On the Collisional Disalignment of Dust Grains in Illuminated and Shaded Regions of IC 63

We used our existing optical and NIR polarimetric observations from Andersson et al. (2013) and Soam et al. (2017). Optical polarization observations toward 12 stars were made at the Nordic Optical Telescope (NOT) on La Palma using ALFOSC and TURPOL instruments in spectropolarimetry and photopolarimetry modes, respectively. The details of the observations are given in Andersson et al. (2013).

For correlating the polarization fraction with grain alignment caused by Purcell mechanism (Purcell 1979), we used the H₂ 1-0 S(1) observations from Andersson et al. (2013). These deep narrow-band imaging observations at 2.122 μm were acquired with the WIRCam instrument (Puget et al. 2004) at the Canada−France−Hawaii Telescope (CFHT). To better analyze the diffuse emission, we had to first perform a star subtraction of the foreground sources. We used the Astropy-affiliated photutils (Bradley et al. 2019) package to construct an effective point-spread function (ePSF) from stars extracted over the entire image. Combined with two-dimensional background estimation and modeling, the ePSF was used to subtract away point sources, leaving the underlying diffuse emission intact.

Additional optical spectropolarimetric observations were acquired on 2013 October 18 and 19 from the Intermediate-dispersion Spectrograph and Imaging System (ISIS) mounted at the ∼f/11 Cassegrain focus of the 4.2 m William Herschel Telescope (WHT) in the Canary Islands, Spain. Observations were acquired with both the red and blue sides of the spectrograph. For the blue arm we used the EEV12 CCD providing good quantum efficiency down to the atmospheric cut-off and the R300B grating centered at 4500 Å. For the red arm we used the Red+ CCD and the R158R grating centered at 6400 Å. The blue observations were corrupted by scattered light and are not discussed here. The red data cover λ ≈ 0.48–0.95 μm. For comparison with earlier data we have extracted the polarization values at 0.65 μm. HD 204827 was used as the high-polarization standard and HD 212311 was observed as a zero-polarization standard. We divided the total integration time into eight half-wave plate (HWP) settings, to minimize the influence of systematic errors. Data reduction was accomplished through standard IRAF routines.

Observations of the J = 1-0 line of HCO⁺ at 89.189 GHz were conducted using the Combined Array for Research in Millimeter-wave Astronomy (CARMA) in the 15-element mode (six 10.4 m antennas and nine 6.1 m antennas). Observations were conducted in three tracks separated by a few days (2014 February 13, 14 and 17), with CARMA in its C configuration (baselines ranging 30–350 m). A six pointing mosaic with the phase center aiming at α_J2000 = 00^h59^m01.22^s and δ_J2000 = +60°53'2340 was implemented. Good atmospheric conditions prevailed for the observations with an average opacity at 230 GHz between 0.15 and 0.3 for the three tracks. The total time on source was 9.4 hr.

The first local oscillator (LO) was set to 91.0163 GHz (3.3 mm). The correlator configuration provided simultaneous observations of the continuum emission (1.9 GHz of total bandwidth) and several lines, including HCO⁺ (1-0) and HCN (1-0) among others. Here we present the HCO⁺ (1-0) data (rest frequency 89.18853 GHz), which lay in one of the ten spectral windows each consisting of 159 channels with 50 KHz each (i.e., 0.16 km s⁻¹ at the observing frequency) and 8 MHz total width (about 26 km s⁻¹).

The data were edited, calibrated, and imaged using the MIRIAD package (Sault & Noordam 1995) in a standard way. Quasars 3C84 and J0102+584 were used as bandpass and phase calibrator, respectively. Observations of Uranus provided the absolute scale for the flux calibration of the data set. The measured flux of J0102+584 was 2.6 Jy and the flux uncertainty for CARMA observations at 3 mm is estimated to be 10%.

A continuum image was created by combining the data set of the three tracks using the Miriad program INVERT with a natural robust weighting. The rms noise of the resulting interferomter-only image has a synthesized beam of 59 × 49 with a P.A. of 48° and an rms noise level of 0.3 mJy beam⁻¹. No continuum emission is detected over a 3σ level. The HCO⁺ (1-0) line image was created using a natural weighting scheme too and the inteferometer-only velocity cube has a synthesized beam of 61 × 47 with a P.A. of 57° and an rms noise level of 97 mJy beam⁻¹.

Single dish observations covering the IC 63 interferometry pointings were also acquired with the EMIR instrument on the IRAM 30 m telescope during 2013 July 21–23. The observations were carried out in on-the-fly (OTF) mapping, position-switching mode, using a velocity resolution of 0.13 km s⁻¹. The final map covering 40 × 28 was obtained.

