A 3D Search for Companions to 12 Nearby M-Dwarfs

1.8 MB·English

by  Cassy L. Davison

A 3D Search for Companions to 12 Nearby M-Dwarfs
Davison, Cassy L.1, White, R.J. 1, Henry, T.J.2, Riedel, A.R.3,4, Jao, W-C.1, Bailey, J.I.,
5 III5, Quinn, S.N.1, Cantrell, J.R.1, Subasavage, J. P.6 and Winters, J.G.1
1 1Department of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
0 2RECONS Institute, Chambersburg, PA 17201, USA
2
3Department of Physics and Astronomy, Hunter College, New York, NY, 10065, USA

n 4American Museum of Natural History, New York, NY 10024
a
J 5University of Michigan, Department of Astronomy, Ann Arbor, Mi, 48109, USA
0 6United States Naval Observatory, Flagstaff, AZ, 86002, USA
2

]
R
S ABSTRACT
.
h We present a carefully vetted equatorial (˘ 30˝ Decl.) sample of all known single (within
p 2
4 ) mid M-dwarfs(M2.5V-M8.0V)extending out to 10pc; their proximity andlow massesmake
-
o them ideal targets for planet searches. For this sample of 58 stars, we provide V , R , I
J KC KC
r photometry,newlowdispersionoptical(6000´9000˚A)spectrafromwhichuniformspectraltypes
t
s are determined, multi-epoch Hα equivalent widths, and gravity sensitive NaI indices. For 12 of
a
these58stars,strictlimitsareplacedonthepresenceofstellarandsub-stellarcompanions,based
[
ona pioneeringprogramdescribedhere that utilizes precise infraredradialvelocities andoptical
1
astrometric measurements in an effort to search for Jupiter-mass, brown dwarf and stellar-mass
v
companions. Our infrared radial velocity precision using CSHELL at NASA’s IRTF is „90 m
2
1 s´1 overtimescalesfrom13daysto 5 years. With our spectroscopicresults the meancompanion
0 masses that we rule out of existence are 1.5 M or greater in 10 day orbital periods and
JUP
5 7 M or greater in 100 day orbital periods. We use these spectra to determine rotational
JUP
0
velocities and absolute radial velocities of these twelve stars. Our mean astrometric precision
.
1 using RECONS 6(Research Consortium on Nearby Stars) data from 0.9-m telescope at Cerro
0 Tololo Inter-American Observatory is „3 milli-arcseconds over baselines ranging from 9 to 13
5
years. With our astrometric results the mean companion masses that we rule out of existence
1
are greater than 11.5 M with an orbital period of 4 years and greater than 7.5 M with
: JUP JUP
v
anorbitalperiodof8years. Althoughwedonotdetectcompanionsaroundoursub-sampleof12
i
X stars,we demonstrate that our two techniques probe a regime that is commonly missed in other
companion searches of late type stars.
r
a
Subject headings: low mass stars, companions, planets
1. Introduction low 4000 K assembled in Batalha et al. (2013)
that were observed with the Kepler mission
Given human-kind’s search for life in the uni-
(Borucki et al. 2010; Koch et al. 2010). This
verse, there is great motivation to find Earth-size
estimate is consistent with but slightly higher
and Earth-mass planets in the habitable zones
than previous studies, which measure occurance
of stars. Recent studies have determined that
rates of approximately one planet per M-dwarf
Earth size planets are common around M-dwarfs.
(Youdin2011;Mann et al.2012;Swift et al.2013;
Morton & Swift (2013) estimate an occurrence
Dressing & Charbonneau 2013). Given the ap-
rate of 1.5 planets per M-dwarf with periods less
parent abundance of Earth-size planets orbiting
than 90 days and radii larger than 0.5R ,
EARTH M-dwarfs, which dominate the stellar population
using the list of 4000 stars with temperatures be-
1
(75%;Henry et al.2006),Dressing & Charbonneau with Vă14 and finds the giant planet (msini =
(2013) predict the nearest non-transiting planet 100-1000 M ) frequency to be 2% for or-
EARTH
in the habitable zone orbiting an M-dwarf is bital periods between 10 and 100 days, and the
within 5 pc of th Sun, with 95% confidence. super-Earth (msini = 1-10 M ) frequency
EARTH
However, how suitable these nearby planets with orbital periods between 10 and 100 days to
within the classically defined habitable zone (e.g. be significantly higher at 52%. Many of the M-
Kasting et al. 1993) may be for life is still under dwarfs not surveyed are faint and chromospheri-
debate (e.g.Tarter et al.2007;Barnes et al.2011; cally active, whichlimits the achievable RV preci-
Guedel et al. 2014). Nevertheless, given their sionandchancestofindEarth-massplanets. Asa
ubiquity and proximity, M-dwarfs are ideal stars result,thesetwosurveys,whicharerepresentative
to search for Earth-size and Earth-mass planets of other spectroscopic M-dwarf surveys, include
in stellar habitable zones. very few mid to late M-dwarfs and can report
M-dwarfshavebeenfavoritetargetsofprecision only preliminary statistics for planet occurrence
searches for low mass planets, because a plane- around such stars.
