Intercomparison of the LASCO-C2, SECCHI-COR1, SECCHI-COR2, and Mk4 Coronagraphs

In order to assess the reliability and consistency of white-light coronagraph measurements, we report on quantitative comparisons between polarized brightness [pB] and total brightness [B] images taken by the following white-light coronagraphs: LASCO-C2 on SOHO, SECCHI-COR1 and -COR2 on STEREO, and the ground-based MLSO-Mk4. The data for this comparison were taken on 16?April 2007, when both STEREO spacecraft were within 3.1^° of Earth??s heliographic longitude, affording essentially the same view of the Sun for all of the instruments. Due to the difficulties of estimating stray-light backgrounds in COR1 and COR2, only Mk4 and C2 produce reliable coronal-hole values (but not at overlapping heights), and these cannot be validated without rocket flights or ground-based eclipse measurements. Generally, the agreement between all of the instruments?? pB values is within the uncertainties in bright streamer structures, implying that measurements of bright CMEs also should be trustworthy. Dominant sources of uncertainty and stray light are discussed, as is the design of future coronagraphs from the perspective of the experiences with these instruments.     

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 R _⊙ as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066). We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50°. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.     

Evolution of CME Mass in the Corona

The idea that coronal mass ejections (CMEs) pile up mass in their transport through the corona and heliosphere is widely accepted. However, it has not been shown that this is the case. We perform an initial study of the volume electron density of the fronts of 13 three-part CMEs with well-defined frontal boundaries observed with the Solar and Heliospheric Observatory/Large Angle and Spectrometric COronagraph (SOHO/LASCO) white-light coronagraphs. We find that, in all cases, the volume electron density decreases as the CMEs travel through the LASCO-C2 and -C3 fields of view, from \(2.6\,\mbox{--}\,30~\mbox{R}_{\odot}\). The density decrease follows closely a power law with an exponent of ?3, which is consistent with a simple radial expansion. This indicates that in this height regime there is no observed pile-up.     

Photometric calibration of the LASCO-C2 coronagraph for Solar System objects

We present a photometric calibration of the SOHO/LASCO-C2 coronagraph appropriate to Solar System objects based on the extensive analysis of all stars down to magnitude V=8 which transited its field-of-view during the past nine years of operation (1996-2004). An automatic procedure was developed to analyze some 143,000 images, and to detect, locate and measure those stars. Aperture photometry was performed using three different aperture sizes and the zero points of the photometric transformations between the LASCO-C2 magnitudes for its three filters (orange, blue and red) and the standard V magnitudes were determined after introducing a correction for the color of the stars. The calibration coefficients for the surface photometry of extended sources were then derived from the zero points. An analysis of their temporal evolution indicates a slight decrease of the sensitivity of LASCO-C2 at a rate of ∼0.7% per year.     

Photometric Calibration of the LASCO-C2 Coronagraph over 14 Years (1996 – 2009)

We present a photometric calibration of the SOHO/LASCO-C2 coronagraph based on the analysis of all stars down to magnitude V=8 that transited its field of view during the past 14 years of operation (1996?–?2009), extending the previous work of Llebaria, Lamy, and Danjard (Icarus 182, 281, 2006). The pre-processing of the images incorporates the most recent determination of the evolution of the LASCO-C2 performances. The automatic procedure then analyzes some 260?000 images to detect, locate, and measure those stars. Aperture photometry is performed using four different aperture sizes, and the zero points (ZPs) of the photometric transformations between the LASCO-C2 magnitudes for its orange filter and the standard V magnitudes are determined after introducing a correction for the color of the stars. A new statistical method (“bootstrap”) is introduced to assess the confidence intervals of the mean yearly value of the ZPs. The correction for finite aperture required to derive the calibration coefficient for the surface photometry of extended sources is based on the reconstructed image of bright saturated stars and a robust model for the growth curve. The global temporal evolution of the sensitivity of LASCO-C2 is compatible with a continuous decrease at a rate of ≈?0.56 % per year. However, it is better described by two separate linear variations with a discontinuity at the time of the loss of SOHO. After the resumption of normal operations in 1999, the linear decrease of the sensitivity amounts to ≈?0.35 % per year.     

