The TESS Input Catalog and Candidate Target List

The TIC point source base catalog is constructed from the full 2MASS point source catalog (Skrutskie et al. 2006) of ∼470 × 10⁶ objects. Next, this catalog is cross-matched against the following catalogs: LAMOST-DR1 and DR3 (Luo et al. 2015), KIC+EPIC (Brown et al. 2011; Huber et al. 2016), RAVE DR4 and DR5 (Boeche et al. 2011; Kunder et al. 2017), APOGEE-1 and APOGEE-2 (Majewski et al. 2015; Zasowski et al. 2017), UCAC4 and UCAC5 (Zacharias et al. 2013, 2017), Tycho-2 (Høg et al. 2000), APASS-DR9 (Henden et al. 2009), hot-stuff-for-one-year (hereafter, HSOY; Altmann et al. 2017), Superblink (Lepine 2017), HERMES-TESS DR1 (Sharma et al. 2018), SPOCS (Brewer et al. 2016), Geneva-Copenhagen (Holmberg et al. 2009), Gaia-ESO (Gilmore et al. 2012), ALLWISE point sources (Wright et al. 2010), and Sloan Digital Sky Survey point sources (SDSS; Alam et al. 2015; Abolfathi et al. 2017; Blanton et al. 2017).

All coordinates are initially drawn from 2MASS. Those objects are cross-matched with Gaia DR1; the coordinates are updated to the Gaia values if a single match, or updated to the flux-weighted Gaia values if a multiple match (see Section 2.1.2). We keep the 2MASS coordinates otherwise. Additional sources originating from a few select small catalogs (e.g., the specially curated Cool Dwarf list) have their coordinates taken directly from those catalogs.

The proper motions and parallaxes for Tycho-2 stars from the Gaia DR1 catalog (de Bruijne 2012; Gaia Collaboration et al. 2016) have also been cross-matched using the 2MASS IDs provided in the Gaia source catalog, and the Gaia DR2 catalog will be cross-matched for future TIC releases. Cross matches are done directly with 2MASS IDs when possible. Otherwise, they are done via cone search, typically with a 10 arcsec search radius—and when possible, a comparison of magnitudes with a tolerance of 0.1 mag.

If entries in multiple proper motion catalogs are available for a given star, then we prioritize the proper motion measurements. We give first preference to those from the Tycho-Gaia Astrometric Solution (hereafter TGAS; Gaia Collaboration et al. 2016), then SUPERBLINK (Lépine & Gaidos 2011), then Tycho-2, then Hipparcos. We have chosen to rank Tycho-2 above Hipparcos because it has a significantly longer time baseline that can help to identify and remove binary motion contamination. SUPERBLINK was ranked above Tycho-2 and Hipparcos because it incorporates a similar ranking for the preference of proper motions using Tycho-2 and Hipparcos.

However, only a small subset of all stars in the TIC have proper motions available in the catalogs described above. To greatly increase the number of stars with proper motions, we include the catalogs UCAC4, UCAC5, and HSOY. We select from either UCAC4, UCAC5, or HSOY, depending on the value of the star's total proper motion. For stars with total proper motions less than 200 mas yr⁻¹, we use HSOY. For stars with total proper motions between 200 and 1800 mas yr⁻¹, we use UCAC5. For stars with total proper motions greater than 1800 mas yr⁻¹, we use UCAC4. This approach was adopted to: (1) use proper motions that incorporate Gaia DR1 for a large number of distant stars (HSOY, Altmann et al. 2017); (2) eliminate the large number of false-positive, high proper-motion stars in HSOY, which are not found in UCAC5; and (3) provide accurate proper motions for the high proper-motion stars, through the UCAC-provided correction catalog.(Zacharias et al. 2013).

Specially curated lists of objects (see Appendix E), such as stars from Hipparcos (Perryman et al. 1997), known cool dwarf stars (Muirhead et al. 2018), known planet hosts, hot subdwarfs, bright stars, and guest investigator targets, are added to the TIC and CTL. The stellar properties supplied by those specially curated lists supersede the default values in the TIC and CTL (see Appendix E for details), but their prioritizations for the transit search are calculated in the same manner as other targets.

Whenever a single match between a Gaia source and 2MASS source exists, we accept the match from the official Gaia DR-1 cross-match table (Gaia Collaboration et al. 2016). However, in many cases, multiple Gaia targets will match to a single 2MASS star. The procedure for identifying the most appropriate Gaia source associated with a single 2MASS source is as follows.

First, we store the flux-weighted mean of right ascension and declination for all Gaia sources matching to the parent star, and accept the weighted means as the stellar coordinates. We then store the flux-weighted mean of the angular distances between each of the matching Gaia sources, and adopt this as the error for the star's right ascension and declination. We do not simply adopt the flux-weighted positional error of an individual Gaia source because that would be unrealistically small. For example, if two equally bright sources are 1'' from a given 2MASS source, the positional error is not ≪1'' (as a flux-weighted combination of Gaia positional errors would imply), but rather 1''. We update the provenance flag for the positions identified in this way from tmass to tmmgaia. The Gaia ID assigned to the TIC star is chosen to be the brightest of the Gaia stars.

We update the Gaia magnitude by combining the fluxes of all matching Gaia stars. We use two provenance flags to differentiate between the original Gaia magnitude and the combined Gaia magnitude: tmgai and tmmga, respectively.

The extended source base catalog is the full 2MASS extended source catalog (Skrutskie et al. 2006). This base catalog is then positionally cross-matched with the ALLWISE extended source catalog (Wright et al. 2010) and the SDSS extended source catalog (Alam et al. 2015), and then merged with the point source catalog.

Early versions of the TIC (up to and including TIC-5) included the full SDSS extended source catalog as a part of the basis of the extended source catalog. However, we found that including the entire SDSS catalog also introduced a large number of artifacts around bright stars caused by diffraction spikes in the SDSS images. These artifacts contributed to source confusion, and led to duplicated bright objects in the flux contamination estimates. Therefore, we added SDSS-colors to 2MASS extended objects, but did not include any extended object from SDSS unless it is also in 2MASS.

The most basic quantity required for every TIC object, aside from its position, is its apparent magnitude in the TESS bandpass (see Sullivan et al. (2015) for a definition of the TESS bandpass and of the TESS photometric system), which we represent as $T$. We estimate $T$ using a set of empirical relations developed from PHOENIX stellar atmosphere models (Husser et al. 2016) to convert the available catalog magnitudes and colors to $T$ magnitudes. The relationships between $T$ and other magnitudes for stars with low surface gravities ($\mathrm{log}g$ < 3.0) and low metallicities ([Fe/H] < −0.5) can be quite different from those of near solar-metallicity dwarfs. Because dwarfs are the targets of greatest interest for TESS, we adopt a single set of relations, which are strictly valid for $\mathrm{log}g$ > 3 and [Fe/H] > −0.5. They are also strictly valid for stars with ${T}_{\mathrm{eff}}$ > 2800 K. We do apply the relations outside these ranges in order to ensure that every star in the TIC has an estimated $T$, but we note that the estimated $T$ are subject to larger errors in such cases.

For each of the color–$T$ relations, we have opted to define a single polynomial relation. As a result, the calibrated relationships have somewhat larger scatter than might otherwise be possible with a more complex relation, but the scatter is still usually smaller than the errors from the original photometric catalogs. Thus, we believe it is a worthwhile tradeoff for the sake of simplicity. The effects of reddening on $T$ are not currently included—many of the highest-priority TESS targets will be relatively nearby and should not experience much reddening—but are expected to be implemented in future versions of the TIC (see Section 4.3.5).

We first present the relations for point sources, then for extended objects, and finally we provide ancillary relations we developed for calculating other magnitudes, such as B and V. We note that, while most of the magnitude calculations are based on Gaia and 2MASS magnitudes, we exclude values from our calculations with the following 2MASS quality flags: X, U, F, E, and D. For the point sources, we report a set of preferred relations, in order of preference, followed by a set of fallback relations that we use for a small number of stars for which it is not possible to apply any of the preferred relations. Column 63 in the TIC specifies which relation was used for any given star (see Appendix A); these flag names are listed below, along with their associated relations.

Regarding the uncertainties in the TESS magnitudes, we have investigated the use of the full covariance matrix, but we find that those errors are typically small in comparison to the scatter of the calibrations. Thus, we believe it is more conservative to simply use the scatter provided with each of the relations below, added in quadrature to the errors propagated from the photometric uncertainties.

Finally, in a small number of cases where we are unable to calculate $T$, we arbitrarily assign a value of $T$ = 25. This is the case for only 645 objects in the TIC.

