4 Results

The clear result of our initial SO( $J_{\rm N}=1_2-1_1$) survey is that emission from this transition is detected only towards regions of known high-density (within our sensitivity limit) - not unexpected in view of the transition's high critical density of >10^6-7 cm^-3 (Green 1994). It is also observed in two molecular outflows, but this may be due to chemical enhancement in the molecular column density. The transition was not detected in Taurus-like dark cloud cores which, however, appeared strongly in our complementary CCS observations. Conversely, the CCS emission is weak or absent in warm star forming regions. The line parameters of the sources observed are presented in Table 2.

   

Table 2: Parameters of sources selected for Zeeman integration

Source	RA	Dec	$t_{\rm {int}}$	$\Delta V_{\rm {ch}}$	$T_{{\rm l}}\,({I})$	$V_{\rm {LSR}}$	$\Delta V_{\rm {line}}$	T(V)/T(I)
	(1950)	(1950)	[h]	[km$\,$s-1]	[K]	[km$\,$s-1]	[km$\,$s-1]	(10-3)
SO Sources
W3-IRS4(S)	02:21:44.0	61:52:32	16.2	0.28	0.16	-42.6	3.4	32.3
Orion-KL	05:32:46.7	-05:24:20	4.3	1.12	0.93	9.0	23.5	8.7
NGC2071A	05:44:20.7	00:22:20	4.4	0.14	0.54	9.5	0.8	23.3
VLA1623	16:23:20.2	-24:16:04	2.8	0.14	1.62	3.0	0.8	7.6
$\rho$ Oph-B	16:24:08.9	-24:22:41	4.5	0.14	0.88	3.7	0.9	16.3
SgrB2(N)	17:44:10.1	-28:21:17	5.4	0.84	2.20	65.1	14.1	4.7
G5.89	17:57:26.8	-24:03:56	7.5	0.56	-0.73	8.3	6.0	9.6
G10.62	18:07:30.7	-19:56:29	8.7	0.56	-0.42	0.2	3.0	13.6
					0.04	-6.6	4.9
S140SO	22:17:42.0	63:04:00	12.3	0.28	0.33	-7.0	2.1	13.6
NGC7538-IRS11	23:11:40.9	61:10:48	15.0	0.28	0.21	-56.2	3.6	21.8
OH Sources
G10.62	18:07:30.7	-19:56:29	12.1	1.09	-0.28	-2.0	6.7	9.1
DR21(OH)	20:37:13.9	42:12:11	19.7	1.09	-0.31	-5.1	4.9	9.4
					-0.09	-10.3	8.3
CCS Sources
L1498	04:07:55.8	25:01:33	25	0.02	1.84	7.82	0.17	5.9
TMC-1C	04:38:31.5	25:55:00	28	0.02	1.83	5.37	0.20	5.8
TMC-1SE	04:38:50.1	25:32:30	23	0.02	2.19	5.66	0.14	4.7

Note: The source names are contained in Col. 1 and the positions (in equatorial coordinates), in Cols. 2 and 3, with the integration time in Col. 4. Column 5 gives the velocity width of the channels. Columns 6 through 8 give the line parameters, based on Gaussian fits to the spectrum. The line intensities, $T_{\rm l}$, are presented as main beam brightness temperatures. The 1$\sigma$ rms noise of the Stokes V-spectrum, normalized to the peak total power I-profile, are given in Col. 9

   
4.1 Description of the Zeeman candidates

In this section we briefly describe the sources selected for the Zeeman study, identifying and detailing the specific sub-regions believed coupled to the observations. We present, in Tables 1 and b, Cols. 2-6, a compilation of their physical characteristics (temperature, size, column density, number density, mass) gathered from the literature.

