Evidence for a systematic offset of -0.25 mas in the Gaia DR1 parallaxes

Evidence for a systematic offset of 0.25 mas in the Gaia DR1 parallaxes

Keivan G. Stassun11affiliation: Vanderbilt University, Department of Physics & Astronomy, 6301 Stevenson Center Ln., Nashville, TN 37235, USA; keivan.stassun@vanderbilt.edu 22affiliation: Fisk University, Department of Physics, 1000 17th Ave. N., Nashville, TN 37208, USA and Guillermo Torres33affiliation: Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
Abstract

We test the parallaxes reported in the Gaia first data release using the sample of eclipsing binaries with accurate, empirical distances from Stassun & Torres (2016). We find an average offset of 0.250.05 mas in the sense of the Gaia parallaxes being too small (i.e., the distances too long). The offset does not depend strongly on obvious parameters such as color or brightness. However, we find with high confidence that the offset may depend on ecliptic latitude: the mean offset is 0.380.06 mas in the ecliptic north and 0.050.09 mas in the ecliptic south. The ecliptic latitude dependence may also be represented by the linear relation,  mas ( in degrees). Finally, there is a possible dependence of the parallax offset on distance, with the offset becoming negligible for  mas; we discuss whether this could be caused by a systematic error in the eclipsing binary distance scale, and reject this interpretation as unlikely.

1 Introduction

The advent of trigonometric parallaxes for 10 stars from the Gaia mission promises to revolutionize many areas of stellar and Galactic astrophysics, including exoplanet science. For example, with eventual expected precision in the parallax of 20 as for bright exoplanet host stars, it should be possible to determine the stellar and planet radii and masses directly and empirically with accuracies of 3–5% (see, e.g., Stassun, Collins, & Gaudi, 2016). Already, the Gaia first data release (DR1; Gaia Collaboration, 2016) provides parallaxes for 2 million Tycho-2 stars (the TGAS stars) with a nominal precision of 0.3 mas and with a quoted systematic uncertainty at present of 0.3 mas.

The results from DR1 are based on only 14 months of observations, and use external information in the form of earlier positions from the Hipparcos (ESA, 1997; van Leeuwen, 2007) and Tycho-2 (Høg et al., 2000) catalogs to help remove degeneracies (the Tycho-Gaia Astrometric Solution; Michalik et al., 2015). Additionally, they rely on very provisional and as yet incomplete calibrations, and as a result the astrometric products including the parallaxes are still preliminary. Nonetheless, the new parallaxes represent such an improvement in both quality and quantity that they are certain to be used by the community for a wide range of astrophysical applications, at least until future Gaia releases supersede them.

It is essential, therefore, to assess the on-sky delivered performance of these parallaxes from Gaia DR1, especially the presence of any unexpected biases. This is particularly important in light of the experience from Hipparcos, which suffered a significant bias in at least the case of the Pleiades cluster (e.g., Pinsonneault et al., 1998). Such a check requires a set of benchmark stars whose parallaxes are determined independently and with an accuracy that is at least as good as that expected from Gaia DR1.

Stassun & Torres (2016) assembled a sample of 158 eclipsing binary stars (EBs) whose radii and effective temperatures are known empirically and precisely, such that their bolometric luminosities are determined to high precision (via the Stefan-Boltzmann relation) and therefore independent of assumed distance. Stassun & Torres (2016) reported new, accurate measurements of the bolometric fluxes for these EBs which, together with the precisely known bolometric luminosities, yields a highly precise distance (or parallax). The precision of the parallaxes for this EB sample was predicted by Stassun & Torres (2016) to be 190 as on average. This is a factor of 1.5 better than the median precision of 320 as for Gaia DR1 (Gaia Collaboration, 2016). It is even somewhat superior to the expected Gaia DR1 precision floor of 240 as. These EB parallaxes can therefore readily serve as distance benchmarks for the trigonometric parallaxes reported by Gaia DR1, and in particular can be used to assess the presence of any systematics.

In this Letter, we report the results of testing the Gaia DR1 parallaxes against the Stassun & Torres (2016) EB benchmark sample. Section 2 describes the EB and Gaia data used. Section 3 presents the key result of a systematic offset in the Gaia parallaxes relative to the EB sample. Section 4 considers potential trends in the parallax offset with other parameters. Section 5 concludes with a summary of our conclusions.

