A correlation between chemistry, polarization and dust properties in the Pipe Nebula starless core FeSt 1-457
Key Words.:Stars: formation – ISM: individual objects: FeSt 1-457, core 109, Pipe nebula – ISM: molecules – Radiative transfer
Context:Pre-stellar cores within molecular clouds provide the very initial conditions in which stars are formed. FeSt 1-457 is a prototypical starless core and the most chemically evolved among those isolated, embedded in the most pristine part of the Pipe nebula, the bowl.
Aims:We use the IRAM 30m telescope and the PdBI to study the chemical and physical properties of the starless core FeSt 1-457 (Core 109) in the Pipe nebula.
Methods:We fit the hyperfine structure of the NH (10) IRAM 30m data. This allow us to measure with high precision the velocity field, line widths and opacity and derive the excitation temperature and column density in the core. We use a modified Bonnor-Ebert sphere model adding a temperature gradient towards the center to fit the 1.2 mm continuum emission and visual extinction maps. Using this model, we estimate the abundances of the NH and the rest of molecular lines detected in the 30 GHz wide line survey performed at 3 mm with IRAM 30m using ARTIST software.
Results:The core presents a rich chemistry with emission from early (CH, HCN, CS) and late-time molecules (e.g., NH), with a clear chemical spatial differentiation for nitrogen (centrally peaked), oxygen (peaking to the southwest) and sulphurated molecules (peaking to the east). For most of the molecules detected (HCN, HCO, CHOH, CS, SO, CO and CO), abundances are best fitted with three values, presenting a clear decrease of abundance of at least 1 or 2 orders of magnitude towards the center of the core. The Bonnor-Ebert analysis indicates the core is gravitationally unstable and the magnetic field is not strong enough to avoid the collapse.
Conclusions:Depletion of molecules onto the dust grains occurs at the interior of the core, where dust grain growth and dust depolarization also occurs. This suggests that these properties may be related. On the other hand, some molecules exhibit asymmetries in their integrated emission maps, which appear to be correlated with a previously reported submillimetre polarization asymmetry. These asymmetries could be due to a stronger interstellar radiation field in the western side of the core.
Pre-stellar cores within molecular clouds constitute the stage previous to the star formation process. They provide the very initial conditions in which stars are formed. They are typically cold ( K) with temperature gradients decreasing towards the center (e.g., Ruoskanen et al., 2011; Wilcock et al., 2012; Launhardt et al., 2013), and densities cm, with a chemistry affected by molecular freeze-out onto dust grains (e.g., Tafalla et al., 2002; Marsh et al., 2014). Their physical structure can be well explained through a Bonnor-Ebert profile (Bonnor, 1956; Ebert, 1955), i.e., the profile corresponding to an isothermal gas sphere in hydrostatic equilibrium (e.g., Evans et al., 2001; Kandori et al., 2005; Roy et al., 2014). However, their density and temperature gradient structures are still under debate (e.g., Sipilä et al., 2011; Hardegree-Ullman et al., 2013) and the implications of heavy molecular depletion on other physical properties, such as dust grain properties and polarization, are not clear.
FeSt 1-457 (Feitzinger & Stuewe, 1984), also known as Core 109 in Lombardi et al. (2006) catalogue, is a prototypical starless core, as previous studies have shown that this core is quiescent with no IRAS nor Spitzer Space Telescope point sources associated (Forbrich et al., 2009, 2015; Ascenso et al., 2013). Indeed, the internal luminosity, estimated using the non-detection from the 70 m Herschel111Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. image ( Jy pixel) and using the relation between the 70 m flux and the internal luminosity (Dunham et al., 2008), is L L. It is also the most chemically evolved starless core among those isolated, embedded in the most pristine part of the Pipe nebula, the bowl, at a distance of 145 pc (Alves & Franco, 2007). Frau et al. (2015) suggest the presence of two filaments with north-south and east-west directions colliding along the northwest-southeast direction at the bowl region, just where FeSt 1-457 is located.
Frau et al. (2012a) carried out a 15 GHz bandwidth molecular survey at 3 mm towards FeSt 1-457 with the Institute of Millimeter Radioastronomy (IRAM) 30m telescope. They find a rich chemistry (specially compared with most of the other Pipe starless cores): many lines are detected from early- (CH, HCN, CS, CS and CN) and late-time (NH, ND and DCO) molecules, suggesting that FeSt 1-457 is an evolved starless core. Aguti et al. (2007) observed the 3 mm lines of NH, HCO, CS and CO with the IRAM 30m. They find evidence of CO and HCO depletion in the center of the core. However, the NH () may be undepleted to depths of mag of visual extinction.
FeSt 1-457 has a mass of M (Frau et al., 2010; Román-Zúñiga et al., 2010), quasi spherical and compact structure and shows signs of gravitational instability (Kandori et al., 2005; Frau et al., 2010). Aguti et al. (2007) find that FeSt 1-457 might be pulsating, based on expansions of the outer layers. However, their Jeans mass measurement is compatible with the mass of the core and they propose a quasi-stable state near hydrodynamic equilibrium.
The core is embedded in a magnetised medium (Alves et al., 2008, 2014; Franco et al., 2010), which suggests that the magnetic field could be a source of external support. Alves et al. (2014), in a multi scale polarization study towards FeSt 1-457, find a polarization ‘hole’ for radii arcsec which they propose to be the result of loss of grain alignment with the magnetic field due to the lack of an internal source of radiation.
In this work we study the starless core FeSt 1-457 through NH (10) observations obtained with the IRAM 30m and Plateau de Bure Interferometer (PdBI) telescopes222IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).. NH is known to be a very good tracer of the densest inner parts of dense cores as it is not expected to be depleted until densities ¿ cm (e.g., Bergin & Tafalla, 2007). In addition, we present mapping information of 15 molecular lines detected at 3 mm within a frequency range spanning 30 GHz obtained with the IRAM 30m which allowed us also to perform a detailed study of the abundance radial profiles and to relate them to the known grain growth and depolarization in the center.
