A statistical analysis of the optical dayside open/closed field line boundary

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2011ja016984, 2012 A statistical analysis of the optical dayside open/closed field line boundary M. G. Johnsen 1 and D. A. Lorentzen 2 Received 6 July 2011; revised 22 November 2011; accepted 19 December 2011; published 28 February [1] In the cusp, the equatorward boundary of the auroral 6300 Å[OI] red line emission can be used as a proxy for the dayside open/closed field line boundary (OCB). In this paper we perform a statistical study based on ground-based optical data from Longyearbyen, Svalbard, covering a period of 15 auroral seasons from 1995 to 2009 (northern hemisphere, winter conditions), concentrating on the time period close to magnetic noon in the dayside part of the auroral oval. Acquiring the OCB latitude from these data, we have compared it to a variety of solar wind coupling functions and geomagnetic indices. The OCB is, according to our findings, located at 75.4 degrees MLAT. The diurnal movement of the OCB latitude follows the poleward edge of the Feldstein auroral oval, confirming the notion that its poleward part is on open field lines. A causal relationship between the latitudinal location of the OCB and the solar cycle is demonstrated. A dependency is clearly seen between the negative Bz component of the interplanetary magnetic field and the OCB latitude. However, when plotting the OCB latitude as function of coupling functions where the solar wind velocity also is taken into account, better correlations are obtained. We are in this work not able to find previously used coupling functions that clearly distinguishes themselves from the others with respect to correlation coefficients. Good correlations with geomagnetic indices such as AE, PC and SYM/H, suggests that both processes at the magnetopause and in the magnetotail are needed in order to best understand the latitudinal location of the dayside OCB. Citation: Johnsen, M. G., and D. A. Lorentzen (2012), A statistical analysis of the optical dayside open/closed field line boundary, J. Geophys. Res., 117,, doi: /2011ja Introduction [2] The cusp is where the solar wind plasma has direct access to the ionosphere allowing for direct energy transfer via magnetopause reconnection. The interaction between the geomagnetic field and the interplanetary medium modulates the location of the cusp, and this has been a subject of research for more than 30 years. There is a broad consensus that the interplanetary magnetic field (IMF) B z component (geocentric solar magnetospheric system (GSM) coordinates) plays an important role in the latitudinal determination of the cusp location, and that the B y component is important for the longitudinal location. Newell et al. [2006, 2007a] examined different coupling functions between the solar wind and the cusp latitude in pursuit of the most efficient one. Many studies have applied statistics to determine the location of the cusp, mainly by means of space-borne instrumentation [Carbary and Meng, 1986; Newell et al., 1989; Zhou et al., 2000; Palmroth et al., 2001; Asai et al., 1 Tromsø Geophysical Observatory, Faculty of Science and Technology, University of Tromsø, Tromsø, Norway. 2 Geophysics Department, University Centre in Svalbard, Longyearbyen, Norway. Copyright 2012 by the American Geophysical Union /12/2011JA ; Newell et al., 2006; Prölss, 2006; Newell et al., 2007a, 2007b]. Ground-based statistical studies of the cusp latitude covering long time series are sparse. Yeoman et al. [2002] used SuperDARN data to study the HF-radar cusp latitudinal location and movement for a data set covering December 1999 and January This is, to our knowledge, the most extensive ground-based study of this type. Owing to its high geographic latitude and relatively mild climate, the archipelago of Svalbard has a unique location for studying the dayside, cusp-related, aurora. In Figure 1 a map indicating the location of Svalbard is shown. Altitude Adjusted Corrected Geomagnetic (AACGM) [Baker and Wing, 1989] latitudes, as of December 2005, are indicated as well as geographic coordinates. The Feldstein auroral oval [Holzworth and Meng, 1975] corresponding to moderate conditions (Q = 3) at UT is indicated. In this study we apply meridian scanning photometer (MSP) data from Svalbard, covering 15 auroral seasons corresponding to two solar minima and one solar maximum, in order to study cusp behavior in relation to the IMF and solar wind - magnetosphere coupling. The blue, dashed line in Figure 1 indicates the MSP field of view down to 20 degrees above the horizon and with an assumed height of 268 km. The equatorward boundary of the 6300 Å[OI] red line cusp aurora has been used as a proxy for the open/closed field line boundary (OCB), and hence the equatorward boundary 1of12

