Inherent Length Scales and Apparent Frequencies of Periodic Solar Wind Number Density Structures Nicholeen Viall 1, Larry Kepko 2 and Harlan Spence 1 1. Center for Space Physics, Boston University 2. Space Science Center, University of New Hampshire, Durham, New Hampshire 2. Space Science Center, University of New Hampshire, Durham, New Hampshire This research was supported through a grant from NSF. We also thank the Wind SWE and GOES magnetic field investigations.

Observations of Magnetospheric Oscillations Two research groups have calculated the occurrence rate of discrete oscillations in the magnetosphere between 1 and 5 mHzTwo research groups have calculated the occurrence rate of discrete oscillations in the magnetosphere between 1 and 5 mHz Ziesolleck and McDiarmid (1995) found occurrence enhancements nearZiesolleck and McDiarmid (1995) found occurrence enhancements near f = 2 and 3 mHz with a smaller enhancement near 4 mHz f = 2 and 3 mHz with a smaller enhancement near 4 mHz Chisham and Orr (1997) found occurrence enhancements nearChisham and Orr (1997) found occurrence enhancements near f = 2.1, 3.1 and 3.9 mHz f = 2.1, 3.1 and 3.9 mHz The multiple, discrete nature suggested a resonance of some kind where the frequencies depend on internal magnetospheric propertiesThe multiple, discrete nature suggested a resonance of some kind where the frequencies depend on internal magnetospheric properties The magnetosphere supports a wide spectrum of oscillationsThe magnetosphere supports a wide spectrum of oscillations Multiple discrete magnetospheric oscillations in the mHz (period ~ minutes) range have been observed throughout the magnetosphereMultiple discrete magnetospheric oscillations in the mHz (period ~ minutes) range have been observed throughout the magnetosphere Of particular interest is the set of multiple discrete frequencies originally observed in event studies by Samson et al. (1992):Of particular interest is the set of multiple discrete frequencies originally observed in event studies by Samson et al. (1992): f = 1.3, 1.9, 2.6, 3.4 mHz

Spectral Estimate Time Series ~1 hour 20 minutes 10 minutes Multiple Discrete Oscillations Driven by Solar Wind Number Density Variations Recent studies show similar oscillations, first in the solar wind number density and then in the magnetosphere [Kepko et al., 2002; Kepko and Spence, 2003; Stephenson and Walker, 2002]. The same spectral peaks observed near f = 0.2, 0.8, and 1.7mHz

Directly Driven Oscillations Kepko et al., 2002, and Kepko and Spence, 2003 showed that in addition to solar wind and magnetosphere time series corresponding well, their spectra exhibit power enhancements at the same frequencies, particularly lower frequenciesKepko et al., 2002, and Kepko and Spence, 2003 showed that in addition to solar wind and magnetosphere time series corresponding well, their spectra exhibit power enhancements at the same frequencies, particularly lower frequencies They showed periodic number density variations = Periodic dynamic pressure variations, so alter the strength of the magnetospheric fieldThey showed periodic number density variations = Periodic dynamic pressure variations, so alter the strength of the magnetospheric field A “forced breathing” of magnetosphere Kepko et al. suggested that, in at least some instances, multiple discrete magnetospheric oscillations are driven externally by periodic number density structures in the solar wind, rather than created through an internal magnetospheric resonance

Frequencies Length Scales High Density Low density Flow speed = 320 km/s L = 400 Mm 400 Mm /320 km/s = 20 minutes (0.8 mHz)  Periodic number density structures remain stationary in the rest frame of the solar wind  Periodicities (frequencies) observed in the time series (spectra) arise from convection of periodic number density structures past the space craft and Earth (Kepko and Spence, 2003)  These observed apparent frequencies can be converted to radial length scales: L = u/f

Motivation and Study 1.We present the results of a rigorous analysis of the relative occurrence rate of statistically significant spectral peaks in the solar wind number density time series 2.We repeat the spectral analysis using radial wave number and present the relative occurrence rate of periodic radial length scales in the solar wind number density 3.We compare our results of apparent solar wind frequencies with our results using the same technique to dayside GOES data  Multiple discrete oscillations have been observed in the magnetosphere  Multiple discrete oscillations have been observed in the solar wind number density  Event studies have shown that the same oscillations sometimes exist both in the solar wind and in the magnetosphere

