The Carnegie Astrometric Planet Search Program
Alan P. Boss, Alycia J. Weinberger, Guillem Anglada-Escude, Ian B. Thompson, Gregory Burley, Christoph Birk, Steven H. Pravdo, Stuart B. Shaklan, George D. Gatewood, Steven R. Majewski, Richard J. Patterson
aa r X i v : . [ a s t r o - ph . I M ] S e p The Carnegie Astrometric Planet Search Program
Alan P. Boss, Alycia J. Weinberger, and Guillem Anglada-Escud´eDepartment of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 BroadBranch Road, NW, Washington, DC 20015-1305Ian B. Thompson, Gregory Burley, and Christoph BirkCarnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101-1292Steven H. Pravdo and Stuart B. ShaklanJet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,Pasadena, CA 91109George D. GatewoodAllegheny Observatory, University of Pittsburgh, 159 Riverview Ave., Pittsburgh, PA 15214Steven R. Majewski and Richard J. PattersonDept. of Astronomy, University of Virginia, 530 McCormick Road, Charlottesvile, VA22903-0818Received ; accepted 2 –
ABSTRACT
We are undertaking an astrometric search for gas giant planets and browndwarfs orbiting nearby low mass dwarf stars with the 2.5-m du Pont telescope atthe Las Campanas Observatory in Chile. We have built two specialized astromet-ric cameras, the Carnegie Astrometric Planet Search Cameras (CAPSCam-S andCAPSCam-N), using two Teledyne Hawaii-2RG HyViSI arrays, with the cameras’design having been optimized for high accuracy astrometry of M dwarf stars. Wedescribe two independent CAPSCam data reduction approaches and present adetailed analysis of the observations to date of one of our target stars, NLTT48256. Observations of NLTT 48256 taken since July 2007 with CAPSCam-Simply that astrometric accuracies of around 0.3 milliarcsec per hour are achiev-able, sufficient to detect a Jupiter-mass companion orbiting 1 AU from a late Mdwarf 10 pc away with a signal-to-noise ratio of about 4. We plan to follow about100 nearby (primarily within about 10 pc) low mass stars, principally late M, L,and T dwarfs, for 10 years or more, in order to detect very low mass companionswith orbital periods long enough to permit the existence of habitable, Earth-likeplanets on shorter-period orbits. These stars are generally too faint and red tobe included in ground-based Doppler planet surveys, which are often optimizedfor FGK dwarfs. The smaller masses of late M dwarfs also yield correspondinglylarger astrometric signals for a given mass planet. Our search will help to de-termine whether gas giant planets form primarily by core accretion or by diskinstability around late M dwarf stars.
Subject headings: astrometry – instrumention: high angular resolution – techniques:high angular resolution – stars: planetary systems – stars: low-mass, brown dwarfs
1. Introduction
There are only 21 known G stars within 10 pc of the sun, but at least 239 M dwarfs(Henry et al. 2006), stars with masses in the range of 0.08 to 0.5 M ⊙ . Given this extremeimbalance in the numbers of the closest stars, M dwarfs are a natural choice for astrometricplanet searches, where closeness is the primary virtue. Young M dwarf stars appear to haveprotoplanetary disks similar to those around T Tauri stars of higher mass (e.g., Andrews &Williams 2005) and perhaps even longer lived (Carpenter et al. 2006). Hence there is noobvious reason to believe that low mass stars should not be able to form planetary systemsin much the same manner as their somewhat more massive siblings. In fact, radial velocityand microlensing searches have begun to discover planetary companions (gas giants andhot or cold super-Earths, respectively) to M dwarf stars in some abundance (e.g., Marcyet al. 1998, 2001; Butler et al. 2004; Bond et al. 2004; Rivera et al. 2005; Bonfils et al.2005; Udalski et al. 2005), and a candidate gas giant planet orbiting an M dwarf (VB10)has been astrometrically discovered (Pravdo & Shaklan 2009). In addition, brown dwarfsshould be more frequent companions to M dwarfs than to G dwarfs, given the smaller massratio involved (e.g., Joergens 2008; Jao et al. 2009). These brown dwarf companions willbe considerably more astrometrically detectable around M dwarfs than gas giant planetcompanions. We are focusing our astrometric search on late M dwarfs and even fainter stars(L and T dwarfs), targets that are not generally included in radial velocity surveys.Our astrometric search will aid in the determination of which of two competingmechanisms for gas giant planet formation dominates by searching for giant planets aroundM dwarfs. Wetherill (1996) found that Earth-like planets were just as likely to form fromthe collisional accumulation of solids around M dwarfs with half the mass of the Sun asthey were to form around solar-mass stars. Boss (1995) studied the thermodynamics ofprotoplanetary disks around stars with masses from 0.1 to 1.0 M ⊙ , and found that the 4 –location of the ice condensation point only moved inward by a few AU at most when thestellar mass was decreased to that of late M dwarfs. In the core accretion model of giantplanet formation, this implies that gas giant planets should be able to form equally wellaround M dwarf stars, and perhaps at somewhat smaller orbital distances. However, thelonger orbital periods at a given distance from a lower mass star mean that core accretionmay be too slow to produce Jupiter-mass planets around M dwarfs before the disk gasdisappears (Laughlin et al. 2004; Ida & Lin 2005). In the competing disk instability modelfor gas giant planet formation, calculations for M dwarf protostars (Boss 2006) have shownthat M dwarf disks are capable of forming gas giant protoplanets rapidly. Gas giant planetsformed by disk instability for host protostars with masses of both 0.5 M ⊙ and 0.1 M ⊙ (Boss 2006), spanning nearly the entire range of M dwarf masses, with no indication thatthe process would not continue to operate for even lower mass dwarfs. Hence a search forgas giant planets orbiting M, L, and T dwarfs should be a valuable means for determiningif disk instability is able to form giant planets in significant numbers around these dwarfs,as core accretion seems to be ruled out for such very low mass stars and brown dwarfs.In this paper, we describe the Carnegie Astrometric Planet Search Cameras(CAPSCam-S and CAPSCam-N), which are the centerpieces of our efforts. We alsopresent data for one target field from the first two years of observations with CAPSCam-S,and use these observations to estimate the short- and long-term astrometric accuracy ofCAPSCam-S on the du Pont telescope.
