Absolute Calibration. IV. Use of G-type Stars as Primary Calibrators

We demonstrate an approach to determine spectral energy distribution (SED) templates that are accurate to the 1% level from the visible through the infrared for nearby (unextincted) solar-type stars. Our approach is based only on measurements of T eff, log(g), and M/H and the use of standard theoretical SED models. The success of this approach confirms that the existing absolute calibration is likely to be accurate to this level throughout this spectral range. We then demonstrate how to measure and correct for extinction, allowing extension of this calibration approach to faint levels (and more distant stars). We provide template SEDs in digital form for 11 G-dwarf stellar calibrators.


Introduction
A number of fields of astronomy will benefit from an absolute calibration extending consistently from the visible through the infrared and accurate to better than 1% (Kent et al. 2009).Examples (Rieke et al. 2023) include (1) combining measurements made with different instruments and particularly between different spectral regions, e.g., optical and infrared; (2) studying phenomena at a range of redshift where the rest wavelengths migrate from one spectral region to another, e.g., Type I supernovae as distance indicators; and (3) providing accurate tests of stellar models over a range of types.Calibrating G-type stars is of specific interest for exoplanet studies, since it enables accurate angular diameters to be estimated for solar-like stars and thus for any solar-systemanalog planets studied using the transit method.This paper is the fourth in a series addressing this goal (see Rieke et al. 2022;Su & Rieke 2022;Rieke et al. 2023).The previous papers have established the basic calibration at the 1% level and addressed transferring it to a few selected stars in the infrared.The ideal for extending such a calibration across the sky is to find a type of reference star that is available in large numbers and where an absolutely calibrated and very accurate spectral energy distribution (SED) can be determined on first principles, e.g., from fundamental parameters such as T eff , log(g), and M/H.Such reference stars would require just normalization at a single wavelength (e.g., V, and correction for extinction), to provide an accurate set of reference fluxes.As discussed in Rieke et al. (2023), finding such a reference type is challenging because (1) white dwarfs are too faint for general use on groundbased telescopes in the mid-infrared; (2) solar-type stars require careful temperature determination and cross-calibration with the Sun; and (3) normal A stars are subject to surface temperature gradients as a result of rapid rotation and to unpredictable near-infrared excesses due to hot dust.
Here, we improve the methods used to certify solar-type stars for accurate calibration.The general approach of basing absolute calibrations on the near-infrared spectrum of the Sun was introduced by Johnson (1965) and applied in the midinfrared by Low & Rieke (1974).The method was employed to greater accuracy by Wamsteker (1981) and Campins et al. (1985).However, a number of more recent works have claimed that this approach is relatively inaccurate (Price 2004;Bohlin et al. 2014Bohlin et al. , 2022)), a situation that must be addressed if they are to be of use.An important issue with G-star calibrators is that their SEDs depend sensitively on their assigned T eff .Rieke et al. (2008) addressed this issue to generate improved G-star templates, and Casagrande et al. (2012) improved on the approach further.However, neither of these references demonstrated SEDs with accuracy compatible with the 1% errors that can now be achieved in the infrared absolute calibration (Rieke et al. 2023), nor with the overall goals for calibration from the visible through the mid-infrared to this level of accuracy.
In this paper, we demonstrate the ability to predict to the 1% level the full visible through mid-infrared SEDs of solar-type stars from just their V magnitudes, effective temperatures, and to a lesser extend M/H and log(g), all taken from a critical review of the literature. 4To do so, we generate spectral models that are traceable to the accurately calibrated solar spectrum but compensate for the variations in spectral type and other parameters among the calibration stars.For comparison with our models we use high-quality K S , Spitzer IRAC, CatWISE, and MIPS 24 μm photometry and find agreement between the derived SEDs and the photometry to the ∼1% level.This establishes the foundation for the use of solar-type stars in the absolute calibration of other targets.
This demonstration has been carried out on very nearby stars where extinction can be ignored.To generate fainter G-star calibrators requires that they be at large enough distances that they are usually significantly reddened.The ability to predict the intrinsic SED as demonstrated by the nearby stars is helpful in dealing with this issue, since it means that with adequate data, the intrinsic SED of a reddened calibration star can be determined accurately and taken as a given in determining the extinction.Nonetheless, correcting for reddening can pose challenges.We illustrate generation of accurate calibrator SEDs for three modestly reddened stars, GSPC P330-E and P177-D (hereafter P330-E and P177-D) and NGC 2506 G-31 (hereafter G-31).Although we do not generate SEDs for additional stars, to facilitate doing that in the future we report on measurements of spectral types and V and infrared JHK photometry for additional members of NGC 2506 and for members of two additional clusters containing good candidates, NGC 2420 and NGC 6811, since they may be useful in expanded sets of calibration stars.
This paper starts with a description of observations obtained with the James Webb Space Telescope (JWST) Near-Infrared Spectrometer (NIRSpec; Section 2), which will be used in discussions of the faint calibration stars P330-E (Section 5) and G-31 (Section 6).The general approach to generating template SEDs is laid out in Section 3. Section 4 demonstrates this approach by generating SEDs for eight nearby stars and demonstrating that only T eff , log(g), and M/H, plus a V magnitude for normalization, can yield templates accurate to 1% through the near-and mid-infrared.Given the proximity of these eight stars, we have set the extinction to them to zero; the consequences of adding an appropriate near-zero level are discussed at the end of Section 4. Extinction is a far more important issue for fainter, and hence more distant, G-star calibrators.Sections 5 and 6 demonstrate the generation of accurate templates for stars where the extinction must be taken into account.The results from this paper are summarized in Section 7. Appendices A and B deal with calibration issues in some of the photometry we use, while Appendix C provides detailed information on the identification and measurement of candidate G-star calibrators in the three open clusters included in our study, NGC 2420, 2506, and 6811.All magnitudes are quoted on the stellar (Vega) system.

Infrared and Spectroscopic Observations of Open Clusters
These observations will be described in Appendix C, where we describe the open clusters we have studied in detail.

