Download Is the Sun anomalous?

The Sun and the stars
he physical
characteristics
of the Sun are
compared to those
of nearby Sun-like
stars, and it is
argued that in
several respects
the Sun is not
typical. A simple
unifying
explanation is
offered to account
for the apparent
solar anomalies.
T
Is the Sun anomalous?
I
s the Sun typical or is it an oddball among
nearby stars? This is an interesting question
that is not answered uniformly by
astronomers. Probably the most frequent
response is that the Sun is indeed quite average.
“Is the Sun typical among nearby Sun-like
stars?”, is another related question. This question sounds circular, but it is a valid one, if one
selects Sun-like stars according to spectral type
and luminosity class and compares other characteristics unrelated to these selection criteria.
In the following, I review those parameters of
the Sun that appear to be anomalous with
respect to nearby stars. I define a quantity mea-
sured in the Sun as anomalous if it appears to
deviate significantly from the average of the
same quantity measured in a group of otherwise similar stars. I begin by listing the apparently anomalous solar characteristics, followed
by a brief evaluation of each. I then propose a
simple unifying idea, which makes sense of
these apparent solar anomalies.
Comparing the Sun to nearby stars
The most basic intrinsic global parameters of a
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0.1
+
0.01
+ +
0.001
+
+
+
+
+
rms variation (mags)
rms variation (mags)
star are its: luminosity, effective temperature,
radius, mass, composition and rotation period.
Of these, luminosity and effective temperature
are the most easily determined. Not surprisingly, then, they are the two parameters plotted on
the most important observational diagnostic in
stellar astrophysics – the Hertzsprung–Russel
(HR) diagram.
The HR diagram is not uniformly populated.
Among the known nearby stars within 10 parsecs, about 88% were less luminous than the
Sun when they formed (Henry 1999) – some of
the originally more massive stars are now
white dwarfs, and hence fainter than the Sun.
Guillermo Gonzalez ponders the
Sun’s place in the universe.
+
+
+
+
0.01
++
+
+ +
+
+
+
0.001
+
+
short term
long term
0.0001
0.0001
– 4.5
–5.0
log R′HK
– 4.0
– 4.5
– 5.0
–4.0
log R′HK
1: Photometric variability of Sun-like stars is shown for long-term (cyclical; left) and short-term (day-to-day; right) timescales plotted against the logarithm of
the chromospheric emission index, R′HK. The figures are adapted from Radick et al. (1998). Only stars that display variability are plotted. F to mid-G stars are
shown as green squares; mid-G to K stars are shown as blue plus signs. The Sun is represented by two red triangles; the upper one represents the correction
for the “inclination effect.” Least-squares fits to the data are shown as dashed lines.
October 1999 Vol 40
5.25
The Sun and the stars
0.6
0.4
0.4
0.2
0.2
[C/Fe]
[O/Fe]
0.6
0.0
0.0
–0.2
–0.2
–0.4
–0.4
–1.0
– 0.5
[Fe/H]
– 0.0
–1.0
– 0.5
[Fe/H]
– 0.0
2: [C/Fe] and [O/Fe] values for nearby single F and G dwarfs are shown in the left (73 stars) and right (50 stars) panels, respectively (data from Gustafsson et
al. 1999). Known spectroscopic binaries have been removed from the samples, and each data point in the two plots has also been corrected for a weak
correlation with galactocentric distance, –0.015 dex/kpc for [C/Fe] and –0.032 dex/kpc for [O/Fe] (these corrections were applied assuming a mean solar
galactocentric distance of 8.8 kpc). Least-squares fits are shown as dashed lines. The Sun is shown as an open circle in both panels.
The distribution according to spectral type can
be found in Henry (1998). Since these are all
main sequence stars (except the white dwarfs),
the shape of the distribution will be similar for
luminosity and for mass. However, it is not yet
clear precisely where we should draw the
boundary between stars and brown dwarfs.
