Observation and Data Analysis - 高質量恆星形成區域的磁場演化

The observations were carried out on 2006 July 27 and 2006 September 10, 2006 using the Submillimeter Array (SMA; Ho, Moran & Lo (2004))¹ in the compact conﬁguration, with seven of the eight antennas available for both tracks. The projected lengths of the baselines ranged from 6.5 to 70 kλ (λ ≈ 870 μm). Therefore, our observational results are insensitive to structures larger than 39. The SMA receivers are intrinsically linearly polarized, and only one polarization is available at the current time. Thus, quarter-wave plates (see Marrone & Rao 2008) were installed in order to convert the linear polarization (LP) to circular polarization (CP). The quarter-wave plates were rotated by 90^◦ on a 5 minutes cycle using a Walsh function to switch between 16 steps in order to sample all the 4 Stokes parameters. The integration time spent on the source in each step was approximately 15 s. The overhead required in switching between the diﬀerent states was approximately 5 s. In each cycle all four cross-correlations (LL, LR, RL, and RR) were each calculated 4 times. The data were then averaged over this complete cycle in order to obtain quasi-simultaneous dual polarization visibilities. We assume that the smearing due to the change of the polarization angles on this timescale is negligible.

The local oscillator frequency was tuned to 341.482 GHz. With a 2 GHz bandwidth in each sideband we were able to cover the frequency range from 345.5 to 347.5 GHz and from 335.5 to 337.5 GHz in the upper and lower sidebands, respectively. The correlator was set to a uniform frequency resolution of 0.65 MHz (∼ 0.7 km s⁻¹) for both sidebands.

While our main emphasis was to map the polarized continuum emission from the dust, we were also able to detect a number of molecular lines simultaneously. These results will be published separately.

Generally, the conversions of the LP to CP of the receivers are not perfect. This nonideal characteristic of the receiver will cause an unpolarized source to appear polarized, which is

1The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica.

known as instrumental polarization or leakage. Nevertheless, these leakage terms (see Sault, Hamaker, & Bregman 1996) can be calibrated by observing a strong linearly polarized quasar. In this study, the leakage and bandpass were calibrated by observing 3c279 for the ﬁrst track and 3c454.3 for the second track. Both sources were observed for 2 hr while they were transiting in order to get the best coverage of parallactic angles. The leakage terms are frequency dependent, ∼1% and ∼3% for the upper and lower sidebands before the calibration, respectively. After calibration, the leakage is less than 0.5% in both sidebands. Besides the calibration for the polarization leakage, the amplitudes and phases were calibrated by observing the quasars 1626-298 and 1924-292 every 18 minutes. These two gain calibrators in both tracks were used because of the availabilities of the calibrators during the observations. Finally, the absolute ﬂux scale was calibrated using Callisto.

The data were calibrated and analyzed using the MIRIAD package (Sault, Teuben, &

Wright 1995). After the standard gain calibration, self-calibration was also performed by selecting the visibilities of G5.89 with uv distances longer than 30 kλ. As a result, the sidelobes and the noise level of the Stokes I image were reduced by a factor of 2. In order to get the images from the measured visibilities, the task INVERT in the MIRIAD package was used. The Stokes Q and U maps are crucial for the derivation of the polarization segments. We used the dirty maps of Q and U to derive the polarization to avoid a possible bias introduced from the CLEAN process. The Stokes I map shown in this paper is after CLEAN.