tary companion will induce a greater reflex mo- Inordertoobtainanunbiasedassessmentofthe
tion on a low mass star than a Sun-like star, companion fraction of the nearest mid M-dwarfs,
making it easier to detect. However, not all M- weconstructavolume-limitedsampleoutto10pc.
dwarfsareequallysuitabletargetsfortheprecision Basedonnew,uniformopticalspectra,wepresent
measurementsneededtofindEarth-masscompan- this sample of 58 stars in §2. We report spectral
ions. Some M-dwarfs have close stellaror substel- types, Hα equivalent widths, and NaI indices for
lar companions that may inhibit the detection of these stars in §3. We list our V , R , I 7
J KC KC
Earth-mass planets. The dynamically disruptive (hereafter without subscripts) photometry in §4.
effectsofthesecompanionscouldalsoprecludethe In §5, we focus on a sub-sample of 12 stars, for
existence of Earth-mass planets; the lack of short which we obtain high dispersion infrared spectro-
period giant planets in multiple planet systems scopicdatadescribedin§6andastrometricdatain
corroborates this hypothesis (Latham et al. 2011; §7. Results forthe remaining starsinourvolume-
Steffen et al.2012;Batalha et al.2013). Some M- limited sample will be presented in a subsequent
starsalso exhibit highchromosphericactivity and paper. We describe our Monte Carlo technique
large rotational velocities, which can hinder the and rule out the existence of massive gas-giant
achievable RV precision (Mohanty & Basri 2003; companions,browndwarfsandstellarcompanions
Reiners & Basri2008;Jenkins et al.2009;Reiners in§8,andweconcludewithabriefsummaryin§9.
2013);thisisespeciallyproblematicformidtolate
(M3 and cooler) M-dwarfs. Given the above con- 2. Sample Selection
siderations, we argue that the best stars to target
2.1. An Equatorial Sample of Nearby Mid
for Earth-mass planet searches are likely the low-
M-Dwarfs
est mass stars (mid to late M-dwarfs) that do not
have a disruptive companion, and are both inac-
Beginning with a parent volume-limited sam-
tive and slowly rotating.
ple of stars extending out to 10 pc (unpublished
Yet, the statistics characterizing companions list; Henry et al. 2006), we assembled a sample
around mid to late M-dwarfs are still incomplete. of mid M-dwarfs for detailed study outlined in
Preliminary surveys show that Jupiter-mass com- Table 1. These stars are within the declination
panions are rare around M-dwarfs. Using ra- range of ˘ 30˝and are thus accessible to the ma-
dial velocity (RV) measurements and high con- jority of observing facilities in both the north-
trast imaging, Montet et al. (2014) found that ern and southern hemispheres. To be inclusive,
6.5˘3.0% of M-dwarfs (M0-M5.5) host a gi- we define mid M-stars using three independent
ant planet (1-13 MJUP) with a semi-major axis measures, including optical spectral type, (V-K)
smallerthan20AU,butthissampleonlyincluded color and absolute magnitude. Starting with the
18 M-dwarfs of M4 or later in their survey of 111
M-dwarfs. Another large M-dwarf survey of 102 7Subscripts: J indicates Johnson and KC indicates Kron-
stars (Bonfils et al. 2013) only included M-dwarfs Cousins.
2
complete 10 pc sample, we include stars meeting rial mid M-dwarfs, only 33 of the stars have been
one of the following criteria: spectral types be- included in past spectroscopic searches for plane-
tween M3.5V and M8.0V classified by the RE- tarycompanions(Barnes et al.2012;Rodler et al.
CONS system (described in §3), V-K “5.0´9.0 2012;Tanner et al.2012;Bonfils et al.2013;Montet et al.
magorM “12.0´19.0mag. Thereare69systems 2014). Inaddition,fourofthe58starsdonothave
V
that meet at least one of these criteria8. Of those knownprojectedrotationalvelocity(vsini)values,
systems, 13 are known binaries, five are known and thus could be rapidly rotating (see Table 1).
triples, one is a quintuple system (GJ 644ABCD-
GJ643)andoneisaknownmulti-planethost(GJ 3. Optical Spectroscopic Measurements
876; Rivera et al. 2010). The 21 close-separation
(ă42) mid M-dwarf binaries9 within the distance 3.1. Observations
and declination range of this sample are listed in We obtained optical (6000 ´ 9000˚A) spec-
Table 2. Also listed are 2MASS coordinates, par-
tra of all 58 stars in the CAESAR sample be-
allaxes,spectraltypes,absoluteV magnitudes,V,
tween 2003´2006and 2009´2011using the Cerro
R, I apparent magnitudes, near infrared photom-
TololoInter-AmericanObservatory(CTIO)1.5-m
etryfrom2MASS(J,H,K apparentmagnitudes)
s Richey-ChretienSpectrograph(RCSpec) with the
and the configuration of the system.
Loral 1200 ˆ 800 CCD camera, as part of the
A sub-sample of mid M-dwarfs is constructed broader RECONS spectral-typing program (e.g.