NIRSpec Observations of Selected Calibration Stars
NIRSpec (Jakobsen et al. 2022;Böker et al. 2023) on JWST was used to observe several flux standard stars during the commissioning period and also as part of the Cycle 1 calibration program (Gordon et al. 2022).These observations were included in JWST program IDs (PIDs) 1536 (white dwarfs), 1537 (A stars), and 1538 (G stars).While the observations included all of the NIRSpec grating settings using both the integral field unit and the fixed slits, the largest number of different standards was observed using the NIRSpec prism together with the S1600A1 fixed slit aperture and the SUB512 subarray.We will use these latter spectra in this paper; they are listed in Table 1.
An initial analysis of these spectra revealed an issue specific to SUB512 and a few other NIRSpec subarrays.Since the SUB512 subarray that contains the short prism spectrum is only 512 × 32 pixels, it does not include any of the reference pixels at the edges of the 2048 × 2048 NRS1 detector.These pixels are normally used to remove correlated noise in the detector pedestal (Rauscher et al. 2007).Comparison of the two separate prism/SUB512 observations of the white dwarf G191 B2B showed inconsistencies in the flux, especially at the red end where the signal is low; in the worst case there were differences as large as 20%-30% between the flux values extracted from the individual dither positions.However, the SUB512 aperture is wide enough that the left and right edges include some pixels that are not illuminated by external light and that can be used in lieu of the missing reference pixels.The current Space Telescope Science Institute (STScI) JWST pipeline does not include this option; however, the NIRSpec IPS Pipeline Software, which was independently developed by the ESA NIRSpec team (Dorner et al. 2011(Dorner et al. , 2015)), includes this capability.It was used to redo the ramp fitting and recreate the rate files, which were then input to the standard STScI pipeline. 5An equivalent capability is in development for the official JWST pipeline and its implementation is expected in the near future.
At the present time the pipeline calibration of extracted point-source spectra with NIRSpec is based on a limited number of commissioning measurements, and in addition the JWST pipeline (Böker et al. 2023) does not currently correct for all of the effects that can have a significant effect on the extracted flux.6However, when comparing observations of different stars for this study, we will assume that we can trust the relative fluxes because we confined ourselves to targets observed using exactly the same observing settings and strategy, and the observations are reduced in the same way.
The observations from PIDs 1536, 1537, and 1538 all use five-point nods in the S1600A1 aperture, without any added spatial or spectral subdithering.This dither pattern has an offset between positions of 0 2571.The FWHM of the NIRSpec PSF varies with wavelength, being about 0 08 at 2.5 μm and 0 17 at 5.3 μm (Jakobsen et al. 2022), while the default extraction region for spectra in the S1600A1 is 5 pixels or about 0''.5 wide.Given the strong overlap at the small spacing, instead of averaging all of the other dither positions to determine the background for each exposure, we excluded the immediately adjacent dither positions from the background average.That is, for the first (top) dither position we subtracted the average of positions 3, 4, and 5; for the second we subtracted the average of positions 4 and 5; for the third, positions 1 and 5; and so on.This allows us to use all five dither positions while reducing the oversubtraction of the PSF wings; however, it does not completely eliminate the impact of the PSF overlap on the flux calibration.We then reran the JWST spec2 pipeline, using appropriately edited association files together with the modified rate files discussed above as input, to produce new "cal" files.The spec3 pipeline was rerun to align and merge the resulting calibrated files into a single rectified "s2d" file.We determined the central location of the spectrum using a simple Gaussian fit to the spectrum collapsed along the dispersion direction, and then reran the jwst extract1d step using a 5 pixel high extraction region.We forced subpixel centering by defining source region coefficients in the extract1d reference file in place of the usual ystart and ystop parameters.
To correct for uncertainties in the calibration as well as the effects of the detailed observing strategy that are not corrected by the pipeline, we start by taking the ratio of each extracted spectrum to an appropriate model spectrum for that star.We then compare the residual errors among the different standards.For this work, we define a baseline correction by using the two prism observations of the white dwarf G191 B2B and the single prism observation of the white dwarf GD 153, giving each observation equal weight, and comparing with the CALSPEC models g191b2b-mod-012 and gd153-mod-011 (Bohlin et al. 2017). 7We smooth these ratios as a function of wavelength using a low-pass filter to remove noise and small scale artifacts that do not repeat from observation to observation.The average smoothed ratio of the pipeline-extracted flux to the model flux was used to define the adopted flux correction vector, which was then applied to all of our extracted prism spectra.That is, we use the white dwarf spectra and models to define the calibration for our analysis of the NIRSpec prism spectra and then see what this implies for the NIRSpec spectra of the other standards.
Our observations should only be compared with others observed and reduced in the same way.Since neither the observing strategy nor the detailed extraction procedure match those originally used to define the current reference files, we do not, with the current state of the reference files and pipeline software, expect perfect agreement between the observed and model spectra.

Template Generation
The unique advantage of using G-dwarf stars for calibration is that the spectrum of the defining G2V star, namely the Sun, provides a foundation that is independent, and in principle more accurate, than any stellar model."In principle" because the quality depends on the accuracy of the absolute measurements of the Sun, which was in question until a few years ago (Gueymard 2018).These issues are now believed to be solved (Coddington et al. 2021).Our starting point for G-star calibrations is the accurate SED of the Sun presented in Rieke et al. (2023), which combines the spectrum of Coddington et al. (2021) with results at longer wavelengths from Gueymard (2018) and with a customized model (used in this case at wavelengths longer than 3.6 μm).As described in Rieke et al. (2008), the model is based on the one constructed by Holweger & Mueller (1974), but has been modified to match the observed strength of the fundamental CO band at ∼4.6-6 μm.Beyond 6 μm, the solar spectral shape is relatively robust in shape against plausible model uncertainties (Vernazza et al. 1976;Engelke 1992).Rieke et al. (2023) also show that this template is in close agreement with both a spectrum in the CO fundamental range of a very similar star and with absolute measurements of the Sun with 1% uncertainties in the 10 μm region.
However, a calibration that depends on finding exact solar twin stars would be limited.It is necessary for a versatile calibration to appeal to models of stars close in type, but not identical, to the Sun.To avoid undermining the accuracy of the solar spectrum more than necessary, we have used the solar spectrum to generate a correction to models that are based on the parameters of the Sun.The application of this correction forces the models to agree more closely with the solar spectrum.One can then apply the correction to similar models of stars of neighboring spectral types to calibrate them relative to the solar spectrum.After describing how we match the models to the solar spectrum in this section, in the following one we demonstrate the approach on eight nearby solar-type stars.

