Velocities of 2046 Nearby FGKM Stars

# Precise Radial Velocities of 2046 Nearby FGKM Stars and 131 Standards

## Abstract

We present radial velocities with an accuracy of 0.1 km sfor 2046 stars of spectral type F,G,K, and M, based on 29000 spectra taken with the Keck I telescope. We also present 131 FGKM standard stars, all of which exhibit constant radial velocity for at least 10 years, with an RMS less than 0.03 km s. All velocities are measured relative to the solar system barycenter. Spectra of the Sun and of asteroids pin the zero-point of our velocities, yielding a velocity accuracy of 0.01 km sfor G2V stars. This velocity zero-point agrees within 0.01 km swith the zero-points carefully determined by Nidever et al. (2002) and Latham et al. (2002). For reference we compute the differences in velocity zero-points between our velocities and standard stars of the IAU, the Harvard-Smithsonian Center for Astrophysics, and l’Observatoire de Geneve, finding agreement with all of them at the level of 0.1 km s. But our radial velocities (and those of all other groups) contain no corrections for convective blueshift or gravitational redshifts (except for G2V stars), leaving them vulnerable to systematic errors of 0.2 km sfor K dwarfs and 0.3 km sfor M dwarfs due to subphotospheric convection, for which we offer velocity corrections. The velocities here thus represent accurately the radial component of each star’s velocity vector. The radial velocity standards presented here are designed to be useful as fundamental standards in astronomy. They may be useful for Gaia (Crifo et al., 2010; Gilmore et al., 2012) and for dynamical studies of such systems as long-period binary stars, star clusters, Galactic structure, and nearby galaxies, as will be carried out by SDSS, RAVE, APOGEE, SkyMapper, HERMES, and LSST.

stars: fundamental parameters — techniques: radial velocities — techniques: spectroscopic — stars: kinematics — stars: late-type — reference systems — Galaxy:kinematics and dynamics — binaries: spectroscopic
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## 1. Introduction

Doppler shifts of stellar spectra provide information about the line-of-sight component of the velocity vector of the target stars in the frame of the telescope. When transformed to the frame of the center of mass of the Solar System, those ”barycentric” radial velocities represent the star’s velocity component measured relative to a well defined, and commonly adopted, inertial frame within our Milky Way Galaxy, suitable for studying the motions of stars in a wide variety of astronomical settings.

Barycentric radial velocities enable study of the kinematics, structure, and mass distribution of the Milky Way Galaxy, including the disk components, bulge, nucleus, and halo. Doppler measurements also provide a primary tool for detecting and characterizing binary stars in many environments such as in the general field, open clusters, star forming regions, planet-hosting stars, globular clusters, and the Galactic center. Radial velocities also serve to measure the dynamics and mass content, both luminous and dark, of star clusters and galaxies. Moreover, radial velocities are vital for measuring the infalling extragalactic matter into our Galaxy, as well as the dynamically important motions of stars within other galaxies in the local group.

When combined with the proper motion and positions measured using, e.g., the Hipparcos telescope or the upcoming Gaia space telescope, one can measure the three dimensional velocity vectors of stars and stellar systems. Such three dimensional velocity measurements offer information about the origin, history, future, and mass distribution of the components of the Galaxy. Precise radial velocities measured over time can reveal the acceleration of stars, caused surely by gravitational forces exerted by unseen nearby objects including orbiting planets, brown dwarfs, and stars, as well as by nearby compact objects such as white dwarfs, neutron stars, and black holes.

Many new observational facilities are now, or soon will be, providing kinematic and positional information about stars in the Galaxy. The RAdial Velocity Experiment (RAVE) is studying the properties and origin of the structure in the Galactic disc (Wilson et al., 2011) by measuring velocities with an accuracy of 2 km sfor up to 500,000 stars. The Sloan Digital Sky Survey and the Sloan Extension for Galactic Understanding and Exploration (SEGUE), with its imaging and radial velocity capability (with 10 km saccuracy) are performing extraordinary measurements on the kinematics of the Galaxy and its halo (Schoenrich et al., 2010). Some groups are combining spectroscopy with these kinematic measurements to gain unprecedented information about the coupled chemical and kinematic properties of the solar neighborhood in the Galactic context (Casagrande et al., 2011). The Gaia-ESO Survey with VLT/Flames will be particularly valuable with its spectroscopy of 100,000 stars in all stellar populations and will nicely complementing the measurements of Gaia (Gilmore et al., 2012).

Radial velocity standard stars of a wide range of stellar types provide useful Doppler calibrators for the many different instruments doing this kinematic work. The radial velocity standard stars provide touchstones of comparions for both zero-points and the velocity scales of the different instruments and observatories.

Despite these current and future uses of radial velocities, one might wonder whether highly precise, absolute radial velocities have value in the modern era. After all, it is relative velocities not absolute barycentric velocities that are used to discover orbiting exoplanets, measure orbits of binary stars, measure velocity dispersions in virialized systems of stars, and to measure masses of compact objects including supermassive black holes. Moreover accurate radial velocities could be obtained by using carefully chosen reference template spectra, either observed (of asteroids, for example) or synthetic. These arguments for the obsolescence of absolute velocities may have some validity for those specialists performing radial velocity measurements. But for the majority of astronomers there remains a widespread need to measure radial velocities as part of a larger project for which exhaustive calibration is not practical. Radial velocity standards offer a sound method at the telescope to place one’s Doppler measurements on a well established scale and to learn their accuracy by observing multiple standard stars with one’s particular (and sometimes peculiar) instrument. Further, new spectrometers on the ground or in space often come online with uncertain wavelength scales, structural and thermal instabilities, or errors that depend on stellar temperature, all of which can be mitigated by a real-time determination of the velocity zero-point and scale. Radial velocity standard stars offer that metric to establish and demonstrate accuracy and internal precision.

