A PRECISION VELOCITY STUDY OF PHOTOMETRICALLY STABLE STARS IN THE CEPHEID INSTABILITY STRIP

T HE A STROPHYSICAL J OURNAL ,494:342È365,1998February 10
1998.The American Astronomical Society.All rights reserved.Printed in U.S.A.
(A PRECISION VELOCITY STUDY OF PHOTOMETRICALLY STABLE STARS IN THE
CEPHEID INSTABILITY STRIP 1
R.P AUL B UTLER 2,3
Department of Physics and Astronomy,San Francisco State University,San Francisco,CA 94132;paul =.au
Received 1997May 21;accepted 1997September 17
ABSTRACT
Results of a precision Doppler velocity survey of 15stars that lie in or near the Cepheid instability strip are presented.Previous studies have shown that these stars are photometrically stable.Long-term radial velocity precision of 15m s ~1has been achieved with the use of an iodine absorption cell and a high-resolution cross-dispersed echelle spectrometer.The stars show a variety of behavior from stability (at the level of 30m s ~1)to variability from 50m s ~1to a few km s ~1.Periodograms of many of the program stars show signiÐcant peaks at 50È80days that are not associated with radial pulsation.Pre-viously undetected binary companions have been found around two of the stars.Line proÐles are com-pared to d Cep.
Subject headings:binaries:spectroscopic ÈCepheids Èstars:oscillations È
techniques:radial velocities
1.
INTRODUCTION
A number of photometric studies have shown that at least one-half of the stars that reside in the Cepheid region of the instability strip are photometrically stable at the level of &Hube 0.01È0.03M V
(Fernie 1971;Schmidt 1972;Percy
Baskerville,&Trevorrow 1975;Fernie 1976;Percy,1979).Studies of these stars have broad implications for several theoretical and observational aspects of Cepheid variable stars.
After seven decades of intensive study,a number of out-standing questions remain unanswered about Cepheids.The radial velocity amplitude of Cepheids with similar color and period can di†er by more than an order of magni-tude.It is not known what sets the radial velocity ampli-tude,or why nonvariable stars exist in the instability strip.The boundaries of the Cepheid instability strip are not well known.It has recently been suggested that the instability strip is much narrower than has traditionally been thought et al.(Fernie 1990;Chiosi 1992).
Historically,small-amplitude variables have been dis-covered because of their photometric variations.Over the last decade,observational advances have improved the pre-cision of Doppler velocity measurements by 2orders of magnitude,from 500to 3m s ~1.Precision velocity tech-niques are now exquisitely sensitive to small amplitude variations.Recent precision velocity studies have found that K giants undergo radial velocity variations of 25È300m s ~1with periods ranging from hours to years McMillan,(Smith,&Merline et al.et al.1987;Walker 1989;Larson 1993;Hatzes &Cochran Other recent studies have 1993,1994).found that F and G supergiants vary by D 100m s ~1&Cochran (Butler 1992;Hatzes 1995).
This paper presents the results of a 6yr survey of 15photometrically stable stars that lie in or near the Cepheid instability strip.The observational technique and stellar
1Based on observations obtained at Lick Observatory,operated by the University of California.
2Also at Department of Astronomy,University of California,Berkeley,CA 94720.
3Current address:Anglo-Australian Observatory,P.O.Box 296,Epping NSW 2121,Australia.
sample are described in The Doppler velocity results °2.and preliminary analysis are presented in Line proÐles °3.are examined in including a comparison with d Cep.A °4,discussion of the results follows in °5.
2.
OBSERVATIONAL TECHNIQUE AND STELLAR SAMPLE
All of the observations presented in this paper were taken at Lick Observatory with the Hamilton,a cross-dispersed coude echelle spectrometer The Hamilton is (Vogt 1987).fed by both the 0.6m Coude Auxiliary Telescope (CAT)and the 3m Shane Telescope.Most of the observations reported in this paper were made with the CAT.
