PARALLAX RESULTS FROM URAT EPOCH DATA

Custom code was used to apply overscan, trim, dark, and flat-field corrections operating on 2-byte-integer FITS files for both the raw data and processed images. Custom code was also used to detect stellar images (4σ above background threshold) and perform 2-dim spherical symmetric Gaussian model profile fits to the observed stellar images of the processed pixel data. Besides the seeing, a significant contribution to the observed point-spread function (PSF) comes from diffraction due to the relatively small aperture, leading to an observed image profile width of typically 2 pixels FWHM. The PSF is very uniform across the entire field of view, thus the same model function was used independent of the location of a stellar images in the focal plane.

An eight-parameter "plate" model was adopted for the astrometric reductions (linear + tilt terms) using the Fourth USNO CCD Astrograph Catalog (UCAC4; Zacharias et al. 2013) for reference stars, restricted to magnitudes R = 8–16. A weighted, least-squares solution with outlier rejection was performed on each individual CCD and exposure with typically several hundred to a few thousand reference stars per astrometric solution. The data are corrected for geometric field distortions (about 10–60 mas effect) and pixel phase errors (0–15 mas) using "look-up" tables generated from preliminary reductions and residual analysis.

Individual epoch positions ($\alpha ,\delta$) of all stars were obtained on the International Celestial Reference System (ICRS) via UCAC4. Depending on brightness and exposure time, typical positional errors of individual observations are 10 to 60 mas. All individual epoch positions have been matched to individual stars with mean data and indexing saved to a separate, large file allowing fast, direct access to the individual observations (42 bytes of binary data each). These URAT data consists of over 392 million individual objects with about 8.4 billion observations. Excluding single detections, the average number of observations per star is about 24. For more details about the astrometric reductions the reader is referred to the URAT1 paper (Zacharias et al. 2015).

The URAT parallax pipeline utilizes routines from Jao (2004), the JPL DE405 ephemeris and Green's parallax factor (Green 1985) for determining parallaxes. We first determined the location of the Earth (rectangular coordinates X, Y, and Z) at each URAT mid-exposure using the JPL DE405 ephemeris. This was done so that the pipeline can be run over all epoch data of all stars and look up the Earth's position by exposure number instead of recalculating these data for each star and epoch, thus significantly reducing the run time of the code. The rectangular coordinates at epoch are then used to determine the parallax factors using the following formulae:

$$\begin{eqnarray}&&{P}_{\alpha }\;=\;X\mathrm{sin}\alpha -Y\mathrm{cos}\alpha \end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{P}_{\delta }\;=\;X\mathrm{cos}\alpha \mathrm{sin}\delta \ +\ Y\mathrm{sin}\alpha \mathrm{sin}\delta \ -\ Z\mathrm{cos}\delta .\end{eqnarray} \tag{ 2 }$$

The parallax factors of all individual data are then used to simultaneously solve for mean position, proper motion, and parallax using all "good" epoch data of a given star in a least-squares adjustment with outlier rejection from the following equations:

$$\begin{eqnarray}&&x(t)\;=\;x({t}_{0})\ +\ {\mu }_{x}(t-{t}_{0})\ +\ \pi {P}_{\alpha },\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&y(t)\;=\;y({t}_{0})\ +\ {\mu }_{y}(t-{t}_{0})\ +\ \pi {P}_{\delta },\end{eqnarray} \tag{ 4w }$$

where $x(t),y(t)$ are the positions of a given star on the tangential plane as a function of time (t), π is the parallax, ${\mu }_{x}\;=\;{\mu }_{\alpha }\mathrm{cos}\delta$ and ${\mu }_{y}\;=\;{\mu }_{\delta }$ represent the proper motions in R.A. and decl., respectively. The initial instant of time (t₀) can be chosen arbitrarily. Here we choose the first observing epoch as zero point for $x,y$ and t.

In Table 1, we show the cuts we have adopted to the URAT epoch data of a given star when solving for parallax. The limits imposed on individual image amplitude, image profile width (FWHM), and position fit error (sigma) are set to not allow saturated stars, stars with too few photons, or poorly determined positions to be used in the parallax solution. Limits on number of individual observations used and epoch span were adopted empirically to obtain "good" results when comparing the URAT parallaxes with the Hipparcos Catalog and the Yale Parallax Catalog and at the same time allow for as many "reasonable" parallax solutions as possible from our data.