Some information about radial velocity standards is maintained by the International Astronomical Union (IAU), Commission 30 found at http://sb9.astro.ulb.ac.be/iauc30/. The IAU has constructed a precise definition of “radial velocity” described by Lindegren & Dravins (2003).

The old standard source of radial velocities was the General Catalog of Stellar Radial Velocities (BCRV) prepared at the Mount Wilson Observatory in Pasadena, California (Wilson, 1953). The modern era of radial velocity standards occurred with the work by the Geneva group led by Michel Mayor and Stephane Udry, the University of Victoria group led by Collin Scarfe and Robert McClure, and the group at the Harvard-Smithsonian Center for Astrophysics led by David Latham and Robert Stefanik (Mayor & Maurice, 1985; Scarfe et al., 1990; Latham et al., 1991, 2002). An excellent summary of the history of radial velocity standards through 1999 is provided by Stefanik et al. (1999).

Three excellent radial velocity programs provided standards with high accuracy and integrity (Stefanik et al., 1999; Udry et al., 1999a, b), all of them constituting a modern velocity zero-point with accuracy better than 0.3 km s. Additional excellent stellar radial velocity measurements were made by Nordström et al. (2004); Famaey et al. (2005) at accuracies of 0.3 km s, and also by the Fick Observatory at Iowa State University, and at the Mt. John University Observatory in Christchurch, New Zealand (Beavers & Eitter, 1986; Hearnshaw & Scarfe, 1999). The Pulkova Radial Velocity Catalog compiles the mean velocities for over 35000 Hipparcos stars (Gontcharov, 2006). The velocities come from over 200 publications, yielding a median accuracy of 0.7 km s.

The largest modern catalog of radial velocity standard stars was established by Nidever et al. (2002) who measured the radial velocities of 889 FGKM-type stars with an accuracy of 0.1 km sin the solar system barycentric frame. Nidever et al. (2002) made multiple radial velocity measurements with the Keck 1 telescope and High Resolution Echelle Spectrometer (Vogt et al. 1994) over a typical time span of 3-7 years, thereby revealing any velocity variability. Use of an iodine cell to impose a wavelength scale yielded relative radial velocities with a precision of 0.003 km s(RMS, with no zero-point) able to detect tiny velocity variability at the level of 0.01 km son time scales of years. Thus, the radial velocity standard stars in Nidever et al. (2002) met the highest standard for constancy in velocity. We adhere to that standard here.

Nidever et al. (2002) contained more stellar radial velocities at the highest viable accuracy of 0.1 km sthan any prevous radial velocity survey, and they provided statistically robust comparisons of the zero-points of other radial velocity surveys. The radial velocity measurements of Nidever et al. (2002) thus uphold high integrity for a wide range of spectral types and provide standard stars at all RA and northward of declination -30 deg.

Here we extend the work of Nidever et al. (2002) with 9 additional years of radial velocity measurements from the same Keck 1 telescope and spectrometer. These measurements supersede those in the Nidever et al. paper by providing more velocity measurements over a longer time baseline, and we include more stars. We include only those 2046 stars for which we obtained Keck-HIRES spectra using the modern CCD detector in HIRES that was installed in June 2004, as we use only the near-IR portion of the spectrum made available at that time. Thus some stars listed in Nidever et al. are not included here. We establish 131 standard stars, with radial velocities measured relative to the barycenter of the solar system for spectral types FGKM that are stable at the level of 0.01 km sduring a decade, and we provide barycentric velocities for 2046 FGKM stars. The final velocities have an precision of typically better than 0.1 km s, and they reside on the Nidever et al. velocity scale. We compare these velocities to extant velocities by other groups.

## 2. Spectroscopic Observations and Velocity Measurements

We obtained spectra using the HIRES echelle spectrometer on the 10-m Keck 1 telescope between 2004 August and 2011 January, as part of the California Planet Survey (CPS) to detect exoplanets by the Doppler technique, using iodine to calibrate both wavelength and the instrumental profile spectrometer at each wavelength (Marcy et al., 2008; Johnson et al., 2011). Before each observing night we positioned the CCD so that the (observatory-frame) wavelengths land on the same pixels within 1/2 pixel as on all previous observing nights. This produced a nearly identical wavelength scale on all nights. At the beginning and end of each observing night, we took spectra of a thorium-argon lamp, providing the linear and non-linear portion of the wavelength scale information, but not the zero-point of the wavelength scale which was instead established by absorption lines formed in the Earth’s atmosphere (see below). We found that the wavelength dispersion of HIRES varies by about 1 part in 2000 over the course of months and years, presumably due to slow mechanical and thermal changes in the spectrometer optics and to changes in air pressure. All 29000 spectra of the 2046 stars and all calibration spectra are available on the Keck Observatory Archive (after the nominal proprietary period of 18 months), made possible by a NASA-funded collaboration between the NASA Exoplanet Science Institute (NExSci) and the W. M. Keck Observatory12.

We employed an exposure meter to set exposure times for each observation, promoting uniform and high signal-to-noise spectra during the seven years of observations (Kibrick et al., 2006). The spectra had a typical S/N  150 per pixel at 720 nm, which is near the center of the near-IR wavelength domain, 654 - 800 nm, used in this paper. The spectral resolution was, R = 55,000 and the pixel spacing corresponds to a Doppler shift of 1.3 km s per pixel at the blaze wavelength of all spectral orders. The dispersion was found to vary by 10% along the free spectral range of each order. The spectrometer instrumental profile had a typical FWHM of 4.2 pixels, varying by 10-20% as a function of wavelength. In this current work, we used both types of spectra obtained as part of the CPS planet-search program, namely those with the iodine cell in front of the spectrometer slit for which the starlight passed through the molecular iodine gas  (Marcy & Butler, 1992) and those with the iodine cell not in the beam that contain no iodine lines. The presence of iodine cell has little effect on the Doppler measurements because the iodine lines are less than 1% deep in the near-IR wavelength regions used here.

