A&A 468, 1099-1102 (2007)
P. Subramanian1 - S. M. White2 - M. Karlický3 - R. Sych4 - H. S. Sawant5 - S. Ananthakrishnan6
1 - Indian Institute of Astrophysics, Bangalore 560034, India
2 - Dept. of Astronomy, University of Maryland, College Park, MD 20742, USA
3 - Astronomical Institute of the Academy of Sciences of the Czech Republic, 25165 Ondrejov, Czech Republic
4 - Institute of Solar Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences (ISTP), PO Box 4026, Irkutsk 33, 664033, Russia
5 - Instituto Nacional de Pesquisas Espaciais, 515, 12201-970, San Jose Dos Campos, SP, Brazil
6 - National Centre for Radio Astrophysics, Tata Institute of Fundamental Research, Pune University Campus, PO Bag 3, Ganeshkhind, Pune 411007, India
Received 22 February 2007 / Accepted 23 March 2007
Aims. To calculate the power budget for electron acceleration and the efficiency of the plasma emission mechanism in a post-flare decimetric continuum source.
Methods. We have imaged a high brightness temperature (109 K) post-flare source at 1060 MHz with the Giant Metrewave Radio Telescope (GMRT). We use information from these images and the dynamic spectrum from the Hiraiso spectrograph together with the theoretical method described in Subramanian & Becker (2006, Sol. Phys., 237, 185) to calculate the power input to the electron acceleration process. The method assumes that the electrons are accelerated via a second-order Fermi acceleration mechanism.
Results. We find that the power input to the nonthermal electrons is in the range -1026 erg/s. The efficiency of the overall plasma emission process starting from electron acceleration and culminating in the observed emission could range from to .
Key words: acceleration of particles - plasmas - Sun: radio radiation - Sun: corona - Sun: flares
The plasma emission process is thought to be operative in several types of meter wavelength emission such as type I, type II and type III bursts and noise emission (e.g., Melrose 1975; Gary & Hurford 2004). The overall emission process comprises several steps: firstly, it is usually assumed that a distribution of nonthermal electrons exists. If these nonthermal electrons have a distribution that is anisotropic in velocity and/or physical space, they are capable of generating a high intensity population of Langmuir waves. These Langmuir waves, in turn, coalesce with a suitable population of low frequency waves to produce the observed radio emission. The efficiency of the last step in this process, the conversion of Langmuir waves into observable radio emission, has been studied (e.g., Robinson et al. 1994; Mitchell et al. 2003). In the context of the plasma emission process, the electron acceleration process that produces the nonthermal electron population in the first place has also been studied recently (Subramanian & Becker 2004, 2006). Subramanian & Becker (2004, 2006) have calculated the power input to the electron acceleration process and the efficiency of the overall process (starting from electron acceleration and culminating in the observed radiation) for noise storm continua. In this paper we use much more reliable observational inputs to calculate such an efficiency for a post-flare decimetric continuum that we have observed. Accurate estimates of the efficiency of the overall plasma emission process are important, for instance, in deducing the shock strength from the intensity of observed type II emission. If the observed intensity can be related to the energy in the nonthermal electrons, one can place reliable constraints on the parameters of the shock that produced the nonthermal electrons. Apart from the conventional type II emission, it is conceivable that meter wavelength emission from standing shocks in the vicinity of a reconnection region (Aurass et al. 2002) can also arise from the plasma emission process.
|Figure 1: 1060 MHz lightcurves from the GMRT images for the M2.8 flare on Nov. 17 2001. Since the GMRT images are not amplitude calibrated, we have normalized the amplitudes to the peak of the 1000 MHz lightcurve from the Nobeyama Radio Polarimeter (NoRP). Top panel: total lightcurve for all the sources (Fig. 8, Subramanian et al. 2003). Bottom panel: lightcurve for the southern (S) source only. It is evident that the high brightness temperature S source is the dominant contributor to the part of the lightcurve after 5:30 UT.|
|Open with DEXTER|
|Figure 2: Contours for the 1060 MHz southern (S) source overlaid on an SXI soft X-ray image.|
|Open with DEXTER|
Figure 3 shows the dynamic spectrum corresponding to this event from the Hiraiso spectrograph. The 1060 MHz emission from the southern source imaged with the GMRT (Fig. 2) is part of the decimetric continuum shown in Fig. 3. The decimetric continuum emission spans a frequency range of approximately 700 to 1100 MHz.
