ESTIMATION OF MAGNETIC FIELD IN THE SOLAR CORONAL STREAMERS THROUGH LOW FREQUENCY RADIO OBSERVATIONS

Magnetic fields play an important role in the dynamics as well as the formation of the structures in the solar corona. The existing direct estimates using optical/infrared and radio emissions are limited to the inner corona, i.e., r < 1.2 R_☉, where R_☉ = radius of the Sun = 6.96 × 10⁵ km (Kuhn 1995; Lin et al. 2000; Gelfreikh 2004; White 2005). In the outer corona beyond r > 3 R_☉, Faraday rotation observations are used to derive the magnetic field (Pätzold et al. 1987; Spangler 2005). But due to lack of observational techniques, measurements in the range 1.2 R_☉ < r < 3 R_☉ (middle corona) are not available until now. As the photosphere, chromosphere, and corona are coupled by the solar magnetic field, the magnetic field strength at these distances is generally obtained by mathematical extrapolation of the observed line-of-sight component of the photospheric magnetic field assuming a potential or force-free model (Schatten et al. 1969; Schrijver & Derosa 2003). It was shown recently by Sastry (2009) that it is possible to extend the radio methods of coronal magnetic field measurements in the inner corona at microwave frequencies (∼ GHz) through bremsstrahlung emission (Gelfreikh 2004) to larger distances in the "undisturbed" middle solar corona. The possibility of using this method is explored in the present work at r ≈ 1.7 and 1.5 R_☉, the plasma levels of enhanced emission in the coronal streamers at 77 and 109 MHz (Newkirk 1961).

The data reported were obtained on 2007 January 30 and March 4 at two frequencies, 77 and 109 MHz, with the east–west one-dimensional radio polarimeter and at 77 MHz with the radioheliograph (Gauribidanur Radioheliograph, GRH) at the Gauribidanur radio observatory² (Ramesh et al. 1998, 2008). The radioheliograph produces two-dimensional images of the solar corona with a resolution of ≈10' × 15' (R.A.×decl.) at 77 MHz, while the polarimeter responds to the integrated and polarized flux densities of the whole Sun. Note that the antennas in the polarimeter array are non-steerable and point toward the local zenith (decl. = 141 N). The width at half-maximum of the response function ("beam") is very broad compared to the Sun in both right ascension and declination ≈ 39 × 90° and ≈ 23 × 90° (R.A. × decl.) at 77 and 109 MHz, respectively. Therefore, a plot of the output data from the polarimeter during the period when Sun transits the local meridian at Gauribidanur is essentially the east–west "beam" of the array. The amplitude of each data point on the plot is proportional to the strength of the emission from the whole Sun multiplied by the antenna gain in that direction. Figure 1 shows the responses of the polarimeter to the integrated (Stokes I) and the circularly polarized (Stokes V) flux densities on the above two days. The corresponding radioheliograms obtained with the GRH at 77 MHz are shown in Figure 2. The details of the heliograph and polarimeter observations are listed in Table 1. The Sun was "undisturbed" and no transient or long-lasting non-thermal activity was present.³ One can note that the integrated flux densities observed with the GRH at 77 MHz on 2007 January 30 and March 4 are close to the Stokes I integrated flux densities observed with the polarimeter at the same frequency during the same period. The estimated peak brightness temperature (T_b) values from the GRH data are less than the electron temperature (T_e ∼ 10⁶ K) of the solar corona. This indicates that the optical depth (τ) of the medium is not large as otherwise T_b ∼ T_e. The spectral index (β) for the Stokes I and V emission listed in Table 1 was calculated assuming that the observed flux density (S) varies as ν^β, where ν is the observing frequency. An inspection of the Hα images obtained at Observatoire de Paris⁴ revealed "long" filaments close to the equator on 2007 January 30 and March 4. The associated active regions are AR 10940 and AR 10945, respectively⁴. The GRH images at 77 MHz presented in Figure 2 show enhanced emission on the disk as well as off the limb close to the location of Hα filaments and in apparent association with them. We also inferred the association between the enhanced radio emission off the limb in the above two figures and the filaments on the solar disk from the model calculations on the coronal streamers and their relationship to the solar active regions reported by Liewer et al. (2001). According to their results, the streamers associated with the above two Hα filaments are expected to be observed in the same region as the off-limb radio emission in the northeast and northwest quadrants in the left and right panel of Figure 2, respectively.

