Carnegie Supernova Project-II: Extending the Near-infrared Hubble Diagram for Type Ia Supernovae to z ∼ 0.1^∗

The primary goal of the CSP-II was to obtain optical and NIR light curves of a sample of at least 100 SNe Ia located in the smooth Hubble flow out to a redshift of z ∼ 0.1. These SNe, which comprise the CSP-II “Cosmology” subsample, were selected for photometric follow-up via the following criteria:

• Discovered before maximum light at optical wavelengths. One of the few disadvantages of observing SNe Ia in the NIR is that maximum brightness occurs 3–5 days before B maximum. Hence, to ensure that NIR photometry was obtained within a few days of NIR maximum, SNe discovered before optical maximum light were given highest priority for follow-up observations.
• Spectroscopically confirmed to be a normal SNe Ia.²⁷ Surveys such as the Sloan Digital Sky Survey-II Supernova Survey, the Supernova Legacy Survey (SNLS), and the Supernova Cosmology Project (SCP) have shown that combining magnitude and color information allows an “educated” guess to be made as to the SN type (Sako et al. 2011; Bazin et al. 2011; Suzuki et al. 2012). Nevertheless, spectroscopy is vital for confirmation purposes and determining the approximate light-curve phase, as well as for eventual sub-typing.
• Discovered preferably in an untargeted search. A weakness of the CSP-I SNe Ia sample is that nearly 90% of the events were found in targeted searches that are strongly biased toward luminous host galaxies (e.g., Kelly et al. 2010). Hence, for the CSP-II, preference was given to SNe Ia discovered in untargeted searches to ensure that the sample was as complete and unbiased as possible concerning host-galaxy type, luminosity, and metallicity.
• Host-galaxy redshift in the range 0.03 ≲ z ≲ 0.10. Many of the SNe Ia in the CSP-II Cosmology subsample appeared in host galaxies with cataloged redshifts. However, approximately one-third of the events were discovered in distant or low-luminosity hosts whose redshifts were unknown. In these cases, we relied on the redshift estimated from the classification spectrum with software tools such as SNID (Blondin & Tonry 2007), SUPERFIT (Howell et al. 2005), and GELATO (Harutyunyan et al. 2008) in deciding whether to obtain follow-up photometry. We have since obtained redshifts for nearly all of these host galaxies (see Section 3.6).

The 125 SNe Ia comprising the Cosmology subsample cover a redshift range of 0.027 < z < 0.137, with a median redshift of z = 0.056. Table 2 summarizes the various supernova surveys from which these SNe were drawn. Fully 96% came from untargeted searches, with nearly half (48%) of the subsample having been discovered by the La Silla-QUEST Low Redshift Supernova Survey (Baltay et al. 2013). The individual SNe belonging to the Cosmology subsample are identified in the final column of Table 1 by the letter “C”.

The top panel of Figure 2 shows a histogram of the heliocentric redshifts of the Cosmology subsample. The arrow indicates the median redshift of the CSP-I sample. In Figure 3, histograms of the epoch with respect to the date of B maximum of the first imaging observations in the optical and the NIR for the Cosmology subsample are displayed. As may be seen, optical imaging was obtained for half of the subsample at −4 days or earlier, and −2 days or earlier in the NIR.

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To realize the full potential of SNe Ia as distance indicators at NIR wavelengths, we must determine accurate K-corrections, which account for the effect of cosmological expansion upon the measured magnitudes (Oke & Sandage 1968). Poorly understood K-corrections directly impact the peak magnitudes of the SNe and inflate both statistical and systematic errors. Prior to the CSP-II, NIR spectra had been published for only 33 SNe Ia, with the total number of useful spectra amounting to 75. Boldt et al. (2014) used this sample to study the errors inherent in NIR K-corrections. Their main finding was that uncertainties due to the diversity of spectral features from object to object are the dominant source of error at maximum light. Boldt et al. demonstrated that, with the small number of spectra in hand, K-correction uncertainties in the Y, J, and H bands amounted to 0.04, 0.06, and 0.10 mag for a SN Ia at z = 0.08. For a sample of 59 spectra of 10 SNe Ia—35 spectra of which overlapped with the Boldt et al. sample—Stanishev et al. (2018) recently found somewhat smaller dispersions of 0.03 and 0.04 mag in the J and H K-corrections at z = 0.08. Much of the diversity in the spectral features is known to correlate with the light-curve decline rate (Hsiao 2009), but to quantify this requires a much larger NIR spectral sample.