2.2.1.1. Point Sources, Preferred Relations

$T$ from Gaia photometry

gaiaj: T from G and J, valid for all [Fe/H] and $\mathrm{log}g$.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & G+0.00106{(G-J)}^{3}+0.01278{(G-J)}^{2}\\ & & -\ 0.46022(G-J)+0.0211\end{array}\end{eqnarray*}$$

with a scatter of 0.015 mag.

gaiah: T from G and H valid for [Fe/H] ≥ −0.5 and $\mathrm{log}g$ ≥ 3.0.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & G+0.00510{(G-H)}^{3}+0.02230{(G-H)}^{2}\\ & & -\ 0.38134(G-H)-0.0058\end{array}\end{eqnarray*}$$

valid for −0.3 ≤ G − H ≤ 2.3, with a scatter of 0.010 mag.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & G+0.01029{(G-H)}^{3}-0.06163{(G-H)}^{2}\\ & & -\ 0.31892(G-H)+0.2113\end{array}\end{eqnarray*}$$

valid for 2.3 < G − H ≤ 5.0, with a scatter of 0.014 mag.

gaiak: T from G and K_S valid for [Fe/H] ≥ −0.5 and $\mathrm{log}g$ ≥ 3.0.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & G+0.00942{(G-{K}_{S})}^{3}+0.00288* {(G-{K}_{S})}^{2}\\ & & -\ 0.35664(G-{K}_{S})+0.0125\end{array}\end{eqnarray*}$$

valid for −0.3 ≤ G − K_S ≤ 2.5, with a scatter of 0.010 mag.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & G+0.02925{(G-{K}_{S})}^{3}-0.29659{(G-{K}_{S})}^{2}\\ & & +\ 0.60877(G-{K}_{S})-0.8676\end{array}\end{eqnarray*}$$

valid for 2.5 < G − K_S ≤ 5.2, with a scatter of 0.019 mag.

gaiav: T from G and V valid for all [Fe/H] and $\mathrm{log}g$ ≤ 5.0.

$$\begin{eqnarray*}&&T=G-6.5(V-G)+0.031\end{eqnarray*}$$

valid for 0.0 ≤ V − G < 0.02, with a scatter of 0.054 mag.

$$\begin{eqnarray*}&&T=G+6.04460{(V-G)}^{2}-3.64200(V-G)-0.0336\end{eqnarray*}$$

valid for 0.02 ≤ V − G ≤ 0.2, with a scatter of 0.018 mag.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & G-0.11179{(V-G)}^{3}+0.57748{(V-G)}^{2}\\ & & -\ 1.28108(V-G)-0.3173\end{array}\end{eqnarray*}$$

valid for 0.2 < V − G ≤ 2.8, with a scatter of 0.015 mag.

T from 2MASS photometry

The following relations are valid for stars with −0.1 < J − K_S < 1.0. In all cases, the J and K_S magnitudes are taken from 2MASS.

vjk: $T$ from V, J, and K_S:

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J+0.00152\ {(V-{K}_{S})}^{3}-0.01862\ {(V-{K}_{S})}^{2}\\ & & +\ 0.38523\ (V-{K}_{S})+0.0293,\end{array}\end{eqnarray*}$$

where the scatter of the calibration is 0.021 mag. In this relation, the V magnitude might be taken from APASS, or calculated from the Tycho-2 B_T magnitude (see below).

bpjk: $T$ from B_ph, J, and K_S, where B_ph is a photographic B magnitude (from 2MASS via USNO A2.0):

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J+0.00178\ {({B}_{\mathrm{ph}}-{K}_{S})}^{3}-0.01780\ {({B}_{\mathrm{ph}}-{K}_{S})}^{2}\\ & & +\ 0.31926\ ({B}_{\mathrm{ph}}-{K}_{S})+0.0381,\end{array}\end{eqnarray*}$$

where the scatter is 0.020 mag.

bjk: $T$ from B, J, and K_S, where B is a Johnson magnitude:

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J+0.00226\ {(B-{K}_{S})}^{3}-0.02313\ {(B-{K}_{S})}^{2}\\ & & +\ 0.29688\ (B-{K}_{S})+0.0407,\end{array}\end{eqnarray*}$$

where the scatter is 0.031 mag. In this relation, the B magnitude might be taken from any of several catalogs.

The following relations are used when there are no Johnson V, Johnson B, or photographic B_ph magnitudes available. In all cases, the J and K_S magnitudes are taken from 2MASS.

jk: $T$ from J and K_S.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J+1.22163\ {(J-{K}_{S})}^{3}-1.74299\ {(J-{K}_{S})}^{2}\\ & & +\ 1.89115\ (J-{K}_{S})+0.0563,\end{array}\end{eqnarray*}$$

valid for J − K_S ≤ 0.70, where the scatter is 0.080 mag.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J-269.372\ {(J-{K}_{S})}^{3}+668.453\ {(J-{K}_{S})}^{2}\\ & & -\ 545.64\ (J-{K}_{S})+147.811,\end{array}\end{eqnarray*}$$

valid for J − K_S > 0.70, where the scatter is 0.17 mag.

There are some stars for which the J − K_S colors are too blue or too red to determine a reliable $T$ from the above relations. For these stars, we use:

joffset: $T$ for J − K_S < −0.1:

$$\begin{eqnarray*}&&T=J+0.5\,(\pm 0.8\,\mathrm{mag}).\end{eqnarray*}$$

joffset2: $T$ for J − K_S > 1.0:

$$\begin{eqnarray*}&&T=J+1.75\,(\pm 1.0\,\mathrm{mag}).\end{eqnarray*}$$

2.2.1.2. Point Sources, Fallback Relations

For a small subset of point sources in the TIC, we have only a few magnitudes listed with passing quality flags from the available catalogs. For these, we adopt the following relations, if needed.

vjh: $T$ from V, J, and H (no K_S available):

$$\begin{eqnarray*}\begin{array}{rcl}T & = & V-0.28408\ {(J-H)}^{3}+0.75955\ {(J-H)}^{2}\\ & & -\ 1.96827\ (J-H)-0.1140\end{array}\end{eqnarray*}$$

where the scatter is 0.063 mag.

jh: $T$ from J, and H (no V or K_S available):

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J-0.99995\ {(J-H)}^{3}-1.49220\ {(J-H)}^{2}\\ & & +\ 1.93384\ (J-H)+0.1561\end{array}\end{eqnarray*}$$

where the scatter is 0.040 mag.

Finally, for faint stars for which only one magnitude is valid, the best we can do to compute $T$ is to apply a simple offset from the one available magnitude. We wish to estimate a $T$ magnitude in these cases, even if only crudely, because we wish to include all known objects in the sky as part of our flux contamination calculations (see Section 3.3.3). Because we rely on a specially curated cool-dwarf catalog to identify faint, cool objects that are known to be bona fide M dwarfs, here we use models to compute $T$ only for ${T}_{\mathrm{eff}}$ > 3840 K. The uncertainties are representative of the spread for a range of ${T}_{\mathrm{eff}}$, and the numerical value is an average.

gaiaoffset:

$$\begin{eqnarray*}&&T=G-0.5\,(\pm 0.6\,\mathrm{mag}),\end{eqnarray*}$$

voffset:

$$\begin{eqnarray*}&&T=V-0.6\,(\pm 0.9\,\mathrm{mag}),\end{eqnarray*}$$

joffset:

$$\begin{eqnarray*}&&T=J+0.5\,(\pm 0.8\,\mathrm{mag}),\end{eqnarray*}$$

hoffset:

$$\begin{eqnarray*}&&T=H+0.7\,(\pm 1.3\,\mathrm{mag}),\end{eqnarray*}$$

koffset:

$$\begin{eqnarray*}&&T={K}_{S}+0.8\,(\pm 1.4\,\mathrm{mag}).\end{eqnarray*}$$

2.2.1.3. Extended Objects

jk: $T$ from J and K_S.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J+1.22163\ {(J-{K}_{S})}^{3}-1.74299\ {(J-{K}_{S})}^{2}\\ & & +\ 1.89115\ (J-{K}_{S})+0.0563,\end{array}\end{eqnarray*}$$

valid for J − K_S ≤ 0.70, where the scatter is 0.080 mag.

$$\begin{eqnarray*}\begin{array}{rcl}T & = & J-269.372\ {(J-{K}_{S})}^{3}+668.453\ {(J-{K}_{S})}^{2}\\ & & -\ 545.64\ (J-{K}_{S})+147.811,\end{array}\end{eqnarray*}$$

valid for J − K_S > 0.70, where the scatter is 0.17 mag. It should be noted that, because these relations were derived from models for dwarf stars, the errors will typically be larger than the formal scatter when they are applied to extended objects.

SDSS $T$ from SDSS g and i (for 2MASS extended sources lacking good 2MASS photometry):

$$\begin{eqnarray*}\begin{array}{rcl}T & = & i-0.00206\ {(g-i)}^{3}-0.02370\ {(g-i)}^{2}\\ & & +\ 0.00573\ (g-i)-0.3078,\end{array}\end{eqnarray*}$$

where the scatter is 0.030 mag. If an SDSS extended source was found to have an unreasonable $T$ magnitude (T ∉ [−5, 25]), then if g = 30, signifying a failure in measuring an SDSS magnitude, and noti = 30, we adopt T = i − 0.5 (±1.0 mag). If $g\ne 30$ and i = 30, then we adopt T = g − 1 (±1.0 mag).

