THE NEXT DECADE - Lowell Observatory

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THE NEXT DECADE OF STELLAR CYCLES RESEARCH
THE NEXT DECADE
OF STELLAR CYCLES RESEARCH
RECOMMENDATIONS DEVELOPED AT A WORKSHOP HELD AT
LOWELL OBSERVATORY, OCTOBER 9-11, 2003
Jeffrey Hall (Lowell Observatory)
G. Wesley Lockwood (Lowell Observatory)
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THE NEXT DECADE OF STELLAR CYCLES RESEARCH
TABLE OF CONTENTS
List of Attendees – 3
Abstract – 4
Executive Summary – 5
Review and Current Status – 6
Recommendations for the Next Decade – 15
Summary – 23
Commentary by Judith L. Lean – 24
Commentary by John A. Eddy – 26
References – 27
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THE NEXT DECADE OF STELLAR CYCLES RESEARCH
WORKSHOP ATTENDEES
Sydney Barnes (Florida Institute of Technology)
Juan Fontenla (University of Colorado / LASP)
Peter Foukal (Heliophysics, Inc.)
Claus Fröhlich (World Radiation Center – Davos)
Mark Giampapa (National Solar Observatory – Kitt Peak)
Jeffrey Hall (Lowell Observatory)
Gregory Henry (Tennessee State University)
Michael Knoelker (High Altitude Observatory)
G. Wesley Lockwood (Lowell Observatory)
Piet Martens (Montana State University)
Richard Radick (National Solar Observatory – Sunspot)
Gary Rottman (University of Colorado / LASP)
Steven Saar (Harvard-Smithsonian Center for Astrophysics)
David Schleicher (Lowell Observatory)
David Soderblom (Space Telescope Science Institute)
O. R. White (High Altitude Observatory)
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ABSTRACT
Long-term, synoptic observations of the spectroscopic and photometric behavior of Sunlike stars has been performed at select observing sites for nearly 40 years. Most of the
spectroscopic data have been collected at the Mount Wilson Observatory (MWO),
beginning in March 1966 with Olin Wilson’s initial observations of the cores of Ca II H&K
lines in a set of 139 Sun-like stars. Since 1994, Ca II H&K and echelle data of the Sun
and 300 Sun-like stars have been gathered at Lowell Observatory using the SolarStellar Spectrograph (SSS), complementing the MWO target set and spectral coverage.
Synoptic photometry was carried out for 18 years at Lowell, and continues today at the
Fairborn Observatory, in a program run by by Tennessee State University. Other
significant ground-based surveys have been performed as well, and since 1980,
continuous observations of the total solar irradiance have provided a large data set
allowing direct comparison of solar with stellar broadband variability.
We convened a workshop at Lowell Observatory on October 9-11, 2003 to plan the next
decade of work in this field. Several speakers gave presentations about the status of
various projects, but the emphasis during the sessions was on open discussion of the
relevant issues. The product of the workshop is this document: a review of the
development and current status of stellar cycles research, and a summation of the
recommendations of the attendees for essential studies to be performed over the next
decade. For our purposes, “stellar cycles research” is taken in its full modern context,
encompassing not only observations of Sun-like stars, but also solar variability on
multiple timescales and its relevance to terrestrial climate change.
We first briefly review stellar cycles research: its historical development and the present
status of the field. We trace the important threads of the past 50 years, and review
current relevant programs, as presented on the first day of the workshop by several of
the participants. The perspectives and discussions of outstanding problems that
emerge from this review clarify the motivation for the workshop, as well as why we need
to do the work outlined in the recommendations. This background material can be
found on pages 4 to 12 of this document.
With the background in place, we present the current results and recommendations
brought forward by workshop attendees. These recommendations present a road map
for lines of study likely to be fruitful over the next 10 years, and begin on page 13.
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EXECUTIVE SUMMARY
Research on the nature, morphology, and physics of stellar activity cycles has had a
fruitful, 40-year history. Beyond its many applications to pure stellar astrophysics, the
field has developed broad relevance to a variety of timely issues.

Understanding the nature of activity cycles in the Sun’s nearest stellar cousins is
essential to understanding the nature of the solar activity cycle itself, as well as
illuminating probable solar behavior during periods of prolonged quiescence such as
the Maunder Minimum of 1645-1715.

Improved understanding of stellar irradiance variability allows development of more
realistic solar irradiance constructions. This impacts assessment of global warming
due to solar forcing, thereby playing a crucial role in supporting the directives of
NASA’s Living With a Star (LWS) program.

With the launch of satellites such as the Solar Radiation and Climate Experiment
(SORCE), which provides ongoing observations of the spectral distribution of solar
irradiance variability, continued analogous observations of stellar variability in
complementary bandpasses, both from the ground and space, becomes imperative
to

Identification of the most nearly Sun-like stars provides critical guidelines for
upcoming searches for true “solar systems,” i.e., stars with habitable, Earth-like
planets with stable orbits and climates.