   

Table 3a: Source physical parameters (OH and SO observations)

Source		$T_{\rm K}$	<size>	n(H2)	N(H2)	Mass	Ref.	$B_{\parallel}^{\rm rms}$	$B_{\rm crit}$	$B_{\rm alf}$	$B_{\rm vir}$
		[K]	[pc]	[cm-3]	[cm-2]	[ $M_{\odot}$]		[mG]	[mG]	[mG]	[mG]
SO Sources
W3-IRS4(S)	(HCN core)	55	0.2	8(5)	2-4(23)	$\sim$200	19-22	0.8	2-3	1.5	1.4
Orion-KL	(doughnut)	200	(0.02)	>1(7)	few(23)	5	1-4	1.5	0.8	$\cdots$	$\cdots$
$\rho$ Oph-B	(halo)	15	0.075	>1(6)	2(23)	6	11,12	0.2	1.6	>0.5	0.3
	(compact core)	$\cdots$	0.03	4(6)	4(23)	4	$\cdots$	$\cdots$	3.2	0.9	0.7
SgrB2(N)	(dense ridge)	100	3.5	1(5)	1(24)	$\cdots$	8,10	0.6	8	<2.3	1.4
	(compact core)	150	0.16	2(7)	1(25)	2(3)	$\cdots$	$\cdots$	80	<32	31
G5.89		90	0.3	$\sim$2(6)	4-6(23)	4-800	16-18	0.6	3-5	4.3	3.0
G10.62		100	0.1	2-4(6)	2(24)	1100	13-15	0.5	16	2.1-3.1	2.2
S140SO	(SMM2)	35	0.04	>4(6)	>5(23)	6.5	23-25	0.4	>4	>2.1	2.8
NGC7538	(20'' E of IRS11)	50*	0.20	6(5)	4(23)	250	5-7	0.7	3.2	1.4	1.6
NGC2071A	(outflow)	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	0.25	$\cdots$	$\cdots$	$\cdots$
VLA1623	(outflow)	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	$\cdots$	0.1	$\cdots$	$\cdots$	$\cdots$
OH Sources
G10.62		100	0.1	2-4(6)	2(24)	1100	13-15	1.2	16	2.1-3.1	2.2
DR21(OH)	(MM1)	>80	<0.1	2-4(7)	4(24)	2-300	26-29	2.0	32	11-16	>6

(1) Plambeck et al. (82), (2) Stutzki et al. (88), (3) Wright et al. (96), (4) Blake et al. (87), (5) Minchin et al. (94), (6) Sandell (priv. comm.), (7) Zylka (priv. comm.), (8) Hüttemeister et al. (93,95) $\&$ ref. therein (10) Vogel et al. (87), (11) Martin-Pintado et al. (83), (12) Wadiak et al. (85) (13) Keto et al. (87) (14) Hauschildt et al. (93), (15) Ho et al. (94), (16) Gomez et al. (91), (17) Cesaroni et al. (91), (18) Cesaroni et al. (92), (19) Helmich et al. (94), (20) Wright et al. (84), (21) Tieftrunk et al. (95), (22) Oldham et al. (94), (23) Ungerechts et al. (86), (24) Zhou et al. (94), (25) Minchin et al. (95), (26) Mangum et al. (91), (27) Mangum et al. (92), (28) Padin et al. (89), (29) Jones et al. (94).

   

Table 3b: Source physical parameters (CCS observations)

Source		TK	<size>	n(H2)	Mass	$M_{\rm J}$	$\sigma_{\rm (H_2)}$	$\sigma_{\rm nt}$	$B_{\parallel}^{\rm rms}$	$B_{\rm alf}$	( $\frac{2{\cal T}}{{\cal W}}$)	( $\frac{2 {\cal T}}{{\cal M}_{\rm alf}}$)	( $\frac{2\cal T}{{\cal M}_{\rm obs}}$)
		[K]	[pc]	[cm-3]	[ $M_{\odot}$]	[ $M_{\odot}$]	[kms-1]	[kms-1]	[$\mu$G]	[$\mu$G]
CCS
L1498		9.7	0.07	8(4)	$\sim$0.6	0.8	0.20	0.040	70	13	1.7	92	>1.1
TMC-1C		9.0	0.11	2-6(4)	0.6-1.9	1.4-0.8	0.19	0.055	78	9-16	0.8-2.6	42	0.2-0.6
TMC-1SE		8.9	$\cdots$	>4(4)	$\cdots$	<1.0	0.19	0.043	51	>10	$\cdots$	70	>0.9

Observables are taken from, (1) Fiebig (90), (2) Cox et al. (89), (3) Cox (priv. comm.).