2.1 IRAM 30m
2.1.1 Line observations
E is the energy of the upper level of the transition.
=A, where A is the Einstein spontaneous emission coefficient and =v is the collisional rate where is the cross section of the collision for each transition and v(3kT/m) is the average velocity of the collisional particles. As H is the most abundant molecule it is used as the dominant collisional particle. We assume T=10 K. The Einstein spontaneous emission coefficients and values are taken from LAMDA database (http://home.strw.leidenuniv.nl/moldata/).
The observations were carried out on July 2012 at the IRAM 30m telescope in Granada, Spain. We used the Eight MIxer Receiver (EMIR) in the E090 configuration. The backend used was the FTS spectrometer with a channel resolution of 195 kHz (0.6 km s at 3 mm), which provided a total bandwidth of 30 GHz covering the frequency ranges from 78.6 to 86.4 GHz, from 87.6 to 102.0 GHz and from 103.2 to 111.0 GHz (see Table 1). In addition, the VESPA (Versatile Spectrometer Array) correlator was used simultaneously with the FTS in order to observe the NH (10) line with a better channel resolution, 20 kHz (corresponding to 0.063 km s), with a total bandwidth of 40 MHz. The observations were done using the frequency-switching mode with a frequency throw of 7 MHz. The maps were done in on-the-fly (OTF) mode covering a region of arcmin 4.5 arcmin centered at RA(J2000), Dec(J2000). In the OTF mode, the maps were done with scans either along the right ascension or either along the declination (with Nyquist separation between scans). This allows to have a better sampling on the observed region. The maps were combined and regrided to have a final pixel size of 6 arcsec. Pointing and focusing were done following the recommended procedure at the telescope, which should give a pointing accuracy of 2 arcsec. Absolute calibration accuracy with EMIR is better than 10%. In this paper we present the spectra in main beam brightness temperature scale, which was obtained by using the efficiencies reported on the IRAM website. The weather conditions were good with system temperatures of 125–192 K and zenith opacities around 0.07. The reduction of the final maps and most of the figures have been done with the gildas333http://www.iram.fr/IRAMFR/GILDAS/ software. Given the highly distorted baselines generated in the frequency switching mode, the spectral baselines were subtracted only over a small frequency range around a given line. The typical rms noise per channel for the VESPA spectral map is K. The half power beam width (HPBW) for each frequency is given in Table 1.
2.1.2 Continuum observations
FeSt 1-457 was observed on April and May 2009 and on January 2010 with the 117-receiver Max-Planck Millimetre Bolometer (MAMBO-II) of the IRAM 30m telescope (previously described in Frau et al. (2010)).
The PdBI observations of NH (10) were performed on several runs in October and November 2011, and March 2012, in the C array configuration, which provides a baseline range from 24 m to 176 m (7.5–55 k at 3.2 mm). The observations were done in mosaic mode with an hexagonal pattern of 12 pointings and with a separation of 18 arcsec. This allows to uniformly cover an area of arcsec centered on RA(J2000), Dec(J2000). The primary beam at 3.2 mm is arcsec. The quasars J1733130 and J1743169 were used as gain calibrators and 3C273, J2015+371, 3C454.3 and J1751+096 as bandpass calibrators. Absolute flux calibration was performed on MWC349 and on the suitable solar system object available at the time of the observations. The absolute flux accuracy is 10%. The NH (10) line was observed in a spectral window of 20 MHz with 512 channels, which provides a spectral resolution of 0.039 MHz (0.125 km s). The system temperatures and the precipitable water vapor values were between –300 K and –6 mm respectively. The data were reduced using clic and mapping packages of the gildas software using the standard procedures. The rms noise per channel achieved was 25 mJy beam. The synthesized beam was 10.6 5.7 arcsec, with a P.A. of 11.94.
2.3 PdBI+IRAM 30m
We combined the NH single dish data taken with the IRAM 30m telescope (with an rms noise per channel of mK) with the PdBI data (rms noise per channel of mK) to add the short-spacing information not detected by the millimetre interferometer. We used the short-spacing processing widget of the mapping package of the gildas software which produces visibilities from the single dish observations with the PdBI spectral resolution and merges them with the PdBI data. After trying different single dish weight factors, we found the best value to be 0.1. This value was the best compromise between adding excessive noise from the PdBI data due to the weak signal and giving to much weight to the single dish data not being able to see the contribution of the interferometer data.
When creating the dirty map we used a -taper of 65 m (20.3 k) to avoid the noise contribution of the longer -distances, recovering the highest signal-to-noise ratio. For the cleaning process we used the Steer, Dewdney and Ito (SDI) algorithm (Steer et al., 1984) to improve some strips that appeared using the Högbom algorithm due to the extended emission. The velocity resolution of the channel maps was 0.12 km s as in the PdBI observations and the cutoff value to stop the cleaning was 1.5 times the rms, 0.06 Jy beam. The synthesized beam was arcsec 6.11 arcsec, with a P.A. of 11.
2.4 Extinction data
We have made use of the high angular resolution extinction maps by Román-Zúñiga et al. (2009, 2010). These maps were constructed from a concerted deep near-infrared imaging survey using several telescopes (ESO-VLT, ESO-NTT and CAHA 3.5 m) as well as the 2MASS data. These maps have a resolution three times higher than the previous extinction map of this cloud by Lombardi et al. (2006), allowing to resolve structures down to AU.
3.1 NH (10)
3.1.1 VESPA IRAM 30m
In Figure 1a we present the moment-zero map (i.e. velocity integrated intensity map) of the NH line emission observed with the IRAM 30m telescope. The moment-zero emission was computed in the km s velocity range, which covers the three central hyperfine lines. The structure is compact with a size of arcmin ( au) and the intensity increases towards the center of the map up to 2 K km s.
