THE MAGNETIC FIELD OF CLOUD 3 IN L204

Lauren R. Cashman; D. P. Clemens

doi:10.1088/0004-637X/793/2/126

1. INTRODUCTION

How are molecular clouds influenced by magnetic fields? Do magnetic fields affect cloud collapse and morphology? Before stars form, molecular clouds and the dense cores within them must form. These processes, however, are not yet well understood. Crutcher (2012) comprehensively reviewed magnetic fields in molecular clouds, concluding that the relative contributions of turbulence, magnetic fields, and gravitational potential to cloud formation and collapse remain unknown. Star-formation theories fall mainly into two magnetic classes: strong-field and weak-field. In strong-field models, cloud collapse occurs primarily along the field lines (e.g., Mouschovias & Ciolek 1999). This leads to cloud long-axes predominantly perpendicular to their magnetic fields. In weak-field models, turbulent flows drive formation of clouds (e.g., Mac Low & Klessen 2004) and as clouds collapse, gas drags magnetic fields along, creating pinched or "hourglass" morphologies.

Magnetic fields may be observed, and different morphologies tested, through near-infrared (NIR) polarimetry of background starlight. The partial linear polarization of optical starlight was discovered by Hall (1949) and Hiltner (1949a, 1949b). This polarization is attributed to dichroic extinction by aligned, asymmetric dust grains. Spinning dust grains become aligned with their long axes preferentially perpendicular to the magnetic field, resulting in partial polarization of background starlight oriented parallel to the magnetic field. The exact alignment mechanism, however, is still unknown. The current leading theory to explain how dust grains become aligned in the presence of a magnetic field is through radiative aligned torques (RATs; Lazarian & Hoang 2007). RAT theory relies on an anisotropic radiation field to spin-up dust grains possessing net helicity and to align the grains with the magnetic field. Therefore, as the opacity to the illuminator increases, there is less radiation available to spin-up dust grains and grain alignment efficiency should decrease.

Differences in grain alignment efficiency can be measured through differences in polarization efficiency (PE), the ratio of polarization percentage P_λ to optical depth or extinction (A_V). Previous studies have shown a decrease in PE with increasing optical depth (Gerakines et al. 1995; Whittet et al. 2008), which is consistent with predictions made by the RAT theory.

Other tests of the RAT theory examine the peak wavelength of polarization (λ_MAX), which corresponds to the size of the dust grains being aligned. Andersson & Potter (2007) searched for correlations between λ_MAX and the illuminating radiation field strength. They found that λ_MAX increases linearly with A_V, concluding that smaller dust grains become unaligned at larger optical depths. Another test, by Andersson & Potter (2010), found that λ_MAX becomes shorter in the presence of a young B9/A0 star, indicating that small dust grain alignment becomes more efficient near such a blue illuminator. Matsumura et al. (2011) showed evidence that grain alignment efficiency is also enhanced at higher dust temperatures.

Another key point from Andersson & Potter (2007) is that A_V represents the line-of-sight (L.O.S.) extinction between some background star and the observer and not necessarily the effective extinction to the illuminator seen by the dust grains. They used I(60 μm)/I(100 μm) as a measure of dust grain temperature, which is correlated with the radiation intensity seen by the grains. Thus, Andersson & Potter (2007) were able to select L.O.S. where the observed extinction corresponded to the actual optical depth seen by the grains.

Here, use of the Mimir (Clemens et al. 2007) wide-field instrument for new NIR polarization measurements of background starlight toward Cloud 3 in L204 is reported. These new observations had a finer spatial sampling than previous L204 studies and so reveal small scale changes in the plane-of-sky magnetic field. Additionally, differences in polarization (grain alignment) efficiency throughout the cloud and with distance from the nearby O star, ζ Oph, were examined. Section 2 introduces the L204 laboratory and Cloud 3 region. The observations and data reduction are described in Section 3. Section 4 explains the analysis of the data. In Section 5, the results of the analyses and their implications are discussed. This work is summarized in Section 6.

2. THE L204 LABORATORY

The nearby dark cloud complex L204 (Lynds 1962) provides a good laboratory to investigate both magnetic field morphology and dust grain alignment efficiency. It is a 4° long, filamentary molecular cloud in Ophiuchus (ℓ = 6 fdg 6, b = 20 fdg 6) that shows no evidence of star formation (Hatchell et al. 2012). L204 appears in absorption in front of a cloud of Hα emission associated with ζ Oph (Sivan 1974), a runaway O9.5 V star (Lesh 1968). This provides an upper limit on the distance to L204 of 112.2 ± 2.5 pc based on the trigonometric parallax of ζ Oph (van Leeuwen 2007). L204 and ζ Oph are separated by ∼2 fdg 8 on the sky, which corresponds to a distance of 5.5 pc if L204 is at the distance of ζ Oph.

McCutcheon et al. (1986) observed optical polarization of background starlight for 60 stars in the L204 region. They found that the magnetic field of L204 is predominantly perpendicular to the long axis of the cloud across several degrees on the sky. The measured polarizations were also generally aligned with the mean polarization position angle in the surrounding interstellar medium, leading McCutcheon et al. (1986) to conclude that L204 collapsed along an existing magnetic field. Their CO observations revealed a steep density gradient on the western, ζ Oph facing, edge of the cloud, implying interaction with that star. They also found the velocity structure and morphological structure of the cloud are correlated. The radial velocities of the less massive sections of the cloud are consistently offset from those of the more massive sections. This correlation implies that some external force is acting on L204, accelerating the less massive sections of the cloud. Based on the assumption that the cloud is in virial equilibrium, McCutcheon et al. (1986) estimated a magnetic field strength of ∼50 μG.

