# Infrared Absolute Calibration I: Comparison of Sirius with Fainter
Calibration Stars

G. H. Rieke  Steward Observatory, University of Arizona, Tucson, AZ 85721,
USA, also Department of Planetary Sciences  Kate Su  Steward Observatory,
University of Arizona, Tucson, AZ 85721, USA  G. C. Sloan  Space Telescope
Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Department
of Physics and Astronomy, University of North Carolina, Chapel Hill, NC
27599-3255, USA  E. Schlawin  Steward Observatory, University of Arizona,
Tucson, AZ 85721, USA

###### Abstract

A challenge in absolute calibration is to relate very bright stars with
physical flux measurements to faint ones within range of modern instruments,
e.g. those on large groundbased telescopes or on the James Webb Space
Telescope (JWST). We propose Sirius as the fiducial color standard: it is an
A0V star that is slowly rotating and does not have infrared excesses either
due to hot dust or a planetary debris disk; it also has a number of accurate
($\sim$ 1 $-$ 2%) absolute flux measurements. We transfer the near infrared
flux from Sirius accurately to BD +60 1753, an unobscured early A-type star
(A1V, V $\approx$ 9.6, E(B-V) $\approx$ 0.009) that is faint enough to serve
as a primary absolute flux calibrator for JWST. Its near-infrared spectral
energy distribution and that of Sirius should be virtually identical. We have
determined its output relative to that of Sirius in a number of different
ways, all of which give consistent results within $\sim$ 1%. We also transfer
the calibration to GSPC P330-E, a well calibrated close solar analog (G2V). We
have emphasized the 2MASS $K_{S}$ band since it represents a large number and
long history of measurements, but theoretical spectra (i.e., from CALSPEC) of
these stars can be used to extend this result throughout the near- and mid-
infrared.

stars: fundamental parameters; infrared: stars; techniques: photometric

##  1 Introduction

Very accurate physical calibration is desired in a number of fields of
astronomy, as summarized in Kent et al. (2009). The highest accuracies are
currently achieved in the visible, with nominal errors of order 0.5 - 1% at
5556 Å (e.g., Bohlin et al., 2014). Nonetheless, work continues in that
spectral range (e.g., Bohlin, 2014; Bohlin et al., 2017; Deustua et al.,
2018), and achieving a robust 1%-quality calibration that can be applied to
routine photometry is very challenging (see, e.g., Bohlin et al. (2019)).
White dwarf stars have proven valuable to provide spectral templates to extend
the calibration spectrally over the entire visible and ultraviolet range
(e.g., Bohlin et al., 2019, 2020). There is increasing interest in extending
use of white dwarf spectral templates into the infrared (e.g., Bohlin et al.,
2011; Gentile Fusillo et al., 2020), which can provide the necessary tests of
their spectral models in the mid-IR. However, they become too faint for
routine use at the longer infrared wavelengths with most instruments. In
addition, many of them may have infrared excess emission due to reradiation of
the white dwarf emission by surrounding dust (Farihi, 2016), a source of flux
that is, of course, not included in the extrapolated spectral templates. Also,
the most fundamental absolute calibrations trace directly to calibrated
reference sources and hence are generally confined to the brightest stars;
white dwarfs are far out of reach for such measurements.

Infrared calibration grew from the main sequence stellar calibration
introduced by Johnson & Morgan (1953), which defined zero magnitude (just for
the U, B, and V bands) on the basis of a suite of A0V stars. Particularly in
the mid-infrared, the original goal of using multiple stars was impractical
and the system has been strongly based on Vega, both because it was readily
measured even through the Q band at 20 $\mu$m, and because it was bright
enough for direct calibration experiments using reference blackbody sources.
Indeed, the resulting photometric system is commonly described as the “Vega”
system. Unfortunately, Vega is not suitable as the defining star for a system
at the accuracy levels we now aspire to. Its shortcomings are legend. First,
it has a huge far infrared excess (Aumann et al., 1984) that persists at a
measureable level down through 10 $\mu$m (Su et al., 2013). Second, the star
is a pole-on rapid rotator with a significant temperature gradient from pole
to equator (Aufdenberg et al., 2006); in fact, rather than defining zero
color, the $V-K$ color of the stellar photosphere is $\sim$ 0.045 (Rieke et
al., 2008). Third, Vega has an excess of $1-2$% in the near infrared above its
photospheric emission (Absil et al., 2006), possibly due to hot dust confined
magnetically (Rieke et al., 2016), which might even be variable (Ertel et al.,
2016).