High-precision Doppler velocity measurements have been made via the iodine absorption cell technique (Butler et al.Butler,&Marcy &Butler 1996;Valenti,1995;Marcy In brief,wavelength calibration is accomplished by 1992).placing an iodine gas absorption cell directly in front of the spectrometer slit.Starlight thus passes through the iodine absorption cell before entering the spectrometer.The super-posed absorption lines of iodine serve as indelible wave-length markers,and their shapes convey the local spectrometer point-spread function (PSF).The wavelength and PSF parameters are determined by constructing a model of the spectrum,which includes the unknown Doppler shift.Relative Doppler errors were D 15m s ~1until 1994November,when improvements in the spectro-meter brought the errors down to 3m s ~1.A number of stable stars are shown in Figure 1of &Butler Marcy (1996),Figure 2of &Marcy and Figures 3and 4of Butler (1996),&Marcy Butler (1997).
The 15stars listed in have been monitored for Table 14È8yr each.These stars are among the brightest apparently stable stars that lie in or near the Cepheid instability strip &Jaschek and can be accessed by the 0.6m (Ho†leit 1982)Coude Auxiliary Telescope at Lick Observatory in the summer months.Eleven of these stars were previously sur-veyed by &Mayor at a precision of 300È400m Burki (1983)s ~1using CORAVEL.With one exception,HR 1884,these stars were found to be stable.Nine of the program stars have been photometrically monitored by &Hube Fernie and Photometric variations ranged (1971)Fernie (1976).from less than 0.005to 0.03mag.writes that Fernie (1976)342
STARS IN CEPHEID INSTABILITY STRIP343
TABLE1
S TELLAR S AMPLE
Star Name HD M
V
Spectral Type
HR157..........HD3421 5.48G2.5IIa
HR213.......58Psc HD4482 5.50G8II
HR461..........HD9900 5.56G5II
HR800.......14Per HD16901 5.43G0Ib-II
HR1017......a Per HD20902 1.79F5Ib
HR1603......b Cam HD31910 4.03G0Ib
HR1884.........HD36891 6.09G3Ib
HR6536......b Dra HD159181 2.79G2Ib-IIa
HR6978......45Dra HD171635 4.77F7Ib
HR7387......32l Aql HD182835 4.66F2Ib
HR7796......c Cyg HD194093 2.20F8Ib
HR7834......41Cyg HD195295 4.01F5II
HR8232......b Aqr HD204867 2.91G0Ib
HR8313......9Peg HD206859 4.34G5Ib
HR8414......a Aqr HD209750 2.96G2Ib
““none of these variations could be assembled into a con-
vincing light curve,and are taken to be just the irregular
variability accepted as normal in supergiants.ÏÏ
The stars in this program span the spectral range from
F2Ib though G5Ib,along with a handful of F and G type II
F IG.1.ÈH-R diagram of the program stars.Solid lines indicate the
““restricted instability stripÏÏof while the dotted line shows a
Fernie(1990),
more traditional red edge.Though the absolute magnitudes of the program
stars are uncertain by D1,most of these stars lie either in or near the
instability strip.
stars.An H-R diagram of the program stars is shown in
along with the boundaries of the Cepheid insta-
Figure1,
bility strip.The approximate boundaries of the““restrictedÏÏ
Cepheid instability strip et al.are
(Fernie1990;Chiosi1992)
indicated by the solid lines,while a more traditional red
edge of the instability strip is indicated by the dashed line.
Although there is signiÐcant uncertainty in the determi-
nation of absolute magnitudes,thisÐgure demonstrates
that most of the program stars lie in or at least very near to
the instability strip.
3.DOPPLER VELOCITY RESULTS
The Doppler velocity measurements of the program stars
are presented here,along with preliminary analysis.Each
star has been observed about50times over4È6yr.The
stars were typically observed on consecutive nights for1or
2weeks during the summer and/or fall from1991through
1995.A few stars have been observed for up to8yr.
periodogram analysis,similar to that
Scargle(1982)
described in&Baliunas is employed in
Gilliland(1987),
searching for periodicities in the data.The signiÐcance of
the periodogram peaks has been determined by Monte
Carlo simulations.The measured Doppler velocities were
randomly reassigned to the observation dates,and perio-
dograms of the resulting scrambled velocity sets were deter-
mined.A total of500trials of each star were run in order to
Ðnd the level at which the peaks were signiÐcant at the1%
level Hearnshaw,&Clark lists the
(Murdoch,1993).Table2
number of observations of each star,the median internal
measurement error the rms of the measured Doppler
(p
INT
),
velocities the most probable period from periodog-
(p
EXT
),
ram analysis,the rms of the sineÐt to the measured veloci-
ties at the most probable period and the
(p
SIN
),
semi-amplitude of the sinusoidalÐt.