Magnetic activity cycles
The typical Sun-like star does not have a constant luminosity. High-precision photometric
observations at Lowell Observatory in Arizona
have revealed that most F to K dwarfs vary at
the millimagnitude level or greater (Radick et
al. 1998). In addition to the well-established
decline in chromospheric activity with age, the
recent data also show that photometric variability declines with age. In fact, both the longterm (cyclic) variability and the short-term
(day-to-day) variability correlate with the Ca II
H&K emission index, R′HK (figure 1) – for a
definition see Radick et al. and references
therein. In both cases, the Sun’s variability
appears to be smaller than stars with a similar
level of chromospheric activity.
Gray (1999) gives a brief review of magnetic
activity cycles in solar-type stars and compares
them to the Sun. He notes that the variation in
temperature lags behind the variation in the
H&K emission index and appears to follow a
simple trend, but that the Sun does not follow
it. It should be noted, though, that Gray only
presents data for four stars apart from the Sun.
Stellar abundances
Recent spectroscopic analyses of nearby Sunlike stars have produced high-quality data on
their physical parameters (e.g. Edvardsson et
al. 1993; Favata et al. 1997). In particular, the
abundances of about 25 chemical elements can
5.26
now be compared among F and G dwarfs ranging in age from less than 1 to about 14 Gyr.
These new data have revealed that most of the
metals are enriched in the Sun by 0.1 to
0.2 dex relative to F and G dwarfs of similar
age and mean galactocentric distance
(Edvardsson et al.; Rocha-Pinto and Maciel
1996; Favata et al.; Gonzalez 1999, hereafter
G99). Recent studies of “zero-age” objects (B
stars and H II regions) have demonstrated that
the Sun is also O-rich relative to the nearby
interstellar medium (see G99 and Gummersbach et al. 1998 and references therein).
Probably the least-biased determinations of
the nearby star metallicity distribution are those
of Rocha-Pinto and Maciel and Favata et al.
Rocha-Pinto and Maciel applied a spectroscopically calibrated equation relating [Fe/H] to uvby
photometry to 287 G dwarfs within 25 parsecs,
obtaining a mean of –0.16±0.23 dex. The mean
[Fe/H] of single G dwarfs (62 stars) from the
sample of Favata et al. is –0.12±0.25 dex.
Therefore the Sun appears to be moderately
metal-rich relative to nearby G dwarfs.
There are also deviations from mean stellar
abundance trends among individual elements
in the Sun’s atmosphere, particularly the light
elements. In a follow-up to their earlier study
(Edvardsson et al.), Gustafsson et al. (1999)
analysed the spectra of a subset (80 stars) of
the original sample (189 stars) for the purpose
of deriving accurate C abundances. The resulting [C/Fe] values display a tight correlation
with [Fe/H], as do the [O/Fe] values from the
Edvardsson et al. study (figure 2).
These data show that the Sun is O-rich and
C-poor relative to solar-like stars of the same
galactocentric distance and hence has a relatively small C/O ratio. If we also remove the
trends of [C/Fe] and [O/Fe] with [Fe/H], we
can compare the distribution of [C/O] at
[Fe/H] = 0. We have done this with the 50 stars
with both [C/Fe] and [O/Fe] data and display
the results in figure 3. Only three stars have
[C/O] values (normalized to the same [Fe/H])
smaller than or equal to that of the Sun. The
mean value of this distribution (not including
the Sun) is 0.12±0.08 dex. Gustafsson et al.
quote a typical measurement uncertainty of
0.09 dex in [C/O]. Thus the intrinsic scatter in
[C/O] among solar-like stars is likely even
smaller than that implied by figure 3.
The Li abundance is observed to range over
two orders of magnitude among nearby field
and open cluster F and G dwarfs (Pasquini et
al. 1994; Jones et al. 1999). Pasquini et al.
(1994) showed that among nearby early G
dwarfs, the Li abundance correlates with temperature, chromospheric activity (which correlates with age), and metallicity; the Li abundance declines with increasing age, with cooler
stars experiencing more rapid depletion. But
even when these are accounted for, a significant scatter remains, especially among stars
with low Li abundances. This scatter is also
seen among single G dwarfs in the solar-age
and solar-metallicity open cluster, M67. The
Sun’s Li abundance is low; about 50% of solartype stars of the Sun’s age have comparable Li.
Unfortunately, Li has only one measurable line
in solar-type stars, and it is already quite weak
in the Sun’s spectrum.
