Sensitivity of large-angle method
to detect deep-seated magneticflux	
Takashi Sekii
NAOJ	

This talk is about…	
 Q: Is going to high latitudes really worthit?

 From the ‘large-angle method’ point of view

Solar-C SDM 18 Nov 2008

The large-angle method	 The p-mode ray paths that reach thetachocline have 45-degree skip angle 	

Solar-C SDM 18 Nov 2008

The large-angle method	 Observing solar wavefield from highlatitudes improves chance of seeing
anything in the tachocline region
 Because then we can observe Doppler
signal at high latitudes without the effectof projection/foreshortening

Solar-C SDM 18 Nov 2008

The large-angle method	 Do we really need two vantage points?

 People have been looking for 45-degree
signal anomaly and nobody has convincingly
found it We may need every little extra help

Solar-C SDM 18 Nov 2008

What do we expect to see anyway?	
 Flux tube: ~100 kG, ~1000-km thick?

 effective ‘soundspeed’ perturbation of ~10-5
 Around 30-degree latitude?

 Flow inside the flux tube: up to ~200 m/s
 v/c~10-3, v/rΩ~0.2

 amplitude large enough but probably too thin to be
seen by rotation inversion
 This flow also exhibits more transient signaturewhen the tubes are rising There is the issue of uncertain crosssection/filling factor
Solar-C SDM 18 Nov 2008

Travel-time signatures	 Rough estimates based on ray theory

 Requires ~a few msec sensitivity for detecting
flux directly by wavespeed anomaly This translates to a few×10‐１sec sensitivity
for flow

Solar-C SDM 18 Nov 2008

Measuring travel times	 It is not just a matter of travel-timesensitivity

 We need a way to disentangle the signaturefrom other sources of perturbations
 However, for the moment, let us forget thisissue What are the difficulties with measuring
travel time with an angle?	

Solar-C SDM 18 Nov 2008

The projection and foreshortening	 There are two effects

 projection: Doppler signal multiplied by cosφ
while the background hardly changes (around3mHz anyway) i.e. noisy cross-correlation function

 foreshortening: loss of spatial resolution leads
to overlaying many cross-correlation
functions with different travel times
 i.e. temporally blurred (noisy) cross-correlation
function

Solar-C SDM 18 Nov 2008

Looking for a flux tube?	
 Suppoe it is located at r/R=0.725, 30-deg
latitude	The projection angle
plot	cos2<θ>~0.6⇒ <θ>~40	

Trajectory of ray-path
end points	
Solar-C SDM 18 Nov 2008

The projection and foreshortening	 A 45-degree ray off equator: how
difficult?

Solar-C SDM 18 Nov 2008

The projection and foreshortening	 A 45-degree ray off equator: how
difficult?

Solar-C SDM 18 Nov 2008

Looking for a flux tube?	
 Cross-correlation function S/N down by afactor ~1.7
 Effective resolution down by a factor 1.3
 What if the full resolution is 1 arcsec?
 =700-km resolution (disc centre)

Solar-C SDM 18 Nov 2008

Simulation	
 Artificially generated stochastically
excited oscillation data for Gabor wavelets with a background noise, some proper parameters (5-min period etc)
 some arbitrary parameters (travel time etc)
 Prescribed spatial resolution and noise level These are fitted by a non-linear LS
method statistic is pretty close to Gaussian

Solar-C SDM 18 Nov 2008

Results	
 Sample curve

Solar-C SDM 18 Nov 2008

Results	 Measurement errors (still tentative)
 1-min cadence, 10-day series

 750-km resolution, 2 per-cent noise: 1.8 sec
 This is 1-arcsec resolution
 900-km resolution, 2.5 per-cent noise: 3.0sec
 1125-km resolution, 3 per-cent noise: 8.5 sec
 This is the relevant case 1-min cadence, 100-day series Errors reduced by about factor 3

 With deep focusing, longer data sets etc,
we may be able to do it
Solar-C SDM 18 Nov 2008

The bottom line is…	
 Going to high latitudes does reduce
measurement errors in travel time by amoderate factor
 This reduction could be crucial

 We seem to be in a twilight zone between theland of possible and the land of impossible
 depends on what the Sun really is doing	

Solar-C SDM 18 Nov 2008

What if…	
 What if the flux tubes are located at 40
degree?
 What if the flux tubes are located deeper?
 Don’t we want to know what is taking
place beneath the tachocline?
Then going to high latitudes iseven more important, not tomention other merits of doing so	Solar-C SDM 18 Nov 2008

This talk was about…	
 Q: Is going to high latitudes really worthit?

 From the ‘large-angle method’ point of view

 A: Most likely YES

Solar-C SDM 18 Nov 2008