Accuracy and Limitations of Fitting and Stereoscopic Methods to Determine the Direction of Coronal Mass Ejections from Heliospheric Imagers Observations

Using data from the Heliospheric Imagers (HIs) onboard STEREO, it is possible to derive the direction of propagation of coronal mass ejections (CMEs) in addition to their speed with a variety of methods. For CMEs observed by both STEREO spacecraft, it is possible to derive their direction using simultaneous observations from the twin spacecraft and also, using observations from only one spacecraft with fitting methods. This makes it possible to test and compare different analysis techniques. In this article, we propose a new fitting method based on observations from one spacecraft, which we compare to the commonly used fitting method of Sheeley et al. (J. Geophys. Res. 104, 24739, 1999). We also compare the results from these two fitting methods with those from two stereoscopic methods, focusing on 12 CMEs observed simultaneously by the two STEREO spacecraft in 2008 and 2009. We find evidence that the fitting method of Sheeley et al. (J. Geophys. Res. 104, 24739, 1999) may result in significant errors in the determination of the CME direction when the CME propagates outside of 60°±20° from the Sun – spacecraft line. We expect our new fitting method to be better adapted to the analysis of halo or limb CMEs with respect to the observing spacecraft. We also find some evidence that direct triangulation in the HI fields-of-view should only be applied to CMEs propagating approximatively toward Earth (± 20° from the Sun – Earth line). Last, we address one of the possible sources of errors of fitting methods: the assumption of radial propagation. Using stereoscopic methods, we find that at least seven of the 12 studied CMEs had a heliospheric deflection of less than 20° as they propagated in the HI fields-of-view, which, we believe, validates this approximation.     

Background Subtraction for the SECCHI/COR1 Telescope Aboard STEREO

COR1 is an internally occulted Lyot coronagraph, part of the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) instrument suite aboard the twin Solar Terrestrial Relations Observatory (STEREO) spacecraft. Because the front objective lens is subjected to a full solar flux, the images are dominated by instrumental scattered light which has to be removed to uncover the underlying K corona data. We describe a procedure for removing the instrumental background from COR1 images. F coronal emission is subtracted at the same time. The resulting images are compared with simultaneous data from the Mauna Loa Solar Observatory Mk4 coronagraph. We find that the background subtraction technique is successful in coronal streamers, while the baseline emission in coronal holes (i.e. between plumes) is suppressed. This is an expected behavior of the background subtraction technique. The COR1 radiometric calibration is found to be either 10 – 15% lower, or 5 – 10% higher than that of the Mk4, depending on what value is used for the Mk4 plate scale, while an earlier study found the COR1 radiometric response to be ∼ 20% higher than that of the Large Angle Spectroscopic Coronagraph (LASCO) C2 telescope. Thus, the COR1 calibration is solidly within the range of other operating coronagraphs. The background levels in both COR1 telescopes have been quite steady in time, with the exception of a single contamination event on 30 January 2009. Barring too many additional events of this kind, there is every reason to believe that both COR1 telescopes will maintain usable levels of scattered light for the remainder of the STEREO mission.     

First Imaging of Coronal Mass Ejections in the Heliosphere Viewed from Outside the Sun – Earth Line

We show for the first time images of solar coronal mass ejections (CMEs) viewed using the Heliospheric Imager (HI) instrument aboard the NASA STEREO spacecraft. The HI instruments are wide-angle imaging systems designed to detect CMEs in the heliosphere, in particular, for the first time, observing the propagation of such events along the Sun – Earth line, that is, those directed towards Earth. At the time of writing the STEREO spacecraft are still close to the Earth and the full advantage of the HI dual-imaging has yet to be realised. However, even these early results show that despite severe technical challenges in their design and implementation, the HI instruments can successfully detect CMEs in the heliosphere, and this is an extremely important milestone for CME research. For the principal event being analysed here we demonstrate an ability to track a CME from the corona to over 40 degrees. The time – altitude history shows a constant speed of ascent over at least the first 50 solar radii and some evidence for deceleration at distances of over 20 degrees. Comparisons of associated coronagraph data and the HI images show that the basic structure of the CME remains clearly intact as it propagates from the corona into the heliosphere. Extracting the CME signal requires a consideration of the F-coronal intensity distribution, which can be identified from the HI data. Thus we present the preliminary results on this measured F-coronal intensity and compare these to the modelled F-corona of Koutchmy and Lamy (IAU Colloq. 85, 63, 1985). This analysis demonstrates that CME material some two orders of magnitude weaker than the F-corona can be detected; a specific example at 40 solar radii revealed CME intensities as low as 1.7×10⁻¹⁴ of the solar brightness. These observations herald a new era in CME research as we extend our capability for tracking, in particular, Earth-directed CMEs into the heliosphere.     