General Approach
Our approach makes extensive use of the BOSZ stellar models, whose general accuracy is demonstrated in Bohlin et al. (2017).To calibrate them against the solar spectrum, we interpolate among the BOSZ models to generate a spectrum that matches the Sun in T eff , log(g), and Fe/H.A comparison with the solar spectrum shows good agreement in shape at wavelengths longer than ∼4 μm, so we normalize the model to the solar spectrum there.This reveals that the model is 1%-1.5% high relative to the solar spectrum in the 1.5-3.5 μm range, as shown in Figure 1.
This comparison is used to derive an empirical correction to the BOSZ model to make it agree closely with the solar spectrum.To do so, we mask the strong absorption lines in the ratio of the BOSZ model to the solar spectrum, 8 smooth the result, and fit a polynomial to it.This takes the form of a multiplicative term that we will apply from 1 to 5.5 μm: where λ is in micrometers.We leave the spectra as modeled in the BOSZ grid for λ < 1 μm and λ > 5.5 μm.Further justification for making no adjustment for λ < 1 μm is provided in the discussion of 18 Sco below, while the need for the adjustment to the BOSZ models between 1 and 5 μm is demonstrated in Section 4.4.1.Applying G stars as calibrators requires that we generate spectra for cases differing by small amounts from G2V.We assume that their BOSZ model spectra need the identical correction we derived for the BOSZ solar model to calibrate them against the solar spectrum.Although this correction applies only to the BOSZ models, a similar procedure is likely to be needed with any set of theoretical models of stellar spectra to take out systematic differences relative to real stars.After applying the correction, we interpolate among the models to find one matching the parameters of the star in question.
In general it is possible that the star in question is reddened.Although small amounts of reddening/extinction can be corrected accurately in the infrared, adjusting models to predict the correct relation of the visible to the infrared is more challenging.To do so, we use the V − K S color difference as an indicator.The reddening (or lack thereof) can be determined by comparing the observed V − K S with the intrinsic value.Predicting the intrinsic V − K S requires an accurate T eff for the star.Sometimes, this is available directly, for example through the line depth ratio method (Kovtyukh et al. 2003) or from very high-resolution spectroscopy.Otherwise, we relate T eff to spectral type.From Gray & Corbally (1994), Kovtyukh et al. (2003), Pecaut & Mamajek (2013), Eker et al. (2018), andMalkov et al. (2020), we find the temperature difference between different spectral types.We then set T eff for G2V equal to that for the Sun (5772 K; Prša et al. 2015), and, based on the averaged results in the above references, we assign temperatures of 5905, 5836, 5772 (by definition), and 5713 K, respectively, to types of G0V, G1V, G2V, and G3V.
With an accurate temperature and estimates of log(g) and metallicity, we can determine the intrinsic V − K S from Masana et al. (2006).We have solved the equation in that reference for V − K S : where: and: where M/H is the metallicity (conventionally taken as Fe/H), log(g) is the surface gravity, and T eff is the effective temperature of the star.Equation ( 2) is valid for 1.15 (V − K S ) < 3.0.Equation (2) can also be used to evaluate the dependence of V − K S on metallicity and surface gravity.The former dependence is very small: for M/H ranging from 0.2 to −0.5, the color difference changes by only −0.006 (holding log(g) = 4.4).For log(g) ranging from 4.5 to 4, the color difference also changes by only +0.006.That is, for normal main-sequence stars, the typical errors in determining the metallicity and surface gravity have a negligible effect on the V − K S color difference.
We used these results to test the fidelity of the BOSZ models.For this test, we assumed log(g) = 4.4 and M/H = 0.A fit to the temperature dependence of V − K S according to these models is: 1.369 10 6.833 10 0.001447, 5 where ΔT = 5772 − T eff , with T eff the stellar effective temperature (we treat this difference as a differential to amplify any deviations).There is a difference of the values from Equation (5) minus Equation (2) of −0.003 for G3, and virtually zero for the G0-G2 spectral types.That is, the models reproduce the observed behavior very closely in this parameter.

Derivation of G-star Spectral Templates
An important aspect of our procedure is the lack of free parameters.The stellar spectrum is obtained by applying the correction to adjust the relevant models according to the difference between the BOSZ model and the absolutely calibrated spectrum of the Sun and then interpolating among the BOSZ models to match the stellar parameters.For low levels of extinction caused by diffuse interstellar material, the comparison of the observed V − K S with the intrinsic value from Equation (2) determines the level of reddening and a standard law can be applied to correct for it.For moderately high extinction, the correction will depend on the appropriate form of the extinction law toward the star, e.g., on R = A V /E(B − V ).We will illustrate approaches to these two situations for the extinction law later in this paper.In all cases, our approach is deterministic, i.e., other than the normalization at V (and correction for extinction if necessary), no fitting adjustments are made in the SED.
We now test the procedure on very nearby G stars, where the extinction should be negligible and the stellar parameters are very accurately measured.The relevant parameters for the stars we will analyze are listed in Table 2, along with notes on their determination and errors.For all eight nearby stars, the error in the observational value for V − K S is about 1%-1.5%, and comparing with the intrinsic values from Equation (2), the extinction is zero within this error.This is indeed as expected given the proximity of these stars within the Local Bubble.However, we have tested this expectation with the local extinction maps in Lallement et al. (2014).It is difficult to obtain accurate estimates of the extinction for an individual star, given the intrinsically modest angular resolution of the Lallement et al. (2014) maps.However, the extinction in units of mag pc −1 in the direction of all of the stars is in the lowest range, except for 16 Cyg B, but even in this case the star is close enough that the net extinction is very small.The average A V for the eight stars from very rough estimates from these maps is 0.004-0.006,which is the same as, or below, the average of the extinction estimates from the V − K S in Table 2.The levels of extinction are also negligible within the errors in the study of Schlegel et al. (1998).9We will therefore assume zero extinction in deriving the SEDs.
Although our procedure discussed above can derive an accurate infrared spectrum, for the visible where there are directly measured calibrated spectra obtained with STIS (Bohlin et al. 2017), they are to be preferred.Our procedure is therefore to merge the spectra at wavelengths where the STIS spectrum is of high quality (using measured spectra for the visible also reduces the effect of any extinction on the final SED).
Figure 2 compares our hybrid SEDs with the available photometry.In general, the measurement errors for the photometry are 1%-1.5%;we (see Figure 2) show 1.5% error bars except in two cases where we make them 2% to reflect the increased scatter in the measurements. 10The agreement between the SEDs and measurements is excellent; we discuss the stars individually below.

16 Cyg B
The spectral merging procedure between STIS and the modified BOSZ models is similar for all the stars and will be discussed in detail for 18 Sco.As is generally the case, for 16 Cyg B in the region of overlap between the STIS and theoretical spectra, the agreement is extremely good.The final spectrum is therefore a hybrid: at wavelengths < 0.8 μm, it is the observed and calibrated spectrum obtained with STIS and retrieved from CALSPEC, whereas at the longer wavelengths it is the infrared model based on the BOSZ library and the spectrum of the Sun.The fidelity of this spectrum can be tested by comparing the resulting fluxes with high-quality infrared photometry, as shown in Figure 2. 11 In effect, we are accepting the normalization of the STIS spectrum with no adjustment by this procedure (other than an 0.3% upward shift to reflect the revised calibration of Rieke et al. 2023).