The Stokes I, Q and U images of the continuum were constructed with natural weighting in order to get a better S/N ratio for the polarization. The ﬁnal synthesized beam is 3.0× 1.9 with the natural weighting. The C¹⁷O images are presented with a robust weighting 0.5 in order to get a higher angular resolution, and the synthesized beam is 2.8

×1.8 with a P.A. of 13^◦. The noise levels of the I, Q, and U images are∼ 30, 5, and 5 mJy Beam⁻¹, respectively. Note that the noise level of the Stokes I image is much larger than the ones in the Stokes Q and U images. The large noise level of the I image is most likely due to the extended structure, which cannot be recovered with our limited and incomplete uv sampling. The strength (I_p) and percentage (P ) of the linearly polarized emission are calculated from: I_p² = Q²+ U²− σ²Q,U and P = I_p/I, respectively. The term σ_Q,U is the noise level of the Stokes Q and U images, and it is the bias correction due to the positive measure of I_p. The noise of I_p (σ_I_p) is thus 5 mJy Beam⁻¹. The presented polarization is

derived using the task IMPOL in the MIRIAD package, where the bias correction of σ_I_p is included.

5.4 Results

In this section, we present the observational results of the dust continuum and the dust polarization at 870μm, and the C¹⁷O 3-2 emission line. No polarization was detected in the CO 3-2 emission line.

5.4.1 Continuum Emission

The total continuum emission at 870 μm, shown in Figure 1(a), is resolved with a total integrated ﬂux density 12.6±1.3 Jy. In general, the morphology of the continuum emission at 870μm is similar to the emission at 1.3 mm by Sollins et al. (2004). However, the 870μm emission peaks at ∼ 1 west of the position of the O5 star, which is oﬀset toward the northwest by∼1.7 from the peak of the 1.3 mm continuum emission. Because there is still a signiﬁcant contribution from the free−free emission to the continuum at 870 μm and at 1.3mm, the diﬀerences between the 870 μm and 1.3 mm maps most likely result from the increasing contribution from the dust emission as compared to the free−free emission at shorter wavelengths. Due to the importance of a correct dust continuum image in the derivation of the polarization, we describe here how the free−free continuum was estimated and removed from the 870μm total continuum emission.

Removing the free−free emission

The free−free continuum at 2cm (shown in a color scale in Figure 1 (a) and (b)) was imaged from the Very Large Array (VLA) archival database observed on 1986 August 7. The VLA synthesized beam of the 2 cm free−free image is 0.92×0.45 with natural weighting of the uv data. Since the free−free shell is expanding at a rate of 2.5 mas yr⁻¹(Acord et al.

1998), at a distance of 2 kpc, this expansion motion over the intervening 20 yr is negligible within the synthesized beam of our SMA observation.

The contribution from the free−free continuum was removed by the following steps.

First, we adopted a spectral index α = −0.154 calculated in Hunter et al. (2008) for the free−free continuum emission between 2 cm and 870 μm. The resulting estimated free−free

continuum strength at 870μm was 4.9 Jy. Second, we further assumed that the morphology of the free−free continuum at 870 μm and at 2cm were identical. We then smoothed the VLA 2cm image to the SMA resolution and scaled the total ﬂux density to 4.9 Jy. Finally, we subtracted this image from the total continuum at 870 μm. The resultant 870 μm dust continuum image is shown in Figure 1(b). The total ﬂux density of the dust continuum is therefore 7.7±0.8 Jy.

Dust continuum: mass and morphology

The corresponding gas mass (M_gas) was calculated from the ﬂux density of the dust continuum at 870 μm following Lis et al. (1998):

Mgas= 2λ³Raρd²

3hcQ(λ)J (λ, Td)S(λ). (5.1)

Here, we assumed a gas-to-dust mass ratio R of 100, a grain radius a of 0.1 μm, a mean grain mass density ρ of 3 g cm⁻³, a distance to the source d of 2 kpc, a dust temperature T_dof 44 K, an observed ﬂux density S(λ) of 7.7 Jy, the Planck factor J (λ, T_d) = [exp(hc/λkT_d)− 1]⁻¹. h, c and k are the Planck constant, the speed of light, and the Boltzmann constant, respectively. The grain emissivity Q(λ) was estimated to be 1.5 × 10⁻⁵ after assuming Q(350μm) of 7.5× 10⁻⁴ and β of 2 (cold dust component), and using the relation Q(λ) = Q(350μm)(350μm/λ)^β (Hunter et al. 2000). As suggested in the same paper, the dust emission can be modeled by two temperature components, with the emission dominated by the colder component at T_d ∼ 44 K. We adopted this value for Td, and therefore, the mass given here refers only to the cold component and is an underestimate of the total mass. The derived gas mass of the dust core M_gasis∼ 300 M, with a number density n_H₂ = 5.3×10⁶ cm⁻³averaged over the emission region. The sizescale along the line of sight is assumed to be 0.13 pc, which is the diameter of the circle with the equivalent emission area.