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The absence of any long and short term non-thermal activity on 2007 January 30 and March 4 implies that the enhanced emission corresponding to the isolated sources on the disk as well as near the limb of the Sun in the GRH images (Figure 2) is thermal. This inference is further confirmed by the fact that the spectral indices of the observed integrated flux densities are consistent with the values expected for thermal emission within the error limits (Table 1). The enhanced low frequency radio emission from sources associated with quiescent Hα filaments are usually manifestations of coronal streamers as suggested by Dulk & Sheridan (1974) and Kundu et al. (1987). The unpolarized thermal radio emission from both the "undisturbed" Sun and streamers will become circularly polarized in the presence of a magnetic field. Due to the latter, the thermal radiation propagates in two orthogonal circular modes, i.e., the ordinary ("o") and the extraordinary ("e") mode. A significant difference between the optical depths and hence the T_b of the two modes will result in a finite value of the degree of circular polarization (dcp), if the corona is not optically thick. The strength of the magnetic field can then be estimated by measuring the dcp. The measured dcp at both the frequencies in the present case can either be due to magnetic field permeating the whole corona or due to the field associated with the streamers. As shown below, the field strength required at the 77 MHz plasma level should be ⩾ 4 G to produce a dcp of ≈15%. It is improbable that a field of such magnitude permeates the whole corona. The average magnetic field strength estimated by either the extrapolation of the measured photospheric field or the interplanetary field turns out to be generally <1 G (Pätzold et al. 1987; Schrijver & Derosa 2003; Spangler 2005). Also, so far it is only on rare occasions, we detected such large values of dcp on "undisturbed" days whereas such fields if they do exist in the corona should result in the occurrence of similar dcp values more often. Therefore, it is possible that the observed dcp in Figure 1 is due to the magnetic field associated with streamers (Wang et al. 1993; Chiuderi Drago 1994; Fineschi et al. 1999).

The classical form of a coronal streamer is that of a "helmet" structure consisting of a bright dome-shaped region of closed field lines in the range r ≲ 1.5 R_☉ surmounted by an arcade of open field lines extending more-or-less radially far outward into the solar atmosphere. The streamers overlie diffuse bipolar magnetic regions on the Sun and have usually a density enhancement of 3–10 over the "background" corona (Pneuman & Kopp 1971; Athay 1976, chapter 2, p. 31; Priest 1982, chapter 1, p. 29). According to Vrsnak et al. (2002), the magnetic field strength in the corona above active regions estimated from radio burst observations decreases from 1to8 G at r = 1.6 R_☉ to 0.3–0.9 G at r = 2.5 R_☉. This result is consistent with other estimates at these radial distances (Dulk & McLean 1978; Krüger & Hildebrandt 1993). From the measured values of dcp in the present case, we estimated the average field strength using the method outlined in Sastry (2009) and the values are ≈ 5 ± 1 G at 77 MHz and ≈ 6 ± 2 G at 109 MHz, on both 2007 January 30 and March 4. The corresponding radial distances are ≈1.7 and 1.5 R_☉, respectively (refer Table 1).

