Asteroseismic Signatures of Stellar Magnetic Activity Cycles
Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 1 November 2018 (MN LATEX style file v2.2)
Asteroseismic Signatures of Stellar Magnetic Activity Cycles
T. S. Metcalfe1,2, W. A. Dziembowski3,4, P. G. Judge1, M. Snow5
1 High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80307-3000 USA
2 Scientific Computing Division, National Center for Atmospheric Research, Boulder, CO 80307-3000 USA
3 Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warsaw, Poland
4 Copernicus Astronomical Centre, Bartycka 18, 00-716 Warsaw, Poland
5 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 80309-0392 USA
1 November 2018
ABSTRACT
Observations of stellar activity cycles provide an opportunity to study magnetic dynamos
under many different physical conditions. Space-based asteroseismology missions will soon
yield useful constraints on the interior conditions that nurture such magnetic cycles, and will
be sensitive enough to detect shifts in the oscillation frequencies due to the magnetic varia-
tions. We derive a method for predicting these shifts from changes in the Mg II activity index
by scaling from solar data. We demonstrate this technique on the solar-type subgiant β Hyi,
using archival International Ultraviolet Explorer spectra and two epochs of ground-based as-
teroseismic observations. We find qualitative evidence of the expected frequency shifts and
predict the optimal timing for future asteroseismic observations of this star.
Key words: stars: activity – stars: individual (β Hyi) – stars: interiors – stars: oscillations
1 INTRODUCTION
Astronomers have been making telescopic observations of sunspots
since the time of Galileo, gradually building an historical record
showing a periodic rise and fall in the number of sunspots every
∼11 years. We now know that sunspots are regions with an en-
hanced local magnetic field, so this 11-year cycle actually traces
a variation in surface magnetism. Attempts to understand this be-
havior theoretically often invoke a combination of differential rota-
tion, convection, and meridional flow to modulate the field through
a magnetic dynamo (e.g., see Rempel 2006; Dikpati & Gilman
2006).
Although we can rarely observe spots on other solar-type stars
directly, these areas of concentrated magnetic field produce strong
emission in the Ca II H and K resonance lines in the optical, and
the Mg II h and k lines in the ultraviolet. Wilson (1978) was the
first to demonstrate that many solar-type stars exhibit long-term
cyclic variations in their Ca II H and K emission, analogous to those
seen in full-disc solar observations through the magnetic activity
cycle. Early analysis of these data revealed an empirical correlation
between the mean level of magnetic activity and the rotation pe-
riod normalized by the convective timescale (Noyes et al. 1984a),
as well as a relation between the rotation rate and the period of
the observed activity cycle (Noyes et al. 1984b), which generally
supports a dynamo interpretation.
Significant progress in dynamo modeling unfolded after he-
lioseismology provided detailed constraints on the Sun’s interior
structure and dynamics. These observations also established that
variations in the mean strength of the solar magnetic field lead to
significant shifts (∼0.5 µHz) in the frequencies of even the lowest-
degree p-modes (Libbrecht & Woodard 1990; Salabert et al. 2004).
These shifts can provide independent constraints on the physical
mechanisms that drive the solar dynamo, through their influence
on the outer boundary condition for the pulsation modes. They are
thought to arise either from changes in the near-surface propagation
speed due to a direct magnetic perturbation (Goldreich et al. 1991),
or from a slight decrease in the radial component of the turbulent
velocity in the outer layers and the associated changes in tempera-
ture (Dziembowski & Goode 2004, 2005).
Space-based asteroseismology missions, such as MOST
(Walker et al. 2003), CoRoT (Baglin et al. 2006), and Kepler
(Christensen-Dalsgaard et al. 2007) will soon allow additional tests
of dynamo models using other solar-type stars (see Chaplin et al.
2007). High precision time-series photometry from MOST has al-
ready revealed latitudinal differential rotation in two solar-type
stars (Croll et al. 2006; Walker et al. 2007), and the long-term mon-
itoring from future missions is expected to produce asteroseismic
measurements of stellar convection zone depths (Monteiro et al.
2000; Verner et al. 2006). By combining such observations with
the stellar magnetic activity cycles documented from long-term sur-
veys of the Ca II or Mg II lines, we can extend the calibration of
dynamo models from the solar case to dozens of independent sets
of physical conditions.