On determining the electron density distribution of the solar corona from K-coronameter data

The electron density distribution of the inner solar corona (r 2 R ) as a function of latitude, longitude, and radial distance is determined from K-coronameter polarization-brightness (pB) data. A Legendre polynomial is assumed for the electron density distribution, and the coefficients of the polynomial are determined by a least-mean-square regression analysis of several days of pB-data. The calculated electron density distribution is then mapped as a function of latitude and longitude. The method is particularly useful in determining the longitudinal extent of coronal streamers and enhancements and in resolving coronal features whose projections on the plane of the sky overlap.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Formation Mechanism of Soft X-Ray Transient Trans-Equatorial Loop System

The Soft X-ray Telescope (SXT) onboard Yohkoh often observed large-scale coronal loops connecting two active regions situated in opposite hemispheres. These are the trans-equatorial loop systems (TLSs). The formation mechanism of TLSs is not yet known. We analyzed a TLS observed simultaneously with Yohkoh/SXT and a coronagraph (SOHO/LASCO-C1). SOHO/LASCO-C1 observed loop expansion and eruption at the west solar limb. Yohkoh/SXT observed a rising motion (chromospheric evaporation) of hot and dense plasmas from the active regions located at the footpoints of the loop. Important results of our analyses are that (1) the loop eruption and the rising motion of the plasmas were simultaneous, (2) the TLS had a cusp-like appearance, and (3) the highest temperature region of the TLS was located above the bright loop seen in soft X rays. These observational results (loop expansion, eruption, and chromospheric evaporation) suggest that this bright (high-density) TLS was created by the same mechanism by which a solar flare occurs, namely, magnetic reconnection. In this paper, we propose a formation mechanism of the TLS that forms between two independent active regions.     

Latitudinal and Solar-Cycle Variations of the White-Light Corona from SOHO/LASCO Observations

SOHO/LASCO data were used to obtain the latitudinal and radial distributions of the brightness of the K- and F-corona in the period of 1996 – 2007, and their solar-cycle variations were studied. Then an inversion method was employed to obtain the radial distributions of the electron density N _e(R,θ) for various latitude values on the coronal images. Our values of N _e(R,θ) are in good agreement with the findings of other authors. We found that in an edge-on streamer belt the electron density, like the K-corona brightness, varies with distance more slowly in the near-equatorial rays than in near-polar regions. We have developed a method for assessing the maximum values of the electron density at the center of the face-on streamer belt in its bright rays and depressions between them. Not all bright rays observed in the face-on streamer belt are found to be associated with an increased electron density in them. Mechanisms for forming such rays have been suggested.     

Small-scale background magnetic field on the sun in solar cycle 23

Based on SOHO/MDI data (an archive of magnetic maps with a resolution of ～2″), we have investigated the dynamics of the small-scale background magnetic field on the Sun in solar cycle 23. The cyclic variations and surface structure of the background magnetic field have been analyzed using the mean estimates of 〈B〉 and 〈B ²〉 of the observed magnetic field strength B for various solar surface areas and at various B levels. We have established that the cyclic variations of 〈2〉 at latitudes below 30° are essentially similar to those of the total radio flux F _10.7. A significant difference between the background magnetic fields in the northern and southern solar hemispheres persisting throughout the solar cycle has been detected. We have found the effect of background magnetic field growth toward the solar limb and concluded that the transversal component in the background magnetic field is significant. The relatively weak small-scale background magnetic fields are shown to form a special population with its own special laws of cyclic variation.     

Addendum to: Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

This addendum uses an alternate fit for the electron density distribution \(N(r)\) (see Figure 1) and estimates the coronal magnetic field using the new model. We find that the estimates of the magnetic field are in close agreement using both the models.

We have fit the \(N(r)\) distribution obtained from STEREO-A/COR1 and SOHO/LASCO-C2 using a fifth-order polynomial (see Figure 1). The expression can be written as

$$\begin{aligned} N_{\text{cor}}(r) &= 1.43 \times 10^{9} r^{-5} - 1.91 \times 10^{9} r^{-4} + 1.07 \times 10^{9} r^{-3} - 2.87 \times 10^{8} r^{-2} \\ &\quad {} + 3.76 \times 10^{7} r^{-1} - 1.91 \times 10^{6} , \end{aligned}$$