2 Data

We adopted the predicted parallaxes for the 158 EBs included in the study of Stassun & Torres (2016). Of these, 116 had parallaxes available in the Gaia first data release. We excluded from our analysis any EBs identified as potentially problematic in Stassun & Torres (2016). This left 111 EBs with good parallaxes from both the EB analysis and from Gaia. These EBs are all relatively nearby, with parallaxes in the range 0.3–30 mas. The EBs and their relevant data are provided in Table 1.

Name Tycho aaEffective temperature for the primary component. bb of SED fit from Stassun & Torres (2016). Stars with were considered unacceptable and are excluded from analysis in this paper also. RA Dec.
K K mag. mas mas mas mas mas deg. deg.
UV PscccFlagged in Stassun & Torres (2016) as a large outlier relative to Hipparcos and excluded from analysis in this paper. 0026-0577-1 5780 100 9.01 2.72 12.47 0.57 0.53 14.392 0.407 19.2297 6.8117
XY Cet 0051-0832-1 7870 115 8.75 1.6 3.62 0.14 0.13 4.542 0.891 44.8897 3.5176
V1130 Tau 0066-1108-1 6625 70 6.66 1.34 14.35 0.36 0.37 14.329 0.332 57.6748 1.5639
EW Ori 0104-1206-1 5970 100 9.78 0.71 5.9 0.22 0.21 5.482 0.233 80.0381 2.0444
U OphddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper (see the text). 0400-1862-1 16440 250 5.9 1.15 4.35 0.14 0.17 3.685 0.775 259.1322 1.2105

Note. – Table 1 is published in its entirety in machine-readable format. A portion is shown here for guidance regarding its form and content.

Table 1: Eclipsing Binary and Gaia Data

3 Results

Figure 1 shows the direct comparison of the EB parallax predictions from Stassun & Torres (2016) versus the Gaia DR1 parallaxes for the study sample. The least-squares linear best fit, weighted by the measurement uncertainties in both quantities (Press et al., 1992), is . While this indicates a good 1-to-1 agreement to first order, the coefficient of 1.030.01 could be interpreted as a modest global difference of scale in the Gaia parallaxes relative to the EB parallaxes. However, considering all of the available evidence instead suggests a small offset in the Gaia parallaxes as we now discuss.

Figure 1: Direct comparison of predicted parallaxes from the eclipsing binary sample of Stassun & Torres (2016) versus the parallaxes from the Gaia first data release. The one-to-one line is shown in black and a least-squares linear best fit is shown in red.

Figure 2 presents the overall distribution of parallax differences in the sense of . The distribution appears roughly symmetric and normally distributed, with perhaps a sharper peak and more extended wings than a Gaussian, and there is a clear offset relative to zero. The mean offset is mas, where the quoted error is the uncertainty of the mean for 111 measurements.

Figure 2: Distribution of (GaiaEB). EBs with known tertiary companions are represented in blue. We find an offset of mas for the entire sample and mas when the triple systems are excluded. Also shown is a best-fit Gaussian with , representing the quadrature sum of the typical random uncertainties from the Gaia and EB parallaxes; see Sec. 1.

Stassun & Torres (2016) noted that a number of the EBs used in that study are known triple or quadruple systems. In general these companions contribute very little to the total system light, and Stassun & Torres (2016) found no evidence for significant systematics in their predicted parallaxes. Nonetheless, the offset that we find above for the Gaia parallaxes is small and could potentially have gone unnoticed in Stassun & Torres (2016). Indeed, the effect of additional light contribution to the EBs by companions would be in the sense of making the EB stars appear brighter, therefore inferred to be closer, and in turn the Gaia distances interpreted as too long (parallax too small).

In Gaia DR1, 12 of our EBs have known companions (see Table 1; one additional EB with a known companion is already excluded by the cuts discussed in Sec. 2). These EBs are indicated in blue in Fig. 2, which shows the two largest outliers to be triples. Excluding all of the triples results in a parallax offset of mas, consistent with that determined for the full sample, though slightly smaller.

Overall, from the EB sample, a systematic offset in the Gaia DR1 parallaxes of to  mas is indicated. For simplicity, we adopt the rounded value between these estimates of  mas.