The L.O.S. magnetic field strength (B_∥) in L204 was measured at several positions by Heiles (1988), using Zeeman splitting of the 21 cm line observed with the Hat Creek 85 foot telescope. Heiles (1988) found a correlation of B_∥ with V_LSR, which he concluded was indicative of gas flowing along the magnetic field. In that case, the magnetic field would be approximately constant throughout the cloud and differences in B_∥ would indicate variations in the direction of the magnetic field. While the maximum B_∥ measured was 9.1 μG, Heiles favored a total field strength of ∼12 μG. No other Zeeman observation of L204 exist.

L204 was also observed by Tachihara et al. (2000a, 2000b) in mm lines of ¹²CO, ¹³CO, and C¹⁸O using NANTEN at angular resolutions as fine as 2 arcmin. They separated L204 into six clouds, the largest of which they called "Cloud 3." It has a semi-major axis of 6.5 pc and a semi-minor axis of 1.5 pc, at their assumed distance of 140 pc. They estimate M = 430M_☉ for Cloud 3, which corresponds to M ≃ 275M_☉ at 112 pc. Tachihara et al. (2000a) saw the same gas structure as McCutcheon et al. (1986) and also found that the denser cores (traced by ¹³CO and C¹⁸O) are on the side of the cloud closest to ζ Oph. Additionally, Tachihara et al. (2000a) examined the possible effects on L204 from the stellar wind and UV flux of ζ Oph. Based on kinetic energy calculations, they concluded that momentum injection from UV photo-dissociation has the largest effect on the velocity structure of the cloud and that the stellar wind from ζ Oph has only a negligible effect.

The L204 region is shown in Figure 1. The red contours represent ¹³CO integrated intensities of the L204 cloud complex from Tachihara et al. (2000a). A solid red circle indicates the location of ζ Oph, with the red line representing its proper motion over 10⁵ yr. The background grayscale image is the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) 12 μm dust map computed by Meisner & Finkbeiner (2014). The map reveals both the almost 1° wide bow shock in front of ζ Oph as well as a 3° radius cavity centered on ζ Oph and with its edge at L204. The black dot-dashed box indicates the 1° × 1 fdg 5 region observed for this work.

fdg — **Figure 1.** Smoothed, grayscale *WISE* (Wright et al. 2010) 12 μm dust map computed by Meisner & Finkbeiner (2014) of the L204 region. Dust emission contours are stepped linearly from 0 to 175 MJy sr⁻¹. The maximum emission in the region is 860 MJy sr⁻¹. The red contours represent ¹³CO integrated intensities from Tachihara et al. (2000a), ranging linearly from 1 to 7 K km s⁻¹. The filled red circle indicates the location of ζ Oph, with the red arrow representing its proper motion over 10⁵ yr. The black dot-dashed box indicates the 1° × 15 region for which NIR linear polarimetry measurements were obtained.
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3. OBSERVATIONS AND DATA REDUCTION

Linear polarimetry measurements were obtained in the NIR H band (1.6 μm) using the Mimir instrument (Clemens et al. 2007) on the 1.8 m Perkins telescope outside of Flagstaff, AZ. Mimir used a 1024² Aladdin III InSb detector array, operated at 33.5 K. The instrument had a field of view (FOV) of 10' × 10' and pixel scale of 0 farcs 58. Polarimetric analysis was performed with a cold, stepping, H-band, compound half-wave plate (HWP) plus a fixed, cold wire-grid analyzer.

Sky observations were planned for a grid of 54 abutting fields (a 6 × 9 field grid) covering a 1° × 1 fdg 5 region of L204 centered on Cloud 3. They were conducted over several nights between 2010 May and 2012 May. To obtain polarimetry measurements, exposures of five second durations were obtained for 16 unique HWP position angles at six sky-dither positions, yielding a total of 96 images per field. The total on-sky integration time of the entire map (eight minutes per FOV) was 7.2 hr. Polarization flat-fields for each HWP position were taken using a lights-on/lights-off method against a uniformly illuminated flat-field screen inside the closed telescope dome.

Polarimetric standard stars from the list of Whittet et al. (1992) and globular cluster stars were observed on the same nights to determine the instrumental polarization, polarimetric efficiency, and HWP position angle offset.

Polarization data were reduced and analyzed using custom IDL software, as described in Clemens et al. (2012b), yielding Stokes U and Q, polarization P, equatorial position angle P.A., and their uncertainties, for 7150 stars contained within the surveyed region. The biased degree of polarization (P') and equatorial position angle (P.A.) were calculated from the Stokes parameters:

$\begin{equation} P^{\prime } = \sqrt{U^2 + Q^2} \end{equation} \tag{ 1 }$

$\begin{equation} \mathrm{P.A.} = \frac{1}{2} \, \mathrm{arctan}\left(\frac{U}{Q}\right), \end{equation} \tag{ 2 }$

where P.A. is in radians. The degree of polarization (P') was then Ricean-corrected, to account for positive bias, following the procedure of Wardle & Kronberg (1974):

$\begin{equation} P = \sqrt{P^{\prime 2} - \sigma _{\rm P}^2}, \end{equation} \tag{ 3 }$

where σ_P is the uncertainty in the polarization percentage. From these quantities, the uncertainty in the polarization position angle σ_P.A., in radians, was calculated:

$\begin{equation} \sigma _{\rm P.A.} = \frac{1}{2} \left(\frac{\sigma _{\rm P}}{P}\right); P \ne 0. \end{equation} \tag{ 4 }$

The stars were separated into three samples, indicated by Usage Flags (UFs: Clemens et al. 2012a) for each star, as shown in Figure 2. Stars with UF = 1 have the highest polarimetric quality, characterized by σ_P ⩽ 2% and m_H ⩽ 12.8 mag. The lower quality UF = 2 sample is comprised of those stars outside of the UF = 1 region, but with σ_P ⩽ 10% and m_H ⩽ 14.6 mag. Stars with UF = 3 are the lowest quality sample and lay outside of both the UF = 1 and 2 regions. The boundary magnitudes were determined by the H-band magnitudes at which the median σ_P were equal to 2% and 10%. As shown by Clemens et al. (2012a), although the UF = 2 and 3 stars have lower polarimetric signal-to-noise ratio (S/N), their Stokes parameters can be averaged spatially (with variance weighting) to provide useful information.

Table 1 lists the Mimir observed polarization properties and Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) photometric magnitudes (where available) for 7150 stars with polarimetric measurements, ordered by R.A. Column 1 lists the star number and Columns 2 and 3 list the R.A. and decl. The Mimir measured quantities Stokes U and Q, polarization P, equatorial position angle P.A., and UF are given in Columns 4 through 8, respectively. For the 6476 that were matched to 2MASS, their J-, H-, and K-band magnitudes are listed in Columns 9–11. For the remaining 674 stars with no 2MASS match, these columns are set to 99.99 ± 0.00 mag. Columns 12 and 13 present the estimated visual extinction and Background Flag (BF), described in Section 4.1.

Table 1. Polarimetry and Photometry of 7150 Stars toward L204-Cloud 3

Star	Mimir							2MASS^a			NICER	BF^f
	R.A. (J2000)	Decl. (J2000)	U	Q	P^b	P.A.^c	UF^d	J	H	K	A_V^e
	(HH MM SS.S)	(DD MM SS)	(%)	(%)	(%)	(deg)	UF^d	(mag)	(mag)	(mag)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)	(13)
1	16 46 04.3	−11 34 18	8.9 ± 7.8	−5.7 ± 7.6	7.2 ± 7.7	61 ± 30	2	14.23 ± 0.03	13.77 ± 0.03	13.62 ± 0.04	−0.71 ± 1.17	1
2	16 46 04.4	−11 37 46	10 ± 12	13 ± 11	11 ± 12	18 ± 31	3	15.15 ± 0.04	14.31 ± 0.04	14.08 ± 0.06	2.00 ± 1.21	2
3	16 46 04.8	−12 04 38	1 ± 20	−13 ± 20	0 ± 20	0 ± 180	3	15.13 ± 0.06	14.45 ± 0.05	14.43 ± 0.09	−0.03 ± 1.29	1
4	16 46 04.8	−11 46 04	3.8 ± 7.8	−0.0 ± 7.6	0.0 ± 7.8	0 ± 180	3	14.82 ± 0.03	14.20 ± 0.03	14.08 ± 0.06	0.04 ± 1.20	1
5	16 46 05.0	−12 38 31	5 ± 13	−1 ± 13	0 ± 13	0 ± 180	3	15.82 ± 0.09	15.31 ± 0.10	15.21 ± 0.14	−0.65 ± 1.47	1
6	16 46 05.1	−11 45 54	2 ± 15	−8 ± 14	0 ± 14	0 ± 180	3	15.73 ± 0.07	14.82 ± 0.07	14.69 ± 0.10	2.06 ± 1.33	2
7	16 46 05.2	−12 35 24	−31 ± 11	−2 ± 12	28 ± 11	133 ± 12	3	16.27 ± 0.12	15.16 ± 0.08	14.92 ± 0.11	3.70 ± 1.47	2
8	16 46 05.3	−12 14 44	−1.7 ± 4.8	1.2 ± 5.0	0.0 ± 4.9	0 ± 180	2	13.86 ± 0.03	13.19 ± 0.03	12.95 ± 0.03	1.07 ± 1.16	2
9	16 46 05.4	−12 31 38	6.6 ± 4.0	−2.1 ± 4.2	5.6 ± 4.1	53 ± 20	3	14.77 ± 0.04	14.16 ± 0.04	13.95 ± 0.05	0.56 ± 1.20	2
10	16 46 05.5	−12 16 59	−3 ± 10	10 ± 11	0 ± 11	0 ± 180	3	14.88 ± 0.05	14.22 ± 0.05	14.03 ± 0.07	0.70 ± 1.23	2

Notes. ^aJ, H, and K values of 99.99 indicate that no matching 2MASS star was found. Magnitude uncertainties of 9.99 indicate measurements that are upper limits.^bP values have been corrected for positive bias. The correction was also propagated into the P.A. uncertainties.^cP.A.s are equatorial, measured East of North.^dUsage Flag: 1 = highest quality; 2 = moderate; 3 = poor.^eA_V values for stars with 2MASS upper limits or without a 2MASS match are set to −9.99 ± 0.00.^fBackground Flag: 2 = background; 1 = foreground; 0 = unknown.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Figure 3 shows a WISE three-color image of the Cloud 3 region observed with Mimir. The WISE image shows that the opaque core of Cloud 3 is rimmed by a filament of warm dust on the western, ζ Oph facing, edge. White vectors represent polarizations of the 188 stars having both UF = 1 and P/σ_P ⩾ 2.5 (σ_P.A. ⩽ 11 fdg 5). The polarization percentages P are encoded as vector lengths and the P.A.s as vector orientations. A 2% reference vector is shown in the bottom right corner. The oversaturated star at R.A. = 16:46:39.11 decl. = −11:38:53.1 is V446 Oph and will be discussed in Section 5.2.

