A Heliospheric Imager for Solar Orbiter

ABSTRACT

We have developed a prototype instrument for use on a near-Sun, three-axis stabilized, solar-oriented platform such as Solar Orbiter. The imager we envision analyzes remotely-sensed observations of coronal and heliospheric brightness in order to provide context for in situ plasma measurements. With this sensitive instrument, the analysis of these data will proceed much as it has from our recent use of Thomson-scattering observations from the Helios spacecraft, together with a recently developed time-dependent tomographic technique for analyzing these observations.

We show a full-scale optical prototype of our heliospheric imager for use on Solar Orbiter. We also show our most recent time-dependent tomographic result with Helios photometer data that depicts CMEs as well as corotating structures in the heliosphere and gives correlations of these data with in situ plasma density measurements at the spacecraft.

INTRODUCTION

There have been numerous attempts to reconstruct coronal structures in the corona and heliosphere in three dimensions. These techniques, reviewed elsewhere (Jackson et al., 1998; Jackson and Hick, 2000a), have been motivated by attempts to determine heliospheric structure morphology in order to determine their physics, their dynamics and most recently to forecast their arrival at Earth using remote sensing techniques.

Rotational tomography of stationary solar structures (streamers) using coronagraph observations have been attempted by Wilson (1977), Jackson (1977), or more recently by Zidowitz et al. (1995). More recently, Jackson and Hick (2000b) have presented results that allow heliospheric 3-dimensional reconstruction from outward plasma flow alone. These "time-dependent" tomographic analyses have been used to determine and successfully forecast the Earth arrival of both heliospheric corotating structures and mass ejections (Jackson and Hick, 2000c) from ground-based interplanetary scintillation (IPS) observations. The same techniques, used with a sufficiently sensitive photometer system on a three-axis stabilized spacecraft, can give context to in situ spacecraft measurements. We illustrate this using Thomson-scattering observations from the Helios spacecraft photometers.

The Helios spacecraft, launched in December 1974 (Helios 1) and January 1976 (Helios 2), each contained three zodiacal light photometers which were originally intended to measure the distribution of dust in the interplanetary medium between the Sun and the Earth (Leinert et al., 1975, 1981a). However, these photometers could also measure brightness variations produced by large-scale differences in the interplanetary electron content. The three photometers were fixed on the spacecraft and rotated at its 1 s spin period on an axis perpendicular to the plane of the ecliptic; they pointed 16°, 31° and 90° north or south of the ecliptic plane. Data from the 16° and 31° photometers were binned into 32 longitude sectors at constant ecliptic latitude around the sky. The photometer data were integrated over 8.6-min periods in turn from each of the three photometers through a set of broad-band ultraviolet, blue, and visual light filters and a set of one clear and three polarizing filters with a time interval of about 5 hours between the same filter combinations.

Richter et al. (1982) first described the use of these data to follow plasma ejections detected by electron Thomson scattering out to 90° solar elongation (angular distance from the Sun). Since then Jackson and Leinert (1985) and Jackson (1985) have used the Helios photometer data to study the characteristics of mass ejections and have traced their motion outward from the Sun into the anti-solar hemisphere. Jackson (1991) has also used the Helios photometer data to study the longer-lasting corotating regions in the solar wind. Because the two Helios spacecraft orbited the Sun with 6-month periods from 0.3 to 1 A.U., the photometers viewed heliospheric structures from a non-Earth perspective and can be used to construct tomographic models of the electron densities required to provide the observed brightness.

The next section describes the tomographic program developed to fit the Helios spacecraft photometer brightness. The third section gives examples of this analysis and compares these tomographic models to Helios in situ densities and to simultaneous coronagraph observations of a CME. The fourth section describes our concept of a Heliospheric Imager that unlike the Helios photometers is designed specifically to optimize information from the electron Thomson-scattering brightness around the spacecraft, and to use this information as input for tomographic reconstructions.

TOMOGRAPHIC ANALYSIS - THEORY AND MODELING

Line of sight Thomson scattering brightnesses for a column of electrons follow the relationship,

where, n_e(s) is the electron density at distance s along the line of sight and W(s) is a ‘weight factor’. For the large distances from the Sun viewed by the Helios photometers,

where s is the Thomson-scattering cross section, F_s the flux received from the solar disk at a distance r₀, r is the distance of the electron from the Sun, and c is the angle between the incident radiation from the Sun and the direction of scattering (Billings, 1966). To evaluate Eq. (1) both rand c are expressed as functions of the distance R of the observer from the Sun, the elongation e of the line of sight and the distance s along the line of sight. W scales as R^-2. For e < 90° W peaks at s = R cos e, the distance of closest approach to the Sun. Figure 1 shows the weight function for elongations 16°, 31° and 90° at a Sun-observer distance of 1 AU.

