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Magnetic Fields in Star-Forming Molecular Clouds. V. Submillimeter Polarization of the Barn


Magnetic Fields in Star-Forming Molecular Clouds. V. Submillimeter Polarization of the Barnard 1 Dark Cloud
Brenda C. Matthews Department of Astronomy, University of California at Berkeley, 601 Campbell Hall, MC 3411, Berkeley, CA 94720 bmatthews@astron.berkeley.edu and Christine D. Wilson McMaster University, 1280 Main Street West, Hamilton, ON L8S 4M1 Canada wilson@physics.mcmaster.ca ABSTRACT We present 850 ?m polarimetry from the James Clerk Maxwell Telescope toward several dense cores within the dark cloud Barnard 1 in Perseus. Signi?cant polarized emission is detected from across the mapped area and is not con?ned to the locations of bright cores. This indicates the presence of aligned grains and hence a component of the magnetic ?eld in the plane of the sky. Polarization vectors detected away from bright cores are strongly aligned at a position angle of ? 90? (east of north), while vectors associated with bright cores show alignments of varying orientations. There is no direct correlation between the polarization angles measured in earlier optical polarimetry toward Perseus and the polarized submillimeter thermal emission. Depolarization toward high intensities is exhibited, but toward the brightest core reaches a threshold beyond which no further decrease in polarization percentage is measured. The polarized emission data from the interior envelope are compared with previously published OH Zeeman data to estimate the total ?eld strength and orientation under the assumption of a uniform and non-uniform ?eld component in the region. These results are rough estimates only due to the single independent detection of Zeeman splitting toward Barnard 1. The uniform ?eld component is thus calculated to be B0 = 31 ? ? ?G [±(0.52N ? 0.01E) ? 0.86?] in the case where we have assumed the ratio of z the dispersion of the line-of-sight ?eld to the ?eld strength to be 0.2. Subject headings: ISM: clouds, magnetic ?elds, molecules — polarization — ISM: individual (Barnard 1) — stars: formation — submillimeter

arXiv:astro-ph/0205328v1 20 May 2002

–2– 1. Introduction

Over the past decade, observational evidence for the presence of magnetic ?elds in molecular clouds and their role in star formation has grown dramatically. However, detection of magnetic ?elds is not synonymous with measuring their geometry or the total ?eld strength. Recent simulations have shown that the low density regimes of molecular clouds may not be in magnetic equilibrium (Padoan & Nordlund 1999), although in high-density cores, the evidence for magnetic and virial equilibrium is stronger (Myers & Goodman 1988; Crutcher 1999; Basu 2000). While models can help interpret data, it is still very rare for evidence of Zeeman line splitting (which traces the line-of-sight ?eld, Blos ) and thermal dust polarization (which traces the plane-of-sky ?eld, Bpos ) both to exist toward regions of similar density in a single cloud. The Perseus molecular cloud complex is one of the closest star-forming regions to the Sun. Its distance is the subject of some debate, but it is thought to be associated with the Per OB2 association at a distance of 334 ± 12 pc (Borgman & Blaauw 1964). However, the complex is likely in front of the OB association (Lynds 1969), and Cernicharo et al. (1985) suggest that there are in fact two clouds along the line of sight toward the complex, the second at a distance more comparable to Taurus at 200 pc. In this paper, we adopt a distance of 330 pc for the Perseus association. CO emission reveals that the complex is elongated, extending over 55 pc along its major axis (at ? 60? east of north), but just 15 pc along the minor axis (Sargent 1979). Along its length, six denser star-forming clouds (L1448, L1455, NGC 1333, Barnard 1, IC 348 and Barnard 5) are connected by low density molecular gas of n ? 102 cm?3 (Bachiller & Cernicharo 1986). The Barnard 1 (B1) cloud has been observed in many molecular transitions and modeled as a multi-phase cloud with a thin outer envelope, denser inner envelope and a central dense core. Bachiller & Cernicharo (1984) observed the cloud in several isotopes of CO, HCO+ and a single transition from NH3 and determined that temperatures are higher toward the outer edges of the cloud, indicating primarily external heating. Three optically visible young stellar objects, LkHα 327, LkHα 328, and LZK 21 are associated with the cloud, two of which show IRAS emission. Three additional IRAS sources are undetected optically; the presence of these sources indicates some recent star formation in B1. In the center of the cloud, Bachiller et al. (1990) observe CS J = 1 ? 0 emission from dense gas over a region ? 2 pc × 5 pc with an accompanying mass of 1200 M⊙ . NH3 (1,1) and (2,2) emission toward the CS “main core” reveal substantial substructure within the gas, showing evidence for two or three condensations (Bachiller et al. 1990). IRAS 03301+3057 lies at the center of the main core, but does not coincide directly with any of the ammonia peaks; it is located approximately 1′ north of the south-western ammonia peak (the “southern clump” of Bachiller et al. (1990)).

–3– High resolution observations of H13 CO+ by Hirano et al. (1999) reveal a strong peak (denoted B1-b) at the position of the south-east ammonia emission detected by Bachiller et al. (1990). As part of the same study, continuum emission at 850 ?m 350 ?m (from the JCMT and CSO, respectively) and 3 mm (from the Nobeyama Millimeter Array) clearly identify two high density dust cores within the single molecular clump. Based on spectral energy distributions, Hirano et al. (1999) conclude that these objects are both extremely young protostars in the Class 0 phase (Andr? et al. 1993). The masses of the central e objects, called B1-bN and B1-bS, are estimated to be no greater than 7×10?2 M⊙ , indicating extremely young ages of less than 2×104 yr for both sources. No out?ows have been detected from either source. One powerful out?ow, associated with IRAS 03301+3057 (B1-IRS), has been identi?ed by Bachiller et al. (1990) in CO (J = 2 ?1). It is con?ned to a region of 40′′ (about 0.07 pc). The dynamical time estimated from the out?ow is 103 to 104 years. Hirano et al. (1997) measured the small scale structure of this CO out?ow and estimate that the driving source is very young and is observed in a pole-on con?guration. The masses of the YSOs seen optically and with IRAS range from 0.2 to 3 M⊙ (Bachiller et al. 1990). Given these low stellar masses, the stellar to gas mass ratio in B1 is ? 0.5%, negligibly small even compared with Taurus where the star formation e?ciency has been recently estimated at 6% (Onishi et al. 1998). The observed rotation velocities within B1 are insu?cient to support the cloud against collapse by a factor of ? 8 (Bachiller et al. 1990). The ages of embedded but optically visible objects LkHα 327 and LkHα 328 are between 4-6 ×106 yr (Cohen & Kuhi 1979). Based on this, Bachiller et al. (1990) conclude that a mechanism must be providing substantial support to the B1 cloud. The mechanism is generally attributed to a magnetic ?eld. Polarization of background starlight from the Perseus cloud due to selective absorption from dust grains within the complex was measured by Goodman et al. (1990a), who ?nd that the distribution of polarization position angles is bimodal, with weaker vectors (less polarized) aligned along the cloud’s projected major axis and stronger vectors (more polarized) lying roughly perpendicular to the ?rst population. Goodman et al. (1990a) hypothesized that two clouds of di?ering magnetic ?eld orientations could be superimposed along the line of sight. A prior argument for a second gas cloud along the line of sight to Perseus and B1 at a distance of 200 pc was presented by Cernicharo et al. (1985). The B1 cloud has been surveyed for evidence of Zeeman splitting in dense OH gas more extensively than any other dark cloud. Lang & Willson (1979) estimated a 3σ limit of 90 ?G toward LkHα 327, located approximately 4′ away from B1’s strong molecular peak. B1 was chosen by Goodman et al. (1989) as a strong candidate for magnetic ?eld detections

