Inherent Length Scales Inherent Length Scales and Apparent and Apparent

Frequencies of Periodic Frequencies of Periodic Solar Wind Number Solar Wind Number Density StructuresDensity Structures

Nicholeen ViallNicholeen Viall11, Larry Kepko, Larry Kepko22 and Harlan Spence and Harlan Spence11

1. Center for Space Physics, Boston University1. Center for Space Physics, Boston University 2. Space Science Center, University of New Hampshire, 2. Space Science Center, University of New Hampshire,

Durham, New HampshireDurham, New Hampshire

This research was supported through a grant from NSF. We also thank the Wind SWE and GOES magnetic field investigations.

Observations of Observations of Magnetospheric Magnetospheric

OscillationsOscillations

•Two research groups have calculated the occurrence rate of discrete Two research groups have calculated the occurrence rate of discrete oscillations in the magnetosphere between 1 and 5 mHzoscillations in the magnetosphere between 1 and 5 mHz

•Ziesolleck and McDiarmid Ziesolleck and McDiarmid (1995) found occurrence enhancements (1995) found occurrence enhancements nearnear ff = 2 and 3 mHz with a smaller enhancement near 4 mHz = 2 and 3 mHz with a smaller enhancement near 4 mHz•Chisham and OrrChisham and Orr (1997) found occurrence enhancements near (1997) found occurrence enhancements near ff = 2.1, 3.1 and 3.9 mHz = 2.1, 3.1 and 3.9 mHz

•The multiple, discrete nature suggested a resonance of some kind The multiple, discrete nature suggested a resonance of some kind where the frequencies depend on internal magnetospheric propertieswhere the frequencies depend on internal magnetospheric properties

http://ase.tufts.edu/cosmos/view_picture.asp?id=112

•The magnetosphere supports a The magnetosphere supports a wide spectrum of oscillationswide spectrum of oscillations

•Multiple discrete Multiple discrete magnetospheric oscillations in magnetospheric oscillations in the mHz (period ~ minutes) the mHz (period ~ minutes) range have been observed range have been observed throughout the magnetospherethroughout the magnetosphere

•Of particular interest is the set Of particular interest is the set of multiple discrete frequencies of multiple discrete frequencies originally observed in event originally observed in event studies by studies by Samson et al.Samson et al. (1992): (1992):ff = 1.3, 1.9, 2.6, 3.4 mHz = 1.3, 1.9, 2.6, 3.4 mHz

Spectral EstimateTime Series

~1 hour20 minutes10 minutes

Multiple Discrete Oscillations Driven Multiple Discrete Oscillations Driven by Solar Wind Number Density by Solar Wind Number Density

VariationsVariations

Recent studies show similar oscillations, first in the solar wind number Recent studies show similar oscillations, first in the solar wind number density and then in the magnetosphere [density and then in the magnetosphere [Kepko et alKepko et al., 2002; ., 2002; Kepko and Kepko and

SpenceSpence, 2003; , 2003; Stephenson and WalkerStephenson and Walker, 2002]. , 2002].

The same spectral peaks observed near f = 0.2, 0.8, and 1.7mHz

Directly Driven OscillationsDirectly Driven Oscillations

•Kepko et al.,Kepko et al., 2002, and 2002, and Kepko and SpenceKepko and Spence, 2003 showed that in , 2003 showed that in addition to solar wind and magnetosphere time series corresponding addition to solar wind and magnetosphere time series corresponding well, their spectra exhibit power enhancements at the same well, their spectra exhibit power enhancements at the same frequencies, particularly lower frequenciesfrequencies, particularly lower frequencies

•They showed periodic number density variations = Periodic dynamic They showed periodic number density variations = Periodic dynamic pressure variations, so alter the strength of the magnetospheric fieldpressure variations, so alter the strength of the magnetospheric field

A “forced breathing” of magnetosphere

Kepko et alKepko et al. suggested that, in at least some instances, multiple discrete . suggested that, in at least some instances, multiple discrete magnetospheric oscillations are driven externally by periodic number magnetospheric oscillations are driven externally by periodic number density structures in the solar wind, rather than created through an density structures in the solar wind, rather than created through an internal magnetospheric resonanceinternal magnetospheric resonance

Frequencies Length Frequencies Length ScalesScales

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 StudyMotivation and Study

1.1. We present the results of a rigorous analysis of the We present the results of a rigorous analysis of the relative occurrence rate of statistically significant spectral relative occurrence rate of statistically significant spectral peaks in the solar wind number density time seriespeaks in the solar wind number density time series

2.2. We repeat the spectral analysis using radial wave number We repeat the spectral analysis using radial wave number and present the relative occurrence rate of periodic radial and present the relative occurrence rate of periodic radial length scales in the solar wind number densitylength scales in the solar wind number density

3.3. We compare our results of apparent solar wind We compare our results of apparent solar wind frequencies with our results using the same technique to frequencies with our results using the same technique to dayside GOES datadayside GOES data

Multiple discrete oscillations have been observed in Multiple discrete oscillations have been observed in the magnetosphere the magnetosphere

Multiple discrete oscillations have been observed in Multiple discrete oscillations have been observed in the solar wind number densitythe solar wind number density