Assessment of the overall variability of a large ensemble of nearby stars guides
astrobiology efforts by placing limits on the range of conditions likely to exist on such
planets as they may have.
Synoptic observations of the Sun and Sun-like stars have been carried out at diverse
locations such as Mount Wilson, Kitt Peak, Lowell Observatory, and Fairborn
Observatory; since about 1978 they have been complemented from space by the solar
irradiance missions as well as by observatories such as IUE and ROSAT. The renewed
focus of the field on closely solar analogous stars and the so-called “stellar-solar
connection,” combined with current imterest in extrasolar planets, origins, and the
critical issue of global warming, makes it imperative that these studies be continued,
and move forward from a well-considered consensus. This workshop report presents a
review of this important field, and some guidelines for the next decade of work.
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REVIEW AND CURRENT STATUS
INTRODUCTION
Research on the astrophysics of activity and variability of Sun-like stars covers an extensive literature.
Recent work on the so-called “solar-stellar connection,” the solar irradiance data and terrestrial climate
reconstructions, and the effect of solar variations on terrestrial climate have diversified the literature even
further. The connections between the various threads are complex enough that reviewing the field by any
one criterion – chronology, method of observation, class of object – does not necessarily provide the path
of least obfuscation. For this review, therefore, we will use results presented at our workshop as
springboards for overviews of how we have reached those results during the modern era of stellar cycles
research, where we define the “modern era” to begin in 1957. That year marks the appearance of two
seminal papers: the observational discovery of the dependence of Ca II H&K emission line widths on
luminosity (Wilson & Bappu 1957), and the first of a series of theoretical papers concerning the NLTE
source function (Thomas 1957) 1; it also incorporates all observations and theory now commonly
referenced, and defines a 46-year period that divides neatly into two parts that lend a useful historical
perspective to the motivation for our workshop.
General developments in the field over this nearly five decade period appear in Figure 1 on the next
page, taken from a slide shown at the opening of the workshop. This diagram shows some (though
certainly not all) of the observational programs of the last 40 years, with arrows indicating their durations,
some of the essential observational quantities (in red), and a few of the references and major reference
series (in green). Shaded ellipses in the background highlight major turning points in the field. We argue
in the sections below that one of these turning points is now, and this explains the timing of the workshop.
We will now briefly describe the major programs and developments in the field, and then turn to the
essential results.
MAJOR PROGRAMS AND DEVELOPMENTS
Long-Term Programs, 1960 - 2000
Long-term programs devoted to observations of the stars appear in blue in Figure 1. Olin Wilson
launched these programs in the mid 1960s with at the Mount Wilson Observatory (MWO). 2 After his
initial investigations of the now well-known age-activity (Wilson 1963, 1964) and rotation-activity (Wilson
1966) relationships, he began synoptic observations of the cores of the Ca II H&K lines a set of 139 stars
“for the purpose of initiating a search for stellar analogues of the solar cycle” (Wilson 1968). The program
continued under his guidance until his publication of the first magnum opus stellar cycles paper (Wilson
1978), which presented the results of the Mt. Wilson HK observations for what was essentially the length
of one solar cycle. Wilson was succeeded in his efforts by a team including individuals from Harvard,
Sacramento Peak, and Utrecht, and following a transition period during which a new HK photometer was
1
This work of course developed from many earlier investigations that go back to the Lucy of the modern
field, a paper first noting the presence of Ca H&K line core reversals in cool stars (Schwarzschild &
Eberhard 1913), who note that “it remains to be shown whether the emission lines of the star have a
possible variation in intensity analogous to the sun-spot period.” Amusingly, this harbinger of a century of
exhaustive research appears immediately under the heading “Minor Contributions and Notes.”
2
The similarity of the names is a coincidence.
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constructed at Mount Wilson, the program continued under the guidance of Sallie Baliunas. Baliunas and
her team authored many papers during this “second phase” of the Mount Wilson program, with the grand
results appearing in a second magnum opus paper (Baliunas et al. 1995), appropriately dedicated to Olin
Wilson, who passed away on July 14, 1994. Wilson’s legacy to the community is the longest and largest
extant database of observations of stellar activity.
FIGURE 1. An overview of stellar cycles research. Far more is omitted than shown, but many of the
essential developments and projects are listed. Major programs appear at left, with descending arrows
indicating their duration. The observational quantities used by workers in the field are shown in red, and
some of the essential references appear in green at right. The shaded blue ellipses in the background
mark major turning points in our approach to stellar cycles research.
The “Lowell” program in Figure 1, which began in 1984, was a photometric survey of 35 targets,
undertaken to address our lack of understanding of irradiance variations in Sun-like stars, or which stars
were the best “solar analogs.” These data were productively compared with the MWO data and yielded
important insights into the behavior of irradiance variations over the course of activity cycles in solar-age
and younger stars (Radick et al. 1987, Radick et al. 1998). Though the Lowell program ended in 2000,
high-precision photometry of Sun-like stars continues at the Fairborn Observatory south of Tucson. High
precision nightly observations of 350 Sun-like stars with four 0.8-meter automated photometric telescopes
(APTs) began at Fairborn in 1993. The longest of these data sets are now 12 years, and they overlap the
Lowell program by several years, and the Lowell and Fairborn data sets have now been merged
(Lockwood et al. 2004). Henry (1999) has described the site and the techniques used to achieve submillimag photometry of a large set of stars that substantially overlap the Mount Wilson set.
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In the late 1980s, an instrument called the Solar-Stellar Spectrograph (SSS) was developed at the High
Altitude Observatory and installed at the Lowell Observatory, designed to complement the Mount Wilson
HK photometer, the SSS incorporates both a single-order instrument covering the HK region as well as
an echelle covering the optical and near IR from λλ 5100 to 9000 Å with 70% spectral coverage. It is also
uniquely equipped to observe both the Sun and the stars directly. Regular observations with the SSS
commenced in 1994, and the initial description of the system and the data reduction techniques appears
in Hall & Lockwood 1995.
Long-term observations of G dwarfs in M67, some nine magnitudes fainter than the Wilson stars, have
been obtained with the WIYN telescope at Kitt Peak by Mark Giampapa, beginning in 1996 (Giampapa et
al. 2000; Giampapa et al. 2004).
Complementing these ground based stellar and solar-stellar observing campaigns is the long-running
series of observations from stations of the National Solar Observatory at Kitt Peak (White & Livingston
1978, White & Livingston 1981, White et al. 1992) and Sacramento Peak (Keil & Worden 1984; Worden,
White, & Woods 1998). The NSO solar Ca K series, shown as one of the solar-oriented programs in
Figure 1, provides the longest continuous database of spectroscopic solar Ca K observations, now
spanning well over a Hale cycle. Full-disk Ca II K images have also been obtained at a regular cadence
at the McMath Observatory, and at the Big Bear Solar Observatory since 1981 (Johannesson, Marquette,
& Zirin 1998), and the upcoming data set from the SOLIS instrument at Kitt Peak will continue these
synoptic solar Ca K observations.
Developments, 1977 - 1982
Stellar cycles research underwent critical changes between 1977 and 1982, about halfway between
publication of the famous Wilson-Bappu relation and the present. This important period in the field is
indicated by the second of three background ellipses in Figure 1, and a perspective on its impact is critical
to projecting fruitful lines of work over the next decade.
Perhaps the most significant of these changes was the advent of the first spaceborne total solar
irradiance (TSI) measurements, which commenced with observations from the Nimbus 7 satellite,
launched in late October 1978, and the Solar Maximum Mission (SMM, launched on Valentine’s Day
1980), beginning a unbroken ongoing time series of TSI data that continues today using instruments
aboard the Solar Radiation and Climate Experiment (SORCE). For the first time, it became possible to
directly compare the irradiance variability of the Sun with its chromospheric activity, and these growing
data sets were part of the impetus behind the initiation of the Lowell solar-stellar photometric program in
1984.
In 1978, Johannes Hardorp launched another important line of study by beginning a systematic search for
solar analogs – the stars most closely resembling the Sun (Hardorp 1978, 1980a). The literature quickly
became contentious (Clements & Neff 1979, Hardorp 1980b), and Hardorp’s methods did result in his
reaching poor conclusions about some stars (positing Van Buren 64, for example, as a solar analog; see
the comments by Garrison 1985). However, Hardorp’s work inspired a second set of investigations
(Cayrel de Strobel et al. 1980, Cayrel de Strobel & Bentolila 1988, Friel et al. 1989), an exhaustive review
of the topic (Cayrel de Strobel 1996), and more recently the identification of the current best (and only)
solar twin, 18 Sco (Porto de Mello & da Silva 1997, Hall 1998). Most significantly for stellar cycles
workers, the search for “the Sun among the stars,” as Hardorp termed it, led to greatly increased interest
in the so-called “solar-stellar connection,” and the idea that understanding putative effects of solar
variability on terrestrial climate can be aided by analyses of activity cycles and irradiance variations of an
ensemble of the most nearly Sun-like stars.
These advances – flux-calibrated data from satellite observations of stars, the growing solar TSI
database, and increased efforts to identify the most solar-like stars – led to commensurate evolution in
interpretation of the data between 1978 and 1984, as is evident in the observational quantities listed in
red in Figure 1. Wilson (1978) expressed his Ca II H&K series in terms of a dimensionless quantity FHK.
that was essentially the ratio of pulse counts from a star to the pulse counts from a standard lamp; this
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
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quantity was not physically interpretable but self-consistent. Wilson’s HK photometer (“HKP-1”) was
upgraded to a new instrument, called the HKP-2, in 1977 (Vaughan, Preston, & Wilson 1978).
Observations from the new instrument were (and are) expressed in terms of a second dimensionless
quantity S, similar to F, defined as the ratio of counts in two 1.09 Å wide triangular bandpasses centered
at the H and K line cores to the counts in two 20 Å wide bandpasses centered at λ4001.1 and λ3901.1.
Today “Mount Wilson S” is universally recognized as a standard measure of stellar activity, but it contains
a color term (due to its dependence on nearby continua) that render it unsuitable for direct physical
comparison of stars of different temperature, or for interpretation in the context of absolutely calibrated
data or models, such as the theoretical flux-calibrated HK profiles being produced at that time by the
Boulder group in their Stellar Model Chromospheres (“SMC” in Figure 1) series of papers (Kelch, Linsky,
& Worden 1979, Linsky et al. 1979, Giampapa et al. 1981). Thus, in 1982, we find the first of the papers
that develop the by-now familiar quantity R’HK (shown in Figure 1 as one of the significant steps in the
development of stellar activity observables). The concept was first formulated by Middelkoop 1982, in
paper IV of the Utrecht group’s long Magnetic Structure in Cool Stars series (“MSCS” in Figure 1).
Middelkoop derived a color-dependent factor Ccf that removes the color term from S, thus making
measurements for different stars directly comparable. (He also provided a prescription for then
converting the color-corrected S to flux F; more on this below). The Harvard group extended Middelkoop’s
relation by first defining RHK ≡ Ccf S, and then deriving the analogous quantity R’HK, which removes the
photospheric contribution from the measured energy in the H&K line cores. Physically, R’HK is the
fraction of the star’s bolometric luminosity emitted by the chromosphere in the cores of the H&K lines, and
it is widely used (e.g., Radick et al. 1998, in their summary of the Lowell photometric program).
The growing IUE, EINSTEIN, HEAO, and TSI databases made it also imperative to understand S in terms
of physical flux, pursuant to the investigation of “flux-flux relations” to illuminate the processes driving
energy transfer between the chromosphere and outer atmospheres in cool stars (indicated by the “FHK –
Fλ” entry in Figure 1). Middelkoop (1982) provided the first prescription, but here the picture, as did the
solar analog picture, became murky. The conversion from color-independent S to flux was refined
several times (Oranje 1983, Rutten 1984, Schrijver et al. 1989), with the effect that many references in
the early 1990s avoid the issue by using the dimensionless, color-independent form of S, which is at least
linearly related to flux. The issue was further examined by Hall & Lockwood 1995 in connection with the
SSS project, with the conclusion that Middelkoop’s original prescription was correct.
To add a final – but enormously significant – thread to the field, interest was renewed in solar-terrestrial
interactions (Eddy 1976, Eddy 1977, Hays 1977), in the volume “The Solar Output and its Variation,”
edited by Dick White. While interest in solar influences on climate had generated lengthy treatises earlier
in the 20th century (e.g., Abbott 1929), the impending availability of quantitative solar irradiance data
finally made formal study tractable. Understanding Sun-like stars as possible proxies of solar activity,
especially in connection with periods such as the solar Maunder Minimum, brought stellar cycles work to
the full attention of the climate community.
By 1984, therefore, stellar cycles research had changed significantly from its state in 1977. Wilson (1968)
posed the question: Does the chromospheric activity of main sequence stars vary with time, and if so,
how? He did not ask specifically about the variability of “Sun-like stars,” nor did he pick his original
targets on the basis of their resemblance to the Sun. Had he written the paper in 1984, the original
question may well have been phrased differently.
Solar Irradiance and Climate, 1980-2000
Many of the recent developments and efforts in stellar cycles research stem from the rapid resurgence of
interest in Sun-climate interactions, especially in light of the rapid global temperature rise observed since
about 1970, as well as from the availability of solar irradiance observations that prompted broader
synoptic stellar observations than pure HK studies (the Lowell photometry program and the effort at HAO
to build the SSS were both outgrowths of this).
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Olin Wilson himself, in fact, presaged these recent broad trends in a comment he made toward the end of
an IAU colloquium on stellar chromospheres (Wilson 1973): “It is important to realize that a chromosphere
is a completely negligible part of a star. Neither its mass nor its own radiation makes a significant
contribution to those quantities for the star as a whole.” Wilson obviously meant to be provocative (and,
judging by the response from the venerable R. N. Thomas, he succeeded), and his suggestion was
certainly not that we ignore chromospheres. Rather, Wilson was likely already considering the
implications of understanding the spectral distribution of stellar variability, both in then inaccessible
regions of the spectrum that obviously would be opened to observation by the impending satellite
observatories, as well as in optical photospheric features more closely tied to phenomena responsible for
a large part of the star’s luminosity variations.
Thus, we find a slightly revised form of Wilson’s original question posed by William Livingston (Livingston
& Holweger 1982): Do the strengths of Fraunhofer lines in the solar integrated flux spectrum (i.e., “the
Sun as a star”) vary with time? If so, with what amplitude and on what time scale? In this paper and
subsequently (Livingston & Wallace 1987), small variations in solar photospheric features over the course
of the activity cycle were documented. The variations are of much smaller amplitude (at most 2% over
the solar cycle) than the Ca II HK variations, but the available proxies are much more numerous.
Contributing to the interest in broadband solar and stellar variability proxies were the accumulating
records of solar irradiance data from a succession of satellites. The composite record appears below.
FIGURE 2. The latest composite record of solar irradiance (not yet including the recent SORCE data).
From presentation by C. Fröhlich, PMOD.
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As these solar irradiance data accumulated through the 1980s, models of the solar luminosity variations
appeared in the literature, typically employing a two-component model in which the positive correlation
between solar activity level and total irradiance is explained by a excess facular brightening slightly
dominating sunspot darkening (Foukal & Lean 1988). Contributions by additional non-facular
components have been proposed (Kuhn & Libbrecht 1991), though Lean et al. (1998) find that these
components are not required to recover the observed TSI variations, and Radick et al. (1998) assumed a
two component model in their analysis of facular versus spot domination of irradiance variations in Sunlike stars of differing ages.
Closely connected with the solar-stellar irradiance analyses has been the application of these data in
reconstructing terrestrial climate variability on both recent and long timescales. Intense interest and
scrutiny surrounded the publication of an apparent extremely tight correlation between the global northern
hemisphere temperature and the length of the solar cycle (Friis-Christensen & Lassen 1991), as well as a
finding, based on Mount Wilson time series of non-cycling stars, that a Maunder Minimum-like phase may
entail a brightness decrease of as much as 0.4%, well in excess of the current solar cycle variation
(Baliunas & Jastrow 1990). However, others have not recovered the Friis-Christensen & Lassen result
and Laut (2003) has published a detailed discrediting of the work. Hall & Lockwood (2004) have likewise
been unable to recover the Baliunas & Jastrow distribution of cycling versus non-cycling stars, and
Giampapa, in his presentation at the Stellar Cycles workshop, showed that he also does not recover a
bimodal distribution of cycling versus flat stars in a 45-star sample of G dwarfs in M67. It appears that
while solar forcing does affect climate and can reproduce much of the climate record until as recently as
the slight cooling from 1940-1960, the magnitude of the effect is not known and is not yet well illuminated
by present stellar results.
A New Turning Point, 2004
As indicated by the lowest ellipse in Figure 1, we are at a timely point to evaluate the status of stellar
cycles research, and to identify future directions for the field. We will first very briefly summarize some of
the results presented at the workshop.
As discussed above, there are two synoptic spectroscopic observing programs underway, the 40-year
Mount Wilson program and the 9-year Solar-Stellar Spectrograph program. Representative data series
for some of the most Sun-like stars in the target sets were presented at the workshop by Wes Lockwood
for Sallie Baliunas, and by Jeffrey Hall, and appear in Figures 3 and 4 below.
Complementing these studies are the ongoing photometric observations of Sun-like stars being carried
out at Fairborn Observatory. Greg Henry from Tennessee State presented an overview of the facility, the
target set, and sample observations. The precision of the averaged observations is better than one
millimagnitude – an essential threshold for observing stellar irradiance variations comparable to the
Sun’s. In many respects, this program is now the most modern synoptic stellar observing program. The
system is fully automated and can acquire data more rapidly and efficiently than either MWO or SSS, and
on a more regular basis.
Significantly, between the Mount Wilson, SSS, and Fairborn programs, we observe only a handful of good
solar analogs (by the conservative definition of Cayrel de Strobel 1996), and only one star (HD 146233 =
18 Sco) that has been repeatedly identified as a real solar twin. Henry’s photometric observations from
the Fairborn Observatory include 350 Sun-like stars, including 18 Sco and most of the other bright solar
analogs, Mount Wilson targets, and SSS targets. The Fairborn results have shown that 18 Sco is
possibly as photometrically quiescent as the Sun – yet another confirmation of its remarkable similarity to
our star (Lockwood et al. 2002; see also Figure 5 below).
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FIGURE 3. Representative Ca II H&K series of Sun-like stars from the Mount Wilson program, presented
at the workshop by Wes Lockwood, on behalf of Sallie Baliunas. Chromospheric activity is expressed in
terms of the well-known Mt. Wilson S index. Presented at the workshop from communication from S
Baliunas, CfA.
FIGURE 4. Representative Ca II H&K series of stars of near-solar color from the Solar-Stellar
Spectrograph program, presented at the workshop by Jeffrey Hall. Activity is expressed in terms of the
HK index (left axis), flux (right axis), and derived S (yellow left axis). Blue bands in each diagram
represent the approximate excursion in S for the star as measured directly by Mt. Wilson. From
presentation by J. Hall, Lowell.
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FIGURE 5. Yearly mean differential magnitudes of HD 146233 = 18 Sco from the Fairborn observatory.
The number in the lower left of each panel is the total magnitude range of the yearly means. Their
standard deviation is given in the lower right of each pane. Precision of the seasonal means is at the 0.2
millimag level and shows that 18 Sco (star "d") varies relative to inactive comparison stars by less than
half a millimag (0.05%). From presentation by G. W. Henry, TSU.
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If solar analog candidates are to be identified, surveys are the way to begin, and they are fortunately
underway. T. J. Henry et al. (1996) have surveyed the Ca II H&K emission in 800 southern stars, which
David Soderblom discussed at the workshop (Figure 6).
FIGURE 6. Chromospheric activity in 800 southern G dwarfs. The quantity log R’HK is a common
measure for expressing the activity level; the Sun lies at B – V = 0.65 and log R’HK ≈ -4.95, in the middle
of the “inactive” star classification band. From presentation by D. Soderblom, STScI.
Soderblom also discussed a large, volume-limited survey he has undertaken of northern G dwarfs to
about 50 pc, or roughly V=9, as determined from HIPPARCOS parallaxes. Surveys such as this one are
an essential starting point for identification of additional targets for the next decade of stellar cycles work.
The paucity of good solar analogs, however, highlights a deficiency in the current stellar databases, at
least as far as comparing solar irradiance with direct stellar counterparts goes: there is only one star
brighter than V=7 that seems to truly resemble the Sun. If stellar cycles work is specifically to provide
insight into solar and Sun-climate work – and this seems a sensible objective given the present
uncertainty in the luminosity effects of Maunder minima, the overall role of solar forcing in climate change,
and federal programmatic objectives in Sun-climate connections and even extrasolar planet searches and
exobiology – then some important gaps in our observational approach must be addressed.
A scan of the review above will reveal a nearly monomaniacal fixation on Ca II H&K – for good reason.
The features in question are accessible from the ground and respond at an easily detectable level to
changes in solar and stellar activity. However, they also lie well off the Sun-like star blackbody peak, with
the line cores at roughly 8% of the already weak continuum. The MWO and SSS measurements have
precisions of no better than a few percent, and, as Wilson reminded us, emerge from “a negligible part of
a star.” A re-evaluation of our observing protocol, identification and expansion of a statistically significant
number of solar analogs and (perhaps) twins, and increased cooperation between complementary
programs is called for. These issues and the specific plans for implementing them appear in the next
section.
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RECOMMENDATIONS FOR THE NEXT DECADE
The purpose of this workshop was to provide a limited, well-directed set of goals for the field of stellar
cycles research over the next decade. The second day of the workshop consisted exclusively of open
discussions intended to identify these goals, and the recommendations below have been distilled from the
discussions that took place. Representatives of the Mt. Wilson stellar cycles program were unfortunately
unable to attend the workshop; however, Dr. Sallie Baliunas sent a PowerPoint summary of the status of
the Mt. Wilson program and her objectives in this arena for the future to Wes Lockwood, who represented
her in absentia during the meeting.
Each of the six recommendations below is presented in the same format. A summary statement appears
first, followed by the reasoning that led to the recommendation and any qualifying points of view.