Radial Evolution of Well-Observed Slow CMEs in the Distance Range 2 – 30 <Emphasis Type="Italic">R</Emphasis><Subscript>⊙</Subscript>

We performed a detailed analysis of 27 slow coronal mass ejections (CMEs) whose heights were measured in at least 30 coronagraphic images and were characterized by a high quality index (≥4). Our primary aim was to study the radial evolution of these CMEs and their properties in the range 2 – 30 solar radii. The instantaneous speeds of CMEs were calculated by using successive height – time data pairs. The obtained speed – distance profiles [v(R)] are fitted by a power law v = a(R−b) ^c . The power-law indices are found to be in the ranges a=30 – 386, b=1.95 – 3.92, and c=0.03 – 0.79. The power-law exponent c is found to be larger for slower and narrower CMEs. With the exception of two events that had approximately constant velocity, all events were accelerating. The majority of accelerating events shows a v(R) profile very similar to the solar-wind profile deduced by Sheeley et al. (Astrophys. J. 484, 472, 1997). This indicates that the dynamics of most slow CMEs are dominated by the solar wind drag.     

<Emphasis Type="Italic">In Situ</Emphasis> Signatures of Interchange Reconnection between Magnetic Clouds and Open Magnetic Fields: A Mechanism for the Erosion of Polar Coronal Holes?

We outline a method to determine the direction of solar open flux transport that results from the opening of magnetic clouds (MCs) by interchange reconnection at the Sun based solely on in-situ observations. This method uses established findings about i) the locations and magnetic polarities of emerging MC footpoints, ii) the hemispheric dependence of the helicity of MCs, and iii) the occurrence of interchange reconnection at the Sun being signaled by uni-directional suprathermal electrons inside MCs. Combining those observational facts in a statistical analysis of MCs during solar cycle 23 (period 1995 – 2007), we show that the time of disappearance of the northern polar coronal hole (1998 – 1999), permeated by an outward-pointing magnetic field, is associated with a peak in the number of MCs originating from the northern hemisphere and connected to the Sun by outward-pointing magnetic field lines. A similar peak is observed in the number of MCs originating from the southern hemisphere and connected to the Sun by inward-pointing magnetic field lines. This pattern is interpreted as the result of interchange reconnection occurring between MCs and the open field lines of nearby polar coronal holes. This reconnection process closes down polar coronal hole open field lines and transports these open field lines equatorward, thus contributing to the global coronal magnetic field reversal process. These results will be further constrainable with the rising phase of solar cycle 24.     

Dynamic and Thermal Disappearance of Prominences and Their Geoeffectiveness

This paper is a qualitative study of 42 events of solar filament/prominence sudden disappearances (“disparitions brusques”; henceforth DBs) around two solar minima, 1985 – 1986 and 1994. The studied events were classified as 17 thermal and 25 dynamic disappearances. Associated events, i.e. coronal mass ejections (CMEs), type II bursts, evolution of nearby coronal holes, as well as solar wind speed, and geomagnetic disturbances are discussed. We have found that about 50% of the thermal DBs with adjacent (within 15° from the DB) coronal holes were associated with CMEs within a selected time window. All the studied thermal disappearances with adjacent coronal holes or accompanied by dynamic disappearances were associated with weak and medium geomagnetic storms. Also, nearly 64% of dynamic DBs were associated with CMEs. Ten (40%) dynamic disappearances were associated with intense geomagnetic storms, even when no CMEs was reported, six (24%) dynamic disappearances corresponded to extreme storms, and five (20%) corresponded to medium geomagnetic storms. The extreme geomagnetic storms appeared to be related to combined events, involving dynamic disappearances with adjacent coronal holes or including thermal disappearances. Furthermore, the geomagnetic activity (Dst index) increased if the source was close to the central meridian (±30°). The highest interplanetary magnetic field (B), longest duration, lowest southward direction B _z component, and lowest Dst were highly correlated for all studied events. The Sun – Earth transit time computed from the starting time of the sudden disappearance and the time its effect was measured at Earth was about 4.3 days and was mainly well correlated with the solar wind speed measured in situ (daily value).     