4 Discussion

The official Gaia DR1 documentation states: “There are colour dependent and spatially correlated systematic errors at the level of 0.2 mas. Over large spatial scales, the parallax zero-point variations reach an amplitude of 0.3 mas…. Furthermore, averaging parallaxes over small regions of the sky will not reduce the uncertainty on the mean below the 0.3 mas level.111http://www.cosmos.esa.int/web/gaia/dr1” Our finding of a mean parallax offset of mas (Sec. 3; Fig. 2) corroborates this statement, and further quantifies it using an independent benchmark sample of EBs with accurately known distances (Stassun & Torres, 2016).

In principle this offset could be due to systematics in one or more of the EB parameters from which the EB distances are determined. If so, one might especially suspect the EB values: unlike the stellar radii, for example, which are determined from simple geometry, the values are determined from spectral analysis and/or spectral typing and/or color relations. The slope of the fitted relation in Fig. 1 would imply an error in the EB distance scale of 3%, which in turn would require a systematic error in of 1.5% (because ) or 105 K given the typical of the EB sample. The sense of the offset is that the EBs would have to be systematically too cool.

However, we do not consider this to be a likely possibility, for multiple reasons. First, Stassun & Torres (2016) found no evidence for a systematic offset of the EB parallaxes relative to the Hipparcos parallaxes which, even at the somewhat poorer precision of 1 mas, should have been apparent. Lindegren et al. (2016) compare the Gaia DR1 parallaxes against 87,000 Hipparcos stars in common, finding a statistically significant average offset just under  mas, smaller than, but in the same sense as the offset we find among our EB sample. Second, while systematics among various scales can be of order 100 K (see, e.g., Casagrande et al., 2011; Heiter et al., 2015), it is unlikely that they should produce a net offset of this entire magnitude in a sample of 111 EBs spanning a large range of , given the different methodologies and calibrations adopted by the various authors. Finally, we have directly examined the degree to which might correlate with in the EB sample (Fig. 3, upper right), finding very weak evidence for a correlation: The regression relation has a coefficient of determination ; this parameter explains only 13% of the variance in . Indeed, a Kendall’s non-parametric correlation test gives a probability of 51% that and are uncorrelated. (We checked that the parallax ratio versus is also not significantly correlated.) Incidentally, this also suggests little to no dependence of with color, since can be taken as a proxy for color.

Figure 3: Potential correlations between and , EB , and mag. Best fitting linear regression lines are shown for each (see the text).

With a current sample of 111 EBs that overlap with the Gaia DR1 parallaxes, it is difficult to ascertain with certainty whether any higher-order dependencies are at work beyond a simple offset. Nonetheless, it is possible that the parallax offset we observe is a function of one or more parameters. We have considered some obvious possible parameters, including distance, and brightness. These are represented in Figure 3. There is some evidence for a dependence of on distance and/or brightness, however it is difficult to gauge whether these modest distance and brightness dependencies are independent of one another. A priori, a possible dependence on brightness may be more likely than a dependence on distance: because of the manner in which the trigonometric parallax measurements are made (linear offsets on the detector), they are more likely to depend on parameters that affect the displacement calibration (e.g., color or brightness) than the displacement itself. Thus there is not strong evidence for a dependence of the offset with brightness or color, at least in our sample.

The apparent correlation of with may be a consequence of the tendency for the EBs with the largest to be located in the ecliptic north, where we find the largest overall offset (see below). In any event, among our 12 EBs with  mas, the average offset is  mas. Thus, it appears that the offset vanishes for very small parallaxes, mas. This would be consistent with the findings of Lindegren et al. (2016) and also Casertano et al. (2016), who find good agreement with the Gaia DR1 parallaxes in separate samples of very distant Cepheids with estimates based on period-luminosity relations. Casertano et al. (2016) also find evidence for a parallax offset, in the same sense as we find, among the small number of very nearby, bright Cepheids in their sample.

Finally, we have considered the possible spatial dependence of . There is evidence for a trend or difference by ecliptic latitude (Fig. 4). The mean parallax offset for EBs in the northern ecliptic hemisphere is statistically significant with  mas, whereas in the southern ecliptic hemisphere it is not significant with  mas. A two-sided Kolmogorov-Smirnov test gives a probability of 0.0001 that this difference could occur by chance. Alternatively, the trend can be represented as a linear variation with latitude,  mas ( in degrees). A Kendall’s test indicates that the correlation between parallax offset and ecliptic latitude is significant with 99.7% confidence.

