THE SOLAR NEIGHBORHOOD. XXIV. PARALLAX RESULTS FROM THE CTIOPI 0.9 m PROGRAM: STARS WITH μ ⩾ 10 yr⁻¹ (MOTION SAMPLE) AND SUBDWARFS

The CTIO 0.9 m telescope has a 2048 × 2048 Tektronix CCD camera with 0401 pixel⁻¹ plate scale (Jao et al. 2003). For both astrometric and photometric observations, we use the center quarter of the chip, yielding a 68 square field of view. Parallax frames are taken through one of four filters, V_J(old), V_J(new), R_KC, or I_KC⁵ (hereafter without the subscripts), so that either science or reference stars have maximum peak counts of ∼50,000 (saturation occurs at 65,535 counts) for better centroiding. The magnitudes of CTIOPI targets are 9 ⩽ VRI ⩽ 19. Depending on the brightness of the science targets, reference stars, and sky conditions, exposure times vary from 20 to 1200 s. With few exceptions, observations are made within ±30 minutes of a science target's transit to minimize the corrections required for differential color refraction. Typically, three to ten frames are taken in each night, depending primarily on the exposure time required. Bias and dome flat frames are taken nightly to enable routine calibration of the science images.

One "event" during the CTIOPI effort warrants special attention here. We have used two V filters, dubbed the "old" Tek#2 V filter (λ_central = 5438 Å, Δλ = 1026 Å) and "new" Tek#1 V filter (λ_central = 5475 Å, Δλ = 1000 Å), during the 11 years of observations because the "old" filter cracked in 2005 February. The "new" V filter was used between 2005 and 2009. In 2009 July, the old V filter was reinstated for use after confirming that the crack in the corner did not significantly affect astrometric residuals. We have found that as long as at least 1–2 years of data (depending on observing frequency) have been taken in both filters, the data can be combined to determine a reliable π_trig (Subasavage et al. 2009). In total, 10 of the 37 systems discussed in this paper were observed astrometrically in the V filter. Further details about the filters and their effects on the astrometry can be found in Subasavage et al. (2009) and Riedel et al. (2010).

The stellar paths traced by science stars on the sky are combinations of proper motions and parallactic shifts. Jao et al. (2005) and Henry et al. (2006) include extensive discussions of the data reduction processes used to separate these two movements. Briefly, we (1) use SExtractor (Bertin & Arnouts 1996) to measure centroids, (2) define a six-constant plate model to find plate constants (given in Equation (4) of Jao et al. 2005), (3) assume that ensembles of reference stars have zero mean parallax and proper motion, (4) solve least-square equations for multi-epoch images (given in Equation (5) of Jao et al. 2005), and (5) convert from relative parallax to absolute parallax by estimating the distance of the reference stars photometrically. The correction from relative to absolute parallax is accomplished using photometric distance estimates by comparing VRI colors to M_V for single, main-sequence, stars in the RECONS 10 pc sample (Henry et al. 1997, 2004). For each reference star, a distance is estimated, and the correction to absolute parallax is then computed using the weighted mean distance of the entire reference field. The error on the correction is determined using Equation (6) in Jao et al. (2005).

We have obtained VRI photometry of these targets at the CTIO 0.9 m telescope using the same instrumental setup used for the astrometry frames. Similar to those astrometry observations, bias and dome flat frames are taken nightly for basic image reduction. Most science stars were observed at sec z < 1.8 or less (a few were observed between 1.8 and 2.0 airmasses because of extreme northern or southern declinations). Various exposure times were used to reach a signal-to-noise ratio (S/N) > 100 for science stars in each of the VRI filters. Combinations of fields that provided 10 or more standard stars from Landolt (1992) and/or E-regions from Graham (1982) were observed several times each night to derive transformation equations and extinction curves. Further details of photometric data reduction, the definition of transformation equations, errors, etc., can be found in Jao et al. (2005) and Winters et al. (2011).