Note: For the calculation of $M_{\rm obs}$ we have assumed $B^2 = 3B^2_\parallel$, a statistical approach that may not apply in this particular case.

SO $\&$ OH associated with dense star forming cores

$\rho$Oph-B -- The SO $J_{\rm N}=1_2-1_1$ emission follows closely the distribution of H₂CO ($J_{\rm K}$ 2 ₁₁ - 2₁₂) 2cm emission (Martin-Pintado et al. 1983) and peaks towards the compact H₂CO cores detected with the VLA (Wadiak et al. 1985). The VLA cores contain $\sim$50$\%$ of the single-dish flux. The H₂CO ridge is 3.2 $\times$0.7 $\hbox{$^\prime$ }$ in size and the SO spectra throughout this region share a singular velocity (V = 3.6 km$\,$s^-1) and linewidth ( $\Delta V = 1.1$ km$\,$s^-1) identical to that of NH₃ line emission observed (Martin-Pintado et al. 1983). Densities in excess of 10⁶ cm^-3 are implied by the detection of the 2cm H₂CO line in emission.
SgrB2(N) -- The complex structure of the Sgr-B2 star forming cloud has been characterized as having three distinct components (see e.g. Hüttemeister et al. 1995, and Ref. therein): embedded in a dense cloud of size $1 \times 2\hbox{$^\prime$ }$ ( $n \sim 10^5$ cm^-3, $N \sim 10^{24}$ cm^-2, $T \sim 100$ K) there are three prominent compact ultra-dense clumps, referred to as N(orth), M(id) and S(outh), with volume densities $n \ge 10^7$ cm^-3 and column densities as high as 10²⁵ cm^-2. The bulk of the mass, however, is contained in an extended envelope of somewhat lower density (10³ cm^-2). Kinematically, it is difficult to discriminate between the dense ridge and the embedded cores in Sgr B2(N), both sharing bulk velocities of $V_{\rm lsr} \sim 65$ km$\,$s^-1 and linewidths of $\sim$15 km$\,$s^-1. The higher velocity component at 81 km$\,$s^-1 seen in our SO $J_{\rm N}=1_2-1_1$ spectrum likely arises from the envelope (Hüttemeister et al. 1995). The SO emission does not show much of variation between the N and S position, therefore we tentatively associate the SO gas with the dense ridge. Any contribution from the ultra-dense cores is difficult to judge with our resolution.
G5.89 (W28 A2) -- A bright ultra-compact H$\,$ II region, whose exciting source (equivalent to a O5 ZAMS object) must be very young and still deeply embedded in its high density parental cloud ( $n_{\rm H_2} = 10^7 {-} 10^8$ cm^-3 along its inner edge; Lightfoot et al. 1984). Associated NH₃ emission is confined to within a 5''radius region centered on the main continuum component (Gómez et al. 1991) and is seen in absorption at velocities of V = 7 km$\,$s^-1, similar to that of the observed SO $J_{\rm N}=1_2-1_1$ line. Virial densities compare nicely with the bulk densities derived from C³⁴S excitation studies (Cesaroni et al. 1991, 1992).
G10.62 -- Our position is centered on the brightest continuum source in the G10.62 star forming region. NH₃ absorption, as well as the kinematics of associated gas, imply that the H$\,$ II region is surrounded by a rotating and infalling gaseous core/envelope structure (Ho & Haschick 1986; Keto et al. 1987). The SO has the same redshifted velocity as NH₃ and H₂CO absorption lines (V = 0 km$\,$s^-1), identifying this component as the dense infalling material of the surrounding ``core'' foreground to the H$\,$ II region. The weak SO emission corresponds kinematically to the dense core previously observed with the optically thin and high-gas density sampling C<sup>18</sup>O (Ho et al. 1994) and C<sup>34</sup>S lines (Hauschildt et al. 1993).
