The Astrophysical Journal, 534:L105–L108, 2000 May 1
q 2000. The American Astronomical Society. All rights reserved. Printed in U.S.A.
CORRECTING RADIAL VELOCITIES FOR LONG-TERM MAGNETIC ACTIVITY VARIATIONS
Steven H. Saar1 and Debra Fischer2
Received 2000 February 15; accepted 2000 March 9; published 2000 April 19
ABSTRACT
We study stars in the Lick planetary survey for correlations between simultaneous measurements of highprecision radial velocities vr and magnetic activity (as measured in an SIR emission index from Ca ii l8662). We
find significant correlations in ≈30% of the stars. After removing linear trends between SIR and vr , we find that
the dispersion in vr in these stars is decreased by an average of 17%, or ≈45% of the dispersion above the
measurement noise. F stars and less active stars with variable Ca ii H and K lines are the most successfully
corrected. The magnitude of the slope of the SIR versus vr relations increases proportional to v sin i and (excepting
M dwarfs) tends to decrease with decreasing Teff. We argue that the main cause of these effects is modification
of the mean line bisector shape brought on by long-term, magnetic activity–induced changes in the surface
brightness and convective patterns. The correlations can be used to partially correct vr data for the effects of
long-term activity variations, potentially permitting study of planets around some (higher mass) younger stars
and planets producing smaller stellar reflex velocities.
Subject headings: convection — planetary systems — stars: activity — stars: late-type — stars: spots —
techniques: radial velocities
presented by Saar et al. (2000). We describe the data and analysis in § 2 and discuss the resulting relations in § 3.
1. INTRODUCTION
High-precision radial velocity (vr ) monitoring has been the
source of nearly all extrasolar planet discoveries to date. All
of these exoplanets induce stellar vr amplitudes due to Doppler
reflex motions of K ≥ 40 m s21 (Marcy, Cochran, & Mayor
2000). The best analysis methods permit long-term accuracies
of 3–5 m s21 (Butler et al. 1996). Thus, there remains a range
of lower K velocity amplitudes in which undiscovered planets
may lie.
This velocity range, however, is also the domain of sources
of intrinsic stellar vr variability, such as magnetic activity (e.g.,
Saar & Donahue 1997). Rotation and evolution of starspots
and regions of magnetically altered convection can generate
vr variations of 10–100 m s21 in moderately active stars (Saar
& Donahue 1997; Saar, Butler, & Marcy 1998). Partly because
of this, most planet search groups have scaled back observations of young, active stars. If a method to correct measured
vr for the effects of magnetic activity existed, however, the
study of younger stars would become feasible, potentially allowing the study of the evolution of planetary systems in time.
Activity corrections to vr for less active stars could permit
detection of planets that cause lower K velocities (i.e., those
more distant or less massive) by reducing the vr noise levels.
This Letter explores one simple method for making an
activity-based correction to vr data, based on the idea that
changes in a star’s activity can lead to changes in its apparent
vr. This concept is supported by the observation that solar line
bisectors are less curved and show smaller velocity spans and
smaller convective blueshifts in plage than the quiet Sun (Livingston 1982; Brandt & Solanki 1990). Changes in the average
plage area over the course of a stellar cycle would then lead
to changes in the mean observed vr (e.g., Dravins 1985). We
therefore study correlations between vr and activity, as measured in a Ca ii infrared triplet (IRT) line in the same Lick
echelle spectra. The analysis here refines a simpler version
2. OBSERVATIONS AND ANALYSIS
The Lick extrasolar planet search has been operating for over
10 years (Marcy & Butler 1998). Since late 1994, improvements in the instrumentation and analysis yielded internal errors
ji ! 5 m s21 and ≈3 m s21 in the best cases. In this Letter, we
study these highest precision vr data from between 1994 November and 1999 June, neglecting only stars added after 1998.
Details of the vr analysis can be found in Butler et al. (1996).3
We averaged vr values taken during a single night.
The Ca ii IRT, a good proxy for chromospheric activity
(Linsky et al. 1979; Chmielewski 2000), was used as our magnetic activity diagnostic. Although all three IRT lines are available in the spectra, several telluric lines surround l8498 and
l8542, introducing seasonal and weather-related variations.