We carefully determined a wavelength scale for each spectrum. We first fit a fifth-order polynomial to the positions of the thorium lines, with their associated wavelengths, to determine a first-approximation to the wavelength scale (called ”thid” files). We used a spline to map the spectra onto a logarithmic wavelength scale, based on the original wavelength scale from the thorium-argon spectra. The new array pixels were designed to be separated by equal intervals in delta . This logarithmic wavelength scale offers the advantage that a certain difference in radial velocity, , causes the spectrum to be displaced by the same distance in units of pixels at all wavelengths, given by . The typical pixel size for a Keck HIRES spectrum corresponds to a Doppler shift of 1.3 km s, and this thorium-based wavelength scale determined the relative wavelength scale to 6 significant digits ( 0.1 pixel), based on the scatter in the fits. The wavelength zero-point remained to be set accurately (using telluric lines, as described below). Instead of cross-correlation, we used the chi-square statistic to determine the relative shifts between a template spectrum and observed spectrum. To measure fractional pixel shifts, we oversampled, at 0.01 km sper pixel, a subarray around the minimum of each chi-squared function and interpolated with a spline function.

To determine a secure wavelength zero-point for each spectrum, we followed the suggestion of Griffin (1973) by using telluric lines to determine the wavelength scale. We used the telluric A and B absorption bands, at wavelengths of 759.4-762.1 nm  and 686.7-688.4 nm  respectively, due to absorption by molecular oxygen in the Earth’s atmosphere. We again used a minimization method to find the displacement of the telluric lines in the program star relative to those in the reference B-type star spectrum of HD 79439. Figure 1 shows the telluric lines in both that reference spectrum and in the representative spectrum of a program star, HD 182488. The program star spectrum has telluric lines clearly displaced by a fraction of a pixel (redward), in this case by +0.437 pixels, an amount representative of the typical shifts in wavelength zero-point from observation to observation over the time scale of days, months, and years covered by the spectra presented here. This measureable displacement of telluric lines provides the key correction to the wavelength zero-point that accounts for small changes (typically less than 1 km s) in the CCD position, the spectrometer optics, and (importantly) for the non-uniform illumination of the starlight on the entrance slit of the spectrometer.

This approach corrects for the dominant systematic errors that often compromise normal radial velocity measurements that do not use an absorbing gas to establish the wavelength scale of a slit-fed (rather than fiber-fed) spectrometer. We subtracted this displacement from the apparent shift of the stellar lines in order to find the net (true) Doppler shift. In this way we found the radial velocity determined by the Doppler shift of stellar absorption lines, including a correction for the shift in the wavelength zero-point. Using telluric lines to set the wavelength zero-point leaves systematic errors of 0.01 km scaused by typical winds in the Earth’s atmosphere. Also, the telluric lines we used (the A and B bands) are not distributed in wavelength coincident with the stellar lines we employed. An additional Doppler error may accrue due to unaccounted for nonlinear errors in the wavelength scale. We find such errors to be several tens of meters per second.

We chose four wavelength segments in the near-IR that are rich in stellar absorption lines in FGKM stars, but nearly free of telluric lines. Using a spectrum of the A5 star, HR 3662, we determined which regions of the spectra in the near-IR of HIRES spectra are largely unpolluted by telluric lines. The resulting four wavelength regions were 679.5-686.7 nm, 706.7-714.6 nm, 739.8-748.9 nm, and 751.8-759.3 nm. In these wavelength regions, we carried out Doppler measurements by using standard chi-square minimization as a function of Doppler shift between the spectra of the program star and template reference star. We averaged the velocities from the four wavelength segments of the spectrum, and we recorded that average value as the star’s radial velocity. We employed two template spectra. For the FGK stars, we used a spectrum of sun-light reflected off Vesta as a solar proxy. As Vesta is unresolved, its use ensured that the spectrometer optics were illuminated in nearly the same way as by the program stars. For M dwarfs we used a spectrum of HIP 80824 (spectral type M3.5). We applied a barycentric correction to the velocity for each spectrum in the frame of the solar system barycenter.

The resulting ”raw” radial velocities were systematically different from those of Nidever et al. (2002) by an arbitrary constant amount due to the radial velocity and barycentric correction of the template spectrum. We calculated this constant by taking a sample of 110 standard FGKM stars in Nidever et al. (2002) and comparing those velocities to our measured raw velocities for those stars. We determined the average difference between our raw velocities and those of Nidever et al. (2002), constituting the constant to be applied to all of our velocity measurements. This automatically forces our radial velocities to have the same zero-point as those of Nidever et al. (2002).

Thus our velocity measurements reside on the scale of Nidever et al. (2002) by construction. These radial velocities of stars are measured relative to a hypothetical inertial frame located at the barycenter of the Solar System. This transformation is accomplished by using the JPL ephemeris of the Solar System to determine the velocity vector of the Keck 1 telescope at the instant of the photon-weighted midpoint of the exposure of the spectrum (accurate to within a few seconds). Our transformation to the barycentric frame is performed using the JPL ephemeris13, accessed and interpreted with utilities from the IDL Astronomy User’s Library14 and custom driver codes written by the California Planet Survey. We carried out extensive tests of our barycentric transformation code, finding discrepancies of 0.1 m sin comparison with TEMPO 1.1 which is similar to that of TEMPO 2 (Edwards et al., 2006). Errors of that magnitude, 10 km s, are negligible compared to other sources of error in this present work.