2
that excludes these close binaries (ă4 ) and the Henry et al. 2004; Jao et al. 2008). The spectra
planetaryhostGJ876. Thissub-sampleincludes7 were obtained with the #32 grating in first order
midM-dwarfsthatarewidecompanionstohigher with a 15.1˝ tilt, which yields a spectral resolu-
mass stars (GJ 105B, GJ 166C, GJ 283B, GJ tion of 8.6˚A; the spectra were acquired through
644C,GJ752B,GJ896B,GJ1230B).Atthestart the OG570 order blocking filter. For consistency
of this program,60 mid M-dwarfsmet the sample checks and to mitigate the effects of cosmic rays,
requirements. Subsequently, GJ 867B has been two spectra of each target were taken consecu-
determined to be a single-lined spectroscopic bi- tively. In addition, the majority of stars have
nary with a period of 1.795 days (Davison et al. spectroscopic observations on multiple epochs.
2014). Likewise,LHS1610hasbeenclaimedtobe To assist with spectral classification, at least one
aspectroscopicbinary(Bonfils et al.2013),butits flux standard was observed each night, and an
orbital properties are unknown. Table 1 lists the ensemble collection of spectral standards from
astrometric,photometric,spectroscopicandphys- Henry et al. (2002) were observed. Some of the
ical properties of the remaining 58 stars, which stars in the CAESAR sample are used as stan-
we refer to as effectively single equatorial mid M- dards, namely GJ 283B, GJ 644C, GJ 752B, GJ
dwarfs. Mass estimates in Table 1 are based on 1065, GJ 1111, GJ 1154, GJ 1207, LHS 292, LHS
mass luminosity relations of Henry & McCarthy 2090 and LHS 3799.
(1993) and Henry et al. (1999); typical errors us-
The data were reduced with standard IRAF
ing these relations are close to 20%. Because the
techniques;biassubtractionanddomeand/orsky
longtermgoalofthisprogramistoconductamore
flatfielding wereperformedonthe datausing cal-
comprehensive 3D search for companion to these
ibration frames taken at the beginning of each
stars, we refer to this sample as CAESAR, which
night. Fringing was effectively removed from the
stands fora CompanionAssessmentofEquatorial
data using a combination of dome and sky flats.
Stars with Astrometry and Radial velocity.
One flux standard per night was used for abso-
Ofthe 58 starsidentified aboveas possible tar- lute flux calibration. Spectra were wavelength
gets for precision planet searches among equato- calibrated using consecutively recorded HeAr arc
spectra. Further details regarding reduction and
8We include GJ 628 with V-K=4.99 in our sample, as its extraction are given in Henry et al. (2004).
V-Kvaluemaybegreaterthan5.0,givenourphotometric
uncertainties.
9ThislistincludesfourmidM-dwarfbinariesthatarewide
companions to more massive stars (LP 771-096BC, GJ
569BC,GJ695BC,GJ867BD).
3
3.2. Results spectraltypesM4orearlierareemission-linestars,
whereas 100% of the 9 stars with spectral type
3.2.1. Spectral Types
M6 or later are emission-line stars. Our fraction
To assign a spectral type, the wavelength cal- of early M-dwarfs with emission is comparable to
ibrated spectra are resampled via interpolation that of Reiners et al. (2012) who find 41% of the
ontoafixed1˚Agrid. TheHαandtelluricfeatures, 115 stars M3 to M4.5 to be active emission-line
basedontheskytransmissionmapofHinkle et al. stars. Likewise, Gizis et al. (2000) reports an in-
(2003) are then given a spectral weight of zero to crease in emission-line stars with lower mass and
essentially remove these features from our analy- finds 100%ofthe M7starsareemission-linestars.
sis. The spectra are normalized to a value of 1 at HealsonotesthatthistrendbreaksdownpastM7
7500˚A. Then, the spectra are then compared to andthatthe fractionoflater type starsthatshow
the library of observed standards (see Figure 1), chromospheric activity is significantly less.
and the adopted spectral type is that of the stan-
dard that yields the lowest standard deviation 3.2.3. Surface Gravity Indices
of the target spectrum divided by the standard
To assess the surface gravity of these stars,
spectrum overthe spectralrange(6000´9000˚A).
as a possible tracer of their evolutionary states,
ThedeterminedspectraltypesrangefromM2.5to
the gravity sensitive NaI doublet (defined in
M8.0, and are listed in Table 1. The uncertainty
Lyo et al. 2004) is measured; this feature is well
in all cases is ˘0.5 spectral sub-classes, based on
known to be weak in giants and strong in dwarfs
consistency between multiple epochs. Additional
(e.g. Allers et al. 2007; Schlieder et al. 2012). For
detailsofthespectraltypedeterminationsarepro-
the NaI doublet index, we use the wavelength
vided in Riedel et al. (2014). region between 8148˚A and 8200˚A. We conserva-
tively estimate our index error to be 0.05; this
3.2.2. Hα Emission
value is the average difference value of our mea-
To assess the amount of chromospheric activ- suredNaI doubletindicesforallofourstarswith
ity that these stars exhibit, we measure equiv- more than one epoch. These values are given in
alent widths of Hα 6563˚A. To do this, we first Table3. Whiletheseindicesderivedfromthelow-
subtractthe linear continuumfrom the regionbe- resolutionspectra area goodindicator ofthe evo-
tween 6550˚A and 6575˚A and then assume the lutionarystateofthe star,high-resolutionspectra
strongest maximum (or minimum) within this re- are needed to ascertain a more quantitative mea-
gion is the Hα line. After determining its loca- sure of the surface gravity. Also, we do caution
tion, we integrate both the continuum and spec- that these lines can be affected by metallicity and
trum over 22˚A, with the central wavelength cor- stellaractivity;metalpoorstarsandchromospher-
respondingto the Hα line to determine the equiv- ically active stars will systematically have lower
alent width. Upon visual inspection of the spec- equivalent widths (EW) (e.g. Hawley et al. 1999).
