The linearly polarized background starlight observed in early studies (Hall 1949;Hiltner 1949a) was suggested to result from dichroic absorption by nonspherical dust grains aligned to B fields (Hiltner 1949b). Hence, polarized starlight is commonly used as a tracer of the B-field structure in the plane of sky (e.g., Chapman et al. 2011;Clemens et al. 2012c;Eswaraiah et al. 2012). The first theory to explain dust alignment used a paramagnetic mechanism (DG alignment; Davis & Greenstein 1951). However, later studies revealed timescale and efficiency problems, so other alignment mechanisms were offered, including superparamagnetic grains (Jones & Spitzer 1967) and superthermal rotation rates (Purcell 1979). Nevethless, most of these mechanisms are only efficient for particular physical conditions, and fail to explain the polarization observed across a wide variety of environments (see review in Andersson et al. 2015).
The model of radiative alignment torques (RATs; Dolginov & Mitrofanov 1976;Draine & Weingartner 1996, 1997;Lazarian & Hoang 2007) can currently best explain how dust grains align with B fields. The RATs theory assumes an anisotropic radiation field impacting nonspherical dust grains. The radiation field can generate net torque on the grains and induce both spin of the grains and precession about the B field. For typical interstellar radiation fields, the RATs alignment timescale is much faster than DG alignment (Lazarian & Hoang 2007), and superthermal rotation tends to enhance RATs alignment more than DG alignment (Hoang & Lazarian 2009). In addition, RATs is efficient across a variety of environments, and thus more likely dominates the grain alignment process.
A key prediction of the RATs theory is the decreasing polarization efficiency (PE, l P /A V ) with increasing A V , because the radiation field required to align the dust grains is decreased through extinction (Lazarian et al. 1997). In order to examine whether the RATs theory can explain observed polarizations, Whittet et al. (2008) performed a numerical simulation based on RATs theory and assuming a starless core with only an external radiation field and a fixed dust grain size distribution for all A V . Their simulation results matched their K-band polarimetry data toward Taurus up to at least à 10
V mag; the K-band polarization degree varied with A V as a power law, with t µ l -P A K V 0.52 . In addition, their simulation predicted that the RATs mechanism would cease as A V approached 10 mag, since the radiation that can penetrate to such high column densities has wavelengths too long to effectively align the grains. However, the single power-law matched their data over the = -A 0 30
V mag range well, which was inconsistent with the predicted cessation of alignment at à 10 V mag. To explain the inconsistency, Whittet et al. (2008) argued that the RAT mechanism may still work in high-A V regions if (1) the dust grains have undergone significant growth and so can couple to longer wavelength radiation, or (2) embedded stars are present to provide radiation at shorter wavelength to enhance the alignment of small dust grains.
To further test the RATs theory in dense clouds, Jones et al. (2015) used both infrared and submillimeter polarimetry data to trace the variation of polarization efficiency (PE) up to à 100
V mag within starless cores. They found a change of power-law index for PE versus extinction from -0.5 to -1 at à 20 V mag, consistent with the cessation of alignment predicted by Whittet et al. (2008). In addition, Jones et al. (2016) found a deeper break point at ÃV hundreds mag and a reversed trend such that the power-law index of PE versus A V changed from -1 to -0.5 within the Class 0 YSO G034.43 +00.24 MM1. The opposite trends shown in these two cases suggest that dust alignment in dense clouds could be strongly affected by environmental effects.
In the RATs paradigm, the polarization degree is expected to be wavelength dependent because the cloud extinction penetration is wavelength dependent and because the highest alignment efficiency occurs at wavelengths similar to the sizes of the grains (Cho & Lazarian 2005;Lazarian & Hoang 2007). Therefore, the polarization wavelength-dependence is determined by both the extinction and the size of dust grains, resulting in a polarization spectrum exhibiting a single peak (l max ). Kim & Martin (1995) showed that l max is sensitive to the small-size cutoff of the grain size distribution, since the dust size distribution is a power law and the small-size cutoff will effectively determine the mean size of the dust grains. Whittet et al. (2008) calculated the l max variation with A V using a RATs model with a fixed grain size distribution over A V , and showed that the RATs theory can explain their observed dependence of l max increasing with A V to ∼6 mag, but that RATs predicts that l max flattens for higher A V in the Taurus cloud.
Recent observational results are mostly consistent with the RATs theory (Whittet et al. 2008;Alves et al. 2014;Cashman & Clemens 2014), although the dust alignment efficiency varies from source to source. As an extreme case, Goodman et al. (1995) found a constant near-infrared polarization degree toward L1755 for A V of 1-10 mag, and argued that nearinfrared polarization can only trace the B field on the surfaces of dark clouds. In contrast, other observations mostly showed a polarization degree increasing with A V , such as µ P A V 0.48 toward Taurus (Whittet et al. 2008) and µ P A V 0.26 toward the L204 cloud 3 (Cashman & Clemens 2014), suggesting that the constant polarization degree found in Goodman et al. (1995) represented a special case and was not the norm.
It is still unclear why the P-A V relation found in L1755 is different from the relation found for other clouds. Whittet et al. (2008) reanalyzed the L1755 polarimetry data with a better background star selection and extinction estimation, but still found the same relation. They speculated that this unique relation might result from a lack of the typical physical conditions leading to grain alignment inside this cloud or a reduction of observed polarization that is due to the complex B-field structure within the L1755 filaments. To examine these possibilities, more polarimetry observations covering both a wider area and more wavebands could help to reveal the alignment conditions for dust grains with different sizes and to probe the detailed B-field structure. In addition, since the Goodman et al. (1995) polarization detections only spanned a small range of A V (2-8 mag), it would be of interest to perform polarization observations with higher sensitivity to investigate this relation to higher A V values.
