Solar structure as seen by high-degree

modes

M. Cristina Rabello Soares

UFMG, Brazil

and

collaborators

Local HelioseismologyNearby Active Region

In collaboration with Rick Bogart & Phil Scherrer (Stanford University)

Rabello-Soares, Bogart & Scherrer (2013):

• Comparison of a quiet tile with a nearby active region (5o to 8o away) with a quiet tile with no nearby active region at the same disk position (same latitude and Stunyhurst longitude)

o using HMI 5o patches from June 2010 to January 2012.

o The HMI ring-digram analysis pipeline uses two fitting methods: rdfitc (Basu & Antia 1999) and rdfitf (Haber et al. 2000, which is also used by GONG pipeline). Looking at the magnetic field from a distance…

The elephant in the room

Ux and Uy : zonal and meridional flows

U⁄⁄ and Uperp in relation to the direction of the nearby AR location

Flow variation

Control set in black:+ fitsc* fitsf

Flow variation in the direction of the

nearby active region

inflow

outflow

Quiet region in the vicinity of AR (50 to 80 away)

fitsf (in red) fitsc (in black)• Best trade-off

parameter:m = 0.0050

• Small errors error of the mean of fitted flows.

• Negative flow means flow away from the nearby AR and

• Positive towards the nearby AR.

inflow

outflow

Quiet region in the vicinity of AR (50 to 80 away)

fitsf (in red) fitsc (in black)

• Surface cooling within the plage results in a downdraft which draws fluid in at the surface (Hindman, Haber & Toomre, 2009): Figure 11. Schematic diagram (side view)

F su

rf

(x 1

03)

F su

rf

(x 1

03)

* fitsf fitsc

AR - Q

QnearbyAR - Q

• Quiet: MAI < 5 G

• Active Region (AR): MAI > 100 G

* n = 1* n = 2* n = 3

In (AR-Q), only a few error bars for fitsc are shown.

ConclusionsWe observe an outflow from about 3 Mm until 6 Mm deep in quiet regions which are 50 to 80 from an active region and some indication of an inflow 0-2 Mm deep.

There is a surface term when comparing a quiet region with a nearby active region and a quiet tile (with no nearby AR).

The two fitting methods give different slopes for Fsurf which is mainly a function of frequency.

This surface term is similar, but present some differences with the surface term for AR – Q.

Global modesSpherical Harmonic Decomposition

Solar Cycle Variations

Frequency shift as a function of solar activity

(20 < l < 900)

Figure 1 of Rabello-Soares (2011)

• Medium-l: MDI Structure Program – Schou (1999) and Larson & Schou (2009)

• High-l: MDI Dynamics Program – Rabello-Soares, Korzennik & Schou (2008)

Solar-radio 10.7-cm daily flux (NGDC/NOAA)

Baldner, Bogart & Basu (2012): analysed 264 regions (from 1996 to 2008) and applied Principal Component Analysis.

Fig. 9 of Rabello-Soares (2012)

Baldner, Bogart & Basu (2012)

Two-layer structure

Global helioseismology: variation between solar max and minimum

Comparison with solar

model

MDI Dynamics 2001

Two different peak-fitting algorithms were used to fit the power spectra and obtain the mode frequencies:

• Medium-l modes: known as the MDI peak-fitting method, is described in detail by Schou (1992) and improved in Larson & Schou (2008, 2009).

• High-l modes: At high degrees, the spatial leaks lie closer in frequency, resulting in the overlap of the target mode with the spatial leaks that merge individual peaks into ridges, making it more difficult to estimate unbiased mode frequencies (also at large frequencies): Korzennik et al. (2013).

Data used:

n > 0

The spatial leaks merge individual peaks into ridges

Figure 1 of Rabello-Soares, Korzennik & Schou (2001)

Medium l

Medium l, but high frequency

High l

Instrumental effects affect the amplitude of the leaks

Figure 7 of Rabello-Soares, Korzennik & Schou (2001)

Observed power

spectra

Simulated power spectra where the leakage matrix was calculated without and with a plate scale error of -0.1%

MDI (2001) - model S

a "surface term" developed by Brodsky & Vorontsov (1993) using a higher-order asymptotic theory suitable for high-degree mode frequencies is used:

To suppress the uncertainties in the surface layers in helioseismic models,

F surf(o

bse

rved)

– F s

urf(fi

tted)

x 1

03

F surf(o

bse

rved)

– F s

urf(fi

tted)

x 1

03

L = 8

n (mHz)

l / n(mHz-1)

n =

obse

rved e

rror

fr

equency

(m

Hz)

obse

rved e

rror

frequency

(m

Hz)

n (mHz)

degree

Medium-l fitting High-l fitting

• Errors for l>200 are divided by sqrt(10), to taken into account that we are fitting every 10th l.MOLA Technique

0.985

0.980

0.960

m = 5e-7, b = 10

Averaging Kernels

Figure 15 of Basu et al. (2009)

Error correlation functionHowe & Thompson (1996)

Figure 1 of Rabello-Soares, Basu & Christensen-Dalsgaard (1999):

Error correlation at r1 = 0.5 Rsun for sound speed based on a medium-l mode set.

Conclusions

The sound speed inversion using Korzennik et al (2013) high-degree (l = 100-1000) mode frequencies agrees with (old) MDI medium-l results (from Basu et al. 2009).

Good averaging kernels until 0.985 R .

More work needs to be done: oscillation in the results are likely due to error correlation invert for every l.

Thank you.

Only fitsc

F su

rf

(x 1

03)

* Fsurf (AR - Q). Fsurf (QnearbyAR - Q) x 15

* n = 1* n = 2* n = 3

Comparison

Variation of the mode parameters with solar cycle

It is well known that amplitudes decrease while mode widths increase in the presence of magnetic fields (for example, Rajaguru, Basu, and Antia, 2001).

Rabello-Soares, Bogart, and Basu (2008) have reported that the relation between the change in width and mode amplitude was very nearly linear.

Figure 4 of Rabello-Soares, Bogart & Basu (2008)

NSO 2013

Fig.3 of Rabello-Soares, Bogart & Scherrer (2013): colors are n=0, n=1, n=2, n=3, n=4

Relative amplitude variation between:

Active and quiet regions

Quiet region with a nearby AR and with no nearby AR.in the direction of the nearby AR

perpendicular to it• For frequencies larger than ≈4.2

mHz, the modes are amplified (acoustic halo) if there is an active region nearby with very little dependence on their propagation direction.

NSO 2013

fistcic=0ic=1 (transparent: black)