tra, we could not reliably determine emission or All of the stars in the ensemble sample ex-
absorptionlines smaller than 0.5˚A. Therefore,we hibit average NaI doublet indices in a typical
conservatively use this number as the error value range for main sequence stars (ą1.1; Lyo et al.
on the Hα measurements, which are given in Ta- 2004; Allers et al. 2007); we therefore classify all
ble 3; we adopt the standard convention of de- 58 CAESAR stars as on the main sequence. This
noting emission with a negative sign. If any star is denoted by adding a ‘V’ to the spectral type
exhibits Hα equivalent widths less than the the listed in Table 1.
typical noise level of 0.5˚A in at least one epoch,
we categorized it as an emission-line star. This is 4. Optical Photometry
denotedwithan‘e’nexttothestar’sspectraltype
in Table 1. Priorto our measurements,four ofthe 58stars
fromCAESARsample did nothavecomplete sets
We classify 35/58 of the stars from the CAE-
of V, R and I photometry. The remaining stars
SAR sample as emission-line stars. We also note
hadphotometric measurementspresentedineight
that the fraction of emission-line stars increases
different publications. Therefore, to establish a
with later spectral type. 37% of the 35 stars with
4
uniform,homogenous,setofphotometricmeasure- classes of these stars range from M3.0 to M5.0.
ments for the ensemble sample of 58 stars,we ob-
tained optical photometric observations using the 6. High Dispersion Infrared Spectroscopy
0.9-m telescope at CTIO. For all of our photom-
6.1. Observations
etry frames, we use the center 1024x1024 pixels
on the Tektronix 2048x2048CCD. The CCD chip
All infrared spectroscopic observations were
has a plate scale of 02.401 pixel´1, which gives
obtained using CSHELL (Tokunaga et al. 1990;
a field of view (FOV) of 6.8 by 6.8 arcminutes
Greene et al. 1993) located on the 3-m telescope
(Jao et al. 2003). All frames were collected at an
at NASA’s Infrared Telescope Facility (IRTF).
airmasslessthan2andwiththetargetstarhaving
CSHELL is a long-slit echelle spectrograph that
asignal-to-noiseratio(SNR) ą100. We use 10or
uses a circular variable filter to isolate a single
morestandardstarsfromLandolt(1992),Landolt
order onto a 256x256 InSb detector. Spectra are
(2007), and Graham (1982) to create extinction
centered at 2.298 microns (vacuum) and cover
curves each night, and transformation equations approximately a 50˚A window. Telluric methane
toobtainV,R andI photometryforallourtarget
absorption features from the Earth’s atmosphere
starsandreferencestarsusedforastrometricmea- that are superimposed on the photospheric 12CO
surements described in §7.2. During the course of
Rbranchlinesat2.3micronsareusedasanabso-
observations, we used two different V filters for
lute wavelength reference (e.g. Blake et al. 2010;
photometry. Jao et al. (2011) demonstrate that
Bailey et al. 2012). The design resolving power
both V filters give effectively identical V band
is 100,000 per pixel. We use CSHELL in the
photometryforstandardstars;thereforeitissuit- 2
high resolution mode (0.5 slit=2.5 pixels), which
able for us to combine photometry from the two
yields a predicted spectral resolving power of R
filters. For additional details on the photometric
„ 40,000. The measured resolving power deter-
reduction and its associated errors, see Jao et al.
mined from the model fits to telluric absorption
(2005) and Winters et al. (2011).
features(describedlater)is„57,000. Thisnumber
The V, R, I photometry and the number of is significantly higher than the predicted resolv-
nights on which observations were made are re- ing power for CSHELL using the 0.52 slit. We
ported in Table 1. Errors at V, R and I are note this discrepancy because CSHELL has an
0.02´0.03 mag. A comparison of five stars (GJ adjustable slit; it may be that the slit is smaller
300, GJ 406, GJ 555, GJ 628 and GJ 729) with than the designed 0.52. Crockett et al. (2011)
Bessel (1990) indicates that the two datasets are and Prato et al. (2008) also report a higher than
consistent to 0.04 mag. Using our photometric predicted spectral resolving power (R„46,000)
measurements and the parallax data given in Ta- for CSHELL in high resolution mode. Also, we
ble 1, the absolute magnitude errors range from note a similar effect of determining a higher spec-
0.03 to 0.08 mag. tral resolving power for Keck is determined in
Bailey et al. (2012), and may be a feature of the
5. A Companion Search of a 12 Star Sub- analysis code.
set
Each night, two spectra of a given star were
obtained in succession at two different positions
We present results of a 3D companion search
2
along the slit, separatedby 10 . Hereafter, we re-
on a sub-sample of 12 CAESAR stars, including
fer to these two positions as nod A and nod B.
