Magnetic field measurement in TMC-1C using 22.3 GHz CCS Zeeman splitting

Starless cores are an ideal place to study star formation in molecular clouds. Here, due to the absence of existing stars, no feedback effect influences the star formation process. Starless cores are broadly divided into two categories: evolved and young starless cores (Tafalla et al., 2004; Roy et al., 2011; Navarro-Almaida et al., 2021). Young starless cores are in the preliminary stages of their evolution and do not have a sufficiently dense central nucleus, whereas evolved cores are believed to be out of the equilibrium stage and in the process of forming stars.

It is well known that stars are formed from dense molecular clouds through gravitational collapse, although the details of the complex processes leading to star formation remain unclear. Although there are several theories on cloud fragmentation and star formation, the debate is still ongoing for whether magnetic field or turbulence is the most dominant factor in the star formation process (Mestel & Spitzer, 1956; Padoan & Nordlund, 1999; Uchida et al., 2001; Crutcher & Kemball, 2019; Das et al., 2021; Li, 2021; Mignon-Risse et al., 2021). To get a better understanding of the process of star formation, it is crucial to measure the magnetic field strength and its morphology in different density regimes in star-forming prestellar cores. In molecular clouds, Zeeman splitting and dust polarization are the two main methods for studying the magnetic field, with the former providing the line of sight magnetic field strength using spectral lines. One of the spectral lines suitable for magnetic field measurements via Zeeman splitting is the 2₁ - 1₀ 22.3 GHz transition of the CCS molecule that has a relatively high Zeeman splitting factor (0.767 Hz $\mu$G^-1). Furthermore, the critical density of CCS, $\sim$ 10⁴ cm^-3, is well matched to the typical densities of prestellar dense cores ($\sim$ 10⁴ $-$ 10⁵ cm^-3; Nakamura et al. 2019). This means that CCS should be observable in these prestellar cores if it is abundant and therefore it is an obvious choice to measure the magnetic field in such prestellar dense cores. Apart from Zeeman splitting measurements, CCS is used to probe density as well as the evolutionary age of dense cores.

The TMC-1C core has been studied extensively using various molecular transitions (Potapov et al. 2016; Spezzano et al. 2016). There are existing single dish Zeeman splitting measurements of similar cores TMC-1 and L1521E at 45.4 GHz (yielding magnetic field strength of $\sim$117 $\pm$ 21 $\mu$G in TMC-1 and $\sim$160 $\pm$ 42 $\mu$G in L1521E; Nakamura et al. 2019; Shinnaga et al. 1999). In this Letter, we present interferometric observations of CCS toward the TMC-1C core with the aim of measuring the Zeeman effect. The kinematical properties of TMC-1C, along with that of TMC-1 and L1544, based on the observations of CCS and NH₃, will be reported in a forthcoming paper (Koley, A., 2022, in prep.). We decided to target TMC-1C based on earlier interferometric observations (Roy et al., 2011), indicating that the CCS 22.3 GHz line intensity and narrow line profile are suitable for Zeeman splitting measurements.

This Letter is organized in the following way. Summary of the observations and data reduction are provided in section §2. The results on the Zeeman splitting measurement and magnetic field estimation are presented in §3, and discussed in §4. Finally, we present the conclusions in section §5.

The data for this work were taken using the Karl G. Jansky Very Large Array (VLA) as part of the proposal VLA/13A-112. The observations were carried out in 2013 February and March (over 13 observing sessions). More details of the observations are provided in Appendix A. All the initial flagging and calibration of the data were performed both in the scripted CASA (Common Astronomy Software Applications package) pipeline of the National Radio Astronomy Observatory (NRAO)¹¹1The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. and manually in AIPS (Astronomical Image Processing System; version 31DEC19). This was done as a consistency check of the analysis. There was no noticeable difference found between the output of the two methods. For imaging, we used the CASA task tclean with the multiscale deconvolver to pick up all the different structures in the core in total intensity. The scales that we used correspond to $3\aas@@fstack{\prime\prime}2$, $7\aas@@fstack{\prime\prime}2$, $16\aas@@fstack{\prime\prime}0$, $24\aas@@fstack{\prime\prime}0$, and $32\aas@@fstack{\prime\prime}0$. We note that multiscale CLEANing produces a single image that is restored with a synthesised beam that corresponds to the full angular resolution of the data. Due to the low signal to noise, we did not CLEAN the Stokes $V$ image cube.