4. ANALYSIS

4.1. NICER Extinctions and Map

Due to the nature of background starlight polarimetry, only stars that are behind L204, and whose polarizations can be attributed to the cloud, are useful for magnetic field analyses. To establish the background status of the stars in the field, visual extinctions were estimated to each of the 6476 stars having a 2MASS match using the Near-Infrared Color Excess Revisited (NICER) technique (Lombardi & Alves 2001).

The NICER method¹ uses NIR colors to estimate extinctions for a region based on comparison to the intrinsic colors of a nearby unextincted stellar population. An existing extinction map of the Ophiuchus cloud from Lombardi et al. (2008) and WISE 12 μm and 22 μm images were used to identify a control field of negligible extinction and dust emission. The control field is centered at R.A. = 16:55:45.3, decl. = −11:34:58 and has a radius of 35 arcmin. All 2MASS stars in the control field having σ_J, σ_H, σ_K ⩽ 0.25 mag were used to calculate the intrinsic colors and color scatter of these presumed unextincted stars. These colors were compared to those in the Cloud 3 region to estimate their visual extinctions (listed in Table 1).

A histogram of these estimated Cloud 3 extinctions is shown in Figure 4. The solid histogram shows the distribution of NICER extinctions for stars in the Cloud 3 region. The dashed histogram shows the distribution of NICER extinctions applied to the stars in the control field. As a result of the large spread of intrinsic colors, the NICER extinctions for both the control field and Cloud 3 region have wide distributions and extend to negative values. These negative values are allowed by the NICER analysis and indicate negligible extinction along the line of sight. As expected, the control sample has a distribution peaked close to A_V = 0 mag. The extincted distribution peaks at A_V ∼ 0.5 mag and may have a weaker higher extinction tail.

To constrain which stars are most likely to be behind Cloud 3, the signature of the unextincted stellar population in the control field needed to be removed from that of the Cloud 3 background stellar population. This was done by direct deconvolution of the distributions shown in Figure 4. Fast Fourier transforms were computed of the histograms of both populations and then ratioed. The inverse fast Fourier transform of the ratio revealed the extinction power spectrum as a function of A_V, shown as the inset in Figure 4. The power spectrum peaks at A_V = 0.5 mag, with an amplitude 5.7σ above the neighboring noise, and no other peak rises above 2.5σ. Thus, Cloud 3 contributes 0.5 mag of A_V on average. Any star showing NICER A_V ⩾ 0.5 mag is deemed to be behind the cloud and has its Table 1 BF value set to two to indicate its background status.

Of the 6476 stars measured polarimetrically and matched to 2MASS, 3896 have A_V ⩾ 0.5 mag and so were judged to be background (BF = 2) while the remaining 2580 are foreground (BF = 1). No visual extinction estimate could be made for the 674 stars with no 2MASS match, and are therefore of uncertain location (BF = 0).

Due to the proximity of L204 and its large angular distance from the Galactic mid-plane (b = 20 fdg 6), all of the extinction along the line of sight is likely due to L204. McCutcheon et al. (1986) estimated that only 0.3 mag of extinction is contributed by foreground material and that the total A_V along a line of sight to the edge of the Galaxy at b = 20°, if there are no molecular clouds, is ∼0.6 mag. Our conclusion of an average 0.5 mag of A_V attributable to Cloud 3 is consistent with their estimates.

To create an extinction map, stars were collected into a rectangular grid of circular, overlapping bins with radii of 8 farcm 5 and separations of 2'. Weighted means were calculated within each bin from the individual stellar (NICER) extinctions, their uncertainty-based variances, and a spatial Gaussian weighting kernel having FWHM of 4'. The FWHM and bins were chosen to meet the Nyquist sampling limit and have 〈A_V〉 S/N ⩾3 over 50% of the grid points. The resulting extinction map is shown in Figure 5 as a grayscale image, which ranges from A_V = 0 to 9 mag. Overlaid as black and white contours are the same ¹³CO integrated intensities from Figure 1 (Tachihara et al. 2000a) to show the location of Cloud 3. As expected, regions of higher visual extinction correspond to high ¹³CO column densities and the dust extinction structure closely matches that of the gas. Additionally, the regions of lower extinction (A_V = 0.5–2 mag) closely match the extended 12 μm warm dust distribution seen in Figure 3.

To test strong-field models, it is necessary to identify the long axis of the cloud. The NICER extinction map in Figure 5 reveals the curve of Cloud 3, as seen by McCutcheon et al. (1986) and Tachihara et al. (2000a), which must be taken into account when determining the location of the long axis. The extinction map was used to locate the locus of peak local extinction of the cloud (i.e., the cloud "ridge"). The R.A. locations of the peak extinction found in decl. strips in the map were fit with a least-squares polynomial. An F-test supported, third-order polynomial fit was found to best describe the spatial variation of the ridge. This ridge locus is plotted in later figures and is featured in the analyses described below.