–4– due to its atypically high non-thermal linewidth components, and a ?eld strength of ?27 ± 4 ?G was measured toward the position of the bright molecular core coincident with IRAS 03301+3057. (The negative sign indicates that the ?eld is oriented toward the observer.) A survey of 12 dark clouds for evidence of Zeeman splitting yielded only one solid detection – toward B1 – with the 140 ft. Green Bank Telescope (Crutcher et al. 1993). In an observation toward the source IRAS 03301+3057, a ?eld strength of ?19 ± 4 ?G was measured, which is consistent with the Arecibo value when beam dilution is taken into account. In order to supplement the Zeeman data toward the dense molecular gas of B1, we have measured polarized emission at 850 ?m from dust toward the “main core” of B1 as identi?ed in CS and NH3 , both tracers of high column densities. Emission from aligned, spinning dust grains is anisotropic and hence polarized. Unfortunately, polarization data reveal no direct information about the ?eld strength, since the degree of polarization is dependent on other factors such as grain shape, composition and degree of alignment. The degree of polarization is in essence a measure of how e?ectively the grains have been “sped up” (Hildebrand et al. 2000). However, even though the grain spin is induced by mechanisms other than the magnetic ?eld, such as the radiation ?eld (Draine & Weingartner 1996) or the production of H2 on the grain surface (Purcell 1979), the magnetic ?eld is expected to provide the alignment. Because of this, continuum polarization data are the principal means of probing the geometry of the magnetic ?eld. The very sensitive Submillimetre CommonUser Bolometer Array (SCUBA) detector now permits the observation of polarized emission from the ambient cloud surrounding dense cores. This paper is the ?fth in a series to examine the magnetic ?eld geometries in starforming molecular clouds using polarized emission at 850 ?m. Barnard 1 is the ?rst dark cloud we have observed, and these data are the ?rst emission polarimetry toward this region. The observations and data reduction techniques are described in § 2. The polarization data are analyzed in § 3. We discuss the possible interpretations of these data and calculate an estimated three dimensional structure for a uniform ?eld component of B1 in § 4. Our ?ndings are summarized in § 5.

2.

Observations and Data Reduction

We have used the UK/Japan polarimeter with the SCUBA detector at the James Clerk Maxwell Telescope1 , to map polarized thermal emission from dust at 850 ?m toward a dense
The JCMT is operated by the Joint Astronomy Centre on behalf of the Particle Physics and Astronomy Research Council of the UK, the Netherlands Organization for Scienti?c Research, and the National Research
1

–5– region of the B1 dark cloud. The observations were taken from 11 to 13 October 1999. The polarizer and general reduction techniques are described in Greaves et al. (2000) and Greaves et al. (2002). To generate a polarization map, a 16-point jiggle map was made at each of 16 di?erent half-waveplate positions. After each 12s integration, the half-waveplate was rotated through 22.5? and the mapping repeated. The data were ?at-?elded, corrected for extinction and dual-beam corrected using the standard SCUBA software. Estimation of systematic errors due to chopping and sky subtraction can be found in (Matthews, Wilson & Fiege (2001), hereafter Paper II). Unfortunately, there are no large scale 850 ?m maps of the B1 cloud in the literature. This made the identi?cation of chop angles and sky removal candidate bolometers more di?cult. The chop angles and throws for each ?eld center observed are summarized in Table 1. The level of precipitable water vapor was very stable over the course of the observations. The estimates of τ (225 GHz) from the CSO ranged from 0.055 to 0.075 over the observations, with 96% in the range 0.060 to 0.070. These data were corrected for an error in the SCUBA clock which placed incorrect LST times in the data headers during the period from July 1999 to May 2000. This error did not a?ect the telescope’s acquisition or tracking, but a?ects data reduction since the elevation and sky rotation are calculated from the LST times in the data headers. The magnitude of this error over time can be evaluated and then corrected retroactively as described on the JCMT website. The error in timing after this adjustment is ±10s. The data were reduced using the Starlink software packages POLPACK and CURSA, designed speci?cally to include polarization data obtained with bolometric arrays. After extinction correction, noisy bolometers identi?ed for each night’s data were ?agged and removed from the data. Between 3 and 5 bolometers were removed per night. Prior to sky subtraction, images were made to examine the ?ux in each bolometer, since bolometers used for sky subtraction should not have negative values (produced if one has chopped onto a location with signi?cant ?ux, for example). The data were sky subtracted using bolometers with mean values close to zero. Between 1 and 4 bolometers were used to subtract the sky. The methods of sky subtraction are discussed in detail in Jenness, Lightfoot & Holland (1998). Finally, the instrumental polarizations (IPs) were removed from each bolometer. All the data sets were then combined to produce maps of three Stokes’ parameters (I, Q, and U), which were then combined to yield the polarization percentage and polarization position angle according to the following relations: p=
Council of Canada.

Q2 + U 2 ; I

θ=

1 arctan(U/Q). 2

–6– The uncertainties in each of these quantities are given by: dp = p?1 [dQ2 Q2 + dU 2 U 2 ]; dθ = 28.6? /σp

where σp is the signal-to-noise in p, or p/dp. A bias exists which tends to increase the p value, even when Q and U are consistent with p = 0, because p is forced to be positive. The polarization percentages were debiased according to the expression: pdb = p2 ? dp2 . Future references to polarization percentage, or p, refer to the debiased value. Absolute calibration is not part of the standard reduction of polarization data since the percentage polarization is a relative quantity. However, from our Stokes’ I map, we can estimate ?uxes by using a reasonable ?ux conversion factor for 850 ?m SCUBA data. This quantity is dependent on the chop throw used, and for a throw of 120′′ , the standard ?ux conversion factor is 219 ± 21 Jy beam?1 V?1 according to the JCMT website. However, the ?ux conversion factor is at least a factor of two greater for polarization data due to the presence of the analyzer which retards half the incoming ?ux on average. In practice, the ?ux conversion factor is ? 2.2 times the standard value due to imperfect transmission through the waveplate (J. Greaves, 2002, private communication). Hence, we have scaled our Stokes’ I map by 480 Jy beam?1 V?1 . The associated uncertainty in this factor introduces an uncertainty of 10% into the resultant ?uxes. Before ?ltering the data to select reliable polarization vectors, it was necessary to estimate the e?ects of sidelobe polarization in the position of the main beam. This is a measure of the minimal believable polarization, pcrit , given the potential for sources in sidelobes to produce arti?cial polarization signals in the central region of the map (see Greaves et al. (2002)). For our worst case scenario in B1, the ?ux contributed at approximately 68′′ from the map center is 16 times that at the center. Examination of polarization maps of Saturn (which has only a small intrinsic polarization ? 0.6%, with a minimum of ? 0.2%) of 13 October 1999 reveal that the relative mean power 68′′ from the main beam center is 0.0067 compared to the main beam itself. The mean polarization percentage at this position on the SCUBA ?eld is 4.3%, which is a measure of the instrumental polarization. The pcrit value is given by: pcrit ≥ 2 × 4.3% × 0.0067 × 16 (see Greaves et al. (2002)) which gives a minimum threshold polarization of 0.92%. Taking into account the intrinsic polarization of Saturn, this leaves ? 0.3?0.7% arising from sidelobe

–7– polarization. We have thus selected vectors for which polarization percentage, p > 1% as reliable data. The vectors selected also have an uncertainty in polarization percentage, dp < 1%, and signal-to-noise in polarization percentage σp > 3. To minimize the systematic e?ects arising from the possibility that we have chopped onto a region of polarized emission, vectors are selected only if they are coincident with Stokes’ I > 20% of the faintest peak in our map. As discussed in Paper II, if the reference position has a ?ux level ? 10% that of the source peak and polarized to the same degree, in the ?nal map the position angle at 20% the peak would be o?set from the correct value by ≤ 10? , while the p value is incorrect by at most a factor of two. For the brighter peaks, the e?ects would be considerably reduced.

3.

850 ?m Polarization Data

Figure 1 illustrates the polarization pattern detected across the B1 “main core” region as identi?ed in CS and NH3 by Bachiller et al. (1990). The polarization data are plotted on a colored greyscale Stokes’ I map estimated by summing together the ?uxes detected at all waveplate positions. Table 2 contains the data (with p > 1%) in tabular form. Four peaks are distinguishable, these are labelled B1-a to B1-d. B1-a and B1-b (N and S) follow the classi?cation of Hirano et al. (1999) as identi?ed in H13 CO+ and 850 ?m SCUBA emission. The presence of two sources within B1-b was con?rmed by 3.0 mm observations with the Nobeyama interferometer (Hirano et al. 1999). NH3 (1,1) and (2,2) emission was observed from peaks corresponding to B1-a, B1-b and B1-c by Bachiller et al. (1990). The B1-d 850 ?m peak lies approximately 1′ south of the B1-a molecular peak (Bachiller et al. 1990) which is likely associated with IRAS 03301+3057 (marked by a blue cross on Figure 1). No ammonia emission is concentrated at the B1-d position (Bachiller et al. 1990), although a very low signal-to-noise peak exists near this position in the H13 CO+ map of Hirano et al. (1999).