2 Figure 1. Map showing the location of Svalbard and MSP field of view. AACGM latitudes are indicated as well as geographical coordinates. of the cusp [Lorentzen et al., 1996]. We have performed a statistical analysis of the dayside OCB latitude as acquired from the MSP over a 15-year period. This represents northern hemisphere, winter conditions. In Svalbard, dayside aurora may be studied from late November to late January. The data set is compared to solar wind coupling functions and geomagnetic indices. We report results that are in accordance with earlier studies. Yearly averaged cusp latitudes are also compared to sunspot numbers, and the result is presented here. 2. Instrumentation and Data 2.1. Meridian Scanning Photometer [3] The MSP used for this study is located close to Longyearbyen (observatory designator: LYR), Svalbard. The MSP, which is owned by the University Centre in Svalbard, is a 5-channel photometer consisting of a rotating mirror that scans from north to south along the geomagnetic meridian, narrow band tilting filters and photo multiplier tubes. The tilting filter mechanism provides a method to subtract the background from the peak emissions. The data, with background subtracted, has an angular resolution of 1 degree and a time resolution of 16 s. The MSP has been taking data from the Auroral Station outside Longyearbyen (GEO: 78.2 N, 15.8 E, AACGM: 75.3 N, E) since it was moved there from Alaska in During the fall of 2007 the MSP was relocated from the Auroral Station to new and modern facilities at the Kjell Henriksen Observatory (KHO) (78.1 N, 16.0 E, AACGM: 75.2 N, E). During the relocation the scanning direction was updated according to the direction of geomagnetic meridian in 2007 (31 degrees west of geographical north), rather than the direction toward Ny Ålesund (43 degrees west of geographical north) which was used at the old station. In Figure 1 the post 2007 scanning direction is shown. Figure 2 shows a keogram of MSP data, for a typical day around magnetic noon (UT ), for the 6300 Å[OI] red line emission. The keogram gives the auroral intensity as function of time and scan angle. The intensity is given in Rayleighs according to the color bar on the right side Sunspot Numbers, Solar Wind Data and Geomagnetic Indices [4] In order to carry out the statistical analysis of the MSP data, information on geomagnetic, solar- and solar wind activity needs to be included. The monthly sunspot numbers were obtained from the Solar Influences Data Analysis Center (SIDC) in Belgium ( June 2011). The solar wind and geomagnetic index data were obtained from the Goddard Space Flight Center OmniWeb Interface (High resolution (1-min, 5-min) OMNI, gsfc.nasa.gov/ow_min.html, June 2011). The OMNI data set used in this study includes 5-min averages of IMF and solar wind velocity components in GSM coordinates, solar wind dynamic pressure, proton density, E-field from the IMP-8, 2of12

3 Figure 2. Typical MSP Keogram for the nm [OI] red line. Scan angle is along the y axis, time along the x axis and light intensity according to the color bar to the right. The black on white curve represents the open/closed field line boundary. Geotail. Wind and ACE spacecrafts as well as the PCN index [Troshichev et al., 2000], the ring current index SYM/H (which is comparable to the Dst index on a one to one basis) and the auroral electrojet indices AE, AL and AU. The solar wind parameters have been time shifted from the measuring spacecraft to the magnetosphere bow shock nose, using techniques described by King and Papitashvili [2005] and on the OMNI-data Web page ( gsfc.nasa.gov/html/omni_min_data.html#6, June 2011). [7] The MSP scan angle is in an instrument centered reference frame, and as such, does not give an absolute measure on the location of the OCB. We therefore transform the scan angle of the obtained OCB into AACGM latitude. To do this we use the mapping height functions of Johnsen and Lorentzen [2012]: ð1þ H ¼ 0:617 e0:0303z þ 322:0; z > 98 ð2þ and 3. Data Processing and Results [5] The time interval chosen for this study was hours magnetic local time (MLT). LYR magnetic noon in Longyearbyen was UT in 1995 and UT in The MSP data set was evaluated manually in order to remove all days of unusable data caused by cloudy weather or instrument malfunction. This resulted in a total of 155 days, spanning the auroral seasons 1994/1995 to 2008/2009, corresponding to an average of 10.3 days of good data per season. Figure 3 summarizes the statistics of the MSP data. Figure 3a shows the number of days of data per season used in this study, while Figure 3b shows the number of data points per season. As can be seen, the two panels are almost identical, the small differences are due to the instrument being turned off parts of some days in the beginning and end of each season owing to sunrise. The gap in the data for seasons 05/06 and 06/07 is due to a major instrument malfunction. [6] In order to find the OCB, the equatorward edge of the aurora must be identified. Here we define this edge as the maximum in the gradient of the intensity along the MSP scan. A semi automatic procedure was developed to locate the OCB in the whole MSP data set, and the results were examined manually in order to remove noisy data and errors or other software dependent difficulties. An example of an OCB determination is shown in Figure 2 (black on white curve). H ¼ 763:6 e 0:0738z þ 262:8; z 98 where z is the