Data Used and Analysis Technique  Solar wind data 11 years, (11 years ~ solar cycle) 11 years, (11 years ~ solar cycle) SWE (solar wind experiment) instrument on Wind spacecraft SWE (solar wind experiment) instrument on Wind spacecraft ~90 s sampling rate, resample to a common 100 s timebase (42 Mm for the radial wave number analysis ~90 s sampling rate, resample to a common 100 s timebase (42 Mm for the radial wave number analysis Dayside GOES magnetic field data Dayside GOES magnetic field data Exclude shocks, discontinuities, jumps, data gaps, magnetospheric and foreshock data Exclude shocks, discontinuities, jumps, data gaps, magnetospheric and foreshock data Analyzed overlapping 6-hour (9702 Mm ) series with a 10-minute step (252 Mm). Analyzed overlapping 6-hour (9702 Mm ) series with a 10-minute step (252 Mm).  Technique Multi-taper windowing analysis (Thomson et al.,1982) Multi-taper windowing analysis (Thomson et al.,1982) Autoregressive background fit and a modified F-test (Mann and Lees, 1996) Autoregressive background fit and a modified F-test (Mann and Lees, 1996) Signal must pass both the F-test (compares the variance of a discrete signal with the spectral variance) and the narrow band (tests for power above the spectral background) test at the 95% confidence level – see poster for details Signal must pass both the F-test (compares the variance of a discrete signal with the spectral variance) and the narrow band (tests for power above the spectral background) test at the 95% confidence level – see poster for details

We make occurrence distributions of all statistically significant frequencies and radial length scales found for three-year intervalsWe make occurrence distributions of all statistically significant frequencies and radial length scales found for three-year intervals We use the bootstrap method to determine which occurrence enhancements are statistically significant – see poster for detailsWe use the bootstrap method to determine which occurrence enhancements are statistically significant – see poster for details The left (right) panel summarizes these results using the occurrence distributions for frequencies (length scales)The left (right) panel summarizes these results using the occurrence distributions for frequencies (length scales) Values indicated on the table are the center of the band that is at least one standard deviation above the backgroundValues indicated on the table are the center of the band that is at least one standard deviation above the background Bars below represent the approximate bandwidthBars below represent the approximate bandwidth Summary of Statistically Significant Frequency Occurrence Enhancements

Direct Wind-GOES Comparison Wind observations propagated to Earth. If GOES on dayside, events are analyzed. within 35 R E, on-axis > 45 R E, off-axis The off-axis events exhibit little similarity in the frequency at which the occurrence enhancements occur Conversely, the occurrence enhancements using on-axis events are very similar between GOES and Wind

Conclusions Our results argue for inherent radial scale sizes to periodic number density enhancements in the solar wind. In Earth’s rest frame these periodic enhancements appear at discrete frequencies. As they convect past the Earth’s magnetosphere, the varying dynamic pressure directly drives global magnetospheric oscillations at the same frequencies We analyzed statistically significant solar wind number density oscillations. With our robust analysis, we find that certain discrete frequencies occur more often than other frequencies. Equivalently, there are certain periodic radial length scales that occur more often than others in the solar wind number density. There is consistency in the value of the occurrence enhancements for both frequencies and length scales across all 11 years of this study. We applied a similar analysis technique to dayside GOES magnetic field data and find that the occurrence distribution of apparent frequencies of on-axis solar wind events and that of the magnetospheric oscillations exhibit occurrence enhancements at the same frequencies. This is strong evidence that these structures directly drive magnetospheric oscillations.

Future Work What is the physical mechanism that causes periodic solar wind number density structures to occur more often at certain length scales? What is the physical mechanism that causes periodic solar wind number density structures to occur more often at certain length scales? Analyze longer time series – occurrence distributions of lower frequencies/longer length scales Analyze longer time series – occurrence distributions of lower frequencies/longer length scales Determine where the solar wind number density structures occur relative to Heliospheric structure Determine where the solar wind number density structures occur relative to Heliospheric structure Examine variations and evolution of solar wind parameters such as temperature, abundance ratios, magnetic field etc. Examine variations and evolution of solar wind parameters such as temperature, abundance ratios, magnetic field etc. Are the structures in pressure balance? Are the structures in pressure balance? Determine if and how they are related to solar surface Determine if and how they are related to solar surface

Occurrence Distributions and the Bootstrap Method We calculate occurrence distributions of statistically significant frequenciesWe calculate occurrence distributions of statistically significant frequencies We take 1000 different randomly generated subsets of the frequencies that were included in the occurrence distributionWe take 1000 different randomly generated subsets of the frequencies that were included in the occurrence distribution For each subset, weFor each subset, we Calculate a new occurrence distribution (panel a, solid line) and fit this occurrence distribution (dashed line)Calculate a new occurrence distribution (panel a, solid line) and fit this occurrence distribution (dashed line) Subtract the background from the occurrence distribution (panel b)Subtract the background from the occurrence distribution (panel b) Calculate the mean value of the 1000 residuals at each frequency (panel c)Calculate the mean value of the 1000 residuals at each frequency (panel c) Occurrence enhancement is statistically significant (marked with dots) if the mean residual at that frequency is at least one standard deviation (indicated with vertical lines) above zeroOccurrence enhancement is statistically significant (marked with dots) if the mean residual at that frequency is at least one standard deviation (indicated with vertical lines) above zero For 1995, there are statistically significant occurrence enhancements at f = , , , and mHzFor 1995, there are statistically significant occurrence enhancements at f = , , , and mHz 1995