In order to infer the physical and chemical properties in FeSt 1-457 from the NH (10) IRAM 30m data, we used the HfS tool444http://ascl.net/1607.011 (Estalella, 2016) to fit the hyperfine structure of our spectra. With the HfS_fit_cube procedure we could fit all the spectra of our data cube pixel-by-pixel. The fit was done only for the spectra with a peak intensity larger than five times the rms noise. We obtained the physical parameters , and and derived the excitation temperature and the column density following Caselli et al. (2002).
|(K)||(km s)||(km s)||(K)||(see Fig. 1c)|
A, product of the amplitude (A, where is the filling factor, is the Planck function in units of temperature, is the excitation temperature and is the cosmic microwave background temperature) times the optical depth of the main component.
, central velocity of the main component.
, linewidth of the hyperfine components.
, optical depth of the main component. (See Estalella, 2016, for further details of the HfS fitting procedure.)
The procedure used for fitting the hyperfine structure of NH (1–0) assumes local thermodynamic equilibrium (LTE) for all the seven hyperfine lines of the transition. However, it has been found that the hyperfine lines F, F=1,01,1 and 1,21,2 can be out of LTE. This is the case of the quiescent core L1512, where these excitation anomalies are attributed to collisional pumping, if the collisional coefficients of the hyperfines were different, or to radiative trapping effects depending on the different optical depth of the hyperfines (Caselli et al., 1995; Daniel et al., 2006). Thus, in order to avoid this problem, we performed the fit of the hyperfine structure of NH (1–0) using only the five hyperfine components without excitation anomalies. In Fig. 2 and Table 2 we show the results from the fit for six selected positions (shown in Fig. 1c) of FeSt 1-457. As can be seen in Fig. 2, although there are some slight discrepancies in the amplitudes of the two hyperfine lines out of LTE (the two with the highest velocity), the synthetic spectra (assuming LTE) fit very well the observed spectra.
In Figure 1b we show the resulting NH column density map overlapped with the 1.2 mm dust continuum emission. The values range from 310 cm at the edges to 9.010 cm towards the center, with hints of an arc-like structure near the continuum peak marginally resolved (see Section 3.1.3 below).
The velocity map shown in Fig. 1c presents a very smooth gradient in the northeast-southwest direction. The velocity ranges from 5.72 km s at the northeast to 5.90 km s at the southwest. Excluding the southwesternmost region, the velocity gradient along the northeast-southwest direction is 1.8 km s pc. Aguti et al. (2007) find a similar velocity pattern in the CO (10) and (21) channel maps.
The typical line widths (see Fig. 1d) are 0.17–0.23 ( km s), except in the southwesternmost region, where it raises up to 0.30 km s (also in agreement with the results from Aguti et al., 2007). Note that the eastern side of the core shows the lowest line widths. The thermal line width for NH has a value of 0.12 km s, for a kinetic temperature of 10 K. Thus, the three-dimensional non thermal dispersion () ranges between 0.09 and 0.21 km s. The isothermal sound speed value is 0.19 km s, which gives a Mach number (defined as /) between 0.46 to 1.1 (following Palau et al., 2015). These values indicate that the non thermal motions seem to be subsonic (as reported by Frau et al., 2010, 2012b; Alves et al., 2014) and the thermal pressure seems to be dominant over the turbulent pressure in the core (in agreement with Aguti et al., 2007) except at the southwestern corner where the ratio seems to be more balanced.
3.1.2 PdBI data
In Figure 3 we show a section of the channel map showing the NH (10) emission detected with the PdB interferometer. The weak emission () is better detected in the second panel corresponding to the strongest line of the three central hyperfine lines, at a velocity of 5.80 km s. The last panel of Fig. 3 shows the spectra (in red) at the position of the detection. The IRAM 30m spectra (in black) is also shown as comparison, and we can see that the hyperfine structure is also seen in the PdBI spectrum indicating that indeed there is a real NH detection from the PdBI. The emission filtered out by the PdBI with respect to the IRAM 30m is estimated to be , from a comparison of the PdBI spectra (convolved with a Gaussian to obtain the IRAM 30m beam size) and the IRAM 30m spectra at the peak position. Given the smallest antenna baseline of PdBI observations, the largest angular scale detectable by the PdBI observations is arcsec or au (following Appendix of Palau et al., 2010). Thus, about of the emission detected with the IRAM 30m comes from structures at scales au.
3.1.3 IRAM 30m+PdBI
In Figure 4 we show the moment-zero map of the merged IRAM 30m and PdBI data (see Section 2.3), overlapped with IRAM 30m MAMBO-II map of the dust continuum emission at 1.2 mm. The peak is 1 Jy beam km s and the arc structure hinted at the column-density single-dish map (panel (b) of Fig.1) is now clearly seen.
3.2 Chemical survey (FTS)
|Molecule||()||S/N||Peak shift ()||()|
Beam size after a Gaussian smoothing of 3 pixels (pixel size ).
Peak shift with respect to the 1.2 mm dust continuum peak.
Position uncertainty given by (Reid et al., 1988).
In this section, we describe the maps of 15 molecular lines detected with the IRAM 30m FTS spectrometer towards FeSt 1-457 (see Figure 5 and Table 1). To generate the maps we performed a gaussian smoothing of 3 pixels and we used the map_aver task of greg software to average the intensity of only the channels with detected emission to obtain a better signal-to-noise ratio and to better characterize the structure of the faintest lines. As presented in previous works (Frau et al., 2010, 2012b) we observed a rich chemistry with emission from early- (e.g., CH, HCN, CS) and late-time molecules (e.g., NH). For the nitrogen-bearing molecules (e.g., HNC and NH; panels (a) to (f)) the gas emission is very compact and the peak coincides well with the peak of the 1.2 mm dust continuum emission. A similar behavior is seen in CH (panels (g) and (h)). However, for CH and molecules containing oxygen in our sample (e.g., HCO, CHOH; panels (i) to (k)) the emission is shifted towards the southwest with respect to the dust. An extreme case of this would be the CO and CO molecules, which present strong extended emission peaking to the southwest, at and of the dust continuum, respectively (panels (l) and (m)). For the molecules containing sulphur (CS and SO, panels (o) and (p)) the emission is located to the east with respect to the dust peak, and , respectively. The peak offsets of the molecular lines with respect to the 1.2 mm dust continuum peak are comparable to the beam sizes of the gaussian smoothed integrated intensity maps (; see Table 3) and therefore significant. Panel (n) shows the emission of a second (and fainter) velocity component of the CO emission at 3 km s.