The Helios photometer brightness data are usually provided in S10 units, the brightness equivalent to one tenth-magnitude solar-type star in degree of sky. Expressing Eq. (1) and Eq. (2) in S10 units requires that the flux F received from the Sun [Eq. (2)] is also specified in S10 units:

where DG is the solid angle subtended by one square degree of sky, and W_s and m are the solid angle and apparent magnitude of the Sun. At 1 AU m = -26.73, and thus ½sF_s is the value specified in Eq. (3) with s in cm.

Figure 1: Thomson-scattering weight function from Eq. (2) as a function of distance s along the line of sight for elongations of 16° (top curve), 31° (center) and 90° (bottom). The observer is assumed to be at R=1 AU from the Sun.

The heliospheric model in our analysis and the iterative procedure that provides the three-dimensional results is explained more thoroughly in Jackson et al. (1998). The tomography program applies corrections to an initial (essentially arbitrary) model, modifying the model until there is a least-squares best fit of modeled and observed line-of-sight brightnesses. Our solar wind model assumes radial outward flow. Where different solar wind speeds interact within a given latitudinal band, solar wind momentum is assumed to be constant, and this is used to determine a new speed. Densities within the model are assumed to change in addition to the outward solar wind r^-2 expansion by assuming that mass is conserved as dictated by the velocity within the latitudinal band. In the current model described here, we assume that the heliosphere can change over time intervals as short as one day. This assumption essentially limits the tomographic reconstruction to rely on outward solar wind flow. For each observed line of sight at a given time, the location of the position along this line in the model is calculated. The model density values along each line of sight defined by the brightness observations are summed using the weighting described in Eqs. (1-3). These model values are then compared with the observed brightnesses, and this comparison is used to change the model.

In the tomographic analysis the model density and a three-dimensional solar wind model is changed in an iterative fashion to fit observations. At the end of each density change, the three-dimensional solar wind model is recalculated. In order that several different perspective lines of sight produce the model values, we require that several lines of sight contribute to each latitudinal and longitudinal resolution element in order that it is changed. In practice we typically require that 10 or more brightness lines of sight contribute to changes in the density model. The computer iterates to a solution, generally converging to an unchanging density within a few iterations. Tests of the program show that the model solutions are not sensitive to the starting input models, and after a few iterations any signature of the input model is lost. Other tests show that the tomographic technique can reproduce simulated heliospheric structures from remote sensing data using these structures as input.

HELIOS SPACECRAFT RESULTS AND COMPARISON WITH OTHER DATA SETS

The Helios photometer data both show the way to analyze the Solar Orbiter heliospheric imager data, and also yield substantial new scientific information about how CMEs expand and propagate through the interplanetary medium. The basic data set from the photometers is brightness time-series information in heliocentric coordinates mapped relative to the Sun. These time series (shown partially for the 16° and 31° photometers in figure 2) have had a zodiacal light model (Leinert et al., 1981b) removed and stellar signals eliminated. To further refine these time series for use with the tomography, we remove an 8-day running mean. This filter removes a portion of the low-frequency response not otherwise accounted for. At this level, the Helios systems act as differential photometers for high-frequency heliospheric signals. In addition, the final time series is searched for "glitches". These generally appear as spikes in the data that are more prominent above the background in the direction opposite the Sun. These spikes are often correlated with high-energy particle flux observed in the Helios particle detectors (Richter et al., 1982). When these spikes are detected in the photometer data, the whole period of time from the Helios photometers is considered suspect and eliminated from consideration even though the high-energy particle spike is not dominant in the photometer observations nearer the Sun.

Figure 2: Helios 2 time series data for the month of May, 1979. Most of the large, slowly varying zodiacal light component has been removed from the data. The 16° and 31° photometer sectors with centers at ecliptic longitudes of 3°, -2°, -8°, and -13° in V light are shown. An additional 31° sector time series at -19° is also shown. The May 7 CME highlighted in the text can be observed along with other heliospheric variations in the data as a bright peak in both photometers on about 8 May.