Nonetheless, there is by now a huge body of photometry based on the A0V star
zero point, which any new approach must preserve. Fortunately, Sirius may in
fact serve as an “ideal” A-star to define a much better-understood zero point,
both as a metric for models of stellar atmospheres and as a photometric
reference. Sirius is of spectral type A0mA1Va (Gray et al., 2003), which means
that it is a mild Am star. The classification indicates that the star is A0V
in type judged by its hydrogen lines (the “a” means it is of high luminosity
for the main sequence) but A1V when judged by lines of metals. This is
different from saying that its spectral type is between A0 and A1; it is an A0
star, but has line strengths like that of an A1 star, meaning that it is
somewhat metal-rich. Both its anomalous abundances and its low vsini $\sim$ 16
km s-1 suggest that it rotates relatively slowly (Royer et al., 2002; Mathys,
2004; Gray, 2014; Takeda, 2020). It appears to have little or no excess due to
a debris disk (e.g., Su et al., 2006), nor does it show a hot excess near 2
$\mu$m (Kervella et al., 2003). Since Sirius is a “model” A0V star, its
spectral energy distribution is well-represented by theoretical models (e.g.,
Bohlin, 2014; Bohlin et al., 2017). Sirius also has a number of accurate
measurements of its absolute flux, most notably by the Mid-Course Space
Experiment (MSX) mission (Price et al., 1999). There have been a number of
previous suggestions to switch to Sirius as the primary defining star for
stellar photometry (e.g., Engelke et al., 2010; Bohlin, 2014; Krisciunas et
al., 2017). This paper takes a step toward completing this goal.

The paper is the first in a series in which we address the issues to establish
an accurate absolutely calibrated infrared photometric system that is based on
Sirius and also is applicable down to standard stars at faint magnitudes. The
challenges in doing so are: (1) to tie the huge output of Sirius (and other
absolutely calibrated stars) accurately to much fainter stars that are useful
for calibration with modern detector systems (Sirius saturates virtually any
modern system in the optical and infrared); and (2) to calibrate the resulting
revised photometric system in physical units (to be discussed in following
papers).

The 2MASS (Skrutskie et al., 2006) photometric system covers the entire sky
uniformly (Cutri et al., 2003) and has become the default system for near
infrared photometry (e.g., Warren et al., 2007; Hodgkin et al., 2009). We
focus on the 2MASS $K_{S}$ photometric band because: (1) it is at a wavelength
where stellar spectral energy distributions (SEDs) are relatively free of
strong absorptions that complicate synthetic photometry; (2) it is far enough
into the infrared that extinction is small for the nearby stars we consider;
(3) it is easily connected to longer infrared wavelengths since the stars we
consider have roughly Rayleigh-Jeans SEDs beyond $K_{S}$ with modest
deviations due to spectrally localized absorptions; and (4) there is a large
database of measurements in this band or similar ones. The goal of this paper
is to derive accurately the brightness of Sirius in the $K_{S}$ band relative
to the much fainter stars that are accessible to photometry by modern
instruments. Extending the recalibrated system to the shorter infrared bands,
e.g., $J$ and $H$, is reserved for future work, since it requires the
establishment of a suitable zero point standard star - the subject of this
paper. In addition, achieving the same level of accuracy in these bands is
made more complicated by the larger interstellar extinction corrections.