2. Carnegie Astrometric Planet Search Cameras
One of the main motivations for this program is to take advantage of the CarnegieInstitution’s du Pont telescope for use in the search for extrasolar planets and brown dwarfstars. The Las Campanas Observatory (LCO) is located at an elevation of ∼ ∼
10 to 12, whereas good astrometricreference stars lying at distances of hundreds of pc to a few kpc have V magnitudes of ∼
15 to 18 or more. CCD cameras will thus saturate on the target star long before sufficientphotons from the references stars are collected.In 2004 we were awarded a grant from the NSF Advanced Technology andInstrumentation Program and Carnegie Institution matching funds to build a state-of-the-art astrometric camera to solve this bright target star problem. CAPSCam uses aHawaii-2RG HyViSI hybrid array that allows the definition of an arbitrary guide window,which can be read out (and reset) rapidly, repeatedly, and independently of the rest of thearray. This guide window is centered on our relatively bright target stars, with multipleshort exposures to avoid saturation. The rest of the array then integrates for prolongedperiods on the background reference grid of fainter stars. This can dramatically extend thedynamic range of the composite image. This HyViSI detector is the heart of the CAPSCamconcept.The Hawaii-2RG array is a three-side buttable, silicon-based hybrid focal plane array,with Si PIN photodiodes indium-bump-bonded to a CMOS readout multiplexer. Theactive, light-sensitive area of the array is 2040 x 2040 active 18 um pixels, surrounded oneach side (window frame style) by 4 rows and columns of reference pixels, for a total of 6 –2048 x 2048 array elements (Bai et al. 2003). However, in order to increase the dynamicrange of CAPSCam-S, we have set the bias voltages at a level such that an addtional 3 rowsand columns of pixels are affected by the bias in the reference pixels, reducing the effectiveactive imaging pixels to 2034 x 2034. The gain in dynamic range more than makes up forthis small loss in imaging area.In our configuration, the detector operates with four output channels at 125 kHz. Eachchannel is a 2048 x 512 stripe of the array. The detector also has a guide window (GW)mode, with programmable size and location, which is read out by one of the four analogto digital converters. This mode allows a selected subarray to be read, without disturbingthe main array (the full frame, or FF). A few simple clock signals and a serial interface areused to select and control the various detector array operations. The readout timing is 8microseconds per pixel.We purchased two Teledyne (formerly Rockwell) HyViSI arrays, one science grade andone engineering grade. The science grade array is mounted in CAPSCam-S, and has a darkcurrent of less than 0.1 electron/s/pixel and a read noise of 12.5 electrons. The gain is 2.1electrons per data number (DN), and the linear full well is 130,000 electrons. The pixel sizeis 0.194 arcsec, while the field of view of CAPSCam-S is 6.63 arcmin by 6.63 arcmin. Theengineering grade array is comparable in performance to the science grade array, exceptwith a read noise of 28 electrons. The engineering grade array has been used to build asecond camera, CAPSCam-N, for use in testing in the laboratories in Pasadena and for usein a northern hemisphere planet search on the Mt. Wilson 2.5-m telescope (see Figure 1).The detector is mounted in our standard single-chip rectangular aluminum housing,coupled to an IR-Labs ND-2 cryostat. The control electronics box is mounted to the sideof the dewar (Figure 2). The system is liquid nitrogen cooled, and has a hold time ofapproximately 13 hours. 7 –The CAPSCam dewar window serves as the system passband filter, with a wavelengthrange of about 800 to 930 nm. Figure 3 illustrates the throughput of CAPSCam as a resultof the combination of the Hawaii-2RG array and the filter/window. The filter/window wasmade with a multilayer coating on a 90 mm diameter λ /30 (peak to valley) fused-silicawindow from Barr Associates.Two of us (GB and IBT) designed and built the electronics boards, and assembledboth CAPSCams in our laboratories in Pasadena. The detector controller is a compact,4-channel digital signal-processor-based system. It is a modified version of our BASE ccdcontrol electronics, which is described in detail on the OCIW website. Tables 1 and 2present more details about the CAPSCam read-out scheme, including the GW, FF, andoverhead readout times.One would normally operate the array without a shutter, using the built-in electronicreset function at the beginning of each FF or GW exposure. However, this would result indifferent sampling of the atmospheric turbulence by the wavefronts from the GW and FFstars, as the FF would continue to integrate during the time used for resetting and readingthe GW. Hence a mechanical Uniblitz shutter and driver was purchased from Vincent &Associates, in order to synchronize the sky time for both the guide window and the fullframe of the array. The optical path then consists solely of the primary and secondarymirrors, the shutter, the Barr filter/window, and the Teledyne array, eliminating opticaldistortions caused by any additional components.CAPSCam-S camera was installed on the du Pont telescope in March 2007 (Figure2) and has been in operation ever since, with several improvements having been made inthe meantime. CAPSCam-S is controlled by a software graphical user interface (GUI)written by one of us (CB), which allows for convenient operation and monitoring of all of itsfunctions. A detailed users manual for CAPSCam-S with a description of the GUI windows 8 –can be found on the Carnegie Observatories web pages.The minimum integration time for the guide window is 0.2 sec, allowing CAPSCam tohandle target M dwarf stars typically as bright as a V magnitude of ∼
12 or an I magnitudeof ∼
3. Target Star Sample Selection
Our top priority sample consists of 44 stars and brown dwarfs closer than 10 pc withspectral types later than M2.5, with another 26 dwarfs from 10 pc to 20 pc, for a total of70 targets with known parallaxes within 20 pc. The majority of these targets have spectraltype M5.5 or later. For observability, we require that the targets not saturate in our 0.2 sminimum integration time, i.e., have I magnitudes greater than ∼ ∼ ∼
100 targets for a decade or longer with CAPSCam-S on the duPont.
