The Astrophysical Journal, 642:523–532, 2006 May 1 # 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.
ELECTRON DENSITY MODELING OF A STREAMER USING LASCO DATA OF 2004 JANUARY AND FEBRUARY A. F. Thernisien Naval Research Laboratory, Code 7663, 4555 Overlook Avenue SW, Washington DC 20375; and Universities Space Research Association, 10211 Wincopin Circle, Suite 620, Columbia, MD 21044;
[email protected]
and R. A. Howard Naval Research Laboratory, Code 7660, 4555 Overlook Avenue SW, Washington, DC 20375;
[email protected] Received 2005 July 29; accepted 2005 December 30
ABSTRACT We present a three-dimensional reconstruction of the electron density of a streamer using a newly developed forward modeling technique. The streamer was observed by SOHO LASCO continuously at the end of 2004 January, but for this study we consider two dates, about 7 days apart. On the first day the streamer was seen ‘‘edge-on,’’ in which the coronal neutral line was perpendicular to the solar limb and the overlying streamer was quite narrow. The second occurred 7 days later, when the streamer had rotated over the solar pole, and the streamer was now seen ‘‘faceon.’’ At this time the neutral line was parallel to the polar limb. Using electron density inversion techniques, we have determined the density profiles characterizing the length and thickness of the streamer. Those density profiles were used to refine a three-dimensional model of the streamer belt, approximated by a Gaussian slab. We find good agreement of the radial profile with previous streamer models, but we find that the electron density can vary by 1 order of magnitude within the streamer structure. Subject headingg: Sun: corona 1. INTRODUCTION
STEREO. Newmark et al. (2004) have also used the model as a test case for an electron density three-dimensional reconstruction program ( Newmark et al. 2003) developed for the STEREO mission. The classical method for deriving the electron density of the white-light solar corona was developed by Minnaert (1930) and Van de Hulst (1950). It is based on the use of the polarized brightness ( pB), which represents the difference between the tangentially polarized brightness and the radially polarized brightness. The photospheric light is scattered by the free electrons present in the corona. The electric vector of the scattered radiation lies in a plane at right angles to the incoming beam. An observer can then separate the measured intensities into two components, the polarized and unpolarized components, or equivalently into the radially and tangentially polarized components. Observations of the solar corona such as those made by whitelight coronagraphs (e.g., LASCO) have four sources of radiation contributing to the brightness: photospheric scattering from electrons and from dust, light from stellar and galactic sources, and instrumental stray light. The K corona, for Kontinuierlich, is due to Thomson scattering of the photospheric light from free electrons. The F, or Fraunhofer, corona is due to various (unknown) scattering processes of photospheric light from dust grains in the interplanetary medium. An important property of the F corona at heights less than 4 R is that it is unpolarized, in contrast to the K corona. Galactic sources, and frequently the instrumental stray light, are also unpolarized. Therefore, calculating pB eliminates the unpolarized components and leaves only the K coronal component. For three decades, space-based coronagraphs have produced more and more data with ever better resolution. The LASCO experiment (Brueckner et al. 1995) on board the SOHO spacecraft, launched in 1995 December, has produced high-resolution
The visible light corona has been observed for many years from the ground during solar eclipses by K-coronameters ( Lyot 1930) and satellite-borne coronagraphs since 1971, and most recently by the Solar and Heliospheric Observatory Large Angle and Spectrometric Coronagraph Experiment (SOHO LASCO; Brueckner et al. 1995). A goal of such measurements is to determine the structural configuration of the corona. The magnetic field, in the low corona, controls the structural configuration and forces the charged particles to follow the field. With increasing height the magnetic energy no longer dominates, and the structures are stretched out by the outward flow of the gas. The problem of determining the structure is then one of locating structures in the corona and then obtaining the electron density distribution in the structures. The Solar Terrestrial Relations Observatory (STEREO) mission, due to launch in 2006, will have two spacecraft, one moving ahead of the Earth and one moving behind, each separating from Earth at the rate of about 22 yr1. It will provide two instantaneous views of the solar corona. With the addition of SOHO, we have three points of view of the scene. In order to anticipate that mission, methods of reconstruction using multiple viewpoints need to be developed. Two approaches are possible: a direct inversion technique, assuming no or little a priori assumptions of the structure, and a forward modeling technique, for which strong assumptions on the morphology and location of the structures have to be made. In this article a forward modeling method has been implemented to model the three-dimensional structure of a streamer. Assuming solid-body rotation, we see that the problem is tractable, even using LASCO as the single point of observation. Nevertheless, the method represents a case study for the future mission 523
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Fig. 1.—WSO source surface field map computed at 2.5 R for CR 2012 [from January 13 (360 ) to February 10 (0 )]. The studied streamer corresponds to the part of the neutral line in the southern hemisphere between longitudes 280 and 360 .