The G2 subgiant β Hyi is the only solar-type star that presently
has both a known magnetic activity cycle (Dravins et al. 1993)
and multiple epochs of asteroseismic observations (Bedding et al.
2001, 2007). In this paper we reanalyze archival International Ul-
traviolet Explorer (IUE) spectra for an improved characterization
of the magnetic cycle in this star, and we use it to predict the activity
related shifts in the observed radial p-mode oscillations. We com-
pare these predictions with recently published asteroseismic data,
c© 0000 RAS
http://arxiv.org/abs/0704.1606v1
2 Metcalfe et al.
and we suggest the optimal timing of future observations to maxi-
mize the amplitude of the expected p-mode frequency shifts.
2 ARCHIVAL IUE SPECTRA
The activity cycle of β Hyi was studied by Dravins et al. (1993),
who used high resolution IUE data of the Mg II resonance lines over
11 years, from June 1978 to the end of October 1989. They consid-
ered these data to be consistent with a cycle period between 15 and
18 years. Since the work of Dravins et al., a significant number of
additional IUE spectra were obtained by E. Guinan from early 1992
to the end of 1995. Our analysis of all of these spectra reveals the
beginning of a new cycle in 1993-1994.
In 1997, the IUE project reprocessed the entire database using
improved and uniform reduction procedures (“NEWSIPS”). Using
the NEWSIPS merged high resolution extracted spectra, we have
reanalyzed the entire IUE dataset containing useful echelle data
of the Mg II lines. Data were excluded when the NEWSIPS soft-
ware mis-registered the spectral orders, when continuum data near
279.67 nm were saturated, or when continuum data were more than
1σ below the mean (to reject additional poorly registered spectral
orders) or more than 1.5σ above the mean.
The classic definition of the Mg II index (Heath & Schlesinger
1986) uses wing irradiances at 276 and 283 nm. The wings in their
formulation had to be so far away from the cores due to the 1.1 nm
spectral bandpass of their instrument. In the IUE spectra, pixels
at those wavelengths are saturated, so the photospheric reference
levels need to be measured much closer to the emission cores.
Snow & McClintock (2005) have shown that at moderate resolu-
tion the variability of the inner wings of the Mg II absorption fea-
ture is very similar to the variability of the classic wing irradiances.
Therefore, we can construct a modified Mg II index using only the
unsaturated IUE data that still captures the full chromospheric vari-
ability.
The chromospheric line cores (0.14 and 0.12 nm wide band-
passes centered at 279.65 and 280.365 nm, in vacuo) and two bands
in the photospheric wings of the lines (0.4 nm wide bands, edge-
smoothed with cosine functions, centered at 279.20 and 280.70 nm)
were integrated, and the ratio of total core to total wing fluxes was
determined. Figure 1 shows the core to wing indices determined
from each usable spectrum from 1978 to the end of 1995. The post-
1992 data permit us to revise the cycle period estimate downwards
to ∼12.0 years, with more confidence than was previously possi-
ble. This period was derived by fitting a simple sinusoid to the data
using the genetic algorithm PIKAIA (Charbonneau 1995). The op-
timal fit yields minima at 1980.9 and 1992.8, and a maximum at
1986.9. The fit suggests that the next maximum occurred in 1998.8,
a minimum in 2004.8, and a future maximum predicted for 2010.8.
The reduced χ2 of the fit was calculated using flux uncertainties
for individual IUE observations of 7%, estimated from the varia-
tion in the ratios of the two wing fluxes, which vary far less than
this in the SOLSTICE solar data. This reduced χ2 has a minimum
value of 0.77. The probability of such a value occurring at random
is 24%, whereas a χ2 of 1.1 has a random probability of 76%. The
2 = 1.1 hypersurface contours suggests that the uncertainties are
roughly ±1 yr for the phase and +3.0−1.7 yr for the period, making our
new period estimate marginally consistent with the range quoted
by Dravins et al. (1993). The χ2 contours are ovals because these
uncertainties are correlated, allowing us to set the following formal
limits on the epochs of maximum: 1986.1–1988.0, 1997.5–2002.4,
and 2007.8–2017.8. These large uncertainties reinforce the need for
Figure 1. Core to wing ratios of the summed Mg II h and k lines determined
from IUE high dispersion observations of β Hyi (small points) and 3-month
seasonal averages with the uncertainties used in the evaluation of χ2 shown
as error bars (large points). The curve is an optimized simple sinusoid fit
obtained using a genetic algorithm applied to the seasonally averaged data,
intended only to estimate the period and phase of the stellar activity cycle,
which is listed in the legend. The IUE index is shown on the left, while the
corresponding NOAA index is shown on the right.
an activity cycle monitoring program specifically for the southern
hemisphere.