4. CAPSCam Data Analysis Pipeline
We present here a brief description of the astrometric data pipeline developed atDTM specifically for CAPSCam. More complete details about the data pipeline andalgorithms employed will be given in a forthcoming publication (see Anglada-Escud´e et al.,in preparation). We have also analyzed CAPSCam data with a completely separate dataanalysis pipeline developed by another of us (SBS), which has been used extensively in theStellar Planet Survey (STEPS) astrometric program in the northern hemisphere on thePalomar 5-m telescope (Pravdo & Shaklan 1996). While the results obtained from the twoapproaches contain significant differences, these differences can be understood in terms ofthe different algorithms and data processing approaches used in the two pipelines.CAPSCam data processing consists of two major steps: source extraction (or one nightprocessing) and the astrometric iterative solution.
A chosen image is used to create an astrometric template of the field for a givennight. Some initial rejection of objects is done based on the roundness (ratio of thefull-width-half-maximum [FWHM] of the point spread function [PSF] in the X and Ydirections) and convergence properties of trying to find an initial rough estimate for 10 –the photocenter of each object (centroid). The 20 brightest objects (typically stars) areidentified in every image and the rest of the objects are then located using the astrometrictemplate. A fine centroiding algorithm is then applied and a catalog with the subpixelpositions of all of the objects is obtained for all of the images of the field for a given night.The centroiding algorithm consists of binning the PSF in the X and Y directionsseparately and fitting a one-dimensional PSF profile in each direction. Several differentwindow sizes (apertures) are used on each object and the centroid position is found byaveraging over all the apertures tried. This scheme has been compared to two-dimensional(2D) approaches (e.g., 2D Gaussian PSF fitting), and found to provide the most robustcentroid determinations. The centroid determinations are very stable numerically, give thesmallest scatter, and are insensitive to the discreteness of the sampling of the PSF.When all the images for a given night are processed, the relative positions of all of thestars are compared, and the resulting scatter is used to estimate the centroid uncertaintiesfor each star. Since we observe with telescope ditherings of 2 ′′ in both X and Y, bad pixelsand other Hawaii-2RG defects will move significantly and can be easily removed at thispoint. A final filtering of bad pixels and detector defects is then done to produce the finalplate catalogs. The processing of each image generates a plate catalog , which contains a listof the X-Y-centroids and their associated uncertainties. One astrometric epoch typicallythen consists of between 20 to 80 plate catalogs obtained in a given night. Once images from a given field have been obtained on different nights spread over along time baseline, an astrometric solution can be obtained and used to derive the positions,proper motions, and parallaxes of all the stars in each target field. 11 –The astrometric solution is an iterative process. An initial catalog of positions isgenerated from a given plate, a transformation is applied to each plate catalog to match theinitial catalog, and the apparent trajectory of each star is then fitted to a basic astrometricmodel. The initial catalog is updated with new positions, proper motions, and parallaxesand a subset of well-behaved stars is selected to be used as the reference frame. Theselection of the reference stars is based on the number of successful observations and themedian of the root-mean-square (RMS) of the residuals for the 100 brightest objects. Atypical field contains around 40–50 of such stars. This process is then iterated a smallnumber of times using only the reference stars for calibration purposes. The convergence ofthe astrometric solution is monitored by following the average RMS of the reference framestars.Since the number of targets followed and images generated by the CAPSCam planetsearch effort is large, the astrometric solution process has been designed to be fullyautomatic. Albeit structurally simple, some steps in this processing are algorithmicallycomplex, especially those related to cross-matching, reference star selection, calibrationweighting, astrometric model selection, etc. A more complete description of each of thesesteps will be given in Anglada-Escud´e et al. (in preparation).The initial catalog is matched to the NOMAD catalog (Zacharias et al. 2005), whichcontains USNO-B1 and 2MASS positions and colors of the brighter objects. This initialmatching is required to better constrain the field rotation and plate scale, and to obtain theresulting astrometric positions in meaningful sky coordinates.The final product is then an astrometric catalog containing five fitted astrometricparameters (effectively X and Y, the proper motions in X and Y, and the parallax),information about the number of observations employed, the RMS of the residuals perepoch, and the reduced χ of the solution for each star: 12 –¯ χ = 12 N epochs − N pars N epochs X i " ( x iobs − x model ) σ i + ( y iobs − y model ) σ i , (1)where N epochs is the number of epochs, N pars is the