3.1.

Polarization Position Angles

Polarized emission is detected both on the bright cores and in regions of lower column density between them. The degree of alignment across the region is evidence for the presence of ordered magnetic ?elds within the main core of the B1 cloud. The data in high intensity regions have been binned to 6′′ sampling, while data in fainter regions are binned to 12′′ to improve the signal-to-noise ratio. The distributions of polarizations associated with faint emission and bright emission are plotted separately on Figure 2.

–8– The distribution for faint I (dashed line) is approximately Gaussian. A ?t to these data yields a mean of 91.3? with a distribution width of 19.0? . Polarization position angles are measured such that values increase east of north. A goodness of ?t measure to the data yields χ2 = 0.6. The statistical mean of the distribution is 88.3? (east of north) with a standard red deviation of 27.7? . The distribution of vectors in regions of bright emission, however, cannot be ?t e?ectively by a Gaussian (or even a series of Gaussians). The solid line of Figure 2 shows several peaks, each of which corresponds roughly to one of the bright peaks. We have indicated the peak sampled on the distribution. Therefore, the polarization pattern in the ambient cloud material around the cores is de?ned by a mean polarization direction where the vectors are distributed about 90? (east of north), while the cores each exhibit di?erent mean position angles. The core B1-b shows systematic variation in position angle. The northern core has < θ >? 65? , while the southern core exhibits < θ >? 120? . The B1-c core has < θ >? 35? , and the B1-d core peaks around 90? east of north, in alignment with the fainter material in the cloud. This could indicate that this core is not strongly di?erentiated from the ambient cloud yet. On Figure 2, we have also plotted the position angles associated with the two peaks observed in the optical absorption polarization data of Goodman et al. (1990a), taking into account the 90? o?set expected for emission polarimetry. These positions (55? and 161? ) are not coincident with any of the peaks in the 850 ?m distribution, either at high or low intensity.

3.1.1. Correlations between Adjacent Vectors To better examine the changes in the nature of the polarization data across the map, we have compared each vector to its closest eight neighbours, calculating the di?erences in polarization percentages and position angles for each pair of values. All the data of Figure 1 were used, except those values for which p < 1% (shown in red). Next, the results were smoothed onto 12′′ grid, by calculating the mean changes in polarization percentage and position angle. The resulting map is shown in vector form in Figure 3, where the vector magnitude is the mean change in polarization percentage in a grid unit and the vector angle is the mean change in orientation. No signi?cant change in orientation is indicated by a vector at 0? east of north. Total intensity contours illustrate the positions of the cores on Figure 3. Only one peak is distinguishable in B1-b, but it is clear this core is elongated. As expected, the changes within the cores are relatively small. The position angles (and even polarization percentages)

–9– are consistent with relatively little change. Based on the histogram of the polarization data toward fainter regions shown in Figure 2, the vectors in this regime were also expected to be well aligned, and the data of Figure 3 show that this is indeed the case. The large variations in adjacent grid units are con?ned to the edge of the map and the boundaries between the B1-b and B1-c cores and the fainter material.

3.2.

Continuum Fluxes Toward Cores in B1

Of the four dense cores detected in our polarization map, two have not been observed previously in continuum emission. These are B1-c and B1-d, although the latter may have been confused with B1-a in large beams (i.e., IRAS) particularly if they are at similar evolutionary stages. The brightest source in our map is B1-c, as revealed by the Stokes’ I contours of Figure 3. We do not detect both peaks toward B1-b although Hirano et al. (1999) do in an earlier SCUBA map; their interferometic observation with the Nobeyama Millimeter Array clearly resolves two peaks toward this source. The slightly enhanced emission coincident with IRAS 03301+3057 is the faintest distinguishable peak at 850 ?m. Table 3 summarizes the peak ?uxes toward each of the four cores (for B1-b, the peak ?ux is that of B1-bS) and positions of these peaks. For a cloud at a distance of 330 pc and assuming κ850?m = 0.01 cm2 g?1 , a mean molecular weight of 2.33 and a dust temperature of 20 K, we ?nd that the column density N(H2 ) = 1023 S850 [Jy beam?1 ] cm?2 . The B1-c peak has a ?ux of 3 Jy beam?1 , which implies N(H2 ) = 3 × 1023 cm?2 , or 300 magnitudes of visual extinction. Toward B1-bS, we estimate N(H2 ) = 2.5 × 1023 cm?2 , which is within 50% of the estimate of Hirano et al. (1999). Assuming a core depth comparable to the FWHM of 30′′ for B1-c yields a volume density of 2 × 106 cm?3 which is typical of prestellar and protostellar core densities.

3.3.

Depolarization in Barnard 1

Figure 3 suggests that changes in polarization percentage are small within the cores of B1. The statistical means of the low intensity and high intensity vector populations are 4.5% and 2.6% in 81 and 74 values respectively. The standard deviations in these populations are 2.3% and 1.4%. In this case, the depolarization e?ect, declining polarization percentage with increasing intensity, may be weak within parts of B1. The easiest way of examining the depolarization e?ect is to plot p versus I for all vectors on the polarization map. In Figure 4, we plot the data for the B1 region as presented in Figure 1 excluding only

– 10 – those data values with p < 1% (plotted in red). The data exist in two populations, where the data at low intensities are binned to 12′′ (shown as crosses) and the data at high intensities are binned to 6′′ (shown as circles). Although these plots are shown in log-log space, the ?ts to the data were done to pro?les of p versus I by minimizing χ2 . This is a more e?ective treatment of the uncertainties since those for low values of p are exaggerated in log space. The ?ts to these two populations produce completely consistent slopes, indicating that both can be characterized by power laws of the form: p = AI γ with an index of γ ≈ ?0.8. At high values of I however, there is a slight thresholding of polarization percentage. To better illustrate this, in Figure 5 we show the same style plot for three cores: B1-b (north and south combined), B1-c and B1-d. Vectors toward the cores B1-b and B1-c exhibit higher values of p than expected given the declining trend below 1 Jy beam?1 . In fact, the distribution of p versus I ?attens at high intensities. In the case of B1-b, this ?attening could be the result of our lack of sensitivity to values of p < 1%. However, for the B1-c core, this constraint removes only a single vector (which has a value of 0.99 ± 0.25%). Thus, in B1-c, the depolarization e?ect does not follow the usual trend of declining polarization percentage as intensity increases. (The B1-d core does exhibit depolarization to its peak, which is signi?cantly lower in intensity than B1-b and B1-c.) The B1-c core is well sampled (with only one vector missing) and de?nitely exhibits a ?at dependence of p on I down to 30% of that core’s peak. The omitted vector (shown in red on Figure 1) does not correspond to the intensity peak of the core, but is associated with an intensity just 2/3 of the peak observed. To our knowledge, this is the ?rst case of a bright core which does not exhibit depolarization over its whole observed intensity range. The observed threshold is not the e?ect of optical depth. We estimate that the optical depth at the B1-c peak is ? 0.015 which is << 1.

4. 4.1.

