SMA Proposal 2015A: Constraining the Depths of Filaments
Herschel observations of nearby molecular clouds find ubiquitous filamentary morphology of dust emission projected on the plane of sky (André et al. 2010). Constraining the “depths" of these filamentary structures along the line of sight is very important as project effects play a critical role in the interpretation of observational results including density profiles (Juvela et al. 2012), mass-size relation (Kauffmann et al. 2010), linewidth-size relation (Shetty et al. 2010), and kinematics (Dib et al. 2010). A filament, as a projected two-dimensional structure, can be consistent with various theoretical models. For example, a “pancake-like" structure in the third dimension has been suggested by numerical simulations with supersonic turbulence and strong magnetic fields (Nakamura & Li 2008) as well as those simulations with converging flows (Ballesteros-Paredes et al. 1999). In addition, a “cigar-like" structure may be generated from pure turbulence-driven MHD simulations (Padoan et al. 2001). A few simulations suggest that gravitationally-driven clouds will collapse to sheet-like structures under the influence of self-gravity (Lin et al. 1965).
Investigating the depths of filamentary structures observationally provides a valuable tool to discern between theoretical scenarios and thus provides insights to the formation mechanism of these structures. However, the spatial structure in the line of sight dimension of a single filament is rarely examined (cf., Li et al. 2012). The line of sight “depths” can be derived from the comparison between volume density and column density, and the dependence of the Spectral Correlation Function on the spatial scales of self-similarity. Here we propose to observe the N_2H^+ (3-2) and the ^13CO (2-1)/C^18O (2-1) molecular line emission in the filament FN1 in the Serpens Main molecular cloud. The proposed observations will allow us to independently derive and compare the depths of filaments using these two methods.
The excitation of molecular transitions is sensitive to the local volume density. The ratio of emission from a higher transition to that from a lower transition is characterized by a sharp transition as a function of volume density (Fig. 1; Green & Chapman 1978, Wernli et al. 2007). For example, by measuring multiple transitions of cyanoacetylene (HC_3N), Avery et al. (1982) and Schloerb et al. (1983) derived a volume density for the TMC-1 region, and thus the line of sight depths of the region by comparing to the column density measurements. Also, Li et al. (2012) applied the same method to the Taurus B213 filament (Li et al. 2012) with HC_3N (4-3) and (10-9) transitions. The result in B213 successfully re-confirms that B213 is a cylindrical filament (Hacar et al. 2013) and has a depth of 0.12 pc in the line of sight direction. This result also conforms with the width in the plane of sky of ~ 0.1 pc, as derived from the density profile across the filament (Pelmeirim et al. 2013).
The Spectral Correlation Function (SPF) measures the degree of similarity between two spectra, and is proposed to be applied on analysis of spectral maps (Rosolowsky et al. 1999). Padoan et al. (2001a) further conclude that there is a dependence of the SPF on the “spatial lag” between the two spectra that the SPF takes into account. This dependence of the SPF on the spatial lag shows a power-law relation, and the spatial scales where this power-law relation exists characterize the spatial scales of self-similarity of turbulence (which is assumed to dominates the spectra; Fig. 2). By computing the self-similar scales characterized by the SPF of HI spectra and assuming that the self-similarity of turbulence is confined to the shortest dimension in the 3D space, Padoan et al. (2001b) measured the “depth” (scale height) to be ~ 180 pc in the line of sight direction of LMC, which has a face-on disk structure and thus the shortest dimension along the line of sight (Fig. 2 & Fig. 3).
Serpens Main is classified as a hub of filaments (Myers et al. 2009). The Herschel observations of dust emission and the CLASSy survey of N_2H^+, HCO^+ and HCN line emission further reveal the filamentary nature of the region (Fig. 4; André et al. 2010; Lee et al. 2014). The CLASSy results provide quantitative estimates of the kinematics in these filaments.
The filament FN1 is identified based on the dendrogram analysis and its continuity in the position-position-velocity (PPV) space (Lee et al. 2014). It is selected as our target to test the two methods above because of its large velocity gradient (3.2 km/s), which makes it well distinguishable in the PPV space. Also, FN1 is not associated with any YSOs, and thus does not suffer from kinematics and chemistry complications around YSOs. It is bright in the N_2H^+ (1-0) emission, which suggests the detection of N_2H^+ (3-2) and makes it an ideal target for testing the 1st method described above. The large velocity dispersion of FN1 indicates that trans-/super-sonic turbulence dominates the region, which follows the assumption of the 2nd method above.
Here we propose to observe the N_2H^+ (3-2) and the ^13CO (2-1)/C^18O (2-1) line emission of the filament FN1 in the Serpens Main molecular cloud. The N_2H^+ 3-2 line (at 279.511760 GHz) will be compared with the N_2H^+ 1-0 line from CLASSy, and the line ratio will be used to determine the volume density using RADEX (van der Tak et al. 2007), a radiative transfer code which constrains physical conditions and abundances from observations. The depth is then estimated by comparing to column density maps based on pixel-by-pixel SED fittings from Herschel observations and the 2MASS/NICEST near-infrared extinction. We plan to compare the volume densities based on the SMA observations with the “averaged" column densities from a bigger beam of Herschel, and therefore we do not plan to match the angular resolutions of the two observations.
The second set of observations (^13CO 2-1 and C^18O 2-1, at 220.398684 GHz and 219.560358 GHz, respectively) allows us to test the 2nd method. By calculating the Spectral Correlation Function of ^13CO (2-1) and C^18O (2-1), we will be able to produce a map of the SCF as a function of the spatial lag. By fitting to a power law, we can then derive the depth from the largest self-similar scale characterized by the power law. The result from this method will be compared with the first method.
To obtain maps that cover a sufficient region along the filament and across the filament, we propose mosaicking observations composed of ten pointings in the hexagonal arrangement to Nyquist-sample the region. At 270 GHz, this will give us a coverage of ~ 100 arcsec (~ 0.23 pc at the diatance of Serpens Main) along the filament, and of ~ 80 arcsec (~ 0.18 pc) across the filament. At 230 GHz, the coverage is ~ 1.3 times larger in length unit. (spectral setup...)