Deflection of Coronal Rays by Remote CMEs: Shock Wave or Magnetic Pressure?

We analyze five events of the interaction of coronal mass ejections (CMEs) with the remote coronal rays located up to 90° away from the CME as observed by the SOHO/LASCO C2 coronagraph. Using sequences of SOHO/LASCO C2 images, we estimate the kink propagation in the coronal rays during their interaction with the corresponding CMEs ranging from 180 to 920 km s⁻¹ within the interval of radial distances from 3 R _⊙ to 6 R _⊙. We conclude that all studied events do not correspond to the expected pattern of shock wave propagation in the corona. Coronal ray deflection can be interpreted as the influence of the magnetic field of a moving flux rope within the CME. The motion of a large-scale flux rope away from the Sun creates changes in the structure of surrounding field lines, which are similar to the kink propagation along coronal rays. The retardation of the potential should be taken into account since the flux rope moves at a high speed, comparable with the Alfvén speed.     

Relation Between the 3D-Geometry of the Coronal Wave and Associated CME During the 26 April 2008 Event

We study the kinematical characteristics and 3D geometry of a large-scale coronal wave that occurred in association with the 26 April 2008 flare-CME event. The wave was observed with the EUVI instruments aboard both STEREO spacecraft (STEREO-A and STEREO-B) with a mean speed of ∼ 240 km s⁻¹. The wave is more pronounced in the eastern propagation direction, and is thus, better observable in STEREO-B images. From STEREO-B observations we derive two separate initiation centers for the wave, and their locations fit with the coronal dimming regions. Assuming a simple geometry of the wave we reconstruct its 3D nature from combined STEREO-A and STEREO-B observations. We find that the wave structure is asymmetric with an inclination toward East. The associated CME has a deprojected speed of ∼ 750±50 km s⁻¹, and it shows a non-radial outward motion toward the East with respect to the underlying source region location. Applying the forward fitting model developed by Thernisien, Howard, and Vourlidas (Astrophys. J. 652, 763, 2006), we derive the CME flux rope position on the solar surface to be close to the dimming regions. We conclude that the expanding flanks of the CME most likely drive and shape the coronal wave.     

The Magnetic Field at the Inner Boundary of the Heliosphere Around Solar Minimum

STEREO A and B observations of the radial magnetic field between 1 January 2007 and 31 October 2008 show significant evidence that in the heliosphere, the ambient radial magnetic field component with any dynamic effects removed is uniformly distributed. Based on this monopolar nature of the ambient heliospheric field we find that the surface beyond which the magnetic fields are in the monopolar configuration must be spherical, and this spherical surface can be defined as the inner boundary of the heliosphere that separates the monopole-dominated heliospheric magnetic field from the multipole-dominated coronal magnetic field. By using the radial variation of the coronal helmet streamers belts and the horizontal current – current sheet – source surface model we find that the spherical inner boundary of the heliosphere should be located around 14 solar radii near solar minimum phase.     

Heliospheric Observations of STEREO-Directed Coronal Mass Ejections in 2008?–?2010: Lessons for Future Observations of Earth-Directed CMEs

We present a study of coronal mass ejections (CMEs) which impacted one of the STEREO spacecraft between January 2008 and early 2010. We focus our study on 20 CMEs which were observed remotely by the Heliospheric Imagers (HIs) onboard the other STEREO spacecraft up to large heliocentric distances. We compare the predictions of the Fixed-?? and Harmonic Mean (HM) fitting methods, which only differ by the assumed geometry of the CME. It is possible to use these techniques to determine from remote-sensing observations the CME direction of propagation, arrival time and final speed which are compared to in-situ measurements. We find evidence that for large viewing angles, the HM fitting method predicts the CME direction better. However, this may be due to the fact that only wide CMEs can be successfully observed when the CME propagates more than 100^° from the observing spacecraft. Overall eight CMEs, originating from behind the limb as seen by one of the STEREO spacecraft can be tracked and their arrival time at the other STEREO spacecraft can be successfully predicted. This includes CMEs, such as the events on 4 December 2009 and 9 April 2010, which were viewed 130^° away from their direction of propagation. Therefore, we predict that some Earth-directed CMEs will be observed by the HIs until early 2013, when the separation between Earth and one of the STEREO spacecraft will be similar to the separation of the two STEREO spacecraft in 2009??C?2010.     