number of model parameters to be fit, x iobs and y iobs are the measured positions of the star in a local coordinate system, x model and y model are the ones predicted by the best fit model, and the summation is over all epochs.Each observation is weighted using its own standard deviation σ i .Values of ¯ χ greater than unity typically indicate the presence of uncalibratedsystematic errors. These can occur for the target star as well as for the reference framestars. The amount of this uncalibrated systematic error is obtained for each iteration byadding an error in quadrature to the estimated uncertainties derived from the calibrationstep until an effective ¯ χ = 1 is obtained. This guarantees that the uncertainties in theparameters from the astrometric least squares solution are more realistic than the onesobtained using only the intra-night scatter. Despite the fact that part of any systematicerror may come from chromatic effects, stars with less extreme colors than the red dwarftarget stars show similar residuals (i.e., RMS deviations and ¯ χ ) pointing to other sourcesof systematic errors related to the mechanical and optical stability of the telescope anddetector on the scale of a few pixels. CAPSCam calibration observations are ongoing to tryto clarify and identify the sources of such night-to-night and long-term systematic errors,which should add more or less in quadrature, with the hope of eventually reducing oreliminating these errors whenever possible. Systematic error sources include dome seeing,dust on the optics, minute changes in the optical alignment (depending on the temperature,humidity, or gravity angle), and the true effective photocenters of the individual pixels onthe Hawaii-2RG.Geometric calibration in the CAPSCam data pipeline accounts for differential opticalaberrations with respect to the plate used as the initial catalog. We note that as long as 13 –we deal with the same instrument, only the time dependent part of the optical aberrationsis relevant. This includes both atmospheric and instrumental-related optical distortions.The CAPS pipeline permits specifying the order of the polynomials to be used in thecalibration. The zero order polynomial corresponds to a translational shift while the firstorder polynomial corrects for a small rotation and a shear. In the language of Zernikepolynomials (see Noll 1975, his Table 1), the second order polynomials account for defocusand astigmatism. While the accuracy of the astrometric solution improves significantly ifsecond order polynomials are used, we find that there is no significant improvement whenusing the third order ones as well; i.e., the third order Zernike aberration (coma) changesvery little over the timespan of these CAPSCam-S observations.
5. Differential Chromatic Refraction
Ideally, astrometric observations are taken as the target star passes the meridian, inorder to minimize atmospheric seeing effects and differential chromatic refraction (DCR,e.g., Pravdo & Shaklan 1996). Uncalibrated DCR leads to systematic errors because thephotocenters of the target and reference stars will be refracted differently as the air masschanges. Pravdo & Shaklan (1996) found that DCR could be calibrated to about 0.13milliarcsec for observations within 1 hour of the meridian and 45 degrees of the zenith withthe Palomar 5-m. We intend to minimize the effects of DCR by using the same calibrationtechnique for the du Pont and expect to be able to remove DCR to a level similar to thatfound to be possible at Palomar. The CAPSCam spectral bandpass has a FWHM of about100 nanometers, centered on 865 nanometers, which also limits DCR effects for our redtarget stars and typically red reference stars.In our first four years of du Pont observations (2003-2006), we used the Tek5 CCDcamera to take Washington+DDO51 photometry (Geisler 1986; Majewski et al. 2000) of 14 –over 250 likely target stars (selected in part from Reyle & Robin 2004; Vrba et al. 2004;and Golimowski et al. 2004) and their reference stars, which is needed in order to removethe effects of DCR and to characterize the luminosity classes of the reference stars (i.e.,distant giants are preferred and are identifiable with these filters; Majewski et al. 2000).Essentially all of the prospective target stars have sufficient reference stars within the6.63 arcmin by 6.63 arcmin field of view of CAPSCam. We have also added Johnson B,Vphotometry (Johnson & Morgan 1953) for most fields, necessary for obtaining absoluteparallaxes through reddening corrections. Hence, the characterization phase of our searchis largely finished, though the occasional addition of new target fields to the planet searchwill require further Tek5 runs to obtain their colors.At present, we apply a prototype of DCR correction in our CAPSCam data analysispipeline which can be turned on or off. It is based on the colors from the NOMAD catalog(B,V from USNO-B1 and J,H,K from 2MASS). Ultimately, the chromatic corrections willbe based on the Tek5 photometric determinations; this process is currently in development.Even with our crude DCR corrections we already see a distinct improvement of the qualityof our astrometric solutions. Observations of a few target fields followed for about 6 hoursthrough airmasses ranging from 1 to 3 are being used to estimate the DCR effects as afunction of the TeK5 colors.