Regarding the intensity of the lines, apart from the CO and CO which do not trace the core well, the brightest lines are HNC, HCO and NH. We found the weaker lines to be CH, NHD and HCN. This is in agreement with the previous observations by Aguti et al. (2007). However, they find the morphology of NH more compact compared to our data. This difference could be due to the better S/N of our observations which allowed us to detect weaker extended emission. As the FTS backend has poor spectral resolution, the specific values of the line intensities cannot be compared with other works due to the spectral dilution. This does not affect the relative positions as the lines are narrow throughout the core. Note that the VESPA and FTS NH maps present very similar structure (see Figs. 1a and 5e).
4.1 The Bonnor-Ebert sphere model fit
A suitable model to fit the Pipe Nebula starless cores is the Bonnor-Ebert sphere (Bonnor, 1956; Ebert, 1955). It describes a self-graviting, pressure-confined, isothermal gas sphere in hydrostatic equilibrium. The density profile can be derived by solving the Lane-Emden equation
where is the non-dimensional radius,
and the logarithm of the density contrast,
, , and are the radius, volume density and central volume density, respectively. The sound speed, , is defined as . , , , and are the gravitational constant, the Boltzmann constant, the temperature, and the mean molecular mass, assumed to be 2.33. Imposing boundary conditions at the core center, forcing the density to be and its derivative to be 0 (i.e., and at ), Eq. 1 can be solved numerically. The last ingredient left is the outer confining pressure, , exerted at the outer radius, , from which one can derive the parameter () that uniquely characterizes the Bonnor-Ebert solution. The critical value is , which corresponds to . For values larger than the equilibrium is unstable to gravitational collapse.
In order to fit the observational data of FeSt 1-457, synthetic 3D cores were generated with density profiles obeying the numerical integration of a Bonnor-Ebert sphere (Eqs. 1, 2, and 3) with a given set of parameters. Then, the emission was integrated along the line-of-sight to generate 2D synthetic maps following a similar recipe as in Frau et al. (2011). We took into account the presence of the molecular cloud surrounding the core by adding a term in the extinction data, , which is constant along the extinction map. Since the IRAM 30m bolometer filters out the extended emission, we assumed that the molecular cloud does not contribute to the 1.2 continuum emission. Two maps were generated, a visual extinction map and a 1.2 mm dust continuum emission map, convolved to the respective observational beams ( and from Román-Zúñiga et al., 2010; Frau et al., 2010, 2012b, respectively). A dust opacity of cm g was adopted for dust grains with thin ice mantles and for gas density cm (Ossenkopf & Henning, 1994). Finally, radial profiles of the observed and synthetic maps were obtained using the ellint task from the Miriad software (Sault et al., 1995). This task averages the intensity in concentric annuli. The quality of the fit was assessed by computing the residual fit of the two radial profiles. Figure 6 shows the comparison between the observational (black lines and dots) and synthetic Bonnor-Ebert emission radial profiles (green (long-dashed) lines).
|( cm)||( au)||()||( cm)||(M)||(mag)||(yr)|
|BE + T||2.7||9.5||No|
Parameters fitted for the isothermal BE model. The uncertainties of the fitted parameters , and were estimated by analyzing the increase of the residual fit by varying the parameters. The uncertainties of the derived physical parameters , and were assessed through error propagation analysis.
Temperature used to determine the sound speed value, .
Based on Aikawa et al. (2005) results following the evolution of a marginally unstable Bonnor-Ebert sphere ( , , where is the internal gravity to pressure ratio).
The best fit was obtained for the values shown in Table 4. The first row lists the fitted parameters of the Bonnor-Ebert profile (, , and ), the physical parameters derived (, , , and mass), the fitted background visual extinction arising from the surrounding ambient medium (), the gravitational stability status, and an estimate of the age (Aikawa et al., 2005). There is no degeneracy between the fitted parameters , , and as the visual extinction map does not depend on temperature and and modify the height and width of the radial profile, respectively. The temperature only modifies the 1.2 mm dust continuum emission map. We found that the temperature derived from the Bonnor-Ebert fit ( K) is in fair agreement with the temperature derived from ammonia observations ( K; Rathborne et al., 2008). The value obtained for the derived parameter was . The error was estimated through error propagation analysis, being and the main contributors to its uncertainty (see Table 4). This value is significantly higher than the critical value (6.5), thus the core is gravitationally unstable, in accordance with Kandori et al. (2005) results.
FeSt 1-457 is observed with an excellent signal-to-noise to test the Bonnor-Ebert scenario. By using the isothermal Bonnor-Ebert sphere we found a good fit for the map but non-negligible differences in the dust emission profile (see green (long-dashed) line in Figure 6). This can be interpreted as a departure from the isothermal approximation because the extinction map (), contrary to the dust continuum emission, is only sensitive to the column density and does not depend on temperature. Previous studies in starless cores (e.g., Crapsi et al., 2007) show that those with cm may have an inner temperature gradient. These cores are colder at the center, reaching temperatures as low as 6 K, than at the outer shells, where they may be heated by the interstellar radiation field (e.g., Marsh et al., 2014). We tested different temperature profiles to check whether the fits improved. We found that a temperature profile following:
( au) with K at the center of the core and increasing until K at a radius of 9000 au fitted much better the data. The second row of Table 4 shows the best fit parameters of the Bonnor-Ebert+temperature gradient model. Figure 7 shows the Bonnor-Ebert density and temperature profiles that appear to fit best the data. In addition, the red line in Figure 6 shows the predicted 1.2 mm dust intensity and extinction radial profile from this Bonnor-Ebert+temperature gradient model. Forbrich et al. (2015) also find a clear decrease of the effective dust temperature towards the center of FeSt 1-457 from Herschel observations. However, they find the lowest value at the center to be 13.5 K, higher than kinetic gas temperature derived from ammonia (9.5 K; Rathborne et al., 2008) and higher than the temperature at the center of the core adopted by us. They argue this difference could be related to the effect of averaging the emission from Herschel along the line of sight which would take into account dust from the cloud at higher temperatures. Note that the temperature profile we found fits well the FeSt 1-457 core is similar to the one found for the L1544 core (Crapsi et al., 2007), a core with significantly higher density, but also to core 16 from Marsh et al. (2014), which has a density similar to that of FeSt1-457.