In order of preference, we adopt high-confidence V magnitudes from Mermilliod that we used for deriving the relation V(G–K), then Hipparcos V, then third-order and linear fits for V(V_T, B_T), then the CCD-based magnitudes listed in the UCAC4 catalog (which are not far from Johnson V; see Figure 3), unless they were flagged as unreliable (i.e., if the "number of images" used is reported as zero), then from APASS DR9, and finally secondary sources, such as those calculated from G − K_s or 2MASS colors only. For V from Hipparcos, Tycho2, UCAC4, and APASS, we compute the Gaia-based V(G − K_s) and compare it to the V reported in the catalog. We accept the catalog value if the difference is less than 0.5 mag, otherwise we assume a bad measurement and use V(G − K_s) as a valid V magnitude. In all cases, whether the V magnitude is observed or calculated from one of the following relations, we convert the adopted V magnitudes to Johnson V using standard conversion relations. Catalog flags that define the source of each magnitude are currently not provided by the TIC schema, but may be provided in future versions.

2.2.2.1. V Magnitude from G

In many cases, we found the observed V magnitudes for bright stars to be discrepant by >2% between catalogs. Therefore, we elected to calculate a Johnson V magnitude using magnitudes from the two largest catalogs in the TIC, Gaia DR1 and 2MASS (see Figure 2). The relations for dwarfs and sub-giants were created by comparing Johnson V magnitudes measured in Mermilliod (1987) with G − K_S color, using 2015 dwarfs and sub-giants within 100 pc and with photometric errors in V of σ_V < 0.1. The relation for giants was created comparing APASS DR9 Johnson V magnitudes with G − K_S color, using 13,580 giants within 400 pc, and with photometric errors in V of σ_V < 0.1. For stars that were used as part of determining these relations, we adopted the V magnitudes from Mermilliod (1987) or APASS DR9 regardless of the prioritization above, for consistency. In both cases, 2.5σ clipping was used to create the fit.

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For dwarfs, the following is adopted for 0.0 < G − K_S < 2.75, with scatter of 0.019:

$$\begin{eqnarray*}\begin{array}{rcl}V & = & G-0.0598208+0.2212224(G-{K}_{S})\\ & & -\ 0.0705395{(G-{K}_{S})}^{2}+0.0363978{(G-{K}_{S})}^{3}.\end{array}\end{eqnarray*}$$

For giants, the relation for dwarfs is adopted when 0.0 < (G − K_S) < 1.45. For 1.45 < G − K_S < 3.7, the following is adopted, with scatter of 0.035:

$$\begin{eqnarray*}\begin{array}{rcl}V & = & G+0.4710164-0.5313155(G-{K}_{S})\\ & & +\ 0.2883704{(G-{K}_{S})}^{2}-0.0274133{(G-{K}_{S})}^{3}.\end{array}\end{eqnarray*}$$

2.2.2.2. V Magnitude from UCAC4

In the case of the UCAC4 aperture magnitudes, there appears to be no published conversion to Johnson V, so we developed our own (shown in Figure 3), based on ∼40,000 stars that we cross-matched between UCAC4, APASS, and 2MASS. The relation is defined as:

$$\begin{eqnarray*}&&V=A-0.09+0.144(A-{K}_{S})\end{eqnarray*}$$

where A is the UCAC4 aperture magnitude and K_S is from 2MASS.

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2.2.2.3. V Magnitudes from Secondary Sources

Johnson B magnitudes are calculated for populating the B magnitude column of the TIC and for ensuring all magnitudes provided in the TIC are on the same photometric system, similar to what is done for the V magnitude calculations above.

• 1.  
  Johnson B magnitude from photographic B_ph and J:

  $$\begin{eqnarray*}\begin{array}{rcl}J & = & {B}_{\mathrm{ph}}-0.00526\ {X}^{3}+0.03256\ {X}^{2}\\ & & +\ 0.14101\ X-0.0149,\end{array}\end{eqnarray*}$$

  where X = B_ph − J. While the overall scatter of the calibration is 0.060 mag, it is better for small X and much worse for large X. Therefore, when propagating errors and adding the scatter of the calibration in quadrature, 0.035 mag should be added to the scatter if X < 3.5, and 0.16 mag if X > 3.5.

The photometric errors for photographic magnitudes in 2MASS come from the USNO-A2.0 catalog. Based on that catalog's description,²⁰ the errors in the photographic B magnitudes are expected to be ∼0.3 mag in the equatorial north and ∼0.5 mag in the equatorial south.

In this section, we describe the methods used to determine ${T}_{\mathrm{eff}}$ for stars in the TIC. Some stars in the TIC have spectroscopically derived ${T}_{\mathrm{eff}}$ values in the literature, and we use these where available. Specifically, we have ingested several large spectroscopic catalogs, and we adopt the spectroscopic ${T}_{\mathrm{eff}}$ if the reported error is less than 300 K, giving preference to the catalogs in the priority order listed in Table 1. Additionally, the proper calculation of parameters such as ${T}_{\mathrm{eff}}$ for cool dwarf stars (${T}_{\mathrm{eff}}$ < 3840 K) is typically very difficult when using ensemble dwarf relations, like we do in this section. Therefore, a specially curated list of cool dwarf stars was created to calculate these parameters; a brief explanation of the techniques used is provided in Appendix E.1.1, but we direct the reader to Muirhead et al. (2018) for more details.

However, the majority of TIC stars do not have spectroscopic ${T}_{\mathrm{eff}}$ values available. Therefore, we have developed a procedure to estimate ${T}_{\mathrm{eff}}$ based on empirical relationships of stellar V − K_S color. Because 2MASS is the base catalog for the TIC, we have a K_S magnitude for nearly every object (though to reiterate, we do not use 2MASS photometry whose quality flags are any of X, U, F, E, or D).

The relation for stars that are not identified as giants (see Section 3.2) is in two pieces:

• 1.  
  For V − K_S in the range [−0.10, 5.05] and [Fe/H] in the range [−0.9, +0.4], we use the AFGKM relation from Huang et al. (2015):

  $$\begin{eqnarray*}\begin{array}{rcl}X & = & V-{K}_{S}\,(\mathrm{de} \mbox{-} \mathrm{reddened})\\ Y & = & [\mathrm{Fe}/{\rm{H}}]\\ \theta & = & 0.54042\,+\,0.23676X-0.00796{X}^{2}\\ & & -\ 0.03798{XY}+0.05413Y-0.00448{Y}^{2}\\ {T}_{\mathrm{eff}} & = & 5040/\theta .\end{array}\end{eqnarray*}$$

  The scatter of this calibration is 2% in ${T}_{\mathrm{eff}}$, which should be added in quadrature to whatever errors come from photometric uncertainties propagated through the above equation.
• 2.  
  For redder V − K_S values in the range [5.05, 8.468], use the relation from Casagrande et al. (2008), shifted by +205.26 K to meet with the Huang et al. (2015) relation at V − K_S = 5.05:

  $$\begin{eqnarray*}\begin{array}{rcl}X & = & V-{K}_{S}\,(\mathrm{de}-\mathrm{reddened})\\ \theta & = & -0.4809+0.8009X-0.1039{X}^{2}+0.0056{X}^{3}\\ {T}_{\mathrm{eff}} & = & 5040/\theta +205.26\end{array}\end{eqnarray*}$$

  According to Casagrande et al. (2008), the scatter of this calibration is only 19 K, which should be added in quadrature to whatever errors come from photometric uncertainties propagated through the above equation. Note that this Casagrande et al. (2008) relation does not include metallicity terms, but those authors claim that the dependence on metallicity is weak for M stars with ${T}_{\mathrm{eff}}$ > 2800 K.

A number of previous studies have compared spectroscopic determinations of ${T}_{\mathrm{eff}}$ to photometric determinations (e.g., Gazzano et al. 2010; Guenther et al. 2012; Sebastian et al. 2012; Damiani et al. 2016), and generally find that the error of the photometric ${T}_{\mathrm{eff}}$ determination depends on the spectral type of the star. The scatter in the color–${T}_{\mathrm{eff}}$ relations noted above implicitly includes this ${T}_{\mathrm{eff}}$ dependence; the reported scatter is a percentage of ${T}_{\mathrm{eff}}$. For example, the formal ${T}_{\mathrm{eff}}$ error is 80 K at 4000 K, and it becomes 160 K at 8000 K.

Color-temperature relations can be especially challenging at cool ${T}_{\mathrm{eff}}$ because of the complexities of the spectral energy distributions of very cool stars. Determining a reliable ${T}_{\mathrm{eff}}$ is crucial to estimating the stellar radii, and thus equally so for estimating the sensitivity to small planets (see below). To validate the above relations at cool ${T}_{\mathrm{eff}}$, we compared the ${T}_{\mathrm{eff}}$ predicted by the relation to the ${T}_{\mathrm{eff}}$ supplied independently by the specially curated cool-dwarf list in the CTL (see Appendix E). The result of this comparison (Figure 4) indicates good agreement with no obvious systematics, except perhaps at the very coolest ${T}_{\mathrm{eff}}$ (V − K_S ≈ 7, ${T}_{\mathrm{eff}}$ ≲ 2600 K). To further verify the ${T}_{\mathrm{eff}}$ that we determine for M-dwarf stars, we compared our calculated ${T}_{\mathrm{eff}}$ with the values in the specially curated cool-dwarf list (see Appendix E, and Muirhead et al. 2018). As shown in Figure 4, the ${T}_{\mathrm{eff}}$ independently determined from the cool-dwarf list closely follows the color-based ${T}_{\mathrm{eff}}$ relation described above, and we find a mean difference of only −19 ± 63 K.