Spectroscopic observations were made using the CTIO 1.5 m with the R-C spectrograph and Loral 1200 × 800 CCD camera. Grating no. 32 was used in first order with a tilt of 151, and observations were made using a 2'' slit. The order-blocking filter OG570 was utilized to provide spectra covering the range of 6000–9500 Å with a resolution of 8.6 Å . Bias frames, dome flats, and sky flats were taken at the beginning of each night for calibration.

At least two exposures were taken for each object to permit cosmic ray rejection, with additional exposures taken if stars were particularly faint. A 10 s Ne+He+Ar or Ne only arc lamp spectrum was recorded after each target to permit wavelength calibration. Several spectroscopic flux standard stars found in the IRAF spectroscopy reduction packages were observed during each observing run, usually nightly. Reductions were carried out using IRAF reduction packages—in particular onedspec.dispcor for wavelength calibrations and onedspec.calibrate for flux calibrations. We use the same set of spectral standard dwarfs discussed in Jao et al. (2008) to assign spectral types for dwarfs and follow the same method discussed in that paper to assign spectral types for subdwarfs.

In addition to the VRI photometry, we take advantage of our long-term observations of these fields (up to 10 years) in the parallax filter (Column 7 in Table 2) to analyze the photometric variability (Column 8 in Table 2) of these parallax targets. The total number of nights used for the variability study for each star is given in Column 9 of Table 2.

Here we examine 130 red dwarfs for evidence of variability, as measured by the standard deviations, σ_mag, of magnitudes derived relative to reference stars in the fields. Combining the 41 stars in this paper with stars in Henry et al. (2006) and Riedel et al. (2010), two previous papers with similar data streams, yields a total of 135 stars. We exclude five stars from the study, as follows. GJ 1207, with σ_mag= 0.263 (Henry et al. 2006), was observed during an obvious flare in a single series of observations. LP 771−095BC, with σ_mag= 0.043 (Henry et al. 2006), exhibited a sudden ∼0.3 mag drop in brightness at V on UT 1999 August 21, but LP 771−095A, the primary star, and none of the reference stars showed this event (one possible cause is an eclipse). LHS 193B, with σ_mag= 0.049 (this work), is a white dwarf that was underexposed in all frames because the primary, LHS 193A, was the star targeted for parallax. Similarly, LHS 2734A was the parallax target, so LHS 2734B with σ_mag= 0.020 (this work) was systematically underexposed and has been omitted from the analysis. Finally, as discussed below in Section 5.2, the photometry for LHS 272 with σ_mag= 0.015 (this work) was corrupted by a background galaxy.

To evaluate variability, we first extracted the instrumental magnitudes using SExtractor with a fixed 6'' diameter aperture. Because most parallax frames were taken on nights when photometric standard stars were not observed, we do not convert instrumental magnitudes to apparent magnitudes; we instead compare the relative fluxes of the target stars to the reference stars used to set the astrometric grid. We follow the methodology discussed in Honeycutt (1992) to handle an inhomogeneous set of exposures. The basic equation of condition used to evaluate inhomogeneous sets of exposures is

$$\begin{equation} m_{i}^{j}=m0_{i}+\delta m^{j}, \end{equation} \tag{ 1 }$$

where m^j_i is the instrumental magnitude of star i on image j (magnitude output from SExtractor), m0_i is the mean instrumental magnitude of star i, and δm^j is the magnitude offset for image j. In other words, δm^j takes into account the differences caused by sky conditions, extinction, and exposure times for each frame in the series. We then utilize a Gaussfit program (Jefferys et al. 1987) to perform least-square calculations to minimize the deviations between the two sides of this equation of condition, as described in more detail in Honeycutt (1992).

After obtaining δm^j, the "corrected" instrumental magnitude (mc^j_i) is

$$\begin{equation} mc_{i}^{j}=m_{i}^{j}-\delta m^{j}. \end{equation} \tag{ 2 }$$

We then calculate the σ_mag values of the corrected instrumental magnitudes, mc^j_i, in a given filter for all science and parallax reference stars in that field. An example output is shown in the top panel of Figure 3. Naturally, the standard deviation is a function of magnitude, where fainter stars have larger standard deviations. In Column 8 of Table 2, we list the standard deviations in magnitudes for the science stars. A high standard deviation value for a science or reference star can be caused by (1) a flare occurring during a series of observations on one night, (2) long-term variability, (3) contaminated photometry from a nearby source, (4) high sky background caused by moon illumination or a twilight sky,⁶ or (5) faint reference stars in the field. Only the first two causes are indicative of true variability.