Even though we did not modify the Bonnor-Ebert density profile (lower panel of Figure 7), which assumes a constant temperature, we finally considered the temperature profile shown in the upper panel of Figure 7 to generate the synthetic maps. This apparent inconsistency is not important in our case. Sipilä et al. (2011) show that the isothermal and non-isothermal Bonnor-Ebert density profiles are fairly similar. In addition, as the gas pressure is proportional to the temperature, reducing the temperature by half, reduces the pressure by half as well, which makes the core even more unstable against gravity. Therefore, this model is good enough to say that FeSt 1-457 has a density profile of a very young core, it is gravitationally unstable and seems to be colder at the center than in the outer parts.
Once the physical model of temperature and density of the core was determined (see previous section), we estimated the abundances for the molecular lines detected with the IRAM 30m observations.
We used the Adaptable Radiative Transfer Innovations for Submillimeter Telescopes (ARTIST; Brinch & Hogerheijde, 2010; Padovani et al., 2011, 2012; Jørgensen et al., 2014) software to generate a synthetic spectral cube of the molecular lines detected. We assume that the source is spherically symmetric with the density and temperature radial profiles derived from the Bonnor-Ebert model derived in the previous section.
For the simulations we assumed the dust temperature equal to the gas temperature. We assumed no velocity field in the core. The velocity gradient in the core is very small ( km s beam at the center of the core), so this does not affect the results. Initially, the only free parameter used in ARTIST was the abundance. First, we assumed a constant value for the abundance. If the model did not fit well the observed intensity profile, we used a step function with two or three different abundances to obtain more accurate fits. We systematically tried different values for the radius at which there was a change in abundance, until obtaining the smallest parameter. One or two step functions (at a radius of arcsec ( au) and arcsec (14500 au)) for the abundance was necessary to obtain good fits for 10 out of the 12 molecules, in which a constant abundance value did not fit well the observed data. We made use of the Leiden Atomic and Molecular Database (LAMDA)555http://home.strw.leidenuniv.nl/moldata/ to load the collisional coefficients of the observed molecules (Green & Thaddeus, 1974; Green & Chapman, 1978; Flower, 1999; Chandra & Kegel, 2000; Daniel et al., 2005; Lique et al., 2006a, b; Rabli & Flower, 2010; Yang et al., 2010). The spectral cube generated with ARTIST was convolved with a Gaussian to mimic the angular resolution of each molecular line observed. The output from ARTIST is given in units of brightness temperature.
In order to compare both the observed and the synthetic molecular line maps, we generated line intensity profiles for both data sets in the same way using the Miriad software. We first computed integrated intensity maps (moment-zero) using the moment task over a velocity range that included all the emission. Then, we used the ellint task for the integrated intensity maps to compute the line radial profiles with annuli of 10 arcsec width, which is a value between one third and one fifth of the angular resolution of the observed molecular lines.
4.2.1 NH abundance fit
To obtain the moment-zero map of NH (see Fig. 1a), we only included the three central hyperfine lines to avoid the anomalous hyperfine lines (see Section 3.1.1) and we obtained a good fit of the data. The high spectral resolution ARTIST fit is shown in the lower panels of Fig. 2 (note that ARTIST handles line overlapping: Brinch & Hogerheijde, 2010). We first used a constant abundance (with respect to H) to fit the radial profile. A value of fitted well the data except for the outer radius where the model gave slightly higher values (blue dashed line of Fig. 8). Thus, we used a step function varying the radius at which there was a change in abundance systematically in steps of 10 arcsec, and a better fit was obtained with values of and for smaller and larger radius than 55 arcsec ( au), respectively (red line of Fig. 8). The error of the radius where the abundance changes is arcsec, estimated from a analysis (e.g., Gibb et al., 2000). We also estimated the abundance uncertainty for the NH line to be less than . This uncertainty was estimated from a analysis using different values of the abundance at the same range of radii of the core.
4.2.2 FTS molecular lines abundance fits
We followed the same procedure used for NH to fit the other molecular lines detected with the FTS spectrometer, except for CH for which the collisional coefficients file was not available in the LAMDA catalogue. HCN and CH 2(0,2)1(1,1) were not fitted as they present weak emission and we had better signal to noise in the similar molecules/transitions HCN and CH 2(1,2)1(0,1). The observed intensity profiles are presented in Fig. 9 (open circles). Our ARTIST modeling indicated that some molecular lines are well fitted with just one abundance value. This is the case of HCN and CH 2(1,2) (see panels (c) and (e) of Fig. 9). HNC and NHD are well fitted with a one step function, one value at the inner part of the core until 55 arcsec ( au) radius and a smaller value at larger radii (see panels (a) and (d) of Fig. 9). However, our ARTIST model revealed that most of the lines needed 3 different abundance values changing at 55 and 100 arcsec ( and 14500 au) radius to obtain a good fit (radii where we assumed a change in abundance are marked in Fig. 9 by vertical dashed lines).
We estimated the abundance uncertainty for the CHOH (one of the molecules with the lowest signal-to-noise ratio) and HCN (one of the molecules with the highest signal-to-noise ratio) following the same procedure as with the NH giving similar results.