Discussion

Interpreting the Polarization Pattern

Optical polarimetry using absorption of light from background stars was used to probe the magnetic ?eld structure through dust at low extinctions in the Perseus cloud complex by Goodman et al. (1990a). They found a bimodal distribution of polarization vector orientations toward the complex such that the vectors lie roughly parallel and perpendicular to the major axis of ? 60?. They ?t two Gaussians to their data set with means 71? and 145? east of north and 1 σ dispersions of 12? and 8? , respectively. Since there is no spatial distinction between the two populations and evidence in observations of molecular gas that two di?erent clouds could lie along the same line of sight, they conclude that the

– 11 – two polarization populations are representative of two distinct clouds at di?erent distances. The foreground cloud was predicted to have a low extinction (AV < 1 mag). Bimodal distributions in polarization vectors had been previously noted by studies toward the Perseus clouds NGC 1333 (Turnshek et al. (1980); Vrba, Strom & Strom (1976)) and Barnard 5 (Joshi et al. 1985). In the process of generating an evolutionary model for the B1 cloud, Crutcher et al. (1994) adopt a mean plane-of-sky ?eld direction along the minor axis of the Perseus (and hence B1) cloud which corresponds to the polarization distribution centered on 145? east of north. In this case, the Goodman et al. (1990a) vectors centered on 71? east of north would most likely be associated with the foreground cloud, at 200 pc distance (Cernicharo et al. 1985). If the interior of the dense B1 main core is threaded with the same ?eld geometry as measured on the periphery of the B1/Perseus cloud, then a ?eld of mean direction 145 ±12? should produce polarized emission from dust at a position angle of 55 ±12? . Figure 2 demonstrates that there is no peak in the polarization data at 850 ?m at 55? , although polarization vectors of B1-c and B1-bN fall roughly in the range of the optical polarization dispersion value. The second distribution measured by Goodman et al. (1990a) peaked at 71? , which corresponds to an emission polarization angle of 161? . Thus, there is no component of position angle in our data set which corresponds directly to either population of the optical polarization data. Hence, based on our emission polarimetry, which is believed to arise only in the regions of dense, cold dust, we cannot conclude which optical polarization direction is more likely associated with the Perseus complex.

4.1.1. Complete Depolarization of the Cores? The polarization vectors across the B1-d peak are aligned with the faint emission polarization angles of 90? , but the brighter peaks, B1-b and B1-c, both exhibit di?erent position angles. Given the previous observations of depolarization in bright peaks and the polarization plateau across these two cores, it would be tempting to think that the cores themselves are completely depolarized and that one might thus measure the polarization toward a different cloud along the line of sight at their positions. There are several reasons why this is unlikely to be the case. In most well-sampled cores, depolarization is a non-linear function of intensity, so the polarization percentage rarely reaches zero (e.g. Henning et al. (2001); Ward-Thompson et al. (2000); Greaves et al. (1999); Greaves, Murray & Holland (1994); Minchin & Murray (1994)), and if it does become unmeasurably small, as it does at places in B1-b, then it does so at the highest intensities. Therefore, one might expect to see a varying position angle

– 12 – across cores that re?ects the varying contribution of the core’s polarized intensity to the vector sum with the second cloud, revealing the second cloud’s position angle only toward the peak of the core. Furthermore, even in the case where the depolarization might atypically be complete across a core, this would e?ectively create a steeper than usual depolarization e?ect rather than a ?at distribution of p with I as we particularly observe toward B1-c (see Figure 5). The reason is that if the polarized emission arose in a cloud other than B1 and were unassociated with the B1-c core (which we know to be in B1 through its associated molecular emission), the increasing contribution to the total intensity from the core (despite its contribution of zero polarized intensity) should produce a variation in p with I which varies exactly as the increase in intensity across the core. The only way this could be avoided would be if, as the intensity across the B1-c core increased, so did the polarized intensity in the second cloud. These increases would have to match each other exactly to produce the ?at pattern we see. We dismiss this scenario as far-fetched. In B1, we see not just a single core which exhibits a di?erent position angle orientation than the ambient cloud, but instead there are two such cores, where B1-b includes systematic variation in θ from north to south. In order to see the optical polarizations from a foreground and background cloud in absorption, Goodman et al. (1990a) point out that the extinction of the nearer cloud must be low (AV ≤ 1 mag) or have signi?cant ?uctuations in order to see through to the background cloud. If the extinction in the cloud is on the order of 1 mag, then the cloud is not self-gravitating and hence is an unlikely source of 850 ?m emission (and certainly 850 ?m polarized emission, which is at most on the order of 10% of the total ?ux). This leaves the possibility of a denser cloud with signi?cant ?uctuations in column density across its projected surface. The angular distance between the B1-b and B1-c cores is approximately 2 arcminutes. At a distance of 200 pc, which is the most probable location of a foreground cloud given previous molecular line observations, this corresponds to 0.12 pc, or about the scale of a self-gravitating core in a molecular cloud. Since we observe di?erent position angles in the two bright cores (and a change in position angle within the B1-b core itself), this would suggest that ?elds of varying orientations are exhibited in the foreground ?uctuations in the nearby cloud. This implies that the ?uctuations in the foreground cloud are comparable to or smaller than the scale of a starless core. Since the two bright cores are associated with NH3 emission (and hence known to be within the B1 cloud), the ?uctuations would have to vary on an angular scale similar to the separation of cores in B1, despite being at a distance nearly a factor of two smaller. We conclude that attributing the polarization seen against the bright cores B1-b and B1-c to a foreground cloud suggests an unlikely con?guration for a nearby cloud not detected in any dense tracers such as CS and NH3 .

– 13 – However, the ?attening of the p versus I relation in B1-c does suggest that this core is unusual in some way. Depolarization within cores is usually attributed to either changing grain or alignment physics with increasing density or varying (ordered or disordered) magnetic ?eld geometry. It is possible that no stellar condensation has formed at the center of B1-c, in which case a ?eld with a straight geometry may thread this core. Also, if no out?ow is present, then theory suggests there should be no disk either, which means the ?eld is unlikely to be tangled on small scales. Further study of this source to search for evidence of out?ow or a protostellar condensation could provide some support for the suggestion that this is a starless core. However, this would not completely explain the pattern, since all the starless cores observed thus far with SCUBA do exhibit depolarization toward their intensity peaks (Ward-Thompson et al. 2000). The cores observed by Ward-Thompson et al. (2000) are all signi?cantly closer than B1 (140-170 pc). The total ?ux from one of these cores (L183) is 2.8 Jy at 800 ?m (Ward-Thompson et al. 1994). Therefore, cores of comparable brightness, both closer and further (i.e., LBS 23’s cores, Matthews, Fiege & Moriarty-Schieven (2002), hereafter Paper III) than B1, do exhibit depolarization to the highest intensities. The p versus I relation of B1-c is thus not easily explained purely by di?ering resolutions.

4.1.2. Polarization in Individual Cores It is worth noting that the degree of alignment across the B1-a, B1-c, and B1-d cores is particularly strong. Figure 3 shows that these three cores are not signi?cantly asymmetric, so the polarization patterns cannot be said to align with any preferred axes of the cores. The elongated core B1-b is the only one which exhibits systematic variation in polarization postion angle. Since this core is composed of two sources, the polarization patterns could be di?erent within each core and then we observe their vector sum where the cores overlap. Several models exist which predict the polarization patterns across cores depending on various physical interpretations. A recent publication by Padoan et al. (2001) predicts the continuum polarization for protostellar cores assembled via supersonic magnetized turbulent ?ows in models of molecular clouds. They ?nd that the universally observed trend of declining polarization percentage with increasing intensity in star-forming cores can be reproduced by their model if grains are aligned only up to a threshold extinction (AV ? 3 mag in their simulation). Several of the resulting p versus I plots do suggest a ?attening in the distribution at high values of intensity. However, one di?erence between their simulations (see Figs. 6 and 7 of Padoan et al. (2001)) and Figure 4 is the population of the bottom left quadrant (low p and low I); vectors exist in this region in the simulations, whereas this region is devoid of vectors in Figure 4, despite complete sampling down to the intensity threshold.

– 14 – Measurement of low levels of polarized emission toward lower intensities will become possible with the next generation of detectors (e.g. SCUBA-2). The fact that there is a potential for confusion between two clouds along the line of sight makes interpretation of the polarization data more complicated in Perseus. However, constraints on the column density and spatial scale of potential variations in extinction of a second cloud suggest that the overwhelmingly predominant source of polarized emission is the B1 cloud and its associated cores. The models of Padoan et al. (2001) and Fiege & Pudritz (2000) relate to cores forming from lower density, ?lamentary structures. B1 is not a signi?cantly elongated cloud (although the Perseus complex itself appears elongated on very large scales), and its cores appear to be forming from density enhancements in its cold interior. A recent model of magnetized cores predicts a relation between the geometry of a core and the measured polarization position angles (e.g. Basu (2000)). However, the B1 cores are not signi?cantly elongated; the only asymmetry is in B1-b, which is resolved into two sources with separate extended envelopes by Hirano et al. (1999).