Figure 4: Parallax differences as a function of ecliptic latitude. A trend is found (black line) with 99.7% confidence, which may also be interpreted as a significant difference in the ecliptic north ( mas) but not in the ecliptic south ( mas). Color represents EB brightness and symbol size is proportional to .

The possibility that systematics in the Gaia DR1 parallaxes are dependent on ecliptic latitude was suggested in the Gaia documentation (Lindegren et al., 2016). These authors reported that a comparison with parallaxes from the Hipparcos mission indicates an overall statistically significant offset  mas, the Gaia values being smaller, but that the northern ecliptic hemisphere shows a larger offset of  mas compared to the southern hemisphere ( mas).

5 Summary and Conclusions

Here we present evidence of a small but systematic offset in the average zero-point of the parallax measurements recently released by the Gaia Mission of about  mas, in the sense that the Gaia values are too small. We also find evidence to suggest that the offset is a function of ecliptic latitude. The offset in the northern ecliptic hemisphere is 0.380.06 mas and 0.050.09 mas in the southern ecliptic hemisphere. Alternatively, the offset may also be represented as a linear function of the ecliptic latitude,  (), according to  mas.

To apply the correction, this (negative) offset must be subtracted from the reported Gaia DR1 parallaxes. At present we can only confirm that the offset is statistically valid for relatively large parallaxes,  mas.

The reference for this determination is a set of more than 100 independently inferred parallaxes from a benchmark sample of well-studied eclipsing binaries with a wide range of brightnesses and distributed over the entire sky. This paper presents evidence of a difference between the Gaia and EB parallaxes, which we have interpreted here as a systematic error in Gaia after discussing the alternative. In particular, we have considered the possibility of a systematic offset in the EB effective temperature scale as a possible, but unlikely alternative explanation.

It is expected that future releases of the Gaia catalog will remove this small shift as the number of observations increases, calibrations are improved, and the astrometric solution transitions to a self-consistent global fit using only Gaia data, independent of external astrometric information. Indeed, these final trigonometric parallaxes may then be used to further refine the EB sample itself, such as improvements to the EB effective temperature scale. In the meantime, investigators using the parallax results from Gaia DR1 are encouraged to keep the systematic error reported here in mind.

This work has made use of the Filtergraph data visualization service at filtergraph.vanderbilt.edu (Burger et al., 2013). K.G.S. acknowledges partial support from NSF PAARE grant AST-1358862. G.T. acknowledges partial support for this work from NSF grant AST-1509375. The authors are grateful to S. Casertano and A. Riess for sharing their results in advance of publication. We are grateful to the referee for critiques and suggestions that improved the manuscript. This work has made use of data from the European Space Agency (ESA) mission Gaia (http://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, http://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