We also focus on three stars that have been used extensively in previous
calibration efforts. First, BD +60 1753 is a fainter Sirius clone at spectral
type A1V. It has a $K_{S}$ magnitude of 9.6, within the range of a number of
modes for all the instruments on JWST as well as being sufficiently faint for
measurement with near infrared imagers on most large telescopes using
narrowband filters. It has more than 400 measurements with Spitzer (Werner et
al., 2004; Gehrz et al., 2007) in the IRAC (Fazio et al., 2004) bands 1 and 2,
and nearly 100 in Bands 3 and 4. Second, we use HD 165459 as a transfer
standard; it is of type A3V and with more than 7000 Spitzer measurements in
IRAC Bands 1 and 2. It is at $K_{S}\sim 6.6$, providing an intermediate step
toward the fainter standards, important for the direct comparison with Sirius
(Su et al., 2021) and for comparison with many of the A-stars with IRAC
measurements in Krick et al. (2021), which are of similar brightness111Beyond
$\sim$ 10 $\mu$m, HD 165459 has a significant debris disk excess (Sloan et
al., 2015); however, this does not compromise its use as a transfer standard
at wavelengths $\leq$ 5 $\mu$m.. The use of both HD 165459 and BD +60 1753 as
IRAC standards allows a direct comparison to transfer measurements to the
latter star at high accuracy. Third, GSPC P330-E is a G2V star that is a close
solar analog and was a prime calibrator for NICMOS (Thompson et al., 1998) on
HST (O’dell & Wen, 1994). At a magnitude of $K_{S}\sim 11.4$, it is even more
accessible to imagers on large groundbased telescopes. All three of these
stars have been very extensively characterized, particularly in the visible
range, with results available in the CALSPEC database (Bohlin et al., 2014,
2017). We remark, however, that steps toward even fainter standard star
systems have proven desirable for some applications (Leggett et al., 2020).
Additional effort will also be necessary to extend the calibration at full
accuracy to the other near infrared bands (e.g, there are $\sim$ 2% offsets
from zero colors for A0V stars in 2MASS $J-H$ and $H-K_{S}$ (Rieke et al.,
2008; Maíz Apellániz & Pantaleoni González, 2018)).

We proceed as follows. In §2, we first introduce the Spitzer/IRAC measurements
that are used in this paper to (1) establish the color-color relation of
$V-K_{S}$ and $K_{S}-$ IRAC1 for main-sequence stars and (2) assess the
stability of the photometry and determine a direct comparison of the routine
calibrators BD+60 1753 and HD 165459 over the entire Spitzer mission. In §3,
we derive the 2MASS-equivalent $K_{S}$ magnitude of Sirius using five distinct
approaches, including that developed in the accompanying paper by Su et al.
(2021) that derives a direct transfer from Sirius to HD 165459 in the IRAC
Bands 1 and 2. The agreement among all of these approaches is excellent,
within $\pm$ 0.006 mag, indicating that systematic errors in any of them are
small. In §4, we extend the work to fainter stars, including BD +60 1753 (A1V
at $K_{S}$ = 9.6) and GSPC P330-E (G2V at $K_{S}$ = 11.4). §5 briefly
discusses the challenges in establishing an accurately calibrated network over
the entire sky. The major results are summarized in §6. In addition, there are
three appendices. §A describes the transformations from heritage photometric
systems into the 2MASS $K_{S}$ band. §B derives the color term between $K_{S}$
and IRAC Band 1 as a function of $V-K_{S}$ and also provides a test of 2MASS
$K_{S}$ magnitudes for moderately bright stars transformed from heritage
photometry. §C tests the transformed $K_{S}$ magnitudes of very bright stars
for accuracy by comparing them with the photometry from the Diffuse Infrared
Background Experiment (DIRBE) instrument on the Cosmic Background Explorer
(COBE) (Mather et al., 1990; Silverberg et al., 1993).

##  2 Spitzer/IRAC Data Processing

Most of the measurements used in this paper were taken from published sources.
However, we carried out our own reductions of the IRAC data we use to (1)
determine the color correction between $K_{S}$ and IRAC Band 1 for main
sequence stars; (2) determine a direct transfer between the two Spitzer IRAC
calibration stars HD 165459 and BD +60 1753, both as a test of the photometric
stability and as the most accurate comparison possible between these stars;
and (3) do a direct transfer from Sirius to fainter stars.