(1)

where \(N_{\text{cor}}(r)\) is in units of cm^?3 and \(r\) is in units of \(\mathrm{R}_{\odot}\). The background coronal electron density is enhanced by a factor of 5.5 at 2.63 \(\mathrm{R}_{\odot}\) during the coronal mass ejection (CME). The estimated coronal magnetic field strength (\(B\)) using radio data indicates that \(B(r) \approx(0.51\text{\,--\,}0.48) \pm 0.02\ \mathrm{G}\) in the range \(r \approx2.65\text{\, --\,}2.82\ \mathrm{R}_{\odot}\). The field strengths for STEREO-A/COR1 and SOHO/LASCO-C2 are ≈?0.32 G at \(r \approx 3.11\ \mathrm{R}_{\odot}\) and ≈?0.12 G at \(r \approx 4.40\ \mathrm{R}_{\odot}\), respectively.

     

Parameters of the Magnetic Flux inside Coronal Holes

The parameters of the magnetic flux distribution inside low-latitude coronal holes (CHs) were analyzed. A statistical study of 44 CHs based on Solar and Heliospheric Observatory (SOHO)/MDI full disk magnetograms and SOHO/EIT 284?Å images showed that the density of the net magnetic flux, B _net, does not correlate with the associated solar wind speeds, V _x . Both the area and net flux of CHs correlate with the solar wind speed and the corresponding spatial Pearson correlation coefficients are 0.75 and 0.71, respectively. A possible explanation for the low correlation between B _net and V _x is proposed. The observed non-correlation might be rooted in the structural complexity of the magnetic field. As a measure of the complexity of the magnetic field, the filling factor, f(r), was calculated as a function of spatial scales. In CHs, f(r) was found to be nearly constant at scales above 2 Mm, which indicates a monofractal structural organization and smooth temporal evolution. The magnitude of the filling factor is 0.04 from the Hinode SOT/SP data and 0.07 from the MDI/HR data. The Hinode data show that at scales smaller than 2 Mm, the filling factor decreases rapidly, which means a multifractal structure and highly intermittent, burst-like energy release regime. The absence of the necessary complexity in CH magnetic fields at scales above 2 Mm seems to be the most plausible reason why the net magnetic flux density does not seem to be related to the solar wind speed: the energy release dynamics, needed for solar wind acceleration, appears to occur at small scales below 1 Mm.     

Magnetic Stereoscopy of Coronal Loops in NOAA 8891

The Solar TErrestrial RElations Observatory (STEREO) requires powerful tools for the three-dimensional (3D) reconstruction of the solar corona. Here we test such a program with data from SOHO and TRACE. By taking advantage of solar rotation, a newly developed stereoscopy tool for the reconstruction of coronal loops is applied to the solar active region NOAA 8891 observed from 1 March to 2 March 2000. The stereoscopic reconstruction is composed of three steps. First, we identify loop structures in two TRACE images observed from two vantage viewpoints approximately 17 degrees apart, which corresponds to observations made about 30 hours apart. In the second step, we extrapolate the magnetic field in the corona with the linear force-free field model from the photospheric line-of-sight SOHO/MDI data. Finally, combining the extrapolated field lines and one-dimensional loop curves from two different viewpoints, we obtain the 3D loop structures with the magnetic stereoscopy tool. We demonstrate that by including the magnetic modeling this tool is more powerful than pure geometrical stereoscopy, especially in resolving the ambiguities generated by classical stereoscopy. This work will be applied to the STEREO mission in the near future.     

Three-Dimensional Properties of Coronal Mass Ejections from STEREO/SECCHI Observations

We identify 565 coronal mass ejections (CMEs) between January 2007 and December 2010 in observations from the twin STEREO/SECCHI/COR2 coronagraphs aboard the STEREO mission. Our list is in full agreement with the corresponding SOHO/LASCO CME Catalog ( http://cdaw.gsfc.nasa.gov/CME_list/ ) for events with angular widths of 45^° and up. The monthly event rates behave similarly to sunspot rates showing a three- to fourfold rise between September 2009 and March 2010. We select 51 events with well-defined white-light structure and model them as three-dimensional (3D) flux ropes using a forward-modeling technique developed by Thernisien, Howard and Vourlidas (Astrophys. J. 652, 763??C?773, 2006). We derive their 3D properties and identify their source regions. We find that the majority of the CME flux ropes (82?%) lie within 30^° of the solar equator. Also, 82?% of the events are displaced from their source region, to a lower latitude, by 25^° or less. These findings provide strong support for the deflection of CMEs towards the solar equator reported in earlier observations, e.g. by Cremades and Bothmer (Astron. Astrophys. 422, 307??C?322, 2004).     