(K
SIN
)
Two of the stars,HR213and HR1884,have Doppler
variations that are consistent with orbiting stellar compan-
ions.The Keplerian orbital parameters for these stars are
given in Less than one-half of the orbit has been
Table3.
observed for HR1884,leaving the derived orbital param-
eters quite uncertain.The individual velocity measurements
for all the program stars are given in Tables4È18.
All of the stars show Doppler velocity variations in excess
of measurement error.Periodograms reveal signiÐcant
periodicities for all of the stars.Many of these periodograms
TABLE2
S UMMARY OF O BSERVATIONS
Number of p
INT
p
EXT
Period p
SIN
K
SIN
Star Observations(m s~1)(m s~1)(days)(m s~1)(m s~1)
HR157.......3211.433.015.19824.935.5
HR213.......349.724.5a.........
HR461.......3110.092.869.18049.7139.6
HR800.......6117.679.051.02658.9102.0
HR1017......6317.3100.877.71756.2108.9
HR1603......4713.263.444.71746.567.0
HR1884......4217.090.7a.........
HR6536......41 5.450.321.29237.358.1
HR6978......4811.036.179.70827.436.0
HR7387......6455.3947.984.126544819
HR7796......10516.4536.774.440353554
HR7834......5112.523.870.67417.521.7
HR8232......7010.5154.5203.4298.8219
HR8313......5212.983.6230.9162.592.5
HR8414......8611.5122.876.15287.1126.1
a After removing Keplerian orbitalÐt.
344
BUTLER Vol.494
TABLE 3
B INARY O RBITAL P ARAMETERS
Parameter HR 213HR 1884a P (d )...............843(4)
9390T p (JD)............2449602.12(3.5)
2448591.9
e ...................0.386(0.013)0.896u 2(deg)...........219.6(0.6)253K 1(m s ~1)........5277(10)21877
a 1sin i (AU)......0.3778.38f 1(m)(M _)........0.01010.89O-C (m s ~1)......
33.3
90.7
a Only D 25%of the orbit has been observed.
bear a ““family resemblance ÏÏwith primary or secondary peaks of 50È80days.Often,there are two or three strong aliased peaks,resulting from uneven data sampling.The problem of periodogram aliasing is studied with a Monte Carlo simulation of the data.A sine is Ðtted to the data at each of the preferred periods,and the rms of the sine Ðt is noted.A model of the data is constructed by adding random noise with an appropriate rms to the sinusoidal Ðt.The window function is maintained by sampling the ““noisy sinusoids ÏÏat the times of the observations.A hundred such models are constructed,and periodograms are determined for each of the resulting models.The periods of the four highest peaks in each of the model data periodograms are stored,then compared to the highest peaks from the perio-dogram of the original data.
3.1.HR 157(G2.5IIa )
The Doppler velocity measurements for HR 157are shown in This is one of the most stable stars in the Figure 2.program.The rms of the measured velocities is 33m s ~1,only 3times larger than measurement error.A periodogram analysis of these velocities Ðnds weak periodicities at 6and 15daysÈthe shortest period of all the program stars.3.2.HR 213(G8II )
The Doppler velocities of HR 213,shown in 3Figure reveal a binary companion.The orbital Ðt is shown as (top ),a solid line.The rms of the residuals to the orbital Ðt (Fig.3,bottom )are 33m s ~1.The orbital parameters are given in The period is 843days,the eccentricity is 0.386,and Table 3.the semi-amplitude is 5277m s ~1.The Bright Star Catalog
F I
G .2.ÈMeasured Doppler velocities of HR 157.The rms of the mea-sured velocities is 33m s ~1,3times larger than measurement error.This is among the most stable of the program stars.