Thus, to avoid spurious periodicities and noise, only the l8662
line was analyzed to generate the IRT equivalent (SIR) of the
Mount Wilson SHK index. The emission flux Fem was measured
in an 11 pixel bandpass (≈0.825 Å wide) centered on the l8662
∗
line core. The median continuum flux Fcon
was calculated in
two 10 pixel wide, line-free regions, on either side of the line.
∗
We then defined S IR = AFem S/Fcon
. A high signal-to-noise ratio
(S/N) template spectrum of each star was used to define the
error jSIR, which we took to be the standard deviation of
(template 2 individual spectrum) in the continuum passbands,
0.5
weighted by S IR
. Typically, jSIR ≤ 2%. A small (≤1%) correction for the effect of the time-variable point-spread function
on S IR was also applied. A “pseudo-S HK” derived using a
B2V–dependent correction to the final SIR values (see Saar &
Cuntz 2000) shows a strong correlation with Mount Wilson
SHK for 35 inactive stars (Pearson r = 0.986; jrms = 0.030 between “pseudo-S HK” and S HK).
We next calculated weighted (by ji) linear least-squares fits
to vr = aS IR 1 b, considering errors in both axes. (The internal
vr error ji is the standard deviation of the velocities from the
1
Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138; ssaar@cfa.harvard.edu.
2
Astronomy Department, University of California, Berkeley, Berkeley, CA
94720; fischer@serpens.berkeley.edu.
3
A list of the targets can be found at http://cannon.sfsu.edu/˜gmarcy/
planetsearch/details.html.
L105
L106
CORRECTING VELOCITY VARIATIONS
Fig. 1.—Left: Correlation between the radial velocity vr and the Ca ii IR
triplet index SIR for Gl 250a from the Lick exoplanet survey. A weighted (in
both axes) linear fit yields vr = (188 5 114)SIR 2 (73 5 34), with x2 = 4.63
and a probability x2 has been significantly improved of px2 = 95.9%. Right:
Time series of vr for Gl 250a before (plus signs with dashed lines) and after
(asterisks with solid lines) correction for the correlation in the left panel. The
weighted vr dispersions before (jv) and after (jv, corr) correction are labeled.
Vol. 534
Fig. 3.—Left: Fractional improvement in jv , Rjv vs. normalized Ca ii H and
K flux R0HK for F (triangles), G (circles), and K (squares) stars; positive-fit
slopes are filled. A tentative envelope of maximum correction is sketched
(dotted line). Right: Rjv vs. v sin i; a weak upward trend is seen.
∼550 spectral segments averaged to produce a single echelle
observation’s Avr S; see Butler et al. 1996 for details.) Note that
ji reflects the combined effects of the spectrum’s S/N and
changes in vr precision due to the strength, width, and number
of the absorption lines (e.g., broader and shallower lines yield
higher ji). We allowed the removal of one “discrepant” point
from each time series if an F-test showed that its removal
significantly improved x2. We applied the resulting vr (S IR ) relations to the time series and compared the “corrected” velocity
scatter jv, corr with the original jv . A fit was deemed acceptable
if jv, corr ! jv, the number of points n ≥ 7, the probability that
the x2 improvement was significant px2 ≥ 0.955 (2 j), and the
slope’s error ja ! FaF. A typical fit and the resulting corrected
vr is shown in Figure 1.
With these conditions, we found significant improvements
in jv for 31 stars out of the Lick sample of 106 (29%). The
average fractional vr noise reduction ARjv S = A1 2 jv, corr /jv S =
17% (Fig. 2, left). Since one cannot expect to achieve
jv, corr & Aji S, we also studied the reduction in the fraction of
jv in excess of the mean measurement noise: Rj0 v = 1 2
[(jv2, corr 2 Aji S2 )/(jv2 2 Aji S2 )]0.5 (Fig. 2, right). By this measure,
the jv improvement is significantly better: ARj0 v S = 45%. However, since the exact value of AjiS is somewhat uncertain (Cumming, Marcy, & Butler 1999) and since Rjv is a robust, conservative measure of jv improvement, we focus on Rjv in the
following.
Six F stars, 12 G stars, 10 K stars, and three M stars were
corrected (comprising 19%, 39%, 32%, and 10%, respectively,
of the F, G, K, and M stars in the sample). F stars were best
corrected (ARjv S = 24%), while the others had ARjv S = 15% 5
2%. One of the K stars is a giant—its correction may be due
to a correlation between low-level pulsations and IRT emission
(e.g., Hatzes & Cochran 1999). Fifteen of the corrected stars
(48%) had negative slopes in their SIR-vr fits, distributed in
nearly equal proportions among the spectral types. There is
some evidence that the maximum Rjv first increases, then de0
creases, as activity (RHK
, the normalized Ca ii H and K flux;
from Baliunas, Sokoloff, & Soon 1996) increases (Fig. 3, left).