6. First Results with CAPSCam-S
The key objective of the CAPSCam program is achieving and maintaining anastrometric accuracy significantly better than a milliarcsecond for a decade or longer. Thenatural plate scale for CAPSCam-S on the du Pont is 0.194 arcsec/pixel, a scale that allowsus to avoid introducing any extra optical elements into the system that would produceastrometric errors. We take multiple exposures with CAPSCam-S, typically 60 seconds for 15 –the full frame, with small variations (2 arcsec) of the image position (dithering), in order toaverage out uncertainties due to pixel response non-uniformity. We typically spend aboutone hour per field for each epoch. The ultimate goal is to achieve a precision of about 0.25milliarcsec, and perhaps as low as 0.15 milliarcsec, which is the level of the atmosphericnoise in one hour found by Pravdo & Shaklan’s (1996) Palomar 5-m study. Here wesummarize our results to date.The goal of this first paper is limited to giving concrete evidence of the astrometricperformance of CAPSCam-S. We do not discuss important issues related to the choice ofthe reference frame or to zero–point parallax and proper motion corrections. Even still, itis remarkable that the proper motions obtained for the objects in the studied target fieldagree fairly well with those given in the USNO-B1 catalog (Monet et al. 2003), especiallythe reference stars.
We present here the performance of CAPSCam-S on Field 453 (Figure 4), whichcontains the target star NLTT 48256 (also known as LP 813-23 and as 2MASS J19483753-1932140). The target star is an M dwarf about which little is known. The field is rich inbackground objects ( ∼ V − K ∼ . No color correction is applied in this first case. After excluding poorly-behaved starsin the first iteration, the reference frame still contains 39 objects that appeared in at least90% of the frames. These 39 objects define a robust reference frame with a median RMSper epoch of 1.1 milliarcsec (mas). The astrometry of the poorly-behaved stars is alsoobtained, but they are not used in the calibration matching step.The RMS of the solution for the target star is 0 .
38 mas/epoch, which is a proxy forthe long-term stability of the instrument. Since our desired target star accuracy is ∼ . . ∼
17 mas, which puts the target star at a distance of 58 pc, considerably beyondour distance cut-off of about 10 pc. However, this star will be kept in the observing programin order to monitor the long-term stability of CAPSCam-S and to support our search forsources of systematic errors. Claims for astrometic planet detections are best supported byobservations showing that other target stars are not being similarly perturbed (so-called“flat-liners”, R. P. Butler, personal communication), so Field 453 will continue to providean invaluable check on the short- and long-term astrometric accuracy of CAPSCam-S.
The same procedure as above has been applied using R − J color as a variable in thecalibration step, which is the color most closely related to the slope of the spectral energydistribution in the CAPSCam working band. The number of useful reference frame starsdrops to 35 in this case because only stars with known R and J colors are used. The RMSof the astrometric solution for the target star decreases to 0 .
35 mas/epoch, showing a slightimprovement in the accuracy. We note that the parallaxes determined with and withoutthe chromatic correction are incompatible at the several σ level. This is caused by thecorrelation of the DCR with the parallax factor, which introduces a small bias into theparallax estimation. Since our current version of the DCR correction is only a prototype,we expect a small but significant increase in the accuracy and a better decoupling of the 18 –true parallax from color dependent effects once we are able to derive a solution with the fullTek5 photometric colors. Once the main astrometric solution is finished, we can fit the plate motion of the targetstar with an astrometric model including a Keplerian component. However, with effectivelyonly five epochs (i.e., 10 measurements of either X or Y), there is not enough information tosolve for a fully Keplerian orbit plus the astrometric solution. Hence, this exercise shouldbe considered purely as an academic one. We can then run a Least Squares periodogramroutine, which consists of fitting for each orbital period P sampled a linearized astrometricsolution with a circular orbit in an arbitrary orientation, i.e., X α = X + µ ∗ α ( t − t ) + Π p α ( t ) + A sin 2 π/P + B cos 2 π/P (2) Y δ = Y + µ δ ( t − t ) + Π p δ ( t ) + C sin 2 π/P + D cos 2 π/P (3)where the offsets X and Y , proper motions µ ∗ α and µ δ , parallax Π and the orbitalcoefficients A,B,C and D are solved simultaneously for each test period P . The functions p α ( t ) and p δ ( t ) are called the parallax factors. They are the projections of the parallacticmotion in R.A. and Declination in the direction of the star. The barycentric instant ofobservation is t and the reference epoch at which the astrometric parameters are defined is t . In order to maximize the sensitivity of our planet search, we have developed a LeastSquares periodogram approach that may perform better than other proposed methods, suchas the Joint Lomb-Scargle periodogram proposed by Catanzarite et al. (2006). Our LeastSquares minimization solves simultaneously for the signal, parallax, proper motion, and 19 –two small offsets in each direction. All of these parameters are intrinstic to the astrometricmeasurements, and can correlate spuriously with the sampling cadence and the true signal,leading to incorrect identification of candidate periods. The Least Squares approach remainslinear in all the free parameters if only astrometric data is involved (see, e.g., Pourbaix1998), which makes it computationally efficient and numerically well-behaved. Black &Scargle (1982) were the first to point out that the coupling between the reflex signal andproper motion will lead to underestimates of both the period and the amplitude of thesignal, even when the data span the entire period of the signal. We go one step further, andinclude both the proper motion and the parallax during our period search, ensuring that werecover the correct orbital period from the start.In this context, we note that the Lomb-Scargle periodogram is a special case of LeastSquares minimization (Cumming 2004), where the Least Squares minima (or the peaks ofthe periodogram) identify the correct periodicities when the true signal is close to a sinusoid(see Frescura et al. 2008). This point was first made by Scargle (1982). A Lomb-Scargleperiodogram works very well with radial velocity data, where the only relevant parameternot related to the periodic motion is a constant offset. This performance breaks down,however, for astrometric data, due to the time dependence of the proper motion and theparallax. If the true signal’s period is well-sampled, the Lomb-Scargle periodogram providesan answer close to the correct one (Traub et al. 2009), but its statistical interpretation interms of significance and confidence level is unclear. We are continuing to investigate thecomparative performance of both approaches when applied to astrometric data, but for thepurposes of this initial paper, we limit ourselves to the Least Squares approach.The purpose of the Least Squares periodogram is to find an initial set of astrometricparameters that can be used as a first approximation for a fully Keplerian solution thatminimizes some merit function (i.e., χ ). The Least Squares periodogram approach allows 20 –the weighting of each observation properly at the initial period-search level, and provides allthe parameters of the best-fit circular orbit (via the Thiele-Innes elements), which can beused as initial values to solve the fully nonlinear Kepler problem (e.g., Wright et al. 2009).If one calculates the ¯ χ as a function of the period (i.e., draw a periodogram, see Figure7), the minimum ¯ χ is the best circular model fitting the data. Currently, the number ofmeasured parameters is comparable to the number of unknowns, and so a large number ofartificial least squares minima with ¯ χ much smaller than 1 appear in the periodogram.However, this periodogram does give information about the most important orbital phasesthat have to be sampled in order to eliminate spurious signals, as shown in Figure 7. Thebest period for NLTT 48256 is at 15 .