A next-generation, automated observatory dedicated to synoptic spectroscopic
observations of Sun-like stars should be constructed in the next 3-6 years.
REASONS
1. Existing synoptic spectroscopic programs are becoming prohibitively expensive to maintain in
their present, non-automated operating mode. W. Lockwood reported the SSS program is
understaffed for the amount of observing needed, and S. Baliunas reported (via Lockwood) that
Mt. Wilson will be operating in the future in “low frequency mode.”
2. Equipment used in the existing programs is aging and/or outdated. The HKP-2 photometer is
more than two decades old. The SSS uses small, noisy CCDs and relies on a hardware system
that has many interrelated, irreplaceable parts; a critical hardware failure would be difficult or
impossible for current program staff to repair.
3. The recommendations listed below will (1) exacerbate the problems outlined above or (2) cannot
be achieved with current instrumentation.
DISCUSSION
The call for an automated facility came most strongly from G. Henry, who operates the automated
photometric telescopes (APTs) at Fairborn Observatory. Attendees concurred with his opinion that
coordinated photometric and spectroscopic observations are vital to progress over the next decade,
and that neither the Mt. Wilson HK project nor the Lowell SSS project can currently keep up with the
data acquisition rate of the Fairborn APTs. The bottleneck in coordinated observations lies clearly on
the spectroscopic side.
Questions followed regarding the feasibility of automating current programs. Attendees concurred
that automation of the Mt. Wilson system was likely neither feasible nor intended. Hall said that the
SSS system would be difficult to automate, and that doing so is probably not desirable given the
system’s present limitations of spectral coverage, detectors, and telescope aperture.
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FIGURE 7. The Fairborn Observatory in sourther Arizona’s Patagonia Mountains, where Tennessee
State University, operates eight 0.4m to 2.0m telescopes. Fairborn is presently the most modern and
efficient site from which synoptic measurements of Sun-like stars are being carried out. From
presentation by G. Henry, TSU.
Attendees considered what would constitute the ideal spectroscopic facility to complement the
Fairborn facility shown above. The requirements of recommendation 6 below suggest an aperture of
1.5-2 meters. The broad spectral coverage and data requirements called for in recommendation 3
below indicate that an echelle spectrograph with at least 2K x 2K CCD is needed, preferably benchmounted and therefore likely fiber-fed. The opto-mechanical system should be dedicated exclusively
to a stellar cycles program. Automated operation is imperative, including weather monitoring, target
selection, and data transfer to the analysis facility. The program requirements and likely target list
require a good, though not necessarily pristine, observing site.