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Finally, for completeness, we provide a similar relation for red giants, also from Huang et al. (2015):

$$\begin{eqnarray*}\begin{array}{rcl}X & = & V-{K}_{S},Y=[\mathrm{Fe}/{\rm{H}}]\\ \theta & = & 0.46447\,+\,0.30156\ X-0.01918\ {X}^{2}\\ & & -\ 0.02526\ X\ Y\,+\,0.06132\ Y-0.04036\ {Y}^{2}\\ {T}_{\mathrm{eff}}({\rm{K}}) & = & 5040/\theta ,\end{array}\end{eqnarray*}$$

which is valid for V − K_S in the range [1.99, 6.09] and [Fe/H] in the range [−0.6, +0.3]. The scatter in ${T}_{\mathrm{eff}}$ is 1.7% (Huang et al. 2015).

The above expressions provide a continuous color–${T}_{\mathrm{eff}}$ relation from 2444 to 9755 K. For stars with V − K_S outside the above ranges of validity, the TIC reports ${T}_{\mathrm{eff}}$ = Null. For stars that are deemed likely to be non-giants according to our reduced-proper-motion (RPM) procedure (see Section 3.2), the ${T}_{\mathrm{eff}}$ is calculated with the above relations but using the dereddened V − K_S color (see Section 3.3.1 for the de-reddening procedure). In general, we do not calculate the ${T}_{\mathrm{eff}}$ for giants using a dereddened color because we only apply our de-reddening procedure for stars identified as dwarfs, which are the stars most likely to be included in the transit candidate targeting list (see Section 3). We note, finally, that in order to be conservative, the final ${T}_{\mathrm{eff}}$ errors from the above polynomial relations include a 150 K contribution added in quadrature to the uncertainties from the photometric errors and the scatter of the calibrations.

Because we estimate stellar ${T}_{\mathrm{eff}}$ principally from empirical color relations, and especially because the favored relations involve the V − K_S color (Section 2.2.4), which is highly susceptible to reddening effects, it is necessary to deredden the colors used for ${T}_{\mathrm{eff}}$ estimation, as we now describe.

3.3.1.1. Basic Approach

Figure 9 (reproduced from Bessell & Brett 1988) shows that stars in the V − K_S versus J − H color–color plane bifurcate between dwarfs and giants at J − H ≈ 0.7. Any star with zero reddening should fall close to one of the two curves. Stars with reddened colors therefore will appear displaced from these curves along a reddening vector toward the upper right. Therefore, to deredden a star, we can move an observed star's colors backward along the reddening vector until it falls on one of the two curves. Note that we update the relation from Bessell & Brett (1988), which used V with JHK to a relation that uses V with 2MASS JHK_S.

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3.3.1.2. Reddening Vector

3.3.1.3. Dereddening Procedure

First, we fit the dwarf and giant sequences from Bessell & Brett (1988) with polynomial functions (Figure 10, green and red curves, respectively). For dwarf stars:

$$\begin{eqnarray*}\begin{array}{rcl}J-H & = & -0.048007+0.20983\ X+0.067020\ {X}^{2}\\ & & -\ 0.036222\ {X}^{3}+0.0049886\ {X}^{4}-0.00021864\ {X}^{5},\end{array}\end{eqnarray*}$$

where X = V − K_S. For giant stars:

$$\begin{eqnarray*}\begin{array}{rcl}J-H & = & -0.033479+0.18300\ X+0.040622\ {X}^{2}\\ & & -\ 0.011824\ {X}^{3}+0.00071399\ {X}^{4},\end{array}\end{eqnarray*}$$

where X = V − K_S.

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Dereddening involves shifting the colors of a given star along the dereddening vector to one of the polynomial curves, or to a certain maximum if dereddening does not intersect one of the curves. Outside the Galactic plane ($| b| \gt 16^\circ$), we take E(B − V) from the Schlegel et al. (1998) dust maps as the maximum, while within the Galactic Plane, we arbitrarily adopt a maximum allowed E(B − V) = 1.5.

We consider stars in the four regions of the color–color plane in Figure 10. In general, we shift the star along the dereddening vector until either: (i) the star intersects the dwarf sequence (green curve), or (ii) we take the tip or tail of the vector—whichever lies closest to one of the (dwarf or giant) sequences. Specifically, we treat their dereddening as follows, using examples of stars in each region.

• 1.  
  Star A: No dereddening applied, as this would only move the star farther away from the dwarf sequence. These stars are flagged as "nondered" in the CTL, and the adopted E(B − V) set to 0.
• 2.  
  Stars B and C: We shift the star along the dereddening vector until the star either: (i) intersects the dwarf sequence (green curve), (ii) reaches the maximum dereddening (see above), or (iii) reaches closest approach to the dwarf sequence (magenta dashed line). Star B is typical for stars outside the Galactic plane that consequently have small reddening values. Star C is an example of a star in the plane for which we therefore adopt a maximum E(B − V) = 1.5 (see above); in that case, we adopt the point at which it intersects the dwarf sequence (marked by a dot). These stars are flagged as "dered" in the CTL, and the adopted E(B − V) is recorded.
• 3.  
  Stars D and E: We shift the stars along the dereddening vector until the star either: (i) intersects either the dwarf or giant sequence (green or red curve), (ii) reaches the maximum possible dereddening, or (iii) reaches the closest approach to one of the sequences (magenta dashed lines). The vector for star D crosses the dwarf/giant sequences four times; in such cases, we store all values (indicated by blue dots) but adopt the smallest reddening value. Star E is an example where the vector crosses neither the dwarf nor giant sequence; in these cases, we instead adopt the value of the closest distance (magenta dashed line) between the dereddening vector and the giants sequence as indicated by the blue dot. These stars are flagged as "dered" in the CTL, and the adopted E(B − V) is recorded.
• 4.  
  For stars earlier than M-type (V − K_S ≤ 2.2241) or within the typical J − H error (0.05 mag) of the dwarf relation (green curve in Figure 10), we assume zero reddening. These stars have been flagged with "dered0" in the CTL, and the adopted E(B − V) set to 0.

Once dereddened as described here, the colors are used to determine an updated ${T}_{\mathrm{eff}}$, following the procedures described in Section 2.2.4. In cases where the reddening cannot be determined (i.e., dereddening would move the star to a region of color space beyond the range of applicability of our color–${T}_{\mathrm{eff}}$ relations), no dereddening is attempted and the star is excluded from the CTL. Effective temperatures included in a specially curated target list supersede temperatures derived by this method.

We have compared our photometrically estimated ${T}_{\mathrm{eff}}$ values to the spectroscopically determined values from the LAMOST survey, which provides ${T}_{\mathrm{eff}}$ estimates for AFGK stars (${T}_{\mathrm{eff}}$ ≳ 3850 K) as both a general check on our ${T}_{\mathrm{eff}}$ estimates and a specific check on the dereddening procedure. We did this comparison for two different photometric dereddening techniques: (1) the scheme described above; and (2) using a 3D Galactic dust model from Bovy et al. (2016), through which we iteratively estimate the distance on the assumption that the star is a main sequence star. The latter procedure was examined because the Schlegel et al. (1998) maps do not provide reliable maximum line-of-sight extinctions within 15° of the Galactic plane, nor do they contain information about the relative amounts of extinction along the line of sight (i.e., they are not 3D). Figure 11 shows the results of these comparisons for the LAMOST spectroscopic sample.

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We find that the method of moving stars in the J − H versus V − K_S plane shows results similar to the 3D dereddening approach outside of the plane (differences relative to LAMOST of −64 ± 115 K, compared to −104 ± 119 K) and inside the plane (178 ± 370 K compared to −157 ± 337 K). This difference is not large, and because the computational effort required for the 3D approach is enormous for the many millions of stars in the CTL, we adopt the method of dereddening the stars in the J − H versus V − K_S plane.

Finally, to provide a sense for the typical range of extinctions for the distances probed by the CTL, Figure 12 shows our derived extinctions versus distance from Gaia for representative CTL stars.

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In order to prioritize the stars based on the ability of TESS to observe transits by Earth-size planets (see Section 3.4), it is essential to estimate the stellar radii and masses. When available, we simply adopt the radii and masses from the specially curated catalogs (Appendix E), such as those provided in the cool-dwarf list. These values are always accepted as the best representation of the true parameters and are given preference over any other values in the TIC. When such specially curated information is not available, we use the procedures described below to calculate each parameter, in order of preference. Note that this approach does introduce heterogeneity in the stellar mass and radius scales, especially as a function of ${T}_{\mathrm{eff}}$. However, we have opted for this approach in order to utilize the best available information wherever possible.