4.2.

An Estimate of the Total Field Strength and Direction in B1

Myers & Goodman (1991) describe a method by which the total ?eld strength and direction can be estimated in a cloud toward which a series of independent Zeeman measurements of Blos and polarization measurements to infer the orientation of Bpos have been made. Their formalism is described for absorption polarimetry, but is easily adapted to emission polarimetry if simple assumptions are made about the relation between the orientations of polarization vectors and the plane-of-sky magnetic ?eld. A distribution of polarization data which can be ?t by a single Gaussian is a good approximation to the precise function described in Myers & Goodman (1991) in the case where the nonuniform ?eld is relatively small and the three dimensional random case can be assumed. As described in § 3.1 above, the polarization vectors associated with the faint lower density gas o? the B1 cores can be ?t with a single Gaussian distribution which has a mean of 91? (east of north) and a width of 19? . At 12′′ sampling, these vectors are not completely independent (since the JCMT beamwidth is 14′′ ), but we use them to get a rough estimate of the ?eld properties. The Myers & Goodman model is based on the presence of both a uniform (B0 ) and non-uniform (Bn ) component to the ?eld in the region. Non-uniform in this case refers to a disordered, possibly turbulent, ?eld component (as opposed to an ordered, but not unidirectional ?eld). Given a distribution of polarization data with mean polarization angle,

– 15 – Θ, (in degrees) and dispersion, s, (in radians) and a series of Zeeman measurements with mean uniform component B 0z and dispersion σBz , the following quantities can be estimated: the inclination, σBz i = arctan ; (1) sB 0z the total uniform mean ?eld strength, B0 = and the dispersion in B, σB = σBz N 1/2 (3) B 0z ; cos i (2)

where N is the number of correlation lengths of the non-uniform ?eld component through the cloud. The correlation length is an expression of how quickly the non-uniform component of the ?eld changes through the depth of the cloud. Values of Bn separated by less than a correlation length are likely to be correlated, while those more spatially separated than a correlation length are independent. Myers & Goodman (1991) derive the relation: Nmax = 69 AV mag B ?G
?1

.

(4)

The maximum number of correlation lengths can be estimated under the assumption that the magnetic and gravitational energy densities are equal. Under this condition, AV /B ≈ 0.17 mag ?G?1, where B is the total ?eld strength (Chandrasekhar & Fermi 1953; Myers & Goodman 1988). This estimate yields Nmax ≈ 12. The r.m.s. ?eld strength and the relative strengths of the non-uniform to uniform magnetic ?eld energy densities can then be calculated according to the relations:
2 2 < B 2 >1/2 = B0 + 3σB 1/2

;

(5)

and

2 Mn 3σB = 2 Mu B0

(6)

where we have assumed a three-dimensional non-uniform ?eld component. We use the detection of ?27±4 ?G toward the position of IRAS 03301+3057 (Goodman et al. 1989) as an estimate of the B0z value. In the absence of other independent detections,

– 16 – there is no estimate of the dispersion in the line-of-sight ?eld strength. Thus, we adopt a parameterized approach to combining the Zeeman and dust polarization data to estimate the three-dimensional ?eld, where the ratio of σBz /B0z takes on a range of values (0.2, 0.4, 0.6 and 0.8). Table 4 then summarizes properties of the magnetic ?eld in B1 based on equations (1), (2), (3), (5), and (6) for N = 1 and N = 10. Finally, the direction of the uniform component of the magnetic ?eld can be estimated: ? ? ? B0 = (N cos ΘB + E sin ΘB ) sin i + cos i?. z (7)

For emission polarization data, we assume the mean magnetic ?eld direction, ΘB , is related to Θ by ±90? . Emission local to each dust grain should be related to the local ?eld direction in this manner (Hildebrand 1988), but for this to be the case in the vector averaged sum of all polarizations through the cloud (which is what we measure at the telescope) is to assume that the magnetic ?eld orientation does not substantially vary through the depth of the cloud. This has been shown to be a poor assumption in some regions, where the polarization data support a more complex ?eld geometry (i.e., OMC-3 in Orion A, Paper II; NGC 2024 in Orion B, Paper III; and NGC 2068, Paper IV). However, B1 is a dark cloud and not part of a giant molecular cloud complex like Orion; therefore, a uniform ?eld structure (at least away from the cores) is not an unreasonable ?rst-order assumption here. We note however that in utilizing this relation in B1, we are also assuming that all the polarized emission is arising in the B1 core, as opposed to in a second cloud as discussed above. Using equation (7) and σBz /B0z = 0.2 (hence i = 31? from the line of sight), ? ? B0 = 31?G ±(0.52N + 0.01E) ? 0.86? . z We note that the direction of the ?eld along the line of sight is toward the observer. The ?eld components can also be expressed in terms of two dimensions, x and z , where ? ? x lies along the plane-of-sky mean ?eld direction, as estimated from the mean polarization ? direction. In this case, (9) B0x = B0z tan i and substitution of B0z and i gives: ? ? B0 = B0x x + B0z z = ±19 ?G x ? 27 ?G ?. ? z (10) (11) (8)

Based on comparisons with theoretical predictions based on the assumptions of equality of magnetic ?elds and kinetic energy and equivalence of magnetic and gravitational energies,

– 17 – Crutcher et al. (1993) found that the z -?eld component measured in B1 agreed well with ? predicted values if the inclination of the ?eld to the line of sight are close to zero. Furthermore, because B1 was the only cloud with a detected magnetic ?eld out of 12 in their survey, there was a concern that B1 might have an atypically strong ?eld. Based on statistical analysis, Crutcher et al. (1993) concluded that this need not be the case if the magnetic ?eld in B1 lies nearly along the line of sight. The B0z value of ?27 ± 4 ?G may be substantially higher than the magnetic ?eld strength at locations away from the dense cores. Therefore, our analysis represents upper limits to the ?eld strenghths in low column density gas. However, our detection of ordered polarization vectors from dust associated with the main core of molecular gas in B1 indicates that at least some of the magnetic ?eld in the region lies in the plane of the sky. Unfortunately, there is no way to unambiguously determine the plane-of-sky ?eld strength from polarization data alone, since the degree of polarization may depend on grain size, shape, composition and degree of alignment or spin, as well as ?eld strength (Hildebrand et al. 2000). We note that the OH Zeeman measurements can e?ectively probe regions with densities as high as n(H2 ) ? 104 cm?3 (Crutcher et al. 1994), quite comparable to the densities associated with the dust emission. Assuming a temperature of 20 K for the main core, the 850 ?m ?ux density (at a level of 0.2 Jy) implies a column density of N(H2 ) ? 2 × 1022 cm?2 , which corresponds to a density of n(H2 ) ? 3 × 104 cm?3 if the emitting dust extends over the main core diameter of 0.8 pc (Bachiller et al. 1990). In reality, the emitting region of dust may be more con?ned along the line of sight, which would imply even higher densities. This is certainly the case where ?ux densities are high. The column density toward B1-c is N(H2 ) ? 3 × 1023 cm?2 . Since Zeeman data have been obtained toward regions of high density, it is possible that the OH Zeeman data and the dust emission polarimetry do not arise in precisely the same spatial regions of the cloud. They could, therefore, be sampling di?erent ?eld geometries, or at least di?erent total ?eld strengths. However, we have applied the Myers & Goodman (1991) method over a size scale comparable to the Arecibo beam at the frequency of the OH Zeeman measurements of Goodman et al. (1989), making our calculation quite reasonable for the lower column density dust.

5.