G 99-49, GJ 300, GJ 406, GJ 555, GJ 628, GJ
Observationswereobtainedbetween2008Novem-
729, GJ 1002, GJ 1065, GJ 1224, GJ 1286, LHS
ber and 2014 January.
1723,andLHS3799,whicharethemostdata-rich
Our exposure times ranged from 180 to 1200
in our sample. The remaining stars in the en-
seconds per nod position, and were set to yield
semble sample will be presented in a subsequent
SNRs of 125 per pixel (or optimally, a combined
paper. These twelve stars have astrometry base-
SNR of 175+) for most of our targets. For the
lines,rangingfrom9toover13years,andhaveat
faintestthree stars(K ą 8.0)in oursample of12
least5infraredradialvelocitymeasurementsspan- s
stars (GJ 1065,GJ 1224,GJ 1286), a SNR of 125
ning fromalmost2weeksto5 years. The spectral
per pixel wasnotachievedas the maximumexpo-
5
suretimeissetto1200secondstolimitcosmicray generating a nightly master flat field image from
events and the dark current. allflatfieldimagesobtainedonaparticularnight.
At the beginning of each night, we obtained The master flat field images were created by first
a minimum of 30 flat and 30 dark images each subtracting the median dark image of the same
with an integration time of ten seconds. Also, exposure time from each of the flat field images.
on November 14, 2009,we collected an additional Then, each flat field image was normalized to the
30 flat and 30 dark images with an integration central 15% of the array, which was the bright-
time of 20 seconds, which were used in creating a est section of the array and the least affected by
bad pixel mask described in §6.2. Most nights we deviant pixels. After normalizing the image, all
also observed bright stars of spectral type early images were median combined.
A, as these stars exhibit no intrinsic absorption Wethenappliedabadpixelmasktoourspectra
or emission lines in this wavelength region and to remove dead and hot pixels from the data. To
therefore can be used to identify telluric features. identifydeadpixels,welocatedanypixelfivetimes
These telluric standards are used to characterize below the standard deviation of the median pixel
the instrumental profile and wavelength solution. value of the master flat field array. To locate hot
When first collecting the data, we did not real- pixels, we subtracted two times the count value
ize how sensitive our final RV measurements were of the 10 second exposure master flat field image
to the initial solutions for the instrumental pro- from the 20 second exposure master flat field im-
fileandwavelengthsolutionobtainedfromthetel- age, and then normalized this number to the 20
luric standards. After reducing part of the data, second exposure master flat field. Because these
we determined that A star observations obtained pixelsshouldincreaselinearlywithtimeandthere-
nightlyyieldthe bestprecision. Inafewcases,we fore have the same values, we identified any pixel
only obtained a few A star observations per run with values greater than three times the standard
leaving us with four nights that containno A star deviation of this median pixel value of the differ-
observations. The four nights the telluric stan- ence image to be a hot pixel. All deviant pixels
dardswerenotobservedaremarkedinTable 4by identified from the bad pixel mask are assigned
an asterisk next to the date. interpolated values using the neighboring pixels.
We aimed to observe each target at least four We optimally extracted each spectrum follow-
nightswithinasingleobservingrun(„1´3weeks) ing the procedures in Horne (1986) as imple-
in orderto searchfor companionswith orbitalpe- mentedfornod-subtractedspectrainBailey et al.
riods of less than a week. Because of inclement (2012). The code used to analyze the data in this
weather we were not able to achieve this ca- work is a modified version of that described in
dence for all targets. On subsequent runs, we re- Bailey et al. (2012), tuned to work for CSHELL
observed our targets at least once to search for data. Theadvantageofoptimallyextractingspec-
companions with longer orbital periods, except tra over the standard extraction is that the opti-
for GJ 1065. For the sample of 12 stars studied malextractionminimizesthenoisycontributionof
here, we obtained between 5´12 RV epochs for the profile wings and eliminates and/or mitigates
each star, spanning a temporal baseline between noisefeatureswithinthespectralprofilecausedby
13 days and 1884 days (see Table 4). cosmic rays and deviant pixels not excluded with
the bad pixel mask.
6.2. Image Reduction and Spectral Ex-
Toobtainanoptimally extractedspectrum,we
traction
summedthepixelsfromthenodsubtractedimages
Wesubtractedeachnoddedpairofimagesfrom overthecross-dispersiontogivethestandardspec-
one another to remove sky emission, dark current trum. We then fitted a second order polynomial
and detector bias assuming that changes in the tomapthecurvatureofthe orderonthe detector.
detector or spectrograph properties were negligi- Next,wefittedthespectralprofileofthestandard
ble over the timescale when the nodded pair of spectrum with a Gaussian to model our spatial
images were obtained. After completing the nod- profiles at each pixel step (column) along the or-
subtraction,wecorrectedeachimageforflatfield- der parallelto the dispersiondirectionofthe nod-
ing. Correctionsforflatfieldingwereperformedby subtractedspectralimage. Fromthis,thevariance
6
of the profile was determined. Then, we summed SNR of the individual spectrum in the nod pair
the pixels weighted by the variance image of the tobegreaterthan50andthereducedχ2 estimate
spectrum’sspatialprofiletocreateourtwodimen- of our modeling prescription (§6.3) to be below
sionaloptimallyextractedspectrum. ForlowSNR 3.5.