Observations using existing synoptic spectroscopic facilities (Mt. Wilson and
Lowell) should continue at least until the next-generation stellar cycles
observatory is in regular operation.
REASONS
1. Although future programs will most productively expand both the set of stars being observed and
the spectral coverage beyond that of Mt. Wilson and SSS, the existing time series are too
valuable to be summarily discontinued. Direct observations of a transition to or from a Maunder
Minimum state are highly desirable, and while the evidence for such is not yet definitive, the Mt.
Wilson time series, and to a lesser extent the SSS series, provide the only present basis for an
internally self-consistent observation of a cycling/non-cycling transition.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
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2. Overlap of the Mt. Wilson series and the SSS series with the data from a new, automated facility
is essential. Failure to achieve direct temporal comparison of one data series with another can
create serious calibration problems.
3. The HK time series have long since reached the point of being usable for application to studies of
differential rotation (Baliunas et al. 1985) and stellar dynamos (e.g., Baliunas et al. 1996,
Brandenburg, Saar, & Turpin 1998; Saar & Brandenburg 1999). While many of the fundamental
astrophysical questions posed about the frequency and morphology of stellar activity cycles by
originators of the field have been answered, useful insights into both the dynamo behavior and
changes in the length, amplitude, or baseline level of the activity cycle in a single target on multicycle timescales (as is well documented for the Sun) are still possible with continued HK
operation of these programs.
DISCUSSION
Program continuity is considered essential. A prime example of the problems in reconciling nonoverlapped data sets appears in Figure 2 above, in which the “PMOD” reconstruction of the solar
irradiance composite shows no change in irradiance from the minimum of solar cycles 21 and 22 to
that of cycles 22 and 23, while the “ACRIM” composite shows a distinct rise. Willson (1997) finds that
the two observed solar minima show a secular rise, while Fröhlich & Lean (1998) find that it does not.
Existing data series must be directly comparable to those from any new program.