F I
G .3.ÈHR 213Doppler velocities.(a )Measured Doppler velocities,spanning slightly more than 4yr,reveal the presence of an orbiting com-panion.The solid line is a Keplerian Ðt to the velocities.The orbital period is 843days,the semi-amplitude is 5277m s ~1,and the eccentricity is 0.386.Assuming that the primary has a mass of 5(consistent with spectral M _type),the companion has a minimum (m sin i )mass of 0.6and a
M _semimajor axis of 3AU.(b )Residual velocities,after subtracting the
Keplerian Ðt.The rms of the residuals is 24.5m s ~1.
does not indicate that HR 213is part of a binary or multiple system.Assuming that HR 213has a mass of D 5(based
M _
on spectral type),the companion would have a minimum mass m sin i of 0.6and a semimajor axis of 3AU.A
M _
periodogram of the residual velocities after subtracting the orbital Ðt Ðnds weak periodicities at 5yr and 16days.3.3.HR 461(G5II )
The measured Doppler velocities for HR 461are shown in The uncertainty of the individual measurements Figure 4.is typically 10m s ~1.The rms of the full data set is 93m s ~1,while the scatter within each of the observing seasons is about 50m s ~1.
A periodogram of the velocities reveals a strong (Fig.5a )peak at 69.180days.shows the velocities phased Figure 6with this period.The sinusoid Ðt (solid line )to the phased velocities has a rms of 50m s ~1.The semi-amplitude of the sine is 140m s ~1.shows a periodogram of the HR Figure 5b 461velocities with the sinusoid subtracted.The peaks seen near 400and 900days in the original periodogram (Fig.5a )fall well below the 1%false alarm level.The remaining peaks are weak,barely reaching the 1%false alarm level,with periods of less than 20days.
No.1,1998STARS IN CEPHEID INSTABILITY STRIP 345
F I
G .4.ÈMeasured Doppler velocities of HR 461.The rms scatter of the velocities is 93m s ~1.Measure errors are typically 10m s ~1.
3.4.HR 800(G0Ib -II )
The measured Doppler velocities for HR 800are shown in The full amplitude of the velocity variations is Figure 7.D 250m s ~1.The rms of the measured velocities is 79m s ~1,while typical measurement error is 18m s ~1.The velocities appear to drop from 1991through 1993,and then begin increasing,suggesting a possible D 10yr period.
F I
G .5.ÈPeriodogram of HR 461velocities.(a )Periodogram of mea-sured velocities.The periodogram peaks at 69.180days,with a number of secondary peaks at much longer periods.The 1%false alarm level is indi-cated by the dashed line.(b )Periodogram of residual velocities,after sub-tracting a best-Ðt sinusoid with a period of 69.180days.The remaining periodogram peaks are signiÐcantly decreased.The long-period peaks seen in essentially disappear.
Fig.5a F IG .6.ÈHR 461velocities phased with a period of 69.180days.The rms to the sinusoidal Ðt is 49.7m s ~1.
The periodogram shows peaks at 491.5,51.0,(Fig.8a )and 293.9days.These peaks are probably aliases.In Figure the observed velocities are phased with the periods of the 9two highest peaks from the periodogram.shows Figure 9a the data phased with the 491.5day period,while Figure 9b has the data phased with the 51.0day period.The rms of the residuals to the sinusoidal Ðt for the 491.5day period is 53.8m s ~1,while the rms of the residuals to the 51.0day Ðt is 58.9m s ~1.
A hundred sinusoidal models of the data have been con-structed at each of the two peak periods found from the periodogram.Random noise with a rms of 55m s ~1was added to the sinusoids,and they were then sampled at the times of the observations to take into account the window function.Periodograms were run on resulting model veloci-ties.For the case of the 491.5day sinusoid,87%of the periodograms found a periodicity of between 50and 52days,while 6%of the periodograms found a period between 278and 308days.For the 51day sinusoid,periodicities between 476and 506days were found in 37%of the perio-dograms,and 52%of the periodograms found periodicities between 278and 308days.Thus,both a 491.5and a 51.0day periodicity can account for all observed peak period-icities,although the 51.0day periodicity is more likely to account for the 293.9day peak.
The star was repeatedly observed for 10or more nights on three di†erent observing runs.The results are shown in
F I
G .7.ÈMeasured Doppler velocities for HR 800.The rms is 79m s ~1.