To attack the NIR K-correction problem, the CSP-II, in conjunction with the Harvard Center for Astrophysics Supernova Group, initiated in 2012 a program of NIR spectroscopic observations of a large “Physics” subsample²⁸ of nearby SNe Ia at z ≤ 0.04. This collaboration is described in detail in an accompanying paper (Hsiao et al. 2018). In order to quantify the light-curve properties of this subsample, it was necessary to obtain optical imaging with a cadence and signal-to-noise ratio comparable to (or better than) that obtained for the Cosmology subsample. Although imaging in the NIR was not a requirement for the Physics subsample, it was nonetheless obtained for 89% of the SNe. The same basic criteria used for the Cosmology subsample were also applied in selecting the SNe to be included in the Physics subsample, although at these lower redshifts, a higher fraction (39%) of the events were discovered in targeted searches. The Physics subsample also includes several fast-declining, SN 1991bg-like (Filippenko et al. 1992a; Leibundgut et al. 1993; Ruiz-Lapuente et al. 1993) events that, because of their low luminosities, are not well represented in the Cosmology subsample.

A total of 90 SNe Ia with a median redshift of z = 0.021 comprise the Physics subsample. Table 3 provides information on the supernova surveys from which these SNe were drawn, and Table 1 lists the individual SNe (identified by the letter “P” in the final column). Their distribution as a function of redshift is plotted in the bottom panel of Figure 2. Note that there is some overlap between the Physics and Cosmology subsamples, with 21 of the SNe (23%) in the Physics subsample also forming part of the Cosmology subsample.

The La Silla-QUEST supernova survey was fundamental to the success of the CSP-II, contributing nearly half of the SNe Ia making up the Cosmology subsample. The LSQ subsample is particularly important because it was an untargeted search with homogeneous selection criteria. The recent dark energy analysis of the Pantheon sample of SNe Ia by Scolnic et al. (2018) found that systematic errors are still a serious problem, particularly in modeling the low-redshift sample because of the uncertainty of whether it is volume or magnitude limited. Calibration errors, which in the Pantheon sample are twice as large for the low-redshift events compared to the high-redshift SNe, also continue to be a significant additional source of systematic error. The LSQ subsample observed by the CSP-II addresses both of these issues.

The CSP-II obtained light curves of a total of 72 SNe Ia discovered by the LSQ survey, spanning a redshift range of 0.009 ≤ z ≤ 0.137. Preliminary photometry of 31 of these SNe was published by Walker et al. (2015). The LSQ subsample is identified in Table 1 by the letter “L” in the last column. Their redshift distribution is plotted in the middle panel of Figure 2. Note that 83% of the LSQ events are also members of the Cosmology subsample, and 13% overlap with the Physics subsample. NIR photometry was obtained for 85% of the LSQ subsample.

Table 1 also includes 11 SNe Ia for which photometric observations were obtained, but which do not fit into any of the three aforementioned subsamples. These objects are identified by a blank entry in the “Subsample” column of the table. All have redshifts too small (z ≤ 0.026) to be included in the Cosmology subsample, and as NIR spectroscopy was not obtained they do not qualify for the Physics subsample. However, the light curves for these SNe are still of value, and so we include them in the full sample of CSP-II SNe Ia.

The emphasis of the CSP-II was on observing the light curves and spectra of normal SNe Ia. Nevertheless, data were obtained for other types, including peculiar SNe Ia (five SN 2002cx-like events and four possible “super-Chandrasekhar” SNe), four super-luminous SNe, and several core-collapse and stripped core-collapse events. The CSP-II observations of these SNe will be presented in future papers.

As was the case for the CSP-I, nearly all of the optical imaging during the CSP-II was obtained with the LCO Swope telescope. Generally speaking, for redshifts less than ≲0.04, the same complement of ugriBV filters used by the CSP-I was also employed. For redshifts greater than this, a subset consisting of the BVri filters was normally used. Each SN was typically observed every 2–3 days from discovery until at least 2–3 weeks past maximum to sample the light-curve maxima and early decline rates as thoroughly as possible. Optical imaging of candidate SNe was often initiated before a classification spectrum was obtained. A quick reduction of the photometry was made the morning after each observation, allowing a nearly “real-time” update of the light curves on the CSP-II webpage, with the calibration improving as data were obtained on more photometric nights. If spectral observations subsequently showed that the target was not a SN Ia, we usually discontinued the optical imaging.