The dust emission presented in Figure 1(b) has an extension toward the northeast (NE), east and southwest(SW), and has a steep roll−oﬀ on the northwestern(NW) edge of the ridge. In the higher angular resolution (0.8) observation at the same wavelength by Hunter et al. (2008), the dust core is resolved into 5 peaks, where the two strongest peaks align in the north-south direction to the west of the O5 star. The dust continuum emission associated with SMA-N, SMA-1 and SMA-2 is called sharp dust ridge hereafter because of its strong emission and its morphology. There is no peak detected at the position of the O5

star. It is likely that the O5 star is located in a dust-free cavity, as proposed by Feldt et al.

(1999) and Hunter et al. (2008).

5.4.2 Dust polarization

We ﬁrst compare the dust polarization derived from the 870 μm total continuum (Fig-ure 1(c)) and from the 870 μm dust continuum (Fig(Fig-ure 1(d)). In both cases the derived polarization is at the same location with the same P.A.s. The only diﬀerence of the polar-ization in Figures 1(c) and (d) is that the percentage of polarpolar-ization near the H II region is increased in Figure 1(d). This is because of the fact that the free−free continuum is not polarized, and the Q and U components are not aﬀected by the free−free continuum sub-traction. Therefore, the expected polarization percentage will increase when the free−free continuum is removed from the 870 μm continuum. The total detected polarized intensity I_p is 59 mJy. All the polarization shown in the ﬁgures besides Figure 1(c) is calculated from the derived dust continuum image. The oﬀset positions, percentages and P.A.s of the polarization segments are listed in Table 1.

Morphology of the detected polarization

The polarized emission is not uniformly distributed (Figure 2(a)). Detected polariza-tions at 2σ_I_p are shown as blue segments, and detections above 3σ_I_p are shown by red segments (Figure 2(b)). Most of the polarized emission is located in the northern half of the dust core close to the HII region and appears as four patches, mostly with σ_I_p ≥ 3 (Figure 2(a) in a color scale). There is a sharp gap where no polarization is detected ex-tending from the NE to the SW across the O star. The southern half of the dust core is free of polarization, except for a few positions at the edge of the dust core. However, the polarization in the southern half of the dust core is at 2 to 3σI_p level only. We will focus our discussions on the more signiﬁcant detections in the core of the cloud.

We separate the polarized emission into two groups. We are guided principally by the fact that one group is associated with the periphery of the total dust emission, while the other group tracks the strongest parts of the total dust emission. The polarized patches to the east of the O star and to the west of the Brγ outﬂow source have similar P.A.s of ∼ 50^◦ (Figure 2(b)). These polarization segments are located at the fainter edges of the higher resolution 870 μm dust continuum image (Figure 2(c); Hunter et al. 2008) and

at the less steep part of the 3 resolution image (this paper). This may suggest that this polarization originates from a more extended overall structure, rather than from the detected condensations. Therefore, these polarization segments are suggested to be the component

”o” (deﬁned in the following section). The rest of the polarization in the northern part is all next to the sharp gap where no polarization is detected. Most of the polarization is on the 870μm sharp dust ridge observed with 0.8 resolution, except for the ones at the NE and SW ends where the polarization patches stretch toward the extended structure. At these NE and SW ends, the polarization is probably the sum of the extended and the condensed structures. These polarization segments are suggested to belong to the component ”x”.