After calibrating the CARMA interferometer visibilities, we combined the HCO⁺ (1-0) with a map taken with IRAM 30 m. For this purpose we created an interferometer image using a robust weighting of 0.5 and converted the IRAM 30 m Dish data to Jy beam⁻¹ using a Jy-per-K factor of 6.0 ⁸ for observations at 86 GHz. We made a jointly−deconvolution of the interferometer and the single-dish data sets using the Miriad program MOSMEM and then restoring the resulting image with a synthesized beam of 58 × 44 with a P.A. of 50°. The final image has an rms noise level of 6 mJy beam⁻¹. Finally, we also made a HCO⁺ (1-0) integrated intensity image, collapsing the emission from −0.9 to 1.5 km s⁻¹. This image has an rms noise level of about 24 mJy beam⁻¹ km s⁻¹.

Purcell (1979) proposed three surface processes to drive grains to suprathermal rotation. Among these three processes, the formation of H₂ molecule at the catalytic site was suggested as the dominant mechanism to produce rotational torques. In addition to the work of Purcell (1979), Lazarian & Draine (1997), and Lazarian & Roberge (1997) presented the detailed calculations for these torques for a brick-like and a spheroidal grain. As noted by Andersson et al. (2013), if the H₂ emission from a region is fluorescent in origin, then the intensity of the emission traces the molecular hydrogen formation rate. This is because H₂ photo destruction proceeds via a two-step process initiated by a line absorption in the Lyman or Werner bands, followed by a relaxation of the electronic excitation. The direct photodissociation of an H₂ molecule requires a photon with energy E > 14.7 eV (Stecher & Williams 1967), well above the ionization energy of atomic hydrogen (E = 13.6 eV) and is thus not important in the atomic ISM. During the relaxation process, the molecule dissociates if the vibrational state of the de-excited molecule has v > 14. If it re-enters the electronic ground state at a lower vibrational quantum number, the molecule will proceed to the ground state through a rotational–vibrational cascade observable chiefly in the NIR. Since the branching ratio between dissociation and fluorescence cascade is determined by quantum mechanics, the fluorescence rate is directly proportional to the molecular destruction rate. As the dynamical timescales in a well-established PDR are much longer than those of molecular formation and destruction (Tielens 2005; Morata & Herbst 2008), the abundance of H₂ is governed by a detailed balance equation where formation and destruction rates equal each other. The fluorescent intensities, therefore, trace the formation rate of the molecule.

The formation of molecular hydrogen on the surface of the dust grains helps in spinning up the grains (Purcell 1979). When the molecule leaves the grain surface, it imparts a net torque to the dust grain which results in spinning of the grain. This phenomena is called the "Purcell rocket effect." These torques cause the grains to rotate suprathermally (i.e., with rotational energies well above the thermal energies of the gas or dust). These spinning grains interact with interstellar magnetic fields and become aligned with the field with spinning axes parallel to the field orientation. These "Purcell torques" play an important role also in modern RAT based grain alignment, where they enhance the radiatively driven alignment allowing a larger fraction of the grains to attain suprathermal rotation.

Andersson et al. (2013), using their spectropolarimetric observation with NOT/ALFOSC and five-band photopolarimetry with NOT/TURPOL for stars toward IC 63, studied the correlation between polarization and diffuse H₂ fluorescence emission in the cloud. They note that the polarization seen in IC 63 is proportional to the level of H₂ fluorescence (i.e., H₂ formation rate) for high intensity H₂ emission fluorescence (i.e ${I}_{{{\rm{H}}}_{2}}\gt {10}^{-5}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}\,{\mathrm{sr}}^{-1}$). They identified this correlation as the signature of enhanced dust grain alignment driven by H₂ formation. No clear correlation was seen for ${I}_{{{\rm{H}}}_{2}}\,\lt {10}^{-5}\,\mathrm{erg}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}\,{\mathrm{sr}}^{-1}$ suggesting that up to this formation rate, only direct RAT alignment dominates. They also note a few outliers. We have used their polarization measurements in addition to values from Soam et al. (2017) to re-investigate the relation between amount of polarization increment with H₂ formation on dust grains (see Figure 5). The star numbered 46 (see Figure 3) is in common in the two studies. For this particular star, we use the polarization values from Soam et al. (2017). ¹⁰ The polarization results from Soam et al. (2017) and Andersson et al. (2013) are consistent within the uncertainties.