To compare the IUE Mg II index measurements to the National
Oceanic & Atmospheric Administration (NOAA) composite data
of solar activity1, we must determine the appropriate scaling fac-
tor. The SOLar-STellar Irradiance Comparison Experiment (SOL-
STICE) on the SOlar Radiation and Climate Experiment (SORCE;
McClintock et al. 2005) measures the solar irradiance every day,
and has a resolution of 0.1 nm in this region. We convolved the
IUE spectra with the SOLSTICE instrument function and then mea-
sured the wings and cores of both solar and stellar data in exactly
the same way. In particular, we used 279.15-279.35 nm as the blue
wing, and 280.65-280.85 nm for the red wing. The emission cores
were defined as 279.47-279.65 nm and 280.21-280.35 nm. We de-
termined the relation between the SOLSTICE modified Mg II index
and the NOAA long-term record using a standard linear regression
method (see Snow et al. 2005; Viereck et al. 2004). Since the mod-
ified IUE data has the same bandpass as the SOLSTICE data, the
scaling factors derived from SOLSTICE solar data will also ap-
ply to the stellar IUE data2. The Mg II index for β Hyi scaled
to the NOAA composite data is shown on the right axis of Fig-
ure 1. For the analysis in Section 3, we adopt a full amplitude of
∆iMgII = 0.015 in the NOAA index.
3 SCALING P-MODE SHIFTS FROM SOLAR DATA
In general, we can evaluate activity related frequency shifts from
the variational expression,
∆ν j =
d3xK jS
2I jν j
, (1)
where
1 http://www.sec.noaa.gov/ftpdir/sbuv/NOAAMgII.dat
2 To transform between indices: NOAA = 0.211 + 0.0708 SOLSTICE;
SOLSTICE = 0.297 + 1.11 IUE; NOAA = 0.232 + 0.079 IUE
c© 0000 RAS, MNRAS 000, 000–000
Asteroseismic Signatures of Activity Cycles 3
I j =
d3xρ|ξ|3 ≡ R5ρ̄Ĩ (2)
is the mode inertia, j ≡ (n,ℓ,m), and we need to know both the
source S(x) and the corresponding kernels K(x). The source must
include the direct influence of the growing mean magnetic field,
as well as its indirect effect on the convective velocities and tem-
perature distribution. Separate kernels for these effects were cal-
culated by Dziembowski & Goode (2004), but there is no theory
available to calculate the combined source. Moreover, it is unclear
whether the model of small-scale magnetic fields, adopted from
Goldreich et al. (1991), is adequate. Therefore, we will attempt to
formulate an extrapolation of the solar p-mode frequency shifts
based on changes in the Mg II activity index measured for the Sun
and for β Hyi in Section 2.
For p-modes, the dominant terms in all of the kernels are pro-
portional to |divξ|2. Thus, we write
K j(x) = |divξ j|
2 = q j(D)Y
ℓ , (3)
where D is the depth beneath the photosphere. A model-dependent
coefficient will be absorbed into the source, which we write in the
S(x) =
Sk(D)P2k(cosθ). (4)
Solar data imply that S is strongly concentrated near the photo-
sphere. Therefore data from all p-modes, regardless of their ℓ value,
may be used to constrain S . We might also expect that the source
normalization is correlated with the Mg II index.
If we want to calculate ∆ν j according to Eq. (1), we need
all terms of S up to k = ℓ. To assess the solar S , we have mea-
surements of the centroid shifts and the even-a coefficients (see
Dziembowski & Goode 2004). For the ℓ = 0 modes we only need
to know the k = 0 term, and for this the centroid data are sufficient.
Let us begin with this simple case.