4.2. Magnetic Field Morphology

As seen in Figure 3, the highest-significance polarization stars are sparsely distributed and do not probe the most opaque parts of Cloud 3. To increase the polarization S/N across the whole cloud and to reach into the opaque cores, variance-weighted mean values of Stokes U and Q were calculated using all 3896 BF = 2 (i.e., background) stars having measured polarizations (i.e., including stars of all UF values). Stokes U and Q maps were generated using the same gridding technique employed for the NICER extinction map. The FWHM of the spatial Gaussian kernel was 6 farcm 6 and the bins had radii of 11' (4σ of kernel) and center separations of 3 farcm 3 (HWHM of the kernel). The kernel and bins were chosen to meet the Nyquist sampling limit and retain P/σ_P ⩾ 3 across 50% of the map area. The Stokes parameter maps were used to determine maps of P and P.A., as well as their uncertainties.

Figure 6 shows the resulting debiased P map as filled color contours. The white contour lines represent the NICER extinctions and are drawn at the same levels as used for the filled gray levels in Figure 5. The dotted white circle in the lower right shows the effective resolution (FWHM) of the P map. The highest mean polarization percentages occur on the southern, western, and northern edges of the highest extinction (A_V ⩾ 6.5 mag) region. A secondary P enhancement occurs at the southern map boundary. This P map will be discussed in Section 5.1.

Figure 7 shows the NICER extinction grayscale map from Figure 5 overlaid with vectors representing the mean P and P.A. calculated for the high significance bins (those exhibiting P/σ_P ⩾ 2.5, equivalent to σ_P.A. ⩽ 11 fdg 5). A 1% vector is shown in the lower right for reference. The thick, white dashed line shows the polynomial representation of the locations of the ridge of the cloud, as described above. The polarization orientations along the southern ridge of the cloud appear to be predominantly perpendicular to the local ridge orientation, while they appear to be predominantly parallel along the northern ridge.

4.2.1. Ridge Magnetic Field Directions

To further test this observation of field-ridge perpendicularity in the southern region of Cloud 3, the polarization properties along the ridge were examined. Stokes U and Q averaging was performed at R.A. positions along the ridge using the same bin sizes that were used in the previous analysis and a declination spacing of 4'. The ridge locations, resulting polarizations P, and polarization P.A.s (P.A._POL) are shown in the left panel of Figure 8.

**Figure 8.** Polarization properties along the extinction ridge of Cloud 3. (A) The mean P and P.A. along the ridge are shown as vector lengths and orientations, respectively. The white dashed line represents the extinction ridge. The extinction map is shown in the background as gray filled regions. (B) The absolute differences (ΔP.A.) between P.A._POL and P.A._RIDGE vs. decl. The black dashed lines represent the mean ΔP.A.s of the northern (decl. ⩾−12°20') and southern (decl. <−12°20') populations. Error bars represent the uncertainties in P.A._POL, only.
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P.A._POL was then compared to the position angle of the ridge (P.A._RIDGE), which was determined at each declination using the tangent to the ridge locations. The differences between the angles ( $\Delta \rm P.A. = |\rm P.A._{POL} - \rm P.A._{RIDGE}|$ ) are shown versus decl. in the right panel of Figure 8. The error bars for ΔP.A. represent only the uncertainties in P.A._POL. Values for ΔP.A. of 90° (0°) indicate that the polarization, and thus the magnetic field, is perpendicular (parallel) to the cloud ridge tangent in those places. The black dashed lines in the right panel of Figure 8 represent the mean ΔP.A.s of the northern (decl. ⩾−12°20') and southern (decl. <−12°20') populations. In the southern region of Cloud 3, the weighted mean ΔP.A. is 78 ± 6°, while the weighted mean ΔP.A. is 26 ± 8° in the northern region of the cloud. This may indicate a transition from a strong-field to a weak-field regime and will be further discussed in Section 5.1.

4.2.2. Application of the Chandrasekhar–Fermi Method

An estimate of the plane-of-sky (P.O.S.) magnetic field can be obtained from background starlight polarimetry using the Chandrasekhar–Fermi (C-F) method (Chandrasekhar & Fermi 1953). The C-F method, modified by Ostriker et al. (2001), estimates the P.O.S. magnetic field as:

$\begin{equation} B_{\rm P.O.S.} = 1.8 \rho ^{0.5} \frac{\delta v_{\rm L.O.S.}}{\delta \phi };\quad \delta \phi \le 25{^\circ }, \end{equation} \tag{ 5 }$

where B_P.O.S. is measured in Gauss, ρ is the mean mass density (in g cm⁻³), δv_L.O.S. is the L.O.S. gas velocity dispersion (in cm s⁻¹), and δϕ is the background starlight linear polarization P.A. dispersion (in radians).

To create a full-cloud magnetic field map, δϕ was calculated across the cloud using the same bins and weighting as was used for the Stokes U and Q maps. Only BF = 2 stars were used for these calculations. A σ_P.A. ⩽ 15° cut retained at least 10 stellar polarizations in each bin across the cloud. Due to the 180° ambiguity of polarization P.A.s (i.e., P.A. = 0° and 180° indicate the same magnetic field orientation), dealiasing the P.A.s was sometimes necessary. This dealiasing was done by finding the biased range which produced the minimum δϕ. P.A. distributions properly centered within biased ranges showed δϕ values smaller than when aliasing was present. At each grid point, the minimum δϕ was found by sweeping through different biased ranges, in bias increments of 10°. The resulting δϕ map had a minimum dispersion of 15 fdg 7 and a median dispersion of 38 fdg 5. Thus, δϕ is greater than 25° for the majority of Cloud 3, making the C-F method inapplicable, as noted by Ostriker et al. (2001).