Saturn's rings. I. Optical thickness of rings A,B, D and structure of ring B

A photometric study of high-resolution (～0″.3) plates of Saturn taken at the Lowell Observatory in 1943 and 1945 is presented. N-S scans were taken over both the planet and rings. The excess brightness due to the planet seen through the rings is found by taking the difference between the central meridian (CM) scans and scans displaced by 5″.7. Adopting a value for the albedo of the planet, it is possible to obtain the optical thickness, τ_CM(r). In particular, for the regions of maximum brightness in rings A and B, we find τ_CM(I_{A max}) = 0.38 ± 0.11 and τ_CM(I_{B max}) = 0.61 ± 0.11. Observations by Barnard made in 1890 show evidence of ring D, recently discovered by Guerin (1969). The value for the optical thickness of this ring is τ_D(I_{D max}) = 0.03 ± 0.01. Ring B exhibits a pronounced (7–10%) decrease in brightness from the extremity of the major axis to the CM. After considering several possible explanations, we conclude that the ring particles are nonspherical and are in synchronous rotation around the planet with their long axis toward it. The mean value for the ratio of major to minor axis for the particles at 15″ is $\text{(a/b)}\text{? 1.08}$. Because of the shape and orientation of the particles, the optical thickness at the extremity of the major axis and at the CM are different for any saturnicentric latitude B ≠ 90°. Under these circumstances, only a minimum value for τ at the extremity can be derived.     

Study of Differences Between Sunspot and White Light Facular Area Data Determined from SDO/HMI and SOHO/MDI Observations

Sunspot and white light facular areas are important data for solar activity and are used, for example, in the study of the evolution of sunspots and their effect on solar irradiance. Solar Dynamic Observatory??s Helioseismic and Magnetic Imager (SDO/HMI) solar images have much higher resolution (??0.5????pixel^?1) than Solar and Heliospheric Observatory??s Michelson Doppler Imager (SOHO/MDI) solar images (??2????pixel^?1). This difference in image resolution has a significant impact on the sunspot and white light facular areas measured in the two datasets. We compare the area of sunspots and white light faculae derived from SDO/HMI and SOHO/MDI observations. This comparison helps the calibration of the SOHO sunspot and facular area to those in SDO observations. We also find a 0.22 degree difference between the North direction in SDO/HMI and SOHO/MDI images.     

Heliospheric Imaging of 3D Density Structures During the Multiple Coronal Mass Ejections of Late July to Early August 2010

It is usually difficult to gain a consistent global understanding of a coronal mass ejection (CME) eruption and its propagation when only near-Sun imagery and the local measurements derived from single-spacecraft observations are available. Three-dimensional (3D) density reconstructions based on heliospheric imaging allow us to “fill in” the temporal and spatial gaps between the near-Sun and in situ data to provide a truly global picture of the propagation and interactions of the CME as it moves through the inner heliosphere. In recent years the heliospheric propagation of dense structures has been observed and measured by the heliospheric imagers of the Solar Mass Ejection Imager (SMEI) and on the twin Solar TErrestrial RElations Observatory (STEREO) spacecraft. We describe the use of several 3D reconstruction techniques based on these heliospheric imaging data sets to distinguish and track the propagation of multiple CMEs in the inner heliosphere during the very active period of solar activity in late July?–?early August 2010. We employ 3D reconstruction techniques used at the University of California, San Diego (UCSD) based on a kinematic solar wind model, and also the empirical Tappin–Howard model. We compare our results with those from other studies of this active period, in particular the heliospheric simulations made with the ENLIL model by Odstrcil et al. (J. Geophys. Res., 2013) and the in situ results from multiple spacecraft provided by Möstl et al. (Astrophys. J. 758, 10?–?28, 2012). We find that the SMEI results in particular provide an overall context for the multiple-density flows associated with these CMEs. For the first time we are able to intercompare the 3D reconstructed densities with the timing and magnitude of in situ density structures at five spacecraft spread over 150° in ecliptic longitude and from 0.4 to 1 AU in radial distance. We also model the magnetic flux-rope structures at three spacecraft using both force-free and non-force-free modelling, and compare their timing and spatial structure with the reconstructed density flows.     