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Name Tycho aaEffective temperature for the primary component. bb of spectral energy distribution fit from Stassun & Torres (2016). Stars with were considered unacceptable and are excluded from analysis in this paper also. RA Dec.
K K mag. mas mas mas mas mas deg. deg.
UV PscccFlagged in Stassun & Torres (2016) as a large outlier relative to Hipparcos and excluded from analysis in this paper. 0026-0577-1 5780 100 9.01 2.72 12.47 0.57 0.53 14.392 0.407 19.22966316 6.8116994
XY Cet 0051-0832-1 7870 115 8.75 1.6 3.62 0.14 0.13 4.542 0.891 44.88971498 3.51756508
V1130 Tau 0066-1108-1 6625 70 6.66 1.34 14.35 0.36 0.37 14.329 0.332 57.67475441 1.56394837
EW Ori 0104-1206-1 5970 100 9.78 0.71 5.9 0.22 0.21 5.482 0.233 80.0381137 2.0444353
V578 Mon 0154-2528-1 30000 740 8.55 0.65 0.75 0.04 0.04 0.855 0.364 98.0025408 4.8780283
AI Hya 0196-0626-1 6700 60 9.35 7.02 1.82 0.07 0.07 1.879 0.353 124.697754 0.283378
FM Leo 0263-0727-1 6316 240 8.45 3.49 7.29 0.64 0.57 7.004 0.322 168.18789591 0.34800926
AQ Ser 0340-0588-1 6430 100 10.65 1.89 1.71 0.06 0.06 0.869 0.366 230.5632692 2.50308
V335 Ser 0353-0301-1 9020 150 7.49 1.99 5.31 0.2 0.21 4.742 0.302 239.7739821 0.5957072
U OphddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 0400-1862-1 16440 250 5.9 1.15 4.35 0.14 0.17 3.685 0.775 259.13215193 1.21054491
V2368 Oph 0404-2156-1 9300 200 6.18 2.84 5.44 0.32 0.29 5.06 0.428 259.05941952 2.18620241
V413 SerddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 0446-0091-1 11100 300 7.99 1.64 5.34 0.35 0.32 3.23 0.853 278.78422403 0.04301045
CoRoT 105906206 0459-0892-1 6750 150 12.21 1.8 0.94 0.05 0.04 0.964 0.249 280.820621 5.966736
IO AqrddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 0511-0960-1 6336 125 8.86 0.87 3.97 0.18 0.17 3.979 0.246 310.18946139 0.93917186
V1388 Ori 0738-0244-1 20500 500 7.5 3.28 1.12 0.06 0.06 1.315 0.381 92.74652296 11.99485667
WZ Oph 0977-0216-1 6165 100 9.12 3.6 6.67 0.27 0.27 6.608 0.238 256.66267585 7.78271678
V2365 Oph 0977-0547-1 9500 200 8.86 1.68 3.81 0.19 0.16 3.542 0.29 257.19075987 9.1861524
V624 Her 1005-2131-1 8150 150 6.2 2.11 7.6 0.29 0.35 7.615 0.489 266.07186051 14.41006621
EE PegddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 1120-0161-1 8700 200 6.98 1.72 7.33 0.41 0.32 7.372 0.298 325.00784071 9.18475409
CF TauddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 1262-0050-1 5200 150 10.24 1.31 4.06 0.26 0.25 3.132 0.513 61.2922271 22.4967133
V1094 Tau 1263-0642-1 5850 100 8.97 0.74 8.4 0.34 0.3 8.256 0.251 63.0149692 21.9473753
CD TauddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 1291-0292-1 6200 50 6.77 4.36 14.73 0.41 0.39 13.559 0.375 79.379796 20.131842
FT Ori 1326-0910-1 9600 400 9.29 7.62 2.32 0.22 0.19 2.222 0.383 93.4923067 21.4275506
BP Vul 1644-2113-1 7715 150 9.95 2.61 2.49 0.11 0.1 2.402 0.294 306.38853349 21.0383264
AD Boo 2015-0216-1 6575 120 9.44 2.31 4.99 0.2 0.19 4.146 0.554 218.8032496 24.6392644