In the least-squares adjustment to solve for parallax (Equations (3) and (4)), weights were used according to the precision of individual observations, which can vary largely due to the different exposure times and amplitudes of individual observations. An error floor of 10 mas was added in quadrature to the random errors (in the astrometric reductions of individual observations) before calculating the weights for an observation in determining the parallax (see Zacharias et al. 2015 for details about the astrometric reductions of individual observations). A 3σ outlier rejection criteria was imposed and in cases where the post-fit error of unit weight exceeded 1.5 times the expected error of the fit solution the largest residual(s) were iteratively removed from the fit solution. This way, typically up to a few percent of observations were rejected for the parallax solution of individual stars.

At this point, we have parallaxes for the target stars that are relative to the set of reference stars used in the reductions of the URAT positions, i.e., with respect to typically many hundreds to a few thousand stars in a 2.65 by 2.65 square degree area of a single URAT CCD detector. To convert from relative to absolute parallax, we use photometric parallaxes for the reference stars. This method is not as reliable as spectroscopic parallaxes, which can determine the spectral type and luminosity class, allowing us to apply correct Mv-color relations to each reference star. Photometric parallaxes were used because of the lack of spectroscopic data for millions of stars in our survey area down to R = 16 mag.

Again we use the UCAC4 catalog here now also for its photometric data. This was done by picking the same UCAC4 stars previously used as reference stars in the astrometric reductions (R = 8–16 mag). These stars are then run through our 16 photometric color–${M}_{{K}_{s}}$ relations (Finch et al. 2014), which use the AAVSO Photometric All-Sky Survey (APASS) BVgri and Two Micron All Sky Survey (2MASS) JHK_s photometry included in the UCAC4 catalog. Using this data, we determine a mean photometric parallax per reference star, assuming that all stars are main sequence due to the lack of information for each star. This is done for all reference stars in a 2 by 2 degree wide area around each target star to determine a mean absolute parallax correction for each target star. The average parallax correction for the target stars in this paper is 1.3 mas varying from 0.5 to 6.6 mas, depending on the field. For any star having an unknown correction, we use the mean to convert to absolute parallax. For stars having a correction greater than three times the average (≥3.9 mas), we adopt this as a cut off and use 3.9 mas to convert to absolute parallax. For these stars, we have added a note in the tables to indicate if the mean or cut off correction was used. Considering the relatively large random errors of our parallax results, this step is not critical for the goal of our investigation.

We do not apply any corrections to our parallaxes for the Lutz–Kelker bias (Lutz & Kelker 1973) because we do not draw conclusions about completeness of a distance limited sample or interpret results regarding absolute luminosity. This is beyond the scope of this paper, which is to present the observed trigonometric parallaxes for a large number of stars. This bias comes into play when "translating" the observed parallax into distances and absolute luminosities.

The Hipparcos Catalog contains 65,546 stars north of $-10^\circ$ decl. While the URAT catalog goes as far south as about $\delta \;=\;-24^\circ$, its completeness begins to drop south of $-10^\circ$ decl. The URAT catalog recovers 65,524 (99.96%) of Hipparcos stars in this area of the sky. Most of the few missed stars are just brighter than the URAT limit or lost due to blended images, which are not taken care of in the URAT reductions.

One of the main goals of this paper is to discover new nearby stars or confirm candidates within 25 pc. To determine how well URAT can detect stars within 25 pc, we used the Hipparcos catalog (2007 version). Hipparcos contains 926 stars north of $-10^\circ$ decl. with a parallax ≥40 mas. URAT recovers 887 (=95.8%) of the Hipparcos 25 pc sample loosing 20 from our amplitude/sigma cuts, 16 having too short of an observational epoch span, 3 having too few observations, and 6 stars not being in the URAT data at all. Of those 887 recovered stars, 778 (=87.7%) have a URAT parallax ≥32 mas. In Figure 1, we show the comparison between the Hipparcos 25 pc sample and URAT results, where the center line indicates agreement and the 2 outer lines indicate a 10 mas difference from the Hipparcos parallax values.