As was also done for the CSP-I, the LCO 2.5 m du Pont telescope was used to obtain most of the host-galaxy reference images in ugriBV. This telescope was also used to obtain a small amount of imaging of SNe being actively followed during scheduled nights.

SNe Ia are excellent standard candles in the NIR when observed at maximum light (e.g., Krisciunas et al. 2004a; Kattner et al. 2012). When combined with optical photometry, NIR observations at maximum also afford the most precise measurement of the host-galaxy dust reddening (Krisciunas et al. 2000; Mandel et al. 2011; Burns et al. 2014, 2018). While the strength of the prominent NIR secondary maximum is a strong function of the decline rate (Hamuy et al. 1996b), there is significant scatter in the correlation (Krisciunas et al. 2001; Burns et al. 2014). Hence, to ensure the highest precision for measuring both the host extinction and distance from optical and NIR observations, it is best that NIR photometry be obtained within ∼1 week of optical (B-band) maximum if at all possible (Krisciunas et al. 2004b). As shown in Figure 3, only a small fraction (11/125) of the SNe in the Cosmology subsample do not meet this condition.

The SNe in the CSP-I sample were sufficiently nearby and bright enough that all of the optical and most of the NIR imaging could be obtained with the Swope telescope. However, extending NIR observations to z ∼ 0.1 requires a larger telescope, and so a more economical approach was necessary for the CSP-II. We requested approximately one week of NIR imaging each bright run with the du Pont 2.5 m telescope during the CSP-II observing campaigns to cover the primary maxima of ∼5 SNe Ia per bright run. For SNe at z ≲ 0.07, imaging was generally obtained in the Y, J, and H bands, while for more distant targets, observations were typically restricted to the Y and J filters. In a few cases (<10%), only the Y filter was used. At least four epochs of NIR imaging were obtained for 66% of the SNe in the Cosmology subsample, and at least three epochs were obtained for 82%. Sparse sampling of the NIR maximum of SNe Ia has been successfully employed in the past by Krisciunas et al. (2004a); Freedman et al. (2009); Barone-Nugent et al. (2012), and Weyant et al. (2014, 2018).

Although most of the NIR photometry for the CSP-II was acquired with the du Pont telescope, we obtained a few epochs of additional imaging (1–2 epochs) with the LCO Magellan Baade 6.5 m telescope for nine SNe Ia. Many of the NIR host-galaxy images were also acquired with Magellan Baade.

Optical spectroscopy near maximum light provides an essential tool for characterizing the diversity of SNe Ia which, in turn, is related to the progenitor systems and explosion mechanism (e.g., Blondin et al. 2012; Folatelli et al. 2013). In total, 308 optical spectra were obtained of more than 100 of the SNe Ia in the Cosmology and Physics subsamples. These spectra were acquired with the du Pont and Magellan telescopes at LCO and with the 2.5 m Nordic Optical Telescope (NOT) at the Observatorio del Roque de los Muchachos with the principal aim of determining the type, phase, and approximate redshift of the SN targets. Through these observations and the NIR spectroscopy described in Section 3.5 and Hsiao et al. (2018), the CSP-II was able to classify ∼20% of the SNe in both the Cosmology and Physics subsamples (listed as “CSP” in the Classification column of Table 1). Many of the remaining targets were classified by the Public ESO Spectroscopic Survey of Transient Objects (PESSTO) with the ESO La Silla 3.6 m NTT (Smartt et al. 2015). With the CSP-II, PESSTO, and other publicly available spectra, 114 of the SNe in the Cosmology and Physics subsamples were observed within ±4 days of maximum light. These data will be presented and analyzed in a future paper (N. Morrell et al., in preparation).