Coronal Mass Ejections,Magnetic Fields,and the Green Corona in Cycle 23

We study a time – latitudinal distribution of CMEs observed by the SOHO spacecraft, their projected speeds and associated magnetic fields, as well as the north – south (N – S) asymmetry of solar surface magnetic fields, and the coronal green line intensities. We have found that (a) there exists an intricate relation between the average projected velocity of CMEs and the mean value of large-scale magnetic fields; (b) there exists a pronounced N – S asymmetry in both the distribution and the number of CMEs; (c) this asymmetry is in favor of the northern hemisphere at the beginning of the cycle, and of the southern hemisphere from 2001 onward, being, in fact, (d) closely related with the N – S asymmetry in the distribution of large-scale magnetic fields and the coronal green line intensities.     

Discovery in 1960 of the Flare Nimbus Phenomenon and Changes with Time in Its Interpretation

During the International Geophysical Year (IGY, 1957/1958) Dunsink Observatory near Dublin in Ireland was a World Data Centre for Solar Activity. In this circumstance, Hα Lyot Heliograph records secured on a daily basis between 07:00 – 14:00 UT at the Cape of Good Hope (then an integral link in a network of similar instruments contributing during the IGY to global monitoring of solar chromospheric activity) were routinely sent to Dunsink for analysis and dissemination. The investigations carried out at Dunsink on these data resulted, inter alia, in the discovery of the Flare Nimbus phenomenon. The nimbus comprises a dark expanding halo seen in the plage regions around major flares at, or within a few minutes of, the time of flare maximum intensity in Hα light. It reaches its greatest extent about 30 minutes after flare maximum. Its maximum dimensions (estimated visually) lie in the range 2 – 4×10⁵ km and its duration ranges from ∼ 1 – 2 hours. Within the nimbus the striation pattern is either completely destroyed or loses its pre-flare configuration. An account of this phenomenon and its interpretation appeared primarily, although not exclusively, in the locally produced Dunsink Observatory Publications which are not now easily accessible to the world community of solar researchers. Also, at around the time when the nimbus was first identified and recorded in Lyot Heliograph data at several observatories, techniques in solar physics shifted towards high resolution narrow field observations. Under these conditions no further examples of the nimbus were recorded and the subject has remained dormant over several decades. The present paper again places the scientific results obtained with regard to the nimbus in the public domain, together with an account of the evolution within the scientific community of an explanation of this phenomenon. It is suggested here for the first time, in the light of present day data concerning coronal mass ejections (CMEs) and coronal dimming, that the nimbus provides a signature of CME-related reorganization of the magnetic field in the chromosphere (such that the transverse magnetic field component decreases and transforms into the line of sight component as the vector field stretches out). Coronal dimming provides a complementary signature of CME-related mass depletion in the corona.     

Relationship between the Parameters of Coronal Holes and High-Speed Solar Wind Streams over an Activity Cycle

The comparison of the brightness and area of coronal holes (CH) to the solar wind speed, which was started by Obridko et al. (Solar Phys. 260, 191, 2009a) has been continued. While the previous work was dealing with a relatively short time interval 2000 – 2006, here we have analyzed the data on coronal holes observed in the Sun throughout activity Cycle 23. A catalog of equatorial coronal holes has been compiled, and their brightness and area variations during the cycle have been analyzed. It is shown that CH is not merely an undisturbed zone between the active regions. The corona heating mechanism in CH seems to be essentially the same as in the regions of higher activity. The reduced brightness is the result of a specific structure with the magnetic field being quasi-radial at as low an altitude as 1.1R _⊙ or a bit higher. The plasma outflow decreases the measure of emission from CH. With an adequate choice of the photometric boundaries, the CH area and brightness indices display a fairly high correlation (0.6 – 0.8) with the solar wind velocity throughout the cycle, except for two years, which deviate dramatically – 2001 and 2007, i.e., the maximum and the minimum of the cycle. The mean brightness of the darkest part of CH, where the field lines are nearly radial at low altitudes, is of the order of 18 – 20% of the solar brightness, while the brightness of the other parts of the CH is 30 – 40%. The solar wind streams originate at the base of the coronal hole, which acts as an ejecting nozzle. The solar wind parameters in CH are determined at the level where the field lines are radial.     