18 Sco
18 Sco is a close solar twin (e.g., Bazot et al. 2011).In principle, a similar approach as used for 16 Cyg B should provide an accurate template for it.However, a number of issues with the photometry of this star need to be resolved first.Its V magnitude from Mermilliod (1994) should be very well determined, but it mixes values of low reliability with those that are more solid.We have just used four high-weight values; their average agrees perfectly with that derived from Hipparcos Hp.The K S value from Casagrande et al. (2012) should be accurate to at least the 1.5% level, but it is discordant with the other data.The star is hardly variable, i.e., in the infrared it should be at the < 0.1% level (Hall et al. 2009), so we attribute the difference to the measurement not being on the standard SAAO system and correct it appropriately (see Appendix B).
In generating the expected spectrum for the star, we again used a hybrid approach, namely the STIS spectrum for the visible and an infrared model generated from the BOSZ library with the two joined as shown in Figure 3.Because 18 Sco is a very close match to the Sun, we explore this overlap region in more detail.Figure 4 compares the spectra from the region where they are joined to the long-wavelength limit of the STIS spectrum.The STIS spectrum has a slightly different slope, shown by it lying about 1% higher than the hybrid spectrum at the longer wavelengths.Given the way the hybrid has been constructed, this difference has to arise from a difference between the measured spectrum and the BOSZ models, since no correction has been applied to those models at wavelengths shorter than 1 μm. Figure 4 also compares with the spectrum of the Sun from Coddington et al. (2021), adjusted in slope by multiplying by the ratio of blackbody fluxes for 5812 K (18 Sco) and 5772 K (Sun).The agreement with the model is virtually perfect, showing that it yields an accurate slope.In Figure 2, we show a spectrum of 18 Sco normalized to the STIS measurement at V (adjusted to the calibration of Rieke et al. 2023) and with the STIS and BOSZ models joined at 0.75 μm (7500 Å).

Other Nearby Solar-type Stars
We have followed procedures similar to those illustrated above for six additional nearby solar-type stars, with the results given in Figure 2. All of them agree to within ∼1% with the photometry, except for HD 106252 as discussed below.This result is achieved with no free parameters, just applying the measured values for T eff , log(g), and M/H from the literature   2, to constrain the extinction.The resulting spectrum shown in Figure 2 shows that the IRAC Band 2 measurement as well as the K S one and those at longer wavelengths fall on the template within the errors and therefore implicates the IRAC Band 1 measurement and supports the use of the K S measurement to deduce zero extinction to the star.The reconciliation of the models with the solar spectrum reaches a peak correction ∼ 1.5% near the K S band at 2.2 μm.We now test the general validity of this reconciliation using the results from the eight bright stars just discussed.Although the individual modeled spectra of these stars hint that the reconciled models may be more compatible with the K S -band photometry than the unreconciled ones, this trend is not definitive for any single star.We have therefore averaged the ratio of the flux density measured at K S divided by the modelpredicted flux density over all eight stars, as summarized in Table 3.This average ratio is 1.000 ± 0.003 for the reconciled model spectrum and 0.985 ± 0.003 for the unreconciled models, with the errors determined from the rms scatter of   the ratios.That is, the unreconciled models lie 1.5% above the photometry, as expected, while the reconciled ones are in exact agreement, again as expected/hoped.

Effect of Extinction
In this comparison, we have applied no extinction correction to the models for the stars; there is some indication that they might overall have a very low level, A V ∼ 0.005.If extinction is applied to the models, since they are normalized in the visible their infrared flux densities will increase.This will increase the discrepancies with the nonreconciled/original models to about 2.0%, while the reconciled models will remain within ∼0.5%.
We conclude that applying the correction quantified in Equation (1) to reconcile the BOSZ models with the spectrum of the Sun also significantly improves the agreement of the model SEDs of the eight solar-type stars with the measured K S -band flux densities.

Spectral Energy Templates
Templates for the SEDs of the eight stars discussed in this section can be found in Table 4.The full templates are supplied electronically.

P330-E
Determining G-star templates for more distant stars requires applying corrections to the intrinsic SEDs for extinction.In this section, we illustrate the approach to this issue with the most thoroughly utilized relatively faint G-star calibrator, P330-E.This star is a central part of the calibration plans for JWST; in addition, it is very well studied and is a calibration stepping stone to fainter stars.Our extinction determination relies on the V − K S color difference and hence we force the template to fit the K S measurement.That is, when extinction is involved, we lose the ability to predict the entire SED just on the basis of a measurement in V plus stellar parameters such as T eff .However, determining the extinction in other ways introduces its own pitfalls, because of the small variations in color differences among photometric systems (e.g., Bessell 1995), errors in the photometry if the indicated extinction is small, and uncertainties in the extinction law.Throughout this section, we use the unified extinction law across the visible and infrared for Gordon et al. (2023).
T eff is a critical parameter.The models for P330-E by Bohlin et al. (2017) suggest possible temperatures of 5840 or 5900 K, i.e., G1V or G0V.The spectral type of the star was measured to be G0V by Colina & Bohlin (1997). 13We have made two additional determinations, one using a spectrum privately communicated by David Rubin and the other using the STIS spectrum in the CALSPEC database.We used the automatic "expert" classification system mkclass (Gray & Corbally 2014) to classify these spectra.This program is different from automated neural networks in that it directly uses the same methods as a human classifier does, rather than being trained on a specific set of data.The mkclass program comes with libraries of standards at 3.6 Å and 1.8 Å resolution.We use three iterations, the mkclass default.Both of these spectra  were best fitted by G1V.It appears that the star is G1V, with a leaning toward G0V.From the discussion in the preceding section, we found T eff to be 5836 and 5905 K, respectively, for G1V and G0V, so we set T eff = 5850 K for P330-E.We take the K S magnitude of the star from Rieke et al. (2022), 11.428.The V magnitude is measured at 13.00 transformed from Gaia (Riello et al. 2021), 13.01 (Altavilla et al. 2021), and 13.028 (Bohlin & Landolt 2015); the latter measurement is the average of 10 individual measurements and has a nominal error of 0.004 mag, while the others have errors ∼ 1%.Based on synthetic photometry from the spectra in the CALSPEC database and assigning a V magnitude of 0.033 to Vega (Mermilliod 1994), the magnitude of P330-E is 13.032.We adopt the latter value since we will join the infrared spectrum to the CALSPEC STIS one, noting that it is generally consistent with the highest weight alternative of 13.028.The resulting V − K S = 1.604.We use the STIS CALSPEC spectrum as the template for wavelengths < 0.8 μm, since it is measured at a high signal-tonoise ratio and should be more accurate than theoretical models.We will derive an optimum theoretical infrared spectrum to merge with the visible one; a similar (but not identical) approach has been taken by Ralph Bohlin to generate an improved CALSPEC SED.From Equations (2)-(4), the intrinsic V − K S is 1.485 (taking M/H = −0.23 and log (g) = 4.4).The resulting value of A V = 0.119/(1 -0.105) = 0.133, where the extinction at K S is 0.105 for the curve we are using when A V = 1.We then interpolated among the BOSZ theoretical templates to create one for 5850 K and the appropriate values of log(g) and M/H.We applied reddening using the unified curve for R = 3.1 and joined the resulting modeled infrared spectrum to the observed one at 0.8 μm.
The proposed spectrum for P330-E can be found in Table 6, and it is compared with the solar spectrum and the available measurements in Figure 5.The agreement is remarkable, confirming the evidence from previous observations that P330-E is a superb match to the Sun.This correspondence results from the combination of its slightly earlier spectral type, making it bluer, with just enough reddening to match the solar colors.As illustrated in Figure 5, this agreement will not hold in detail in spectral features, the most dramatic case being the CO fundamental at ∼4.3 μm.A further perspective is provided in Figure 6, where we show the spectrum of the star obtained in the prism mode of NIRSpec plus the two relevant photometric points, given as a ratio relative to the model template.We have selected the NIRSpec reduction based on an average of the white dwarf standards, which have very few spectral features in the infrared.This average is in close agreement with the overall calibration from the visible to 5 μm (and presumably beyond; Rieke et al. 2023).The spectrum agrees within ±1% with the template for P330-E deduced from photometry and our general approach, except for the fundamental CO absorption feature at 4.3 μm.The strength of this feature does not follow monotonically with spectral type (nor does the better documented case of the first overtone band at 2.3 μm-see the variations among G stars found by, e.g., Ali et al. 1995;Cesetti et al. 2013)-so it should be avoided in using solar-type stars for calibration.