The pioneering work of the Calán/Tololo Project showed that SNe Ia luminosities are correlated with host-galaxy morphologies and colors (Hamuy et al. 1995, 1996a, 2000). More recently, evidence has been presented that SNe Ia Hubble diagram residuals correlate with global host-galaxy parameters such as total mass and star formation rate (Kelly et al. 2010; Lampeitl et al. 2010; Sullivan et al. 2010; Rigault et al. 2013; Uddin et al. 2017). To examine these effects for the CSP-II sample of SNe Ia, a program of integral field unit (IFU) host-galaxy spectroscopy is being carried out with both the Multi Unit Spectroscopic Explorer (MUSE) on the ESO VLT (Bacon et al. 2010) as part of the All-weather MUse Supernova Integral-field Nearby Galaxies (AMUSING) survey (Galbany et al. 2016), and the Potsdam Multi-Aperture Spectrophotometer (PMAS) on the 3.5 m Calar Alto telescope within the PMAS/PPak Integral-field Supernova hosts COmpilation (PISCO) program (Galbany et al. 2018) for those targets in the northern hemisphere. In addition to the global host properties, these IFU data will provide spectral information on the immediate environments of the SNe—e.g., line-of sight gas-phase and stellar metallicity, stellar age, and star formation rates—allowing a detailed study of the correlations between the SNe Ia Hubble diagram residuals and the local environmental properties.

NIR spectroscopy was a new and vital component of the CSP-II. During the four campaigns, NIR spectra were obtained of 157 different SNe Ia. These observations were carried out using the Folded-port IR Echellette (FIRE) on the LCO Magellan Baade telescope and through target of opportunity (ToO) time obtained principally with the Gemini North and South 8.1 m telescopes, the NASA Infrared Telescope Facility (IRTF), and the ESO Very Large Telescope (VLT). This set of NIR spectra is more than 15 times larger than the previous largest sample (Marion et al. 2009). The FIRE spectra account for 80% of the total spectra obtained, but the ToO observations were crucial for obtaining spectral coverage at the earliest epochs. More than 70% of the SNe Ia observed have at least 3 epochs of NIR spectral observations, and more than 10 epochs were obtained for 15 SNe. Whenever possible, we also attempted to obtain simultaneous optical spectroscopy to match the NIR observations. The NIR spectroscopy part of the CSP-II is presented in detail in the accompanying paper by Hsiao et al. (2018).

The majority of the SNe Ia in both the Cosmology and Physics subsamples were discovered in untargeted searches. Approximately one-third of the events selected for follow-up appeared in distant or low-luminosity hosts whose redshifts were unknown. A program of host-galaxy spectroscopy was initiated to measure redshifts for these SNe. Spectra of 40 of the hosts were obtained with the Wide-Field CCD (WFCCD) spectrograph on the du Pont telescope. For the faintest galaxies, it was necessary to use the Magellan telescopes. Spectra of 19 hosts were taken with the Inamori Magellan Areal Camera and Spectrograph (IMACS) on the Baade telescope, and another five galaxies were observed with the Low-Dispersion Survey Spectrograph (LDSS3-C) on the Clay telescope. Redshifts were obtained for an additional 11 host galaxies from our optical integral-field spectroscopy program.

The resulting redshifts are listed in Table 4, which gives the number of absorption and emission lines used to calculate the redshifts for each host-galaxy spectrum, and the rms errors of the final redshift values. These redshifts are also included in Table 1. Note that there are eight galaxies in Table 1 for which a redshift has not yet been measured.

As detailed in Krisciunas et al. (2017), the CSP-I employed the “SITe3” CCD camera and a set of Sloan Digital Sky Survey ugri and Johnson BV filters on the LCO Swope telescope to obtain optical light curves of the target SNe. The same setup was used for the first two campaigns of the CSP-II.²⁹ However, for the third and fourth campaigns, the SITe3 camera was replaced with a new camera housing an e2V 4112 × 4096 pixel, deep depletion CCD with 15 μm pixels, four read-out amplifiers, and a two-layer anti-etalon, anti-reflection coating. At the focal plane of the Swope telescope, this corresponds to a 30′ × 30′ field with 0435 pixels. This is a larger field than was required for the CSP-II observations, so we used only quadrant 3 of the detector since it had the best linearity characteristics.

The relative throughputs of the ugriBV passbands with the new e2V CCD were measured in 2013 October using a monochromator and calibrated detectors (Rheault et al. 2014). As expected, the quantum efficiency of the e2V CCD was found to be more uniform and sensitive, both in the blue and the red, than the SITe3 CCD. The response functions (telescope + filter + CCD camera + atmosphere) for the SITe3 camera are plotted in cyan in Figure 4. These are based on measurements made at the telescope in 2010 January and July using the same monochromator (see Stritzinger et al. 2011b for the calibration details). Plotted in red in Figure 4 are the response functions for the e2V camera. The curves for both detectors have been normalized using the r band. The B, g, V, and i filters with the e2V CCD show increased sensitivity compared to the r filter than was the case with the SITe3 detector.