RT CrB 2039-1337-1 5134 100 10.22 1.84 2.54 0.11 0.11 2.475 0.268 234.5126246 29.48720441
LV Her 2076-1042-1 6060 150 10.97 1.17 2.82 0.16 0.15 2.675 0.243 263.8850083 23.1751667
DI Her 2109-0775-1 17000 800 8.47 0.65 1.58 0.16 0.15 1.354 0.346 283.35933236 24.27799733
BK Peg 2254-2563-1 6265 85 10.04 0.82 3.38 0.11 0.1 2.911 0.482 356.7852704 26.5666433
AR Aur 2398-1311-1 10950 300 6.14 1.83 7.43 0.43 0.41 7.047 0.611 79.57875162 33.76734788
HP AurddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 2401-1263-1 5810 120 11.17 1.31 5.01 0.23 0.21 5.273 0.22 77.590762 35.796286
V432 Aur 2416-0768-1 6080 85 8.05 4.61 7.72 0.29 0.28 8.118 0.255 84.38545384 37.08673876
WW Aur 2426-0345-1 7960 420 5.82 3.06 12.42 1.46 1.26 11.026 0.5 98.11326959 32.45489819
KX Cnc 2484-0592-1 5900 100 7.19 1.05 21.97 0.83 0.77 20.542 0.378 130.69254478 31.86260197
HD 71636 2489-1972-1 6950 140 7.9 0.92 8.59 0.41 0.35 8.403 0.402 127.48463115 37.07096799
CV Boo 2570-0843-1 5760 150 10.99 1.64 3.83 0.23 0.21 3.997 0.253 231.5813963 36.9815092
V501 Her 2606-1905-1 5683 100 11.12 0.5 2.36 0.09 0.09 2.129 0.231 263.93108 30.64308
V885 Cyg 2655-1877-1 8150 150 9.99 2.27 1.17 0.05 0.04 0.744 0.608 293.2077342 30.0213972
MY Cyg 2680-1529-1 7050 200 8.34 1.79 4.22 0.27 0.25 3.952 0.235 305.01412547 33.94306105
V453 Cyg 2683-3326-1 27800 400 8.4 1.62 0.58 0.02 0.02 0.683 0.288 301.6456979 35.7406322
V442 Cyg 2685-1903-1 6900 100 9.7 1.68 2.98 0.1 0.09 2.44 0.346 306.9679333 30.791195
CG CygddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 2696-2945-1 5260 180 10.16 3.26 11.68 0.89 0.8 9.438 0.545 314.556071 35.174911
Y Cyg 2696-3486-1 33200 600 7.32 1.58 0.65 0.03 0.03 0.613 0.291 313.01490655 34.65763334
KIC 8410637 3130-2385-1 4800 80 11.33 2.63 0.98 0.04 0.04 0.373 0.238 282.1587429 44.4860661
KIC 3858884 3135-0651-1 6800 70 9.28 10.6 2.05 0.07 0.07 1.776 0.224 293.69543217 38.98278969
V380 Cyg 3141-3692-1 21700 400 5.68 0.9 1.02 0.05 0.04 0.685 0.696 297.65553032 40.59976051
V478 Cyg 3151-2222-1 30479 1000 8.68 5.82 0.59 0.05 0.04 0.297 0.214 304.91144903 38.33588957
V364 Lac 3215-0971-1 8250 150 8.36 2.3 2.37 0.1 0.1 2.166 0.423 343.06170498 38.74573119
V342 AndddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 3246-2531-1 6200 100 7.82 24.15 12.15 0.69 0.69 4.915 0.333 2.5133037 46.3903136
CO AndddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 3268-0398-1 6140 130 10.77 1.34 2.71 0.13 0.13 3.087 0.274 17.8534604 46.9637042
V570 Per 3314-1225-1 6842 50 8.09 1.98 8.26 0.19 0.18 7.847 0.264 47.39559997 48.62463695
IM PerddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 3323-1123-1 7580 150 11.28 3.91 1.68 0.09 0.07 1.814 0.291 47.9262975 52.2117222
IQ Per 3331-1175-1 12300 230 7.73 3.2 3.65 0.16 0.15 2.92 0.281 59.93615716 48.15124737
HS Aur 3394-0326-1 5350 75 10.05 1.71 7.89 0.3 0.29 7.53 0.282 102.82698688 47.67338091
FL Lyr 3542-1492-1 6150 100 9.36 1.53 7.51 0.33 0.29 7.25 0.217 288.02025709 46.32412867