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If a reference star's magnitude appears to have a high standard deviation, as illustrated with an open box shown in the top panel of Figure 3, we remove this outlier and perform another round of least-square calculations to obtain the δm^j values for the frames and the final mc^j_i and derived σ_mag values. Such outliers can be caused by any of the five reasons listed above. Usually, after the second round of calculations to get mc^j_i, we determine the final magnitudes for the science star for each frame, which represents its variability around its mean magnitude, as shown in the bottom panel of Figure 3.

We have carried out three specific tests to support the variability results, including analyses of (1) the two V filters used, (2) reference star selection, and (3) the target star brightness ranking relative to the reference stars.

Two V filters. To check that slight differences between the two V filters ("old" and "new") do not cause significant extra variability for those parallax stars observed using both filters, we have evaluated the photometric time series of three white dwarfs, LHS 145, GJ 440, and GJ 781.3, observed during CTIOPI (Subasavage et al. 2009). These three stars have rich data sets taken using both filters and are known to be non-pulsating white dwarfs, which ensure extremely low levels of intrinsic variability. The results given in Table 3 show that in both filters, our "observational floor" for detecting variability is ∼0.008 mag (discussed further in Section 5.2). Thus, the use of different V filters may introduce small additional uncertainties. However, the "observational floor" in V stays below 0.010 mag.

Reference star selection. To investigate whether or not the reference stars' brightnesses affect δm^j, and consequently our measurements of variability, we have selected the reference star-rich field of LHS 3045 for a series of tests in which we keep the total number of reference stars constant. Figure 4 shows results using four different sets of reference stars. Setup 1 is the one used for the parallax reduction reported in Table 1 and the variability result given in Table 2. Setup 2 includes three stars that differ from those in Setup 1 so that the mean magnitude of Setup 2 reference stars is brighter than for Setup 1. Setup 3 includes a set of faint reference stars that could be selected in this field (but would not, given much more suitable reference stars). Setup 4 also includes reference stars that are all fainter than LHS 3045, but which are generally brighter than in the case of Setup 3.

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Setups 1 and 2 have identical standard deviations for all stars in common. Setup 2 was not chosen for the parallax work because some stars are on the edge of the CCD chip, where their PSFs are slightly distorted and degrade the astrometric results. Predictably, Setup 3 yields the highest standard deviations among the tests because all of the reference stars are fainter than mag 19.8. In practice, these stars cannot be selected for astrometric work because they are too faint to determine reliable centroids if the target star is kept unsaturated. As discussed in Section 2.1, to derive good centroids for astrometric measurements, we expose long enough to let either parallax or reference stars reach peak counts of ∼50,000 for centroiding, which consequently provides a high S/N for all stars used in the astrometric reduction. In fact, because the target/reference star configuration used in Setup 3 will not provide a reliable parallax, we would drop this target from the parallax program. We did not select Setup 4 because suitable brighter stars were available for both astrometric and photometric work. The σ_mag values from Setup 4 are 0.001 mag higher than for Setups 1 and 2 because of four stars of mag 19.7 or fainter. Nonetheless, the σ_mag value for the target star remains less than 0.010 mag and is only 0.001 mag higher than for Setups 1 and 2. We therefore conclude that all realistic reference star configurations yield variability measurements consistent at the 0.001 mag level.

Target star brightness. To better understand how variability measurements change with the brightness ranking of the target star, in Figure 5 we plot the σ_mag values versus magnitude for the 130 sample stars and show the brightness ranking of the target stars in the right panel. A science star with a brightness ranking of 85% means that 85% of reference stars in that field are fainter than the science star. A science star with brightness ranking of 100% has a field similar to Setup 4 in Figure 4. The mean brightness ranking of all 130 stars is ∼85%, marked as a vertical dashed line. The right panel of Figure 5 shows that there is no clear relation between a science target's brightness ranking and its variability for most stars, which are found in the 50%–100% region.