An ideal target for a detailed testing of the RATs paradigm is the system of dark cloud filaments associated with the reflection and emission nebula IC5146, a nearby (∼460 pc) star-forming region in Cygnus. The system consists of a young cluster inside an H II region and a long main dark cloud filament with several subfilaments branching out from the main filament. The HerschelGould Belt Survey (Arzoumanian et al. 2011) revealed a complex network of filaments within the long dark cloud, highlighting the locations of young forming stars. The Planck polarization map of IC5146 (Planck Collaboration et al. 2016c) revealed that the B field is nearly uniform, with the millimeter-wavelength-traced B field oriented perpendicular to the elongation orientation of the main filament. This apparently uniform B field gives the IC5146 dark cloud system an advantage for testing the RATs model because the high angular resolution of stellar polarizations can be used to test for, and quantify, complex B fields along the multiple line of sights.
In a series of papers, we will report measurements and analyses of the polarizations of stars behind the IC5146 filamentary cloud. The polarimetry of background starlight was performed at both optical and infrared wavelengths to probe the large-scale B field in the cloud. In this paper, we focus on the dust properties and the dust alignment conditions revealed by our data in order to identify where the B fields were accurately probed by our observations. The observations and data reduction are described in Section 2. In Section 3 we present the polarization measurements toward IC5146. Section 4 presents an initial analysis of the data to show how the dust grain alignment conditions vary with A V and regions. In Section 5 we discuss the evolution of dust grains and how the dust properties influence the PE. The consequences of these results for the investigations of the role of B fields in cloud evolution will be offered in the forthcoming Paper II.
We measured the polarization of background stars toward the IC5146 filamentary cloud system with several instruments: the Aryabhatta Research Institute of Observational Sciences (ARIES) Imaging Polarimeter (AIMPOL; Rautela et al. 2004) and Triple-Range ( ¢ g , ¢ r , ¢ i ) Imager and POLarimeter (TRIPOL; S. Sato et al. 2017, in preparation) provided optical R c -and ¢ i -band polarimetry data, respectively. Mimir (Clemens et al. 2007) measured the H-and K-band polarizations at nearinfrared wavelengths. Figure 1 shows the target fields for each instrument overlaid on the Herschelarchive 250 μm image (Griffin et al. 2010;Arzoumanian et al. 2011). The dust continuum map shows an east-west main filament connected to the bright cluster complex, known as the Cocoon Nebula. Numerous "subfilaments" are extended from the main filament, with the largest subfilament located on the northwest side of the main filament. Almost all parts of the cloud were observed with Mimir, while the fields observed with AIMPOL were chosen to be mainly in the edge of the cloud in order to cover as many optically bright stars as possible. The TRIPOL observations focused on the northwestern region, with longer exposure time, where bright stars are rare at both optical and infrared wavelengths. The detailed information of the observations with the different instruments is described below.
The R c -band (0.67 μm, bandwidth=0.14 μm) polarimetric observations were carried out toward the IC5146 filamentary cloud system using AIMPOL, which is mounted at the Cassegrain focus of the 104 cm Sampurnanand telescope of the ARIES, Nainital, India. AIMPOL consisted of a half-wave plate (HWP) modulator and a Wollaston prism beam-splitter illuminating a fraction (370×370 pixel 2 ) of the Tektronics 1024×1024 pixel 2 CCD camera. The pixel size of the CCD was 1.73″and the typical seeing was ∼2″. The observations spanned the nights of 2011 November 4-8 and 2012 November 8-15 and covered 37 fields (see Figure 1), with each field having a useful diameter of ∼8′. In order to obtain Stokes Q and U, we took images at four independent HWP orientations (0°, 22°.5, 45°, and 67°.5; Schaefer et al. 2007). The Wollaston prism analyzer produced offset, but simultaneous, ordinary and extraordinary overlapping images for each HWP orientation. Hence, each image resulted in one measurement of Stokes Q or U. The integration time was set to 10 minutes for each HWP orientation, so the total integration time for each field was 40 minutes.
The polarization measurements were calibrated for instrumental polarization and offset angle by observing standard polarized and unpolarized stars drawn from Schmidt et al. (1992). The data were reduced using standard IRAF procedures. 6 The fluxes in the ordinary and extraordinary beams for each observed source were extracted using standard aperture photometry. Sources with stellar overlap, fewer than 10% of the total sources, were excluded. The polarization degree and angle for each star were derived from the relative fluxes in the ordinary and extraordinary beams. We removed the Ricean bias with the asymptotic estimator
where P is the debiased degree of polarization, Q and U are normalized Stokes Q and U, and s P is the uncertainty in the polarization percentage (Wardle & Kronberg 1974). The details of the observing facility and procedures used to estimate the polarization degree and polarization angles (P.A.) are described in Eswaraiah et al. (2011Eswaraiah et al. ( , 2012)).
Polarimetric observations focused on the northwestern region of IC5146 in the ¢ i bands (0.77 μm, bandwidth 0.15 μm) on 2012 July 27-28 and 2014 July 6 with TRIPOL installed on the Lulin-One-meter Telescope in Lulin Observatory, Taiwan. Seven fields, each with a size of 4′×4′, were observed (see Figure 1). TRIPOL consisted of dichroic mirrors and three ST-9 512×512 pixel 2 CCD cameras, which enabled simultaneous observations in the ¢ g , ¢ r , and ¢ i bands; however, only the ¢ i -band data were able to detect background stars behind this dark cloud. The pixel sizes of the CCDs were 0.5 arcsec and the average seeing was ∼1 5. A rotatable achromatic half-wave plate and a fixed wire-grid were used to analyze the incoming light. Each field was measured at four HWP orientations (0°, 22°.5, 45°, and 67°.5, with pairs of images yielding stellar Stokes Q and U values.). The integration time for each position angle was 22.5 minutes, so each field required a total of 1.5 hours.
Standard reduction procedures were applied using IRAF, and the photometry of each background star was obtained using Source Extractor (Bertin & Arnouts 1996). The debiased polarization degree and angle for each background star were derived from the fluxes measured through each of the four HWP orientation angles and calibrated against observations of polarized and unpolarized standard stars from Schmidt et al. (1992).