As usual for such transformations to the Solar System barycenter, we do not include the effects of the solar gravitational potential at that location (near the surface of the Sun) that would cause a (meaningless) gravitational blueshift. Similarly, we do not account for the gravitational blueshift caused by starlight falling into the potential well of the Sun at the location of the Earth, a 3 m seffect. We also do not take into account the gravitational redshift as light departs the photosphere of the star, an effect of hundreds of m sthat depends on stellar mass and radius.

We further ignore the convective blueshift of the starlight caused by the Doppler asymmetry between the upwelling hot gas and the downflowing cool gas. Convective blueshift depends on spectral type (Dravins, 1999), and we do not include any theoretical estimates of this photospheric hydrodynamic effect here. Both gravitational redshift and convective blueshift amount to a few tenths of a kilometer per second, and while they are opposite in sign they may not cancel each other. However see Section 4 for a quantitative discussion of these two effects, that appear to largely cancel each other. We note that several efforts have been successful at measuring the convective blueshift in a few stars, especially for the Sun and the alpha Centauri system (Ramírez et al., 2010; Dravins, 2008; Nordlund, 2008; Pourbaix et al., 2002).

### 2.1. Radial Velocity Standard Stars

We identified standard stars from among the 2046 total sample of stars based on several criteria. We examined the iodine-based relative velocities, having a precision of 3 m s, for each of the 2046 stars. We established a severe criterion of stability during 10 years in order for a star to be qualified as a ”radial velocity standard star”. All standard stars must exhibit an RMS of their iodine-based relative velocities under 0.03 km s(Marcy & Butler, 1992) and a duration of such velocity measurements of at least 10 years. Figure 2 displays the iodine-based relative velocities for three representative standard stars. The absolute radial velocity relative to the Solar System sets the zero-point and the relative velocities come from the iodine-based Doppler measurements. The velocities of the three representative cases exhibit an RMS of under 0.010 km s(10 m s) and span over 10 years, typical of the standard stars, promoting their integrity as standard stars at the more relaxed level of 0.1 km s.

Thus, our radial velocity standard stars must demonstrate constant velocity during a decade within a tolerance of 30 m sRMS during that time. We required that at least 3 spectra be obtained over a 10 year time period to demonstrate the decade-long stability. We identified 131 standard stars based on these criteria. Among them, only 12 exhibit an RMS scatter in their iodine-based RVs of more than 0.01 km s, and none over 0.03 km s, during 10 years of observations. Thus, the 131 standard stars all exhibit radial velocity stability during a decade at the level of 0.03 km s.

The barycentric radial velocities for the 131 standard stars are reported in Tables 1 and 2. In Table 1, primary and alternate star names are given in the first three columns, and the spectral type is given in column 4. Columns 5, 6, and 7 give the Julian dates of the first and last observations, and the duration of observations in years. Column 8 lists the radial velocity of the star relative to the solar system barycenter given by Nidever et al. (2002). Column 9 lists the unweighted average of all radial velocity measurements from this current work. In the next two columns we list the standard deviation of the multiple velocities we measured here for the star and the number of spectra used. We report the final velocity for each standard star as the average of the Nidever et al. (2002) and present velocities. We consider this final radial velocity to be robust as both sets of velocities have high integrity and we do not rank one set significantly higher in integrity than the other. Importantly, the Nidever et al. velocities and these new velocities were determined using completely different Doppler algorithms and different wavelength regions. Thus the Nidever and present radial velocities offer considerable resistance to unexpected errors associated with any particular method or wavelength. The Nidever et al. velocities had a wavelength scale rooted in the iodine lines and measured using the 500-600 nm wavelength region, quite different from the wavelength scale here rooted in telluric lines at 670 and 760 nm and measured using the near IR spectrum.

The radial velocity uncertainty recorded in Tables 1 and 2 is the largest of three values: the difference between our present velocity and Nidever’s, the uncertainty in the mean, or 0.03 km s, which we deemed our base accuracy, to prevent artificially low uncertainties. Table 2 lists the same standard stars, but in a format more suitable for observing. We give the primary name, position in RA and DEC, magnitude, spectral type, final absolute radial velocity, and uncertainty.

Establishing and maintaining a single, well-defined velocity scale, including zero-point accuracy and precision, is important to make the radial velocities more useful. The velocity scale must be compared to other well–known scales. In particular, our velocities are compared here to those from Geneva, Harvard-Smithsonian, and the California Planet Survey15.

We compared our ”present” velocities to those of the standard stars of Udry et al. (1999a). The average of the differences (i.e. zero–point difference) is:

 =+0.063 km s−1.

Thus there is a statistically significant difference in the zero-points. That this difference is less than 0.1 km soffers some scale to the integrity of the discrepancies in the two systems of radial velocities. The RMS of the differences is 0.072 km s(RMS) for the 30 standard stars in common, as shown in Figure 3. Thus the two sets of velocities agree within 0.1 km sin zero point and scatter. However, the differences in the velocities appear to be correlated with stellar B-V color, suggesting a systematic error. Inspection of Figure 3 shows that it is the M dwarfs, with B-V 0.9 where the systematic difference resides of (present - Udry) = +0.10 km s. Thus, while the FGK stars of Udry et al. and the present set have different velocity zero-points by 0.063 km s, the M dwarfs differ by 0.10 km s.

We also compared our velocities to those of Stefanik et al. (1999). Considering the 25 standard stars in common, as seen in Figure 4, the average of the differences is:

 (Vpresent−VStefanik)=+0.15 km s−1.

The differences in the 25 velocities have a scatter of 0.13 km s(RMS). Thus the present velocities differ in zero-point from those of Stefanik et al. (1999) by a statistically significant amount (see Section 4 for the explanation).