scan angle, and where z = 0, 98, 180 corresponds to the northern horizon, magnetic zenith and the southern horizon, respectively. Then, by means of trigonometry, we calculate the geographic latitude and longitude and the distance from the center of the Earth. The geographic coordinates are further transformed to AACGM coordinates. Figure 4 shows a histogram of the AACGM latitudinal distribution of the OCB for the whole data set. The vertical line indicates the mean OCB latitude (75.4 ). Owing to the fact that we know very little about the vertical volume emission rate profiles of the cusp aurora, equations (1) and (2) are in reality only valid for a pre defined reference aurora constructed upon parameters considered to be typical for the cusp. The implication of this is that the further the OCB is determined away from magnetic zenith the greater uncertainty in the latitudinal mapping we will get. Taking a large variety of auroral shapes into account, Johnsen and Lorentzen [2012] estimated the uncertainty introduced by the mapping height functions defined for the reference aurora. They found the uncertainty in the interval 67 to 130 degrees scan angle (corresponding to magnetic latitudes of 73.2 to 77) or degrees off magnetic zenith, to be within one degree. See their work for a thorough discussion on mapping heights, errors and the use of MSP data for cusp auroral studies. Johnsen et al. 3 of 12

4 Figure 3. (a) Number of days and (b) data points per auroral season with usable data. [2012] shows that the OCB as obtained from the energetic particle instrumentation onboard the NOAA-16 satellite fits well within the calculated uncertainties of the MSP method. [8] Owing to the fact that the earth is rotating under the auroral oval, Svalbard, which is situated inside the polar cap most of the time, will be closest to the oval near magnetic noon. For a static oval, the aurora would from the ground on Svalbard, appear to be expanding northward in the dawn sector and retract southward in the dusk sector. As a time interval of 6 hours per day, is rather large, it is interesting to check for this diurnal effects in our data, and this was examined by taking the mean of the OCB over half hour Figure 4. Histogram showing the OCB latitudinal distribution for the whole data set. Bin size is 0.5 degrees. 4of12

5 Table 1. Correlation Coefficients Between Sunspot Number and Median OCB Latitude Lag (Auroral Season) Correlation Coefficient Figure 5. The mean OCB AACGM latitude as function of universal time. Error-bars represents standard deviation. The solid curves represents the theoretical Feldstein auroral oval (Q = 3) and the vertical line represent UT which is approximately magnetic noon in Longyearbyen. intervals throughout the whole data set. The result can be seen in Figure 5. We have included the theoretical Feldstein auroral oval (Q = 3) for reference [Holzworth and Meng, 1975]. [9] In order to check for variation of the OCB location over the solar cycle, the median OCB latitude was calculated per auroral season. This was further compared to the sunspot number. As the day-side auroral season, i.e. when the solar elevation is sufficiently low in Longyearbyen, is from late November to late January, the mean sunspot number for December and January was used for comparison. The resulting median OCB latitudes and sunspot numbers as function of auroral season, can be seen in Figure 6. The two curves were cross correlated, and the resulting correlation coefficients are presented in Table 1. The best correlation is Figure 6. Median OCB AACGM latitude as function of auroral season (dots and left axis), the error bars represent the standard deviation. Corresponding sunspot numbers averaged over December and January (solid line and right axis). observed to be at 2 years (the results are similar, but poorer if we use mean instead of the median OCB latitude). [10] In order to compare the optical OCB to the 5 minute high resolution OMNI data, the OCB (as obtained from the 16 second MSP data) temporal resolution was reduced by averaging over the same times as in the OMNI data. 5 minute resolution OMNI data was chosen, rather than 1 minute, to reduce ambiguities caused by the transport time from the magnetospheric bow-shock to the ionosphere, and to filter out rapid and noise like changes in both the solar wind and MSP data. The part of the OMNI data set that came from spacecraft measurements was time delayed further by 10 min, in order to take the propagation time from the bow shock, through the magnetosheath and down into the ionosphere into account. Because of gaps in the OMNI data, the amount of usable data was reduced further: The high resolution OMNI data set is only available from the 1st of January 1995, and 5 days of good 1994 MSP data have, thus, been discarded in this work. [11] For each of the used OMNI data parameters, appropriate bin sizes were chosen and the corresponding OCB magnetic latitudes were averaged for each bin. [12] In Figure 7a, a scatterplot showing all the OCB latitudes in the data set plotted as function of the IMF Bz component is presented. In Figure 7b the data seen in