We carried out H-(1.6 μm) and K-band (2.2 μm) polarization observations toward IC5146 on 2013 September 17-27, using the Mimir instrument (Clemens et al. 2007), which is mounted on the 1.8 m Perkins telescope located near Flagstaff, AZ, and operated by Lowell Observatory. Fifty-seven fields covering the IC5146 cloud were observed in the H band, and 12 fields were observed in the K band toward the dense regions (see Figure 1). The pixel size of the InSb detector array was 0.58 arcsec and the average seeing was ∼1 5. The field of view was 10′×10′ for Mimir, and we set 1′ overlap between adjacent fields. Each field was observed in six sky-dither positions where images were taken at 16 orientation angles of the HWP. A total of 96 (16×6) images were taken for each field with 10 sec of integration time for each image for both the H and K bands, and thus the total integration time was 16 minutes for each field. We took an additional short integration for fields with bright stars, which took 4 minutes per field.
In order to calibrate the nonlinearities of the InSb detector array, a series of images were taken with an increasing exposure time toward an illuminated flat-field screen, and the response curve of each pixel was fitted with a polynomial model to obtain a linearity correction. Flat fields for each HWP position were taken using a lights-on/lights-off method toward a flat-field screen inside the closed dome during the observation run. The data were calibrated using the Mimir Software Package Basic Data Processing (MSP-BDP), and the Photo POLarimetry tool (MSP-PPOL) was used to extract Stokes Q and U values for each observed source from the calibrated data. The detailed processes used in the Mimir Software Package are described in Clemens et al. (2012aClemens et al. ( , 2012bClemens et al. ( , 2012c)).
We matched the polarization data to the 2MASS catalog (Skrutskie et al. 2006) to obtain positions accurate to 0.5 arcsec. Table 1 lists all the observed polarization properties as well as photometric magnitudes from 2MASS and WISE (Wright et al. 2010). Column 1 lists the star number, and columns 2 and 3 list the R.A. and decl. The measured Stokes Q, U, debiased P, and position angle P.A. in the R c , ¢ i , H, and K bands with their uncertainties are listed in columns 4-35. The J-, H-, K-, W1-, and W2-band magnitudes and uncertainties are listed in columns 36-45. Column 46 presents the estimated visual extinction described in Section 4.1. Column 47 present the Usage Flag (UF; stars with UF=1 were selected for further analyses, and stars with UF=0 were not used). The usage data were selected with the polarization degree divided by its uncertainty s P p 3 for the R c and ¢ i bands, and s P p 2 and s p < 5% for the H and K bands; the selection criteria were relaxed for near-infrared data, since the number of 3σ nearinfrared detections was too small for adequate statistics.
In total, 2022 independent background stars have polarization detections in at least one of the four bands, 239 stars were detected in two bands, 24 stars were detected in three bands, and only 3 stars were detected in all four bands. About 71% of the background stars were detected in the H band, 24% in the R c band, 10% in the ¢ i band, and 8% in the K band. Figure 2 shows all of the polarization measurements on the HerschelSPIRE 250 μm image. The inferred B field is seemingly perpendicular to the main filament on large scales but parallel to the subfilaments. The bimodal perpendicular or parallel alignment is similar to that seen in previous polarimetry work toward filamentary clouds, and has been ascribed to B-field confinement of sub-Alfvénic turbulence or gravitational contraction channeled by strong B fields (Li et al. 2013). We will discuss the B-field structure in detail and estimate the B-field strengths with the Chandrasehkar-Fermi method to determine the dynamical importance of the B fields in Paper II.
To test whether the results from AIMPOL, TRIPOL, and Mimir were consistent and thereby capable of revealing wavelength-dependent effects in the probed dust columns, we selected the stars that had detections at multiple wavelengths, and we examine their P.A.s in the different wavelengths in Figure 3. In total, 143, 31, and 65 stars were selected in R c -¢ i , R c -H, and H-K band pairs. The mean P.A. differences in these three band pairs were -4°.6±0°.8, 6°.2±0°. 8, and -2°.9±1°.6, respectively. The standard deviation of the measured P.A. differences were 8°.7, 16°. 3, and 26°.6 for the R c -¢ i , R c -H, and H-K band pairwise samples. The average expected uncertainties of P.A. difference, propagated from observational uncertainties (s
2 ), were 4°.2, 9°.3, and 12°. 3 for the R c -¢ i , R c -H, and H-K band pairwise samples. The P.A. difference standard deviations obtained from these sets are 1-2 times to the propagated instrumental uncertainties, which are acceptable values since the P.A.s may be intrinsically different at different wavelengths because they may trace the polarizations to different depths.
We attempted to identify and exclude foreground stars whose polarizations do not trace the B field of the IC5146 cloud system. To obtain enough star samples to represent the foreground polarization near IC5146, we selected stars with known distances and V-band polarization measurements from van Leeuwen (2007) and Heiles (2000), within a 10°radius sky area near IC5146. Figure 4 shows the V-band polarization degree (P V ) versus distance for these 41 stars. The distance of -+ 460 60 40 pc to the IC5146 cloud system (Lada et al. 1999) was used to separate these stars into foreground and background groups. The polarization degree rises significantly at a distance of ∼400 pc, which is possibly due to nearby clouds in the Gould Belt. For most of the stars with distances smaller than 400 pc, the polarization degrees are below 0.3%. This value was chosen as the upper limit of the foreground V-band polarization for the sky area near IC5146.
In the interstellar medium (ISM), the polarization in the V band is greater than that in the R c , H, or K bands (Serkowski 1973). Hence, based on the foreground star values in Figure 4, the foreground polarization in the R c , H, and K bands is expected to be lower than ∼0.3%. This foreground polarization upper limit is similar to the instrumental uncertainties of our data (~-0.2% 0.5%). Hence, any foreground stars were likely to have been already excluded by our selection criteria ( s > P 3 p for the R c and ¢ i bands and s > P 2 p for the H and K bands). Thus, we concluded that contamination by foreground stars was negligible in our sample set, and furthermore, that no foreground polarization correction to the remaining data was necessary.
Visual extinction provides an estimate of how many dust grains are responsible for the observed starlight polarization, and thus is required for estimating dust alignment efficiency and testing the RATs theory. We used the technique called near-infrared color excess revisited (NICER; Lombardi & Alves 2001)foot_2 to calculate the visual extinction over the IC5146 cloud system. The NICER technique uses multiband colors to obtain extinction for a target field, using extinction coefficients derived from Indebetouw et al. (2005). We selected a total of Note.
a The uncertainties of A V are 0.93 mag, estimated in Section 3.1.