Because the very bright zodiacal light component is inseparable from the heliospheric time series signal except by its rapid (less than ~8-day) variation over time, the tomographic analysis must deal with the fact that there is a steady background Thomson-scattering signal component as well as the time-varying one. Several techniques have been devised to include an estimate of this signal in our Thomson-scattering analysis. One of the first methods was to simply analyze the variations relative to the mean datum formed by the running 8-day average (Jackson and Hick, 2000a). After the 3-D analysis was complete, a small additional r^-2 density was added to the data to provide a total density at 1 AU commensurate with the mean value for that time interval at Earth. In the current tomographic analysis shown here, an additional r^-P density with a constant value at 1 AU is added to the model data prior to the tomographic analysis. The sum of the modeled background brightness and the variable component above the mean datum are now compared with total modeled brightness from the three-dimensional model. The Helios spacecraft densities (rather than those at Earth) are now also compared over the time interval in question with the densities derived by our model in order to provide a best interval fit to the value of P and the density at 1 AU. For the period of time during May 1979, P was found to be 2.07 with a density at 1 AU of 7.0 e^- cm^-2. For a less active time in 1977 (Carrington Rotation 1653) P was found to be ~2.10 with a 1 AU value of 8.5 e^- cm^-2. The different techniques used in background density fitting make little difference in the location of the heliospheric structures reconstructed, but they do somewhat change the overall density.

Figure 3: Carrington synoptic map of heliospheric structure at 1.0 AU at 12 UT 10 May 1979. At this time the Helios 2 spacecraft is ~90° west of Earth in heliographic longitude (indicated) at a solar distance of 0.3 AU.

Once a three-dimensional result is available, it can be viewed from any perspective or extrapolated to any position in space. Figure 3 is a Carrington synoptic map of heliospheric density 1.0 AU at 12 UT on 10 May 1979 obtained from the Helios 2 photometer data. The number of lines of sight from the Helios 2 spacecraft allow sufficient model coverage to determine structures using a one-day temporal cadence and a 10°´10° latitude-longitude heliographic spatial resolution at locations near the spacecraft (indicated on the map). Structures near the spacecraft are reconstructed more redundantly than those farther from it. Locations where line-of-sight coverage is poor are left blank. Since only Helios 2 photometer observations are used, there is no data coverage at southern heliographic latitudes. A remote-observer view of northern heliospheric density shows the heliospheric manifestation of the 7 May 1979 CME (Jackson et al., 1988, figure 4) at the same time as the 1 AU Carrington map of figure 3. Figure 5 shows this remote view. Figure 6 is a comparison plot of heliospheric density at the Helios 2 spacecraft and the reconstructed density in the time-dependent kinematic model extracted at the location of the spacecraft. The in situ density values at Helios 2 are averaged using an 18-hour filter in order that they have the same approximate temporal resolution as the 10°´10° daily spatial model.

Figure 4: Solwind coronagraph image of the 7 May CME observed at the time indicated. The coronagraph outer field of view extends to 8 R_S.

Figure 5: Remote observer view of heliospheric density at the time indicated. An r^-2.07 density gradient fit to the observations over the Carrington rotation 1681 interval has been removed from the kinematic model ambient (fit from Helios 2 in situ measurements at 7.0 e^- cm^-2 at 1 AU), and to the reconstructed structures to aid in viewing them. The observer is located at 3.0 AU 30° above the ecliptic plane ~45° west of the Sun-Earth line.

Figure 6: Comparison plot of heliospheric densities at the Helios 2 spacecraft and least squares correlation.

The major structure observed in figure 5 is a coronal mass ejection (CME) that was observed by the Solwind coronagraph (Poland et al., 1981) to arise from the Sun to the solar northwest at midday 7 May, 1979. This well-studied CME (Jackson, 1985; Jackson and Leinert, 1985; Jackson et al., 1988; Jackson and Froehling, 1995) was termed "three-pronged" by the Solwind coronagraph group. At the time of figure 5 the front portion of the CME is estimated to have a solar distance of ~1.0 AU (see Jackson et al., 1988). This CME had an estimated excess mass of 10¹⁶ g (Poland, 1981) by assuming its entire excess mass was located in the plane of the sky observed by Solwind. The CME underwent considerable evolution by the time it reached the Helios viewing position, expanding both outward and in north-south size. By summing over time and space in the 3-D matrix using the current tomographic reconstruction, this CME is estimated to have an excess mass of ~4´10¹⁶ g at 1.0 AU. If the total CME mass above zero within the CME volume is included, the CME mass is estimated to be ~1´10¹⁷ g and the CME takes from 18 UT 9 May to 18 UT 13 May, 1979 to completely pass 1 AU! This compares with values of 6´10¹⁵ g and 9´10¹⁵ g respectively for the outer portion of this CME obtained by the two-spacecraft tomographic reconstruction technique (Jackson and Froehling, 1995). The two-spacecraft technique shows approximately the same type structure reconstructed. In the 3-D reconstruction techniques, the northern portion of the CME is directed away from Earth and northerly while the southern feature is directed primarily northwest of the Sun-Earth line.