Summary

We have detected polarized emission at 850 ?m arising from the dense interior of the Barnard 1 dark cloud. Our observations are centered on the molecular “main core” observed by Bachiller et al. (1990), in which three ammonia peaks were identi?ed. Submillimeter emission is detected coincident with each of the ammonia peaks. In total four dust cores are

– 18 – identi?ed, one of which has been resolved into two sources (Hirano et al. 1999). Two of the dust condensations, B1-c and B1-d, have not been previously observed in continuum. The B1-a core is likely the 850 ?m counterpart of IRAS 03301+3057. This source appears quite faint at long wavelengths. We note that the detection of two new dense dust condensations, plus the B1-b binary sources identi?ed as young Class 0 sources by Hirano et al. (1999), increases the number of YSOs or pre-protostellar objects in B1 by almost a factor of 2. This indicates that the star formation e?ciency in B1 is likely much larger than the 0.5% estimate by Bachiller et al. (1990) since there may be other as yet unobserved pre-protostellar or protostellar cores in the cloud of which we have observed only a fraction. The polarized emission can be separated somewhat arbitrarily into two sub-groups by the coincident ?ux levels. Strong polarizations are measured toward faint dust emission regions where the mean polarization percentage is 4.5% (standard deviation 2.3%). The position angles are distributed about 90? (east of north) and can be ?t by a Gaussian of mean 91.3? and dispersion 19? . The polarizations associated with high intensities (i.e., the cores) show smaller polarization percentages, with a mean of 2.6% and standard deviation 1.4%. The vectors show alignment across the cores, but each core does not exhibit the same mean position angle. A comparison of each vector to adjacent values shows that vectors are strongly aligned with their neighbours in position angle. The largest discrepencies are observed at the “boundaries” between the dense cores and the lower column density dust emission in which they are embedded. Over the whole mapped area, we see evidence of the depolarization observed toward many star-forming cores. Interestingly, when the polarization percentages are plotted against intensity for individual cores, the p versus I relation ?attens out at 30% and 40% of the peak emission from the B1-c and B1-b cores, respectively. The B1-c core exhibits only one vector with a value of p < 1%, and thus the ?attening in that core is real and not just an artifact of a lower limit on detectable polarizations or increasing optical depth. The observation of depolarization at the highest intensities of cores closer (Ward-Thompson et al. 2000) and further (Paper III) than B1 makes it unlikely that this e?ect is directly related to our resolution of B1 at 330 pc. None of the orientations of polarization vectors measured by SCUBA are directly related to the two mean magnetic ?eld directions detected with optical polarimetry of the Perseus complex (Goodman et al. 1990a). In the case where the B1 dense cores could be completely depolarized, the polarized emission along the line of sight to those cores would arise completely in the foreground cloud (proposed to be at 200 pc). If such a cloud contains ?uctuations in extinction, those ?uctuations must be on scales similar to the separation of cores in B1 at approximately half the distance. This is required to account for the di?ering

– 19 – orientations measured in the two bright cores, B1-b and B1-c. We dismiss this scenario as unlikely since, unless the polarized emission from the foreground cloud rises in such a way as to o?set the increasing intensity toward the B1-c core peak, we should see a steeper depolarization toward B1-c than in typical cores, not the threshold we observe. Finally, following the method of Myers & Goodman (1991), we have estimated the net ?eld geometry in the B1 main core using our polarized emission data toward faint regions (centered on 90? east of north) and the line-of-sight ?eld strength toward B1 measured by Goodman et al. (1989). We ?nd that the total uniform ?eld component is described by: ? ? B0 = 31?G ±(0.52N ? 0.01E) ? 0.86? , z (12)

under the assumption of σBz /B0z = 0.2. The ratio of the magnetic energy of the nonuniform component of the ?eld to the uniform component ranges from 0.09 to 0.9 for this case, depending on the number of correlation lengths of the non-uniform component through the cloud. This result is roughly consistent with the theoretical predictions based on virial and magnetic equilibrium in the cloud, for which the line-of-sight ?eld was comparable to the total predicted ?eld. The high degree of ordering in the polarization data itself suggests that some component (possibly a signi?cant amount) of the magnetic ?eld could lie in the plane of the sky. The authors would like to thank J. Greaves, T. Jenness, and G. Moriarty-Schieven at the JCMT for their assistance during observing and with subsequent data reduction. A. Goodman provided clari?cation regarding the status of Zeeman observations toward B1, suggestions on the interpretation of patterns across the cores, and a detailed referee report which led to signi?cant improvements to this paper. G. Petitpas and J. Wadsley provided helpful discussions on the most e?ective means of comparing adjacent vectors. The research of CDW is supported through grants from the Natural Sciences and Engineering Research Council of Canada. This work was partially supported by NSF grant AST-99811308.

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A This preprint was prepared with the AAS L TEX macros v5.0.

– 23 –

Table 1. Observing Parameters for Jiggle Mapping of B1 Pointing Center R.A. (J2000) Dec. (J2000)
s 03h 33m 17.9 s 03h 33m 19.6 s 03h 33m 18.3 ′′ +31? 09′ 32. 3 ′′ +31? 08′ 28. 25 ′′ +31? 07′ 03. 8

Number of Times Observed 16 12 30

Note. — The chop throw used for all observations was 120′′ at a chop position angle of 65? (east of north).

– 24 –

Table 2. Barnard 1 850 ?m Polarization Data ? R.A.a ? Dec. (′′ ) (′′ ) p (%) dp (%) σp θ (? ) dθ (? )

Vectors associated with I > 720 mJy beam?1b ?58.5 ?136.5 3.74 0.56 6.7 ?85.3 ?64.5 ?136.5 5.24 0.83 6.3 ?78.3 ?52.5 ?130.5 1.86 0.50 3.7 68.1 ?58.5 ?130.5 2.36 0.46 5.2 85.0 ?64.5 ?130.5 3.85 0.59 6.5 ?80.9 ?70.5 ?130.5 9.06 0.76 11.9 ?80.6 ?46.5 ?124.5 2.49 0.63 3.9 67.3 ?52.5 ?124.5 3.10 0.46 6.7 64.0 ?58.5 ?124.5 1.79 0.44 4.1 85.4 ?64.5 ?124.5 2.29 0.61 3.7 ?72.8 ?46.5 ?118.5 4.10 0.52 7.9 79.3 ?52.5 ?118.5 3.68 0.41 9.0 79.8 ?58.5 ?118.5 2.25 0.43 5.2 ?87.8 1.5 ?112.5 2.50 0.51 4.9 ?89.0 ?4.5 ?112.5 2.47 0.46 5.4 ?88.7 ?10.5 ?112.5 4.79 0.43 11.0 66.7 ?16.5 ?112.5 4.52 0.48 9.5 89.1 ?22.5 ?112.5 1.74 0.50 3.5 85.6 ?46.5 ?112.5 4.25 0.55 7.7 84.6 ?52.5 ?112.5 2.25 0.47 4.8 78.3 ?58.5 ?112.5 1.46 0.48 3.0 ?66.1 ?64.5 ?112.5 2.13 0.54 3.9 ?80.1 13.5 ?106.5 4.00 0.50 8.0 89.8 7.5 ?106.5 2.59 0.35 7.5 89.2 1.5 ?106.5 1.05 0.32 3.3 81.9 ?4.5 ?106.5 1.57 0.32 4.8 ?82.1 ?10.5 ?106.5 2.75 0.38 7.2 ?86.7 ?16.5 ?106.5 4.26 0.44 9.7 ?86.8 ?22.5 ?106.5 3.99 0.43 9.3 ?89.1

4.3 4.5 7.7 5.6 4.4 2.4 7.3 4.3 7.1 7.6 3.6 3.2 5.5 5.9 5.3 2.6 3.0 8.2 3.7 6.0 9.5 7.3 3.6 3.8 8.7 5.9 4.0 3.0 3.1

– 25 –

Table 2—Continued ? R.A.a ? Dec. (′′ ) (′′ ) 13.5 ?10.5 ?16.5 7.5 1.5 ?10.5 ?16.5 19.5 ?4.5 ?10.5 13.5 7.5 1.5 ?4.5 ?10.5 13.5 7.5 1.5 ?4.5 ?10.5 13.5 7.5 1.5 ?4.5 7.5 1.5 ?4.5 ?28.5 ?34.5 ?22.5 ?100.5 ?100.5 ?100.5 ?94.5 ?94.5 ?94.5 ?94.5 ?88.5 ?88.5 ?88.5 ?82.5 ?82.5 ?82.5 ?82.5 ?82.5 ?76.5 ?76.5 ?76.5 ?76.5 ?76.5 ?70.5 ?70.5 ?70.5 ?70.5 ?64.5 ?64.5 ?64.5 13.5 13.5 19.5 p (%) 1.28 2.08 2.86 1.13 1.01 1.28 2.53 2.38 1.18 3.40 1.09 1.15 1.35 1.52 4.02 1.53 1.50 2.35 1.91 4.48 3.00 4.50 1.98 1.35 5.30 4.13 2.98 3.56 1.25 2.04 dp (%) σp θ (? ) dθ (? ) 7.2 4.5 4.1 4.0 4.4 8.1 5.1 4.9 5.8 3.4 7.4 4.4 3.9 4.9 3.3 6.9 4.2 2.4 4.1 3.2 6.1 2.4 4.0 7.3 3.5 3.1 4.9 3.4 8.4 6.5