observations of the total brightness of the white-light corona out to 30 R . Que´merais & Lamy (2002) applied the pB method to process the C2 polarized data. Beyond 5 R the polarization of the F corona cannot be ignored ( Koutchmy & Lamy 1985; Mann 1992). For the C3 coronagraph, the pB-based inversion method becomes then more problematic and is still to be improved. Hayes et al. (2001) extended the Van de Hulst (1950) technique to invert the equations for the total B. This was a very important new capability, since most of the LASCO images are not polarized, enabling inversions to be made for these total B images. However, the F corona has to be extracted from the total brightness images, which requires additional and careful processing. Also, both the Hayes et al. technique and the Van de Hulst technique assume that the corona has spherical symmetry, which in the case of localized structures is not valid. The streamer belt is observed as a bright and radial structure mostly located around the solar equator during solar minimum, but as solar activity increases, it becomes more and more warped. Wang et al. (1997) have demonstrated that the position of the streamer belt is predicted by the position of the neutral line. They derived the location of the belt using magnetogram observations of the solar surface, extrapolated to higher altitude in the corona by the potential-field source-surface model (PFSS; Wang & Sheeley 1992). Guhathakurta et al. (1996) and later Gibson et al. (2003) developed a three-dimensional model of the solar corona that reproduces most of the features seen on Carrington maps. Their models fit pB observations of Mauna Loa Mark III K-coronameter and LASCO C2, going from 1.15 to 2.5 R . Compared to their work, we focus only on a portion of the streamer belt in a small range of longitudes, with observations going from 2.5 to 30 R ( LASCO C2–C3 fields of view [FOVs]). 2. STATEMENT OF THE PROBLEM AND METHOD During the Carrington rotation 2012 (CR 2012), the coronal magnetic field is characterized by a simple tilted dipole. The source surface field map from the Wilcox Solar Observatory
(WSO) calculated at 2:5 R is presented in Figure 1. The neutral line in the southern hemisphere remains at a constant latitude (50N5 south) around longitude 270 . On 2004 January 23, the LASCO C2 and C3 images show a bright and narrow streamer at 51 of the west limb, corresponding to that portion of the neutral line seen edge-on ( Fig. 2, left). Due to the rotation of the Sun and assuming that the streamer evolves slowly enough in time, the streamer is seen face-on 7 days later (Fig. 2, right). The references of the LASCO images are given in Table 1. We have used these two views to derive the electron density and the morphology of that portion of the streamer belt. Until now, streamer models have been considered to have a uniform density along the orthoradial direction, following the streamer neutral sheet. However, this does not seem to be supported by our observations. Looking at the image data, we observe a fanlike structure with brightness enhancements and depletions. Moreover, using a running difference synoptic map (Fig. 3) tends to show that those brightness enhancements really
Fig. 2.—LASCO data of the streamer viewed edge-on (left) and face-on (right). The images are a composite of the C2 and C3 coronagraph FOV: the inner FOV is 2.6 R at the edge of the occulter, and the outer FOV is 30 R . In the face-on view, the region of interest where we focus our modeling is from position angle ( P:A:) ¼ 115 to 219 ( P:A: ¼ 0 is the vertical axis). The image names are given in Table 1. The intensity scaling is inverted to enhance visibility: the dark features have higher brightness and are denser in electrons.
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MODELING OF STREAMER USING LASCO DATA TABLE 1 Reference of the LASCO Images Used for the Study C2
C3
View
Filename
Date
Time
Filename
Date
Time
Face-on............................. Edge-on ............................
