Locations of Auroral Kilometric Radiation
Using a 4-station Space-Based Interferometer
Robert Mutel, Ivar Christopher
University of Iowa
URSI, Boulder, Jan 2006
Auroral displays
Image from ISS
Altitudes of Aurora
(Red)
(Green)
Aurora: caused by precipitating
keV Electrons
Magnetic reconnection: Source of
energetic particles for aurora, AKR (?)
Auroral Kilometric Radiation
Mechanism: Electron Cyclotron Maser Instability
Conditions needed for Cyclotron Maser Instability
•
• Requires fpe/fce << 1
• Requires ∂f/ ∂vperp > 0
e.g. ‘Horseshoe’ velocity
distribution
• Terrestrial AKR: occurs
on B-field lines in
acceleration region
above auroral zone
• AKR also detected
from all Jovian planets
• May also be
responsible for radiation
from active stars, AGN
Begelman, Ergun, Rees
2005 ApJ
CMI gain, bandwidth
CMI Dispersion relation”
For γ<<1, expand:
Growth rate (imaginary part
of ω):
AKR Time-frequency spectra
Scientific Question addressed by
VLBI location studies of AKR:
What is the detailed
correspondence between
AKR bursts (at 2-4 Re) and
auroral features (at 80-300
km)?
This addresses the
magnetosphereIonosphere coupling
problem
AKR location measurements using VLBI
(differential delays)
Cluster 4 S/C VLBI array
Requires real-time
waveform downlink
(4 DSN antennas!)
Cross-correlate
waveforms to measure
differential delays
Note: CCF delay peak
width Δτ~ 1/BW
Note: When S/C widely separated,
only small fraction of AKR bursts
are common to all S/C!
Location-finding
algorithm
1. In order to determine the AKR source position, the
differential delay is measured between the waveform
arrival time for each baseline between pairs of spacecraft.
For baseline connecting spacecraft i and j, the differential
delay is given by
2. The resulting differential delays are further vetted by
examining the signed sum of delays on each of the four
independent baseline triangles. For an unresolved
source, the signed sum of all delays on baseline triangle
(i, j, k) must be zero within the delay uncertainty
3. A cubic grid of 512,000 points is examined, delays
calculated for each grid point. All points with delays
within uncertainty are cobnsidered valid solutions.
VLBI technical details
• Snapshot mode! (bursts lasts only ~1s -10s)
•Timing uncertainty ±10 μs << 1ms delay
uncertainty
• Clock: ‘ultra’ stable crystal: δt ~ 10-10 s/s
• Real-time downlink (waveforms, 8-bit)
• Time: DSN stamped ±1 μs
• Essentially no location determination along z
(l.o.s.)
• 6 baselines: over-determined position
solution (3 unknowns: X,Y,Z)
• Source unresolved (coherent emission, high
Tb)
• New VLBI maps every 300ms x 12 freq chan
• Frequency channels 12 x 1 KHz
• Only delays used – not phases (yet)
• S/C positions uncertainty ~1km (3 μs error)
Position
Uncertainty
If we displace a source in the plane
perpendicular to the line of sight by distance
x along the direction of B, the
corresponding differential delay will be
Assuming x << B << z, we can
easily solve for x
~ 500 -1,000 km
Assuming x << B << z, a calculation
similar to the above, but for a source offset
by B/2 in the perpendicular plane results in
a position uncertainty
~ 5,000 - 20,000 km
AKR VLBI
science results
1. Association of AKR burst locations with
discrete auroral arcs, but:
1. Some (up to 50%) AKR bursts have
no associated auroral features
2. Some discrete arcs have no AKR
emission
2. Motion of AKR burst centroids (V ~ 100
m/s)
3. Radiated beamwidth of AKR bursts are
much smaller than previously reported
(HPBW~ 5°)
4. Striated AKR triggered by ion stationary
structures
Time variations in AKR burst
locations
9 Nov 2003 (3 hours)
(125, 250, 500 KHz)
29 Dec 2002 (1 ½ hrs)
Simultaneous AKR location/UV
imaging of aurora
Correlating Narrowband (Striated) AKR bursts
•
Problem: Narrow bandwidth implies large
uncertainty in delay and location:
– Δν ~ 50 Hz → Δτ ~ 20 ms → Δx ~ 4 Re!
•
Solution: Cross-correlate using longer time
window, isolated bursts
•
Example below: cross–correlation of
Synthetic Monochromatic Chirp Signals (τ =
10 ms, Signal + UDP phasor)
Δτ ≈ 0.5 ms
Summary
1. VLBI Technical Summary
1. 4 S/C VLBI successfully done from space (no ground stations)
2. Real-time data downlink to DSN (37 kbps) – time stamps added
3. Software Correlator (IDL)
4. Onboard crystal Local oscillator, stability: 10-10 s/s (100s)
5. Uses differential delays from CCF peak (no phase)
6. Position determination only - no source structure (unresolved)
7. Position uncertainties ~ ± 200km - 400km at Earth
8. Narrowband AKR drifting bursts can be mapped using chirp analysis
2. AKR Science
1. AKR emission occurs on B field lines associated with discrete auroral
arcs
2. AKR activity center drifts at 80-100 m/s over hours
3. AKR beam sizes are much smaller than previously assumed (~5°)
4. Striated AKR triggered by ion stationary structures