdata manipulation \colorblackwas performed in the Herschel Interactive Processing Environment (HIPE version 11) including the Zero Point Correction function for the SPIRE maps. The resulting maps were smoothed to 35.2 resolution by convolving with Gaussian kernels of an appropriate size and then re-gridding to match the Herschel 500\colorblack-m map.
We attempted to separate the Galactic foreground and background dust emission from the emission of Vela C following the procedure described in section 5 of fissel2016. Modified blackbody spectral energy distribution (SED) fits were made for each map pixel using the methods described in hill2011 and \colorblackwith the dust opacity law presented in hildebrand1983 \colorblackfor a dust spectral index . The result of these fits are column density () and dust temperature () maps, both at 35.2 resolution. It should be noted that above a temperature of approximately 20 K, the dust emission is expected to peak at wavelengths shorter than 160 m. For these warmest lines of sight (LOSs) our estimates will have a higher degree of uncertainty. Note \colorblackalso that we computed maps of the column density of atomic hydrogen, , while hill2011 calculated the column density of molecular hydrogen, .
4.1 The histogram of relative orientations
We quantifi\colorblacky the relative orientation between the iso- contours and using the histogram of relative orientations (HRO, soler2013). In this technique, the structures are characterized by their gradients, which are, by definition, perpendicular to the iso- curves. The gradient constitutes a vector field that we \colorblackcan compare pixel by pixel to the orientation inferred from the polarization maps.
We compute the angle between and the tangent to the contours,
For each observation band, characterized by its central wavelength , we assume that is perpendicular to the unit polarization pseudo-vector . The orientation of is defined by the polarization angle calculated from the observed Stokes parameters using
In Eq. 1, as implemented, the norm carries a sign when the range used for is between 0 and 90. For the sake of clarity in the representation of the HROs, we cho\colorblackose the range , in contrast with the HROs presented in soler2013 and planck2015-XXXV, where . This selection does not imply any loss \colorblackof generality\colorblack, given that the relative orientation is independent of the reference vector, that is, is equivalent to .
4.2 Construction of the histograms
We construct the HROs using the BLASTPol observations of polarization at 250, 350, and 500 m and the gradient of the total gas column density map, , estimated from the Herschel observations. The upper panels of Fig. 3 present the maps used in the construction of the HROs. For completeness, we present the HROs calculated from the BLASTPol polarization and the gradient of the intensity observed by BLASTPol in the 500\colorblack-m band, , in Appendix LABEL:appendix:HROI.
The HROs have the advantage of providing a more precise estimate of the total gas column density, but the disadvantage of being estimated with a different instrument and at a different angular resolution. \colorblackThe improvement in angular resolution provides a larger dynamic range for evaluating the HROs at different column densities.
We calculate the gradient of the (or ) maps using the Gaussian derivatives method described in soler2013. To guarantee adequate sampling of the derivates in each case, we appl\colorblacky a derivative kernel computed over a grid with pixel size equal to one third of the beam FWHM in each observation; that is .83 for the BLASTPol map (discussed in Appendix LABEL:appendix:HROI) and .21 for the Herschel map.
We compute the relative orientation angle, , introduced in Eq. 1, in all the pixels where BLASTPol polarization observations in each band are available. We select the polarization observations in terms of their polarized intensity , such that we only consider where the polarization signal-to-noise ratios (S/N) . These values of the polarization S/N correspond to classical uncertainties in the orientation angle 9 .5 and it guarantees that the polarization bias is negligible (serkowski1958; naghizadeh-khouei1993; montier2015).
We compute the HROs in 15 bins, each with equal number\colorblacks of values. This selection is intended to \colorblackexamine the change in with increasing with comparable statistics in each bin. The lower panels of Fig. 3 present the HROs for the lowest bin, an intermediate bin, and the highest bin.
4.3 Relative orientation parameter
The changes in the HROs are quantified using the histogram shape parameter , defined as
where is the area under the histogram in the range . and is the area under the histogram in the range . .. The value of is \colorblacknearly independent of the number of bins selected to represent the histogram if the bin widths are smaller than the integration range.
A histogram peaking at 0, corresponding to mostly aligned with the contours, would have . A histogram peaking at 90, corresponding to mostly perpendicular to the contours would have . A flat histogram, corresponding to no preferred relative orientation between and the contours, would have .
The uncertainty in , , is obtained from
The variances of the areas, and , characterize the “jitter” of the histograms. If the jitter is large, is large compared to and the relative orientation is indeterminate. The jitter depends on the number of bins in the histogram, but does not.
We compare the maps computed from the Herschel observations with the estimates from the BLASTPol polarization observations. Given the distance to the cloud, this corresponds to comparing structures on scales larger than 0.12 pc to on scales larger than 0.6 pc. This difference in scales implies that we are evaluating the relative orientation of structures with respect to a larger-scale component of .