0.32 4.0 ?80.5 0.33 6.4 83.2 0.41 7.0 ?78.2 0.16 7.2 ?63.3 0.15 6.6 ?49.0 0.36 3.5 47.2 0.45 5.6 ?82.8 0.41 5.8 33.8 0.24 5.0 46.4 0.41 8.4 58.5 0.28 3.9 28.0 0.18 6.5 58.9 0.18 7.4 67.5 0.26 5.8 68.0 0.46 8.8 66.9 0.37 4.1 ?50.2 0.22 6.8 73.7 0.20 11.9 66.6 0.27 7.0 71.2 0.51 8.8 65.5 0.64 4.7 ?80.1 0.37 12.1 ?87.4 0.28 7.2 76.8 0.34 3.9 64.7 0.65 8.2 87.8 0.45 9.3 77.1 0.51 5.9 71.7 0.42 8.5 61.2 0.37 3.4 72.4 0.47 4.4 ?56.5

– 26 –

Table 2—Continued ? R.A.a ? Dec. (′′ ) (′′ ) p (%) dp (%) σp θ (? ) dθ (? ) 7.8 5.1 4.4 4.0 3.4 3.1 2.9 4.9 3.9 3.0 4.5 3.2 3.9 4.9 6.9 6.8 5.5 2.3 2.2 2.7 2.3 3.2 1.7 3.0 3.5 1.5 3.2 3.7 3.6

?28.5 19.5 1.22 0.33 3.7 9.7 ?34.5 19.5 1.41 0.25 5.6 27.9 ?40.5 19.5 1.45 0.22 6.5 19.8 ?22.5 25.5 3.12 0.43 7.2 ?24.0 ?28.5 25.5 2.62 0.31 8.3 24.8 ?34.5 25.5 1.77 0.19 9.1 31.6 ?40.5 25.5 1.69 0.17 9.9 31.9 ?28.5 31.5 1.83 0.31 5.8 30.0 ?34.5 31.5 1.34 0.18 7.4 44.9 ?40.5 31.5 1.86 0.20 9.4 47.0 ?46.5 31.5 1.88 0.30 6.3 50.3 ?52.5 31.5 4.29 0.48 9.0 64.6 ?34.5 37.5 2.15 0.29 7.4 47.1 ?40.5 37.5 1.77 0.30 5.9 46.9 ?46.5 37.5 1.58 0.38 4.1 40.6 Vectors associated with I < 720 mJy beam?1b ?10.5 ?139.5 3.44 0.81 4.2 47.8 ?22.5 ?139.5 4.58 0.87 5.3 ?78.7 ?34.5 ?139.5 11.66 0.93 12.6 88.1 ?46.5 ?139.5 6.88 0.52 13.2 ?70.8 ?58.5 ?139.5 4.05 0.38 10.6 ?65.0 ?70.5 ?139.5 8.00 0.64 12.4 ?73.1 13.5 ?127.5 8.54 0.96 8.9 89.9 1.5 ?127.5 9.42 0.57 16.5 ?81.3 ?10.5 ?127.5 3.99 0.41 9.7 87.1 ?22.5 ?127.5 3.64 0.44 8.2 73.3 ?34.5 ?127.5 8.27 0.45 18.5 ?86.2 ?46.5 ?127.5 2.94 0.33 8.9 67.2 ?82.5 ?127.5 5.19 0.68 7.7 ?88.7 25.5 ?115.5 5.15 0.64 8.0 ?87.1

– 27 –

Table 2—Continued ? R.A.a ? Dec. (′′ ) (′′ ) 13.5 1.5 ?22.5 ?34.5 ?82.5 25.5 ?34.5 ?46.5 ?70.5 ?82.5 ?22.5 ?34.5 ?46.5 ?58.5 ?70.5 ?82.5 25.5 ?22.5 ?34.5 ?46.5 ?58.5 ?70.5 ?10.5 ?22.5 ?46.5 ?58.5 ?70.5 13.5 1.5 ?10.5 ?115.5 ?115.5 ?115.5 ?115.5 ?115.5 ?103.5 ?103.5 ?103.5 ?103.5 ?103.5 ?91.5 ?91.5 ?91.5 ?91.5 ?91.5 ?91.5 ?79.5 ?79.5 ?79.5 ?79.5 ?79.5 ?79.5 ?67.5 ?67.5 ?67.5 ?67.5 ?67.5 ?55.5 ?55.5 ?55.5 p (%) 8.13 2.91 2.37 1.18 1.77 6.52 4.63 2.64 1.46 2.14 3.11 3.41 1.16 2.03 1.65 9.54 3.43 3.92 3.78 4.09 1.67 3.06 3.89 6.48 2.37 4.19 3.29 7.64 2.23 2.71 dp (%) 0.43 0.30 0.28 0.32 0.58 0.46 0.31 0.30 0.42 0.63 0.31 0.36 0.34 0.32 0.46 0.92 0.62 0.51 0.46 0.36 0.32 0.43 0.31 0.62 0.41 0.33 0.49 0.86 0.43 0.41 σp θ (? ) 82.0 ?85.2 84.0 56.5 86.0 74.8 81.2 ?85.3 ?89.6 87.1 89.5 ?87.3 84.4 79.1 22.2 ?17.0 88.8 75.4 ?85.8 80.9 35.8 54.1 83.2 83.5 82.5 57.9 15.0 0.1 ?76.8 70.5 dθ (? ) 1.5 3.0 3.4 7.7 9.4 2.0 1.9 3.3 8.2 8.4 2.8 3.0 8.3 4.6 7.9 2.7 5.2 3.7 3.4 2.5 5.5 4.0 2.3 2.7 5.0 2.2 4.3 3.2 5.5 4.4

18.7 9.6 8.3 3.7 3.1 14.1 15.1 8.7 3.5 3.4 10.2 9.4 3.4 6.2 3.6 10.4 5.5 7.7 8.3 11.5 5.3 7.2 12.7 10.5 5.7 12.8 6.7 8.9 5.2 6.6

– 28 –

Table 2—Continued ? R.A.a ? Dec. (′′ ) (′′ ) ?22.5 ?46.5 ?58.5 1.5 ?10.5 ?22.5 1.5 ?10.5 ?22.5 1.5 ?10.5 ?22.5 ?34.5 ?46.5 13.5 1.5 ?10.5 ?22.5 ?34.5 ?46.5 1.5 ?10.5 ?22.5 ?34.5 ?58.5 13.5 1.5 ?10.5 ?58.5 1.5 ?55.5 ?55.5 ?55.5 ?43.5 ?43.5 ?43.5 ?31.5 ?31.5 ?31.5 ?19.5 ?19.5 ?19.5 ?19.5 ?19.5 ?7.5 ?7.5 ?7.5 ?7.5 ?7.5 ?7.5 4.5 4.5 4.5 4.5 4.5 16.5 16.5 16.5 16.5 28.5 p (%) 8.82 3.04 4.43 2.54 2.53 7.08 6.44 5.43 9.13 8.57 4.18 4.86 2.73 4.25 3.89 3.95 3.63 4.78 4.93 4.13 4.15 4.05 1.25 1.86 7.14 8.55 3.23 4.10 4.97 7.91 dp (%) 0.72 0.98 0.81 0.72 0.59 0.90 0.70 0.59 0.94 0.79 0.68 0.79 0.67 0.76 0.78 0.76 0.58 0.54 0.45 0.62 0.74 0.55 0.36 0.30 0.87 0.93 0.65 0.45 0.63 0.73 σp θ (? ) ?85.7 56.5 ?72.3 74.5 86.9 78.9 ?70.8 ?67.9 90.0 ?84.0 ?60.5 61.7 ?84.6 ?78.6 ?68.9 ?80.3 ?89.6 ?79.0 ?88.6 ?79.5 66.9 ?74.2 ?51.8 54.0 42.9 ?58.2 ?63.8 ?59.4 ?86.8 ?84.6 dθ (? ) 2.3 9.2 5.3 8.1 6.7 3.7 3.1 3.1 3.0 2.6 4.7 4.7 7.0 5.1 5.7 5.5 4.6 3.2 2.6 4.3 5.1 3.9 8.2 4.6 3.5 3.1 5.8 3.2 3.6 2.6