Substantial effort must be directed in the next 1-3 years to ensuring the crosscalibration, internal consistency, and accessibility of the existing synoptic data
sets.
REASONS
1. The evolution of instrumental performance is critical in the reduction and analysis of data
obtained by the long-term programs. Both the SSS and MWO data sets are known to have
systematic artifacts. The SSS data show a slight long-term evolution manifested in gradually
increasing intensities in the wings of the Ca K line. Though this evolution is small, it results in
measurable systematic increases in the measured K indices (Figure 8). Baliunas reported, via
Lockwood, that one of the MWO priorities was to “rework calibration for increased precision and
improved archival access.” Lockwood noted that the S indices of the MWO series of Sun-like
stars show a systematic decrease (Figure 9).
2. Although the calibration of MWO S to SSS derived S is good, discrepancies that remain for some
stars need to be reconciled.
3. Results from stellar cycles work are presented in myriad ways (K index, S, log R’HK, F), and the
various archives are either scattered about the Web or not accessible at all. Improved crosscalibration of these quantities, and access and documentation of reduction and analysis
procedures for any of the relevant programs (not necessarily just the spectroscopic efforts), is
vital for broad evaluation of the results.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
18
FIGURE 8. Systematic trend in SSS data. Shown is the mean intensity in the Ca K line wings in SSS
spectra of the solar twin 18 Sco, approximately 0.5 Å from the line core. A slight rise of about 0.005 of
continuum intensity over 7 observing seasons is apparent. This same rise appears in the time series of
many of the SSS stars. From presentation by Hall, Lowell.
FIGURE 9. Systematic trend in MWO data. All stars in this sample of Sun-like stars with significant
secular changes in S trend downward. From presentation by Lockwood, Lowell.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
19
DISCUSSION
The general opinion of the workshop was that although many detailed investigations had been carried out
to resolve cross-calibration discrepancies, there is still no consensus on the correct reconciliation of the
databases. Several conversions of S to flux have been presented, and even the widely used R’HK has
two different formulations.
The large data archives are also generally not published in electronic format. Soderblom noted that the
results of his large Ca HK survey will be published on the web, and attendees encouraged other
programs to follow suit. To some extent, the task of publishing each archive rests with the individual
investigators, though there was some discussion of a central Web site that, even if not actually containing
all the individual data, contained summaries, essential results, and a concise set of links to external sites
containing the archival data from the various stellar cycles programs.