Interplanetary Scintillation Observations of Stream Interaction Regions in the Solar Wind

We present a summary of results from ten years of interplanetary scintillation (IPS) observations of stream interaction regions (SIRs) in the solar wind. Previous studies had shown that SIRs were characterized by intermediate-velocity solar wind and – in the case of compressive interactions – higher levels of scintillation. In this study we considered all cases of intermediate velocities in IPS observations from the European Incoherent SCATter (EISCAT) radar facility made at low- and mid-heliographic latitudes between 1994 and 2003. After dismissing intermediate-velocity observations which were associated with solar-wind transients (such as coronal mass ejections) we found that the remaining cases of intermediate velocities lay above coronal structures where stream interaction would be expected. An improved ballistic mapping method (compared to that used in earlier EISCAT studies of interaction regions) was used to identify the regions of raypath in IPS observations which might be expected to include interaction regions and to project these regions out to the distances of in-situ observations. The early stages of developing compression regions, consistent with their development on the leading edges of compressive stream interaction regions, were clearly detected as close to the Sun as 30 R _⊙, and further ballistic projection out to the distances of in-situ observations clearly associated these developing structures with density and velocity features characteristic of developed interaction regions in in-situ data in the cases when such data were available. The same approach was applied to study non-compressive interaction regions (shear layers) between solar-wind streams of different velocities where the stream interface lay at near-constant latitude and the results compared with those from compressive interaction regions. The results confirm that intermediate velocities seen in IPS observations above stream boundaries may arise from either detection of intermediate-velocity flow in compression regions, or from non-compressive shear layers. The variation in velocity about the mean determined from IPS measurements (representing the spread in velocity across that part of the raypath associated with the interaction region in the analysis) was comparable in compressive and non-compressive regions – a potentially interesting result which may contain important information on the geometry of developing SIRs. It is clear from these results that compressive and non-compressive interaction regions belong to the same class of stream – stream interaction, with the dominant mode determined by the latitudinal gradient of the stream interface. Finally, we discuss the results from this survey in the light of new data from the Heliospheric Imagers (HI) on the Solar TErrestrial RElations Observatory (STEREO) spacecraft and other instruments, and suggest possible directions for further work.     

A Study of Surges: II. On the Relationship between Chromospheric Surges and Coronal Mass Ejections

Liu et al. (Astrophys. J. 628, 1056, 2005a) described one surge – coronal mass ejection (CME) event showing a close relationship between solar chromospheric surge ejection and CME that had not been noted before. In this work, large Hα surges (>72 Mm, or 100 arcsec) are studied. Eight of these were associated with CMEs. According to their distinct morphological features, Hα surges can be classified into three types: jetlike, diffuse, and closed loop. It was found that all of the jetlike surges were associated with jetlike CMEs (with angular widths ≤30 degrees); the diffuse surges were all associated with wide-angle CMEs (e.g., halo); the closed-loop surges were not associated with CMEs. The exclusive relation between Hα surges and CMEs indicates difference in magnetic field configurations. The jetlike surges and related narrow CMEs propagate along coronal fields that are originally open. The unusual transverse mass motions in the diffuse surges are suggested to be due to magnetic reconnections in the corona that produce wide-angle CMEs. For the closed-loop surges, their paths are just outlining stable closed loops close to the solar surface. Thus no CMEs are associated with them.     

2D Feature Recognition And 3d Reconstruction In Solar Euv Images

EUV images show the solar corona in a typical temperature range of T >rsim 1 MK, which encompasses the most common coronal structures: loops, filaments, and other magnetic structures in active regions, the quiet Sun, and coronal holes. Quantitative analysis increasingly demands automated 2D feature recognition and 3D reconstruction, in order to localize, track, and monitor the evolution of such coronal structures. We discuss numerical tools that “fingerprint” curvi-linear 1D features (e.g., loops and filaments). We discuss existing finger-printing algorithms, such as the brightness-gradient method, the oriented-connectivity method, stereoscopic methods, time-differencing, and space–time feature recognition. We discuss improved 2D feature recognition and 3D reconstruction techniques that make use of additional a priori constraints, using guidance from magnetic field extrapolations, curvature radii constraints, and acceleration and velocity constraints in time-dependent image sequences. Applications of these algorithms aid the analysis of SOHO/EIT, TRACE, and STEREO/SECCHI data, such as disentangling, 3D reconstruction, and hydrodynamic modeling of coronal loops, postflare loops, filaments, prominences, and 3D reconstruction of the coronal magnetic field in general.     