The 1979 time period during Carrington Rotatation 1681 is at the extreme maximum of CME activity for Solar Cycle 21. Far more CMEs can be observed throughout this period and related to CMEs observed by the Solwind coronagraph, and some of these CMEs and CME sequences are far more massive than the single isolated 7 May CME. In particular this is the case with a CME that began eruption from the Sun on 25 May 1979. A more complete data set and a video of over 40 days of this northern hemisphere Helios 2 reconstruction of heliospheric density can be found on the Web at: http://casswww.ucsd.edu/solar/tomography/. An additional video sequence and images of an earlier (and less active) temporal interval (Carrington rotation 1653, in the year 1977) can be found at the same location. In this sequence, both Helios 1 and Helios 2 photometer data are used in the reconstruction of northern and southern heliospheric features, and both corotating and CME structures can be observed in the remote-observer views. The correlation with Helios 2 densities for the entire 1653 Carrington rotation is 0.86.

HELIOSPHERIC IMAGER

The group at UCSD has designed a heliospheric imager for inclusion on Solar Orbiter (Buffington et al., 1996; Buffington, 1998a; Buffington et al., 1998b; Buffington, 2000). If a hemisphere free from illuminated obstructions can be made available on the spacecraft, then a simple and light-weight imager design results. Figure 7 gives a diagram of this imager design, and figure 8 shows a full-scale optical prototype of the instrument designed specifically for Solar Orbiter. The instrument will be able to view an entire hemisphere of sky with ~0.1% photometric precision to within about 4° of the solar surface. Closer-view heliospheric imager options may be desirable to overlap more with other Solar Orbiter instruments, and these options will be studied more fully at a later date. The heliospheric imager functions like a coronagraph in that there is an external occulter to exclude unwanted sunlight and spacecraft glints and a Lyot stop to further reduce scattered light. Table 1 gives mass estimates for the imager designed for Solar Orbiter. We expect that power requirements for an advanced CCD camera design would be less than 5 watts. Additional power is required for the imager share of the DHU. We expect the instrument to be held stable to 0.1° during an exposure. Telemetry is expected to amount to approximately one summed CCD image per hour that has been cleansed of cosmic ray contamination by the DHU. The telemetry requirement in this case amounts to ~5 kbits s^-1 for an uncompressed image.

Figure 7: Solar Orbiter heliospheric imager schematic.

Figure 8: Image of a working instrument model designed specifically for Solar Orbiter.

Table 1: Mass estimates for the Solar Orbiter Heliospheric Imager.

* Graphite-Epoxy construction for minimum weight: for aluminum, triple the mass.
** Excluding DHU, harness

CONCLUSIONS

The tomographic analysis handles density both nearby density and distant from the spacecraft as accurately as the modeling and data precision allow. We continue to upgrade our tomographic analysis techniques as newer solar wind models are incorporated. In particular, the simple kinematic model currently used in the reconstruction is somewhat crude, and we expect to replace this within a few years with a more precise optional model version that can be used in the final tomographic iterations. Primarily data quantity, precision, and computational convenience restrict spatial and temporal resolution of the heliospheric structures that are reconstructed. The heliospheric imager for Solar Orbiter that we envision will be able to reconstruct the density over an entire heliospheric hemisphere with approximately 1°´1° heliospheric latitude-longitude spatial resolution and a 1-hour temporal cadence. Although structures near the Solar Orbiter spacecraft can be more accurately reconstructed than can those more distant from it, we expect that other instruments (SMEI, STEREO, etc.) may operate during the same times as Solar Orbiter. If so these other instruments may help fill in heliospheric regions not observed well from the spacecraft in order to help complete the Solar Orbiter far-field view.

ACKNOWLEDGEMENTS

The work of B.V. Jackson, A. Buffington and P. P. Hick was supported at the University of California at San Diego by AFOSR grant F49620-01-1-0054 and NASA grants NAG5-8504 and NAG5-9423.

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