A useful compilation of velocities was provided by Crifo et al. (2010) based on various past surveys. They show that the velocities from Nidever et al. (2002) are valuable because of the accuracy ( 0.1 km s), the large number of observations, and the long duration of the velocity time series. They compare the Nidever et al. velocities to those from past CORAVEL measurements that have typical accuracy of 0.3 km s, finding good agreement within errors. They offer a preliminary list of standard stars drawn heavily from Nidever et al. (2002). Thus the zero-point and scale of the velocities in Crifo et al. naturally agree with those here.

We also compare our measurements of M dwarfs to those of Marcy et al. (1987). We find that the velocity differences scatter by 0.26 km s(RMS) and our zero–points are different by

 =0.007 km s−1

for the 17 stars in common (see Figure 5). As the velocities from Marcy et al. (1987) are expected to carry precision of only 0.2 km s, this scatter of 0.26 km sRMS is consistent with most of the error residing in Marcy et al. (1987) and only 0.1 km sresiding in the errors in the present velocities of M dwarfs.

The differences in the velocities between those of Nidever et al. (2002) and those of both Udry et al. (1999a) and Stefanik et al. (1999) exhibted a scatter of less than 0.1 km s(RMS), and our present velocities differ from those previous standard measurements within a margin of 0.1 km s(RMS). Thus, the velocities reported here agree with the best established standard stars to within 0.1 km sin precision, with modest zero-point differences of comparable magnitude.

We show in section 2.3, that the radial velocities measured here for 428 stars in common with Nidever et al. (2002) agree within 0.13 km s(RMS) and that there is little dependence on the color of the stars. This comparison of 428 stars offers further weight to the suggestion that the standard stars in Tables 1 and 2 have integrity at the level of 0.1 km s. We also show in Section 4 that the zero-point of the velocity scale has integrity at the level of 0.1 km s.

### 2.2. Uncertainty in the Velocities of Standard Stars

We compute the uncertainty of the radial velocity for each of the 131 standard stars by considering two separate estimates of the uncertainty. The first estimate is the uncertainty of the mean velocity measurement, defined as , where is the standard deviation of the ensemble of velocities for a particular star. This estimate offers a measure of the internal uncertainty revealed by the scatter in the individual velocity measurements. As a second estimate of uncertainty we compute the difference between the radial velocity measured here and the radial velocity published in Nidever et al. (2002). This difference in radial velocities offers a measure of agreement in the two radial velocity measurements despite two different methods used to compute them and two different sets of spectra used to measure them in the two papers. The largest of these two uncertainty estimates, but not less than 0.030 km s, is listed in Tables 1 and 2 as the final estimate of the 1-sigma uncertainty for the radial velocity of each standard star. We adopted this floor 0.030 km sfor the stated uncertainty because this was the uncertainty of the velocities given in Nidever et al. (2002). Any fortuitous agreement between the current velocities and those in Nidever et al. that happens to be smaller than 0.030 km scould well be spurious. This adopted floor at 0.030 km sprevents our quoted measurement uncertainty from dropping lower than the level below which we have no useful comparison with the Nidever et al. velocities.

To broaden the scope of this uncertainy assessment for the standard stars, we compared the measured radial velocities here to those in common with Nidever et al. (2002) among the full set of 2046 stars, not just the standard stars. We display the difference between our present radial velocities and those of Nidever et al. (2002) in Figure 6 for FGK stars and Figure 7 for the M dwarfs. For the 428 FGK stars in common, the differences have an RMS of 0.13 km s. Thus the combined errors in the present work and in Nidever et al. amount to 0.13 km sfor the FGK stars, as described in more detail in Section 2.3. For the 52 M dwarfs in common, the differences exhibit an RMS of 0.13 km s(with three outliers near 0.4 km s) indicating the level of combined errors among M dwarfs in the two studies. The errors in the final velocities for the standard stars will be smaller than quoted above for the entire set of 2046 stars because the standards typically have more observations and have constant radial velocities by their selection.

### 2.3. Radial Velocities of 2046 Stars

Table 3 reports the radial velocities of all 2046 stars (including the standards) relative to the solar system barycenter. The same technique that was used to determine the radial velocities of the standard stars was used to determine the radial velocities for all 2046 stars. In Table 3, the primary star name is given in column 1, and the template type in column 2. The symbol ”V” represents the Vesta spectrum (solar), and ”M” represents the constructed M-dwarf template described above. The 3rd column gives the unweighted mean of the Julian Dates of our observations, and the 4th column gives the number of days between the first and last observation. For each star, we compute the unweighted average of all radial velocity measurements from all spectra we obtained for that star. The 5th column gives that average radial velocity for the star, measured in the frame of the barycenter of the solar system. The 6th column gives the number of radial velocity observations, and the 7th column gives the standard deviation of all radial velocity measurements of that star, a measure of both the uncertainty and of the intrinsic variation of the radial velocities.

Examination of Table 3 shows that among the 2046 stars with measured radial velocities, some stars have only one or two velocity measurements while others have over 30 measurements. The time span between the first and last spectrum is typically over a year, and often many years. The standard deviation of the velocities given in the last column is a measure of the combined errors and acceleration of the star during the time span of observations. The median standard deviation is 0.12 km s, representing the uncertainty of our individual velocity measurements, but increased slightly by the actual velocity variations of the stars.

One measure of the 1-sigma errors of the radial velocities in Table 3 is given by the uncertainty in the mean, namely, . However, because of systematic errors caused by convection of 0.1 km sdescribed in Section 4, we prefer to avoid stating the formal uncertainties that could be misinterpreted as useful uncertainties. Also, some stars exhibit intrinsic velocity variation caused by unseen orbiting companions, thus artifically augmenting the formal uncertainty in the mean.