However, for the 15 bins meeting the Ostriker et al. (2001) requirement of δϕ ⩽ 25° and having ¹³CO measurements, an estimate of the plane-of-sky magnetic field could be made. The average ¹³CO line profile for each L.O.S. was used to determine ρ and δv_L.O.S.. The H₂ column density (in cm⁻²) was first found using:

$\begin{equation} N_{\rm H_2} = (4.92 \times 10^{20}) \: T \: \sigma _v \end{equation} \tag{ 6 }$

from Simon et al. (2001), where T is the peak antenna temperature in K and σ_v is the velocity FWHM. To convert this column density to a volume density, two different effective diameters were estimated, the full-width at half-power (FWHP) and the full-width at zero-power (FWZP). Assuming cylindrical symmetry, B_P.O.S. estimates were determined for all 15 bins using the FWZP diameters and 13 bins using the FWHP diameters (the other 2 bins lay outside the FWHP radius).

The 15 bins are located in three distinct regions, so an average estimate of B_P.O.S. (in μG) was calculated for each region, as shown in Figure 9. The lower average estimates (∼11–14 μG) are derived from the FWZP diameters, which are larger and thus yield lower values of ρ. Within each region, the standard deviation of B_P.O.S. is ∼2 μG. The bins used in these calculations are denoted by black "X"s. The higher average estimates (∼13–26 μG) are derived from the FWHP diameters. The standard deviation within each of the three regions is ∼3 μG. The bins used in these calculations are denoted by the black crosses, which lie on top of the "X"s.

These average estimates of B_P.O.S. reveal a moderate strength magnetic field, which is consistent with the total field strength estimate of Heiles (1988), but are much smaller than the McCutcheon et al. (1986) estimate. These new B_P.O.S. estimates also indicate that the field strength may be somewhat greater in the dense core of the cloud.

4.3. Polarization Efficiency

The mean A_V through the Cloud 3 region is low (∼ 0.5 mag) and should allow for RAT aligning radiation to penetrate into the cloud. To study grain alignment efficiency in L204, the polarization efficiency² (PE ≡ P_H/A_V) was examined, as a function of A_V, for the entire surveyed region. To increase S/N, background stars (BF = 2) with UF = 1 and 2 were placed into 12 logarithmically spaced extinction bins, based on their nominal A_V values (from Table 1). Weighted mean PE and A_V values were calculated using the nominal values, variance-weighted by their uncertainties. Bin uncertainties for A_V and PE were computed from the summed variance weights. For some low A_V bins, these bin uncertainties exceed the bin widths. Figure 10 shows the resulting 〈A_V〉 and 〈PE〉, as well as the bin boundaries (top axis). A power-law index was found by linear regression to:

$\begin{equation} \log\left(\frac{P_{\rm H}}{A_{\rm V}}\right) = \alpha \log(A_{\rm V})+\beta, \end{equation} \tag{ 7 }$

where α is the power-law index and β is a constant offset. The dashed line in Figure 10 represents the least-squares fit, with an α index of −0.74 ± 0.07.

However, there may be problems with this technique. As pointed out by Andersson & Potter (2007), the extinctions used are representative of the optical depth along the line of sight to each background star, but more important is the optical depth between the illuminator and the aligned dust grains, which is harder to measure. To try to account for this "true" optical depth, PE was also examined as a function of distance from ζ Oph. The surveyed region was divided into six regions, shown in Figure 11. The region boundaries were chosen based on R.A. (i.e., distance from ζ Oph) and the shape of cloud, determined by examining the extinction map. The regions are labeled "1"–"6," with larger region numbers corresponding to larger angular offsets from ζ Oph.

**Figure 11.** Regions for mean PE determination. Region boundaries were chosen to reflect the shape of Cloud 3 and to test for changes in PE with distance from ζ Oph. Region numbers are indicated at the bottom. Figure 5 extinctions are shown in gray-scale.
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The weighted mean PE and its uncertainty were calculated within each of these regions, and the resulting values are shown in Figure 12. With the exception of Region 3, the center of the cloud, the mean PE is well fit by a linear regression with a slope of −0.027% ± 0.008% polarization per mag per region (or −0.09% ± 0.03% mag⁻¹ pc⁻¹). This indicates that as the distance from ζ Oph increases, the PE decreases. Additionally, in the core of the cloud, which is well shielded from radiation, the mean PE is 9.8σ less than that predicted by the fit to the rest of the cloud. (This difference decreases to 2σ when also taking into account the uncertainties in the fitted line coefficients.)

To further test for shadowing effects in Cloud 3, stars in the field were assigned to one of three larger zones: the ridge (Region 3), the west side of the cloud (Regions 1 and 2), and the east side (Regions 4–6). Within each zone, the stars were placed into the same 12 logarithmically spaced extinction bins used in Figure 10. Linear, least-squares fits of 〈PE〉 versus 〈A_V〉 were calculated in each of the three zones, using only bins with at least 5 stars and Equation (7), to find the power-law index α in each zone. The α indices and their uncertainties are shown in Figure 13. A power-law index of α = −1, shown by the black dashed line, is characteristic of uncorrelated polarizations and extinctions (i.e., forced to be −1 because PE ∝1/A_V).