346BUTLER Vol.494
F IG.8.ÈPeriodogram of HR800velocities.(a)Periodogram of mea-
sured velocities.The three highest periodogram peaks have periodicities of
491.5,51.0,and293.9days.The1%false alarm level is indicated by the
dotted line.(b)Periodogram of residual velocities,after subtracting a best-
Ðt sinusoid with a period of491.5days.The remaining periodogram peaks
are signiÐcantly decreased.(c)Periodogram of residual velocities,after
subtracting a best-Ðt sinusoid with a period of51.0days.The remaining
periodogram peaks are signiÐcantly decreased.
The velocity zero point of each of the observing
Figure10.
runs is arbitrary.The circles are from an observing run that
began in1991early October,and they span11nights.The
squares are from1992late September and span10nights.
The diamonds are from1993mid-August and span13
nights.On several occasions the velocity of the star is seen
to change by D150m s~1over1È3days.The full amplitude
of the velocity variations seen in is only D250m
Figure7
s~1,suggesting that the longer periods(293.9and491.5
days)seen in the periodogram are the aliased periods.
A periodogram of the residual velocities,after subtracting
the491.5day sinusoid,is shown in while
Figure8b,Figure
shows the periodogram of the residuals after subtracting
8c
the51.0day sinusoid.
3.5.HR1017(F5Ib)
Doppler velocity variability in HR1017wasÐrst report-
ed by&Cochran based on24observations
Hatzes(1995),
made between1991October and1993August.A total of63
observations made between1991August and1995October
are shown in The rms of the measured velocities
Figure11.
is101m s~1,while the full amplitude of the velocity varia-
tions is D350m s~1,in agreement with&
Hatzes Cochran.
A periodogram of these velocities is shown in Figure12a.
A single dominant period is seen at77.717days.In contrast,
F IG.9.ÈPhased Doppler velocities for HR800.(a)Doppler velocities
phased with a491.483day period.The rms to the sinusoidalÐt is54m s~1.
(b)Doppler velocities phased with a51.026day period.The rms to the
sinusoidalÐt is59m s~1.
Hatzes&Cochran report possible periodicities of87.7and
9.8days.shows14observations of HR1017taken
Figure13
over25nights,beginning in1993early August.The veloci-
ties are seen to increase by220m s~1over this interval,
ruling out the9.8day periodicity.The velocities are phased
F IG.10.ÈNightly velocity variations of HR800from three observing
runs.The velocity zero point of each of these runs is arbitrary.Circles:
Observing run that began in1991early October;squares:observing run
that began in1992late September;diamonds:observing run that began in
1993August.Velocity variations within a single run are typically D150m
s~1,about one-half of the full range of variation seen over the4yr observ-
ing span.
No.1,1998STARS IN CEPHEID INSTABILITY STRIP 347
F I
G .11.ÈMeasured Doppler velocities for HR 1017.A total of 63observations span 4.2yr.The rms of the velocities is 101m s ~1,and the full amplitude of the velocity variation is D 350m s ~1.
with a period of 77.717days in The solid line is a Figure 14.sinusoidal Ðt.The rms to the sinusoidal Ðt is 56.2m s ~1.A periodogram of the residual velocities,after removing the sinusoidal Ðt,is shown in Several peaks lie Figure 12b .above the 1%false alarm level.These peaks may be real,or they may be an artifact of subtracting the overly simplistic sinusoid et al.(Larson 1993).
F I
G .12.ÈPeriodogram of HR 1017velocities.(a )Periodogram of mea-sured velocities.The dominant peak has a period of 77.717days.The 1%false alarm level is indicated by the dotted line.(b )Periodogram of residual velocities,after subtracting a best-Ðt sinusoid with a period of 77.717days.The remaining periodogram peaks are signiÐcantly decreased,although several rise signiÐcantly above the 1%false alarm level.
F I
G .13.ÈFourteen measured Doppler velocities of HR 1017,spanning 25nights in 1993August.The velocities climb by more than 200m s ~1.
3.6.HR 1603(G0Ib )
The velocity measurements of HR 1603are shown in Measurement uncertainty is D 13m s ~1,the rms Figure 15.of the measured velocities is 63.4m s ~1,and the full ampli-tude of the velocity variations is D 250m s ~1.Velocities
F I
G .14.ÈHR 1017velocities phased with a 77.717day period.The rms to the sinusoidal Ðt is 56m s ~1.
F I
G .15.ÈMeasured Doppler velocities for HR 1603.The rms is 63m s ~1,and the full amplitude of the velocity variation is D 250m s ~1.