GSPC P177-D
P177-D is being used in the calibration of JWST, although the prior information about it is less complete than that for P330-E.We have derived parameters for this star as summarized in Table 2 and built the corresponding model.It accurately reproduces the V and V − K S values (by construction) but its fidelity cannot be tested against other infrared photometry since CatWISE is all that is available (with which it agrees satisfactorily given the errors).The derived spectral template can be found in Table 6.It is probably somewhat less accurate than, e.g., the P330-E template.Rieke et al. (2023).The error bars are 1% at 2.2 and 3.6 μm, but larger at the longer wavelengths, where they show effects of increased statistical measurement errors (i.e., they are 2% for IRAC Bands 2 and 3, 3% for Band 4, and 4% at 24 μm.The NIRSpec prism spectrum is the version set as a ratio to the average of the white dwarf spectra and has been smoothed to suppress noise.Contrary to the model, it indicates that the CO fundamental is actually similar in strength to that in the Sun.

Identification of Very Faint Solar-type Calibration Stars
In this section, we illustrate finding and characterizing solartype stars that are significantly fainter than P330-E, to allow more flexible use in calibration with very large telescopes, including JWST.We identified three clusters as possible venues for these stars.We show that only one of them, NGC 2506, meets all our criteria except for its modestly subsolar metallicity.This is acceptable because the dependence of infrared colors on metallicity for wavelengths shorter than 2 μm is very small (see Section 3) and for those longer than 2 μm is also tiny, <3% in K S for [Fe/H] changing from 0 to -0.5 (Sheehan et al. 2010).We will first demonstrate how the solar-type members of this cluster were identified, and then derive a template for the best-characterized one.We summarize the selection of other G-star candidates and measurements of them for all three clusters in Appendix C.

Selection of Suitable Clusters
We used the WEBDA database (Mermilliod 1995) 14 to find open clusters most suitable for flux calibration of the JWST instruments with solar-type stars.We considered: 1. Age.Obviously, the solar-mass stars must be on the main sequence.A more subtle requirement is that they be 1 Gyr old to reduce the probability of them having debris disk infrared excesses (Gáspár et al. 2013).Furthermore, the age should be 7 Gyr to avoid mainsequence turnoff F-type stars that have similar colors and could be confused with solar analogs (we used the isochrones from Dotter et al. 2008).2. Extinction.Should be as small as possible.Of the clusters found, A V < 0.3.3. Distance modulus.The clusters should be distant enough that they do not saturate the JWST near-infrared imagers NIRCam and NIRISS in their wide-band filters in full frame mode.This means the distance modulus (m − M) should be 12.6 for a solar absolute K magnitude of 3.28 (Binney & Merrifield 1998).Given typical levels of extinction at the distances of candidate stars, there is a bit of margin (perhaps 0.15 mag) on this limit.4. Metallicity.Ideally, the clusters should have near-solar metallicity.5. Compactness.The clusters should be relatively compact to allow efficient observation within the field of view of NIRCam ( ¢ ´¢ 2 2 per module).We selected clusters with WEBDA diameter < 15′.6. Ancillary data.The clusters should have ancillary photometry from multiple observatories for cross-calibration.We preferred clusters with 2MASS, Wide-field Infrared Survey Explorer, and IRAC measurements.
Table 5 shows the properties of these clusters.With all these considerations in play, we selected NGC 2506 as the best fit for the multiple criteria.The only parameter that is not satisfied by NGC 2420 is the distance modulus (i.e., the G-star members are too bright for some of the JWST modes), so additional sources or conversions are needed for a few JWST bands.NCG 6811 is closer and brighter, but has been included as being useful in other applications.
Appendix C describes the process we used to select candidate G stars in these clusters, the photometry and spectra we obtained of them, and our procedure for classifying them