3.3.2.1. Stars with Parallax

When a parallax is available, we calculate the radius from the Stefan–Boltzmann equation, as follows. We first calculate the V-band bolometric correction, BC_V, using a polynomial formulation by Flower (1996), which is purely empirical and has been found to work reasonably well for solar-type and hotter stars. (The choice to use the V-band was driven by the availability of bolometric corrections over the widest possible range of ${T}_{\mathrm{eff}}$.) The coefficients for three different ${T}_{\mathrm{eff}}$ ranges are shown in Table 3 (see Torres 2010), where BC_V = a + b log T_eff + c (log T_eff)² + d (log T_eff)³ + e (log T_eff)⁴ + f (log T_eff)⁵. We add the following offsets to the above polynomial relations to make the three ${T}_{\mathrm{eff}}$ ranges meet smoothly: For log ${T}_{\mathrm{eff}}$ < 3.7, add −0.022 mag to the polynomial result; for 3.7 ≤ log ${T}_{\mathrm{eff}}$ < 3.9, no offset; and for log ${T}_{\mathrm{eff}}$ ≥ 3.9, add −0.003 mag to the polynomial result.

Table 3.  BC_V Relation Coefficients Adopted from Flower (1996)

	Cool Regime	Middle Regime	Hot Regime
	log ${T}_{\mathrm{eff}}$ < 3.7	3.7 ≤ log ${T}_{\mathrm{eff}}$ < 3.9	log ${T}_{\mathrm{eff}}$ ≥ 3.9
a	−0.190537291496456d+05	−0.370510203809015d+05	−0.118115450538963d+06
b	+0.155144866764412d+05	+0.385672629965804d+05	+0.137145973583929d+06
c	−0.421278819301717d+04	−0.150651486316025d+05	−0.636233812100225d+05
d	+0.381476328422343d+03	+0.261724637119416d+04	+0.147412923562646d+05
e	⋯	−0.170623810323864d+03	−0.170587278406872d+04
f	⋯	⋯	+0.788731721804990d+02

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With BC_V in hand, we next calculate the bolometric luminosity, ${L}_{\mathrm{bol}}$, as follows.

• 1.  
  Correct the apparent V magnitude for extinction (A_V): V₀ = V − A_V.
• 2.  
  Calculate absolute V-band magnitude: M_V = V₀ − 10 + 5 log π, where π is the parallax in milli-arcseconds.
• 3.  
  Compute the absolute bolometric magnitude: M_bol = M_V + BC_V.
• 4.  
  Compute the bolometric luminosity in solar units: log L/L_⊙ = −0.4 (M_bol − M_bol,⊙), where M_bol,⊙ ≡ 4.782.²¹

The final formula for ${L}_{\mathrm{bol}}$ is therefore: log L/L_⊙ = −0.4 (V − A_V − 10 + 5 log π + BC_V − 4.782).

Next, we calculate the radius from ${T}_{\mathrm{eff}}$ and the Stefan–Boltzmann law using T_eff,⊙ ≡ 5772 K, as recommended by the IAU (2015 Resolution B3). The above methodology is valid for ${T}_{\mathrm{eff}}$ ≥ 4100 K. The stellar radii for cooler stars will be obtained using other methods, as described in Section 3.3.2.2.

To compute the error in the radius, we propagate the observational uncertainties for all of the above quantities. For the Gaia DR1 parallax, we have adopted as the total error a quadrature sum of the nominal uncertainty and 0.3 mas systematic error (Gaia Collaboration et al. 2016), to be conservative. For BC_V, we have chosen to add 0.10 mag in quadrature to the BC_V uncertainty that comes from the ${T}_{\mathrm{eff}}$ error via the Flower (1996) polynomials. The error in M_bol,⊙ is taken to be the estimated error in V_⊙, which is 0.02 mag.

Using the radius and stellar mass calculated as discussed below, we derive $\mathrm{log}g$. A $\mathrm{log}g$ derived from a known and measured parallax supersedes a spectroscopic $\mathrm{log}g$, and is reported in the CTL.

3.3.2.2. Stars without Parallax but with Spectroscopic Parameters

3.3.2.3. Stars with neither Spectroscopic Parameters nor a Parallax Available

When none of the above sources of stellar radii are available, we use a single relation to estimate the stellar radii as well as the masses for each quantity, based on ${T}_{\mathrm{eff}}$. These relations were derived from high-precision empirical measurements of masses and radii of eclipsing binaries (Torres et al. 2010), which in the case of the radii show relatively little scatter for hot and cool stars, but a considerably larger scatter for intermediate-temperature stars where subgiants are more common. However, the sample of eclipsing binaries in this regime was found to be sparse, and was therefore supplemented with simulations based on the TRILEGAL code (Girardi et al. 2005) to generate a population of stars that is complete in both mass and radius at a given ${T}_{\mathrm{eff}}$. The TRILEGAL sample was created using 12 representative sight lines at a Galactic longitude of 90° and Galactic latitudes between 30° and 85°. Each sight line covered 10 deg² and excluded binaries, which led to ∼390,000 objects brighter than $T$ = 20. We included both dwarfs and subgiants, because these are the largest sample populations in the TIC.

We drew spline curves through the middle of the distribution of points in the mass–temperature and radius–temperature diagrams, and also along the upper and lower envelopes (considering both the eclipsing binaries and the simulated stars from TRILEGAL), so as to provide a means to quantify the mass and radius uncertainties from their spread. The nodal points of these spline functions are provided in Tables 4 and 5, and the final relations are shown in Figure 13.

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Table 4.  Nodal Points of the ${T}_{\mathrm{eff}}$–radius Spline Relations

Type	${T}_{\mathrm{eff}}$ (K)	Mean Radius (${R}_{\odot }$)	Lower Radius Limit (${R}_{\odot }$)	Upper Radius Limit (${R}_{\odot }$)
O5	42000	11	9.0	14.2
B0	30000	6.2	5.12	8.0
B5	15200	3	2.38	4.3
B8	11400	2.6	1.83	4.39
A0	9790	2.4	1.66	4.54
A5	8180	2.1	1.53	4.45
F0	7300	1.8	1.40	4.32
F5	6650	1.55	1.23	4.2
G0	5940	1.2	1.00	4.0
G5	5560	1.05	0.90	3.84
K0	5150	0.9	0.79	3.67
K2	⋯	⋯	⋯	0.889/3.4
K5	4410	0.72	0.65	0.79
M0	3840	0.60	0.52	0.67
M2	3520	0.47	0.35	0.59
M5	3170	0.28	0.20	0.37

Note. The K2 spectral type has a discontinuity in the upper radius limit; see Figure 13.

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Table 5.  Nodal Points of the ${T}_{\mathrm{eff}}$–mass Spline Relations

Type	${T}_{\mathrm{eff}}$ (K)	Mean Mass (${M}_{\odot }$)	Lower Mass Limit (${M}_{\odot }$)	Upper Mass Limit (${M}_{\odot }$)
O5	42,000	40.0	36.0	44.0
B0	30,000	15.0	13.5	17.0
⋯	22,000	7.5	6.9	8.5
B5	15,200	4.4	3.95	5.0
B8	11,400	3.0	2.6	3.5
A0	9790	2.5	2.15	3.0
A5	8180	2.0	1.7	2.48
F0	7300	1.65	1.40	2.15
F5	6650	1.4	1.18	1.80
G0	5940	1.085	0.965	1.22
G5	5560	0.98	0.87	1.11
K0	5150	0.87	0.78	0.98
K5	4410	0.69	0.615	0.77
M0	3840	0.59	0.51	0.67
M2	3520	0.47	0.37	0.59
M5	3170	0.26	0.19	0.35

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In the range of ${T}_{\mathrm{eff}}$ occupied by significant numbers of subgiants, the asymmetric spread toward larger radii is very large, but it decreases sharply below about 4800 K (because for the age of the Milky Way, all stars at such cool ${T}_{\mathrm{eff}}$ are either main sequence dwarfs of very low mass or else evolved red giants of higher mass). It was found convenient to split the upper envelope of the radius–temperature relation into two regimes at 4800 K, which introduces a discontinuity that matches what is seen in Figure 13.

As discussed in Section 3.2, we find that our RPM_J-based procedure for removal of red giants does not effectively remove subgiants, and therefore the largest radius errors are for G-type stars because there are large numbers of G subgiants. On the other hand, because there are no cool subgiants, typical radius errors for cool stars are small, reflecting only the small spread on the main sequence. Radius errors are also small for hotter stars (A and F types), as mentioned before, because massive subgiants evolve extremely quickly through the Hertzsprung gap and there are few blue giants in the local neighborhood. As currently defined, the TIC (and therefore the CTL) permits only a single value for radius error or mass error; we are currently unable to supply asymmetric errors. Therefore, for the radius error, we adopt the average of the upper and lower asymmetric errors from Table 4, capped at 100% of the radius; for the mass error, we report the average of the upper and lower errors from Table 5, which is always smaller than 100% of the mass.