Magnetic field values in the interstellar medium are relatively low ($\sim$ $\mu$G - mG). Thus, the expected Stokes $V$ signal for typical magnetic field values in a dense core is very weak, requiring deep observations with high spectral resolution to detect the Zeeman splitting signal. In astrophysical environments, spectral lines are significantly broadened by thermal and non-thermal motions. Therefore, the Zeeman splitting is much smaller than the line width, which in turn results in the measurement of only the line-of-sight component ($B_{\rm los}=B{\rm cos}\theta$) of the magnetic field (Crutcher et al., 1993; Sault et al., 1990). In this small splitting approximation, the fitting formulae for Stokes $V$ with Stokes $I$ is:

where $a$ is the gain difference between the left circular polarization (LL) and the right circular polarization (RR), $b=zB\mathrm{cos}\theta$, and $z$ is the Zeeman splitting factor (Greisen, 2017). We used XGAUS and ZEMAN in AIPS to fit the observed Stokes $I$ and $V$ profiles.

The integrated intensity map of the CCS 22.3 GHz emission in TMC-1C is shown in Figure 1. This figure reveals a very patchy appearance spread over the field of view. Figure 2 shows the Stokes $I$ and $V$ profiles toward the region highlighted by the black box in Figure 1. The Stokes $V$ profile (bottom panels of Figure 2) has an S-shape that usually suggests a Zeeman splitting detection. Typically, at least 6 channels across the spectral line is considered to be necessary in order to claim a Zeeman splitting detection. Since the profile in Figure 2 marginally spans 6 channels “null-to-null”, we claim that the observations reported in this Letter represent a detection. To eliminate the possibility of any systematic effects that may lead to a false S-curve, we checked each individual session’s data, and found that the Stokes $V$ profiles were indeed noise-like with no spurious features that may be attributed to instrumental effects. We obtained the magnetic field value in two different ways: (1) We fitted the observed Stokes $I$ profile with a single Gaussian component, then found the derivative of that component and fitted it to Stokes $V$ using equation (1) to derive $B_{\text{los}}=-1.80\pm 0.38$ mG, and (2) We calculated the one-sided derivative of the observed Stokes $I$ profile and fitted it to Stokes $V$, again using equation (1) to find $B_{\text{los}}=-2.44\pm 0.44$ mG. Within the errors, both methods agree on the magnetic field value, which we adopt to be 2 mG for further analysis in section §4.

We note that, for single dish observations, the beam squint can produce false Zeeman signal in presence of velocity gradient of the line emission. For interferometric observations, the prominent effect is leakage of Stokes I into Stokes V (Sault et al., 1990). In our modeling, leakage is included in Eqn. 1 to account for this. Further, our detected Stokes V signal indicates a magnetic field strength of $\sim 2$ mG. As the observed line profile is fairly narrow, we can clearly rule out, from our observations, any large velocity gradient that will be required, along with beam squint, to produce a Zeeman-like signal.

This work presents the interferometric study of CCS 22.3 GHz emission from the TMC-1C region. The emission is found to be widespread and patchy, while the line profile is very narrow and consistent with earlier shallow observations (Roy et al., 2011). For one region within the primary beam of the VLA, we also have a detection of the magnetic field, based on the Zeeman splitting of the transition. If the signal is real, the determined magnetic field is about 2 mG.

We have observed the 22.3 GHz CCS line toward the starless core TMC-1C with the VLA. We report in this Letter the detection of CCS Zeeman splitting, the first of its kind, with a radio interferometer. Our inferred line of sight magnetic field toward TMC-1C is $\sim$2 mG. Future observations with higher sensitivity and higher spectral resolution will be necessary to confirm these results. The Zeeman detection is toward a region to the southwest of the 1200 $\mu$m dust peak. If we interpret the dust peak to be the core of TMC-1C, then our observed magnetic field may be associated with the envelope region around the core. This is consistent with the general expectation of a supercritical core and a subcritical envelope in an accreting starless core like TMC-1C where the magnetic field in the envelope may be dynamically important, and the accreting core grows via the ambipolar diffusion process. The ambipolar diffusion timescale of core formation is found to be in agreement with the mass infall timescale for TMC-1C reported by previous authors. The detection reported here is a crucial step highlighting the possibility of future interferometric measurements of magnetic fields in dense molecular clouds using CCS transitions.

We thank the reviewer for many useful comments and valuable suggestions that have helped in improving this paper significantly. We are grateful to Thushara Pillai for useful discussions and valuable inputs. A.K. would like to thank DST-INSPIRE (IF160553) for a fellowship.

All data used in this study are available publicly from the VLA online archive. All reduced data will be shared at reasonable request to the corresponding author.