(This table is available in its entirety in machine-readable form.) 186,319 stars from the 2MASS catalog and 46,100 stars from the WISE catalog that cover the IC5146 cloud system. To estimate the stellar intrinsic colors, a square control field, centered at R.A.=330°. 153, decl.=+47°.794 with a side length of 15′, was compared to the target field.
To examine the quality of the estimated extinctions, the NICER extinction map shown in Figure 5 was created and compared with the Herschelmap. The extinction map was created from the variance-weighted mean of NICER extinction of each individual star within a pixel grid with a pixel size of 30″. The pixel grid was smoothed using a Gaussian weighting kernel with an FWHM of 90″. The black contours in Figure 5 show the Herschel250 μm data. The morphology of the extinction map is almost identical to that of the 250 μm map.
Figure 6 shows the histogram of A V values derived from the NICER analysis. The uncertainties in A V arise both from the uncertainties of the spectral types and from the propagated photometric uncertainties. In order to estimate the overall uncertainty of A V , we selected all the stars that NICER assigned with negative A V , and assumed that the negative A V values were only due to A V uncertainties. This negative A V portion of the full distribution was duplicated and reflected about A V =0 to generate a new pseudo-A V distribution. Fitting this with a Gaussian centered at A V =0, we derived a standard deviation of 0.93 mag. Because this includes uncertainties from both spectral typing and observations, we adopted this value as our A V uncertainty.
To test whether the polarization measurements trace the magnetic field structure inside the IC5146 cloud system, we examined whether embedded dust grains align with the B fields via estimating how the degree of polarization varied with extinction. PE is defined as polarization percentage divided by A V . It describes how much polarization is contributed by dust grains in the line of sight. We used PE versus A V to test whether the dust grains are better aligned in the diffuse region, as predicted by the RATs model.
Figure 7 shows PE versus A V for the R c -band data. The data probability density over the PE-A V space, represented by the contours, was calculated using the kernel density estimation (Rosenblatt 1956;Parzen 1962); for each source, the probability distribution function was described by a Gaussian kernel, and the width of the Gaussian kernel was determined by the uncertainties of PE and A V . The probability density for the entire data set was represented by the summation of the Gaussian kernels.
To reduce the uncertainty from A V and also avoid the bias due to uneven sampling over A V , the variance-weighted means of PE and A V were calculated in bins of width log(A V )=0.1. The uncertainties of the weighted mean of PE and A V for each bin were propagated from the instrumental uncertainty and A V uncertainty for each sample. Stars that NICER assigned with negative A V were not used for PE determination, since their extinctions were negligible.
Similarly, PE versus A V plots for the ¢ i , H, and K bands are shown in Figures 8,9, and 10, respectively. In the ¢ i band, the last bin (A V =5 mag) was found to have significantly higher PE and the bin only contained two stars. This bin was judged to be an outlier, and was excluded from further analysis. In the four bands, PE always decreased with A V , but with different slopes. In addition, the PE at à 20 V mag is still half of the PE at à 4 V mag, suggesting that the dust grains in high-A V regions are still being aligned with some degree of efficiency.
The power-law behavior of PE-A V has been shown in previous studies (e.g., Whittet et al. 2008;Chapman et al. 2011;Cashman & Clemens 2014) and apears to match the prediction of the RATs theory well. However, recent studies have also discovered changes in the index of the power law for highextinction regions (Alves et al. 2014;Andersson et al. 2015). To test whether in the IC5146 dark cloud system the power-law index changes with A V , we fit l P /A V versus A V with both a single power law (hereafter, Model 1), and with a broken power law (hereafter, Model 2),
The four parameters a 1 , b 1 , and b 2 , and BP were all taken as free parameters in the fit to Model 2.
The goodness-of-fit on the binned data to the two models was examined using the F-test and the bias-corrected Akaike information criterion (AICc, Akaike 1974;Sugiura 1978). The two different model comparison methods may exhibit different preferences. For example, Ludden et al. (1994) used Monte Carlo simulations to examine the performance of these methods, finding that the F-test tends to choose the simpler model more often than does the AICc, even when the more complex model is correct. To avoid possible bias, we used both methods to compare the model fits, and the preferred model was chosen to be the one for which (1) the F-test probability was below 0.05 (95% confidence level) and (2) had the lower AICc value. The results of the fitting and model comparisons are listed in Table 2. Both the F-test and AICc show consistent results; the broken power law is the better model for H bands, and the single power law is the better model for the R c , ¢ i , and K bands.
The PE-A V relations were empirically found to be insensitive to observing wavelengths (e.g., Andersson et al. 2015, and references therein), although our observed PE-A V relations might be expected to show some differences among the observing bands, since each data set covered different A V and spatial ranges. The R c -and ¢ i -band data mostly probed the regions with A 4
V mag, and thus the derived PE indices mainly characterize the low-A V regions. The power index of -0.71±0.10 for the R c band is very different from the index for the ¢ i band, namely -1.23±0.10. In addition, the power index of -0.95±0.30 for the H band for low-A V values is in between the indices for the R c band and the ¢ i band. For high-A V regions, the index of -0.25±0.06 for the H band is softer than the index for the K band (-0.53 ± 0.09), and both are flatter than all of the indices characterizing low-A V regions. This finding may indicate that the physical properties of grains, as well as their alignment efficiencies, change significantly beyond ~-A 3 4
V mag (see Section 5.4). The R c , ¢ i -, and H-band data all covered the A 4
V mag regime; however, the power-law indices for these three bands were all different. One major difference between the R c -, ¢ i -, and H-band data was that the H-band observations covered almost all of the IC5146 cloud system, while the R c -band observations mostly covered the main filament, and the ¢ i -band observations only probed the northwest filament (see Figure 1).