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The methodology of the CSP photometric reductions is explained in detail in Krisciunas et al. (2017), but we briefly reproduce it here for completeness. First, we solve for color terms and extinction based on observations on photometric nights of Landolt (1992) and Smith et al. (2002) standard stars. We then fit the instrumental magnitudes, ugribv, via the following equations:

where u’g′r’i′BV correspond to magnitudes in the standard system, k_λ are the extinction coefficients, X is the airmass, _λ are the color terms, and ζ_λ are the zero-points. During the CSP-I project, ∼10 standard stars were observed per photometric night to determine the extinction and color terms. These were found to be highly stable over five years (see Figures 4 and 5 of Krisciunas et al. 2017). Hence, a slightly different calibration strategy was implemented for the CSP-II. The number of standard stars observed per night was decreased to ∼4–5, but standard-star observations were taken on as many clear nights as possible. As a result, data for determining extinction and color terms were obtained on considerably more nights during the CSP-II compared to the CSP-I.

Figure 5 displays the evolution of the nightly values of the zero-points during the CSP-II. As mentioned above, the detector in use for the first two years was the same SITe3 CCD used during the CSP-I. The significant jump in sensitivity at the end of year 2 is due to two nearly equal effects. The first is the washing of the primary mirror (indicated by the vertical gray dashed line), and the second is the higher quantum efficiency of the e2v CCD, which was put into operation immediately following the mirror washing. Each of these effects separately appears to have produced an increase in sensitivity of ∼50%. The steady decline in sensitivity observed for both detectors is due to the accumulation of dust and aerosols, principally on the primary mirror. The periodic dips in sensitivity correspond to the Chilean midsummer and most likely are due to an increase in atmospheric haze that is typical at this time of the year (Krisciunas et al. 2017).

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Table 5 compares the final mean extinction and color coefficients for the Swope+e2V system with those of the Swope+SITe3. As was observed for the CSP-I (Krisciunas et al. 2017), the extinction terms were remarkably consistent during the four years of the CSP-II, testifying to the photometric stability of the atmosphere above LCO. As expected, some small differences are observed between the color coefficients, with the largest changes being in the blue (the u and B filters) and the red (the i filter).

To measure final light curves for the SNe, we first established local sequence stars in each of the SN fields from observations of Landolt (1992) and Smith et al. (2002) standard stars. The underlying host-galaxy light was then subtracted from each SN image using host-galaxy reference images acquired after the SN had disappeared. These images were obtained mostly with the SITe2 CCD imager on the du Pont telescope. However, reference images for a number of SNe were acquired with the SITe3 CCD on the Swope telescope in good seeing (<1″) conditions. Magnitudes for the SN were then measured differentially with respect to the local sequence stars using point-spread-function (PSF) photometry (for further details, see Krisciunas et al. 2017). As a matter of policy, the CSP has been publishing all of its optical (and NIR) light curves in the natural photometric system of each telescope/instrument/filter combination, which is the “purest” form of the data (see Section 5.1 of Krisciunas et al. 2017).

The LCO du Pont 2.5 m telescope was used with the facility Tek5 CCD camera to obtain host-galaxy reference images as well as a small amount of SN follow-up photometry. As discussed in detail in Section 6.1.2 of Krisciunas et al. (2017), experiments carried out on two SN fields observed in both the Swope  SITe3 and du Pont+Tek5 systems confirm that the SN photometry obtained in the ugriBV filters with the du Pont+Tek5 is on substantially the same natural system as the Swope+SITe3 camera.

NIR imaging in the YJH filters of the CSP-II SNe was obtained with RetroCam on the du Pont telescope. RetroCam employs a Rockwell 1024 × 1024 HAWAII-1 HgCdTe array with 18.5 μm pixels. This is the same NIR imager used at the Swope telescope during the CSP-I.³⁰ RetroCam on the du Pont telescope gives a field of 34 × 34 and a pixel size of 0201. For host galaxies that were larger than the dither pattern, separate sky images were obtained.