In all cases where we introduced a 2 step function profile in the abundance, values are higher in the outer part of the core and decrease towards the center. We consider a slightly different analysis for the abundances of CO and CO lines. As their emission is very asymmetric presenting their peak at the southwest part with respect to the dust continuum (see panels (l) and (m) in Fig. 5), we divided the image in two sections, one including the strongest emission (southwest) and the other including the faintest emission to the northeastern part, which resembles more the emission pattern of the other species. Thus this part should trace more reliably the behavior of this molecule in the core. We performed the same procedure for the two sections separately. Both molecular lines show very flat profiles fitted with a 2 step function for the abundance as the emission is very extended (see panels (j) and (k) of Fig. 9). Table 5 summarizes the abundances for each molecule. Note that by using the main beam brightness temperature scale the intensity of the lines with extended emission, namely CO and specially CO, may be overestimated. This may result in some overestimation of their abundances but not of the observed relative drop within the core.
4.3 Estimation of the magnetic field strength
We made use of the polarization data presented in Alves et al. (2014) to estimate the magnetic field strength on the plane of the sky. The observations were performed at the APEX 12m telescope at 345 GHz obtaining a FWHM of . The magnetic field lines are relatively uniform with a weighted mean position angle of (from north to east direction).
Using the Chandrasekhar-Fermi technique we are able to estimate the magnetic field strength. We used the Ostriker et al. (2001) approximation for estimates of the plane-of-sky field strength under strong-field cases (). The projected field strength () is given by:
where the number density of molecular hydrogen is taken as , is the observed line width and is the dispersion of the polarization angles.
The observed dispersion , is produced by contributions from the measurement uncertainty of the polarization angle and the intrinsic dispersion . Taking into account every pair of polarization angles (PA) and their uncertainties according to the equation
where is the number of data pairs, we obtained
5.1 Molecular depletion
After our analysis with ARTIST (see Section 4.2), we found that molecular abundances are well fitted with three values, presenting a decrease of abundance towards the inner region of the core in most of the molecules detected (7 out of 12). The simplest explanation for the decrease of molecular abundance is that the molecules are depleted onto the dust grains once the density of the core increases and the temperature decreases. Some of these molecules are strongly depleted in the core interior with a decrease of abundances by at least 1 or 2 orders of magnitude. The strongest depletion is found in CO and CO with a difference in abundance of 2 orders of magnitude, from to and to , respectively. Aguti et al. (2007) find CO is depleted only by a factor of but by averaging the abundance along the line of sight. CS and SO also present strong depletion with a decrease of abundance of a factor of (it is known that sulphurated molecules tend to deplete quite fast in chemical models of dense cores, e.g., Ruffle et al., 1999). Similar results are found in Tafalla et al. (2002, 2004) in several starless cores. We also found a decrease in abundance of 1 order of magnitude in HCN and HCO. The HCN shows emission peaks at both sides of the continuum peak in an east-west strip. The decrease of emission around the continuum peak is probably an indication of heavily depletion at that position. Curiously, the shape of the HCN and HNC emissions are quite different close to the continuum peak. Loison et al. (2014) found that the HCN/HNC ratio tends to decrease when carbon atoms or CO are depleted, due to isomerisation of HCN into HNC. In fact, we see an increase of abundance of a factor of of HNC at the inner region of the core. Thus, the combination of depletion of HCN plus the conversion of HCN into HNC could be enough to explain the observed difference in emission.
Our best studied molecule, NH, is well fitted with two abundance values with a small increase towards the interior of the core (see Section 4.2.1). The abundance value is in agreement with Aguti et al. (2007) results. In Section 3.1.1, we showed that the NH column density follows an arc-structure around the 1.2 mm continuum peak (see Fig. 1b) which is clearly seen using the combined emission of IRAM 30m and PdBI (see Figure 4). This might not be seen in the ARTIST analysis because we averaged the emission in concentric annuli and the feature is only present at a very small scale of 5 arcsec or 725 au, suggesting that NH might be frozen-out onto the dust grains at this scale, which corresponds to a density of cm. Aguti et al. (2007) also suggest posible depletion of NH in FeSt 1-457 at depths ¿40 mag of visual extinction, which corresponds to radii au and densities cm. Our results are consistent with previous observations towards starless cores, where NH is depleted at densities cm (e.g., Belloche & André, 2004; Pagani et al., 2007). The arc-like structure is not likely due to opacity effects as in the calculation of the column density we already took opacity into account. Higher angular resolution and with even better sensitivity observations are needed to discard other explanations for the arc structure seen in NH (such as a real physical structure).
NHD appears to have a significant abundance only in the inner region of the core, at radius arcsec ( au). Previous observational studies have shown evidence of NHD abundance increase towards starless cores (e.g., Busquet et al., 2010; Masqué et al., 2013). Deuterated ammonia is expected to be abundant in the coldest and densest parts of starless cores, where the depletion of CO enhances the deuterium fractionation through a combination of gas phase (e.g., Roberts et al., 2004; Hatchell et al., 2013) and surface reactions (e.g., Fedoseev et al., 2015; Fontani et al., 2015).
Finally, HCN and CH are well fitted with a constant abundance value throughout the core. Tafalla et al. (2006) study the molecular abundances of two starless cores (L1498 and L1517B) and find depletion of 1 order of magnitude of HCN towards the center of L1498 and of only a factor of 2 in L1517B. However, they find that HCN seems to survive in the gas phase to higher densities than other species as CO and SO. They also find a similar behavior in L1498 for CH and suggest that the chemistry of CH and HCN could be related. In our case, we can only see some depletion effect in the molecular profiles of HCN and CH in the innermost position closer to the center of the core ( arcsec, see panels (c) and (e) of Fig. 9).
In summary, for most of the molecules detected in our sample (HCN, HCO, CHOH, CS, SO, CO and CO), we found a clear decrease in their abundance towards the inner region of the core.
5.2 Chemical differentiation in the core’s outskirts
As we have seen in Section 3.2, FeSt 1-457 presents a clear chemical differentiation for nitrogen, oxygen and sulphurated molecules. Their emission appears with different offsets with respect to the peak of the 1.2 mm dust continuum emission (see Section 3.2 and Table 3).