To test whether the indices characterizing low-A V regions differ from region to region, the stars with H-band detections and < A 3
V mag were assigned to one of the five zones delineated in Figure 11. Within each zone, single power-law indices were derived, and they are shown in Figure 11. Powerlaw indices ranging from -0.81±0.13 to -1.80±0.38 were fit to the assigned H-band data within the different zones. The indices were significantly softer in the eastern part of the cloud than in the western and northern part. In addition, the index derived within the northern zone was -1.18±0.14, nearly identical to the index for the ¢ i band, namely -1.23±0.06, covering a substantially similar region. Hence, the PE-A V relation varies by region in the low-extinction regions. The different indices derived for the different wavelengths for the whole cloud could then merely arise from the combination of a variety of PE-A V relations. The possible origin of the diverse PE relation is discussed further in Section 5.3.
The polarization of starlight is known to be wavelength dependent, resulting in a polarization spectrum. Since this wavelength dependence originates from dust properties and alignment conditions, the polarization spectrum can be used to investigate the evolution of dust grains. The polarization spectrum is well-fit by the empirical "Serkowski relation,"
where P max is the peak polarization degree at wavelength l max (Serkowski 1973). In later studies, the parameter K was shown to follow the relation = - + K 0.1 l c max (Wilking et al. 1982), where c was found to depend on dust properties, such as Note. The preferred model is determined by (1) a p value from the F-test below 0.05 (95% confidence level) or (2) a lower AICc value. geometric shape (e.g., Voshchinnikov et al. 2013;Voshchinnikov & Hirashita 2014).
To fit the Serkowski relation for its three parameters, detections in at least four bands are required to obtain uncertainties in the parameters. However, it is difficult to do so in the presence of high extinction. Thus, most of the previous studies have been limited to low-extinction regions. Even in our data, only three stars were detected in all four wavebands. The Serkowski relation fit results for these stars are shown in Figure 12. The range of fitted l max is ∼0.72-0.83 μm, significantly greater than the typical value ∼0.55 μm characterizing the general diffuse interstellar medium (Serkowski et al. 1975).
It is difficult to obtain the necessary multiple wavelength polarization detections needed to fit Serkowski relations in the presence of strong extinction. In order to have more samples to constrain l max , we examined the "polarization color" (the ratio of polarization degrees at two bands) as a partial descriptor of the polarization spectrum. Polarization color can be easily obtained from a limited set of wavebands without presumption of the spectrum shape. The Serkowski relation has been suggested to be only valid for a limited wavelength range, mostly UV through optical. Martin (1989) found that the polarization spectrum between 1.6 and 5 μm wavelength behaved more like a power law than like the Serkowski relation, and Clayton et al. (1992) found that the polarization spectrum in the ultraviolet showed an excess with respect to the Serkowski relation.
In the wavelengths where the Serkowski relation is valid, polarization color can constrain l max . Following the Serkowski relation, the ratio of the polarization degree of a star at two wavelengths can be written as
To reduce the free parameters, we also assumed the relation K=-0.1+ l c max , where c is expected to be a constant over A V . Via Equation (5) and the assumptions regarding K, the polarization color (ratio) is determined by only one free parameter, l max . Thus, only one polarization color is required to constrain l max , although for wavebands right near l max , the uncertainties will be large. Clemens et al. (2016) used this approach with Mimir H-and K-band data to identify grain growth in the moderate-to high-extinction regions of L1544, finding l max in the 1.0-1.2 μm range.
The polarization color P P R H c versus A V values shown in Figure 13 reveal how the polarization spectrum varies with A V . The observed P P R H c distribution seems diverse and can hardly be described with a simple function. To try to find some order, we separated the stars into four A V groups by eye, based on the similarities in the distribution. They span A V ranges of <1, 1.0-2.5, 2.5-4.0, and >4.0 mag, labeled as regions A, B, C, and D, respectively. The blue horizontal lines show the unweighted average±standard deviation (STD) of P P than the other regions. Since the A V of this region was comparable to the expected foreground extinction <0.3 mag (Lada et al. 1994), the depolarization due to any foreground medium might significantly affect the polarization spectrum. Thus, the polarization color in this group might not accurately trace the dust properties. The average P P 5) is known. The varianceweighted mean c of 2.3 was derived from the four-band fitting to the three stars shown in Figure 12. This c value was higher than the value of 1.66 found in Wilking et al. (1982) and the value of 1.86 found in Whittet et al. (1992). 3. For each P P R H c , two possible l max solutions from the Serkowski relation are possible, as can been seen in Figure 14. These two solution regions were colored in gray for the lower l max values and in red for the greater l max values. If we assume that l max across the cloud system does not dramatically change within a few magnitudes of extinction, then only one set of solutions is likely to be true. Since the values of l max derived from the fourband fitting to the three stars shown in Figure 12 were all in the range of 0.72-0.83 μm, l > 0.4 max μm selects the better solutions.
Hence, the average P P R H c values correspond to l max of 0.75, 0.78, and 0.73 μm for groups B, C, and D, respectively. These l max are all greater than the average value for the ISM of 0.55 μm (Serkowski et al. 1975), suggesting that the dust grains across most of the IC5146 cloud system have grown significantly with respect to dust grains in the diffuse ISM. In addition, the large dispersion of l max in group B implies that Figure 13. P Rc /P H vs. A V from the stars with R c -and H-band polarization detections. These stars were separated into four groups, based on their A V values as defined by the black dashed lines. The blue horizontal lines show the s 1 excursions above and below the average of P Rc /P H for each group. The distribution of P Rc /P H is narrowest when A V =2.5-4 mag. The stars with negative A V values have negligible extinction: these values result from uncertainties in the NICER extinction estimation. . Uncertainties were calculated from the means and the propagated uncertainties of the means, assuming c=2.3. b The intrinsic dispersions and the uncertainties of the dispersions. The intrinsic dispersion cannot be defined if the observed dispersion is lower than the instrumental uncertainty.
the dust grain size distributions are more diverse in this A V range than in the other extinction regions.
Similarly, we plot P P H K versus A V in Figure 16 to trace the variation in polarization spectrum in the infrared. The data were separated into five groups, in a fashion similar to Figure 13 ( < A 1
V , 1.0-2.5, 2.5-4.0, 4.0-10.0, and >10.0 mag, labeled as A, B, C, D, and E, respectively). The statistical properties of P P H K for these groups are listed in Table 4. The average P P H K changes significantly with A V , with the greatest value found in group B.