The 0.8 resolution observations show that there is a hole in the southern part of the detected dust continuum. This hole is not resolved with the 3 synthesized beam of our map. That may explain why polarization is not detected at this position. Here, and also for the dust ridge sharply deﬁned with 0.8 resolution, the dust polarization is sensitive to the underlying structures and can help to identify unresolved features which are smaller than our resolution.

Distribution of the polarization segments

The detected P.A.s vary enormously over the entire map, ranging from −60^◦ to 61^◦ (Figure 3(a)). Nevertheless, they vary smoothly along the dust ridge and show organized patches. We have roughly separated the polarized emission into two diﬀerent components according to their locations (as discussed in Sec. 4.2.1) and their P.A.s. The ”o” component is probably from an extended structure with P.A.s ranging from 33^◦to 61^◦. The mean P.A.

weighted with the observational uncertainties of component ”o” is 49±3^◦, with a standard deviation of 11^◦. The ”x” component associated with the sharp dust ridge has P.A.s ranging from −60^◦ to 4^◦. Its weighted mean P.A. is−24±1^◦, with a standard deviation of 18^◦. If the polarization were not separated into two components, the weighted mean P.A. is −9^◦ with a standard deviation of 39^◦.

The relation between the percentage of polarization and the intensity is shown in Fig.

3(b). The percentage of polarization decreases towards the denser regions, which has already been seen for other star formation sites, such as the ones listed in Sec. 1. This is possibly due to a decreasing alignment eﬃciency in high-density regions, because the radiation torques are relatively ineﬀective (Lazarian & Hoang 2007). It can also be due to the geometrical

eﬀects, such as diﬀerences in the viewing angles (Gon¸calves et al. 2005), or due to the results from averaging over a more complicated underlying ﬁeld morphology.

5.4.3 C

¹⁷

O 3-2 emission line

In order to trace the physical environments and the gas kinematics in G5.89, we choose to use the C¹⁷O 3-2 emission line because of its relatively simple chemistry. The critical density of C¹⁷O 3-2 is∼ 10⁵ cm⁻³, assuming a cross-section of 10⁻¹⁶ cm⁻² and a velocity of 1 km s⁻¹, and therefore, it will trace both the relative lower (n_H₂ ∼10⁵cm⁻³) and higher (n_H₂∼ 10⁶ cm⁻³) density regions. Although its critical density is much smaller than the estimated gas density of 5.3×10⁶ cm⁻³ from the dust continuum, it is apparently tracing the same regions as the dust continuum because of the similar morphology of the integrated intensity image, shown in the next section. We therefore assume that the kinematics traced by C¹⁷O represents the bulk majority of the molecular cloud and that it is well correlated with the dust continuum.

Morphology of C¹⁷O 3-2 emission

The emission of the C¹⁷O 3-2 line covers a large velocity range, from−7 to 28 km s⁻¹, as shown in the channel maps in Figure 4. The majority of the gas traced by the C¹⁷O 3-2 line is relatively quiescent and has a morphology similar to the 870μm dust continuum emission. Besides the components which trace the dust continuum, an arc feature is seen in the south-east corner of the panel covering 10−15 km s⁻¹. There is no associated 870μm dust continuum detected at this location, probably due to the low total column density or mass of this feature. Another feature seen in the more quiescent gas is the clump extending towards the south of the dust core (see the panel covering 6−10 km s⁻¹ in Figure 4). This clump has a similar morphology as seen in the 870 μm dust continuum where no polarization has been found. At the higher velocity ends, i.e. from −7 to −3 km s⁻¹ and from 23 to 28 km s⁻¹, the emission appears at the 870μm dust ridge. This suggests that at the sharp dust ridge, there are high−velocity components besides the majority of quiescent material.

Furthermore, the brightest HII features appear correlated with the strongest C¹⁷O emission, especially at low velocities (v_lsr= 6 to 15 km s⁻¹), which may point toward an interaction between the molecular gas and the H II region.