Figure 7a has been averaged over 2 nt bins and the averages have been plotted with their standard deviation. The curve in Figure 7c shows how many data points contributed to each average. Averages were calculated only in bins with more than 20 points. A linear fit was performed on OCB latitude as function of Bz (Figure 7a) for southward IMF, and the resulting line is indicated as the black, solid line (y = A + Bx) in Figures 7a and 7b. The fitting parameters (A and B) are printed in the lower right corner of Figure 7a together with the correlation coefficient (r). The other lines in Figure 7b are the results of similar fits from the works of Prölss [2006] (red), Newell et al. [1989] (green), Pitout et al. [2006] (turquoise) and Zhou et al. [2000] (purple). [13] In earlier studies, a wide range of solar wind coupling functions have been examined in relation to the OCB latitude. In Figure 8 scatterplots of our obtained OCB latitudes and the half-wave rectifier (E HW = B z V SW ), for B z < 0 and E HW = 0, for B z > 0, the Kan-Lee Electric field (E KL = B T V SW sin 2 ( q 2 )), the intermediate WAV (Wygant, Akasofu, Vasiliunas) (E WAV = B T V SW sin 4 ( q 2 )) and the Newell coupling function ( df MP dt = B 2/3 T V 4/3 SW sin 8/3 ( q 2 )) are presented, where the IMF clock angle q = arctan( B y B z ). Least squares linear fits were 5of12

6 Figure 7. (a) Scatterplot showing the OCB latitude as function of IMF Bz with linear fit to the data indicated as solid black line. Blue and red colors indicate southward and northward pointing IMF, respectively. (b) 2 nt binned means of the OCB latitude as function of IMF Bz. The error-bars indicates the standard deviation of the binned average latitudes (dots) the black line indicates a linear fit to the binned averages, the colored lines represents similar results obtained by other (see text for references). (c) The number of points available in the calculation of the averages in Figure 7b. Only averages with more than 20 points were considered. performed (only for negative values for the half-wave rectifier) and the resulting fitting parameters and correlation coefficients are printed inside each plot. As discussed by Newell et al. [2007a] the correlation with sine of the OCB latitude generally proves better, and we have therefore included it here. Indeed, a small, but hardly significant, improvement of the correlations is seen. [14] In Figure 9 the OCB latitude as function of three different geomagnetic indices is shown. In the left column scatterplots of the whole data set are shown, in the middle column the binned averages are shown and in the right column the number of points contributing in each bin are shown. The top, middle and bottom rows shows the AE [Davis and Sugiura, 1966], PCN [Troshichev and Andrezen, 1985; Troshichev et al., 1988] and SYM/H (Dst) [Wanliss and Showalter, 2006, and references therein] indices, respectively. Linear fits have been performed on the data and the fitting parameters (A, B and r) are written in top of each plot. 4. Discussion [15] The number of statistical studies of the cusp location with respect to solar wind or geomagnetic parameters is rather large. However, the previous studies are based on satellite data with the exception of one using HF radars [Yeoman et al., 2002]. Low earth orbit satellites only traverses the cusps a few times per orbit and then only gets a snapshot of it, thus it is impossible to study the time dependent morphology of the cusp from such satellites. Ground-based optics are therefore powerful tools with respect to cusp studies; from a fixed location one do not have to consider aspects like dipole tilt, hemispherical asymmetries and local time sector effects that may introduce ambiguities to the statistical results. However, there are challenges with this method as well; from the ground, the cusp will only be accessible optically under clear tropospheric conditions, only for certain hours during the day owing to the Earth s rotation and only when it is sufficiently dark (late November to late January for Svalbard). A low earth orbit satellite for instance, may encounter the cusp in both hemispheres resulting in two measurements approximately every 90 min throughout one whole day. Also when obtaining the optical dayside OCB from a single ground station there is a height ambiguity that will introduce an uncertainty in the determination of the horizontal location [Johnsen and Lorentzen, 2012]. It is certain that this uncertainty contributes to the spread of data points as seen in the comparisons between the OMNI data and the obtained OCB latitudes in this study. However, as shown by Johnsen and Lorentzen [2012], this uncertainty is much less than the variations observed here. [16] Figure 4 shows the distribution of the OCB latitude independently of time, and as can be seen, the majority of the observed OCB latitudes are between 70 and 80 MLAT. The vertical line shows the average OCB latitude for the whole data set (75.4 ); thus, half of the time the cusp aurora (which is north of the OCB) will be located north of Longyearbyen. [17] From Figure 5 we see that the average latitude of the