data, we implemented a clipping routine that in-
terpolatesoverapixelthatis morethan5σ above 6.3. Method to Determine Spectral Prop-
orbelowtherunningaverageofthefivepixelsnext erties
to the pixel in question to remove any remaining
Wefiteachobservationtohighresolutionspec-
deviant features.
tral models that are convolved to the resolution
To obtain an estimate of the SNR for each of CSHELL. Each model spectrum is formed by
spectrum, we use a simplified version of the CCD combining a synthetic stellar spectrum and an
equation from Mortara & Fowler (1981) modified empirical telluric spectrum. The synthetic stel-
to account for the noise introduced by subtract- lar spectra are created from NextGen models
ing pairs of images. When performing a nod (Hauschildt et al. 1999). The telluric model spec-
pair subtraction we remove the sky background, tra are extracted from observations of the Sun
dark current and bias simultaneously. Therefore, fromanultra highresolutionKPNO/FTStelluric
we cannot distinguish between these values and spectrum(Livingston & Wallace1991). Weadopt
refer to them collectively as the uncertainty in the stellar template closest in temperature to our
background. Executing a pair subtraction means star, using the assigned spectral types and the
that we have to deal with this uncertainty in the temperature scaleofKraus & Hillenbrand(2007).
background twice and the read noise associated We fix the surface gravity log(g) to 4.8 dex (cgs)
with eachof those backgroundestimates. In most for all of our stars, which is consistent with mea-
cases, the background of the first image (Image surementsassembledinMentuch et al.(2008)and
A)shouldequal(withintheuncertainty)theback- Hillenbrand & White (2004) for field M-dwarfs.
groundofthe secondimage(ImageB).Therefore,
Themodelspectrumconsistsof19freeparame-
we simply double the noise contribution from the
ters to fit. The linear limbdarkeningcoefficientis
background and the read noise. The equation to
setto0.6forallstars,whichisappropriateforcool
calculate the SNR per pixel is as follows:
starsatinfraredwavelengths(Claret2000). Three
oftheparametersmakeupaquadraticpolynomial
S
e
SNR“ that characterizes the wavelength solution. Nine
aSe`2¨npBe`Re2q oftheparametersareGaussiansusedtomodelthe
where S is the total number of counts per inte- line spread function (LSF) of the spectrum; we
e
gratedcolumnofaspectrumextractedfromanod- assume that the LSF along the order is constant.
subtracted image in electrons, n is the number of Theremainingsixparametersarethedepthofthe
pixels in the spatial direction that are integrated telluric features, the depth of the stellar features,
over during the extraction, B is the integrated the projected rotational velocity (vsini), the RV,
e
backgroundcountsofthecorrespondingskyimage a normalization constant, and a linear normaliza-
beforeimagesubtractionisperformed,inelectrons tion term.
per pixel, and Re2 is the read noise set to be 30 We fit the empirical telluric spectrum to our
electrons/pixel from Greene et al. (1993). rapidly rotating A star for each night we pro-
Following the above description, we determine curedobservationsofAstars. Fromthismeasure-
the SNR foreachintegratedpixelofthe spectrum ment, we estimate the wavelength solution and
and set the final SNR for the spectrum to be the the instrumental profile. The instrumental pro-
meanofthesevalues. TheSNRsarethenaddedin file is solved for by interpolating the input spec-
quadratureforthenodAandnodBmeasurements trum onto a log-linear wavelength grid and con-
to give a combined SNR value. volving it with a Gaussian kernel set to the spec-
tral resolution of the instrument determined by
Because of occasional poor weather conditions
fitting the telluric spectrum. We tested both sin-
leading to low SNR, not all observations are suit-
gle and multiple Gaussian functions to obtain the
able for precision RV analysis. We require the
instrumental profile of CSHELL. We favor multi-
7
pleGaussianstofittheinstrumentalprofile,aswe extracted spectrum fit to our telluric and stellar
had better agreement between the RV estimates models is shown in Figure 2.
fromtheABnodpairsandsmallerRVdispersions Rather than use the full 256 pixels along the
overall. The Gaussian kernel is composed of one order,the modeling analysisis restrictedto pixels
central Gaussian and four satellite Gaussians on between10and245,whichcorrespondsto asmall
eachsidefollowingcloselythetechniquedescribed continuum area on the spectra. These boundaries
in Valenti et al. (1995). We set the positions of are setto preventstrongabsorptionfeatures from
the centers of the Gaussians and the widths of movinginandoutofthe analysisregionondiffer-
the satellite Gaussians so that the curves barely entepochs,becauseofdifferentbarycentriccorrec-
overlap. The amplitude of the central Gaussianis tions. Partialfeaturesthatarecut offbythe edge
constrainedbythenormalizationfactor,while the of the chip can cause our RV value to change on
width of the central Gaussian is allowed to vary. the order of 100 m s´1. Using the restricted pixel
The amplitudes of the satellite Gaussians are al- range, our average precision improved by 27% for
lowed to vary. Optimization of these values is ac- the 12 stars analyzed here.
complished by minimizing the variance weighted
reduced chi-squared as described in Bailey et al. 6.4. Spectroscopic Results
(2012) to best reproduce the observed spectrum.