W3-IRS4 -- Our position is located $\sim$20'' south of IRS4 (the second brightest infrared source in the W3 star forming complex; Wynn-Williams et al. 1972) and corresponds to the dense core identified by other molecular tracers (HCN, Wright et al. 1984; C<sup>18</sup>O, Oldham et al. 1994; C<sup>34</sup>S, Tieftrunk et al. 1995) as well as with one of two maxima in 800 $\mu$m continuum emission (Richardson et al. 1989). The velocity and linewidth of the SO emission are in agreement with those of C<sup>18</sup>O measured by Tieftrunk et al. (1995). The nonisotopic CO lines, in contrast, are nonsymmetric, double peaked, and display larger linewidths ranging between $\Delta V = 9$ and 18 km$\,$s<sup>-1</sup> (Hasegawa et al. 1994; Dickel et al. 1980).
Orion-KL -- Following up on the detection of SO emission by Gottlieb et al. (1978), the interferometric studies by Plambeck et al. (1982) and Wright et al. (1996) indicated that SO $J_{\rm K} = 2_2 - 1_1$ emission is localized to within a $11''\,\times\,19''$ region centered on the IRC2 source, known now as the low-velocity part of the ``plateau'' feature. Our measurements are consistent with these findings; the SO $J_{\rm N}=1_2-1_1$ line parameters are similar to those determined by Gottlieb et al., and substantial emission is recorded only within a single beam centered near the IRC2 source. Plambeck et al. (1982) hypothesize that the SO emission arises from an expanding torus which surrounds and perhaps collimates a bipolar outflow arising from IRC2.
S140SO -- S140 is a crescent shaped H$\,$ II region bordering the edge of the dark cloud L1204. The SO $J_{\rm N}=1_2-1_1$ emission is centered $\sim$15'' north-east of S140-IRS1, the location of strongest C⁽³⁴⁾S (Zhou et al. 1994) and NH₃ (Ungerechts et al. 1986) emission. The SO peak does, however, coincide with SMM2, a dense compact core identified by its dust continuum emission (Minchin et al. 1995), but not observed in previous molecular line studies.
NGC7538 IRS11 -- The only position in the NGC7538 star forming cloud where appreciable SO $J_{\rm N}=1_2-1_1$ emission was detected is offset 20'' east of the embedded IRS11 source. Towards this position a dense dust core has been detected (see reference in Minchin et al. 1994). The physical parameters for this compact core, given in Table 1, are deduced from unpublished dust continuum observations (Sandell & Zylka, priv. comm.), assuming T = 50 K.
DR21(OH) -- This position, also referred to as W75S (Wilson & Mauersberger 1990) and DR21(OH)M, is located $\sim$3' north of the DR21 H$\,$ II region toward the site of a prominent maser and far IR maximum. DR21(OH) is toward the strongest of four CS peaks, separated by 30-50'', in the DR21(OH) region (Chandler et al. 1993). Judging from the velocity of the OH emission, it arises from the dust core MM1 (Padin et al. 1989).