The procedure used is to determine the radio ray paths for the o and e modes separately in the anisotropic corona for a given magnetic field strength (B). The model used for the latter is B(r) = B_o(r − 1)^−1.5. The constant B_o is adjusted to give the assumed value of the magnetic field strength at the plasma level of the observing frequency (Sastry 2009). The coronal electron density used for the calculations is that of Newkirk (1961) with the following parameters: (1) coronal electron temperature, T_e = 10⁶ K; (2) density enhancement factor (D) in the streamer compared to the "background" corona is ≈ 5; (3) the width (σ) of the streamer at 77 MHz is ≈ 0.6 R_☉ and that at 109 MHz is ≈ 0.4 R_☉ (Schmahl et al. 1994); and (4) the streamer is in the equatorial plane with an azimuth (ϕ) ≈ 75°–85°. The latter was estimated from the GRH images at 77 MHz (Figure 2). The coordinates of the radio enhancements that relate to the Hα filaments mentioned in Section 2 are (≈ 50°E 5°N) and (≈ 60°W 10°N) on 2007 January 30 and March 4, respectively. The corresponding azimuth value is ≈ 80° on both the days. The absorption coefficient (κ) integrated along the path of each mode and their corresponding brightness temperatures T^o_b and T^e_b are calculated as described in Sastry (2009). The dcp is then estimated using the expression $\frac{T_{b}^{e}-T_{b}^{o}}{T_{b}^{e}+T_{b}^{o}}$. This procedure is repeated for different values of B until the computed dcp matches with the measured values. We would like to note here that the radial distances at 77 and 109 MHz obtained using the density model of Newkirk (1961) agree closely (≈±0.1 R_☉) with the corresponding values given by the other frequently used coronal electron density models (Saito et al. 1977; Baumbach 1937; Allen 1947).

It should be pointed out that the observed dcp in the present case could be due to the presence of weak noise storm continuum sources on the Sun as the dcp of a noise storm continuum source located close to the limb would be small (Kai 1962). But the absence of short duration bursts which usually accompany the noise storm continuum and more importantly the fact that the spectral index of the observed polarized flux (Stokes V emission) is close to that of thermal emission argue against radio emission of noise storm continuum. Note that according to Benz & Zolliker (1985), the polarized flux from the noise storm continuum is expected to decrease with increase in the observing frequency. The recent observations of Ramesh et al. (2010) also indicate the same. As mentioned earlier, no noise storms were reported from other solar observatories also on both 2007 January 30 and March 4 as well as a few days before and after.

The possibility of determining the magnetic field in the solar coronal streamer using low frequency radio observations is explored in the present work. The advantage seems to be in the straightforward manner in which radio measurements can be obtained. But circularly polarized observations of the type described here are not so frequent at present. The radio heliograph and the polarimeter at the Gauribidanur observatory are in near continuous operation since 2004. However, only on rare occasions when the Sun is "undisturbed," the detected circularly polarized signal can be attributed to the "undisturbed" Sun and/or streamers (Ramesh & Sastry 2005; Ramesh et al. 2008). One of the reasons for this could be the limited angular resolution and sensitivity of the Gauribidanur radioheliograph and the polarimeter. The other is the frequent presence of non-thermal radio bursts of various types. We expect that future observations, particularly at low radio frequencies, with existing large arrays like the Very Large Array, the Giant Metrewave Radio Telescope, and the proposed as well as upcoming arrays like the Murchison Widefield Array, the Low Frequency Array, and the Frequency-Agile Solar Radio Telescope might provide similar observations in a more routine and unambiguous manner as they have higher angular resolution and better sensitivity. To note, radio emission at different frequencies originate from different radial distances in the solar corona. So, simultaneous multi-frequency observations is desirable as it will be useful in determining the radial variation of the magnetic field strength, which in turn could be useful in understanding activity over specific locations in the solar atmosphere. For example, in one particular case study, Borovik et al. (2002) reported a slow increase in the longitudinal component of the coronal magnetic field during the initial evolution of a coronal mass ejection event from observations in the 1–17 GHz range. The authors explained the same in the framework of bremsstrahlung emission in the presence of weak magnetic field (Gelfreikh 2004).

We thank the staff of Gauribidanur radio observatory for their help in data collection and maintenance of the antenna and receiver systems there. We thank the referee for his/her critical comments which helped us to bring out the results more clearly.