If a TESS target is blended with a foreground or background star, the flux from the nearby source will fall into the TESS aperture of the target star, decreasing the ability to detect transits of the target. We use the catalogs described in Section 2.1 to identify all flux-contributing sources near each TESS target.

We identify all potential point-source contaminants for each TESS target, down to the limiting magnitudes of APASS and 2MASS ($T$ ∼ 17–19), and we calculate the fraction of contaminating flux in the aperture for the TESS target. That calculation relies on: (1) the distance out to which a star might possibly contaminate a target, (2) the shape and size of the TESS PSF, and (3) the size and shape of the TESS aperture.

In order to calculate expected contamination ratios for TESS targets before the launch of the mission in a computationally practical manner, we made a set of assumptions for each of the quantities involved. For the maximum angular distance out to which a source might contribute contaminating flux, we adopted a distance of 10 TESS pixels. Although especially bright stars at larger distances will have wings of the PSF extending to distances significantly larger than that, their density on the sky is small.

For the shape and size of the TESS PSF, we used a preliminary empirical PSF determined by the TESS mission. Although the small focal ratio of the TESS optics means that there will be significant non-circularity of the PSF and focal plane distortions in the TESS images, the exact location of the targets on the TESS cameras was not known at the time of this writing. Therefore, we selected the empirical TESS PSF determined for the center of the TESS field of view, which generally represents the most compact PSF—and therefore also represents a lower limit of the rate of flux contamination for a given star. We have considered but ultimately declined to add the calculation of the flux contamination for other choices of assumed PSF size, for two reasons. First, the flux contamination calculation is by far the most computationally expensive operation in the creation of the catalog, and it is not feasible to do this calculation for multiple choices of assumed PSF size. Second, the precise PSF properties are in fact not yet determined sufficiently well from in-flight tests to warrant a more detailed treatment at this time.

We fit both a Moffat model and a 2D Gaussian model to the empirical PSF. While there is virtually no difference between the empirical PSF and the Moffat model in integrated flux, the relative errors reveal that the Gaussian model underestimates the total flux by 5%. However, because it does this both for the target and the nearby contaminating stars, the effect partially cancels out. The main difficulty with a 2D Moffat profile is that there is no analytical solution for the integral over the function, and we would have to integrate numerically—which requires considerable computing resources. Therefore, we select a circular 2D Gaussian model (see Figure 14).

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Just as the TESS PSF is not fully determined at this time, the size of the aperture used for a given TESS target is not known precisely. As TESS prepares to observe each sector, the mission will define the set of pixels to be acquired for each two-minute target. After those pixels are downloaded, the SPOC will determine the optimal pixels to be used from the downloaded pixel set for the mission-derived light curves. The size of the pixel set depends on the size and shape of the PSF, the brightness of the target star, the placement of the target star in the TESS field, and the location of nearby objects.

For the analysis here, the size of the aperture is adaptive based on the TESS magnitude of the star. We determine the radius of a circle around a given target for a given $T$, and then derive the side length of an enclosing square and the side length of an area-preserving square. Both are averaged, and this average is the size of the aperture. We calculate a given star's PSF using the formula below, requiring the PSF to be no smaller than one pixel and limiting the brightest stars to have a PSF size equal to that of a $T$ = 4 star:

$$\begin{eqnarray*}&&{N}_{\mathrm{pix}}={c}_{3}\,{T}^{3}+{c}_{2}\,{T}^{2}+{c}_{1}\,T+{c}_{0}\end{eqnarray*}$$

where c₃ = −0.2592, c₂ = 7.7410, c₁ = −77.7918, and c₀ = 274.2898.

We calculate the contamination ratio as the ratio of flux from nearby objects that falls in the aperture of the target star, divided by the target star flux in the aperture. The nominal parameters we adopt for these calculations are as follows:

• 1.  
  Pixel size: 20.25 arcsec.
• 2.  
  Contaminant search radius: 10 pixels.
• 3.  
  Standard deviation for the 2D Gaussian model: $\mathrm{FWHM}/(2\sqrt{2\mathrm{ln}2})$.

The flux contamination for ∼3.8 million stars in the CTL is shown in Figure 15.

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We have made a set of decisions to assemble comprehensive information about potential TESS targets, and also to construct the CTL with a goal of maximizing the detection of small planets. That process has led to a CTL that has a great deal of heterogeneity in the sources of star information, and in some places displays discontinuities in the distribution of stellar parameters.

A good example of such structure is shown in Figure 16. Here, we plot the priority of CTL stars versus stellar radius, portrayed in a heatmap with color indicating average contamination ratio in each two-dimensional bin. Overall, the highest-priority targets typically have small radii and relatively low contamination ratios. In the top panel, only stars outside the Galactic plane ($| b| \gt 15$°) are displayed; in the bottom panel, no such cut is imposed. Sharp vertical edges in the distributions are visible around R = 0.65 R_⊙ and R = 1.03 R_⊙. Those features are due to the elimination of stars with $T$ > 12 and ${T}_{\mathrm{eff}}$ > 5500 K, and $T$ > 13, except for those in special lists as described in Section 3.1. The bottom panel includes the stars near the Galactic plane. Because those stars had their priorities de-boosted, they show up below the existing population, with similar patterns.

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As described in Section 2.2.4, stars with valid V and K_S magnitudes from 2MASS should have a temperature calculated from the V − K_S color. While the final reported ${T}_{\mathrm{eff}}$ follows the preference order of (1) specially curated lists (Cool Dwarf and Hot Subdwarf), (2) spectroscopic ${T}_{\mathrm{eff}}$, (3) dereddened ${T}_{\mathrm{eff}}$, and (4) non-dereddened ${T}_{\mathrm{eff}}$, we expect ${T}_{\mathrm{eff}}$ to generally follow the trend of our initial V − K_S relation. Indeed, Figure 17 shows general agreement between the V − K_S color and the "best" selected ${T}_{\mathrm{eff}}$ using the order of precedence above.

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However, as also shown in Figure 17, there is a significant amount of structure present that cannot be explained by the V − K_S relation. This structure is the result of the combination of numerous selection criteria explained in previous sections, as well as the forced validity ranges of parameter calculations. Each feature is well-understood, as follows:

• 1.  
  Stars with V − K_S < −0.1 and ${T}_{\mathrm{eff}}$ > 3840 K. These stars either do not have valid V magnitudes or were too blue for the validity range of the V − K_S relation, so they were required to fall back to the (J − K_S)-to-${T}_{\mathrm{eff}}$ relation. Given that their V − K_S color is so blue and yet their ${T}_{\mathrm{eff}}$ is cool, this suggests either V or K_S are incorrect, due either to a mismatch or a problem with the original photometry. At present, we do not have a mechanism to flag such cases—the quality flags from the original photometric catalogs do not otherwise suggest problems—so we simply caution that such cases do occasionally make their way into the TIC despite our best efforts.
• 2.  
  The three populations with ${T}_{\mathrm{eff}}$ < 3840 K. These values come from the Cool Dwarf list and the variety of color relations used to determine ${T}_{\mathrm{eff}}$. See Muirhead et al. (2018) for more details.
• 3.  
  Stars just to the left and below the V − K_S relation. These temperatures come from spectroscopic sources and will generally follow the relation without exactly landing on it.
• 4.  
  Stars to the right and above the V − K_S relation. These temperatures come from the de-reddening routine—a star's effective temperature increases when dereddened.
• 5.  
  The jagged edges at 5500 and 4800 K. These result from the T < 13 and T < 12 limits imposed on the CTL.
• 6.  
  The jagged edge at ∼9800 K. This edge is the result of the limits on the de-reddening routine.
• 7.  
  Stars with ${T}_{\mathrm{eff}}$ > 10,000 K. These temperatures mainly come from spectroscopic values.

If we make a simple histogram of the ${T}_{\mathrm{eff}}$ values in the CTL, we also notice a significant deviation from a smooth distribution, as shown in Figure 18. There are four particularly noticeable features of the distribution: (1) the distribution of targets with ${T}_{\mathrm{eff}}$ < 4000; (2) the lack of targets with 5000 < ${T}_{\mathrm{eff}}$ < 4000 K, i.e., "missing" K dwarfs; (3) a peak and sharp drop near ${T}_{\mathrm{eff}}$ = 5500 K; and (4) a peak and smooth decline in the number of targets with ${T}_{\mathrm{eff}}$ > 5500 K.

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Features 1, 3, and 4 can be explained by the selection function of the CTL (Feature 2 is discussed in Section 4.2.3). The large distribution of targets with ${T}_{\mathrm{eff}}$ < 4000 K (1) comes from the specially curated Cool Dwarf list, as shown in the top part of Figure 19. The sharp drop-off of targets near ${T}_{\mathrm{eff}}$ = 5500 K is from the combination of magnitude limits of T < 12 for all stars with T > 5500 and T < 13 for ${T}_{\mathrm{eff}}$ < 3480 K. In fact, if we only display stars with T < 12, this feature disappears, as shown in the bottom panel of Figure 19.