Coordination between complementary stellar cycles programs, both groundbased and space-based, must be improved, and should be incorporated in future
proposals by the various groups involved.
REASONS
1. The newest generation of space-based solar irradiance observatories also incorporates
spectroscopic instruments covering spectral regions directly comparable to those observed by
current ground-based programs, opening a new way to directly compare data sets of solar and
stellar spectral variability
2. Important problems remain in our understanding of the spectral distribution of solar cycle
variability, such as the discrepancy between the cycle amplitude of solar coronal emission and
that observed by ROSAT for many stars, which is the new factor-of-three problem in solar
astrophysics.
DISCUSSION
The most recent solar irradiance mission, the Solar Climate and Radiation Experiment (SORCE) has not
only a TSI monitor on board, but a suite of instruments including the Spectral Irradiance Monitor (SIM),
which have begun synoptic spectroscopic observations of the Sun from space. The spectral coverage of
these instruments and the irradiance variability models one can construct using these data were
discussed by Gary Rottman and Juan Fontenla of the SORCE project.
Piet Martens (Montana State) discussed the X-ray variability of the Sun and stars, and proposed
programs to specifically address this problem from space. There was agreement that proposals and
observing programs to explore this and similar problems require formal target coordination between the
various groups. To date, with the exception of the Lowell photometry – MWO S irradiance variations
program (Radick et al. 1998), these “multiwavelength” efforts have been somewhat casual.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
20

Future ground-based observations must take advantage of large-format CCDs to
provide ongoing ing of currently unexplored regions of the spectrum particularly
that from λ4000 to λ5000.
REASONS
1. Carefully chosen proxies other than HK, obtained in regions of the spectrum where greater S/N is
possible than in the HK line cores, have the potential to provide more robust measures of activity
than single-line proxies
2. To more fully understand the origin of luminosity variations in stars, we need to observe a variety
of proxies, as has been done for the Sun by Livingston and his collaborators. Long-term
observing of features of varying degrees of sensitivity to brightness changes in magnetic
structures, for example, will let us directly examine the relative importance of these structures in
stellar irradiance variations and, by extension, TSI variability.
DISCUSSION
The increased interest in using spectral features other than Ca II H&K as activity proxies (e.g., Livingston,
White, & Wallace 1987, Hall & Lockwood 2000) led to extended discussion of the utility of these features
in stellar cycles work. Foukal mentioned the CH G band at ≈λ4300 as a likely example of such a proxy,
and drew our attention to a fortuitously timed paper (Schussler et al. 2003) on this very feature that
appeared shortly after the workshop. Observations of this and other proxies with varying degrees of
sensitivity to magnetic structures, and with different places of origin (e.g., chromosphere vs. quiet
photosphere), if then compared with the star’s HK cycle and irradiance variability, might more fully
quantify the origin of luminosity variations over the course of the activity cycles.
The discussion also highlighted some important gaps in our current stellar cycles database, summarized
in Figure 10 on the next page. The spectrum between λ4000 and λ5000 contains numerous features that
might productively be used as new activity proxies (including the G band and Hβ), yet spectroscopic time
series from this part of the spectrum do not exist. The SSS echelle does cover the region from λ5100 to
λ9000, but with gaps in the spectral coverage due to the small size (512 x 512) of the CCD. Given the
ongoing b – y observations from Fairborn, and the full spectral coverage of instruments like SIM aboard
SORCE, the need for the spectroscopic programs to include this portion of the spectrum is acute.