Event studies have shown that the same oscillations Event studies have shown that the same oscillations sometimes exist both in the solar wind and in the sometimes exist both in the solar wind and in the magnetospheremagnetosphere

Data Used and Analysis Data Used and Analysis TechniqueTechnique

Solar wind dataSolar wind data 11 years, 1995-2005 (11 years ~ solar cycle)11 years, 1995-2005 (11 years ~ solar cycle) SWE (solar wind experiment) instrument on Wind spacecraftSWE (solar wind experiment) instrument on Wind spacecraft ~90 s sampling rate, resample to a common 100 s timebase ~90 s sampling rate, resample to a common 100 s timebase

(42 Mm for the radial wave number analysis(42 Mm for the radial wave number analysis Dayside GOES magnetic field dataDayside GOES magnetic field data Exclude shocks, discontinuities, jumps, data gaps, Exclude shocks, discontinuities, jumps, data gaps,

magnetospheric and foreshock datamagnetospheric and foreshock data Analyzed overlapping 6-hour (9702 Mm ) series with a 10-Analyzed overlapping 6-hour (9702 Mm ) series with a 10-

minute step (252 Mm).minute step (252 Mm).

TechniqueTechnique Multi-taper windowing analysis (Multi-taper windowing analysis (Thomson et al.,1982Thomson et al.,1982)) Autoregressive background fit and a modified F-test (Autoregressive background fit and a modified F-test (Mann Mann

and Lees,and Lees, 1996) 1996) Signal must pass Signal must pass bothboth the F-test (compares the variance of a the F-test (compares the variance of a

discrete signal with the spectral variance) and the narrow discrete signal with the spectral variance) and the narrow band (tests for power above the spectral background) test at band (tests for power above the spectral background) test at the 95% confidence level – see poster for detailsthe 95% confidence level – see poster for details

•We make occurrence distributions of all statistically significant We make occurrence distributions of all statistically significant frequencies and radial length scales found for three-year intervalsfrequencies and radial length scales found for three-year intervals

•We use the bootstrap method to determine which occurrence We use the bootstrap method to determine which occurrence enhancements are statistically significant – see poster for detailsenhancements are statistically significant – see poster for details

•The left (right) panel summarizes these results using the occurrence The left (right) panel summarizes these results using the occurrence distributions for frequencies (length scales)distributions for frequencies (length scales)

•Values indicated on the table are the center of the band that is at least Values indicated on the table are the center of the band that is at least one standard deviation above the backgroundone standard deviation above the background

•Bars below represent the approximate bandwidth Bars below represent the approximate bandwidth

Summary of Statistically Significant Summary of Statistically Significant Frequency Occurrence EnhancementsFrequency Occurrence Enhancements

Direct Wind-GOES Direct Wind-GOES ComparisonComparison

•Wind observations propagated to Earth. If GOES on dayside, events are analyzed.

• within 35 RE, on-axis

• > 45 RE, 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

ConclusionsConclusions

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 WorkFuture Work What is the physical mechanism that causes What is the physical mechanism that causes

periodic solar wind number density structures to periodic solar wind number density structures to occur more often at certain length scales?occur more often at certain length scales?

Analyze longer time series – occurrence distributions of lower Analyze longer time series – occurrence distributions of lower frequencies/longer length scalesfrequencies/longer length scales

Determine where the solar wind number density structures Determine where the solar wind number density structures occur relative to Heliospheric structureoccur relative to Heliospheric structure

Examine variations and evolution of solar wind parameters such Examine variations and evolution of solar wind parameters such as temperature, abundance ratios, magnetic field etc.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 surfaceDetermine if and how they are related to solar surface

Occurrence Distributions and Occurrence Distributions and the Bootstrap Methodthe Bootstrap Method

•We calculate occurrence distributions of We calculate occurrence distributions of statistically significant frequenciesstatistically significant frequencies

•We take 1000 different randomly generated We take 1000 different randomly generated subsets of the frequencies that were included subsets of the frequencies that were included in the occurrence distributionin the occurrence distribution

•For each subset, we For each subset, we •Calculate a new occurrence distribution Calculate a new occurrence distribution (panel a, solid line) and fit this occurrence (panel a, solid line) and fit this occurrence distribution (dashed line)distribution (dashed line)

•Subtract the background from the Subtract the background from the occurrence distribution (panel b)occurrence distribution (panel b)

•Calculate the mean value of the 1000 Calculate the mean value of the 1000 residuals at each frequency (panel c)residuals at each frequency (panel c)

•Occurrence enhancement is statistically Occurrence enhancement is statistically significant (marked with dots) if the mean significant (marked with dots) if the mean residual at that frequency is at least one residual at that frequency is at least one standard deviation (indicated with vertical standard deviation (indicated with vertical lines) above zerolines) above zero

•For 1995, there are statistically significant For 1995, there are statistically significant occurrence enhancements at occurrence enhancements at ff = 0.5-0.7, 2.1- = 0.5-0.7, 2.1-2.4, 2.7-2.9, 3.6-4.0 and 4.7-4.9 mHz2.4, 2.7-2.9, 3.6-4.0 and 4.7-4.9 mHz

1995