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As noted above, the distribution of stellar temperatures in the CTL shows a "gap" among the K dwarfs (Figure 18). This may seem surprising, as K dwarfs are surely more abundant than G dwarfs. However, we have verified using a TRILEGAL population synthesis simulation (Figure 20) that this is mostly an expected consequence of the fact that we prioritize according to a combination of stellar brightness (brighter stars receive higher priority) and stellar radius (smaller stars receive higher priority). The G dwarfs benefit from the boost according to brightness, whereas M dwarfs benefit from the boost according to size, where we have intentionally inserted a specially curated sample of (generally faint) M dwarfs into the CTL. K dwarfs suffer in priority due to being relatively faint but not as small as M dwarfs.

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The TRILEGAL simulation does, nonetheless, predict somewhat more K dwarfs than we observe in the real CTL. Another important factor may be that the RPM cuts are more prone to fail for K dwarfs (because the RPM relation "flattens" out at colors corresponding to K stars, small errors in RPM can push a star above or below the cut). A similar effect was reported in the stellar properties for the EPIC (cf. Section 5.4 in Huber et al. 2016).

It is also especially worth noting the nature of the ${T}_{\mathrm{eff}}$ distribution in Figure 18 between the stars in the continuous viewing zone (CVZ) and elsewhere. The area outside the CVZs includes a set of early-type stars in the F and G regime, a smaller population of K dwarfs, and a large number of cool dwarfs in the late-K and early- to mid-M ranges. However, in the CVZs, there are simply not many late-type stars above the TESS detection limits, so the priority boost in those areas results in larger numbers of relatively fainter G stars. The sharp cutoff at 5500 K is an artifact of the cuts applied in selecting stars for the CTL.

Note that these features, which will complicate statistical analyses of the ensemble planet properties discovered by TESS, could in principle be ameliorated by different choices in the targeting strategy. However, as noted in the introduction, the primary purpose of TESS as defined by the mission is to maximize the discovery of small planets; statistical purity of the sample is a secondary consideration. Thus, certain features of the target sample, such as those discussed here, are likely to remain in future updates to the TIC and CTL.

Figure 21 shows the calculated mass and radius for the top ∼400,000 stars in the CTL. While the majority of CTL stars had their radii and masses calculated from the unified spline relations described above, there are a number of objects that had their parameters calculated from spectroscopy, from parallaxes, taken from the independent cool-dwarf list, or a combination of these methods. Therefore, Figure 21 shows a large number of stars with masses and radii from the spline relation but also shows a cloud of points around the relation. While there is a significant spread of radii and masses for a particular ${T}_{\mathrm{eff}}$, it is encouraging that in general the distribution of values is more or less centered on the ridge coming from our spline relation. Thus, a TIC/CTL user should expect to find stars with similar ${T}_{\mathrm{eff}}$ but differing radii or masses.

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One of the primary purposes of the TIC and CTL is to provide a list of the top 200,000–400,000 targets to be observed in the two-minute cadence. If we investigate the distribution of these targets in the celestial sphere, significant features begin to arise as shown in Figure 22.

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The most notable feature is the dearth of stars in the Galactic Plane. Because source confusion is large in the plane, we de-boosted stars that do not have spectroscopic ${T}_{\mathrm{eff}}$ or that are not included in any specially curated list. Second, there is a clear demarcation at about −35° in declination. This is due to the proper motions of the majority of TIC stars coming from the UCAC4/5 survey, which is based on the PPMXL catalog; as described above, this catalog is incomplete at these southern declinations.

Third, the stars in the ecliptic plane ($| \beta | \lt 6$) are bright stars with priorities set to 1. Finally, the two elliptical regions at the northern and southern ecliptic poles ($| \beta | \gt 78^\circ$) are the CVZs. Because the priority increases with ecliptic latitude, they are quite overdense compared to the rest of the sky.

So far, the prioritization of candidate transit targets has been based on estimates of the detectability of transits produced by small planets, as well as assumptions on the geometric parameters (e.g., stellar radius) and measurement noise (e.g., stellar brightness and flux contamination by neighbors). However, in principle it should be possible to also prioritize based on the likely photometric and/or radial-velocity quiescence of the star. Photometric noise from, e.g., magnetic activity could complicate the detection of small transit signals, whereas radial-velocity noise (e.g., "jitter") could complicate the confirmation of planets and the measurement of stellar masses. With regards to photometric noise, there are a number of long-term photometric monitoring campaigns of bright stars across the sky that could be used to obtain a measure (or at least an upper limit) on the amplitude of photometric variability. Surveys that could be utilized for this purpose include SuperWASP and KELT, as well as ASAS (Pojmanski 1997; Pepper et al. 2007, 2012; Smith & WASP Consortium 2014).

With regards to radial-velocity jitter, most RV surveys cover relatively few stars. However, in principle it would be possible to use a proxy such as stellar rotation, either spectroscopic (v sin i) or photometric (rotation period). For example, Vanderburg et al. (2016) give empirical relations linking radial velocity jitter to stellar rotation period as a function of stellar ${T}_{\mathrm{eff}}$.

We have determined stellar rotation periods and variability amplitudes for nearly the entire KELT data set (Oelkers et al. 2018). Because the KELT and TESS pixel scale, field of view, and depth are comparable (see Pepper et al. 2007, 2012), we anticipate that the KELT photometric variability measures may prove useful in further winnowing the CTL of stars that might otherwise be too photometrically or Doppler-noisy.

It is known that most stars are in gravitationally bound pairs or stellar systems of higher multiplicity (e.g., Duchêne & Kraus 2013). All-sky or wide-field catalogs of stars are often able to separately identify the individual stellar components of especially wide binary pairs, in which both stars are bright enough for detection, but generally are not able to resolve the components below a certain angular separation, nor detect fainter companions. Furthermore, even when all components in a multiple system are individually identified, it is typically not possible to reliably match the bound stars without good proper motion or other dynamical information. Therefore, we expect a large fraction of the stars in the TIC to represent blended, unresolved multiple stars.

Binarity and higher-order multiplicity affects the reliability and integrity of the TIC because an unresolved companion will cause the photometric magnitudes ascribed to a star to be incorrect, along with any derived stellar properties, such as ${T}_{\mathrm{eff}}$, mass, and radius. Furthermore, the presence of stellar companions specifically affects the suitability of a star as a TESS mission target, even if the stellar properties of the target star are correctly described. That can be caused by introducing signals that complicate or confuse the transit search, or by creating conditions that would not permit the presence of any planet that TESS is capable of detecting. In the first category, if a stellar companion is in orbit about the target with a period shorter than the TESS dwell time on the target and it happens to be eclipsing, the system can mimic the photometric signal of a transiting planet. That can happen if the companion is in a grazing orbit, or if the companion is a small enough star to create an eclipse comparable to the transit of a planet. Alternatively, if there is a planet transiting the target on a stable interior orbit, the photometric signal of the eclipsing companion can interfere with the ability to detect the transit signal. Furthermore, the presence of a luminous stellar companion unresolved from the target will dilute the photometric transit signal.

In the second category, the presence of a stellar companion indicates that there could not exist a planet in an orbit around the target star that TESS could detect, meaning that the target could potentially be excluded from the two-minute target list if the presence of the companion were known. In general, the presence of a stellar companion in an orbit of a given size will dynamically exclude planetary companions in a range of orbits (e.g., Kraus et al. 2016). Furthermore, a stellar companion with a short orbital period may indicate the absence of any circumbinary planets.

For those reasons, it would be advantageous to know about the existence of all stellar multiplicity for each potential target star. That information is generally not available, but will be critical for establishing the correct planetary radii (Ciardi et al. 2015; Bouma et al. 2018). We are endeavoring to obtain whatever information is available, through lists of known multiple systems from stellar spectroscopy that can identify single- and double-lined spectroscopic binaries, photometric surveys that can identify eclipsing systems, proper motion catalogs that can identify co-moving companions, and eventually time-series astrometric catalogs to identify astrometric binaries. However, we expect all such efforts to be quite incomplete due to various observational biases.

While beyond the scope of this paper, in principle one could attempt to estimate the fraction of binaries in the TIC and CTL by using empirical estimates of binarity as functions of spectral type and other factors. The study by Duquennoy & Mayor (1991) was concerned with solar-type stars; though we do have many solar-type dwarfs in the CTL, TESS emphasizes M-dwarfs as being more valuable targets, and those have a lower intrinsic binary frequency. Duchêne & Kraus (2013) provides a more updated and comprehensive view of the frequency of binaries. In lieu of performing such an analysis, we suggest that the CTL is likely missing essentially all physical binary companions, so the percentage of unknown binaries in the catalog should be essentially the same as the frequency of binaries of different spectral types as given by Duchêne & Kraus (2013).

Therefore, such information about stellar multiplicity will be primarily useful for the evaluation of TESS transit candidates after observations are taken, rather than usable for target selection during the prime mission. Indeed, our selection of targets independent of multiplicity considerations could well prove to be a major benefit for studying the effect of multiplicity on planet occurrence.