3.1 Radial modes
Theoretical arguments and the observed pattern of solar frequency
changes suggest that the dominant source must be localized near
the photosphere. Therefore, it seems reasonable to try to fit the mea-
sured p-mode frequency shifts by adopting
S0(D) = 1.5× 10
−11A0δ(D − Dc) µHz
, (5)
with adjustable parameters A0 and Dc. The numerical coefficient is
arbitrary, and was chosen for future convenience. With Eqs. (3-5),
we get from Eq. (1)
∆ν j = A0
Q j(Dc), (6)
where R and M (as well as L below) are expressed in solar units,
frequencies are expressed in µHz, and
Q j = 1.5× 10
−11 q j
ν j Ĩ j
. (7)
The solar values of A0 and Dc can be determined by fitting the
centroid frequency shifts ∆ν j from SOHO MDI data for p-modes
with various spherical degrees, ℓ. Since at n = 1 the approximation
inherent in Eq. (3) is questionable, we use data only for the higher
orders.
For the Sun, we have
A0,⊙(Dc) =
w j∆ν j
, (8)
Figure 2. Determinations of A0,⊙ from SOHO MDI data with Dc fixed at
0.3 Mm (top panel), and using the optimal value of Dc for each set (middle
panel), with the corresponding changes in the Mg II index from the NOAA
composite data (bottom panel).
where ∆ν j are the measured shifts and w j are the relative weights.
The values of Q j are calculated from a solar model. The best value
of Dc is that which minimizes the dispersion,
σ(Dc) =
A0,⊙ −
. (9)
It is also reasonable to assume that A0 should be proportional to
the change in the Mg II activity index, ∆iMgII, and that Dc is pro-
portional to the pressure scale height at the photosphere. Thus, we
A0 = A0,⊙
∆iMgII
∆iMgII,⊙
Dc ∝ Hp = Dc,⊙L
0.25 R
. (11)
To determine A0,⊙, we used SOHO MDI frequencies for all
pn modes with n > 1, ℓ from 0 to ∼181, and ν between 2.5 and
4.2 mHz. The data were combined into 38 sets, typically cover-
ing 0.2 years. We averaged the frequencies from the first 5 sets,
corresponding to solar minimum (1996.3-1997.3), and subtracted
them from the frequencies in subsequent sets to evaluate A0,⊙ using
Eq. (8). The results are shown in Figure 2, where the points in the
top panel were obtained at fixed Dc = 0.3 Mm, which is represen-
tative of the highest activity period. In the middle panel, the value
of Dc was determined separately for each set and the error bars
represent the dispersion. In the bottom panel, we show the corre-
sponding changes in the solar Mg II index calculated from NOAA
composite data. A tight correlation between A0,⊙ and ∆iMgII,⊙ is
clearly visible.
Although the optimum value of Dc is weakly correlated with
the activity level, the dispersion changes very little between Dc =
0.2 and 0.4 Mm, so we fixed the value of Dc,⊙ to 0.3 Mm. In Fig-
c© 0000 RAS, MNRAS 000, 000–000
4 Metcalfe et al.
Figure 3. The observed p-mode frequency shifts averaged from four sets
of data obtained near the solar maximum in 2002.0 (top panel), and the
same shifts normalized by Q j (bottom panel) showing that most of the
frequency and ℓ-dependence is included in our parametrization. Different
symbols show the roughly equal number of modes with ℓ ≤ 30 (circles),
31 ≤ ℓ≤ 75 (squares), and 76 ≤ ℓ≤ 181 (triangles).
ure 3, we show the quality of the fit to the observed frequency
shifts for selected p-modes using Eq. (6) with the adopted value
of Dc. The upper panel shows the frequency shifts averaged from
four sets of data near the activity maximum in 2002.0, while the
lower panel shows ∆ν j/Q j . Note that most of the frequency and
ℓ-dependence appears to have been fit by our parametrization. The
slight rise at frequencies below 3 mHz could be eliminated by al-
lowing a spread of the kernel toward lower depths. However, since
the signal is more significant at higher frequencies, we believe that
adding a finite radial extent would be an unnecessary complication.
There were two activity maxima during solar cycle 23. The
first was centered near 2000.6 and the second at 2002.0. The av-
erage values of (A0,⊙,∆iMgII,⊙) are (0.3116, 0.0135) for five data
sets around the first maximum and (0.3669, 0.0178) for four data
sets around the second maximum. For future applications, we adopt
A0,⊙/∆iMgII,⊙ = 22.