To determine the intrinsic color difference between $K_{S}$ and IRAC Band 1,
we used the observations obtained in Spitzer PID 70076. We focus on Band 1 to
avoid the effects of the strong CO absorption in Band 2 for stars later than
mid-F-type. The data were processed by the Spitzer Science Center (SSC) with
the final IRAC pipeline (Lowrance et al., 2016). We used the BCD (basic
calibrated data) images, which have a native scale of 1$\farcs$22 pixel-1. We
performed aperture photometry using an on-source radius of 3 pixels and a sky
annulus between 3 and 7 pixels, with an aperture correction factor of 1.1233,
as in Krick et al. (2021). The BCD photometry was corrected for the pixel
solid angle (i.e., distortion) effects based on the measured target positions
using files provided by the SSC. We also discarded any photometry when the
target was too close to the edge of the detector array, and obtained weighted
average photometry for each of the astronomical observation requests (AORs) by
rejecting the highest and lowest photometry points in the same AOR. The same
procedures were also conducted on the mosaic post-BCD products for comparison.
A few photometry points from the post-BCD products were significantly fainter
(up to 10%) than the values obtained from the individual BCD images.
Inspection of those AORs found that one or two BCD frames have poor WCS (world
coordinate system) information, likely causing misalignment in the post-BCD
products. Thus, we adopted our final photometry based on the weighted average
of the BCD images, which were not subject to this issue.

We also made a high weight direct comparison between BD +60 1753 and HD 165459
based on the huge number of observations of each of these stars as primary
IRAC calibrators. Since they are of similar spectral type and low extinction,
we can compare the signals from the two stars directly to obtain an accurate
difference. We used an automated pipeline to compute the IRAC photometry of
the two stars throughout the cold mission and through August 2018 in the warm
mission. This pipeline reduces all of the observations of these stars in a
uniform way, using aperture photometry. The initial steps were similar to
those described in the preceding paragraph. The signal was extracted with an
aperture on the source of 10 pixels radius, relative to a sky annulus of inner
radius 12 pixels and outer radius 20 pixels. These parameters were selected
after experiments to determine the values giving the most reliable and
accurate photometry. Outliers were rejected per AOR by discarding the maximum
and minimum flux values if the spread of the distribution was greater than 2%
and the AOR had at least 10 files.

Finally, we make use of IRAC photometry of very bright stars based on the
wings of the saturated point spread functions. This work is described in
detail in Su et al. (2021).

##  3 The $K_{S}$ magnitude of Sirius

Figure 1 provides an overview of the steps we have implemented to relate
Sirius accurately to fainter stars in the $K_{S}$ band. The extreme left
column shows infrared magnitudes progressing from nearly -2 for Sirius to
fainter than 11 for GSPC P330-E. The next column to the right indicates the
various stars and stellar samples that we use as reference standards. The
double ended arrows connecting them indicate the existing photometry that
provides measurements of their relative brightnesses. The center two columns
show the various steps taken to relate these references to Sirius and the
other target stars. The rightmost column includes the target stars and also
some of the processing steps we have used to relate them directly to each
other without passing through the details of a photometric system. As shown in
Figure 1, we depend heavily on heritage $K$ photometry transformed into 2MASS
$K_{S}$. Details of the individual transformations are given in Appendix A. By
construction, such transformations should not introduce substantial biases.
Specifically, in Appendix B, we show that any bias is $0.0014\pm 0.0021$
magnitudes, i.e., negligible. In Appendix C, we utilize DIRBE photometry for
comparison on bright stars, finding that the transformed $K_{S}$ magnitudes
are generally accurate to $\sim$ 2%, similar to the accuracy of 2MASS itself
for sufficiently bright but unsaturated stars (Skrutskie et al., 2006).
Appendix B finds a similar result for fainter stars.

Figure 1: Overall approach to calibration of Sirius at $K_{S}$ and to transfer
this calibration to fainter stars relative to Sirius. The leftmost column
shows fiducial magnitudes at K. The first column to the right of this one
shows the starting points for the photometry, while the central two columns
identify the steps we have used to put the outputs of these starting points
onto a common photometric system. Where we started from photometry of the star
to be calibrated, this is also registered in the center columns. The rightmost
column shows the calibrated sources. Where additional calibration steps were
taken among these sources, they are indicated within this column.

###  3.1 Determination of Sirius $K_{S}$ with Traditional Photometry

The most straightforward approach to calibrating Sirius is to use heritage
photometry of the star, row 2 of Figure 1. Before standard infrared
photometers lost the ability because they no longer had sufficient dynamic
range, there were a number of measurements of Sirius. To make use of this
photometry, we need to: (1) discard any measurements of questionable quality;
and (2) put the remaining ones on the 2MASS photometric system. We only
consider observing programs that addressed measurements of a significant
number of stars per se222Studies using Sirius as a calibration star in a
program addressing some scientific priority other than photometry of large
numbers of normal stars were rejected, since the heritage of the Sirius
photometry for the rejected programs is difficult to determine and usually
leads back to one of the accepted programs. .