22164263.fts 22163759.fts
2004 Jan 30 2004 Jan 23
11:06:06 02:30:05
32118543.fts 32118187.fts
2004 Jan 30 2004 Jan 23
11:18:05 02:42:05
follow the neutral sheet during the solar rotation and are not isolated structures, such as jets or polar plumes, that might be present at higher or lower latitude, in front of or behind the streamer fan. We have then included in our model an orthoradial modulation of the electron density. To sum up the different steps of the modeling, we first preprocess the data images in order to extract the K coronal component. Then we locate the studied streamer in space, using synoptic maps and source surface field Carrington maps. We chose to fit the portion of the streamer with a simple slab model. We see that it is a good approximation of the streamer morphology regarding the synoptic map and the source surface field map. A simple model, such as the slab, also makes the electron density inversion easier: the radial and orthoradial model parameters can be fitted independently (orthogonal sets of parameters), which allows a freezing of the set of parameters associated with the radial density, while fitting the parameters associated with the orthoradial direction of the streamer. We also use a Powell multivariate minimization method to obtain a best fit of the parameters including both the edge-on and face-on views. Finally, we discuss and compare the results with several electron density models.
observations, which is 10% (Morrill et al. 2006; Thernisien et al. 2006). For the face-on view, the results are more problematic, since the brightness of the face-on streamer is more than 1 order of magnitude lower than for the edge-on view. At high altitudes we are at the limit of the signal-to-noise ratio (S/ N ). 4. SIGNAL-TO-NOISE RATIO Using a method described in Newberry (1991) we can estimate the S/N. This is what limits our reconstruction: we want to fit the signal, not the noise. For LASCO, the dominant noise is the Poisson photon noise. For the edge-on view, the S/ N remains at an acceptable level (from 50 to 10) up to 20 R . For the brightness enhancements of the face-on view, the S/ N is lower since the structures are less bright. It remains acceptable in the C2 FOV but decreases rapidly in C3. Its level becomes less than 3 above 10 R , where the signal falls into the noise. 5. SLAB MODEL DEFINITION Based on the work of Guhathakurta et al. (1996) and Vibert et al. (1997), the slab model we used is described by the following equation:
3. BACKGROUND REMOVAL The electron density inversion method we have developed here is not a pB-based method, but rather uses the total brightness data. It could actually use either, but LASCO has better temporal and spatial resolution in total B, than for the pB data. Due to telemetry restrictions the pB images were taken much less frequently and at half the resolution. The drawback is that the separation between the K and F coronae is not as straightforward. Nevertheless, three methods can be used. First, we can still use the nearest pB image assuming that the F corona evolves slowly compared to the K component. The problem is that it can only be applied for the C2 data, as the polarization of the F corona cannot be neglected above 5 R . The second method is to use a preevent image. That technique is very simple and is commonly used with very good results when estimating the mass ejected during a coronal mass ejection (CME; Crooker et al. 1997). Nevertheless, the ‘‘event’’ we study here is less transient than a CME, and the problem of selecting the proper preevent image arises. The third method is to use a minimum image, which is obtained by finding the minimum brightness for each pixel in the sequence of images around the observation date. The computation of that type of background has to take into account the Poisson noise due to the photon detection to avoid any underestimation. It contains also the fraction of the K corona that remains constant during the sequence. As a test, in our study, we use the three methods briefly described above to calculate the background. Then we perform the inversion of the electron density of the streamer seen edge-on using the three different backgrounds. The comparison of the three methods gives results within 5% of each other, which is satisfying since it is comparable to the absolute accuracy of the
Ne(r; ; ) ¼ Neradial (r)Neshape (r; )Neface ( );
ð1Þ
with r as the radial distance (or height), as the width angle in the plane of the slab, and as the angle between the line defined by a point in the corona and the Sun center to the central symmetry plane of the slab (see Fig. 4). The three functions, Neradial , Neshape , and Neface , are described hereafter. The function Neradial gives the radial dependence of the electron density. Its formulation is Ne(r) ¼
4 X
ai ri ;
ð2Þ
i¼1
where the ai or a coefficients have to be determined (see x 9). Hayes et al. (2001) found that four terms in the polynomial are sufficient to give a robust fit, while avoiding unwanted instabilities common to high-degree polynomial fits. The function Neshape represents the orthoradial section shape of the streamer seen edge-on. A Gaussian function has been used previously as in the Guhathakurta et al. (1996) and Vibert et al. (1997) models. In our case we made use of a slightly improved function that allows a better fit of the observed streamer profiles. It is given in the following equation: 8 2 > > > exp ; < 1 (r) Neshape (r; ) ¼ > > > exp ; : (r) 2
1 (r) ; 2:2 (r) 1 (r) : 2:2 (r)