There is also some tendency for Rjv to increase with v sin i
(Fig. 3, right). For Rj0 v (Fig. 2, right), F stars are again the best
corrected and trends with v sin i and activity similar to Figure 3. Eight stars showed Rj0 v ≈ 1 (i.e., jv reduced to the measurement error); these all fell in the narrow activity range
0
0.9 ≤ 10 5RHK
≤ 1.5.
Analysis of the fit results shows the maximum magnitude
of the slope FaF decreasing with decreasing Teff in F–K stars,
perhaps increasing again in the M dwarfs (Fig. 4, left). The
slope also increases with v sin i (Fig. 4, center); values of
v sin i were gathered from Saar & Osten (1997), Gray (1982a,
1984, 1986), Soderblom (1983), and Fekel (1997). A leastsquares fit for the 24 stars with v sin i data yields FaF ∝
( v sin i) 0.76, with j fit = 0.39 dex and a correlation coefficient
r = 0.965. The corrected M dwarfs have only poorly determined upper limits for v sin i and were excluded from the fit.
0
There is also a trend of increasing FaF with RHK
(Fig. 4, right;
0
again excluding M dwarfs, where RHK is not calibrated).
Fig. 2.—Left: Histogram of the fractional improvement in jv, Rjv (binned
by 0.05) in the Lick survey stars after removing linear SIR-vr trends; the solid
line indicates all stars, while shaded areas indicate those for which fit slopes
FaF = Fdvr /dSIRF ! 0, ARjv S = 17%. In all cases, px2 1 95%, n 1 6, and FaF 1
ja. Right: The modified jv improvement Rj0 v (adjusted for ji, see text) for the
Lick stars; AR0jv S = 45%.
Fig. 4.—Left: Amplitude of the (unsigned) slope FaF = Fdvr /dSIRF of the
linear fits to vr vs. SIR (e.g., Fig. 1) plotted against B2V; the symbol size is
in proportion to v sin i, and plus signs are v sin i upper limits. The approximate
upper envelope is given as a dotted line. The maximum FaF decreases with
B2V until the M stars. Values of FaF tend to increase with v sin i at fixed
B2V. Center: Fdvr /dSIRF vs. v sin i; symbols as in Fig. 3. A power-law fit to
24 stars yields Fdvr /dSIRF ∝ (v sin i)0.75 with a dispersion of jfit = 0.39 dex
(solid line). Right: Fdvr /dSIRF vs. R0HK showing FaF ∝ R00.89
HK (solid line) with
jfit = 0.30 dex (excluding one high-a F star).
No. 1, 2000
SAAR & FISCHER
3. DISCUSSION
Many of the characteristics of the corrected stars and the fits
can be explained in the framework of stellar activity and convection. (We set M dwarfs aside, since there is evidence [Saar
et al. 1998] that some additional factor, possibly flares, enhances their Dvr.) Inactive, low v sin i F to mid-G stars show
“/”- or C-shaped bisectors with both convective blueshifts and
the velocity spanned by the bisector vspan decreasing toward
lower Teff (Gray 1982b, 1988). We assume that active region
(AR) bisectors on these stars, as on the Sun, are constricted to
smaller convective velocity shifts (vcs ) and smaller vspan. Increased numbers of ARs on these stars should then lead to
decreased blueshifts and thus positive SIR-vr correlations and
slopes a. Late G dwarfs and early K dwarfs have more vertical
bisectors and (possibly) even convective redshifts (Gray
1982b). Integrated line profiles from granulation models of
K1 V stars do not show redshifts (Dravins & Nordlund 1990),
but do indicate a strong temperature sensitivity, with higher
excitation lines more blueshifted. If such blueshift-temperature
correlations are typical at K1 V, increased warm AR plage area
in these stars could cause either decreased redshifts (Gray
1982b) or increased blueshifts (Dravins & Nordlund 1990),
and thus a ! 0. Higher v sin i (Smith, Huang, & Livingston
1987; Gray 1986; Bruning & Saar 1990) or activity (Toner &
Gray 1988) can significantly alter bisector shapes; these stars
may also show a ! 0. There are slightly more F to mid-G stars
corrected (16) than late-G and K stars (13), but the four with
v sin i (≥5 km s21) stars are all F stars. Thus, we might expect
roughly equal numbers of positive and negative slopes, as observed (Fig. 2), with some a ! 0 at all spectral types, due to
complications at higher v sin i/activity. Increased v sin i tends
to amplify vspan (Gray 1986; Smith et al. 1987) and correlates
with increased activity; both amplify the change Dvcs, resulting
in increased FaF (Fig. 4). The range in FaF at fixed B2V is
thus likely due in part to the range in v sin i at a given color
(Fig. 4, left). The reduced slopes in K stars relative to F and
G stars can be understood as due to their lower Av sin iS and
lower Avspan S (Gray 1988) and macroturbulent velocities (Gray
1988; Saar & Osten 1997), resulting in lower vcs and Dvcs.