Space motion
While not an intrinsic stellar property, the
space velocity relative to the Local Standard of
Rest, υlsr, has been measured for thousands of
nearby stars. It has been known for several
decades that older stars have a larger υlsr than
younger stars (see figure 11 of Gaidos 1998 for
October 1999 Vol 40
The Sun and the stars
3: The linear trends
with [Fe/H] have
been removed from
the [C/Fe] and
[O/Fe] data in figure
2, and the resulting
data used to
produce a
histogram for [C/O].
The mean value is
indicated with a
solid vertical bar,
and the location
where C/O =1 is
shown with a
dashed vertical bar.
20
N
10
0
0.2
0.0
0.4
[C/O]
a recent dataset showing this). This is understood as the accumulation of perturbations to
a star’s trajectory due to close encounters with
other stars and giant molecular clouds, which
perturbs (or “heats up”) its galactic orbit from
an originally nearly circular motion in the
plane. The trend of υlsr with age can be seen in
figure 4, which employs the stellar sample from
G99. The typical uncertainty in a velocity estimate is only 1 to 2 km s–1, and the typical
uncertainty in age is 1 to 2 Gyr. The Sun’s υlsr
value is now well-determined, with three recent
Hipparcos-based studies (Kovalevsky 1998;
Dehnen and Binney 1998; Bienaymé 1999)
yielding a mean value of 13.4±0.4 km s–1. The
mean value of υlsr for the 37 stars with age estimates between 3 and 6 Gyr in the top panel of
figure 4 is 42±17 km s–1. Only one star in this
sample has a smaller value of υlsr than the Sun.
The probability of finding ourselves at a
given location in the Milky Way can be calculated from the space-distribution of stars. Our
location is notable in two ways. First, we are
presently only about 10–12 parsecs from the
mid-plane (Reed 1997), but the Sun (and other
old stars) spends most of its time at least
40 parsecs from it. So, if we could take a random snapshot of the Sun’s location in the
Milky Way at any time during its 4.5 Gyr history, finding it within 10 parsecs of the midplaneit would be rather unlikely. Secondly, we
are very near the corotation circle (Mishurov
and Zenina 1999). At the corotation radius in
a spiral galaxy, the angular speeds of the spiral
pattern and the stars are equal.
Incompleteness and selection bias
The datasets discussed above suffer from a
number of incompleteness factors and selection
biases that we cannot neglect. There may also
October 1999 Vol 40
be some systematic errors. We will summarize
these complications in the following and
briefly note how they affect the interpretation
of the apparently anomalous solar parameters.
The nearby star surveys still suffer from
incompleteness. Based on the number of
known stellar systems within 5 parsecs, Henry
et al. (1997) estimate that about 130 systems
are missing from the 10 parsec sample. The
vast majority of the missing stars are M
dwarfs. Even the 5 parsec sample is still incomplete, though less severely. Considering this,
the Sun is likely to be among the top ~9% of
stars by mass in the solar neighborhood.
Among the categories of solar anomalies listed in the previous section, perhaps the weakest
case is the low photometric variability of the
Sun. The number of nearby Sun-like stars with
long-term high-precision photometry is still relatively small. More problematic, though, is the
fact that the Sun is monitored with equipment
very different from that used to observe other
stars. Differential photometry through Strömgren filters is used to monitor bright stars in the
night sky from the ground, while bolometers in
space are used to monitor solar irradiance variations, which cover a much larger portion of
the electromagnetic spectrum. So it is possible,
for instance, that flux variations in the UV part
of the Sun’s spectrum partially compensate for
the flux variations in the optical region, where
the stellar observations are made.
However, Radick et al. do make an attempt
to correct the solar bolometric flux measurements to be consistent with optical observations – we have certainly not heard the end of
this story. Apart from this, there is very likely
to be a bias in the solar data. We observe the
Sun from a low angle relative to its equator,
while nearby stars are observed at random ori-
entations relative to their spin axes. This
would not be a problem if there were no
dependence of variability on heliographic latitude, but there is indeed reason to expect such
a dependence (Schatten 1993; Radick et al.).