19 days and has a semi-amplitude of 1 . too well , as shown in the phased representation of the bestorbit in Figure 8 (top). Other minima in the periodogram are due to the aliasing of the noisewith the sampling cadence (Figure 8, center) and the coupling of the astrometric motionwith natural periodicities, such as the parallax (Figure 8, bottom). External constraintscan be used to suppress such unrealistic least squares minima, however the best strategy issimply taking more data and optimizing the cadence to minimize the effects of the discretesampling cadence.In general, the minimum number of observations needed to constrain with confidencean orbital model is a complicated function of the number of observations, signal-to-noiseratio, spacing of the observational epochs, orbital period and eccentricity, and the choice ofthe statistical tests used to choose the best orbital model (e.g., Sozzetti 2005; Casertanoet al. 2008; Ford 2008; Cumming et al. 2008; Wright & Howard 2009). However, a lowerbound on the number of observational epochs required to solve for a planetary companioncan be determined simply from linear algebra theory: at least n independent observationsare needed to solve a system with n unknown factors. For a circular Keplerian orbit, there 21 –are a total of 10 free parameters in the astrometric solution for the orbit, proper motion,and parallax, while for an eccentric orbit, there are 2 more free parameters (eccentricityand the argument of periastron), for a total of 12 free parameters. For a circular orbit,then, at least 5 observational epochs in two coordinates (R.A. and Dec.) are required fora solution, and at least 6 epochs for an eccentric orbit. Clearly, such minimal solutionsmust be considered dubious, and require additional epochs for their validity to be properlyassessed. We expect that at least 10 or 12 epochs (20 or 24 measurements in R.A. orDec.) will be necessary to constrain circular or eccentric orbits, respectively. In cases whereadditional information is available (e.g., radial velocities, or catalog proper motions), theseestimates might be relaxed somewhat.
7. STEPS Data Analysis Pipeline
The STEPS data reduction process (Pravdo et al. 2004) begins by extracting squareregions containing the target and reference stars from the raw frames and organizing theminto a single file, from which positions for all stars are determined. The cross-correlationof the reference star positions relative to the target star is determined by the weightedslope of the phase of the Fourier Transform of the images after summing them intohorizontal and vertical distributions. This algorithm is insensitive to the background level,robust against changes in the shape of the point spread function (PSF), and maintains asignal-to-noise ratio comparable to matched filtering. Centroiding is then performed, anda preliminary astrometric solution is obtained by fitting a conformal six-term (three peraxis) transformation for each CCD frame to a reference frame. The transformation is thenapplied to the target star as well, allowing the target star position to be measured relativeto the surrounding reference stars. An automated program then searches for frames whoseastrometric noise is above a user-defined threshold. Generally, the threshold can be set 22 –to be very high, because the major cause of unusable data is missing reference stars orselection of the wrong star. After removal of the bad frames, the conformal transformationis run again to form an intermediate astrometric solution.The DCR effect is proportional to the tangent of the zenith angle and leads to alinear shift in right ascension and a parabolic shift (relative to the meridian position)in declination. The relative DCR coefficient for each star is determined empirically byfitting the right ascension shift. A single coefficient for each star is defined as the weightedaverage of the nightly coefficients, used to adjust the centroid positions, and the conformaltransformation is rerun once again. The position of the target star relative to the referenceframe is then known for that night.The final STEPS processing step is to fit the motion of the target star to a model of theits parallax, proper motion, and radial velocity. STEPS uses relative, rather than absolute,proper motions and parallaxes. The USNO subroutine ASSTAR is used to compute theastrometric wobble, and the NAIF subroutine CONICS is used to determine the positionand velocity of a suspected companion from an assumed set of elliptic orbital elements,which are then varied in order to find the best fit.The analysis of NLTT 48256 using the STEPS pipeline is in good agreement with theanalysis obtained using the CAPSCam data reduction scheme. However, the intra-nightscatter and corresponding single epoch uncertainties are larger using the STEPS pipeline.We attribute this to the STEPS centroiding approach, which requires a finer sampling ofthe stellar PSF than is obtained using CAPSCam-S – the seeing-disk to pixel ratio is about15 to 20 with the STEPS camera on the Palomar 5-m telescope, while the ratio is about 5for CAPScam-S on the 2.5-m du Pont.It is also significant that the reference stars used in the two analyses are not exactlythe same. We attribute the discrepancy in the obtained proper motions to these differences. 23 –In spite of these differences, both astrometric solutions agree to within the errors (see Table5). A refined centroiding algorithm using an analytic approximation of the PSF is beingimplemented on the STEPS pipeline in order to achieve improved compatibility with theCAPSCam pipeline. Table 6 presents the R.A. and Dec offsets as a function of time forthose who may wish to try their own fit to this CAPSCam-S data.