Nonetheless, examination of in the last column of Table 3 shows scatter of typically 0.15 km sfor individual velocity measurements, serving as an upper limit to the typical errors. Thus any values of in Table 3 greater than 0.45 km s(3 sigma) are likely “real”, i.e. indicating actual changes in the radial velocity of that star by an amount given by that standard deviation on a time scale constrained by the time span of the observations.

We have compared the present velocities to those of Nidever et al. (2002). Nidever et al. used the iodine lines and the visible portion of the spectrum to measure Doppler shifts, a method quite independent of that used here. Thus a comparison of the two sets of the velocities for stars in common offers a method of identifying random and systematic errors that stem from the Doppler methods themselves. Figure 6 shows the difference between the present velocities and those of Nidever et al. (2002) as a function of stellar color, B-V, for all 428 stars in common classified as F, G, or K spectral type. The plot shows that the differences in the velocities are typically less than 0.2 km s, with an RMS of the differences of 0.13 km s, and there is no evidence of a dependence on stellar color. (We removed HD 217165 from the RMS calculation, which is a binary star.) This suggests that the accuracy and zero-points of the present and Nidever et al. velocities are similar within 0.13 km s(RMS).

However, Figure 6 reveals six stars (with one off scale) for which the difference between present and Nidever et al. velocities are over 0.5 km s(3 sigma differences). These stars are HD 87359 (+0.81 km s), HD 114174 (+0.58 km s), HD 180684 (+0.61 km s), HD 196201 (+0.65 km s), HD 91204 (-0.74 km s), and HD217165 (-2.2 km s). Examination of the iodine-based relative velocities (precise to 0.002 km sRMS) for these six stars reveals all of them to exhibit long-term trends of velocity of over 0.5 km s. These are certainly long period binary stars. The difference between the present velocities and those of Nidever et al. (2002) is simply due to the orbital motion that has occurred since the spectra were taken for the work of Nidever et al. (prior to 2002) and those here that were taken after 2004 June. Thus, the present velocities offer a sieve for binary stars,

Figure 7 shows a similar comparison of present velocities and those of Nidever et al. (2002) for the 52 M dwarfs in common. The RMS of the differences of 0.13 km sindicates larger errors for the M dwarfs than for the FGK-type stars. This error is reminiscent of that seen in Figure 4 for which the difference between the present velocities and those of Udry et al. (1999a) among the M dwarfs was 0.15 km s. These metrics suggests that the M dwarf velocities in general, from all surveys, remain uncertain at the level of 0.2 km s(RMS) and harbor uncertain zero points at the level of 0.15 km s.

Figure 8 shows the location of the stars in equatorial coordinates in a Mollweide projection on the sky. The broad distribution at all RA, and northward of DEC = -50 offers a set of secondary standard stars. The dots are color-coded with blue representing stars approaching and red representing stars receding from the barycenter of the solar system. The size of the dots is proportional to the square root of the absolute value of the radial velocity, an arbitrary functional form for ease in display. The solar apex is shown as a cross, the direction of the motion of the sun relative to the G dwarfs in the solar neighborhood (Abad et al., 2003). Analysis of such all-sky measurements of Doppler shifts can, in principle and after removal of the solar apex motion, reveal effects from gravitational redshift including tests of general relativity (Hentschel, 1994).

Those stars exhibiting a standard deviation of their measured velocities less than 0.1 km sas listed in Table 3 (last column) and having a time span of observations over a few years constitute secondary standard stars. Their lack of radial velocity variation above 0.1 km sduring several years indicates a constant velocity suitable for many purposes. In contrast, the standard stars listed in Tables 1 and 2 met a higher standard of constant radial velocity within 0.1 km sduring a time span of a full 10 years and all of them also exhibted precise radial velocities (using iodine as wavelength reference) constant to within 0.025 km s, thereby ensuring their integrity as standard stars.

## 3. Binary Stars

We compared our radial velocities with those previously published, noting a subset of stars that show differences of over 2 km s, indicating likely binary stars. We made great use of the Pulkovo Catalog of Radial Velocities (Gontcharov, 2006). The Pulkovo catalog gives the weighted mean absolute velocities for over 35000 Hipparcos stars drawn from over 200 publications. Despite the inhomogeneous sources, the median accuracy of the final radial velocities in the Pulkovo Catalog is 0.7 km s, adequate to identify binaries in comparison with the absolute velocities presented here. The times of observations from the Pulkovo Catalog were typically 10-30 years ago, offering a time difference of typically over 10 years between those measurements and the radial velocities presented here. Thus, binary stars with periods over a decade can be identified. Thanks are due to Charles Francis and Erik Anderson for their critical evaluation of the velocities in this work compared to those in the Pulkovo Catalog of Radial Velocities.

Among the 2046 stars reported here in Table 3, we identified those having a difference between the present velocities and those in the Pulkovo Catalog of more the 3 , i.e. 2 km s. Velocity differences of over 2 km soffer a sign, but not convincing evidence, of long term binary motion with orbital periods over a year. For binaries with periods of between a year and several decades, the velocity variation will be many km son time scales of a decade, allowing some of them to be detected.