The effect results from: 1) the fact that
sunspots and faculae are confined to low heliographic latitudes, and 2) they have different
angular irradiance dependencies on distance
from the disk center. Radick et al. have modeled this “inclination effect” and determined
that the Sun’s long-term RMS variation needs
to be increased by about 30% over the
observed value (see figure 1). The short-term
variations are not expected to suffer from this
bias as strongly.
Also not very convincing is Gray’s (1999) discovery that the lack of a lag in the temperature
variations relative to H&K index variations in
the Sun is an anomaly. Five data points are
simply not enough upon which to build a
strong case.
Selection bias is important for the [Fe/H] and
υlsr distributions. Both are affected by our particular location in the Milky Way – a mere 10
to 12 parsecs above the disk mid-plane. As a
result, stars with large velocities perpendicular
to the galactic plane (the so-called W velocity),
which spend most of their time far from the
mid-plane, are under-represented in a sample
that is restricted to a volume of space within 10
or 20 parsecs of the Sun. This means that the
average value of υlsr derived from the data in
figure 4 is an underestimate – making the Sun’s
small υlsr value even more anomalous. Similarly, older stars typically have smaller [Fe/H] and
larger W, so a local sample overestimates
[Fe/H]. This bias against metal-poor stars is
partly the cause of the asymmetry of the [Fe/H]
distribution. Rocha-Pinto and Maciel applied a
scale-height correction factor to their nearby G
dwarf sample, obtaining a mean [Fe/H] of
–0.19±0.27, which is only 0.03 dex smaller
than the raw mean.
The Li abundances and [C/O] distribution
are not likely to suffer from significant systematic errors or selection biases. The Li, C and O
abundances have been determined in differential spectroscopic analyses calibrated with the
solar spectrum. Larger samples would be
worthwhile, though.
Anthropic considerations
Certainly these anomalies could just be due to
chance. But “just chance” is not a very satisfying answer. In the following we propose to
unify the apparent solar anomalies within a
single, simple hypothesis. To a significant
degree, we can remove the anomalous label
from the solar parameter values if we consider
them within the framework of the Weak
Anthropic Principle (WAP). Briefly, the WAP is
the recognition that the particular values that
5.27
The Sun and the stars
30
solar-age stars
150
20
υlsr (km s–1)
N
100
10
50
0
0
100
50
υlsr (km s–1)
0
0
5
10
age (Gyr)
15
4: Velocity with respect to the Local Standard of Rest (υlsr) is plotted against age for 179 F and G dwarfs in the left panel; the Sun is represented by an open
circle. The data are from Gonzalez (1999) and references therein. The histogram of υlsr values for 38 Sun-age (3.5–6 Gyr) stars from this dataset is shown in
the right panel. The mean of this subsample is indicated with a solid vertical bar, and the Sun’s υlsr value is indicated with a dashed vertical bar.
we observe in our physical environment must
be consistent with our existence. This implies
that we, as observers, are relevant to the proper interpretation of our observations. Thus the
WAP is just a type of observer selection bias.
To take a simple example, we should not be
surprised to find that we are living on a planetary body with oxygen in its atmosphere,
because we require it for our survival. The
apparent anomaly of our living on the only
planet in the solar system with a high abundance of oxygen in its atmosphere is thus
solved, but the more fundamental question of
the source of the Earth’s high oxygen abundance is not addressed. Thus, while the WAP
can remove some of the apparent anomaly of a
particular observation, it has only limited
explanatory power.
While the arguments presented here are necessarily speculative at this stage, we believe
there are reasonable physical mechanisms that
relate each solar anomaly to our existence.
Before we begin, though, we should note that
the requirements for habitability we are considering refer specifically to observers (i.e.
humans who can observe and write) and
advanced life (i.e. mammals), not to simple life.
We begin with the most obvious anomaly –
the Sun’s high mass relative to the average
nearby star. There are several reasons to prefer
an early G dwarf to a K or M dwarf as our parent star: 1) the habitable zone (HZ) is located
sufficiently far from a G dwarf such that tidal
locking does not occur in 4.5 Gyr (Whitmire
and Reynolds 1996); 2) a G dwarf produces
more blue light, which is important for photosynthesis; 3) stellar flares are a greater threat
around K and M dwarfs, given that the HZ is
closer to the parent star; and 4) Wetherill
5.28
(1996) has argued that the formation of terrestrial planets around a star is insensitive to its
mass and that their distribution peaks near
1 AU; since the location of the HZ is highly
sensitive to stellar mass, then the probability of
forming a terrestrial planet in the HZ is greatest for stars near one solar mass.