OCB moves northward with about one degree from UT to UT and then about one degree southwards from UT to UT This is similar to what the theoretical Feldstein oval does. We also observe, from the standard deviations for each time interval, that the spread in the data, caused by other effects than the earth rotation, is much bigger than the diurnal effect. We therefore do not need to be concerned about the diurnal effect affecting our results to a great extent. The average OCB latitude is within one degree of the poleward boundary of the Feldstein oval. This is in accordance with the idea that the cusp constitutes the poleward part of the auroral oval [Murphree et al., 1990] and that the oval is dominated by harder precipitation from the central plasma sheet (CPS) equatorward of the OCB. It is probably this part of the oval which in early studies has been recognized as the dayside oval [e.g., Akasofu, 1972]. [18] In Figure 6 we compare the average OCB latitude - as function of auroral season - to the average sunspot numbers for the same months. A visual comparison of the two curves 6of12

7 Figure 8. Scatterplots of the obtained OCB latitude and the (top left) half-wave rectifier, (top right) Kan-Lee Electric field, (bottom left) WAV electric field and (bottom right) the Newell intermediate coupling function. Results of linear fits are indicated inside each plot. shows similarities, and the distance between the maxima of the OCB latitudes is 11 years. The season of the lowest average OCB latitude lags the sunspot maximum by two years. The result of the cross correlation seen in Table 1, confirms our visual observations, and the correlation between the two curves is fairly good for the 2 year lag. As reported by Hathaway and Wilson [2006] the interplanetary component of the aa (aa I ) index reached its maximum in October just one to two months before the auroral season where we observe the OCB latitude to be furthest south. Feynman [1982] discusses the interpretation of the aa I index, and she attributes it to solar wind source structures on the solar surface which are long-lived compared to the solar rotation period. Such long-lived structures may be coronal holes that are the source of the high speed solar wind. As will be seen below, the solar wind velocity contributes to the reconnection rate on the magnetopause and thus this may be interpreted as the reason for the solar cycle dependence on the average OCB latitude. However, the results that are presented here needs further studying in order to ascertain the relationship between the OCB latitude and the aa I index or any other solar cycle variations. In order to find any clear relationships between the solar cycle and the OCB latitude, much longer time series and a greater statistical basis is needed. [19] As can be seen in Figure 7, the latitude of the OCB behaves in accordance to expectations with respect to the IMF Bz component. For a northward IMF, which favors lobe reconnection, the latitude changes little with the magnitude of the solar wind magnetic field. However, for southward IMF, which favors reconnection on the sub-solar magnetopause, reconnection erodes the Earth s magnetic field bringing the x-line closer toward the Earth and consequently the OCB in polar regions equatorward. The black line (in Figure 7b) is a linear fit to our OCB latitudes when IMF Bz is negative. As can be seen, it is in fairly good accordance with the satellite-based results of Prölss [2006] (red), Newell et al. [1989] (green) and [Pitout et al., 2006] 7of12

8 Figure 9. (left) Scatterplots of the obtained OCB latitude and the AE, PCN and SYM/H indices. (middle) The OCB latitude has been averaged over appropriate bin sizes. (right) The number of points in each bin is indicated. Results of linear fits are indicated inside each plot. (turquoise). We also see that the results from high altitude ( Earth radii) [Zhou et al., 2000] (purple) diverges from ours. Still, their fit is relatively parallel to the one obtained by us. This may be explained by the increased deformation of the Earth dipole field as you approach the magnetopause and how the magnetic field line tracing routines fails to intersect the Earth s surface on the correct latitude. From the above, since we are able to confirm the well known results of previous studies using a different method, we conclude that the ground-based, optical technique we apply, produces reliable and meaningful results. [20] As discussed in detail by Newell et al. [2006] and Newell et al. [2007a] the solar wind velocity and IMF clock angle are also critical parameters for the latitude of the OCB. In Figure 8 we present scatterplots between some of the coupling functions discussed by them and our obtained optical OCB latitude. We generally find that our correlation coefficients are about 0.1 to 0.15 lower than theirs. Unlike 8of12