In 2013 October, Rheault et al. (2014) made spectrophotometric measurements of the RetroCam YJH bandpasses on the du Pont telescope, which can be compared with similar data collected in 2010 January with the same monochrometer when RetroCam was on the Swope telescope (Krisciunas et al. 2017). This is shown in Figure 6, where the total relative throughputs (telescope + filter + camera + atmosphere) are shown for RetroCam on the Swope and du Pont telescopes. As may be seen, the transmission functions of the Y and J bands did not change significantly between the two measurements. The most significant difference is in the H filter and is likely ascribed to variations in either or both of the reflective and transmissive properties of the optics of the two telescopes. Most importantly, for all three bandpasses, the filter edges have not shifted significantly in wavelength.

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The NIR imaging of the SNe was calibrated to local sequence stars established in the fields of each of the SNe. Calibration of the local sequence stars was carried out through observations on photometric nights of ∼4–5 of the Persson et al. (1998) standard stars. In analogy to the optical filters, the photometric transformation equations for the measured instrumental magnitudes, yjh, are

where k_λ are the extinction coefficients, X is the airmass, _λ are the color terms, and ζ_λ are the zero-points. In these equations, J_std and H_std are the magnitudes given in Persson et al. (1998), and Y_std is the magnitude in the RetroCam Y-band standard system defined by Krisciunas et al. (2017).

Zero-points derived from RetroCam during the 4+ years of the CSP-II are plotted in Figure 7. Note that these do not show the steady decline in sensitivity observed for the CCD detectors on the Swope telescope (cf. Figure 5). This is likely because the primary mirror of the du Pont telescope is cleaned with CO₂ on an approximately weekly basis, whereas the closed-tube design of the Swope telescope does not permit this.

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Extinction coefficients in the Y, J, and H filters for RetroCam on the du Pont telescope were derived through a simultaneous Markov chain Monte Carlo fitting in the mixture model framework (Hogg et al. 2010) of all the CSP-II RetroCam nights. This procedure assumes a unique free parameter for the extinction coefficient, a fixed value of the color term estimated from synthetic photometry of model stellar atmospheres (see below), and the nightly zero point values. The resulting values are given in the top half of Table 6. We note that these differ slightly from the extinction coefficients measured with RetroCam on the Swope telescope during the CSP-I, but fall within the dispersion of the latter values (see Figure 8 of Krisciunas et al. 2017).

The NIR color terms could not be measured at the telescope due to the small color range, +0.19 ≤ (J − H) ≤ +0.35 mag, of the Persson et al. (1998) standard stars employed for the nightly photometric calibration. However, as we have precise spectrophotometric measurements of the NIR filter bandpasses, color terms can be estimated from synthetic photometry of model stellar atmospheres. This was done for the RetroCam J_RC2 and H filters on the du Pont telescope in Appendix C of Krisciunas et al. (2017), and the resulting values, reproduced in Table 6, were shown to be consistent with observations made of the red stars listed in Table 3 of Persson et al. (1998). As expected from the close agreement of the RetroCam Y filter bandpasses on the Swope and du Pont telescopes (see Figure 6), the color term for this filter is negligible since the standard system is defined to be the natural system of RetroCam on the Swope telescope (Krisciunas et al. 2017).

Final measurement of the SN light curves was carried out in an analogous way to the optical photometry. Local sequence stars were established in each of the SN fields and magnitudes for the SNe were measured differentially with respect to these.

Host-galaxy reference images were obtained mostly with the FourStar imager (Persson et al. 2013) on the Magellan Baade telescope, due to the superior throughput and image quality of this instrument. (Some reference images were also obtained with RetroCam on the du Pont telescope on nights of excellent seeing.) As mentioned in Section 3.2, a few active SNe were also observed with FourStar. FourStar employs four HAWAII-2RG detectors that cover a 108 × 108 field of view with a pixel scale of 0159. Filter response functions for the FourStar filters are illustrated in Figure 8. Note that FourStar does not have a Y filter, but the J1 filter provides a useful alternative. When imaging CSP-II SNe, the target was centered typically in chip 2. If the host galaxy was larger than the dither pattern, the target was alternately positioned in chip 2 and chip 4 to construct sky images in both chips.

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The Persson et al. (1998) red stars are far too bright to be observed with FourStar on the Magellan Baade telescope, and so we must also estimate the color terms for this instrument from synthetic photometry of model atmospheres. The resulting values are listed in Table 6.