The programs we have considered further are Johnson et al. (1966); Glass
(1974); Engels et al. (1981); Alonso et al. (1994); van der Bliek et al.
(1996) and the UKIRT (United Kingdom Infrared Telescope) bright standard star
list (UKIRT, 2018). We found, as discussed below, that consistent results for
Sirius were obtained for the first five of these programs, but not for the
UKIRT standards333Sirius is marked as “a Mauna Kea (primary standard); JHKLL′M
magnitudes for these objects should be accurate to $\pm$0.01 mag.” Leggett et
al. (2003) gives a general description for the selection of the UKIRT
standards, but she does not provide details to review the values for a
specific star. However, we found Sirius in a listing of bright standards for
the Infrared Telescope Facility (IRTF) at
http://irtfweb.ifa.hawaii.edu/IRrefdata/Catalogs/bright_standards. The values
are identical to those in the UKIRT list but they have a rather different
notation: “CIT (unpublished) … SJ sources; lower accuracy. Avoid use.”
Combined with our finding that the Sirius value on this list is an outlier, we
have adequate cause to discard it.. As discussed further in the footnote, we
have rejected the UKIRT value for Sirius from further consideration.

These programs are in differing photometric systems, since they were in an era
when there was no completely uniform such system. We therefore need to
transform the $K$-band measurements from them accurately to the 2MASS
photometric system. Doing so achieves two goals: (1) it reconciles the
measurement frameworks by putting all the measurements on a consistent
calibration; and (2) by adopting 2MASS $K_{S}$ for this calibration, it
relates the brightness of Sirius to those of all the stars measured in the
2MASS survey. Accurate transformations can be derived in the infrared, where
virtually all of the relevant calibration stars (typically late B-type through
early M-type dwarfs) have spectral energy distributions past $\sim$ 1.5 $\mu$m
that are close to Rayleigh Jeans behavior, with modest deviations at spectral
features (e.g., CO bands).

The general transformation of all heritage photometry onto the 2MASS system is
useful in many ways for our study, as will become apparent as we proceed. To
achieve high accuracy, we need to be mindful that, early in the development of
near infrared photometry, systems of standard stars may have been updated as
measurements were improved without the changes being documented. The
measurements of Johnson et al. (1966) are homogeneous and extensive, but the
stars are too bright for useful overlap with 2MASS; Appendix A describes the
derivation of the transformation for them. To obtain the best results for
Sirius from Glass (1974) and Engels et al. (1981), we carried out
transformations using only the stars in the specific reference along with
Sirius. We adopted this precaution because, as an example, although Carter
(1990) and Koen et al. (2007) have derived high quality transformations for
the South African system, it is likely that the standard star values utilized
in the reference we use, Glass (1974), had been updated in the ensuing time.
As an example, Carter (1990) introduced a change in the zero point. For the
two remaining references, Alonso et al. (1994); van der Bliek et al. (1996),
the general transformations were in fact based on photometry contemporaneous
with the measurement of Sirius although not in the same reference. Given that
the Johnson et al. (1966) measurements have fairly large scatter, we averaged
the results (in magnitudes) on Sirius for $J$ and $K$. The final results are
summarized in Table 1. Although this value, $-$1.394, is based on only five
sets of measurements, they agree well and also agree with a large number of
independent determinations to be discussed below. It is difficult to assign a
priori errors to photometric transformations; we characterize the errors by
the $rms$ scatter of the results.