**Figure 13.** PE power-law α index vs. zone in the survey region. Error bars represent 1σ uncertainties in the fitted α indices. An α index of −1 (black dashed line) is expected if the distributions of P_H and A_V are fully uncorrelated.
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The α index changes across the cloud and appears to decrease with distance from ζ Oph. The α index in the western zone closely matches that seen for the entire Cloud 3 region in Figure 10 (−0.77 ± 0.25 versus −0.74 ± 0.07). This suggests that the stars in the western zone may be dominating the power-law fit for the entire cloud. Due to the small number of stars in each zone, the uncertainties in their α indices are significant and none of the zones differ significantly from α = −1. Taken at face value, even though the mean PE decreases with distance from ζ Oph, the PE slope with A_V has not been found to vary significantly with that distance. These results will be further discussed in Section 5.2.

5. DISCUSSION

The NIR background starlight polarizations observed toward Cloud 3 of L204 have revealed a wealth of information about conditions within and around the cloud. Through Stokes U and Q averaging of the many background starlight polarizations, including those with low individual significance, the magnetic field structure of Cloud 3 has been revealed. Combined with NICER extinctions, the stellar polarizations also provided insight into the dust grain alignment efficiency throughout the cloud. In the following sections, these properties are highlighted.

5.1. Magnetic Field Characteristics

Previous optical polarimetric observations of stars behind L204 (McCutcheon et al. 1986) revealed that the magnetic field is predominantly perpendicular to the long axis of the cloud complex and is coherent over separations of several parsecs. The new observations presented here, however, reveal a more complex magnetic field on smaller scales. The mean polarization percentage map in Figure 6 does reveal that larger polarizations tend to be associated with regions of modest extinction, implying that the magnetic field being probed is associated with the cloud and is aligning internal dust grains.

Figure 14 shows a similar view of the L204 region as that in Figure 1, overlaid in red by the mean polarization map from Figure 7. This map reveals a wide range of P.A.s in the vicinity of Cloud 3. Though there are changes in P.A. within and across the cloud, the direction of the magnetic field is predominantly perpendicular to the long axis of the cloud in the southern region, as seen in Figure 8. This axis-perpendicular field, which is shielded by the rest of the cloud and less likely to have been influenced by ζ Oph, may be a remnant signature of the collapse of L204. This would indicate that L204 collapsed under strong-field conditions, e.g., along the magnetic field lines.

However, at the northern and western edge of the cloud (facing ζ Oph), the P.A.s are parallel to the extended 12 μm dust emission, appearing to be compressed against the side of the cloud. This may indicate that while clearing out a cavity, the UV flux from ζ Oph has pushed the magnetic field on the western side of L204 up against the high density core. This discrepancy between the northern and southern regions of Cloud 3 may be a sign of a transition between strong-field collapse and present weak-field conditions.

Though the P.A.s appear to vary smoothly in Figure 14, the dispersions of local sets of individual stellar polarizations are large, up to 50° in some parts of the cloud. As discussed in Section 4.2, these large dispersions are unsuitable for estimating the P.O.S. magnetic field strengths for most of the cloud using the C-F method (which seems more applicable to quiescent conditions, e.g., Marchwinski et al. 2012). However, an estimate of the P.O.S. magnetic field strength was possible for 15 positions and yielded an average B_P.O.S. ∼ 11–26 μG. These estimates are consistent with the estimates of Heiles (1988), but smaller than the (McCutcheon et al. 1986) estimated value. The large P.A. dispersions found in Cloud 3 suggest that there may be significant turbulent motions and tangled magnetic fields present. Tachihara et al. (2012) performed CO J = 1–0 and 3–2 observations of the western edge of Cloud 3 and found evidence of turbulence driven by thermal instability.

5.2. Grain Alignment

Polarization efficiency, and grain alignment efficiency, are known to decrease in the dense cores of molecular clouds (Goodman et al. 1995). This decrease is predicted by many grain alignment theories, including RAT theory. A unique prediction of RAT theory (Lazarian & Hoang 2007), however, is that in the presence of a strong, anisotropic radiation field, dust grains will remain aligned deep into molecular clouds.

For the entire surveyed Cloud 3 region, the PE versus A_V fit power-law index α, shown in Figure 10, is −0.74 ± 0.07. This is significantly steeper than similar indices found for other clouds. In the Taurus Molecular Cloud, Gerakines et al. (1995) found an index of −0.56 ± 0.17 at K band. Whittet et al. (2008) found indices of −0.52 ± 0.07 and −0.45 ± 0.10 for the Taurus and Ophiuchus clouds, respectively, at K band. Together, these imply that grain alignment in Cloud 3 in L204 becomes less efficient as extinction increases than in the other clouds. Thus, it would appear that the strong radiation field from ζ Oph is less able to boost grain alignment efficiency in L204, relative to these other clouds.

However, as mentioned in Section 4.3, the extinctions used are representative of the optical depth along the L.O.S. to background stars and are not providing the optical depth between ζ Oph and the dust. Figure 12 tries to take this effect into account by testing how the PE changes with distance from ζ Oph. With the exception of Region 3, the PE steadily decreases with increasing distance from ζ Oph. This relation indicates that where they are exposed to a stronger radiation field, dust grains are more efficiently aligned.