Damped Oscillations of Coronal Loops

A mechanism of damped oscillations of a coronal loop is investigated. The loop is treated as a thin toroidal flux rope with two stationary photospheric footpoints, carrying both toroidal and poloidal currents. The forces and the flux-rope dynamics are described within the framework of ideal magnetohydrodynamics (MHD). The main features of the theory are the following: i) Oscillatory motions are determined by the Lorentz force that acts on curved current-carrying plasma structures and ii) damping is caused by drag that provides the momentum coupling between the flux rope and the ambient coronal plasma. The oscillation is restricted to the vertical plane of the flux rope. The initial equilibrium flux rope is set into oscillation by a pulse of upflow of the ambient plasma. The theory is applied to two events of oscillating loops observed by the Transition Region and Coronal Explorer (TRACE). It is shown that the Lorentz force and drag with a reasonable value of the coupling coefficient (c _d ) and without anomalous dissipation are able to accurately account for the observed damped oscillations. The analysis shows that the variations in the observed intensity can be explained by the minor radial expansion and contraction. For the two events, the values of the drag coefficient consistent with the observed damping times are in the range c _d ≈2 – 5, with specific values being dependent on parameters such as the loop density, ambient magnetic field, and the loop geometry. This range is consistent with a previous MHD simulation study and with values used to reproduce the observed trajectories of coronal mass ejections (CMEs).     

Kinematic Evolution of a Slow CME in Corona Viewed by STEREO-B on 8 October 2007

We studied the kinematic evolution of the 8 October 2007 CME in the corona based on observations from Sun – Earth Connection Coronal and Heliospheric Investigation (SECCHI) onboard satellite B of Solar TErrestrial RElations Observatory (STEREO). The observational results show that this CME obviously deflected to a lower latitude region of about 30° at the beginning. After this, the CME propagated radially. We also analyze the influence of the background magnetic field on the deflection of this CME. We find that the deflection of this CME at an early stage may be caused by a nonuniform distribution of the background magnetic-field energy density and that the CME tended to propagate to the region with lower magnetic-energy density. In addition, we found that the velocity profile of this gradual CME shows multiphased evolution during its propagation in the COR1-B FOV. The CME velocity first remained constant: 23.1 km s⁻¹. Then it accelerated continuously with a positive acceleration of ≈7.6 m s⁻².     

Grad–Shafranov Reconstruction of Magnetic Clouds: Overview and Improvements

The Grad–Shafranov reconstruction is a method of estimating the orientation (invariant axis) and cross section of magnetic flux ropes using the data from a single spacecraft. It can be applied to various magnetic structures such as magnetic clouds (MCs) and flux ropes embedded in the magnetopause and in the solar wind. We develop a number of improvements of this technique and show some examples of the reconstruction procedure of interplanetary coronal mass ejections (ICMEs) observed at 1 AU by the STEREO, Wind, and ACE spacecraft during the minimum following Solar Cycle 23. The analysis is conducted not only for ideal localized ICME events but also for non-trivial cases of magnetic clouds in fast solar wind. The Grad–Shafranov reconstruction gives reasonable results for the sample events, although it possesses certain limitations, which need to be taken into account during the interpretation of the model results.     

Intensity and Magnetic Field Distribution of Sunspots

We study the relationship between the brightness (I) and magnetic field (B) distributions of sunspots using 272 samples observed at the San Fernando Observatory and the National Solar Observatory, Kitt Peak, whose characteristics varied widely. We find that the I – B relationship has a quadratic form for the spots with magnetic field less than about 2000 G. The slope of the linear part of the I – B curve varies by about a factor of three for different types of spots. In general the slope increases as the spot approaches disk center. The I – B slope does not have a clear dependency on the spot size but the lower limit appears to increase as a function of the ratio of umbra and penumbra area. The I – B slope changes as a function of age of the sunspots. We discuss various sunspot models using these results.