We computed the CS/CS, SO/SO and CO/CO line intensity ratios from the integrated spectra of an area of 30 arcsec radius around the position where the main isotopologue line is brighter. Because these ratios are done for the same rotational transition, they depend only on the optical depth and abundance ratio of the isotopologues (we adopted an abundance ratio of 5.6 for CO/CO and 24 for S/S: Wilson & Matteucci, 1992; Chin et al., 1995). The optical depth for CS (21), SO 3(2)2(1) and CO (10) transitions is 1.54, 2.11 and 2.14, respectively. We expect this value to decrease as we go away from the peak. Thus, the observed different morphologies are not likely due to opacity. In addition, the critical densities and energies of the upper level of NH (10), CS (21) and HCO (10) are similar, cm and K, respectively (from LAMDA database; see Table 1). Therefore, we can exclude different excitation conditions as well. This suggests that different types of molecules are tracing different chemical conditions in the core.
The characteristic asymmetries in the emission of CH, HCO and CHOH, peaking (south)west of the dust peak, could be evidence of the penetration of UV radiation into FeSt 1-457.
Moreover, HCN and HCN also show a slight displacement of their emission peak towards the southwest. This may be a similar situation to the emission enhancement of these molecules in PDRs (photo-dominated regions) and in molecular condensations ahead of Herbig-Haro objects (e.g., Hollenbach & Tielens, 1997; Girart et al., 1998, 2002; Viti et al., 2006). In the second case, chemical models show that this enhancement is due to the UV radiation arising from the Herbig-Haro objects (Viti & Williams, 1999; Viti et al., 2003). Viti et al. (2003) find that the UV radiation affects the chemistry enhancing HCO and CHOH for mag, meaning that the enhanced emission should trace the most outer layer of the core. Additionally, PDR models show that CH reach higher abundances at somewhat less deep layers (lower values) than HCN. Indeed, CH has been found to peak close to the edge of PDRs as its production is enhanced by the UV radiation field in a relatively narrow range of visual extinction values (e.g., Pety et al., 2005; Morata & Herbst, 2008; Rimmer et al., 2012). Moreover, in some PDR models (e.g., Morata & Herbst, 2008; Rimmer et al., 2012), HCN also has an abundance peak at similar layers to HCO.
FeSt 1-457 is, in projection, embedded in a diffuse molecular cloud with average mag. Thus, the enhanced CH, HCO and CHOH emission could only happen if the core is near the border of the molecular cloud, such that one side of the core is exposed to the interstellar UV radiation without much absorption. We do not expect the penetration of the UV photons to be too large, but it is probably strong enough to produce some differences in the distribution of the molecular emission. Infrared extinction maps show that FeSt 1-457 is surrounded by gas with relatively low extinction, mag (Román-Zúñiga et al., 2010). If the medium around FeSt 1-457 is not homogeneous, some UV radiation from a nearby OB star or the interstellar radiation field could be penetrating quite deep into the (western side of the) core. Indeed, Gritschneder & Lin (2012) proposed that the Pipe Nebula might be an H II region shell swept by the nearby Ophiuchi (a B2 IV Cephei star). Ophiuchi lies in a direction approximately west-northwest of FeSt 1-457 and might be the source of the UV radiation required to explain the morphology of the emission of CH, HCO and CHOH. Future works must be done to confirm this possible scenario.
Regarding the asymmetries of CS and SO emission (see panels (o) and (p) in Fig. 5, respectively), it has been studied that in PDRs (see Morata & Herbst, 2008) CS has a relatively shallow abundance closer to the edge of the PDR (around or inwards the CH peak) and a higher abundance in inner layers, while SO has high abundances in even deeper layers into the PDR. The combination of depletion and the influence of the UV field could explain the shape of the emission of these maps. If the eastern side of the core is more shielded from the radiation, these molecules will reach higher abundances and have their emission peaks there, while they will have lower abundances on the western side of the core (more markedly for SO), and they will be depleted towards the center of the core. Finally, NH and deuterated molecules, from both the observational and chemical point of view, are supposed to be abundant in the inner and most shielded parts of the cloud (e.g., Roberts et al., 2003; Crapsi et al., 2005), which is what our emission maps show (see Fig. 5 and 9).
5.3 A correlation between depletion, grain growth and polarization
As we have seen in Section 4.2, and discussed in Section 5.1, molecular abundances are well fitted with two or three values, presenting a decrease of abundance towards the inner region of the core in most of the molecules detected. This change in the chemical properties suggests FeSt 1-457 experiences a variation in the physical properties of its inner region.
It is interesting to note that Forbrich et al. (2015) find evidence of grain growth at the inner region of the core from Herschel-derived dust opacity results and near-infrared extinction measurements. Depletion of the molecular gas onto the dust grains due to a decrease of temperature and increase of density in the center of the core could make easier for the grains to stick together and contribute to the grain growth seen by Forbrich et al. (2015). This is supported by the fact that we found a depletion radius very similar to the radius where Forbrich et al. find grain growth. It has been studied that water ice on the surface of dust particles enhance grain-grain adhesion favoring grain growth (e.g., Gundlach & Blum, 2015; Wang et al., 2005). Furthermore, Liu et al. (2013) find that CO depletion positively correlates with a decrease of the dust emissivity index, which could be related to the size of the dust grains (e.g., Lommen et al., 2007; Ricci et al., 2012; Piétu et al., 2014). This also agrees with our results of low abundance of CO at the center of the core (see Fig. 5) and the grain growth seen by Forbrich et al. (2015).
In a different work, Alves et al. (2014) present a study of the polarization properties in FeSt 1-457 at different wavelengths and find that the emission is more polarized to the western side of the core (see Alves et al., 2014, figure 1). It is globally accepted that non-spherical dust grains are aligned perpendicularly with respect to magnetic field lines producing linearly polarized thermal continuum emission (Davis & Greenstein, 1951; Hildebrand, 1988). One of the most important theories for the dust grain alignment is via radiative torques (Dolginov & Mitrofanov, 1976; Draine & Weingartner, 1996, 1997; Lazarian & Hoang, 2007). Thus, the stronger polarized emission to the west also supports the idea of a UV radiation field penetrating into the core from the west which would be affecting not only the polarization properties but also the chemistry in the core (see previous section).
