Presentation - National Solar Observatory

**Volume Title**
ASP Conference Series, Vol. **Volume Number**
**Author**
c○ **Copyright Year** Astronomical Society of the Pacific
Solar Cycle Variation of High-Degree Acoustic Mode Frequencies
Sushanta C. Tripathy, Kiran Jain, Rudolf Komm, and Frank Hill
National Solar Observatory, Tucson, AZ 85719, USA
Abstract. We investigate the temporal variations of the high-degree mode frequencies
measured over localized regions of the Sun though the technique of ring-diagrams.
We observe that the high-degree mode frequencies have a solar cycle variation similar
to those of intermediate-degree modes but ten times greater. We also find that the
averaged frequency shifts are linearly correlated with routinely measured solar activity
indices e.g. 10.7 cm radio flux. We do not, however, find any evidence of a quadratic
relation between the frequencies of individual multiplets and solar activity indices as
reported earlier from the study of global high-degree modes.
1. Introduction
The characteristics of low- and intermediate-degree global modes with the solar activity
cycle has been investigated by many authors, and it has been established that the
mode frequencies vary with the phase of the solar cycle (see Jain, Tripathy, & Hill
2009, and references therein). In the context of high-degree modes, such studies are
limited due to the inherent difficulties in determining the mode frequencies (Korzennik,
Rabello-Soares, & Schou 2004). Applying global helioseismology techniques to
Michelson Doppler Imager (MDI) dynamics data, Rabello-Soares, Korzennik, & Schou
(2008) have analyzed high-degree mode frequencies and showed that the changes are
in good agreement with the medium-degree results, except for the years when the MDI
instrument was highly defocused. This was later extended to include data up to 2008
(Rabello-Soares 2011). However, these studies analyze discrete data sets spanning a
period of two to three months in a year. In this paper, we present results obtained from
the analysis of a continuous high-degree data set covering a period of about 11 years
during the descending and ascending phase of cycle 23 and 24.
2. Analysis and Results
We use the ring-diagram technique (Hill 1988) to investigate the temporal as well as latitudinal
variations in high-degree mode frequencies in the range of 180≤l≤ 1000. The
mode frequencies corresponding to the 189 dense-pack overlapping tiles spanning the
period from 26 July 2001 to 9 September 2012 and processed through the ring-diagram
pipeline (Corbard et al. 2003) are extracted from the Global Oscillation Network Group
(GONG) data archive (http://gong.nso.edu). Figure 1 shows the distribution of the duty
cycle. For this analysis, we exclude all data where the duty cycle is less than 70%.
This yielded usable data for 3213 ring-days (1 ring-day= 1664 minutes) consisting of
more than 600,000 tiles. The characteristicl−ν diagram constructed from fitted mode
1

2 Tripathy et al.
Figure 1. Left panel: Distribution of the duty cycle of GONG ring pipeline data.
Right panel: Example of mode coverage in different data sets; modes obtained by
the MDI medium-l program (filled circles) and GONG high-l data (open circles).
parameters are shown in Fig 1(b). The filled circles represent the mode set from MDI
intermediate-degree modes while the open circles represent the high-degree modes. It
is evident that the high-degree modes nicely follow the intermediate degree ridges.
In order to characterize the temporal evolution of the mode frequencies, we calculate
the mean frequency shift,δν, using a formula which is analogous to the frequency
shifts calculated for the global modes,
δν =
∑
n,l
∑ 189
i=1 δν n,l(t) ∑
σ 2 /
n,l
n,l
1
σ 2 n,l
, (1)
whereδν n,l is the frequency difference with respect to the frequency corresponding
to a quiet day (ring-day of 11 May 2008) as measured by the magnetic field strength
over the disk andσ n,l is the uncertainty in the frequency measurement. Since the mode
parameters measured by the ring-diagram analysis are influenced by the foreshortening,
we correct the frequencies following the procedure described by Tripathy, Jain, & Hill
(2013) before calculating the frequency shifts.
Figure 2(a) displays the temporal variation ofδν. In order to reduce the random
fluctuations produced by daily variations, we smooth the data by calculating a running
mean over 35 points. This is shown by the solid line and clearly depicts the descending
phase of cycle 23, the extended minimum period and the ascending phase of cycle
24. The dashed line in the same figure shows the intermediate-degree frequency shifts
obtained from time series of 36 days for global modes. We note that the shifts corresponding
to high-degree modes are ten times greater than the intermediate-degree
modes, a result similar to those of global frequencies (Rabello-Soares 2011). We also
find that both intermediate and high-degree frequency shifts are linearly correlated with
a Pearson’s correlation coefficient of 0.88.
We further investigate the correlation of the frequency shifts with solar activity
represented by the 10.7 cm radio flux, F 10 . Figure 2(b) showsδν and F 10 interpolated
to the same temporal grid of frequency shifts, and smoothed by a running mean over
71 points. The correlation between the two parameters except during the extended
minimum period can be clearly seen. The Pearson’s linear regression analysis yielded

Solar Cycle Variation of High-Degree Mode Frequencies 3
Figure 2. (a) Temporal evolution ofδν. The open circles denote the shifts corresponding
to each ring-day. The solid line represents the running mean over 35
points. The dashed line shows the frequency shifts calculated from global modes obtained
from 36-day time series (globalδν). (b) Temporal evolution of localδν (solid
line) and 10.7 cm radio flux (dashed line), interpolated to the same grid of frequency
shifts. Both the quantities are represented by a running mean over 71 points.
a correlation coefficient of 0.98 confirming that the high-degree frequency shifts track
the solar activity in a manner similar to the low- and intermediate degree modes.
Since Rabello-Soares (2011) found evidence of a quadratic relation between frequencies
of individual modes and F 10 , we further investigate the existence of such a
relationship. In Figure 3, we show the frequencies of two modes (n=2,l=314 and
n=3,l=427) as a function F which is defined as the value of the solar radio flux
divided by the maximum flux during the period of analysis. The solid line shows the
result from linear fitting with a linear correlation coefficient of 0.95 and 0.97 for the two

4 Tripathy et al.
Figure 3. Example of frequency variation with the relative activity index, F, as
defined in text for two different modes (a) n=2,l=314 and (b) n=3,l=427.
The solid and dashed lines represent linear and quadratic fits.
multiplets. We also fitted these two modes with a quadratic relation, the fitted result is
shown by dashed lines. We do not see any difference between the two fitting methods.
Similarly, the correlation coeffecients do not show any significant difference between
the two fitting methods. Thus, we conclude that the the frequencies are linearly correlated
with the activity indices and do not show any evidence of a quadratic relation.
It is possible that the quadratic relation seen by Rabello-Soares (2011) could be due to
the small number of data sets present in their analysis.
In summary, we find that the frequency shifts of high-degree modes calculated
using ring-diagrams are ten times greater than the intermediate-degree modes which is
consistent with the study of high-degree mode frequencies calculated from global helioseismology.
We also note that both individual multiplets and disk-averaged frequency
shifts are linearly correlated with the solar activity index as represented by the 10.7 cm
radio flux. Further, we do not find any evidence of a quadratic relationship between the
frequencies of individual modes and activity index.
Acknowledgments. This work utilizes data obtained by the NSO Integrated Synoptic
Program (NISP), managed by the National Solar Observatory, which is operated
by AURA, Inc. under a cooperative agreement with the National Science Foundation.
References
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