|Figure 3: The dynamic spectrum for this event from the Hiraiso spectrograph. The decimetric continuum emission feature is labelled in the figure.|
|Open with DEXTER|
We have fitted a two-dimensional Gaussian to the southern source shown in
Fig. 2 and derived a full width at half-maximum (FWHM) size of
The beam size in the images is
and we use this to
deconvolved source size of
We use the 1 GHz Nobeyama
Radio Polarimeter (NoRP) lightcurve to determine that the peak post-flare flux
(which, as we know, arises almost exclusively from the S source) is around 430 SFU. The brightness temperature
(in K) of a source is given by
We assume the acceleration volume to be the same as that from which the observed
emission emanates. We envisage this region to be a rectangular column. The
dimensions of the face of this column would be equal to the observed source
which is equivalent to 15 500 km 69 600 km. Its depth can be calculated from the bandwidth of the emission as
evident from the Hiraiso dynamic spectrum (Fig. 3). The dynamic spectrum shows
that the post-flare emission feature starting at 05:30 UT that we have
imaged with the GMRT at 1060 MHz ranges from 700 to 1100 MHz. Using the
height-density model developed in Aschwanden & Benz (1995), we find that this
frequency extent corresponds to a depth of 6300 km for the emission
column. The volume of the acceleration region is thus taken to be
We now turn our attention to estimating the power in the observed decimetric
continuum. As noted earlier, the 1060 MHz post-flare radiation imaged with the
GMRT is part of the decimetric continuum feature starting at around 05:30 UT and
spanning a frequency range of 700 to 1100 MHz (Fig. 3). The peak
intensity of this post-flare emission is
SFU (Fig. 1). We
assume that this is the intensity of radiation emitted throughout the bandwidth
1100 - 700 = 400 MHz. The radiation flux is therefore
power in the observed radiation
can be related to
using (e.g., Elgaroy 1977; Subramanian & Becker 2006)
The numbers quoted here for and are the best estimates of these quantities for the plasma emission process that we are aware of. There have been attempts to calculate these quantities for noise storm continua (e.g., Subramanian & Becker 2006), but the observational inputs for these estimates were not as good as the ones used here. In particular, they used oft-quoted, but nonetheless rather rough estimates for the emission volume V and the output power . These quantities are determined much more reliably from observations for the calculations presented here.
Before concluding, it is appropriate to reiterate the following caveats: one of the key observational inputs to this calculation is the size of the post-flare decimetric continuum source as determined from the 1060 MHz GMRT images. The source is significantly more elongated in one dimension as compared to the other, suggesting that it might be oriented along a loop. The actual transverse dimension might then be somewhat smaller than the measured size of . Scattering due to coronal turbulence is known to be anisotropic (e.g., Chandran & Backer 2002). The contrast between the longitudinal and transverse dimensions might thus also be accentuated by preferential scattering along the longitudinal dimension. The other important observational input we use in our calculations is the column depth of the radiating source, which we calculate in an approximate manner from the extent of the decimetric continuum feature on the Hiraiso dynamic spectrograph (Fig. 3). In calculating the power in the observed radio emission , we also assume that the flux at 1 GHz is the same as that emitted throughout the 700-1100 MHz extent of the decimetric continuum emission. In the absence of calibrated multifrequency measurements, these are the most reasonable assumptions we can make. The formalism of Subramanian & Becker (2006) that we have used to calculate the power fed to the nonthermal electrons, , accounts only for anisotropy in velocity space of the nonthermal electrons (the gap distribution). In reality, the nonthermal electrons are likely to be anisotropic both in physical space (as in a losscone distribution) as well as in velocity space (e.g., Thejappa 1991; Zaitsev et al. 1997). Finally, we have asumed a coronal temperature of 1 MK in our calculations. There are indications that the temperature might be as high as 2 MK, especially above active regions (e.g., Hayashi et al. 2006). As shown in Subramanian & Becker (2006), doubling the value of the ambient coronal temperature will result in the efficiency estimate of the overall process being enhanced by a factor of 10.
We appreciate insightful comments from the anonymous referee that led to improvements in the content of this paper.