With this specification, we get from Eqs. (6) and (10)
∆ν j = 3.3× 10
∆iMgII
q j(Dc)
ν j Ĩ j
, (12)
where
Dc = 0.3L
0.25 R
mM (13)
and again frequencies are expressed in µHz, while R, M, and L
are in solar units. This is our expression for predicting the radial
p-mode frequency shifts on the basis of changes in the NOAA
composite Mg II index. In Table 1, we list the frequency shifts
(∆ν j) calculated from Eq. (12) for the radial modes of β Hyi
observed by Bedding et al. (2007), adopting ∆iMgII = 0.015. The
mode parameters q j and Ĩ j were calculated from a model of β Hyi
generated using the Aarhus STellar Evolution Code (ASTEC;
Christensen-Dalsgaard 1982).
Table 1. Predicted radial p-mode frequency shifts between activity max-
imum and minimum for β Hyi, calculated with Eq. (12) and adopting
∆iMgII = 0.015. Frequencies are from Table 1 of Bedding et al. (2007).
n Frequency (µHz) ∆ν j (µHz)
13 833.72 0.061
14 889.87 0.091
15 945.64 0.116
16 1004.21 0.139
17 1062.06 0.168
18 1118.93 0.199
19 1176.48 0.234
3.2 Non-radial modes
Now from Eqs. (1) and (4). we have
∆νnlm =
Skκk,lm
2Inlνnl
, (14)
where,
κk,lm =
dθdφ|Y mℓ |
2P2k(cosθ) sinθ. (15)
As in Eq. (5), we can adopt
Sk(D) = 1.5× 10
−11Akδ(D − Dc,k) µHz
. (16)
For k > 0, the solar amplitudes Ak and effective depths, Dc,k
can be determined by fitting measurements of shifts in the a2k co-
efficients. The relation is
∆a2k,ℓm = AkZk,ℓQk,nℓ(Dc,k), (17)
where
Zk,ℓ = (−1)
k (2k − 1)!!
(2ℓ+ 1)!!
(2ℓ+ 2k + 1)!!
(ℓ− 1)!
(ℓ− k)!
(cf. Dziembowski & Goode 2004, their Eq. 2), and
Qk,nℓ = 1.5× 10
−11 qnℓ(Dc,k)
ν j Ĩnℓ
(compare to our Eq. 7).
The prediction of frequency shifts for non-radial modes re-
quires an additional assumption of the same scaling for all required
Ak amplitudes, which amounts to assuming the same Butterfly di-
agram as observed on the Sun. Moreover, since the shifts depend
on |m| and multiplets are not expected to be resolved, we need to
adopt the inclination angle (i) to correctly weight the contributions
from all of the components. Since we do not know i for β Hyi, we
restrict our numerical predictions to the radial modes.
4 ASTEROSEISMIC OBSERVATIONS
The detection of solar-like oscillations in β Hyi was first reported
by Bedding et al. (2001), and later confirmed by Carrier et al.
(2001). These two detections of excess power were based on data
obtained during a dual-site campaign organized in June 2000 using
the 3.9-m Anglo-Australian Telescope (AAT) at Siding Spring Ob-
servatory and the 1.2-m Swiss telescope at the European Southern
Observatory (ESO) in Chile. Both sets of observations measured
a large frequency separation between 56-58 µHz, but neither was
sufficient for unambiguous identification of individual oscillation
modes.
c© 0000 RAS, MNRAS 000, 000–000
Asteroseismic Signatures of Activity Cycles 5
Nearly 30 individual modes in β Hyi with ℓ=0-2 were detected
during a second dual-site campaign organized in September 2005,
and reported by Bedding et al. (2007). The authors also reanalyzed
the combined 2000 observations using an improved extraction al-
gorithm for the AAT data, allowing them to identify some of the
same oscillation modes at this earlier epoch. Motivated by the first
tentative detection of a systematic frequency offset between two
asteroseismic data sets for α Cen A (0.6±0.3 µHz; Fletcher et al.
2006), they compared the two epochs of observation for β Hyi and
found the 2005 frequencies to be systematically lower than those in
2000 by 0.1±0.4 µHz, consistent with zero but also with the mean
value in Table 1.