In Fig. 10 we show the emission of 4 molecules peaking to the southwest (CH and HCO) and to the east (CS and SO) of the dust peak, overlaid with the position angles of the polarization data from Alves et al. (2014). The CH and HCO emission seem to correlate with the stronger polarized emission towards the west. On the other hand, the emission peaks of CS and SO seem to present an anti-correlation with the polarized emission. To study further these possible correlations, we performed a 1-D slice across the core passing through the CH and CS peaks (black arrows in Fig. 10). In Fig. 11 we show the polarization intensity (blue) and the emission of CH (black) and CS (red) along the slice. The polarization intensity presents a similar distribution and seem to correlate well with the CH emission and anti-correlate with the CS emission. To quantify these correlations we performed the statistical tests Kendall’s and Spearman’s 666http://www.statsoft.com/textbook/nonparametric-statistics/ and found a good correlation (, ) between CH emission and polarization intensity and anti-correlation values (, ) between CS and polarization intensity. More observations are necessary to further study these results.
On the other hand, Alves et al. (2014) also find a steep decrease in the polarization efficiency at visual extinctions () larger than 30 mag. Alves et al. (2014) propose the lack of an internal source of radiation results in a loss of grain alignment with the magnetic field, which is consistent with the theory of dust grain alignment via radiative torques. Our work suggests that depolarization could be produced as a combination of lack of internal source and dust grain growth possibly affected by molecular depletion. Due to the ‘grain clustering’ yielding to larger grains, the elongated shape of the grains could be distorted. The paramagnetic nuclei of the grains would be surrounded by a thick layer of ice (unpolarized) and the alignment of the grains could be harder to achieve resulting in a depolarized inner region as seen by Alves et al. (2014).
Therefore, we conclude that depletion, grain growth and depolarization seem to be correlated in FeSt 1-457.
5.4 Magnetic properties of FeSt 1-457
Previous studies in star forming cores have shown that magnetic fields can play an important role in their evolution (e.g., Girart et al., 2006).
Magnetic forces could prevent a cloud from collapsing if its mass-to-flux ratio is below the critical value,
where M is its mass and is the magnetic flux through it, derived from the mean magnetic field and the radius of the cloud cross-section perpendicular to the magnetic field. The critical mass-to-flux ratio is (Nakano & Nakamura, 1978), where is the gravitational constant. We used the ratio in terms of the column density following eq.(7) of Pillai et al. (2015)
Frau et al. (2010) obtain a core+cloud column density cm. From our Bonnor-Ebert model fit (see Section 4.1) we found the background visual extinction arising from the surrounding medium () to be 9.5 mag which corresponds to a column density of cm. Thus, we adopted a column density for the core of cm. On the other hand, we assumed G as Alves et al. (2014) find the magnetic field direction mainly onto the plane-of-sky. We obtained a ratio of 6.5 (magnetically supercritical) which implies that gravity dominates over the magnetic support. Our Bonnor-Ebert model fit showed that the core is gravitationally unstable (see Section 4.1). Finally, we can see that the magnetic field is not enough to avoid the collapse.
We have used the IRAM 30m telescope and the PdBI to study the chemical and physical properties of the starless core FeSt 1-457 (Core 109) in the Pipe nebula. Our main conclusions are as follows:
We fit the hyperfine structure of the NH (10) IRAM 30m data. This allows to measure with high precision the velocity field and line widths in the core. The NH emission shows a clear southwest-northeast velocity gradient of 1.78 km s pc, and larger line widths (0.3 km s) at the southwest part of the map. The typical line widths are km s. The column density map presents an arc-structure around the the 1.2 mm dust continuum peak.
Combining both IRAM 30m and PdBI NH (10) data we can resolve the arc-like structure hinted at the single dish map.
The core presents a rich chemistry with emission from early (CH, HCN, CS) and late-time molecules (e.g., NH), with a clear chemical spatial differentiation for nitrogen (centrally peaked), oxygen (peaking to the southwest) and sulphurated molecules (peaking to the east).
The chemical difference in the core could be due to an external UV radiation field penetrating into the core from the (south)west which could be also affecting the polarization properties. This implies that the core should be close to the edge of the molecular cloud.
FeSt 1-457 is well fitted with a Bonnor-Ebert sphere model and introducing a temperature gradient decreasing towards the center from 12 to 6 K. We found the core is gravitationally unstable and that the magnetic field is not enough to stop the collapse.
We have analyzed the abundances of the molecular lines using the ARTIST software. For most of the molecules detected (HCN, HCO, CHOH, CS, SO, CO and CO), abundances are best fitted with three values, presenting a clear decrease of abundance of at least 1 or 2 orders of magnitude towards the inner region of the core. This is consistent with chemical models of starless cores, that show that there is a significant depletion of molecules onto the dust grains. On the other hand, NH, HCN and CH are well fitted with a constant abundance throughout the core and the abundance of HNC and NHD increases in the inner region of the core (at radius arcsec).
Finally, we have seen that depletion of molecules onto the dust grains, grain growth and depolarization take place at the inner region of the core. This strongly suggests that these properties could be correlated in FeSt 1-457.
Acknowledgements.We would like to thank the referee for her/his useful comments. We also thank Phil Myers and Jan Forbrich for thoughtful discussions. CJ, JMG and RE acknowledge support from MICINN (Spain) AYA2014-57369-C3 grant. CJ and RE also acknowledge MDM-2014-0369 of ICCUB (Unidad de Excelencia ‘María de Maeztu’). JMG also acknowledges the support from the MECD (Spain) PRX15/00435 travel grant and from the SI CGPS award “Magnetic Fields and Massive Star Formation”. AP acknowledges financial support from UNAM-DGAPA-PAPIIT IA102815 grant, Mexico. OM is supported by the MOST (Ministry of Science and Technology, Taiwan) ALMA-T grant MOST 103-2119-M-001-010-MY to the Institute of Astronomy & Astrophysics, Academia Sinica.
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