The RV results of the spectroscopic modeling
In the cases when no A stars were observed on
are given in Table 4 with objects listed alphabeti-
a night, we use the mean values determined on
cally. MultipleRVmeasurementsonasinglenight
nights close to the night when A stars were ob-
are averaged to provide a single epoch value. All
served.
RV measurements are corrected to the Solar Sys-
After fitting the telluric spectrum, the nine pa-
temBarycenterusingacorrectionprescriptionac-
rameters used to characterize the LSF are kept curate to „ 1 m s´1 (G. Basri; priv. communica-
constant for all remaining fits. We use an itera-
tion).
tive process where we fit the target spectrum to
Under the assumption that the stars do not
the combined synthetic stellar model and empiri-
have companions, the observed dispersion is
caltelluricmodel. Onthefirstiteration,wefitthe
thoughttobecausedbyacombinationoftheoret-
wavelengthsolution,thedepthofthetelluricspec-
ical photon noise error, intrinsic stellar error and
trum, the RV, the normalization constant, and
instrumental error (σ 2 “ σ 2 ` σ 2
the linear normalization term. With an improved obs photon stellar
` σ 2). The theoretical error for each spec-
guess on our second iteration, we allow the vsini, instr
trum is calculated based on the prescription by
the depth ofthe telluric model,the depthofspec-
Butler et al. (1996). For our 12 stars, the average
tralmodelandthetwonormalizationconstantsto
theoretical photon noise error is 57 m s´1, with a
fluctuate. The vsini is determined following the
standard deviation of 14 m s´1. The stellar error
description provided in Gray (2005). We adopt
is assumed to be zero, as we are observing a field
the average vsini value from this iteration for all
population of slowly rotating M-dwarfs. This is
epochs as the vsini value for the star. Finally,
supportedbyresults ofBonfils et al.(2013)show-
we repeat the first iterative process allowing the
ing that the observed RV dispersions based on
wavelengthsolution,thedepthofthetelluricspec-
optical spectral for nine of the stars in this sub-
trum,theRV,thenormalizationconstant,andthe
samplearebelow10ms´1. Wesolvetheequation
linear normalization term to vary in order to de-
abovetodeterminetheinstrumentalerror(σ 2
termine the absolute RV of the star. Computa- instr
“σ 2 ´σ 2)foreachstar,inwhichtheob-
tionally, the optimization of the model spectrum obs photon
served dispersion is the standard deviation of the
is completed using AMOEBA, which is a routine
nightly radialvelocity measurements and the the-
used for minimization of multiple variables using
oretical photon error for each star is the average
the downhill simplex method of Nelder & Mead
ofthenightlytheoreticalphotonerrors. Theaver-
(1965). We note that AMOEBA is very sensi-
age instrumentalerrorfor this subset is 73 m s´1,
tive to initial guesses and is given user specified
with a standard deviation of 42 m s´1. We adopt
ranges to restrict the answers to physically rea-
this number as the instrumental error for all tar-
sonable solutions. An example of an optimally
gets in our sub-sample. In Table 4, we report the
8
final error assigned to each measurement, which
is calculated as the instrumental error added in
quadrature with the theoretical photon noise er-
ror.
In Table 5, we summarize the infrared spec-
troscopic results, including the absolute RV, the
number of epochs, the time span of observations,
the standard deviation of the RV measurements
andthe vsinivalueanditsuncertainty. Theabso-
luteRVisthemeanoftheRVmeasurementsfrom
different nights. We note that systematic uncer-
taintiesinthe adoptedsynthetictemplate(log(g),
T ), and the wavelength region used in the fit
eff
can cause RV shifts of „ 100 m s´1. Therefore,
wesettheuncertaintyoftheabsoluteRVmeasure-
Fig. 1.— CTIO spectra of five CAESAR stars ments to be 100 m s´1 for all 12 stars. All of our
(black) normalized to 7500˚A. The comparison stars have previous absolute radial velocity mea-
spectra (red) are from the library of standards surements and those measurements are less than
from Henry et al. (2002). Small discrepancies at 3sigmafromourmeasurements(Gizis et al.2002;
the longest and shortest wavelengths are due to Nidever et al. 2002).
minor errors in the flux calibrations. The vertical The vsini value is the average of the nightly
line represents the position of Hα (6563 ˚A). best fit vsini measurements. The error on the
vsini value is calculated as the standard devia-
tion of the best fit nightly vsini measurements.
We do caution that the spectral resolving power
ofCSHELLisnothighenoughtofullyresolvethe
lines of the slowest rotators. Line broadening be-
comes measurable for vsini values in excess of 3
km s´1, therefore we set this value as our vsini
detection limit. This detectionthresholdis in line
with those reported by Reiners et al. (2012) of 3
km s´1 and Browning et al. (2010) of 2.5 km s´1
for similar resolution spectra (R=45,000-48,000).