348BUTLER Vol.494
F I
G .16.ÈEleven measured Doppler velocities of HR 1603,spanning 13nights in 1993August.The velocities descend by about 200m s ~1.
spanning 13nights show a clear downward trend (Fig.16)of 200m s ~1.
The periodogram of the velocities,shown in Figure 17a ,reveals two peaks of almost equal strength at 44.717and 51.575days,with a third strong peak at 25.922days.Sinus-oids have been Ðtted to the data with the 44.717and 51.575
F I
G .17.ÈPeriodogram of HR 1603velocities.(a )Periodogram of mea-sured velocities.The three highest periodogram peaks have periodicities of 44.717,51.575,and 25.922days.The 1%false alarm level is indicated by the dotted line.(b )Periodogram of residual velocities,after subtracting a best-Ðt sinusoid with a period of 44.717days.Power at periods longer than 10days is signiÐcantly reduced.(c )Periodogram of residual velocities,after subtracting a best-Ðt sinusoid with a period of 51.575days.A few peaks near 20and 30days nearly rise to the 1%false alarm level.
day periods.The rms Ðt of the 44.717day sine is 46.5m s ~1,while that of the 51.575day sine is 49.7m s ~1.Figure 18a shows the velocities phased with the 44.717day period,while shows the data phased with the 51.575day Figure 18b period.Two sinusoidal models of the data have been created,with periods of 44.717and 51.575days,as in the case of HR 800.Random noise with a rms of 50m s ~1was added to each of the sinusoids,and the sinusoids were then sampled at the same times as the observations.A total of 100such models was constructed for each of the two periods,and periodograms were run for each case.The 44.717day sinusoid produced strong peaks between 50.575and 52.575days 74%of the time,and between 24.9and 26.9days 30%of the time.For the case of the 51.575sinusoid,strong peaks between 43.7and 45.7days were generated 62%of the time,and between 24.9and 26.9days 14%of the time.Both sets of models also typically produced periodo-gram peaks near 400and 1000days,as in Thus,Figure 17a .both a 44.717and a 50.575day period are consistent with the observed periodogram,although the 44.717day period is more likely to produce the aliased peak near 26days.
A periodogram of the residual velocities,after removing a sinusoid with a 44.717day period,is shown in Figure 17b .The periodogram of the residual velocities,after subtracting a sinusoid with a 51.575day period,is shown in Figure 17c .3.7.HR 1884(G3Ib )
This star is listed as a possible spectroscopic binary by &Mayor shows a total of 42Burki (1983).Figure 19observations over 5.2yr.There is a 4]104m s ~1jump in velocities between the Ðrst and second observing runs.Sub-sequently,there is a monotonic 8]103m s ~1decline in the velocities.The solid line in shows a possible Figure 19orbital Ðt.The orbital period is 9390days,and the rms of the orbital Ðt is 91m s ~1.Only about a quarter of the proposed period has been sampled,so the orbit is quite tentative.It will not be possible to search other periodicities until the orbit has been more completely sampled.
3.8.HR 6536(G2Ib -IIa )
The measured Doppler velocities of HR 6536are shown in These velocities have a rms of 50.3m s ~1.A Figure 20.periodogram of the Doppler velocities is shown in Figure
F I
G .18.ÈPhased Doppler velocities for HR 1603.(a )Doppler veloci-ties phased with a 44.717day period.The rms to the sinusoidal Ðt is 47m s ~1.(b )Doppler velocities phased with a 51.575day period.The rms to the sinusoidal Ðt is 50m s ~1.
No.1,1998STARS IN CEPHEID INSTABILITY STRIP 349
F I
G .19.ÈMeasured Doppler velocities for HR 1884.A total of 42observations span 5.2yr.A possible Keplerian orbit is indicated by the line.The rms of the Keplerian Ðt is 90.7m s ~1.The orbital period is D 26yr,and the eccentricity is 0.89.Less than a quarter of the orbit has been observed,leaving the orbital parameters quite uncertain.
The periods of the three highest peaks are 21.292,21a .20.073,and 108.065days,respectively.Sinusoids Ðtted to the data with these periods scatter by 37.6,38.8,and 38.2m s ~1,respectively.
shows 13observations of HR 6536taken over Figure 2214nights,beginning in 1993mid-August.Over this 2week interval the velocities change by the full amplitude of the variations in the entire data set,suggesting that the 108day period is an alias of a shorter period.