V2080 Cyg 3551-1744-1 6000 75 7.4 2.15 12.63 0.36 0.35 11.439 0.252 291.69977628 50.14549388
KIC 9246715 3559-0102-1 4930 190 9.65 3.92 1.68 0.15 0.13 1.272 0.279 300.9513421 45.6041192
V1061 Cyg 3600-0472-1 6180 100 9.21 2.29 6.54 0.26 0.21 5.768 0.291 316.83549669 52.04956061
RW Lac 3629-0740-1 5760 100 10.81 1.83 5.15 0.21 0.2 4.942 0.301 341.2378975 49.6576586
AP And 3639-0915-1 6565 150 11.19 1.02 2.89 0.15 0.14 2.433 0.388 357.3779521 45.7892364
IT Cas 3650-0959-1 6470 100 11.23 1.13 2.02 0.07 0.07 2.52 0.339 355.5058137 51.7435558
V505 PerccFlagged in Stassun & Torres (2016) as a large outlier relative to Hipparcos and excluded from analysis in this paper. 3690-0536-1 6510 50 6.88 0.99 16.93 0.41 0.37 15.563 0.323 35.30401536 54.51007761
V1143 Cyg 3938-1983-1 6450 100 5.9 2.02 26.11 0.96 0.88 24.746 0.354 294.6715988 54.97379118
RT AndccFlagged in Stassun & Torres (2016) as a large outlier relative to Hipparcos and excluded from analysis in this paper. 3998-2167-1 6100 150 9.04 5.42 9.17 0.54 0.5 10.053 0.225 347.79207917 53.02584476
V396 Cas 4006-1219-1 9225 150 9.58 1.82 1.85 0.08 0.06 1.661 0.279 348.3999133 56.7381106
PV Cas 4010-1411-1 10200 250 9.86 3.77 1.56 0.09 0.08 1.057 0.276 347.51073 59.2017072
MU Cas 4014-1119-1 14750 800 10.8 3.1 0.56 0.07 0.06 0.528 0.24 3.96483911 60.43156742
V459 Cas 4030-1001-1 9140 300 10.36 3.94 1.6 0.12 0.11 1.028 0.318 17.8746546 61.1466544
SZ CamddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 4068-1651-1 30320 150 6.93 3.57 1.25 0.03 0.03 1.578 0.484 61.95538446 62.33293757
WW Cam 4073-1191-1 8350 135 10.09 3.26 2.41 0.11 0.1 2.062 0.303 67.8553362 64.3626378
ZZ UMa 4144-0400-1 5960 70 9.83 1.74 5.27 0.15 0.14 5.638 0.469 157.5133057 61.81150639
WX Cep 4268-0138-1 8150 250 9 12.47 2.01 0.16 0.14 1.873 0.234 337.81577827 63.52265463
AH Cep 4273-0857-1 29900 1000 6.88 5.84 1.31 0.11 0.1 1.315 0.341 341.97059463 65.06216647
YZ Cas 4307-2167-1 10200 300 5.65 4.63 11.71 0.41 0.37 10.3 0.488 11.41282179 74.98807249
BF Dra 4435-1750-1 6360 150 9.76 1.42 2.9 0.16 0.13 2.77 0.224 282.74730236 69.88263435
UZ Dra 4444-1595-1 6200 100 9.6 4.95 5.55 0.24 0.23 5.206 0.253 291.4793554 68.9353192
EK Cep 4466-2120-1 9000 200 7.89 4.61 6.14 0.32 0.3 5.316 0.308 325.33960392 69.69280812
VZ Cep 4470-1334-1 6670 160 9.72 1.82 4.47 0.25 0.24 3.876 0.348 327.5463979 71.4439708
EY Cep 4521-0349-1 7090 150 9.81 0.77 3.37 0.16 0.15 2.957 0.314 55.0169708 81.0191858
AY Cam 4540-1742-1 7250 100 9.72 0.99 1.94 0.06 0.06 2.035 0.225 126.4657754 77.2185686
EI Cep 4599-0082-1 6750 100 7.61 1.93 5.32 0.2 0.17 5.066 0.243 322.11752646 76.40349679
GG Ori 4767-0857-1 9950 200 10.49 3.43 2.25 0.11 0.1 2.396 0.673 85.792592 0.687461
V530 Ori 4786-0571-1 5890 100 9.96 1.09 9.77 0.41 0.38 9.897 0.224 91.1408646 3.1976719
V501 Mon 4799-1943-1 7510 100 12.32 2.48 1.1 0.04 0.04 0.939 0.325 100.173871 1.111114
CoRoT 102918586 4800-1540-1 7400 90 12.43 0.99 1.03 0.03 0.03 0.513 0.443 102.226296 0.873125