An exploratory SO observation was also made toward W3(OH) where, in an earlier OH Zeeman absorption line study, Güsten et al. (1994) found a 3 mG line-of-sight field within its dense gas at V = -45 km$\,$s^-1. We indeed detected SO toward W3(OH), but only in emission, and at a velocity (V = -47 km$\,$s^-1) similar to that of a second OH absorption component observed (in the earlier study) which gave no indication of a magnetic field above a limit of $\sim$0.4mG. We therefore did not integrate further in the attempt to make an SO Zeeman measurement toward W3(OH). The -47 km$\,$s^-1 component of gas is apparently distributed in a relatively extended envelope ($\sim$2') around the H$\,$ II region (Wilson et al. 1991; Dickel & Goss 1987), whereas the -45 km$\,$s^-1 component containing the strong Bfield is of somewhat higher density (10^6.8 cm^-3) and more closely borders the H$\,$ II region along its western edge (Wink et al. 1994; Reid et al. 1987; Guilloteau et al. 1984). So, unfortunately, no independent confirmation of the earlier OH results has been possible.


SO associated with molecular outflows.

NGC2071A -- We have centered on an SO emission peak, mapped by Schmid-Burgk & Muders (1994), located $\sim$3' northwest of the NGC2071 bipolar outflow (Bally 1982; Snell et al. 1984; Scoville et al. 1986; Moriarty-Schieven et al. 1989). Both the $J_{\rm N}=1_0-0_1$emission lines observed by Schmid-Burgk & Muders and the $J_{\rm N}=1_2-1_1$ emission lines observed in this study are relatively narrow ( $\Delta V = 0.9$ km$\,$s^-1), in contrast to high excitation SO $J_{\rm N} = 6_5 - 5_4$ emission observed by Chernin & Masson (1993) which have complex line structure and large velocity width and are correlated to the ends of the high velocity CO outflows (Chernin & Masson 1992). The CS emission is distributed symmetrically, within a 0 0=.00 0=' 005 region, on the cluster of infrared sources (IRS 1, 2, and 3; Persson et al. 1981) central to the outflow activity (Zhou et al. 1991). Our position (NGC2071A) is outside of the region mapped previously by molecular line studies. We detect no SO line emission towards a second position, NGC2071, 22'' south of IRS 1.
VLA1623 -- A compact VLA continuum source and class 0 protostellar candidate centered on well-collimated molecular outflow, the only such flow found in the $\rho$-Oph starforming complex to date (André et al. 1993; André et al. 1990). Our position is toward the tip of the 2'-scale redshifted molecular lobe. Indeed, the SO $J_{\rm N}=1_2-1_1$ spectrum appears to be slightly asymmetric, perhaps possessing a modest redward tail. The FWHM of the SO line is 0.8 km$\,$s^-1. By comparison, the ¹²CO spectra (André et al. 1990) associated with the molecular flow have velocity widths on the order of $\Delta V = {\sim}$8 km$\,$s^-1 and are likely blends of several velocity components. Also coinciding with our position is the bright infrared source GSS30 (Graasdalen et al. 1973).


CCS towards dark cloud cores

From our survey of dark cloud cores in the Orion and Taurus region we selected three dark cores for deep Zeeman integrations: L1498, TMC-1C, and TMC-1SE. To identify the best suited positions (strongest lines with cleanest possible Gaussian profiles) the cores were first mapped in the CCS( $J_{\rm N} = 2_1 - 1_0$) transition at 22.34 GHz (42'' angular resolution). Their kinetic temperatures were determined using observations of their lower NH₃ rotational transitions (Fiebig 1990) and their H₂ densities were estimated from a multi-transition study of C₃H₂ (Cox et al. 1989; Cox, priv. comm.) (Table 2, Col. 4).

4.2 B field determinations

We detect no line-of-sight magnetic field ( $B_{\scriptsize {\parallel}}$) above the 3$\sigma$uncertainty level toward any of the sources observed, either by their SO $J_{\rm N}=1_2-1_1$ OH $^2{\rm\Pi}_{\rm 3/2}\;\; J=7/2$ or CCS line emission/absorption. Figures 1a-c display the Stokes-V and Stokes-I spectra for the SO line. With exception only to SgrB2(N), no large-scale deviations in the V-spectra are seen within the velocity limits of their respective lines. The SgrB2(N) displays a signature in its V-spectrum consistent with a field at the 1$\sigma$ level ( $B_{\parallel} = 0.57$ mG). The broadness and complex shape of the line, however, makes its interpretation difficult at this level.

In Table 2, Col. 9, we present the 1$\sigma$ limits on V/I. In Table 1 (Col. 8) and 2 (Col. 9), the corresponding 1$\sigma$ limit on the magnetic field strength $B_{\parallel}$ for each region is given.

Figure 1: The SO $J_{\rm N}=1_2-1_1$ Stokes-V difference spectra (thin solid line) and the Stokes-I total power spectra (thick line) toward the sources indicated in upper left corner of each panel. Note that there is no sign in any of the Stokes-V spectra of a Zeeman response above the level of the noise

Figure 2: The SO $J_{\rm N}=1_2-1_1$ Stokes-V difference spectra (thin solid line) and the Stokes-I total power spectra (thick line) toward the sources indicated in upper left corner of each panel. Note that, with exception of SgrB2(N) (which is marginal), there is no sign in any of the Stokes-V spectra of a Zeeman response above the level of the noise

Figure 3: The SO $J_{\rm N}=1_2-1_1$ Stokes-V difference spectra (thin solid line) and the Stokes-I total power spectra (thick line) toward the sources indicated in upper left corner of each panel. Note that there is no sign in any of the Stokes-V spectra of a Zeeman response above the level of the noise