The most nearly Sun-like stars down to visual magnitude 10-11 must be identified
via surveys and targeted for frequent observation.
REASONS
1. The broad interest in the use of stellar observations to provide perspective on solar irradiance
variations and proxy reconstructions of long-term solar variability makes identification of a
statistically significant set of Sun-like stars imperative. Statistics indicate that the observations
must be pushed to at least V=10 for this to be possible.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
21
FIGURE 10. Deficiencies in the current overall ground-based database, displayed on a time series – V
magnitude – wavelength phase space. The spectroscopic programs cover a long duration with minimal
spectral coverage (MWO) or broader coverage with a much shorter time series (SSS). Broad wavelength
coverage on the time scale of stellar cycles and Maunder minima is largely lacking, and the important
region between 4000 and 5000 Å is unexplored spectroscopically. The “Lowell” cube is the 18-year b – y
program discussed in the text; this program has concluded but the Fairborn observations have kept these
observations going (Lockwood et al. 2004). Giampapa’s M67 work is indicated as well. Importantly, the
region of the phase space where solar twins are likely to be found is largely unexplored. The surveys of
Henry et al. (1996) and Soderblom (2004) have recently provided the first broad look at Ca II emission at
fainter magnitudes, but long-term observations of promising targets do not exist.
DISCUSSION
Identification of the closest solar analogs per se was largely considered merely a means to an end.
Soderblom considered finding a true solar twin extremely unlikely, and similar suggestions about the
scarcity of such stars are found in the literature (Cayrel de Strobel 1996, and in her presentation in Hall
1998).
However, the current state of knowledge regarding the current only solar twin, 18 Sco = HD 146233,
suggests that finding more stars as nearly similar to the Sun as possible is worthwhile. Originally
identified as the best solar twin by de Mello and da Silva (1997), 18 Sco was confirmed as a solar twin, on
the basis of a spectral snapshot revealing its gross parameters, at the Solar Analogs workshop at Lowell
(Hall 1998).
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
22
Time series observations of 18 Sco’s chromospheric behavior confirmed that it has a reasonably Sun-like
activity cycle (Hall & Lockwood 2000), and the Fairborn photometry subsequently revealed that it is
photometrically extremely quiescent (Lockwood et al. 2002, and Henry, this workshop). Thus, the one
star brighter than V=7 most similar to the Sun in its instantaneous appearance also is found to be more
similar to the Sun in its combined temporal spectroscopic and photometric behavior than its nearest
counterparts.
Several essential questions may be addressed with comprehensive, multiwavelength observations of
good solar analogs. Do solar age stars with gross parameters extremely close to those of the Sun also
exhibit highly Sun-like photometric quiescence, as 18 Sco does? Do they also in general exhibit similar
chromospheric cycles, as 18 Sco does? If we find an 18 Sco counterpart that does not cycle, is this a
true stellar Maunder Minimum, and if so, can we observe the spectral distribution of its irradiance
variability with some confidence that this reflects the real Sun during its own period(s) of quiescence?
While the broad astrophysical goals of synoptic observations of cool stars must not be ignored, the
specific potential for future observations of truly Sun-like stars presents at least one well-defined objective
for the field in the next decade, which is roughly the timescale for a complete solar cycle, and which is
well aligned with current broad programmatic goals.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
23
SUMMARY
The stellar cycles workshop developed six broad programmatic recommendations that,
if followed, should produce (1) a unified database of stellar parameters, activity records,
and irradiance variability and (2) maximally productive observing programs during the
next decade. Attendees specifically suggested:

Ground-based spectroscopic programs dedicated to observations of stellar cycles
must be made more compatible with other modern observing programs through
construction of a dedicated, automated observing facility, employing a 1-2 meter
class telescope, and a spectrograph providing as nearly complete spectral coverage
from the near UV to near IR as possible. Existing programs should continue at least
until this facility is in operation, to ensure accurate cross-calibration of the data sets
is possible.

Existing ground-based data sets should be rendered into a publicly accessible final
format as the programs wind down. Centralized electronic access to the various
datasets pertinent to the field should be made available.