The total integrated intensity (zeroth moment) image (Figure 5(upper-panel) of the

C¹⁷O 3-2 emission line shows a similar morphology as the 870 μm dust continuum. The morphology of the C¹⁷O gas to the west of the O star is similar to the dense dust ridge, i.e. there is an extension from north to south. The steep roll oﬀ of the dust continuum in the NW and an extension from NE to the west of the O star are also seen in C¹⁷O. Besides these similar features to the dust continuum, a strong C¹⁷O peak is found at position A, where no dust continuum peak is detected. This feature A likely does not have much mass, and we will not discuss its properties further in this paper.

Total gas mass from C¹⁷O 3-2 line

The total gas mass Mgas in this region can be derived from the C¹⁷O 3-2 line. This provides a complementary estimate, which is independent from the mass derived from the dust continuum in Eq. 1. Assuming that the observed C¹⁷O 3-2 line is optically thin and in local thermal equilibrium (LTE), the mean column density N_C17O is calculated following the standard derivation of radiative transfer (see Rohlfs & Wilson 2004):

N_C17O = 1.3× 10¹³× T_R3₋₂ V

D(n, T_k) (5.2)

Here, the T_R3−2 V term is the mean ﬂux density of the entire emission region in K km s⁻¹. The D parameter depends on the number density n and the kinetic temperature T_k and is given by

D(n, T_k) = f₂[J_ν(T_ex)− Jν(T_bk)][1− exp(−16.597/Tex)],

where f₂ is the population fraction of C¹⁷O molecules in the J =2 state. T_ex and T_bk are the excitation and background temperatures, respectively. The adopted value of D is 1.5 from the LVG calculation by Choi, Evans II & Jaﬀe (1993). In their calculation, this D value is correct within a factor of 2 for 10 < T_k< 200 K in the LTE condition. The total gas mass M_gas is given by

Mgas= μmH₂d²ΩN_C17O

X_C17O

. (5.3)

Here μ is 1.3, which is a correction factor for elements heavier than hydrogen. m_H₂ is the mass of a hydrogen molecule. d and Ω are the distance to the source and the solid angle of the emission, respectively. The C¹⁷O abundance X_C17O is assumed to be 5× 10⁻⁸ (Frerking et al. 1982; Kramer et al. 1999). The derived mean N_C17O is 2×10¹⁶ cm⁻². The

mean gas number density n_H₂ is 1.6×10⁶ cm⁻³, assuming the size of the molecular cloud is 0.13 pc along the line of sight, which is the diameter of the circle with the equivalent emission area. The derived M_gas from the C¹⁷O 3-2 emission is∼100 M.

The gas mass calculated using the C¹⁷O 3-2 line is a factor of 3 smaller than the value derived from the dust continuum (300 M). This diﬀerence has also been seen in the C¹⁷O survey towards the UC H II regions by Hofner et al. (2000). Their M_gasestimated from the measurement of the C¹⁷O emission tends to be a factor of 2 smaller than the measurement from the dust continuum. The uncertainty of the estimate here possibly results from the assumptions of the dust emissivity, the gas to dust ratio, the abundance of the C¹⁷O, and from the possibility that C¹⁷O might not be entirely optically thin.

5.5 Discussion

We discuss the possible reasons of the nondetected polarization in the CO 3-2 line in the next paragraph. In order to interpret our results, we have also analyzed the kinematics of the molecular cloud in G5.89 using the C¹⁷O 3-2 ﬁrst and second moment images, the position−velocity (PV) diagrams, and the spectra at various positions. The strength of the B ﬁeld inferred from the dust polarization is calculated using the Chandrasekhar−Fermi method. A possible scenario of the dust polarization is discussed based on the calculation of the mass−to−ﬂux ratio and the energy density.

5.5.1 CO 3-2 polarization

Under the presence of the B ﬁeld, the molecular lines can be linearly polarized if the molecules are immersed in an anisotropic radiation ﬁeld and the rate of radiative transitions is at least comparable with the rate of collisional transitions. This eﬀect is called the Goldreich−Kylaﬁs (G−K) eﬀect (Goldreich & Kylaﬁs (1981); Kylaﬁs (1983)). The G−K

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