The unusually low mean polarization efficiency in Region 3 is not unexpected, because this region contains the highly extincted Cloud 3 core. As seen in Figure 3, the core of the cloud (R.A. ≃ 16:47:30, decl. ≃ −12:15:00) is opaque even at 4.6 μm, making it unlikely that short λ radiation, from ζ Oph or elsewhere, is reaching these grains, and so prevents background starlight from finding aligned grains to easily reveal any magnetic field there.

Further evidence of a possible change in grain alignment efficiency with distance from ζ Oph was shown in Figure 13. Though all three power-law indices are marginally consistent with the polarization being independent of extinction, there remains an apparent change in α with distance from ζ Oph. On the ζ Oph facing (West) side of Cloud 3, the α index is flatter, suggesting dust grains remain better aligned to higher column densities. Farther away from ζ Oph (East), the α index is steeper, indicating less polarization per mag of A_V. A linear fit to the data in Figure 13 (not shown) produces a slope of 0.20 ± 0.16. This, however, is not a significant change and does not exclude a constant α index throughout the cloud.

As with Figure 10, the polarization efficiencies in Figures 12 and 13 were calculated using L.O.S. extinctions. Though these are not strictly correct optical depths, they are readily available. Truer estimates of the optical depths between ζ Oph and the aligned dust grains may reveal stronger correlations.

Due to the projection of L204 in front the H ii region surrounding ζ Oph, the relative placements of L204 and ζ Oph are known, but the exact geometry of the system is unknown. The decay in PE with offset from ζ Oph in Figure 12 falls far faster than r⁻², even assuming ζ Oph and Cloud 3 are at the same distance. Thus, distance dilution of the radiation field alone is insufficient to account for the PE decay and another factor, such as extinction, has a lead role. This implies that the assumption that L204 and ζ Oph are at the same distance is not a bad one and that the eastern side of the cloud is being shielded by the western side.

5.2.1. V446 Oph

Due to its bright appearance in Figure 3, one might conclude that V446 Oph, not ζ Oph, is illuminating Cloud 3. However, V446 Oph is probably much more distant and unlikely to interact with L204. It is a semiregular variable star with a B-band amplitude of ∼1 mag (Samus et al. 2009), has a spectral type of M8 (Hansen & Blanco 1975), and hosts an SiO maser (Hall et al. 1990). Based on these, V446 Oph is likely a red supergiant. If an absolute K_S magnitude of −6.5 mag is assumed for all M I-II stars (Nikolaev & Weinberg 2000), then with K_S = 0.923 mag (Skrutskie et al. 2006), V446 Oph would have to experience 24 mag of visual extinction to be at the same distance as L204. This is inconsistent with its NICER estimated extinction of A_V = 5.5 ± 2.6 mag, which places it at a minimum distance of ∼243 pc. This is well beyond the L204 complex, reaffirming that V446 Oph is not the illuminator for L204.

6. SUMMARY

We have used NIR H-band linear polarization of background starlight to probe the magnetic field of Cloud 3 in L204. The mean polarization properties of the cloud were determined through spatial averaging of the Stokes U and Q values for the 3896 background stars with measured polarizations and exhibiting A_V ⩾ 0.5 mag.

These mean properties revealed that Cloud 3 has a coherent magnetic field, oriented predominantly perpendicular to the long axis of the cloud in its southern region. There, the mean deviation of the field from being cloud-perpendicular is 12°. The small deviations from cloud-perpendicular in the southern portion of the main cloud ridge support strong magnetic field models and suggest that this portion of the cloud collapsed (or has been pushed or driven) along the magnetic field lines. The corresponding mean deviation of the field from the cloud long axis in the northern region is 64°. The direction of the field in this region implies that the UV flux from ζ Oph has compressed the (weak) magnetic field against the face of Cloud 3.

The B_P.O.S. field strength is estimated to be ∼11–26 μG, using the C-F technique, for the small number of locations exhibiting sufficiently small P.A. dispersions.

The dust-grain alignment was probed via measuring the P_H/A_V versus A_V power-law index α. For the entire Cloud 3 region, this index is −0.74 ± 0.07, which is steeper (i.e., shows less grain alignment at high extinctions) than similar indices found by others for other molecular clouds. However, the polarization efficiency and, thus, dust grain alignment efficiency changes with location and extinction within Cloud 3. Specifically, grain alignment efficiency decreases with increasing distance from ζ Oph and is also significantly lower in the dense core of Cloud 3.

The authors thank M. Pavel and A. Pinnick for performing some of the observations and for helpful discussions. The authors thank K. Tachihara for making the mm CO data available. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center (IPAC)/California Institute of Technology (CalTech), funded by NASA and NSF and the from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and JPL/CalTech, funded by NASA. This research made use of the C. Beaumont IDL library, available at www.ifa.hawaii.edu/users/beaumont/code. This research was conducted in part using the Mimir instrument, jointly developed at Boston University and Lowell Observatory and supported by NASA, NSF, and the W. M. Keck Foundation. This work and the analysis software for Mimir data were developed under NSF grants AST 06-07500 and 09-07790 to Boston University.

Facility: Perkins (Mimir) - Lowell Observatory's 72in Perkins Telescope

THE MAGNETIC FIELD OF CLOUD 3 IN L204

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ABSTRACT

1. INTRODUCTION

2. THE L204 LABORATORY

3. OBSERVATIONS AND DATA REDUCTION