A comparison of the individual modes from these two data
sets (T. Bedding, private communication) allows a further test of
our predictions. Of the 14 modes that were detected with S/N> 4
in both 2000 and 2005, only one was known to be a radial (ℓ = 0)
mode, while four had ℓ = 1, three had ℓ = 2, two were mixed modes,
and four had no certain identification. Without a known inclination,
we can only calculate the shifts for radial modes, but the magnitude
of the shift is largest at high frequencies (see Table 1). Fortunately,
the radial mode that is common to both data sets (ℓ = 0, n = 18) has a
frequency above the peak in the envelope of power, improving our
chances of measuring a shift. The best estimate of the mode fre-
quency from each data set comes from the noise-optimized power
spectrum, since this maximizes the S/N of the observed peaks. The
noise-optimized frequency for the ℓ = 0, n = 18 mode was 1119.06
and 1118.89 µHz in the 2000 and 2005 data sets, respectively.
Considering the quoted uncertainty for this mode from Table 1 of
Bedding et al. (2007), the frequency was 0.17±0.62 µHz lower in
2005 than in 2000, again consistent with zero but similar to the
predicted shift for this mode in Table 1.
5 DISCUSSION
Our reanalysis of archival IUE spectra for β Hyi allows us to test
our predictions of the relationship between the stellar activity cy-
cle and the systematic frequency shift measured from multi-epoch
asteroseismic observations. The optimal period and phase of the ac-
tivity cycle from Section 2 suggest that β Hyi was near magnetic
minimum (2004.8) during the 2005 observations (2005.7), while it
was descending from magnetic maximum (1998.8) during the 2000
campaign (2000.5). The systematic frequency shift of 0.1±0.4 µHz
reported by Bedding et al. (2007) between these two epochs, and
the observed shift of 0.17±0.62 µHz in the only radial mode (ℓ = 0,
n = 18) common to both data sets are not statistically significant.
They are both nominally in the direction predicted by our analysis
of the activity cycle (lower frequencies during magnetic minimum)
and they have approximately the expected magnitude (cf. Table 1),
but the formal uncertainties on the period and phase of the activity
cycle do not permit a definitive test.
Future asteroseismic observations of β Hyi would sample the
largest possible frequency shift relative to the 2005 data if timed
to coincide with the magnetic maximum predicted for 2010.8+7−3 .
Long-term monitoring of the stellar activity cycles of this and other
southern asteroseismic targets (e.g. α Cen A/B, µ Ara, ν Ind),
which are not included in the Mt. Wilson sample, would allow
further tests of our predictions. For asteroseismic targets that have
known activity cycles from long-term Ca II H and K measurements
(e.g. ǫ Eri, Procyon), it would be straightforward to calibrate our
predictions to this index from comparable solar observations.
While our current analysis involves a simple scaling from so-
lar data, future observations may allow us to refine magnetic dy-
namo models by looking for deviations from this scaling relation
and attempting to rectify the discrepancies. By requiring the models
to reproduce the observed activity cycle periods and amplitudes—
along with the resulting p-mode shifts and their frequency depen-
dence for a variety of solar-type stars at various stages in their
evolution—we can gradually provide a broader context for our un-
derstanding of the dynamo operating in our own Sun.
ACKNOWLEDGMENTS
We would like to thank D. Salabert for inspiring this work with an
HAO colloquium on low-degree solar p-mode shifts in May 2005,
Keith MacGregor and Margarida Cunha for thoughtful discussions,
and the Copernicus Astronomical Centre for fostering this collab-
oration during a sponsored visit in September 2006. We also thank
the SOHO/MDI team, and especially Jesper Schou for easy access
to the solar frequency data, Tim Bedding for providing frequency
data for β Hyi, and Jørgen Christensen-Dalsgaard for the use of his
stellar evolution code. This work was supported in part by an NSF
Astronomy & Astrophysics Fellowship under award AST-0401441,
by Polish MNiI grant No. 1 P03D 021 28, and by NASA contract
NAS5-97045 at the University of Colorado. The National Center
for Atmospheric Research is a federally funded research and devel-
opment center sponsored by the U.S. National Science Foundation.
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	Introduction
	Archival IUE spectra
	Scaling p-mode shifts from solar data 
	Radial modes
	Non-radial modes
	Asteroseismic Observations
	Discussion