The slope’s dependence on v sin i can be explored by writing
a=
dvr
dvr
dS IR
≈
dS IR d( v sin i) d( v sin i)
[
21
]
.
Since for nonsaturated stars the X-ray luminosity L X ∝
( v sin i) 2.5 (Dorren, Güdel, & Guinan 1995) and L X /L bol ∝
(L CaHK /L bol ) 2.1 (Piters et al. 1997), we have L HK ∝ L IR ∝
S IR ∝ v sin i 1.2, and so dS IR /d( v sin i) ∝ v sin i 0.2. Saar & Donahue (1997) showed that for spots Dvr ∝ v sin i and gave evidence (through the behavior of vspan) that for plages Dvr ∝
( v sin i)11g, with g 1 0. Thus, we would predict dvr /dS IR ∝
( v sin i)g20.2, but must await models of vr effects of inhomogeneous plages to estimate g and compare with the observed
result g ≈ 1.0 (Fig. 4, center). Note that if Dvr ∝ vspan and
vspan ∝ ( v sin i) 2 (Smith et al. 1987), then g = 1 in agreement
with observations.
Explaining the proportion of stars corrected may also be
possible. First consider how spots and plage affect vcs and vr.
Spots act as “holes” in the background convective pattern, decreasing the net Avcs S by an amount proportional to AS vcs, where
AS is the new spot’s area. Spots are even more effective, however, at generating large Dvr on rotational timescales, adding
considerable short-term noise to any SIR-vr relation. Take the
L107
simple case of a black, equatorial spot on a star with i = 907
and no limb darkening. Here, rotation causes an apparent
brightness decrease proportional to the spot’s projected area,
cos fDAS, where f is the phase angle measured from disk
center and DAS is the area inhomogeneity introduced by the
new spot. (Note that this differs from the area AS itself; it takes
an asymmetry in the spot coverage to generate a rotational
effect.) The apparent vr is deflected by the “missing” velocity
at the spot’s location scaled by the projected area: Dvr ∝
cos f sin fDAS v sin i. Thus, equal DAS’s at 5f yield Dvr’s of
opposite signs, adding scatter to a S IR -vr relation. Since typically
DAS v sin i 1 AS vcs, spots tend to add more short-term rotational
noise than long-term change in vcs and vr.
Rotating plages have more complex f behavior, since they
combine Teff and velocity inhomogeneities (see Saar et al.
2000). The hot upflows and cool downflows add additional
vr terms proportional to cos f, while tangential flows connecting them will add a term proportional to sin f. Nevertheless, it is primarily the change in the mean activity level that
produces a systematic Dvcs and Dvr. Here, the change is not
due to the “blanking” of part of vcs due to a dark spot, but
rather the perturbation d vcs due to the altered (suppressed) vcs
in the plage. Thus, if AP is the area of the new plage,
ADvcs S ∝ AP d vcs. In the Sun, d vcs ≈ 0.5 vcs or more (Livingston
1982). Since AP k AS on the Sun and likely most stars as well
(although the spot-to-plage ratio increases with activity; Radick, Lockwood, & Baliunas 1990), we expect AP d vcs k AS vcs.
Thus, plages should dominate the systematic changes in vcs and
vr. We must therefore look to dynamo cycles or long-term
variations in plage as the main contributors to the SIR-vr
correlations.