The HROs, shown in the lower panels of Fig. 3, are flat in the lowest \colorblackrange and peak at 90 in the intermediate and highest \colorblackranges across the three BLASTPol wavelength bands. The HROs corresponding to the highest and intermediate \colorblackranges clearly show fewer counts \colorblackfor and more \colorblackfor .
Fig. 4 \colorblackpresents the behaviour of in different bins and across the BLASTPol wavelength bands. The plot shows considerable agreement across the wavelength bands and \colorblackshows that only in the highest bin \colorblackis there a clear indication of perpendicular orientation between and \colorblack, while \colorblackfor the rest of the bins is consistent with no preferred relative orientation.
As in planck2015-XXXV, we characterize the trends in relative orientation \colorblackby assuming \colorblackthat the relation between and can be fit roughly by a linear relation
The measurements \colorblackin each of the BLASTPol wavelength bands are in principle independent determinations of . Consequently, we use the estimates of in each wavelength band as independent points in the linear regression that we use to estimate the values of and .
We observe that the relative orientation is consistent across the three wavelength bands observed in polarization by BLASTPol. This finding \colorblacktakes the results of planck2015-XXXV, which were based exclusively on 353-GHz (850\colorblack-m) polarization observations, \colorblackand extends them not only to a different cloud, but also to the morphology observed in three bands at higher frequencies. The interpretation of the agreement of the HRO analysis across these three wavelength bands is discussed in Section. 5.1.
The results of the \colorblackHRO analysis in Vela C suggest that, as in the MCs studied in planck2015-XXXV, the magnetic field \colorblackplays a significant role in the assembly of the parcels of gas that become MCs, as \colorblackalso suggested by the analysis of simulations of MHD turbulence (soler2013; walch2015; chen2016). We discuss this in Section. LABEL:sec:RegionalStudy \colorblackalong with the possible relation between the relative orientation and \colorblackthe distributions of column density in different \colorblacksub-regions of the Vela C clouds.
5.1 Polarization angles \colorblackat different wavelengths
Figure 4 shows that the relative orientation between the structures and inferred from the three BLASTPol wavelength bands is very similar. This agreement is expe\colorblackcted if we consider the small differences between the polarization angles in the different wavelength bands, which we compute directly and present in the top panel of Fig. 5. The average differences between orientation angles in different bands are \colorblackall less than 7, \colorblackand hence have a negligible effect on the shape of the HROs and the behaviour of as function of .
The most widely accepted mechanism of dust grain alignment, \colorblackthat of radiative torques (RATs, lazarian2000), \colorblackexplains the changes in polarization properties across these bands \colorblackas arising from the exposure of different regions to the interstellar radiation field (ISRF) and to internal radiation sources, such as RCW 36. According to RATs, dust grains in a cold region deep inside the cloud and far from internal radiation sources will not be as efficiently aligned as the dust grains in regions \colorblackwhere they can be \colorblackspun up by \colorblacka more intense radiation field.
To investigate whether the polarization properties across the BLASTPol wavelengths depend on the environment in different regions of the clouds, gandilo2016 evaluated the variations of the polarization fractions, , in different ranges of and temperature, , across the Vela C region. gandilo2016 report\colorblacked that no significant trends of were found in different ranges, and additionally, no trends over most of the -ranges, except \colorblackfor a particular behaviour \colorblackfor the highest data coming from the vicinity of RCW 36.
blackIn a similar way, we \colorblackhave evaluated the differences in polarization orientation angles between different BLASTPol wavelength bands in different ranges in Vela C and summarize the results in Table 5.1, where, for the sake of simplicity, we present only two ranges, \colorblacknamely and , which are the most relevant for the change in relative orientation between \colorblackstructures and . We observe that the differences in orientation angles between bands are \colorblackall less than 7, and although the differences change \colorblacksomewhat with increasing column density, their values do not significantly affect the HROs in the different bins.
Towards the bipolar nebula around RCW 36 (minier2013), the ionization by the H ii region and the related increase in dust temperature can potentially introduce differences in the orientation across the BLASTPol wavelength bands. To test this, we evaluated the difference between the orientation inferred from the observations at different wavelengths in the region around RCW 36, where the dust temperature, derived from the Herschel observations, is larger than 20 K. The results, presented in the bottom panel of Fig. 5, indicate that the mean differences in \colorblackfor the different BLASTPol wavelength bands are not significantly different \colorblackfrom those found in the rest of the cloud. This implies that the magnetic field\colorblack, and the dust that dominates the observed orientations, are approximately the same for \colorblackthe three wavelength bands. This is \colorblacknot unexpected, given that the observed is the result of the integration of the magnetic field projection weighted by the dust emission, and \colorblackmost of the dust is in the bulk of the cloud, which is most likely unaffected by RCW 36.