9 them, we are not able to conclude, based on our results, that any of the coupling functions are better than the others. However, when only considering the cases where IMF Bz is negative (not shown), we get higher correlations and a hint that the df MP dt coupling function is slightly better than the rest (r = 0.71 versus 0.69 on the two other). As pointed out by Asai et al. [2005], when the IMF points northward, the reconnection is taking place poleward of the cusp and hence any flux erosion will bring the reconnection site (and its ionospheric footprint) polewards. As we are taking the equatorward boundary of the cusp aurora as a proxy for the OCB, it will in fact not map to the reconnection site during periods of northward IMF, and thus it is impossible to claim that the location that we find is directly controlled by the rate of magnetopause reconnection during these intervals. Thus, it is also reasonable that we observe an increase in the correlation coefficients when we remove the Bz positive cases. [21] When considering a time interval closer to noon MLT (12.00 MLT 50 min) and restricting the dataset to IMF Bz negative cases, we see an increase in the correlation coefficients for all coupling functions. The half wave rectifier function now has the lowest correlation coefficient (r = 0.72), while the others show higher, but similar correlations (E KL : r = 0.77; E WAV : r = 0.76 and df MP dt : r=0.77). Hence, the df MP dt (Newell) function is now on the same level as the other two coupling functions. The reason for the improvement in correlations is most likely attributed to the substantially decreased cusp width (1 hour 40 min) compared to the cusp width of 6 hours (noon MLT 3 hours) used elsewhere throughout this paper. Narrowing down the time span around noon means that the probability for observing pure auroral emissions on open field lines (cusp aurora) becomes larger. With a wider time span, there is a probability that auroral emissions on closed field lines are included in the data set. Depending on the shape of the auroral oval and the length of the reconnection x-line (which will increase with increasing B T ), this may contribute to the scatter in the obtained OCB latitudes. Another reason may be that if we narrow down the interval of interest, we are also closer to the magnetic noon meridian: Considering the geometry of the Earth s dipole and the definition of the clock angle, we may assume that the coupling functions discussed above looses their validity away from noon [Kan and Lee, 1979]. [22] Nevertheless, from Figure 8 we can conclude that the correlation between the OCB latitude and the coupling functions are better when using the southward IMF Bz component exclusively (Figure 7), and clearly demonstrating the importance of the solar wind speed. [23] Several studies on the cusp location with respect to the IMF Bz component have been performed during the last decade using ultraviolet imagers from satellites [Fuselier et al., 2002; Frey et al., 2003; Zhang et al., 2005]. Fuselier et al. [2002] studied the cusp during northward IMF conditions, and found that the cusp aurora under these conditions is separated poleward from the main auroral oval. Furthermore they used a magnetic field tracing technique to show that their aurora mapped to the high latitude magnetopause indicating lobe reconnection. This is consistent with the type of cusp aurora termed Type 2b by the groundbased, optical community [Sandholt et al., 2002]. Frey et al. [2003] followed up with a similar study for southward IMF conditions. They found that the center of the latitudinal location of the cusp aurora moved southward by 0.45 degrees per unit of decreasing Bz (nt). They compared their result with the result of Newell et al. [1989] and found the latter to have a much steeper slope. The result of Newell et al. [1989] agrees well with our result as shown in Figure 7b (green and black lines). Frey et al. [2003] suggested as an explanation for this difference that they used the center of the aurora for the cusp location while Newell et al. [1989] used the equatorward boundary (as in our study). The difference would then be due to a mixing of the variations of the cusp latitudinal size and motion of its equatorward boundary. We find this to be a reasonable explanation since the cusp latitudinal width is known to vary from less than one to more than five degrees [cf. Carbary and Meng, 1988; Newell et al., 2006; Wing et al., 2001]. In another, similar, study by Zhang et al. [2005], they found that the latitudinal location of the center of the cusp aurora moved by 1.1 degrees per unit Bz (nt), which is twice as steep as in our study. Furthermore, they found that for Bz < 15 nt there is a tendency that the cusp latitude saturates toward extreme values of Bz. Studying our results in Figure 7, there is in fact a similar tendency for Bz values less than 10nT. The OCB does not reach as far south as in their study and is more comparable to the Dipole Model they show in their Figure 5. We do, however, need to emphasize that our observation is based on very few data points, as shown in Figure 7c, which makes it hard to draw any decisive conclusions. A potential problem with the results of Zhang et al. [2005] is that they do not mention if they correct their result with respect to changes of cusp latitude owing to dipole tilt. This might make their results difficult to compare with