The habitable zone
A brief note concerning the HZ concept is in
order. The most-often quoted estimate for the
size of the HZ in the solar system is that of
Kasting et al. (1993). Its extent is determined
by the requirement that liquid water exist on
the surface of an Earth-like planet. The inner
edge is bounded by runaway greenhouse, and
the outer edge is set by formation of CO2
clouds, which increase albedo, and hence produces cooling. However, this standard definition is not sufficiently restrictive for our application of the WAP. Advanced land life can only
tolerate a relative narrow range of mean surface temperature and atmospheric composition; towards the outer edge of the HZ, the
CO2 content of the atmosphere must be very
high in order to maintain warm surface temperatures. One can make a strong case on
physiological grounds that advanced mobile
life requires high O2 and low CO2 abundances
in the atmosphere.
Given the increasing evidence for a link
between solar irradiance variations and the
global terrestrial climate (see Lean and Bind
1998 for an up-to-date review), it is likely that
the habitability of the Earth is not independent
of the Sun’s rapid (compared to its evolutionary timescale) changes. Therefore, advanced
life may only be able to tolerate a relatively low
level of variability of its parent star. This also
has implications for the timing of our appearance, given that the photometric variability
amplitude of Sun-like stars steadily declines
with age. Gray (1999) speculates that the
unusually stable terrestrial climate of the past
10 000 years may be a result of the Sun going
through a “superstable state”. However, irradiance variations may not be the only Sun–
climate link; interactions between the geomagnetic and interplanetary magnetic field and the
solar wind might also be important (Baranyi
and Ludmany 1994).
There must be a strong correlation between
the metallicity of a star and the habitability of
its environment for the simple reason that terrestrial planets are composed primarily of metals (i.e. elements heavier than H and He). This
point was made recently by Trimble (1997) and
Whittet (1997). While the functional dependence of the mass of the largest terrestrial planet in a planetary system on the metallicity of the
parent star is not yet known, there is little doubt
that Earth-like planets do not exist around
metal-poor stars (such as in a globular cluster).
There is now empirical evidence that at least
giant planets favour metal-rich stars (see Gonzalez et al. 1999 and references therein). This
finding relates to habitability in two ways: 1)
Wetherill (1994) has shown that the gas giants
in the solar system act to shield the inner planets from frequent cometary impacts; with
fewer or with less massive giant planets, the
shielding effect is weakened, and 2) if the number of massive gas giants depends on metallicity, then the probability of large gravitational
perturbations among them is increased (Weidenschilling and Marzari 1996). A high metallicity will also likely result in a large number of
debris (asteroids and comets) left over from the
October 1999 Vol 40
The Sun and the stars
formation of planets around a star, thus
enhancing the probability of impacts. A high
metallicity may also make it more likely for
giant planet migration to occur (Murray et al.
1998). If these speculations are correct, then
habitability is optimized within a narrow range
in [Fe/H].
The possible connections between [C/O] and
habitability are less obvious. However, there
should be little doubt that the C/O ratio is an
important factor in determining the final state
of a terrestrial planet. Oxygen is the most
abundant element (by number) in the Earth
(Kargel and Lewis 1993), forming many oxides
with heavier elements. Carbon is present in
trace quantities, but its role as a climate regulator via CO2 and CH4 greenhouse gases is
extremely important for habitability; had there
been significantly more C in the Earth, perhaps
too much CO2 would have been produced.
One could argue that self-regulation processes can modify an atmosphere hospitable to
advanced life, but they can only go so far. In
addition, the C/O ratio may have been an
important factor in the earliest stages of the
formation of the proto-solar nebula. Interstellar chemistry is very sensitive to the C/O ratio
(Watt 1985; Pratap et al. 1997). Most of the C
and O atoms go into CO, and the more abundant species forms additional molecules, mostly with H. Thus a low C/O ratio results in a
high abundance of O-rich molecules, OH and
H2O, and a high C/O ratio results in C-rich
molecules, CHn. The dividing line between Cand O-rich molecules occurs at C/O =1, but
even small departures from the solar ratio can
result in large changes in the abundances of
some species (C+, O2, H2CO, and CH4; Watt).