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In order to investigate how reliabel the URAT parallax formal errors are, we took the 25 pc sample of 887 stars common to Hipparcos and applied two different cases of cuts to filter "reasonably good" data. Selection criteria and results are summarized in Table 2. The number of observations per target star, the epoch span of these observations, and the formal errors of both the Hipparcos and our URAT data were restricted. For the stars remaining in the sample, the unweighted difference in parallax was calculated. A few outliers were further eleminated at this stage (see Table 2) before the rms of the parallax difference and the formal errors were calculated. We see that formal errors on our URAT parallaxes are underestimated by about 10%–20% when compared to the observed scatter of the data (the errors for the Hipparcos parallaxes are much smaller, typically 0.5–2 mas, than the URAT parallax errors). Distributions of the URAT parallax formal errors are shown in Figures 2 and 3 for the Hipparcos 25 pc sample and all Hipparcos stars north of $-10^\circ$ decl., respectively. This shows that the URAT errors for these samples peak around 8 mas with typical errors between 4 and 15 mas.

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In Figure 4, we show the relation between the URAT parallax error and epoch difference of the available URAT data for the Hipparcos 25 pc sample. For Figure 5, we use the same sample but show the relationship between the URAT parallax error and number of observations. These plots indicate that the URAT parallax errors drop below about 8 mas for solutions having an epoch span greater than 2.0 years and more than 40 individual epochs.

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Hipparcos and YPC have 698 stars in common north of $\delta \;=\;-10^\circ$ with a V magnitude range of 2.83–11.70. Of these 698 stars, we obtained a URAT parallax for 696 stars. Figures 6–8 show the comparison of URAT versus Hipparcos, URAT versus YPC, and YPC versus Hipparcos, respectively. The center line indicates perfect agreement while the two outer lines have been added to show a difference of 10 mas. URAT compares relatively well with both the Hipparcos and YPC results, but does show a somewhat larger scatter not present in the YPC versus Hipparcos plot, as expected from mean formal errors.

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A similiar parallax investigation was completed using images from the MEarth photometric survey (Dittmann et al. 2014) having a large overlap with our URAT parallaxes. The typical error on the MEarth parallax data is reported to be 4 mas, while that for URAT data is about twice as large. In Figure 9, we compare the parallax results reported in Dittmann et al. (2014) for the 572 stars matched with the URAT parallax data. The center line represents perfect agreement while the outer lines show a ±10 mas difference.

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In Figure 10, we show a comparison between URAT and 1387 published trigonometric parallaxes ≥40 mas from the 11,878 parallaxes described in Section 4.3 pulled from the 44.7 million parallaxes from the entire URAT data. A 60 arcsec radius was used when searching SIMBAD, published papers, and vizeir for published trigonmetric parallaxes.

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We first took a list of 9737 nearby stars having previously published distance estimates based on photometry from the publications listed in Section 1. After cutting these to the area of sky being searched in this survey ($\delta \geqslant -10^\circ$), we are left with 4853 candidate nearby stars. These are then run through our parallax pipeline and list of constraints resulting in 3093 parallax results. These constraints include the same as those listed in Table 1 with an additional constraint to the parallax error of ≤1/2 the parallax and ≤25 mas. Of the remaining 3093 stars, 1906 were found to not have a published parallax result after searching SIMBAD, Vizier, and published papers. After removing 182 duplicate entries, which came from combining all systems from the published papers, we are left with 1724 parallax results. We then only keep the 545 stars having a URAT parallax ≥40 mas, which is the focus of this paper. Of these 545 stars, 10 have a URAT parallax ≥100 mas.

Data for all of these 545 stars (picked from the photometric list and having a URAT prallax distance within 25 pc) are given in Table 3 (sorted by parallax). We include the names, R.A. and decl. coordinates (at epoch 2014.0 on the ICRS; derived from input data in corresponding published paper), URAT magnitude, epoch span, number of observations, number of rejected observations, absolute parallax, parallax error, parallax correction, proper motion in R.A. and decl. with associated errors, and JHK_sBV_gri photometric data from UCAC4 along with any notes. All 545 stars have no previously published trigonometric parallax. The average formal parallax error for this sample is 7.8 mas. Notes on specific individual stars from this sample are reported in Section 5.

In Figure 11, we compare the URAT trigonometric parallax to the previously published photometric parallaxes for the 545 stars in this sample. In Figure 12, we show an example of a good fit for G165-058 (π = 80.1 ± 4.4 mas, pmra = 6.4 ± 2.8 mas yr⁻¹, pmdc = 298.1 ± 2.7 mas yr⁻¹). This plot shows all URAT epoch data for this star. A histogram of the parallax error for this sample is given in Figure 13, showing the peak around 6 mas with the majority of the errors falling in the 4–10 mas range. In Figure 14, we present a histogram of total proper motions for the same sample, which shows a significant number of nearby stars with small proper motions (between 100 and 450 mas yr⁻¹). The errors for this sample are somewhat smaller than for the Hipparcos and YPC sample used above due to the more stringent restrictions applied here.