The values of l max converted from P P H K were listed in Table 4. The range of l max derived from the group averaged c max . The horizontal dashed lines represent the range of observed P Rc /P H , seen as the range spanned by the blue horizontal lines shown in Figure 13. Only the relation characterized by c 2.2 can cover the range of observed P Rc /P H . The yellow curve shows the relation for = c 2.3, which was used to convert P Rc /P H into l max .
Figure 15. Ranges of l max with A V group. The colored regions represent the ranges of the distributions of l max values in each A V group, estimated from the observed P Rc /P H values, the Serkowski relation, and the c=2.3 curve from Figure 14. The red and gray sets of zones identify the two degenerate sets of solutions to the Serkowski relation. The three stars whose four-band polarimetry data were fitted to the Serkowski relation (see Figure 12) are plotted as filled colored circles with error bars and are consistent with the set of red zone solutions corresponding to greater values of l max .
P P H K was 1.46-1.93 μm, significantly higher than the 0.73-0.78 μm range derived from P P R H c . The inconsistency implies that the Serkowski relation may not describe the polarization spectrum at near-infrared wavelengths well. Martin (1989) suggested that the near-infrared polarization spectrum can be better described by a power law
where b -1.6 2.0. In the infrared, polarization color can still constrain the power-law index by
The β derived from our data are listed in Table 4. These indices probably vary with A V and have a peak at » -A 2.5 4
V mag, as shown by Figure 16. Kim & Martin (1995) showed that the index could depend on the amount of micron-sized dust grains. Our results indicate that the population of micron-sized dust grains might evolve with A V , and a significant change occurs at A V of 2.5-4 mag.
The derived l max values obtained in previous studies (e.g., Whittet & van Breda 1978;Wilking et al. 1982) are expected to be related to the small-size cutoff of the grain size distribution. Whittet & van Breda (1978) found that l max is related to the ratio of total to selective extinction
5.6 0.3 V max , tracing the reddening changes with grain size distribution changes. However, with more observations, Andersson & Potter (2007) found no correlation between l max and R V for individual clouds; the empirical relation could only be recovered by combining the data for all of their observed clouds. They further argued that l max may depend on both grain size distributions and dust alignment conditions.
Figure 16. Same as Figure 13, but for P H /P K vs. A V . The dispersions of P H /P K are almost the same over the different A V groups, while the P H /P K means appear to change with A V . . Uncertainties were calculated from the means and the propagated uncertainties of the means, assuming c=2.3. b The intrinsic dispersions and the uncertainties of the dispersions. The intrinsic dispersion cannot be defined if the observed dispersion is lower than instrumental uncertainty. Whittet et al. (2008) showed in their RATs simulations with constant grain size distribution that l max increases with A V because small dust grains become less well aligned as a result of the decaying and reddening of the external radiation field by extinction. Their model predicts a smooth increase of l max from 0.45 to 0.75 μm as A V increases from 0 to 6 mag. However, our derived l max values, 0.73-0.78 μm, do not significantly change with A V . In addition, our data show a significant decrease of the intrinsic dispersion of l max from 0.11±0.08 ( = A V -1.0 2.5 mag) to <0.07 ( = -A 2.5 4.0 V mag), possibly due to changes of the grain size distribution.
The change in the dispersion of l max implies that the grain size distribution in the dense regions could be more uniform than in the diffuse regions. We speculate that the difference is due to the evolution of the dust grain size. In grain-grain collision models (Jones et al. 1996;Hirashita & Yan 2009;Ormel et al. 2009), the grain size distributions are expected to be modified by the competing effects of fragmentation and coagulation. Steady-state grain size distributions are eventually reached when these two effects achieve equilibrium. As a result, the apparent uniform grain size distribution in the dense regions may indicate the existence of stabilized grain-grain collision processes. Together with the increase of l max , this non-evolution of grains in the dense regions favors the notion that grain growth has already taken place before A V reaches 2.5-4.0 mag.
In Figure 17 we show that the l max derived from a Serkowski relation based on an analysis of P P H K yielded an average l max of 1.46-1.93 μm. This was inconsistent with l max derived from P P R H c , which yielded an average l max of 0.73-0.78 μm. To reach a l max of 0.73-0.78 μm, P P H K would need to be >2.3, which is much higher than the observed range of mean values from 0.96±0.28 to 1.71±0.21. This indicates that at least the measured K-band infrared polarization exceeds the predictions of the Serkowski relation. This excess infrared polarization was also found in early studies (e.g. , Jones 1990;Martin & Whittet 1990;Nagata 1990) and is better fit by a power law (Equation ( 7)). We found that a power law with β ranging from -0.14±0.69 to 1.78±0.41 can explain our data for different A V . The β index appears to vary with A V and has its highest value for = -A 2.5 4.0 V mag. Our β are similar to, or smaller than, the value of 1.6±0.2 measured toward ScO-Oph and CyG OB2 (Martin et al. 1992), and 1.76±0.25 measured toward the Galactic center (Hatano et al. 2013).
Two models have tried to explain the physical origin of the excess infrared polarization over the Serkowski relation. Kim & Martin (1995) showed that a model with a dust grain mixture with sizes of 0.3 μm and 0.6-1 μm can reproduce the observational Serkowski relation while also exhibiting a power-law excess infrared polarization. Li & Greenberg (1997) showed that an organic refractory-mantled dust grain model with a Gaussian grain size distribution could reproduce the observed excess infrared polarization without requiring a high abundance of micron-sized dust grains. Our results show that the observed power-law index might vary with A V , providing new constraints for future models.
Reveal B fields?