8. Comparison With Other Ground-Based Programs
Considerable progress has been made in the adaptation of CCDs to the field ofastrometry. Most notable is its application in an astrometric instrument called STEPS,which has been used at Keck and at the Palomar 5-m telesope (Pravdo & Shaklan 1996).STEPS is able to achieve high precision (approximately 0.25 to 0.5 milliarcsec) on 30 minuteexposures of intrinsically faint M dwarfs in fields with bright, well-distributed referencestars. STEPS has detected a low-mass M6-M8 binary companion to the M dwarf GJ 164,with a noise floor of ∼ ∼ ∼ ∼ ∼
9. Comparison With Space-Based Programs
The European Space Agency (ESA) Hipparcos satellite (1989-93) and the resultantcatalog comprise the most successful astrometric effort in history. Hipparcos obtainedthe parallaxes of nearly 120,000 stars with a median precision of about 1 milliarcsecond.Hipparcos’ ability to detect an astrometric planet perturbation was limited primarily bythe mission’s duration of only 3.36 years and by its annual precision of approximately 2milliarcseconds.Astrometric efforts with the Hubble Space Telescope (HST) have been almost entirelyconfined to use of the interferometers of the fine guidance system (FGS) instead of HST’sCCD cameras. The resulting studies are among the highest precision (approximately 0.5milliarcsec) planet searches to date (Benedict et al. 1999). Unfortunately these searcheswere of limited duration. The FGS has also been used to place an upper limit on themass of the short-period companion to 55 Rho Cancri of about 30 M Jup (McGrath et al.2002), a result that differed considerably from the Hipparcos evidence for a wobble largeenough to require the presence of an M dwarf companion with a mass of 126 M Jup . TheFGS measurements, with an accuracy of about 0.3 milliarcseconds, rule out the Hipparcos 27 –claim. More importantly, Benedict et al. (2002) used the FGS to determine the mass ofthe outermost planet of the GJ 876 system to be 1 . M Jup , the first time that astrometryhas determined the mass of an extrasolar planet. The low mass of the GJ 876 primarystar (0 . M ⊙ ) enabled this detection, along with knowing basic orbital parameters fromthe original spectroscopic detection of the star’s planets. While the FGS evidently can bea potent astrometric instrument, the difficulty of obtaining precious HST time for lengthyastrometric surveys limits its use to following up on particularly promising spectroscopicdetections, such as GJ 876.
10. Conclusions
Our analysis of the target star NLTT 48256 shows that an astrometric accuracy betterthan 0 . . < ∼ < . M ⊙ is largely unprobed. Dopplersearches of small samples of young stars have so far revealed an 18 Jupiter-mass objectaround a brown dwarf (Cha H α
8; Joergens & Muller 2008). Optical Doppler surveys havetargeted very few of these faint stars because integration times are prohibitively large, andinfrared Doppler surveys are in their infancy. Direct imaging studies can only search forplanets widely separated from young brown dwarfs (e.g., 2MASS1207; Chauvin et al. 2004).Astrometry searches closer in, and removes the orbital inclination ambiguity of Dopplersurveys. Hence we believe that by targeting late M, L, and T dwarfs for astrometricmonitoring for a decade or more, CAPSCam will make an important contribution to thecensus of planetary systems.We believe that a sample of around 100 stars is sufficiently large to ensure areasonable statistical measure of the frequency of long-period gas giant planets (and binarycompanions) around late M and later type dwarfs, companions with orbital periods longenough to permit habitable rocky planets to orbit these stars on shorter period orbits. Mdwarfs have recently been recognized as attractive targets in the search for life beyond theSolar System (Segura et al. 2005; Tarter et al. 2007), yet late M dwarfs are not beingstudied by optical Doppler surveys in any great number. While CAPSCam will not be ableto detect habitable terrestrial planets, we will be able to point the way for searches by futureground- and space-based telescopes designed to discover new Earths around the closest 29 –stars. In fact, the report of the Exoplanet Task Force (Lunine et al. 2008) specifically callsfor planet searches around M dwarfs to be a fast-track effort for ground-based and existingspace telescopes (see their Figure 1).We thank Paul Butler, Sandy Keiser, and Dave Monet for their key contributions tothis effort, and Wendy Freedman, Mark Phillips, and Miguel Roth for their steady supportof this ambitious program at Las Campanas. Oscar Duhalde, Javier Fuentes, Gast´onGuti´errez, Herman Olivares, David Osip, Fernando Peralta, Frank P´erez, Patricio Pinto,and Andr´es Rivera have provided valuable assistance at Las Campanas. We thank thereferee as well, whose comments have helped to improve the paper. This work has beensupported in part by NSF grants AST-0352912 and AST-0305913, NASA Planetary Geologyand Geophysics grant NNX07AP46G, NASA Origins of Solar Systems grant NNG05GI10G,and NASA Astrobiology Institute grant NCC2-1056. This research has made use of theSIMBAD database, operated at CDS, Strasbourg, France. 30 –