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The entire URAT data was run through the parallax pipeline giving 44.7 million parallax solutions. We then implemented several cuts to get this to a more manageable sample, keeping only stars with (1) a parallax ≥40 mas, (2) an epoch span of at least 1.5 years, (3) at least 30 individual epochs, and (4) a parallax error ≤20 mas and ≤1/4 the absolute parallax. These cuts left us with a sample of 6571 new candidate nearby stars. We then used SIMBAD, Vizeir, and published papers to remove 1753 stars having a previous published parallax or having a match with Table 3, leaving us with 4818 nearby star candidates. Of these new nearby star candidates, 35 have a URAT parallax ≥100 mas.

The current URAT reduction process does not take provisions for close doubles (blended images) of arcsecond-level separations. Many of our candidates, particularly those with large parallax solution errors are possibly blended images. This means a visual inspection (residual plots as well as real sky image using Aladin) must be completed to verify the integrity of the solution. This would not be practical for the entire sample.

However, this visual inspection was completed for the 35 candidate stars in our 10 pc sample. For this sample, we find that the majority of the stars are blended or elongated even if the fit solution looks reasonable. All stars considered "suspect" from this visual inspection are flagged. In Figure 15, we show an example of a poor fit case for the star UPM 1304+8611 (π = 42.5 ± 7.3 mas, pmra = 40.1 ± 8.6 mas yr⁻¹, pmdc = −33.4± 8.4 mas yr⁻¹), which is marked as suspect in our table. This plot shows all URAT epoch data for this star similarly to the previous Figure.

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While sifting through the 10 pc nearby star sample, we notice that UPM2340+4631 and UPM2340+4625 both have large parallaxes with a separation of less than 7 arcmin. We also notice that UPM1758-0055, UPM1758-0057, UPM1758-0058, and UPM1758-0104 also share a large parallax and are all separated by less than 12 arcmin, indicating that they may all be part of the same group. More information on these stars is reported in Section 5.

For the remaining 4783 stars, comprised of nearby star candidates between 10 and 25 pc, we were not able to search the entire sample. Instead, we sorted the list by (1) number of epochs, (2) parallax error, and (3) image elongation in that order. We then started visually checking the fits to verify the quality. During this process, we also randomly looked at sky images using Aladin. For this sample, we did not see any examples of an elongated or blended image in our random search. The fits for this sample also seemed of higher quality than the 10 pc sample; however, we did see some fits that might be suspect, which are noted in the table. We were able to search 1221 of the 25 pc nearby star candidates that we felt had the highest chance of being a real nearby star with a quality parallax solution.

This search produced 558 new discoveries within 25 pc of the Sun, of which 24 have a URAT parallax putting them within 10 pc. All of the fits and sky images have been visually inspected for the 10 pc sample. For new discoveries between 10 and 25 pc all fits have been visually inspected and sky images randomly inspected for issues.

In Table 4, we present details for the 558 new nearby stars having an absolute parallax ≥40 mas (sorted by parallax). These stars have no previously published photometric distance or trigonometric parallax information. We have added a note in the table to indicate if the sky image was found to be elongated or blended, or for which the fit was suspect. We include the names, R.A. and decl. coordinates (ICRS epoch 2014; derived from the mean URAT position at mean epoch from all epochs used in the fit along with the URAT proper motions), URAT magnitude, epoch span, number of observations, number of rejected observations, absolute parallax, parallax error, parallax correction, proper motion with associated errors, and JHK_sBV_gri photometric data from the URAT1, along with notes. We have given a USNO Proper Motion (UPM) name for the 281 entries having no previous proper motion information reported from SIMBAD. The average absolute parallax error for this sample is 6.3 mas. Details about individual stars are reported in Section 5.

We present a histogram of the parallax error for this sample in Figure 16, showing the peak around 5 mas with the majority of the errors falling in the 4 to 8 mas range. In Figure 17, we show a histogram of total proper motions for the same sample which shows the majority of the new nearby star discoveries have small proper motions (less than 200 mas yr⁻¹). The errors for this sample are the smallest out of any other sample due to the most stringent selection criteria applied here for searching the best possible nearby star candidates.

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