others. Nevertheless, we make a very interesting finding if we introduce the solar wind speed into their results. Zhang et al. [2005] points out that their observations were made during periods of high solar wind speeds. We interpret this to be speeds that are higher than the average speed of 400 km/s. If we assume that the speed is between 500 and 1000 km/s, we may easily assess their results assuming a half wave rectifier coupling function. This is simply done by dividing the slope of their latitude-bz linear relation by 500 and 1000 km/s. The resulting slope is found to be in the range of to degrees/nt*km/s. Our linear fit of the half wave rectifier (Figure 8, top left), is perfectly within this range. Taking into account the solar wind speed as shown above, we conclude that the results of Zhang et al. [2005] are in good accordance with our own results. [24] The results for the AE and PCN indices (Figure 9) are very similar with respect to the correlation and they are higher than the correlations with solar wind parameters and coupling functions. The PCN index is designed to describe the cross polar cap current/convection, while the AE index is supposed to describe the overall current in the auroral zone. Vennerstrom et al. [1991] did a study where the two indices were compared and he also found that they tend to act equally. However, as pointed out by Kamide and Rostoker [2004], the use of the AE index is problematic; the index has no clear physical interpretation and should, thus, be avoided in scientific work. The PCN index, on the other hand, shows an excellent linear trend with respect to the OCB latitude, and this can be attributed to its clear 9of12

10 relationship to the geo-effective or merging electric field (Kan-Lee Electric field) [Stauning et al., 2008]. [25] As seen in Figure 9 there also seems to be a relationship between the SYM/H index and the OCB latitude. For increasing negative values of the SYM/H index, which is interpreted as increasing current density in the ring current, the OCB seems to move southwards. The physical interpretation of this is simply that an increased ring current will increase Earth s magnetic moment and thus the size of the magnetosphere. In order for the magnetosphere to retain its shape (the constant shape assumption) the total amount of magnetic flux in the tail lobes needs to increase in order to balance the solar wind dynamic pressure, hence the area of the polar cap will increase, moving the OCB southwards [Siscoe, 1979]. This can again be related to the fact that the OCB latitude seems to have a dependence upon the solar cycle as seen in Figure 6 and that the Dst (and thus the SYM/H) [Wanliss and Showalter, 2006] depends on the solar wind electric field. Comparing the slope of the linear fit of the SYM/H index with respect to the OCB latitude, we get a very steep slope compared to the theoretical calculations of Siscoe [1979]. However, the fact that our data set only contains relative low values of the SYM/H index (majority > 50, see Figure 9) leads us to conclude that our results are not directly comparable to his work. [26] As seen in the comparisons between OCB latitude and the OMNI data, there is a large spread around the estimated linear fits performed (Figures 7, 8, and 9). This clearly illustrates the complexity of the determination of the physical processes behind the location of the cusp/ocb. Some part of the spread in the results is due to uncertainties in the method for obtaining the OCB. These are the height ambiguity of the cusp aurora causing an uncertainty in the determination of the horizontal location of the OCB. Another uncertainty is that we have no method of determining exactly if the aurora we are looking at is cusp or not, the width chosen for the cusp (6 hours) will certainly cause an inclusion of obtained OCB locations that are not from cusp aurora but from auroral forms that are on the flanks of the cusp. However, as we may assume that these uncertainties are as arbitrary as the location of the cusp, and therefore are uniformly distributed in latitude, they will only contribute to the spread of the data, rather than causing systematic errors, which is confirmed by the fact that our results are very similar to those of previous studies. [27] Moreover Cowley et al. [1991] described how a combination of the IMF Bx and By will modulate the magnetic local time dependence of the dayside OCB latitude owing to a partial penetration of these components into the magnetosphere [Cowley, 1981a, 1981b]. We have not been able isolate and visualize this effect (owing to the rapid decay of statistical significance when trying), but it cannot be ruled out as a contributing effect to the large scatter seen in our plots. [28] However, the factors mentioned above, are not the main contributing effects causing the large spreads observed. The spreads are also very visible in other studies [e.g., Yeoman et al., 2002; Asai et al., 2005; Pitout et al., 2006; Newell et al., 2006] and we may explain them by several factors. First the asymmetry between reconnection on the magnetopause and in the magnetotail: Continuous reconnection on the