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36 –Table 3. Catalog information on NLTT 48256. Proper motion and coordinates are fromthe NLTT catalog (Salim & Gould 2003) and color is from the NOMAD catalog (USNO-B1+ 2MASS, Zacharias et al. 2005).Reference epoch JD 2000RA 19 48 37.5Dec −
19 32 14.3 µ RA − ±
20 mas/yr µ Dec − ±
20 mas/yrR 16.84R − J 3.63 37 –Table 4. Log of observations of Field 453. The SNR on NLTT 48256 is always over 1000and the faintest reference frame star has a typical SNR of 200-300. Exposure times aregiven in seconds while the seeing is in arcseconds.Date FF Exptime GW Exptime a STEPS b Achromatic ChromaticRA 19 48 37.488 19 48 37.488Dec −
19 32 15.926 −
19 32 15.925muRA(mas/yr) − ± − ± − − − ± − ± − − ± ± − a Parameter uncertainties in CAPSCam are given as the standard deviationsobtained from the covariance matrix of the linearized least squares solution. b Parameter uncertainties in STEPS are given as the interval with a 68% confi-dence level. 39 –Table 6. Astrometric shifts of NLTT 48256 in local plane coordinates, uncertainties, andpostfit residuals after fitting an offset, parallax, and proper motion only. All angles given inmilliarcseconds (mas).Julian Date RA Shift Dec Shift RA unc Dec unc O-C RA O-C Dec2454285.726960 -1.566825 -3.984330 0.143 0.205 -0.008 -0.8012454289.733512 -2.872852 -5.162385 0.304 0.383 0.187 0.2712454343.589780 -22.608162 -35.169847 0.184 0.263 -0.117 0.5662454661.673801 -45.457509 -197.023902 0.085 0.259 -0.030 -0.0542454722.625970 -66.343008 -230.239554 0.218 0.472 -0.070 0.8832454928.216687 -59.445586 -332.217484 0.295 0.335 0.090 -0.472 40 –Fig. 1.— The Teledyne Hawaii-2RG array can be seen mounted in the center of CAPSCam-N, shown here with the Barr Associates filter/window removed. The Hawaii-2RG array isapproximately 2” by 2” in size. 41 –Fig. 2.— CAPSCam-S is shown mounted at the Cassegrain focus of the 2.5-m du Ponttelescope at Carnegie’s Las Campanas Observatory in Chile. 42 –Fig. 3.— CAPSCam-S throughput in percent as a function of wavelength. The throughputis the product of the quantum efficiency of the Hawaii-2RG detector and the transmissionfunction of the filter/window. CAPSCam is optimized for the study of M dwarf stars, witha bandpass of about 100 nanometers centered at about 865 nanometers. 43 –
64 pix p i x p i x
120 sec. exposure time 30 sec. 30 sec. 30 sec. 30 sec.
NE 19h 48m 37.5s -19º 32’14.3’’
NLTT 48256
CAPSCam Full Frame+ Guide Window mode
Fig. 4.— CAPSCam-S Full Frame image of Field 453, with NLTT 48256 located in theGuide Window. 44 – R . A . ( m a s ) D ec ( m a s ) O - C R . A . ( m a s ) O - C D ec . ( m a s ) Fig. 5.—
Top.
R.A. (left) and Declination (right) shifts as a function of time for NLTT48256. The parallax wobble can be clearly seen on the R.A. motion.
Bottom.
R.A. andDeclination residuals (observed minus computed) with respect to the best fit model. Allvertical axes are in milliarseconds (mas). The right-most data point is based on GuideWindow and Full Frame data, while the others are Full Frame only. Use of the GW doesnot introduce any significant bias or jitter to the data. 45 – -100 -50 0 50 100R.A.(mas)-400-300-200-1000100 D ec . ( m a s ) Best fit solutionAll imagesAveraged epochsGuide window epoch -30 -20 -10 0-40-30-20-10010-90 -80 -70 -60-370-360-350
Fig. 6.— Motion of NLTT 48256 on the sky (R.A. vs. Dec.) in mas. On the top right, azoom-in of the first two epochs is shown. The small crosses are the positions as measuredfrom each individual image. The scatter is consistent with a standard deviation of ∼ ∼
10 100 1000Period (days)0.0010.010.1110 χ Fig. 7.— Best ¯ χ as a function of the period (periodogram) for NLTT 48256. The minimarepresent the candidate periods. Since the number of observations is still small, most ofthe minima are spurious and can be attributed to well-known issues related to poor datasampling (see Figure 8). 47 – R . A . ( m a s ) D ec ( m a s ) R . A . ( m a s ) D ec ( m a s ) R . A . ( m a s ) D ec ( m a s ) Fig. 8.— False minima in the periodogram for NLTT 48256 can lead to spurious solutions.
Top.
Best fit period, showing R.A. and Dec. as functions of the orbital phase, for P ∼ χ is much smaller than 1 because the number of parameters being fitted almostmatches the number of observations. Center.
Aliasing with the observing cadence ( P ∼ Bottom.
Couplingwith the parallax. Here the apparent period is P ∼
349 days, about one Earth year. Theparallax obtained for this solution is − ii