Analysis of the limited data on plage (S HK) variations (Soon,
Baliunas, & Zhang 1994) suggests that among less active stars,
variability amplitudes rise from an average of 22% in G stars
to 36% in early-mid K stars, perhaps dropping again to 31%
in late (B2V 1 1.00) K stars (we have only considered stars
with cycles, and we assign HD 81809’s cycle to the K dwarf
secondary; see Baliunas et al. 1995). F stars appear to generally
show smaller activity variation amplitudes (Baliunas et al.
1995), perhaps because they are more spatially homogeneous
(Rucinski & VandenBerg 1986). Photometric variability amplitudes tend to increase with B2V from minimal levels in
early F stars (Lockwood, Skiff, & Radick 1997). The long01.35
term photometric rms is proportional to RHK
, while long-term
01.15
chromospheric rms varies as RHK (Radick et al. 1998, their
Figs. 6 and 7). Hence, the ratio of spot-to-plage rms increases
00.2
as RHK
(see Radick et al. 1990). More active stars show more
stochastic variability and often lack clear cycles (Baliunas et
al. 1995).
Thus, we expect that F stars, unless very active with high
v sin i, will typically show less variation due to their more
homogeneous surfaces. The number of F stars with v sin i 1
0
8 km s21 or RHK
1 2.5 # 1025 in the Lick sample is eight; we
correct 38% of these. K stars have lower Av sin iS and more
common and higher amplitude cycles, but also have more nonuniform surfaces and more spots (Krishnamurthi et al. 1998),
increasing the short-term vr noise. Thus, we expect good SIRvr correlations only in inactive cyclic K stars for which
v sin i is low and spots are fewer. The number of K stars with
0
v sin i ! 2 km s21 or RHK
! 1.5 # 1025 (≈ the Vaughan Preston
gap) in the Lick sample is 21; we correct 48% of these. G stars
show intermediate behavior, having more long-term activity
variation and lower v sin i than F stars, but lower spot amplitudes than K stars. It is thus reasonable that G stars show the
L108
CORRECTING VELOCITY VARIATIONS
highest fraction of correctable long-term activity-driven Dvr.
0
The number of G stars with v sin i ! 3 km s21 or RHK
!
25
1.5 # 10 in the Lick sample is 28; we correct 36% of these.
Thus, if we have a correction “efficiency” of ≈40%, there is
reasonable agreement between the predicted and observed
numbers of F, G, and K stars corrected. This relatively low
efficiency is expected, given that the data span only ≈4–5 yr,
less than half of a typical dynamo cycle period, and that the
average number of observations per corrected star is only
AnS = 17.2 (AnS = 13.4 for the sample as a whole). Sampling of
the longest timescale variations is thus likely incomplete. In
comparison, of the 37 stars we expect to be less successful at
correcting (low-activity, low v sin i F stars and moderate and
higher activity/v sin i G and K stars), only five (13.5%) show
significantly improved jv.
The apparent peak in the maximum Rjv at low activity
0
(log RHK
∼ 25; Fig. 2, left) likely arises from a combination
0
of two effects. At low RHK
, maximum corrections increase with
activity along with the rise in the number of ARs (and thus
correctable Dvr). At some point, however, increased short-term
vr noise from spots and reduced numbers of well-defined cycles
begin to dominate and reduce the maximum Rjv. F stars have
Vol. 534
the best ARjv S since Av sin iS is larger (Fig. 3, right), but spots
are unimportant. There is a significant range in Rjv at a given
0
v sin i or RHK
due to a range of n, cycle amplitudes and lengths,
and amounts of short-term vr noise.
Activity-vr correlations like those derived here can partly
correct for vr “noise” due to long-term magnetic activity variations. Precisions of ji & jv0 /3 (with jv0, the activity-induced
vr scatter, estimated from, e.g., Saar et al. 1998) will be needed
to permit significant vr correction. Such corrections should improve chances of detecting planets around active F stars and
low K planets around more inactive G and K stars. When
combined with techniques under development to correct for
shorter term vr variations using changes in line bisectors (Saar
& Snyder 1999; Saar et al. 2000), these methods may significantly reduce systematic noise in vr data.
This work was based on observations obtained at Lick Observatory, which is operated by the University of California.
We gratefully acknowledge support from NSF grants AST 9731652 and AST 95-28563 (S. H. S.) and from NASA grant
NAG5-8861 (D. F.). We thank the referee for comments and
suggestions.
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