The next-generation target set should focus first on the most nearly Sun-like stars
available, to a limiting magnitude of at least V = 10. The target set should include
stars on the Fairborn list and on current and future space-based missions, and the
groups involved should coordinate observing lists to the maximum extent possible.
The research begun 40 years ago by Olin Wilson is increasingly relevant today, and
unification of extant databases with the observing facilities and observational
requirements specified for future programs supports several timely science goals.
Foremost among these is surely the role of solar forcing of terrestrial climate,
particularly in the context of the recent rapid global warming, which is a critical scientific
and public policy issue. Understanding the Sun in the context of an expanded sample
of Sun-like stars, particularly in terms of total stellar irradiance, spectral distribution of
stellar variability, long-term (multi-cycle) trends in stellar irradiance, and the behavior of
stars during periods of minimal activity, is a vital complement to solar and climatic
research. Additional relevance exists in identifying optimum targets for extrasolar planet
searches, and for understanding the ensemble properties of Sun-like stars and the
attendant implications for astrobiological conditions in their habitable zones. The
attendees of the workshop look forward to what the next decade of observations will
show us.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
24
COMMENTARY
Judith L. Lean
[Editors’ note: This invited commentary is reproduced almost exactly as received. Some brief comments
pointing out minor errors in the original report text have been edited following corrections. The editors
thank Dr. Lean for her thoughtful commentary.]
This concise synopsis of the evolution and current state of primarily ground-based stellar monitoring is
both illuminating and instructive. It is to the authors (and workshop attendees) credit that they have
attempted such a broad assessment of their field, and are motivated by the need to define priorities for
the next decade of research.
The following comments are offered from an outsider of this field, and are intended not to detract from the
report’s overall strengths, but to provide what is a hopefully a helpful additional and even broader
perspective.
1) Spectral Irradiance Variability
The report aims at elucidating stellar cycles research in “its full modern context”. Yet the text primarily
discusses just two types of stellar variability, namely total (bolometric) irradiance and the Ca HK flux.
These are the two types of stellar monitoring that have been mainly conducted thus far. But they do not
compose “the full modern context.” In fact, the Ca K (or Ca HK) flux is used in solar irradiance variability
modeling as a proxy for the bright faculae that alter not just total solar irradiance at visible and IR
wavelengths, but also the UV and EUV irradiance. The variability of spectral irradiance at different
wavelengths depends on a balance between the bright facular and the dark sunspots, and this balance is
strongly wavelength-dependent. It is also a function of time– the balance differs during rotation versus the
activity cycle, and it apparently changes also on very long time scales; younger more active stars are
dominated by spots, whereas older, less active stars are dominated by facular.
Thus quantifying the total irradiance and the Ca HK time series is actually a subset of what is a broader
goal – to understand the mechanisms/sources of solar and stellar spectral irradiance variability at all
wavelengths, on all time scales. Included in this are the UV, EUV and X ray fluxes which the report
mentions only briefly (but does appropriately include as one of the recommendations), since it does not
describe much about the space-based stellar variability research. The text would benefit from a coherent
unifying statement of current knowledge and future needs of stellar spectral irradiance cycles, including
observations from space-based observatories of X rays and EUV fluxes, and of time scales. For example,
the X-ray solar stellar comparison are mentioned briefly (see recent paper by Judge et al, Ap. J. 2003) yet
the relative relationships of irradiance variations from the photosphere, chromosphere and corona is
potentially even more powerful in discerning solar-stellar relationships than a study of just the
photosphere (total) and chromosphere (UV).
The discussion about what Wilson might have been considering, at the top of page 10, is a very nice
statement of this broader view.
The report would benefit from a table, for example, giving the amplitude and time scales of variability at
different wavelengths in the Sun. This would identify the type of variability being sought in the stellar
cycles.
2) Solar Analog
Much is made about what constitutes a “solar analog” and the answer seems to be that there really is no
such thing. One solar analog is named. But this is not the same solar analog as, for example, Judge et al
(2003) cite when considering X ray fluxes. And the behavior of only one star is unlikely to be, in the end,
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
25
totally convincingly relevant for the Sun’s behavior. A great value of stellar cycles research is the ability
to access many stars at different states of activity, and to statistically quantify how they behave so as to
place the Sun in perspective. Even if no star is perfectly identical to the Sun, the insights of average
stellar behavior has much value for understanding solar variability. It is, for example, interesting to know
that younger stars are thought to be dominated by spots and older stars by faculae. Knowledge like this
can help in developing scenarios for long-term solar variability needed for solar terrestrial research.
Rather than continue the apparently not very fruitful search for THE solar analog (or two), perhaps stellar
cycles research should seek broader categorization of cycles, and their relevance of the Sun. In a sense,
this is reversing the focus of the past decade to goals that appeared to inform the first few decades of
stellar monitoring.
3) Relevance for the Earth
The report makes a strong point of the relevance of stellar variability for understanding the Sun’s
influence on climate change. The information that the stellar cycle research can provide is limits on the
range of variability that we expect for the Sun. Even if actual values are elusive, plausible, defendable
limits on solar irradiance variations are important to have – both lower and upper limits. An important
aspect of such upper and lower limits is that their level of certainty (or uncertainty) be quantified. The
original distribution of sun-like stars that Baliunas and Jastrow reported has now been discredited. But
why was it so in error? What mistaken assumptions were made? In retrospect, what caveats might have
been applied? What were the uncertainties of that distribution? Why should the revised distribution be
more believable? There are lessons to be learned from this, for reporting future stellar distributions
results.
Also important is the frequency with which the Sun can be expected to reside in, for example, Maundertype states (or super active states?) relative to “normal” cycling conditions. Aside from the magnitude of
the cycle, might stellar cycles research be able to determine such probabilities of high, medium, low
activity? Baliunas and Jastrow actually attempted this, and compared their stellar distribution with the
cosmogenic isotope record of Maunder-type events in the Sun. More generally, the focus of this report for
future stellar cycles record is on utilizing the contemporary solar irradiance datasets, but much can also
be learned from studying the very long-term proxies of solar activity (14C and 10Be) since they provide
distributions of activity for the Sun.
Furthermore, the relevance of stellar cycles research is broader than just sun-climate – it also applies to
the Sun’s influence on the ozone layer, and the upper atmosphere and space weather. Knowing how the
upper atmosphere and ionosphere differed in the Maunder Minimum is equally interesting as knowing
how climate changed. This means that plausible limits be discerned from stellar data for cycles and longterm variability for the entire solar spectrum – including the RUV, EUV and X rays.
4) Science Goals for the Future
The recommendations for the next decade are in each case a statement of hardware needs and
measurement techniques. The report would be strengthened by translating these recommendations into
science goals. The instrumentation and the monitoring techniques would then flow down from the science
goals.
For example, the science goal of achieving a high statistical sample from which to make meaningful
assessments about average stellar cycles requires as much observing time as possible, and hence
automated equipment. The science goal of quantifying the spectral irradiance variations in stellar cycles
requires a spectral device with wide wavelength coverage and relatively high spectral resolution, rather
than a few broad band monitors. The science goal of detecting true trends requires that all new observing
devices be properly and carefully connected radiometrically to existing observations.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
26
COMMENTARY
John A. Eddy
[Editors’ note: This invited commentary is reproduced exactly as received. Dr. Eddy is chairman of
NASA’s Living With a Star working group. The editors thank him for his comments.]
The Stellar Cycles Workshop held at the Lowell Observatory in the autumn of 2003 was, it seems to me,
science in its purest form: the kind of thing that Percival Lowell would have applauded. For one, it
stepped up to a vexing question in pure astronomy that has pressing, practical implications for national
environmental policies, through what other Sun-like stars tell us about our own. It succeeded in bringing
together, in the right place, almost all of those who know the most about this important but seldom
heralded area of research, to review and discuss and then propose a prudent course for action in the next
decade. In the process it also helped illuminate the present limits of what stellar cycles can and cannot
support, with certainty, of the long-term behavior of solar irradiation.
As we all know, panels and workshops are common phenomena in science today. Nor is there any
shortage of the reports that follow, inevitably, in their wake: laying out, in pontifical terms and with the full
Weight and Authority of Those in Attendance, what needs to be done, by whom, and how soon. I was
once told that the principal sources of such publications—the NAS and NRC—release about one such
report each day, year after year, much like a hen laying eggs.
The product of the Lowell Workshop—The Next Decade of Stellar Cycles Research—is different, for it
reports on an effort that was called and organized and put together, on a shoestring, not by those who
dwell in the hallowed halls of science, but those who have labored long in the fields. And who, we can
hope, will continue their important work for another forty years.
THE NEXT DECADE OF STELLAR CYCLES RESEARCH
27
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