Panel (a) of Figure 5 shows robust linear model (RLM) fitting in distribution of amount of polarization we have from observations and the intensity of H₂ fluorescence measured at the same locations where we detected polarization. Panel (b) also shows the distribution of same quantities but with linear regression model (LM) fit to the data and uncertainty in the fit model is shown with shaded blue region. These two different models have different functions when fit to the data. LM is just ordinary least square fitting which reduces the residuals, whereas in RLM, all data points are not treated equally. Robust fitting is not sensitive to outliers but LM is very sensitive to the outlying data points. If the uncertainties are of a fully random nature LM is the more appropriate technique. However, RLM fitting is useful for samples where additional unaccounted for parameters may be producing significant systematic errors in the data. The distribution shown in Figure 5 is quite scattered. Therefore, we used both RLM and LM methods. In both the panels, a trend of increase in polarization with intensity of H₂ fluorescence can be noticed. The correlation is not as good as seen by Andersson et al. (2013) who had a lesser number of targets. Although more data should nominally improve the sampling of an underlying relationship, this is only true if the noise in the data set is statistical/random in nature. If the noise is instead systematic, more sampling may not yield tighter correlations. Because of the good correlation seen in Andersson et al. (2013), the formal correlation seen in this larger sample and the highly successful ab initio modeling of the alignment in this [physically simple] system by Hoang et al. (2015), we feel justified in probing for a "third parameter" in these data (where RAT alignment and H₂ enhanced alignment are the first two).

The most prominent outliers in the plots (here and in Andersson et al. 2013) seem to be associated with large column density regions in the mm-wave maps, especially the compression ridge region at the side of the nebula facing γ Cas. If the column density can be used as a proxy for space density (i.e., if the cloud can to first order be approximated with a slab geometry) this is where the collision rate would be especially large. We therefore probe the hypothesis that the outliers represent enhanced collisional disalignment in the material.

To probe for a dependence of the measured polarization on the collision rate, we assume that the direct radiative alignment rate of the grains in IC 63 is close to constant. This is supported by the fact that the opacity in the gas to photons capable of direct RAT alignment is relatively low as these are only constrained to have λ < 2a (the opacity to H₂ dissociating photons is much smaller than the cloud size since they are much harder with λ < 1108 Å). We then find a nominal correlation with the H₂ fluorescent flux to account for the H₂ formation enhancement (as done in Andersson et al. 2013; Hoang et al. 2015). Based on this nominal P versus I(H₂) relation we can investigate the possible role of collisions by comparing the deviations from this relationship (ΔP) with the integrated intensity of the HCO⁺ line (${W}_{{\mathrm{HCO}}^{+}}$). We use the HCO⁺ column density rather than visual extinction as it has higher accuracy and is assured to probe the IC 63 cloud only, rather than possible background gas. Other gas tracers, such as CO (J = 1-0) or its isotopomers might have been preferable, but are not available at the spatial resolution required to match the pencil beams of the polarimetry.

The result is shown in Figure 6. The overall distribution of points shows a weak anticorrelation (with a ∼45% probability based on a Spearman rank-order test). However, a bifurcation in the points is also evident. To explore this dichotomy, we plot the locations of the polarization lines of sight on a heavily stretched map of HCO⁺ (Figure 3). This map allows us to separate the lines of sight into those that pass through IC 63 in front of, or behind, a dense clump in the cloud. We have marked the former with red symbols in both Figures 3 and 6 and the latter with blue symbols. A number of lines of sight do not clearly fall in either category and are plotted as white symbols in Figure 3. If the distinguishing separations between the different lines of sight is the illumination of the gas (and dust) by γ Cas, then these latter points shown with white color should be more closely related to the ones in front of a clump (red symbols), as the distinguishing characteristic is whether the radiation from the background star has been damped or not by the dense gas.

Considering the color scheme in Figure 3, we notice a clear separation of the full sample into two populations. The population with blue symbols which are in the shaded region behind HCO⁺ clumps (Figure 3), show significantly shallower slope (−0.99 ± 0.06) than that of the population with the red symbols (−2.18 ± 0.46) which are in front of the HCO⁺ clumps (see Figure 6). The two slopes here suggest different rates of drop in amount of polarization with the gas density.