A Faint G-star Calibrator in NGC 2506
In this section, we will derive a spectral template for a solartype star in NGC 2506.As shown in Table 5, the extinction toward this cluster is significant.The effects of extinction and the relatively incomplete observational data set pose challenges that were not obvious in the preceding sections.These challenges are common to many calibration stars subject to extinction, so the discussion in this section illustrates the general set of issues to be faced.
G-31 has been observed as a potential JWST calibration star, and therefore relative to all the other members of NGC 2506, it has the most complete set of data.Obtaining highly accurate photometry for this star is challenging.Although it appears that the field around G-31 is clear for a radius of a few arcseconds, the field in general is crowded and that puts emphasis on obtaining photometry with a sufficiently small PSF and using reference areas sufficiently clear to get accurate numbers.Given that we want photometry to the 1% level, these requirements are quite demanding.They could be violated without any apparent evidence, i.e., visual inspection may not go deep enough to find sources in the reference area bright enough to affect the results.Therefore, for the K S magnitude, we have used only data from the VISTA catalog (McMahon et al. 2021), plus dedicated photometry for this paper and synthetic photometry from the low-resolution JWST NIRSpec spectrum.All of these references have 1″ or smaller effective PSFs.To enhance the signal-to-noise ratio, we have stacked the J measurement from McMahon et al. (2021) and both J and H from our photometry onto K S , with corrections for the intrinsic colors (Pecaut & Mamajek 2013) and the reddening assuming A V = 0.26.The K magnitudes for WFCAM were then transformed to the 2MASS system as in Dye et al. (2006) and Hodgkin et al. (2009), as checked in our measurement campaign.No adjustment is required for the VISTA magnitudes (González-Fernández et al. 2018).We have taken errors of 0.05 for VISTA K S , 0.06 for the stacked VISTA result, 0.03 for WFCAM K S , and 0.03 and 0.04 for the stacked results, respectively, for H and J.The NIRSpec data present a unique opportunity because there is also a spectrum of P330-E, calibrated against the average of the white dwarf calibration stars.This provides the possibility of essentially a direct transfer from P330-E to G-31.As a result, we have done synthetic K S photometry on both spectra; any issues with the white dwarf calibration stars will tend to cancel in this calculation.This approach along with the similarity of the stars should also minimize the observational issues discussed in Section 2. We then take the magnitude difference and add it to the very accurate K S magnitude of P330-E from Rieke et al. (2022).We assign a 1.5% error to this determination.The weighted average of all these measurements is K S = 16.242 ± 0.011 For V band, there is potential confusion with a nearby cataloged cluster member very close in brightness and colors to G-31.Again, small effective beams and accurate registration are key.We have taken V-band measurements from Gaia, transformed as in Riello et al. (2021), Pan-STARRS transformed as in Kostov & Bonev (2018), and synthetic photometry from the CALSPEC STIS spectrum, for which we assumed a V magnitude of Sirius of −1.436.We assume errors of 0.03 for the Gaia and Pan-STARRS values, 0.02 for the STIS one, and obtain a weighted average of 17.934 ± 0.015.Synthetic photometry on the STIS spectrum also yields 0.71 for B − V, or E(B − V ) = 0.09 ± 0.03 To derive the best-fitting template, we started with one matched to the properties of NGC 2506 and G-31: Fe/H = −0.30,log(g) = 4.5, and T eff = 5836 K (the temperature appropriate for a G1V star).Because of the modest signal-tonoise ratio of the STIS spectrum in CALSPEC, we do not use it but continue the BOSZ-based model down to 4000 Å.The template was determined by interpolation among the BOSZ models, and the correction to rationalize to the observed spectrum of the Sun was applied (Equation ( 1)).We required that no adjustments were permitted in this intrinsic stellar template and that its departure from the observed spectrum of G-31 is due purely to extinction.
The results of Schlafly et al. (2017) indicate values of R = A V /E(B − V ) ∼ 3.6 at the Galactic longitude of NGC 2506; although the cluster is at a latitude of 10°, most of the extinction is likely to occur close to the Galactic plane, so this high value of R is a possibility.To help measure the results of extinction in view of this possibility, we compare the shape of the template spectrum with the shape of the NIRSpec spectrum (Figure 7).That is, other than entering its result for the K S magnitude of G-31, we do not worry about its normalization, but use it just to assess whether the simulated SED of G-31 is returning the right slope and shape.Since the white dwarf average has been shown previously to be closely consistent with the overall calibration over the 0.5-5 μm range (Rieke et al. 2023), this should give an accurate comparison free of the influence of spectral features (e.g., the CO fundamental depth in P330-E).To optimize the extincted spectrum, the slope of the ratio of the template spectrum to the observed spectrum was fitted from 0.6 to 4.2 μm, and this parameter plus B − V and V − K S were combined as a metric for the quality of the fit, with the slope weighted 10 times the weight of the other two.Models were run for R V = 3.1, 3.5, 4.0, and 4.5, using extinction curves from Gordon et al. (2023).The metric of quality of fit was best for the R V = 3.5 case.The indicated level of extinction is A V = 0.25, in good agreement with that generally adopted for this cluster (Dias et al. 2021).
The final SEDs for P330-E, P177-D, and G-31 are provided in Table 6.

Conclusions
The goal of a consistent optical/infrared calibration to within 1% includes the challenge of finding suitable stellar types to convey a calibration at selected wavelengths on bright stars down to the faint stars in the range of interest for observation with large telescopes.In Rieke et al. (2023), we demonstrated a consistent calibration to this level of accuracy using Sirius as a reference star.However, as discussed there, using A stars to extend this work to faint levels suffers from the effects of rapid rotation, which can significantly affect the nominal SEDs, and from the possibility of emission by hot dust, which can on average add 1%-1.5% of flux to the modeled SEDs.White dwarfs provide a convenient solution for the visible and ultraviolet, and their use can be extended into the near-infrared.However, they are much too faint to be useful at the longer infrared wavelengths (except in limited cases for JWST).
Solar-type stars in principle can provide a solution for the visible through the mid-infrared.However, the generation of model SED templates to the necessary accuracy has been a challenge.In this paper, we have developed methods to achieve that goal.They involve an empirical correction to reconcile SED models with the accurately measured solar spectrum, plus methods to combine the reconciled spectra in ways consistent with the relevant stellar parameters: T eff , log(g), and M/H.This approach successfully yields SEDs from the visible through the infrared accurate to the 1% level on eight nearby solar-type stars.This result provides an independent confirmation that the proposed calibration (Rieke et al. 2023) is consistent across this range to 1%.It also provides templates useful for calibration at relatively bright flux levels.Extending this calibration approach to faint levels requires the use of G stars sufficiently distant that they are likely to be reddened significantly.We therefore demonstrate how to measure the extinction levels to correct the model templates.We do this for three cases: P330-E and P177-D illustrate the approach where a"normal" extinction law, R = A V /E(B − V ) = 3.1 is expected; and G-31 illustrates an approach for a case where the value of R may be larger.
The work in this paper addresses specifically generating accurate spectral templates referenced to the solar spectrum and for stars very close to the solar type (G2V).The approach is based on the CALSPEC database at STScI and the BOSZ stellar models.However, the procedures are general, and can use any set of stellar spectral models: (1) generate a model for the Sun; (2) compare it with the accurate solar spectrum to determine any corrections needed to force agreement; and (3) apply these corrections to models from the same set for stars close to the Sun in spectral type.If the resulting templates are customized for carefully determined parameters for calibration stars (including reddening), templates with similar accuracy to those derived here should be obtained.
The latter reference is claimed to be of higher accuracy, but for our purposes we are also interested in the consistency with the photometric system used in Rieke et al. (2022Rieke et al. ( , 2023)).Both are stated to be on the system defined by Carey et al. (2012).However, as shown in Figure 8, there is a photometric offset between the two reductions in IRAC Band 1 that is approximately constant at ∼1% up to ∼600 mJy, increasing for brighter stars to ∼5%.Within these zones, the two sets of photometry appear to be in agreement to the ∼1% level, supporting the claims of high accuracy; however, it appears that there is a photometric zero-point shift.This possibility is particularly worrisome for our use of the IRAC Band 1 photometry to compare with models of bright G stars, where a 5% offset is indicated.
Because of the high quality and consistency of its photometry, we have used 16 Cyg B to test the consistency of these two sets of measurements with the overall IRAC photometric system (Carey et al. 2012).We have started with the expected K S -W1 color difference from Pecaut & Mamajek (2013).A fit to this color difference versus V − K S indicates an expected K S − W1 = 0.019 for 16 Cyg B. We carried out synthetic photometry on our spectrum of 16 Cyg B (versus Sirius) to find W1 − IRAC1 = 0.013,15 for a net expected value of K S − IRAC1 = 0.032.An independent determination can be made from the equation in Rieke et al. (2022); it gives an expected value K S − IRAC1 = 0.034, in excellent agreement.Using the measurement of Krick et al. (2021), we find K S − IRAC1 = 0.021, while the measurement of Bohlin et al. (2022) gives K S − IRAC1 = −0.035,all under the conversion from flux units to magnitudes using the Carey et al. (2012) calibration.The former value is consistent with expectations, within the expected errors.The latter value is clearly inconsistent.We therefore use the Krick et al. (2021) value to compare with the proposed spectrum of the star.
The history of calibration constants for IRAC can be found in Table 4 in 2014) is transformed to K S as in Koen et al. (2007).From a comparison with other sources of photometry the results do not appear to be sufficiently accurate for our purposes.We have therefore derived our own transformation, using direct 2MASS magnitudes when they are available and adding values from stars too bright for unsaturated 2MASS measurements using transformation procedures as described in Rieke et al. (2022).The result is shown in Figure 9; the fit is:

C.1. Selection of G-star Candidates
We selected G-star candidates in the clusters listed in Table 4 using photometric data.At the time this was carried out, Gaia photometry was not available so we took the grizy photometry from Pan-STARRS for all three clusters (Schlafly et al. 2012;Tonry et al. 2012;Magnier et al. 2013).For NGC 6811, we added the B and V photometry from Janes et al. (2013).We also estimated the Pan-STARRS gr and B -V colors from a Pickles G2V spectrum using pysynphot (Lim et al., 2015), the extinction estimates available at that time, and assuming a Milky Way diffuse R(V ) = 3.1 (Cardelli et al. 1989) extinction law. Figure 10 shows the H-R diagram for NGC 2506; those for the other clusters are similar.The main sequence in each cluster was fit with a polynomial and then three priority levels were chosen for follow-up spectroscopy.Candidate solar-type stars were selected using the appropriate colors for each cluster: g − r = 0.42, g − r = 0.43, and B − V = 0.67 for NGC 2420, NGC 2506 and NGC 6811, respectively.The first priority targets had near-solar g − r or B − V colors (±0.04, 0.03, and 0.05, respectively) and were within ±4′ of the cluster center (to concentrate in the NIRCam field of view).The second priority was near-solar g − r or B − V colors but with a wider field of view (1°) to include G2V stars that could be observed with larger dithers.Third, any remaining main-sequence stars that were within a 1°field of view with reasonable a signal-to-noise ratio were selected to allow for errors in photometric color predictions and enable star cluster science at the main-sequence turnoff point.

C.2. Near-infrared Photometry
We observed the three open clusters with WFCAM on the UKIRT in queue mode on 2016 October 11, 25, and 26, November 11, and December 29, (UTC).This is the same instrument, pipeline, and telescope used for the UKIDSS survey for the infrared JHK bands.The data were processed automatically by the CASU IR Reduction Software v1.202 (Irwin et al. 2004), which created photometric catalogs for every detector array.We focused primarily on the one detector centered on the cluster.As recommended by the UKIRT pipeline team (Mike Irwin, private communication), we used aperture photometry number 3 (1″ radius) to measure the fluxes in the J, H, and K bands.
We identified over 1000 WFCAM sources in common with the 2MASS survey.We used these overlapping stars to check for offsets between the 2MASS survey on the WFCAM photometry.Fainter than K S = 14 gets into the low signal-tonoise ratio regime for 2MASS, whereas K < 11.5 approaches saturation with WFCAM, so the stars between those ranges are the most useful on cross-checking photometry.We find an offset of UKIRT K -2MASS K S = 0.007 if using all 2MASS and WFCAM points with 11.5 < K 14.

C.3. Spectral Typing
We obtained spectra of the candidate stars with Hectospec on the MMT (Fabricant et al. 2005;Mink et al. 2007) and LRIS on Keck (Oke et al. 1995).The spectroscopy confirms cluster membership and allows an accurate type to be assigned.We describe each set of observations here, followed by a description of the steps used to determine the spectral types for the stars.

C.3.1. Hectospec on the MMT
We observed NGC 2420 with Hectospec using two fiber configurations in the spring and fall of 2016.We used the 600 gpm grating (1.9-2.2Å resolution element) to match with existing spectral template libraries with 3.6 Å resolution.We selected the central wavelength to be 4800 Å, which means that the wavelength range is about 3550-6050 Å, covering several important features for G-star classification (many of which are concentrated between 4000 and 4400 Å).We obtained exposure times of 1.7 hr (spring 2016) and 2 hr (fall 2016).A minimum fiber separation ∼ 20″ is required when we observe in the two configurations to increase the density of stars for which we could obtain spectral classifications.
We processed the data with the standard IDL routine HSRED2, which applies automatic bias and flat-field corrections, spectral extraction, and wavelength calibration.HSRED can apply flux calibration for F-type stars, but we elected to rectify the spectra.Flux calibration is not crucial to spectral typing G-type stars because the library standards are normalized (Chris Corbally, private communication).We normalized the raw spectra provided by HSRED before passing them to a spectral classification program, mkclass (Gray & Corbally 2014).The first step in the normalization was to get an approximately normalized curve from the strongly curved spectrum.We fit a cubic spline in log space to the flux as a function of wavelength.The fit was iterated three times with 2σ outlier rejection to account for strong spectral lines and cosmic rays.It is important to do the fit in log space in flux because in linear space there are regions (near 3800 Å) where the best-fit cubic spline drops to low values and a spline fit in linear flux space can have zero crossings.The second step in the spectral rectification process is to normalize by the pseudocontinuum and remove any residual curvature.This is again fit with a cubic spline with three iterations of outlier rejection.The modification for the second step is to do it in linear space (now that zero crossings will not occur) and also to select only points greater than 95% of the normalized value to ensure they are continuum points.