The four elements H, C, N, and O are
responsible for most of the ices in interstellar
space. Thus, since the C/O ratio is so central to
light-element astrochemistry, it is likely to have
a bearing on the condensation of ices. However, the C/O ratio will have differing effects over
the wide range in temperature and pressure of
the early solar nebula. Why a low C/O ratio
should be preferred overall is not clear.
Implications of space motion
The large deviation of the solar υlsr value from
the mean of nearby solar-age stars implies that
this parameter may be strongly related to habitability. Solutions to this problem should be
sought among those phenomena that can
threaten advanced life on the Earth and that
relate to the Sun’s galactic orbit. In this regard,
it is helpful to decompose the Sun’s galactic
orbit into two orthogonal components: motion
in the plane (characterized by an eccentricity, e)
and motion perpendicular to the plane (characterized by a maximum distance above the
plane, Zmax). A small value of υlsr requires that
both e and Zmax must be small.
October 1999 Vol 40
Two oft-discussed threats are nearby supernovae and perturbations of the Oort comet
cloud leading to comet impacts. Both are sensitive to the particular galactic orbit of the Sun.
Furthermore, the Sun’s galactic orbit is very
close to the corotation circle. A star with a circular orbit near the corotation radius will cross
the spiral arms infrequently. The observed surface density of supernova remnants in the
Milky Way rises steeply inside the solar circle
(Clark and Caswell 1976); supernovae in nearby galaxies are also observed to be centrally
concentrated (van den Bergh 1997). If the
Sun’s e were greater, its perigalacticon distance
would be smaller and the probability of spiral
arm crossings would be greater, hence increasing the threat from nearby supernovae.
In a similar way, excursions of the Sun into
the inner disk of the Milky Way increase the
probability of perturbations to the Oort cloud
comets due to nearby star and molecular cloud
encounters and the changing galactic tide
One obvious application of our
proposal is the calculation of
the probability of ETI.
(Matese et al. 1995; Matese and Whitmire
1996). Since a star located near the corotation
circle will encounter spiral arms infrequently,
“dynamical heating” of its orbit will be small.
So it could be that our proximity to the corotation circle is the key galactic-scale requirement for habitability – low e and Zmax values
may simply be natural by-products of this configuration. The reader is referred to Gonzalez
(1999), where this is discussed in greater detail.
One obvious application of our proposal is
the calculation of the probability of ETI. Once
we are confident that a given solar parameter
value is relevant to habitability, we can add it
to a Drake-like equation, as an additional constraint. A crude estimate of the degree of finetuning required for the constraint can be had
from the deviation of the solar value from the
mean among nearby stars.
So, for example, since the Sun is among the
9% most massive stars in the solar neighbourhood, we can infer that about 9% of nearby
stars have the required minimum mass for habitability. However, this should be considered
only as a first-order approximation, since we
have to allow the possibility that a given parameter must lie within a range in a probability
distribution (as opposed to a simple inequality).
A more refined estimate must make use of theoretical arguments. Therefore, we can argue
that significantly more massive stars than the
Sun are less favourable for habitability for a
number of reasons relating to luminosity
evolution, mass loss, UV light luminosity, etc.
Taking these other factors into account, then,
probably less than 9% of nearby stars have a
mass in the range required for habitability of
advanced life.
Summary
We have argued (admittedly, at a rather speculative level) that the apparently anomalous
solar parameter values are clues about the habitability of the Earth. We have offered some
possible links between them and habitability,
but much more can be said about this topic.
We close with a simple suggestion. The
approach outlined here can serve as a guide to
direct astrobiology research programmes looking to determine the basic requirements for
advanced life on a terrestrial planet. We especially encourage research on a careful comparison of the Sun’s chemical abundance pattern
to those other nearby G dwarfs. ●
Guillermo Gonzalez is research assistant professor
of astronomy at the University of Washington. He
studies the chemical abundance patterns of stars.
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