The anticorrelation seen in the distribution is expected for the collisional disalignment, whose rate (C) is proportional to the gas density (n_gas) and gas velocity (v_gas)

$$\begin{eqnarray}&&C\propto {n}_{\mathrm{gas}}\cdot \sqrt{{T}_{\mathrm{gas}}}\end{eqnarray} \tag{ 5 }$$

where, for thermal motion, the gas temperature (T_gas) is related to average velocity of the gas (v_gas) by relation ${T}_{\mathrm{gas}}=\tfrac{\mu {m}_{{\rm{H}}}}{{k}_{B}}{v}_{\mathrm{gas}}^{2}$. As discussed above, we are here applying the local density variations in a perturbation mode around the steady-state solution described by Equation (4), which means that ΔP versus n_gas should show linear anticorrelation with a slope proportional to the square root of the gas temperature. If we, as suggested above, approximate the cloud as a slab geometry, then the integrated HCO⁺ intensity can be used as a proxy for gas density. Figure 6 shows two separate slopes fit to the two populations of targets shown in red and blue symbols with the point tracing more intensely illuminated gas following a steeper plot in ΔP versus ${W}_{{\mathrm{HCO}}^{+}}$. This would be expected if the gas is heated by the radiation from the star and gas in the shade is cooler than the gas in the direct illumination of γ Cas radiation. Similar to the opacity differences between H₂ photodissociation and the subsequent re-formation, the photons responsible for heating the gas, through photoelectric emission from small grains will likely also have a higher effective opacity into the cloud than those responsible for the direct RAT alignment. This assumes that the small grain population is present in both "hot" and "cool" gas, which is likely as the clumps are not dense or dark enough to support significant grain growth (Ysard et al. 2013; Vaillancourt et al. 2020). This depends on the poorly known work function of the grain material, but if we assume a work function of 4.4 eV (equivalent to a photon wavelength of λ = 2820 Å) for graphite (PAHs) and 8 eV ( ⇔ λ = 1550 Å) for silicates (Weingartner & Draine 2001), then also the gas heating is likely to be more spatially structured that the direct RAT alignment, and it is reasonable to thence separate the alignment from the disalignment dependence of the radiation field.

To probe the [dis-]alignment efficiency, the ideal probe would be the normalized fractional polarization (P/A_V), which removes changes due to total column density. However, while we have some A_V measurements of the targets shown in Figure 6 some line of sight extinction measurements are fully missing, while for others the existing ones are of marginal accuracy. Therefore, performing the analysis in P/A_V introduces additional uncertainties. Doing this analysis shows that the parameters of the two slopes in this figure are within the mutual uncertainties of those utilizing the normalized fractional polarization P/A_V, and implies that the approximation of the cloud as a plane-parallel slab is reasonable.

The two slopes in Figure 6 are consistent with the two-temperature hypothesis of Thi et al. (2009). The ratio of the square roots of the two temperatures 106 K and 685 K of warm and hot regions, respectively, in Figure 2 is 2.54 ± 1.83. The ratio of the two slopes obtained in Figure 6 is 2.20 ± 0.49. These values are consistent within their joint uncertainty of ∼1.89. The higher rate of gas–grain collision in the hot regions leads to higher disalignment rate of the aligned dust grains and hence stronger decrements in polarization, as seen in Figure 6.

The steady-state solution of the alignment (Equation (4)) has a 1/(${n}_{\mathrm{gas}}\cdot \sqrt{{T}_{\mathrm{gas}}}$) dependence in the RAT term, and, therefore, the ΔP = 0 location should depend on these parameters. Figure 6 shows dotted lines plotted for ΔP = 0 and the corresponding two integrated intensities of HCO⁺ on the x-axis. This "critical density" for the hotter gas (toward higher temperature) occurs at a lower value than for the colder gas as would be expected from the above dependence. This supports our conclusion that the two sub-sets and their associated linear anticorrelations represent the two—warm and hot—phases of the gas in IC 63 PDR. It is possible to an unknown degree that the rotational disruption by RAT (RATD; Hoang et al. 2019) may play a minor role in affecting the critical density.

It is worth noting that a dual temperature distribution in the molecular hydrogen line excitation is a well known phenomenon in UV observations of diffuse gas. There, the J = 1, J = 0 excitation shows a temperature of typically ∼80–130 K (Naslim et al. 2015) consistent with the cool neutral medium. For J = 3 and higher, a typically much higher excitation temperature is derived ∼500–1000 K (Shaw et al. 2005). As shown by Lambert et al. (1990), the column density in the high J-levels is correlated with that of CH⁺. Since the formation path of this radical requires an endothermic reaction with an activation energy exceeding 4600 K:

$$\begin{eqnarray}&&{{\rm{C}}}^{+}+{{\rm{H}}}_{2}\to {\mathrm{CH}}^{+}+{\rm{H}}-4640\,{\rm{K}}\end{eqnarray} \tag{ 6 }$$

(Pineau des Forets et al. 1986, and references therein), this implies that some gas along the line of sight either is now in warm/hot regions or recently was. Hence the two-temperature excitation seen in UV observations likely corresponds to distinct thermal components along the line of sight. Our proposed separation of thermal components corresponds to a similar structure, albeit in the plane of the sky.