12.2 3.1 5.4 3.5 4.3 7.8 9.2 9.1 9.7 10.9 6.1 6.1 4.1 5.6 5.0 5.2 6.3 8.9 11.0 6.7 5.6 7.3 3.5 6.2 8.2 9.2 5.0 9.1 7.9 10.8

– 29 – Table 2—Continued ? R.A.a ? Dec. (′′ ) (′′ ) ?10.5 ?58.5 ?10.5 ?22.5 ?58.5 ?34.5 ?58.5
a

p (%) 4.22 3.48 5.84 2.24 4.96 2.08 2.88

dp (%) 0.47 0.43 0.76 0.39 0.54 0.69 0.72

σp

θ (? ) ?77.2 68.6 ?61.6 ?3.1 72.1 ?71.1 ?47.1

dθ (? ) 3.2 3.6 3.7 5.0 3.1 9.5 7.2

28.5 28.5 40.5 40.5 40.5 52.5 52.5

9.0 8.0 7.7 5.8 9.1 3.0 4.0

Positional o?sets are given from the J2000.0 cos ′′ ordinates α = 03h 33m 20.9 and δ = +31? 09′ 03. 7 s ′′ (α = 03h 30m 15.0 and δ = +30? 59′ 00. 0 in B1950.0). Vectors are binned to 12′′ sampling below the chosen threshold in total intensity and 6′′ sampling above. The total intensity at each vector position exceeds 20% of the faintest compact peak, B1-d. This minimizes the chances of systematic e?ects from chopping to a reference position, as discussed in Appendix A of Paper II.
b

Using a calibration factor of 480 Jy beam?1 V?1 .

Table 3. Peak ?ux densities at 850 ?m Core R.A. (J2000)
s 03h 33m 16.4 s 03h 33m 21.3 s 03h 33m 17.7 h m s 03 33 16.2

Dec. (J2000) +31? 07′ 51′′ +31? 07′ 28′′ +31? 09′ 31′′ +31? 06′ 49′′

Speak (Jy beam?1 ) 0.68 2.5 3.0 1.1

Notes

B1-a B1-bS B1-c B1-d

IRAS 03301+3057 (B1-IRS) Hirano et al. (1999) ?rst continuum detection ?rst continuum detection

– 30 –

Table 4. Magnetic Properties of Barnard 1 ib σBz a (?G) (degrees) 5.4 10.8 16.2 21.6 31 50 61 68 B0 (?G) 31 42 56 71 N σB < B 2 >?1/2 (?G) (?G) 5.4 17.1 10.8 34.2 16.2 51.3 21.6 68.4 32.4 42.9 46.0 72.6 62.6 105 80.3 138 Mn /Mu

1 10 1 10 1 10 1 10

0.09 0.91 0.20 2.00 0.25 2.50 0.28 2.80

For all calculations, the following values were used: |B0z | = 27 ?G; s = 0.33 radians.
b

a

Inclination is measured from the line of sight.

– 31 –
Right ascension (B1950) 22.2 18.2 14.2 10.2 03:30:6.2 31:00:56.3

B1-c
59:56.3 (J2000)

Declination (B1950)

58:56.3

B1-bN B1-a
57:56.3

B1-bS
56:56.3

B1-d

30:55:56.3

5%

(J2000)

Fig. 1.— 850 ?m polarization pattern toward the “main core” of Barnard 1 is overlaid on the Stokes’ I map. The greyscale range is ?1σ to 3σ. Polarization data were sampled at 3′′ and have been binned to 6′′ (approximately half the JCMT beamwidth of 14′′ ) on the bright cores where signal-to-noise (σp ) is high and 12′′ in the fainter regions. All vectors are associated with Stokes’ I values greater than 20% the B1-d peak ?ux, σp > 3, and an uncertainty in polarization percentage, dp, < 1%. Red vectors have polarization percentage, p, < 1% and were not included in any analysis of the polarization pattern. The vectors are accurate in position angle to better than 10? . The peaks B1-a, B1-bN and B1-bS have been labeled according to the designations of Hirano et al. (1999). We have designated the other two peaks B1-c and B1-d. The position of IRAS 03301+3057 is marked in blue where the lines denote the extent of the uncertainty in the IRAS position. The mean polarization percentage of the plotted vectors is 3.6% with a standard deviation of 2.2%. Coordinates in J2000 and B1950 are shown.

– 32 –

Fig. 2.— Distributions of position angle in B1 are shown using histograms of the θ measured toward faint (dashed) and bright (solid) regions separately. The threshold used to discriminate between faint and bright regions was a Stokes’ I value of 720 mJy beam?1 , as discussed in §3.2. The vectors associated with lower column densities exhibit a Gaussian distribution with a mean of 91? and dispersion of 19? . The distribution of vectors toward the cores is not Gaussian, with each core dominating a di?erent part of the total histogram. The position angles are labeled with the core dominating each peak. The dotted lines show the emission polarization position angles which correspond to the peaks observed in the Goodman et al. (1990a) distribution of optical absorption polarimetry (i.e., they are rotated by 90? ).

– 33 –

B1-c

B1-a B1-b

B1-d 5%

Fig. 3.— Core positions and the variation between neighbouring vectors. The positions of the cores are shown with contours of the Stokes’ I emission. Contours plotted are: 0.2 to 1.0 Jy beam?1 in steps of 0.2 Jy beam?1 , and 1.4 to 2.6 Jy beam?1 in steps of 0.4 Jy beam?1 . (These correspond to visual extinction magnitude contours of 20 to 100 in steps of 20 magnitudes, and 140 to 260 in steps of 40 magnitudes.) We have compared each polarization vector shown in Figure 1 to its nearest neighbours in eight directions to a maximum radial separation of 17′′ . The data were then smoothed to 12′′ sampling. The length of the vectors plotted is the mean change ?p in the smoothed grid point, while the vector orientations indicate the mean change in direction ?θ. Zero change in angle is indicated by 0? (east of north). These data reveal that within cores, and between them, the position angles are strongly consistent, while the large vectors o?sets from 0? at the boundaries show where the changes in vector character occur. Coordinates are J2000.

– 34 –

γ

?0.80 +/? 0.05 Alow = 2.1 +/? 0.1

low =

γ high = ?0.82 +/? 0.04 A high = 2.6 +/? 0.1

Fig. 4.— Depolarization in regions of low and high column density. Polarization is plotted against intensity on a log-log scale for our two populations of vectors. Low column density data are plotted with crosses while circles illustrate vector magnitudes associated with the cores. The slopes derived from ?ts to the p versus I pro?les yield the same power law index, γ (where p = AI γ ), plotted as the slope on the logarithmic scale. We note, however, that despite the scatter in the plot, the vectors at higher intensities seem to ?atten in p. This can be seen more clearly in Figure 5.

– 35 –

Fig. 5.— Depolarization toward individual cores. To better examine the change in polarization percentage at high intensities, we plot log p versus log I for individual cores. Essentially, we take all vectors around each core above the intensity threshold discussed in Figure 1. By plotting the three bright cores separately, it is clear that B1-b and B1-c show higher values of p than expected given the slope of the relation below 1 Jy beam?1 . The threshold corresponds to ? 30% of the peak of B1-c and ? 40% of B1-b. In the text, we discuss possible systematic e?ects which could explain this ?attening (i.e., the truncation of the data set below 1% and optical depth). We conclude that the threshold is a real e?ect for the B1-c core.



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