As mentioned in Section 2, it had been hoped from the start of planning for TESS target selection that the highly anticipated Gaia DR2 parallaxes might become available sufficiently in advance of TESS launch to be incorporated into the TIC. Unfortunately, the DR2 parallaxes did not become public until after launch, which necessitated creation of a TIC and CTL for use in the TESS Year 1 operations without the benefit of DR2 parallaxes. Nonetheless, we are now working to incorporate parallaxes and other information from Gaia DR2. We expect that the Gaia DR2 data set will be incorporated into the next version of the TIC before Year 2 of the mission when TESS observes the northern ecliptic sky.

There is at least one specific area in which the incorporation of the Gaia DR2 parallaxes could dramatically enhance target selection: elimination of subgiant contaminants. As discussed by Bastien et al. (2014) in the context of the bright Kepler targets, roughly half of the putative dwarf stars are in fact modestly evolved subgiants. Recent assessments of the full Kepler planet sample find subgiant contamination of ∼25% (Berger et al. 2018). In any event, the slightly lower $\mathrm{log}g$ of subgiants can be too subtle for discernment by photometric and even some spectroscopic methods. Moreover, as discussed above (Section 3.2), the RPM method that we employ to screen out giants is also ineffective at removing most subgiants. As laid out in Section 3.3.2, with an accurate parallax for most if not all TESS targets, we can accurately determine the stellar radius and thereby screen out subgiants with high fidelity. In the meantime, a large proportion of subgiant contaminants are to be expected among the putative dwarf stars in the CTL. We should note that such a step should only be undertaken after careful consideration, because there is also significant value specifically in detecting planets transiting subgiants, which are prime targets for asteroseismic studies (Campante et al. 2016).

Finally, with Gaia magnitudes available for virtually all stars in the TIC, it should be possible in principle to redetermine accurate $T$ magnitudes for all TIC stars.

In addition to the standard two-minute cadence of measurements for the primary 200,000–400,000 bright transiting planet candidates, TESS will provide FFIs with a cadence of 30 minutes. These FFIs can in principle be used to also identify planetary transits, and specialized pipelines for extracting precise light curves from the FFIs are available or in preparation (e.g., Lund et al. 2017; Oelkers & Stassun 2018). Thus, it may be beneficial to consider which types of transit hosts can be effectively studied at a 30 minute cadence so as to reserve as many two-minute slots for those types of systems that most require the higher cadence. Here, we consider two types of situations where such a consideration could lead to further optimization of the CTL.

4.3.4.1. Transits of M Dwarfs and White Dwarfs by Earth-sized Planets

4.3.4.2. Transits of Hot Subdwarfs and White Dwarfs by Earth-sized Planets

Hot subdwarfs and white dwarfs represent other potentially interesting classes of transiting planet host stars that, because of the small stellar radius, may require the two-minute cadence observations in at least a subset of cases. The respective transit durations of a 0.47 ${M}_{\odot }$ subdwarf star and a 0.64 ${M}_{\odot }$ white dwarf by a 1 ${R}_{\oplus }$ planet are shown in Figures 23 and 24, as a function of orbital period and the $\mathrm{log}g$ of the host star.

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In a future version of the TIC, we will need to account for the effects of reddening and extinction on $T$. The color relations we are using are derived from model atmospheres that assume the fluxes are not affected by extinction, which is not true in practice. We plan to overcome this approximation by correcting our V + JHK_S magnitudes for extinction and then, using the de-reddended fluxes, we will derive an extinction-free TESS magnitude with the previously described relations and coefficients. We will then apply the appropriate extinction for the TESS band to recover an "observed" TESS magnitude. Using the Cardelli et al. (1989) extinction law with a weighted mean wavelength for the passband and ignoring the spectrum of the star, we estimate A_T = 0.656 E(V − K_S), A_J = 0.325 E(V − K_S), and A_G = 0.901 E(V − K_S), where G is the Gaia magnitude we expect to incorporate into a future version of the TIC. The conversion from E(V − K_S) to E(B − V) can be made with E(B − V) = 0.372 E(V − K_S), and similarly E(G − J) = 0.576 E(V − K_S). For stars that do not have a reliable V magnitude, no extinction correction will be computed.

Figure 25 shows the expected differences between TESS magnitudes calculated without proper consideration of extinction and those with extinction accounted for, for extinction levels of A_V = 1 and A_V = 3. For most stars in the TIC experiencing modest extinction, the impact of not properly modeling the effect amounts to a systematic error of ∼0.1 mag for the coolest stars. However, for areas of high extinction, such as in the Galactic plane, the effect can be as large as several tenths of a magnitude for ${T}_{\mathrm{eff}}$ ≲ 4000 K.

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The Cool Dwarf list is a carefully vetted list of stellar parameters for K- and M-dwarf stars (${T}_{\mathrm{eff}}$ < 4000 K). We provide a basic overview of the catalog here, but direct the reader to Muirhead et al. (2018) for a more detailed discussion.

The catalog itself is created using the SUPERBLINK catalog, cross-matched with 2MASS and APASS. Dwarf stars are separated from giant stars using parallax measurements, when available, or the RPM criteria of Gaidos et al. (2014). ${T}_{\mathrm{eff}}$ is calculated from r − J, r − z, and V − J color, with an additional J − H term to account for systematic effects of [Fe/H]. For stars with trigonometric parallax, masses and radii are calculated using the ${M}_{{K}_{S}}-{R}_{* }$ relation from Benedict et al. (2016) and Mann et al. (2015) respectively. For stars without trigonometric parallax, radius and mass are calculated using the ${T}_{\mathrm{eff}}$–R_* relation from Mann et al. (2015) and a newly developed relation between ${T}_{\mathrm{eff}}$ and M_*.

The Cool Dwarf list is treated like an override catalog and the values provided replace default calculated values for T, ${T}_{\mathrm{eff}}$, stellar radius, and stellar mass. The catalog provides a value for V from the SUPERBLINK catalog, but these values do not override the V column in the TIC at this time.

The Bright Star list is a catalog of all (∼10,000) bright (T < 6) sources in the TIC. These objects are included in the CTL regardless of whether the star passes the RPM_J cut. We compared the list of bright TIC objects to the Yale Bright Star catalog (hereafter, YBC) (Hoffleit & Jaschek 1991) and found ∼80% of the YBC to be in our Bright Star list. Nearly ∼90% of objects that are in the YBC but missing from the Bright Star list are stars where V > 6 or V is not provided.

These stars have contamination calculated in the normal way. However, because many of these stars may not be typical dwarf stars (with 3850 < ${T}_{\mathrm{eff}}$ < 10,000), parameters such as radius and mass are not calculated unless that star already appears in the Cool Dwarf list or was previously identified as an RPM_J dwarf. Additionally, in TIC-7, these stars have an arbitrary priority value of 1, as their priorities could not be effectively calculated using the schema described in Section 3.4. We emphasize that this priority value of 1 is for identification purposes only and does not represent the true final prioritization of these targets.

The Hot Subdwarf list identifies all known evolved compact stars down to V ∼ 16. For the most part, they belong to the extreme horizontal branch and beyond (spectral types sdB, sdOB, and sdO; see Heber (2016)). The list is constructed from the Geier et al. (2017) catalog, completed with newly identified bright objects of the kind from recent or ongoing ground-based surveys carried out at the Steward Observatory (Green, priv. comm.), the NOT (Telting, priv. comm.), and the SAAO (Kilkenny, priv. comm.). The T_eff and log g values are evaluated from asteroseismology (Fontaine et al. 2012) or spectroscopy (Geier et al. 2017), or else they are given a representative value based on spectral classification if nothing else is available. Stellar mass is from asteroseismology when available (Fontaine et al. 2012). Otherwise, it is set to the canonical value of 0.47 M_⊙, considering that typical hot subdwarfs have a narrow mass distribution around that value. Radius is computed from log g and mass. $T$ is estimated from (V-$T$) and (J − $T$) color indices calculated from hot-subdwarf NLTE model atmospheres (interpolation in a T_eff − log g grid; Fontaine et al., priv. comm.). If both V and J measurements are available, the TESS magnitude is an average of the two; otherwise, transformation is from V-band only. The value of V is, by order of availability, from APASS_V or GSC_V. The J, H, and K values are, by order of availability, from 2MASS or UKIDSS. More information about each target can be found by any registered user on the TASC Working Group 8 wiki page at the URL https://tasoc.dk/wg8/.

The list of known exoplanet host stars continues to evolve because the number of known exoplanets is constantly being updated. The most frequently updated source of information regarding exoplanetary systems is the NASA Exoplanet Science Institute,²² which is described in more detail by Akeson et al. (2013). We extracted a subset of the data from this source for each star, including stellar coordinates, the number of planets, and fundamental stellar properties including effective temperature, mass, radius, log g, V mag, and v sin i. The stellar properties were checked with respect to the literature and updated where necessary. The final vetted list was then cross-matched with the TIC in order to include alias information and ancillary data, such as TESS magnitudes, resulting in a first version of the list containing ∼2800 exoplanet host stars.