We detect rotationalbroadening above our detec-
tion threshold for two stars, G 99-49 and GJ 729,
out of the twelve. The previous vsini value for G
99-49 of 7.4˘0.8 km s´1 by Delfosse et al. (1998)
is within 2 sigma of our measurement of 5.8˘0.3
km s´1. Likewise, the previous vsini value for GJ
729 of 4.0˘0.3 km s´1 by Browning et al. (2010)
iswithin0.7sigmaofourmeasurementof3.8˘0.6
Fig. 2.— Spectral Modeling of GJ 300. Spectra km s´1.
aremodeledbycombiningatelluricspectrum(top
Our observed dispersions for these 12 stars
spectrum) with a synthetic stellar spectrum (2nd
range from 47 m s´1 to 139 m s´1. Our average
spectrum);thetelluricspectrumprovidesanabso-
observed dispersion is 99 m s´1, with a standard
lute wavelength reference. The CSHELL spectra
deviation of 27 m s´1. Figure 3 shows the RV
of GJ 300 are shown (black) in comparison with
measurementsfor allepochsfor eachofthe target
the the bestfit(red;3rd spectrum). Theresiduals
stars. The median RV error for high SNR spec-
of the fit are shown (bottom spectrum).
tra ofthe 10slowly rotatingstars(vsini ă 3.0 km
s´1)is88ms´1. Thisisdominatedbytheinstru-
9
mentalerror(73ms´1),whichsuggestsalimiting require all stars used as reference stars to have a
precision of „90 m s´1 for high SNR, slowly ro- minimum of 100 counts. Our reduction routine
tating mid to late M-dwarfs. We note that some accountsforplatescalingandrotationeffects,but
of the instrumental uncertainty could be a conse- ignores higher-order terms (astigmatism, coma,
quence of our modeling prescription; a more so- chromatic aberration; see Jao et al. 2005).
phisticatedapproachmayyieldbetterresults. We Exposuretimesaresetsuchthatthetargetstar
also note that a precision of 58 m s´1 has been or in some cases a very close bright reference star
reported for multiple epoch measurements of the does not saturate. Our maximum exposure time
M0 star GJ 281 using CSHELL (Crockett et al. is 600 seconds. We aim to obtain exposure times
2011). These precisions are nevertheless consid- of atleast30 secondsfor every star,althoughthis
erably better than the design specs for CSHELL is not always possible for our brightest stars.
(Tokunaga et al. 1990; Greene et al. 1993), espe-
Frames are only collected under seeing condi-
cially considering the small wavelength coverage, 2
tions better than 2.4 , determined by the FWHM
and are credited to the talents of the instrument
of the stars in the field to be used in our reduc-
team.
tion. Also, the target star and its reference stars
must have an ellipticity less than 20%, in order
7. Astrometry
to determine the centroid of the stars with the
most accuracy and to eliminate frames with pos-
7.1. Observations
sible tracking/guiding errors. The guider is typi-
All optical astrometric observations were made cally used for any exposure times longer than 300
using the 0.9-m telescope at CTIO. The astrome- seconds.
tryprogrambeganasanNOAOSurveysProgram
Eightof the twelve stars discussed here are ob-
in 1999 August and continued from 2003 Febru- served astrometrically with the V filter. During
ary as part of the SMARTS (Small and Moder- the course of observations, the first V filter was
ateApertureResearchTelescopeSystem)Consor- crackedandreplacedbyanotherV filter. Theuse
tium. Starshavebeenintermittentlyaddedtothe ofthe secondV filter from2005Februaryto 2009
observing list since 1999 and stars discussed here
July causes a few milli-arcseconds (mas) offset in
continue to be observed. The Cerro Tololo In-
astrometric residuals of known singles from other
teramerican Observatory Parallax Investigation
techniques. In 2009 July, we switched back to the
(CTIOPI) program was originally designed to original V filter, as the minor crack on the filter
measure accurate parallaxes of nearby stars. We
edgedoes notaffectthe dataacquiredonourcen-
are now using the same data and techniques to
tral quarter region of the CCD. Using data from
look for perturbations that remain in our astro-
both filters gives the same parallax measurement,
metric signal after solving for the parallactic mo-
but with slightly higher errors (Subasavage et al.
tion and the proper motion of our targets. The
2009; Riedel et al. 2010) and the average residual
presence of a periodic perturbation in our data
deviation for the stars is still less than 4 mas for
might signify that our star is orbiting around a our 12 stars (see §7.3). Therefore, we choose to
common center of mass with an unseen compan-
use data obtained in both filters to maximize the
ion. To do this, we use the same instrumental
time coverage.
setupasthatusedforthephotometryframes. We
observe each star in one of the V, R, or I filters. 7.2. Astrometric Reductions
Starsareobservedthroughthefilterthatgivesthe
We correct all centroids of reference stars and
strongest reference field, while not compromising
the target star for differential chromatic refrac-
the counts of the target star (the filter and num-
tion (DCR; Jao et al. 2005). We measure accu-
ber of reference stars used are given in Table 6).
rate positions using the SExtractor Centroiding
Strong reference fields that give the most precise
algorithm from Bertin & Arnouts (1996) and use
parallax measurement include 5 to 12 reference
the Gaussfit program (Jefferys et al. 1987) to si-
stars that are bright (peak counts greater than
multaneously solvefor the parallaxrelativeto the
1000), close on the chip to the target star, and
reference stars and proper motion on all available
in a configuration that surrounds the target. We
10