magnetopause will make the OCB move equatorward, while unbalanced reconnection events in the tail will cause a contraction of the polar cap and, thus, a poleward movement of the OCB [see, e.g., Moen et al., 2004, references therein]. If we only consider the reconnection electric field on the magnetopause, we are not able to account for the dayside OCB latitude with respect to reconnection events in the magnetotail. Second, the history of the solar wind - magnetosphere interaction: In this study we look at the one to one correlation between different parameters and the OCB latitude. However, the history or integral of previous values of these parameters might have influenced or pre-conditioned the magnetospheric system in such a way that they in conjunction with the current values - they determine the latitude of the OCB. Hence, the amount of current density in the ring current or the absence or initiation of a substorm might cause the deviation from the predictions by coupling functions only reflecting the current magnetopause reconnection rate as the ones discussed above. As an example of the former, it may be mentioned that when successfully modeling the Dst index, a driving term defined by the solar wind electric field and a decay term with a decay rate of 7 hours are taken into account [Temerin and Li, 2002, and references therein]. [29] As we have seen, there are clear relationships between the dayside OCB latitude and a wide range of physical parameters, coupling functions and indices that have different manifestations or physical interpretations. Finding a direct physical mechanism (or mechanisms) responsible for the latitudinal movement and location of the OCB proves challenging. The strong correlation between the PCN index and the latitudinal position of the OCB indicates that convection/hall currents in the polar cap are driven by similar physical mechanisms as the drivers of the OCB location. 5. Conclusion [30] We have performed a statistical study based on ground-based optical data from Longyearbyen, Svalbard, covering a period of 15 auroral seasons from 1995 to 2009, corresponding to northern hemisphere, winter conditions, concentrating on the time period close to magnetic noon in the dayside part of the auroral oval. Acquiring the OCB latitude from these data, we have compared it to a variety of solar wind coupling functions and geomagnetic indices. [31] The study reveal that the average optical OCB is located at 75.4 degrees magnetic latitude, implying that the cusp aurora, which is located immediately north of the OCB, half of the time will be located north of Longyearbyen. [32] The average OCB latitude follows the diurnal movement of the theoretical Feldstein auroral oval of moderate geomagnetic conditions (Q = 3) very well. The average optical OCB is located less than one degree south of the poleward edge of the Feldstein oval, confirming the notion that the poleward part of the oval is on open field lines. [33] Using a cross correlation between the seasonal median of the OCB latitude and the corresponding sunspot number, the study indicates a causal relationship between the latitudinal location of the OCB and the solar cycle. A twoyear lag between the lowest average OCB latitude and the sunspot maximum is observed, and yields a cross correlation coefficient of of 12

11 [34] We have shown how our results for IMF Bz < 0, using data from a ground based instrument, is in very good accordance with earlier studies based on satellite data. The study illustrates that there is a systematic error in determining the cusp latitude owing to the uncertainties in the geomagnetic field models causing the statistical results to deviate more as one moves away from the Earth s surface, rather than the time resolution of the data sets used as suggested by Zhou et al. [2000]. [35] A variation of solar wind coupling functions have been correlated with the obtained OCB latitudes and linear relationships have been obtained. However, we have been unable to clearly identify a coupling function superior to others. The physics determining the OCB latitude has been discussed in the light of its relationship to the solar wind coupling functions and several geomagnetic indices. We claim from our findings, that the pre-conditioning of the magnetosphere from the history of the solar wind - magnetosphere interaction has to be considered in order to successfully make empirical coupling functions or successfully model the cusp/dayside OCB latitude. Last, we have also shown how well the PCN index relates to the mean, dayside OCB latitude, and, thus, how well the OCB latitude reflects the degree of interconnection between the solar wind and the magnetosphere. [36] Acknowledgments. The OMNI data were obtained from the GSFC/SPDF OMNIWeb interface at We thank the ACE MAG and SWEPAM instrument teams and the ACE Science Center for providing the ACE data. We thank Wind MFI and SWE instrument teams, the Geotail CPI and MGF instruments teams and the IMP-8 magnetometer and solar wind plasma instrument teams for providing the Wind, Geotail and IMP-8 data. 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