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Overall, we conclude that none of the three tests indicates any systematic effects on the variabilities measured for the target stars.

Figure 6 shows stellar variability, measured using σ_mag, as a function of color for the 130 dwarfs and subdwarfs included in this study, separated into panels that include all stars and split into subsets for stars observed in the V, R, and I filters. Points with ×'s are the five stars omitted from the statistical study for reasons given in Section 5.1. For the sample of 108 dwarfs (open circles in Figure 6), the mean variabilities at V, R, and I are 0.013 (51 stars), 0.013 (39 stars), and 0.008 (18 stars) mag, respectively. These results indicate that as a group, red dwarfs are more variable in the V and R bands than in the I band. We also perform a Kolmogorov–Smirnov test for 51 stars at the V band and 18 stars at the I band. The result shows a probability of 99.87% that distributions of these two bands are statistically different.

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For the sample of 22 cool subdwarfs, the average variabilities are 0.007 at V (3 stars), 0.008 at R (13 stars), and 0.007 at I (6 stars) mag, which are lower than for dwarfs at V and R. A Kolmogorov–Smirnov test for the R-band sample, in which we have the largest number of subdwarfs, indicates a probability of almost 100% that the dwarf and subdwarf cumulative distributions are different, where the greatest absolute difference between the two distributions is equal to 0.74, highly indicative of different samples. Thus, it appears that the variability in subdwarfs is lower than that of dwarfs, at least in the R band, implying that their atmospheres are less active. More subdwarfs need to be observed in the V band to confirm our suspicion of less activity than for subdwarfs than for dwarfs at V, although the data do point in that direction. We also note that subdwarf variability is similar in all three filters, rather than increasing at shorter wavelengths, which is the case for dwarfs. This may be indicative of quiet atmospheres in the subdwarfs, for which we have reached our "observational floor" (about 0.008 mag) in our ability to measure variability in the current data sets, which suspiciously also matches the value for the least variable I filter measurements for dwarfs. Although this comparison is based on relatively small samples, it is the first time the long-term variability of cool subdwarfs has been investigated.⁷

Overall, most subdwarfs' variability is less than 0.01 mag, with two notable exceptions, both of which have been excluded in the statistical evaluations of the subdwarf sample above.

LHS 272. This star is relatively bright (V= 13.16), yet has the largest σ_V= 0.015 of the 11 stars measured in that field. For comparison, a relatively faint (V= 14.17) reference star has σ_V= 0.007. However, LHS 272 was observed on the wing of a bright background galaxy ∼17''distant at a position angle of 217° in 2001. In our frames, LHS 272 has moved quickly away at μ = 1.439 yr⁻¹ at 2792, but the galaxy may corrupt the variability measurements for those images taken during the first few epochs of observations, causing an erroneously high variability measurement.

LHS 2734B. This is the fainter star of a pair of science targets in the field; the primary, LHS 2734A was targeted for parallax so the B component was systematically underexposed, resulting in a high variability measurement due to poor S/N, with σ_I= 0.020 mag. This is also the faintest star observed among all 130 systems, with I= 16.79.

So far, we have only observed a few dozen subdwarfs over these long time periods, and with limited numbers of reference stars. At present, we are comparing subdwarfs observed at R with V − I< 2.4 to dwarfs observed at R with V − I> 2.4, as shown in Figure 6. In order to make a systematic comparison of dwarfs and subdwarfs of similar color, we need long-term photometric monitoring campaigns that cover large swaths of sky, such as the Hungarian-made Automated Telescope Network (HATNet) or the All Sky Automated Survey. For example, Hartman et al. (2009) reported variability for 27,560 K and M dwarfs using HATNet data, but this rich data set has not yet been applied to subdwarfs. The catch is that these surveys typically reach σ_mag∼ 0.01 mag at I∼ 11, a magnitude limit too bright to reach many cool subdwarfs. To reach large numbers of faint, cool, subdwarfs, we will need the next generation of survey projects like the Large Synoptic Survey Telescope, Pan-STARRS, and the SkyMapper project.