Table 4 gives a list of the stars showing differences of over 2 km sbetween the present and Pulkovo velocities, indicating a possible binary. The first and second columns give the HD and Hipparcos identities of the star. The third column gives the radial velocity from the present work, and the fourth column give the radial velocity from the Pulkovo Catalog (Gontcharov, 2006). For each of the stars in Table 4, we examined the relative, precise iodine-based radial velocities (precision of 2 m s) to detect any obvious velocity variations. Indeed, for many of the stars in Table 4, the precise, iodine-based RVs reveal large velocity variations of over 1 km s, confirming the binary nature. For them, we note the measured time derivative of the variation of precise radial velocities (”PRV var”) in the last column of Table 4 under ”Comments”. For the remaining stars in Table 4, we do not have precise relative RVs, and must rely on the difference between the present and Pulkovo velocities as the indicator of a binary star. Certainly a few of these entries may be false binaries, due to unavoidable errors in the Pulkovo compilation. But we suspect that the vast majority of the stars in Table 4 are actual binaries, and we are alerting the community to this likelihood. In addition, we discovered several double-line spectroscopic binaries among our target stars, so indicated in the Comments in Table 4.

## 4. Velocity Zero Point

The present velocities share, by construction, the zero-point of the velocity scale with that of Nidever et al. (2002). The Nidever zero-point in velocity was determined by using spectra of both the day sky and of the asteroid, Vesta, yielding a zero-point accurate to within 0.01 km sfor G2V stars. The present velocities have a similarly accurate zero-point for G2V stars.

However one must consider the effects of general relativistic gravitational redshifts upon departure of the light from the star (but we do include the general relativistic blueshift caused by entry of light into the potential wells of the solar system, an effect of only 0.003 km s). One must also consider the “convective blueshift” caused by the hydrodynamic effects in the photospheres of FGKM stars (Dravins, 2008). We emphasize that our present velocities were constructed to have the correct velocity for the Sun and Vesta, thus automatically accounting for gravitational redshift and convective blueshift for G2V stars. Here we estimate these two effects on the velocity zero-point as a function of stellar mass along the main sequence.

The gravitational redshift of light upon departure from stars is = 0.635() where K is given in km sand M and R are the stellar mass and radius given in solar units. As is nearly proportional to along the main sequence, the gravitational redshift varies little among the main sequence stars, and remains 0.6 km sfor FGKM stars.

But the convective velocities decrease substantially for the lower mass stars that have lower luminosities, requiring lower convective velocities to carry the energy. Scaling the convective energy transport with stellar mass suggests that convective velocities will vary linearly with stellar mass. Indeed, the RV “jitter” decreases from 2 m sfor G dwarfs to less than 1 m sfor M dwarfs, in part caused by the decrease in sub-photospheric convective hydrodynamics, not necessarily due to spots. We note that convective blueshift depends on the technique used to measure radial velocity because it stems from a net displacement and distortion of the absorption line profiles. These displacements and shapes of the lines arise from the integrated velocity field with depth in the photosphere, implying that each radial velocity technique with its particular set of absorption lines will sample a different portion of that velocity field. Given this physical situation, it is noteworthy that the present velocities and those of Nidever et al. (2002) show negligible discrepancies as they sample the near-IR and green/optical portions of the spectrum, respectively.

One may anticipate that M dwarfs of 0.5 solar masses will suffer a convective blueshift that is only half that of solar type stars, and hence half that necessary to cancel the gravitational redshift. This suggests that the radial velocities of M dwarfs presented here may suffer from a net surplus of gravitational redshift compared to convective blueshift of 0.3 km s.

To quantify this imbalance of convective blueshift against gravitational redshift, Nidever et al. (2002) draw from hydrodynamic models of stellar atmospheres of Dravins (1999) to estimate the resulting systematic errors. Based on them and on computed gravitational redshifts, we estimate that our present radial velocities are too low by 0.56 km sfor F5V stars. For those stars convective blueshift causes a greater blueshift than the gravitational redshift. For G2V stars, our present radial velocities have a zero-point accurate to within 0.01 km s, by construction (using the Sun and Vesta). For K0V and M0V stars, our present velocities are probably too high by 0.15 and 0.30 km s, respectively.

We caution that the asymmetries in absorption lines leading to convective blueshift vary from line to line depending on the velocity fields at their depth of formation, with variations of 0.1 km/s. The asymmetries also vary with time during a magnetic cycle as the surface fields influence the convective flow patterns. Moreover, the convective blueshift will be a function of spectral resolution and of the algorithm used to measure it, i.e. cross-correlation or other, that implicity apply weights along the line profile.

Thus, to obtain kinematically robust measures of radial velocity, d/d, we recommend applying the corrections listed above, to the velocities in Tables 1, 2, and 3, i.e. adding 0.56 km sto our velocities of F5V stars, zero for G2V, subtracting 0.15 km sfor K0V, and subtracting 0.3 km sfor M0V. A useful linear relation that approximately represents the correction (in km s) to be applied is:

 VCorr=1.3×10−4(Teff−5780K)

This correction to our radial velocities is pinned to the zero-point established by the spectra of the Sun and asteroids, and applies only to main sequence stars.

We check the velocity zero-point assessment described above, as follows. A careful assessment of gravitational redshifts is provided by Pasquini et al. (2011). They compared the radial velocities of main sequence stars and giants within the open cluster, M67, expecting to find a larger gravitational redshift from the main sequence stars due to their smaller radii. Remarkably, their radial velocities of main sequence stars and giants showed no difference in systemtic velocities of the two stellar populations. Pasquini et al. (2011) find an upper limit of 0.1 km sin the net difference in the systemic radial velocities between main sequence stars and giants. This lack of RV difference indicates that the spectral lines in main sequence stars are sufficiently blueshifted, compared to those in giant stars (that suffer only a small gravitational redshift due to their large radii), such that the gravitational redshift and convective blueshift nearly cancel each other in FGK main sequence stars, at the level of 0.1 km s. This cancellation provides some assurance that our velocity zero-point, which is forced to be zero for G2V stars, is not highly sensitive to changes in convective blueshift along the main sequence.

