281 research outputs found
The art of fitting p-mode spectra: Part II. Leakage and noise covariance matrices
In Part I we have developed a theory for fitting p-mode Fourier spectra
assuming that these spectra have a multi-normal distribution. We showed, using
Monte-Carlo simulations, how one can obtain p-mode parameters using 'Maximum
Likelihood Estimators'. In this article, hereafter Part II, we show how to use
the theory developed in Part I for fitting real data. We introduce 4 new
diagnostics in helioseismology: the echelle diagramme, the cross
echelle diagramme, the inter echelle diagramme, and the ratio cross spectrum.
These diagnostics are extremely powerful to visualize and understand the
covariance matrices of the Fourier spectra, and also to find bugs in the data
analysis code. These diagrammes can also be used to derive quantitative
information on the mode leakage and noise covariance matrices. Numerous
examples using the LOI/SOHO and GONG data are given.Comment: 17 pages with tex and ps files, submitted to A&A,
[email protected]
The art of fitting p-mode spectra: Part I. Maximum Likelihood Estimation
In this article we present our state of the art of fitting helioseismic
p-mode spectra. We give a step by step recipe for fitting the spectra:
statistics of the spectra both for spatially unresolved and resolved data, the
use of Maximum Likelihood estimates, the statistics of the p-mode parameters,
the use of Monte-Carlo simulation and the significance of fitted parameters.
The recipe is applied to synthetic low-resolution data, similar to those of the
LOI, using Monte-Carlo simulations. For such spatially resolved data, the
statistics of the Fourier spectrum is assumed to be a multi-normal
distribution; the statistics of the power spectrum is \emph{not} a
with 2 degrees of freedom. Results for shows that all parameters
describing the p modes can be obtained without bias and with minimum variance
provided that the leakage matrix is known. Systematic errors due to an
imperfect knowledge of the leakage matrix are derived for all the p-mode
parameters.Comment: 13 pages, ps file gzipped. Submitted to A&
Evidence for solar frequency dependence on sunspot type
High degree solar mode frequencies as measured by ring diagrams are known to
change in the presence of the strong magnetic fields found in active regions.
We examine these changes in frequency for a large sample of active regions
analyzed with data from the Michelson Doppler Imager (MDI) onboard the SoHO
spacecraft, spanning most of solar cycle 23. We confirm that the frequencies
increase with increasing magnetic field strength, and that this dependence is
generally linear. We find that the dependence is slightly but significantly
different for active regions with different sunspot types.Comment: 13 pages, 4 figures, accepted in ApJ letter
Characterization of solar-cycle induced frequency shift of medium- and high-degree acoustic modes
Although it is well known that the solar acoustic mode frequency increases as
the solar activity increases, the mechanism behind it is still unknown. Mode
frequencies with 20 < l < 900 obtained by applying spherical harmonic
decomposition to MDI full-disk observations were used. First, the dependence of
solar acoustic mode frequency with solar activity was examined and evidence of
a quadratic relation was found indicating a saturation effect at high solar
activity. Then, the frequency dependence of frequency differences between the
activity minimum and maximum was analyzed. The frequency shift scaled by the
normalized mode inertia follows a simple power law where the exponent for the p
modes decreases by 37% for modes with frequency larger than 2.5 mHz.Comment: Proceedings of GONG-SoHO 24: A new era of seismology of the sun and
solar-like star
On the choice of parameters in solar structure inversion
The observed solar p-mode frequencies provide a powerful diagnostic of the
internal structure of the Sun and permit us to test in considerable detail the
physics used in the theory of stellar structure. Amongst the most commonly used
techniques for inverting such helioseismic data are two implementations of the
optimally localized averages (OLA) method, namely the Subtractive Optimally
Localized Averages (SOLA) and Multiplicative Optimally Localized Averages
(MOLA). Both are controlled by a number of parameters, the proper choice of
which is very important for a reliable inference of the solar internal
structure. Here we make a detailed analysis of the influence of each parameter
on the solution and indicate how to arrive at an optimal set of parameters for
a given data set.Comment: 14 pages, 15 figures. Accepted for publication on MNRA
On The Determination of MDI High-Degree Mode Frequencies
The characteristic of the solar acoustic spectrum is such that mode lifetimes
get shorter and spatial leaks get closer in frequency as the degree of a mode
increases for a given order. A direct consequence of this property is that
individual p-modes are only resolved at low and intermediate degrees, and that
at high degrees, individual modes blend into ridges. Once modes have blended
into ridges, the power distribution of the ridge defines the ridge central
frequency and it will mask the true underlying mode frequency. An accurate
model of the amplitude of the peaks that contribute to the ridge power
distribution is needed to recover the underlying mode frequency from fitting
the ridge.
We present the results of fitting high degree power ridges (up to l = 900)
computed from several two to three-month-long time-series of full-disk
observations taken with the Michelson Doppler Imager (MDI) on-board the Solar
and Heliospheric Observatory between 1996 and 1999.
We also present a detailed discussion of the modeling of the ridge power
distribution, and the contribution of the various observational and
instrumental effects on the spatial leakage, in the context of the MDI
instrument. We have constructed a physically motivated model (rather than some
ad hoc correction scheme) resulting in a methodology that can produce an
unbiased determination of high-degree modes, once the instrumental
characteristics are well understood.
Finally, we present changes in high degree mode parameters with epoch and
thus solar activity level and discuss their significance.Comment: 59 pages, 38 figures -- High-resolution version at
http://www-sgk.harvard.edu:1080/~sylvain/preprints/ -- Manuscript submitted
to Ap
- …