PE has been used to indicate how deep into a cloud, in A V , the dust grains remain aligned. Goodman et al. (1995) found a PE-A V power-law index of -1 in L1755 in the JHK bands. This constancy of P with A V was used to argue that nearinfrared polarization does not trace the B field within dense clouds. In contrast, Whittet et al. (2008) found an index of -0.52 in Taurus at the K band, showing that polarization can trace the B field, at least up to à 10 V mag. The power-law PE versus A V indices characterizing these two cases can be found in our data, but for different A V ranges. The power index of -0.95±0.30 measured for the H band in 15, but the l max range was estimated from P H /P K using the Serkowski relation with c=2.3. The l max values derived from P H /P K are much greater than the l max values derived from P Rc /P H shown in Figure 15. In addition, the distribution of l max is inconsistent with the best-fit Serkowski relations to the three stars with four-band polarimetry data shown in Figure 12, suggesting that the Serkowski relation may not be valid, at least in the K band. low-A V regions is similar to the results found in L1755 at the R band (Goodman et al. 1995) for < -A 8 10
V mag. Our index of -0.53±0.09 for the K band is close to the value found in Taurus at the K band (-0.52 ± 0.07) by Whittet et al. (2008) and the value found in numerous starless cores at the K band (∼-0.5) for < A 20
V mag by Jones et al. (2015). In addition, the intermediate index -0.71±0.10 found in the R c band is similar to the results found in Pipe-109 using the R band (-0.76 ± 0.14, Alves et al. 2014) and in L204 using the H band (-0.74 ± 0.07, Cashman & Clemens 2014). We found our steepest index, of -1.23±0.10, in the ¢ i band and our softest index, of -0.25±0.06, in the H band in high-A V regions.
The softer indices of -0.25 to -0.53 are only found in high-A V regions in the H and K bands, while a variety of steeper indices are found in low-A V regions. The ∼-0.5 indices match predictions of RATs models with constant grain size distributions (Whittet et al. 2008). The same models predicts a steepening of PE as A V approaches 10 mag, caused by the strong extinction of external radiation. Here, however, the indices we measure for high-A V regions show that the dust with A V up to ∼20 mag still contributes to the measured polarization: the PE at A V =20 mag is only a factor of ∼2 lower than that at A V =4 mag. Thus, the notion that only the dust on the surfaces of clouds is aligned, as concluded by Goodman et al. (1995), is not supported here.
It is interesting that a variety of PE versus A V power-law behaviors are seen across the IC5146 cloud system. We showed that the indices derived using the H band varied with region location in Figure 11. The diverse PE-A V relations likely depend more on A V and region choice and less on wavelength, as the indices derived from ¢ i and H bands in the same region are almost the same. If all the stellar values from all of the low-A V regions are combined into a single plot and fitted, the location dependence of the PE-A V relation would be mixed and thereby lost. The index of -0.95 derived from the H band using all data with low-A V is merely the average from the mixed PE-A V relation shown in Figure 11. This is different from the suggestion by Goodman et al. (1995) that a power-law index of ∼-1 indicates that starlight polarization only traces the dust grains on the surfaces of clouds.
Three possibilities could explain the origin of the wide variation of the PE-A V relation.
(i) The grain size distributions could be diverse and vary greatly from region to region for low A V . In Section 4.3 we showed that the dispersion of l max , estimated from P P R H c , is significantly larger for < A 2.5
V mag, suggesting that grain size distributions are diverse. This diversity is likely regiondependent, since the different l max values were derived from different sightlines. The grain size distribution is a key element of the RATs theory; radiation can efficiently align dust grains with sizes comparable to its wavelength, and wavelength determines radiation penetration ability.
(ii) Depolarization effects may occur if multiple polarizing layers exist. In Figure 11 we showed that the PE versus A V indices derived in the western part of the IC5146 cloud were steeper than -1, hence the polarization percentage must decrease with A V . This may be a result of depolarization. If a multiple layer structure, in which the layers have different B-field orientations, exists along a line of sight, the net transferred polarization from the different layers would be reduced. Arzoumanian et al. (2011) found rich and hierarchical filamentary structure in the IC5146 cloud system. These filaments can naturally produce a multiple layer structure if the projections of such structures overlap along the line of sight. In addition, they further found that most of the filaments in the western part of the IC5146 cloud system were supercritical, which might twist to cause complex B fields. This could explain the steeper indices found in the western part of the cloud.
(iii) The degree of dust alignment may be affected by one or more bright illuminators, such as the stars in the Cocoon Nebula. Cashman & Clemens (2014) found a possible dependence of PE-A V index for regions in the L204 cloud 3 with distance from a nearby illuminator. Brighter stellar radiation can boost alignment of the dust, and the alignment efficiency will mainly depend on the optical depth to the illuminator. In IC5146, the Cocoon Nebula stellar cluster could be a strong illuminator that is able to affect grain alignment. However, the radiation from the Cocoon Nebula is also highly shadowed by the main filament structure, making the optical depth from the Cocoon Nebula to the other regions difficult to estimate.
In Section 4.2 we showed that PE decays with A V and a breakpoint (BP) of = A 2.88 0.67
V mag are rarely seen. Pipe-109 shows a breakpoint at 9.5 mag with power index changing from -1.00 to -0.34 (Alves et al. 2014). LDN 183 shows a breakpoint at à 20 V mag with power index changing from -0.6 to -1 (Crutcher 2004;Clemens 2012;Andersson et al. 2015). Jones et al. (2015) also found a break point at à 20 V mag with power index changing from -0.5 to -1 toward several starless cores. Jones et al. (2016) found an break point at very high A V , ∼hundreds mag in the Class 0 YSO G034.43+00.24 MM1 with a change of power index from -1 to -0.5.
Three mechanisms could change the power-law indices with A V , although in opposite directions. Radiation into the deepest regions could be too faint to align the dust grains, so the powerlaw index for high-A V regions should steepen (Whittet et al. 2008). If grains grow at higher A V , however, the alignment efficiency will be higher for dust with sizes comparable to the wavelength (Lazarian & Hoang 2007), hence the power-law index will become flatter in the dense regions where only radiation with longer wavelengths can penetrate and the dust grains are believed to grow. In addition to the change of dust properties, internal radiation fields from embedded sources within dense clouds could also enhance dust alignment and flatten the power-law index. Andersson et al. (2015) suggested that the origin of the breakpoint found in LDN 183 is likely due to the extinction of external radiation because their power-law index in low-A V regions, of -0.6, is consistent with prediction of the RATs model assuming constant grain size (Whittet et al. 2008). Similar trends were also found within several starless cores by Jones et al. (2015), and they further showed that the RATs theory can explain the break point of ∼20 mag, where the dust optical depth, for the wavelength comparable to the maximum grain size, becomes optically thick.