C.3.2. LRIS on Keck
We observed NGC 2506 on 2018 December 6 with Keck LRIS using custom slit masks, with the target priority as described above.We designed masks with slit widths of 0 7 × 5″, which matched well to the seeing on that night, which was ∼0 7. We used the D560 dichroic and 600/4000 grating to collect blue spectra from 3300 to 5600 Å at a resolution ∼ 3 Å.As with the Hectospec setup, this arrangement sampled well the temperature-sensitive absorption lines between 4000 and 4400 Å.The LRIS red arm was not used for spectral typing.We took dome flats and HgNeArCdZnKrXe arc lamp exposures for wavelength calibration and direct imaging observations of the NGC 2506 field for source identification and alignment.
We used the pypeit pipeline to extract spectra of all sources (Prochaska et al. 2020).Some additional adjustments were needed to find spectral types of the stars.A −35 km s −1 velocity adjustment correction was needed to shift all spectra to match the stellar templates from the mkclass (Gray & Corbally 2014) library.As with the Hectospec data, we rectify the spectra by fitting to a third-order spline with a 2σ iterative clipping rejection and four spline knots.

C.3.3. Spectral Classification
We used the automatic "expert" classification system mkclass (Gray & Corbally 2014) to classify the stars, as already discussed in Section 5.As recommended by C. Corbally, the mkclass classifications of near-solar stars were  checked by eye.A graphical user interface explorer was made to compare template classification spectra with the observed Hectospec spectra.Figure 11 shows the Hectospec spectrum of a source at 07:38:28.4+21:33 that mkclass identifies as G2V, and compares it with G1.5V and G2V standards.The line ratios of Ca I 4226 Å, Hδ, Hγ, and Fe I lines are most consistent with a G2V type.

C.3.4. Results
Table 7 summarizes the results for NGC 2506.Since this was selected as the preferred cluster for JWST calibration stars, the members have been vetted for crowding and confusion by visual inspection in both the UKIRT WFCAM images and the IRAC Band 1 ones.We suspect issues not apparent in the visual inspections if the extinction to a star appears to depart significantly (more than 0.06 mag) from that for the cluster.Stars that pass these tests for purity are indicated by a footnote in the table.Solar-type stars in NGC 2420 are listed in Table 8, and similar information for NGC 6811 can be found in Table 9.These stars have not been vetted with the care applied to NGC 2506, but we have used crowding as judged from the Gaia and Pan-STARRS source detections, agreement in extinction, and consistency of the two V magnitude b The infrared photometry is on the WFCAM system.The nominal errors are 1%.c These stars are attractive for development as calibrators, given that there is no indication of confusing sources in the Pan-STARRS data, the V − K values agree with the average for the cluster to within 5%, and they have good JHK photometry.Notes.
a The V magnitudes are the average of values transformed from Gaia (Riello et al. 2021) and Pan-STARRS (Kostov & Bonev 2018), so long as the two values agree to within 2%.
b The infrared photometry is on the WFCAM system.The nominal errors are <1%.c These stars are attractive for development as calibrators, given that there is no indication of confusing sources in the Gaia and Pan-STARRS data, the V magnitudes agree within 1.5%, and they have good JHK photometry.

Figure 1 .
Figure 1.Upper panel: comparison of the solar spectrum with a BOSZ model with parameters matched to the Sun, and normalized to the solar spectrum at wavelengths > 4 μm.The model is high between ∼1.5 and 3.5 μm, by up to 1%-1.5%.[The conventional units for absolute calibrations are in the mixed units of W cm −2 μm −1 , originating with Johnson 1966, as used in this figure.They can be converted to Janskies by multiplying by 3.3357 × 10 15 × λ(μm) 2 .]Lower panel: correction factor to reconcile the BOSZ model with the spectrum of the Sun.

Figure 3 .
Figure 3. Region of overlap for the STIS and BOSZ/solar spectra of 18 Sco, showing how they were joined.

Figure 4 .
Figure 4. Comparison of the spectra of 18 Sco after joining, out to 1 μm.The spectrum of the Sun has been adjusted by the ratio of blackbody spectra at 5812 K (18 Sco) and 5772 K (Sun).It is hardly distinguishable from the BOSZ/solar spectrum.

Figure 5 .
Figure 5.Comparison of the solar spectrum with the model for P330-E.The agreement is extremely good (in general, maximum differences are 0.3%), except for the shallower CO fundamental band in the model, which does not behave monotonically with spectral type.The small excursions in the P330-E model spectrum around 10 μm are from silicate absorption in the extinction law.The photometry is from Rieke et al. (2022) for K S , Krick et al. (2021) for IRAC Band 1 (3.6 μm), Bohlin et al. (2022) for IRAC Bands 2-4 (see footnote in Section 4.1), and IRSA SEIP for the MIPS 24 μm point.All are based on the calibration of Rieke et al.(2023).The error bars are 1% at 2.2 and 3.6 μm, but larger at the longer wavelengths, where they show effects of increased statistical measurement errors (i.e., they are 2% for IRAC Bands 2 and 3, 3% for Band 4, and 4% at 24 μm.The NIRSpec prism spectrum is the version set as a ratio to the average of the white dwarf spectra and has been smoothed to suppress noise.Contrary to the model, it indicates that the CO fundamental is actually similar in strength to that in the Sun.

Figure 6 .
Figure 6.Ratio of the NIRSpec prism spectrum to the P330-E model.The two relevant photometric points are also shown, both with 1% error bars.

Figure 7 .
Figure 7.Comparison of the model for G-31 (red line), the NIRSpec prism spectrum (orange line), and the K S -band photometric point.
Krick et al. (2021); current Spitzer pipeline products use the Carey et al. (2012) values.Appendix B Casagrande et al. (2014) Infrared Photometry If the infrared photometry in Casagrande et al. ( The indicated K Casagrande − K S = 0.031 for 18 Sco (J − K = 0.35).Alternatively, one could interpret Figure 9 as a scatter diagram, in which case the average K Casagrande − K S = 0.030 (in both cases we have rejected one high and one low point).The value of 4.006 from Casagrande et al. (2014) therefore transforms to K S = 3.975.

Figure 10 .
Figure10.The H-R diagram for the field containing NGC 2506.The main sequence is well defined, and most of the brighter detections off it are foreground stars (i.e., too bright for their gr color).The vertical line is at the expected color difference for solar-type stars, and candidates are selected where they cross the main sequence.

Table 3
Test at K S of Reconciliation with the Solar Spectrum

Table 7
Solar-type Stars in NGC 2506