The Double Structure of the Coronal Streamer Belt

Increasing the effective spatial resolution when analyzing LASCO-C2/SOHO data helped to reveal the existence of double-ray structure in the streamer belt, both in the absence and presence of belt bends. Streamer-belt rays located in the plane of the sky are demonstrated to deviate poleward (north- and southward, respectively, in the N and S hemispheres) at distances R < 4{–}5R_⊙ from the Sun center. These new results concerning streamer belt structure are important as the basis for checking a theory claiming to adequately describe physical processes in the corona.     

Comparison of Ground-Based and Space-Based Longitudinal Magnetograms

We compare photospheric line-of-sight magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) instrument with observations from the 150-foot Solar Tower at Mt. Wilson Observatory (MWO), the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO), and the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO). We find very good agreement between VSM and the other data sources for both disk-averaged flux densities and pixel-by-pixel measurements. We show that the VSM mean flux density time series is of consistently high signal-to-noise ratio with no significant zero offsets. We discuss in detail some of the factors ?C spatial resolution, flux dependence, and position on the solar disk ?C affecting the determination of scaling between VSM and SOHO/MDI or SDO/HMI magnetograms. The VSM flux densities agree well with spatially smoothed data from MDI and HMI, although the scaling factors show a clear dependence on flux density. The factor to convert VSM to HMI increases with increasing flux density (from ??1 to ??1.5). The nonlinearity is smaller for the VSM vs. SOHO/MDI scaling factor (from ??1 to ??1.2).     

Omnidirectional induced compton scattering by relativistic electrons

Quasars, pulsars and other cosmic sources of intense radiation are known to have large brightness temperature (kT _b?mc ²) and relativistic electron density values. In this case the induced Compton scattering by relativistic electrons should be considered. The probability of scattering with decreasing radiation frequency is derived for isotropic radiation scattering. When induced scattering takes place, the relativistic electron obtains its energy by transforming high-frequency quanta into the low-frequency ones. In the most intensive sources electrons would receive energiesE?mc ² ××(kT _b/mc ²)^1/7 due to the heating rate proportional toE ^?5 with the cooling rate proportional toE ². Considerable distortion of the quasar spectrum is possible for reasonably large values of relativistic electron density (N?10⁶cm^?3) notwithstanding that the heating is negligible. In pulsars relativistic electron heating and spectrum distortion appear to depend more on the induced Compton scattering.     

Antarctic substorm events observed by sounding rockets,ionization of the D- and E-regions by auroral electrons

The ionization structure of the auroral arc was measured on a sounding rocket which penetrated into a bright auroral arc. The E-region electron density becomes large (2 ～ 5 × 10⁵ el/cm³ only in the moving auroral arc, whose N₂⁺ 4278 Å brightness is 1 ～ 2·5 kR. The electron density in the D-region beneath the lower boundary of the arc (75 ～ 98 km in altitude) is also considerably enhanced to 2 ～ 5 × 10⁴ el/cm³.The observed E-region electron density can be interpreted theoretically as due to the direct ionization by precipitating electrons, whose energy spectrum is approximately represented by an exponential type having the characteristic energy of 2 keV. The correlation between the electron density and the N₂⁺ 4278 Å brightness can be reasonably explained by considering the simultaneous effects on the ionization and the optical excitation caused by the primary electrons having a flux of 9 × 10⁹ el/cm²/sec per 1 kR of the 4278 Å emission.Further analyses using the electron density data from four other sounding rockets have shown that the D-region ionization has good correlations to the cosmic noise absorption (CNA) and the magnetic substorm activities observed simultaneously at the ground station, whereas it has poor correlation to the same quantity of the E-region measured in the same experiment. It is found that the observed D-region ionization is much larger than that predicted by the theory which takes into account the Bremsstrahlung X-ray ionization along with the direct impact ionization when it is applied to the precipitating electron flux spectrum consistent to the E-region ionization and optical excitation.After all the present experimental results suggest a dual nature of the electron precipitation spectrum in the substorm, i.e. the softer part which is localized in the auroral arc and the harder part which is spatially wide-spread over the substorm area.