HI Mon 4809-0245-1 29500 600 9.45 4.1 0.45 0.02 0.02 0.776 0.274 103.9544438 4.0432744
FS Mon 4825-2374-1 6715 100 9.68 2.17 3.13 0.1 0.1 2.937 0.261 111.1762621 5.1540478
VZ Hya 4874-0811-1 6645 150 9.06 0.8 6.95 0.35 0.32 6.936 0.235 127.9225553 6.31876784
IM Vir 4955-0912-1 5570 100 9.69 1.39 11.3 0.48 0.45 12.12 0.342 192.4112337 6.0791283
BH Vir 4968-0569-1 6100 100 9.68 1.81 6.46 0.28 0.27 6.306 0.296 209.60358735 1.66082075
EG Ser 5099-0149-1 9900 200 8.24 4.57 4.59 0.21 0.2 4.342 0.445 276.5091796 1.6809489
LL Aqr 5236-0883-1 6080 45 9.32 0.9 8.68 0.19 0.19 7.746 0.271 338.67563291 3.5994906
EF Aqr 5248-1030-1 6150 65 10.04 0.67 5.66 0.15 0.14 5.056 0.499 345.3295333 6.4375969
PV Pup 5422-3294-1 6920 300 6.93 85.13 11.98 1.49 1.28 11.969 0.334 116.36971411 14.68613454
GZ CMa 5965-0860-1 8800 350 7.98 2.25 3.5 0.32 0.28 3.36 0.311 109.08002714 16.71669043
SW CMa 5976-0630-1 8200 150 9.16 3.87 1.77 0.07 0.08 1.596 0.601 107.06348559 22.4403521
HW CMa 5976-1266-1 7700 150 9.18 2.14 3.21 0.15 0.14 3.056 0.305 107.0910854 22.4082975
HS Hya 6069-1131-1 6500 50 8.12 1.04 10.01 0.23 0.16 9.676 0.268 156.15319885 19.09248835
AK For 6446-0342-1 4690 100 9.36 5.68 30.65 1.88 1.8 32.222 0.247 52.34530926 24.10085907
V3903 Sgr 6843-0543-1 38000 1900 7.31 0.47 0.77 0.08 0.07 1.029 0.348 272.32374524 23.98839603
TZ For 7026-0633-1 5000 100 6.89 0.75 5.33 0.25 0.21 5.436 0.254 48.66705279 35.55766586
HD 187669 7443-0867-1 4330 70 8.88 1.13 1.64 0.07 0.07 1.467 0.549 298.0920162 32.5610378
PT Vel 7690-2859-1 9250 150 7.03 13.27 7.31 0.38 0.35 6.145 0.451 137.74049908 43.26748036
V4089 Sgr 7936-2270-1 8433 97 5.91 2.66 6.86 0.18 0.18 6.748 0.489 293.53535674 40.03463968
AI Phe 8032-0625-1 5010 120 8.6 0.52 5.98 0.31 0.3 5.938 0.238 17.39247871 46.26558121
V467 Vel 8151-1072-1 36200 2500 10.9 10.29 0.19 0.03 0.02 0.339 0.777 130.95325 46.125928
V636 Cen 8285-0847-1 5900 85 9.09 0.25 13.91 0.43 0.4 13.962 0.991 214.24130865 49.94510016
TV Nor 8322-0334-1 9120 150 9.06 1.99 3.55 0.13 0.12 3.389 0.33 241.0385217 51.5444425
GV Car 8627-1797-1 10100 300 8.91 2.72 2.19 0.17 0.13 2.075 0.325 166.387038 58.730517
SZ Cen 8676-2330-1 8100 300 8.59 17.76 1.94 0.18 0.16 1.769 0.263 207.646219 58.49919382
DW Car 8957-1314-1 27900 1000 9.85 3.76 0.39 0.03 0.03 0.423 0.432 160.79195 60.0365947
EM Car 8959-0569-1 34000 2000 8.52 0.99 0.47 0.06 0.05 0.464 0.232 168.0187762 61.0952586
V349 Ara 9038-0641-1 9074 200 8.58 3.91 1.7 0.09 0.09 1.6 0.392 249.8442192 60.9617075
UX MenddIdentified in Stassun & Torres (2016) as a known triple system; these are retained in the analysis in this paper but discussed separately in the text. 9378-0190-1 6200 100 8.24 1.15 9.91 0.39 0.38 9.718 0.214 82.51326739 76.24870878
RZ Cha 9422-0104-1 6450 150 8.09 0.68 5.61 0.28 0.28 5.685 0.259 160.60043486 82.0372742
TZ Men 9496-0590-1 10400 500 6.18 2.04 8.63 1.01 0.81 8.022 0.488 82.557857 84.78510291
Table 1: Eclipsing Binary and Gaia Data
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