One hundred sinusoidal models of the data have been constructed with each of the three peak periods from the periodogram.Random noise with a rms of 38m s ~1has been added to the models,and periodograms have been taken of the results.Models constructed from 108.065day sinusoid produced strong periodogram peaks between 17and 24days in 2%of the simulations.Models constructed from the 20.073and the 21.295day sinusoids produce strong peaks between 103and 113days for 1%and 13%of the time,respectively.Thus,it is likely that the 108day periodicity seen in the periodogram is an alias of the 21.292day period.
A periodogram of the residual velocities,after subtracting the sinusoidal Ðt at the 21.292period,is shown in Figures A few peaks are seen above the 1%false alarm level
21b .F IG .20.ÈMeasured Doppler velocities for HR 6536.The rms of the velocities is 50m s ~1.
F I
G .21.ÈPeriodogram of HR 6536velocities.(a )Periodogram of mea-sured velocities.The three highest peaks have periods of 21.292,20.073,and 108.065days.The 1%false alarm level is indicated by the dotted line.(b )Periodogram of residual velocities,after subtracting a best-Ðt sinusoid with a period of 21.292days.
that are possibly artifacts of subtracting the overly simplis-tic sinusoid.
shows the velocities phased at the 21.292day Figure 23a period,and shows the velocities phased with the Figure 23b 108.065day period.
F I
G .22.ÈThirteen measured Doppler velocities of HR 6536,spanning 14nights in 1993August.The amplitude of the velocity variations from this run are nearly as large as those from the entire data set.
350BUTLER Vol.494
F I
G .23.ÈPhased Doppler velocities for HR 6536.(a )Doppler veloci-ties phased with 21.292day period.The rms to the sinusoidal Ðt is 37.6m s ~1.(b )Doppler velocities phased with a 108.065day period.The rms to the sinusoidal Ðt is 38.2m s ~1.
3.9.HR 6978(F7Ib )
The measured Doppler velocities of HR 6978are shown in Meaurement uncertainty is D 11m s ~1,the Figure 24.rms of the velocities is 36m s ~1,and the full amplitude of the velocity variation is D 150m s ~1.A periodogram of the Doppler velocities is shown in The periods of Figure 25a .the three highest peaks are 79.708,65.000,and 157.690days,respectively.Sinusoids Ðtted to the data at these periods have rms residuals of 27.4,29.3,and 28.0m s ~1,respec-tively.
A hundred sinusoidal models of the data have been con-structed at each of the three peak periods.Random noise with a rms of 28m s ~1has been added to the models,and periodograms have been determined for the results.The 79.708day sinusoid produced strong periodogram peaks between 152.7and 162.7days 60%of the time,and between 64and 66days 59%of the time.The 65.000day sinusoid produced peaks between 152.7and 162.7days 10%of the time,and between 78.5and 81days 29%of the time.The 157.690day sinusoid produced peaks between 64and 66days 13%of the time,and between 78.5and 81days 26%of the time.Thus it is likely that both the 65and the 157day periodicities are aliases of the 79.708day period.A perio-dogram of the velocity residuals,after removing the 79.708
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G .24.ÈMeasured Doppler velocities for HR 6978.A total of 48observations span 3.0yr.The rms of the velocities is 36m s ~1.F IG .25.ÈPeriodogram of HR 6978velocities.(a )Periodogram of mea-sured velocities.The three highest peaks have periods of 79.708,65.000,and 157.690days.The 1%false alarm level is indicated by the dotted line.(b )Periodogram of residual velocities,after subtracting a best-Ðt sinusoid with a period of 79.708days.
day sinusoid,is shown in There are no signiÐ-Figure 25b .cant remaining peaks at the 1%false alarm level.Figure 26shows the observed velocities,phased with the period of 79.708days.
3.10.HR 7387(F2Ib )
The measured Doppler velocities of HR 7387are shown in This is the earliest spectral type of the program Figure 27.stars.As a result,the spectral lines are broader and less than
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G .26.ÈHR 6978Doppler velocities phased with a period of 79.708days.The rms to the sinusoidal Ðt is 27.4m s ~1.。