Our results showed an opposite trend as compared to the case of LDN183: steeper indices ranging from -0.71 to -1.23 were found in low-A V regions, while flatter indices ranging from -0.25 to -0.53, consistent with the Whittet et al. (2008) model, were found in high-A V regions for all observed wavebands. The results from Alves et al. (2014) toward Pipe-109 and Jones et al. (2016) in G034.43+00.24 MM1 show similar trends as ours, but with different breakpoints. The flattened slopes in high-A V regions more likely originate from efficient grain alignment due to either grain growth or internal radiation fields. Because Pipe-109 is a starless object but G034.43+00.24 MM1 is a Class 0 YSO, the change of slope for the former likely results mainly from grain growth, while internal radiation might play an important role in the latter. Since the breakpoint of A V ∼ 2.8 mag shown in our data is consistent with the A V of the regions where the intrinsic dispersion of l max drops significantly (A V =2.5-4.0 mag), our observed trend is more likely caused by grain growth.
An open question is why the breakpoint we measure is so different from the 9.5 mag value in Alves et al. (2014), although both breakpoints likely result from grain growth. The difference could originate from two possible reasons. First, Alves et al. (2014) lacked samples in low-A V regions, and thus a broken power law with breakpoint at à 3 V mag would be difficult to identify. Second, the difference may come from different grain growth conditions. Ormel et al. (2009) simulated the evolution of dust grain size, based on grain-grain collisions. They found that dust grains with ice-coatings are more likely to aggregate and grow than are grains without ice-coatings, due to the increased surface stickiness. Chiar et al. (2011) found that H O 2 -ice in IC5146 only exists in regions exhibiting extinctions exceeding A V ∼ 4 mag, a value quite similar to the breakpoint we found. Thus, H 2 O-ice mantling could induce a breakpoint via enhanced grain growth. Similarly, Whittet et al. (2001) found that the observed R V in Taurus changed from R V ∼ 3 to 4 around = A 3.2
V mag, coincident with the extinction threshold for H 2 O-ice mantling in Taurus, and suggested that mantle growth is an important process in initial grain growth. We conclude that such mantling also enables greater efficiency of dust grain alignment, permitting magnetic field to be traced deeper into clouds than if such mantling is not present.
We performed optical and infrared polarimetry observations toward background stars seen through the IC5146 dark cloud system using AIMPOL at the ARIES Observatory, TRIPOL at the Lulin Observatory, and Mimir at the Lowell Observatory Perkins Telescope. A total of 2022 stars showed significant polarization detection in at least one of the four wavebands observed. From the analysis of these data, we found the following results.
1. The polarization efficiency ( º l P A PE V ) decreases with A V as a power law or broken power law. The values of the power-law indices likely depend more on the choice of targeted regions and local extinction, and less on observing wavelength. 2. A cloud-averaged power-law index of -0.95 for PE versus A V was found in the H band for low A V , the same as the index found in L1755 by Goodman et al. (1995). However, we showed that the index of -0.95 resulted from the admixture of a variety of PE-A V relations, whose local-regional indices varied from -0.8 to -1.8, different from the suggestion by Goodman et al. (1995) that the index of ∼-1 indicates that background starlight polarization only traces the dust grains on the surface of clouds. 3. A broken power law relation for PE versus A V in the H band exhibits a breakpoint at about A V ∼ 2-3 mag. The power-law index in high-A V regions is shallow and consistent with predictions from RATs models (Whittet et al. 2008), while the indices in low-A V regions are steeper and vary with region. The shallow index in high-A V regions is likely due to grain growth. 4. Excess infrared polarization, over that predicted by the Serkowski relation, was observed in P P H K , possibly resulting from abundance enhancements of large micronsized dust grains. The average P P H K varies with A V from 0.96±0.20 to 1.71±0.21, and exhibits its highest value of 1.71±0.21 for A V in the 2.5-4.0 mag range. This implies that the abundance of such micron-sized dust grains might change with A V . 5. The polarization color
) is a useful tool to constrain l max , the peak of the Serkowski relation, which may trace the small-size cutoff of the grain size distribution. We found that both the average and dispersion of P P R H c decreased from the < < A 1.0 V 2.5 mag range to the < < A 2.5 4.0 V mag range. These variations suggest that the small-size cutoffs of grain size distributions are most likely due to efficient grain-grain collisions, and thus indicate that grain growth could already take place by ~-A 2.5 4.0 V mag, possibly enhanced at this relatively low-A V range by the presence of ice mantles on the grains.
In conclusion, this study revealed that dust grains in the diffuse molecular regions ( < A 2.5
V mag) of the IC5146 dark cloud system have diverse size distributions. As A V approaches ∼3 mag, submicron dust grains grow significantly due to graingrain collisions. The size distributions may also become more uniform as A V increases as a balance is reached between fragmentation and coagulation. In addition, the larger micronsized grains likely already exist in the diffuse regions, and their abundances and sizes likely change with A V . In the next paper of this series, we will use these polarization data to characterize the magnetic field morphology and strength across this system of filamentary dark molecular clouds associated with IC5146.
Facilities: ARIES:ST, LO:1m, Perkins. Software: IRAF, Source Extractor (Bertin & Arnouts 1996), Mimir Software Package (Clemens et al. 2012c), PNICER (Meingast et al. 2017), Astropy (Astropy Collaboration et al. 2013), NumPy (van der Walt et al. 2011), SciPy (Jones et al. 2001), Aplpy (Robitaille & Bressert 2012).
Jia-Wei Wang https:/ /orcid.org/0000-0002-6668-974X Shih-Ping Lai https:/ /orcid.org/0000-0001-5522-486X Chakali Eswaraiah https:/ /orcid.org/0000-0003-4761-6139 Dan P. Clemens https:/ /orcid.org/0000-0002-9947-4956 Wen-Ping Chen https:/ /orcid.org/0000-0003-0262-272X
The Astrophysical Journal, 849:157 (18pp), 2017 November 10 Wang et al.
IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation.
Using the PNICER python package developed byMeingast et al. (2017).
The Astrophysical Journal, 849:157 (18pp), 2017 November 10 et al.