We further check our velocity zero-point by comparison with Center for Astrophysics (CfA) radial velocity results that targeted asteroids having known ephemerides to establish the instantaneous velocity vectors relative to the observatory (Latham et al., 2002). This effort is similar to that employed by Nidever et al. (2002) who used Vesta to set their zero-point. The CfA group finds that their native radial velocities require a correction of +0.139 km sto achieve agreement with the actual dynamical orbital velocities of the asteroids (Latham et al., 2002).

This asteroid-derived correction of +0.139 km sto the CfA radial velocities may be combined with the measured zero-point difference between the present radial velocities and those from the CfA. In Section 2.1 we noted that the velocities of the present standard stars differed from those of the CfA (Stefanik et al., 1999), with a zero–point difference: = +0.15 km s. But the CfA radial velocities should be corrected by +0.139 based on their asteroid reference. Doing so reduces the difference between the present and (corrected) CfA velocity zero point to 0.15-0.139 km s= 0.011 km s. Thus, the radial velocities presented here differ from the dynamically derived velocity zero-point at the CfA by only 0.011 km s.

The lines of evidence presented in this section indicate that the radial velocities presented here are accurate measures of the time rate of change of the distance of the star from the solar system barycenter for solar type stars. In summary, our velocity zero-point was pinned to Nidever et al. (2002) that stemmed from spectra of the Sun and Vesta. Pasquini et al. (2011) show that gravitational redshift and convective blueshift nearly cancel for main sequence FGK stars. The asteroid measurements at the CfA (Latham et al., 2002) yield a zero-point of the velocity scale that agrees with that here, within 0.01 km s. Thus, the present velocities represent the actual time rate of change of distance, d/d, of the solar-type stars. For other spectral types, corrections to velocities should be applied for convective blueshift, as noted above. We caution that even after applying such corrections, the present radial velocities may carry systematic errors of 0.1 km sor more, especially for spectral types far from G2V.

## 5. Discussion

We have provided barycentric radial velocities with an internal precision of 0.1 km sfor 2046 stars, of which 131 are standards. The error estimates come from both the internal errors found from our measurements and from the comparison with the standard velocities of Nidever et al. (2002), Stefanik et al. (1999) and Udry et al. (1999a). Our absolute radial velocities were constructed to share the velocity zero–point defined by Nidever et al. (2002) and apparently the resulting velocity scale differs by only 0.063 km sfrom that of Udry et al. (1999a), by 0.15 km sfrom that of Stefanik et al. (1999), and 0.007 km sfrom that of Marcy et al. (1987), which adds confidence to the zero points of all four sets of velocities.

The 1-sigma errors of the radial velocities in Table 3 are 0.12 km s. Any stars exhibiting a scatter among their individual velocity measurements, listed as in the last column of Table 3, that is greater than 0.36 km srepresents a 3-sigma departure from a constant velocity. Such scatter likely indicates physical changes in the radial velocity of that star by an amount given by that standard deviation and occurring on a time scale constrained by (shorter than) the time span of the observations. In such cases of velocity variability, the individual radial velocities and their times of observation offer information about the coherence, if any, and the time scale of the acceleration of the star. Certainly long term trends and periodicities in the radial velocities offer information on the cause of the velocity variation and on the orbital or physical behavior.

Such accelerations are likely caused by gravitational forces within a multiple star system. Other possible causes are gravitational forces exerted by orbiting giant planets, passing stars including compact objects, structural pulsations in the star itself, rapid rotation coupled with surface inhomogeneities such as starspots, Rossiter McLaughlin effect from orbiting objects, or stochastic surface velocities from magnetic events such as flares.

The precise barycentric radial velocities presented here may serve as useful reference measurements for calibrations of other spectroscopic programs. They may be used to construct velocity metrics for studies of the kinematics of the Galaxy or of other galaxies. We intended for these velocities to be useful to surveys of Galactic kinematics and dynamics such as Gaia, SDSS, RAVE, APOGEE, SkyMapper, HERMES, and LSST. They may assist in Doppler searches for long-period binary stars. Indeed, these velocities will help identify long period orbiting or passing companions to the 2046 stars themselves, most of which reside within 100 pc thus making them interesting targets for future high contrast imaging.

We are indebted to the University of California and NASA for allocation of telescope time on the Keck telescope. We thank Charles Francis and Erik Anderson for a critical review of the velocities compared to past measurements. We thank Guillermo (Willie) Torres and Dimitri Pourbaix for valuable suggestions that improved the manuscript. This work benefited from valuable discussions about radial velocity standard stars with Dave Latham, Stephane Udry, and Dainis Dravins. We are grateful to UCLA for hospitality during the writing of some of the paper. This work made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at www.exoplanets.org. All 29000 spectra are archived and publicly available, thanks to the Keck Observatory Archive made possible by a NASA-funded collaboration between the NASA Exoplanet Science Institute and the W. M. Keck Observatory. We acknowledge support by NASA grants NAG5-8299, NNX11AK04A, NSF grants AST95-20443 (to GWM) and AST-1109727 (to JTW), and by Sun Microsystems. This research was made possible by the generous support from the Watson and Marilyn Albert SETI Chair fund (to GWM) and by generous donations from Howard and Astrid Preston. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. This research has made use of NASA’s Astrophysics Data System and the SIMBAD database, operated at CDS, Strasbourg, France. We thank R.Paul Butler and Steven Vogt for help making observations. We thank the staff of the W.M Keck Observatory and Lick Observatory for their valuable work maintaining and improving the telescopes and instruments, without which the observations would not be possible. We appreciate the State of California for its support of operations at both observatories. We thank the University of California, Caltech, the W.M. Keck Foundation, and NASA for support that made the Keck Observatory possible. We appreciate the indigenous Hawaiian people for the use of their sacred mountain, Mauna Kea.