Table 1: Transformed Photometry of Sirius to 2MASS $K_{S}$ Magnitudes Reference |  $K_{S}$ (2MASS)
---|---
Johnson et al. (1966) | -1.376
Glass (1974) | -1.374
Engels et al. (1981) | -1.400
Alonso et al. (1994) | -1.398
van der Bliek et al. (1996) | -1.424
mean (average) | -1.394
rms scatter | 0.020
standard error of the mean | 0.010

###  3.2 Use of DIRBE All-Sky Photometry to transfer from Bright Standards

We now discuss row 1 in Figure 1. As demonstrated in Appendix C, the DIRBE
photometry is very accurate (errors no more than $\sim$ 1%) if care is taken
to apply it only to stars with no contamination within the DIRBE beam. The
calibration of DIRBE was based on a then-contemporary model of Sirius, so it
cannot be used directly to determine the flux from this star. However, we can
use the DIRBE measurements in a relative sense to compare the fluxes from
Sirius with those from other stars. There are five stars that meet the anti-
contamination criterion for accurate DIRBE measurements and for which there
are accurate near-infrared spectral templates from Engelke et al. (2006) so
the color corrections can be calculated as needed to transfer the DIRBE 2.2
$\mu$m relative measurements accurately to the 2MASS passband (see Table 2).
The $K_{S}$ magnitudes for these stars are based on very high weight heritage
photometry, e.g., their use as standards by Johnson et al. (1966) and a
similar use for all but $\gamma$ Dra at the UKIRT. That latter star has a high
weight measurement from Kidger & Martín-Luis (2003). Appendix B shows that our
transformations of heritage photometry to $K_{S}$ are accurate to the 1% level
and given the high quality of the heritage photometry for these five stars, we
believe that the $K_{S}$ values for each approach this level of accuracy. The
results from transferring the $K_{S}$ magnitudes of these stars to Sirius via
the DIRBE measurements are in Table 2; their average yields a value of
$-$1.402 for the $K_{S}$ magnitude of Sirius.

Table 2: $K_{S}$ magnitude of Sirius Using DIRBE Photometric Transfer  Star | alt name | Spec. Type |  $K_{S}$ mag | rel Sirius | color correction | Sirius mag
---|---|---|---|---|---|---
$\alpha$ Tau | HR 1457 | K5III | -2.837 | 1.474 | -0.018 | -1.381
$\alpha$ Aur | HR 1708 | G3III | -1.807 | 0.428 | -0.005 | -1.384
$\beta$ Gem | HR 2990 | K0III | -1.118 | -0.279 | -0.009 | -1.397
$\alpha$ Boo | HR 5340 | K1.5III | -3.014 | 1.628 | -0.017 | -1.403
$\gamma$ Dra | HR 6705 | K5III | -1.334 | -0.079 | -0.018 | -1.413
mean (average) |  |  |  |  |  | -1.402
rms scatter |  |  |  |  |  | 0.020
standard error of the mean |  |  |  |  |  | 0.010

###  3.3 Sirius Magnitude via that of Vega

Another approach is to relate Sirius to Vega, for which there are a number of
accurate transfers, and to then use the flux determinations for Vega to
determine the flux of Sirius, as indicated in row 3 of Figure 1. We proceed by
(1) comparing the brightness of the two stars; (2) deriving the Vega flux; and
(3) combining these results with some additional corrections to determine a
2MASS $K_{S}$ magnitude for Sirius.

####  3.3.1 Sirius relative to Vega

To determine an accurate magnitude difference in the infrared between Vega and
Sirius, we focus on wavelengths between 1.25 and 7$\mu$m.This range avoids at
the short wavelengths the strongest effects of the temperature gradient over
the surface of Vega and at the long wavelengths, the debris disk infrared
excess beyond 7$\mu$m. Comparing two stars of very similar spectral type has
the major advantage that the details of the photometric system become largely
irrelevant, since they affect the results for both stars in very similar ways.
This is particularly true here, since both stars have smooth, Rayleigh-Jeans
spectra (the hot dust excess adds a small contribution above the photosphere
of Vega, but it also appears to be roughly Rayleigh-Jeans). All of the high-
quality comparisons of Vega and Sirius in the infrared that we could find
(high stability space observatories or groundbased measurements carefully
reviewed for quality) are listed in Table 3. Nearly all of the entries are
already known to be high-quality photometry. As discussed in Appendix C, the
DIRBE photometry is also likely to be highly accurate since there are no stars
within the DIRBE beam brighter than $\sim$ 1% of either Sirius or Vega, and,
coincidentally, the brightest nearby star for each target is nearly the same
fraction of the target flux, so no adjustment is required. We boosted the
signal to noise of the DIRBE measurements by taking a weighted average of the
magnitude differences at 2.2, 3.5, and 4.9 $\mu$m.

In making this comparison, we need to take account of the temperature gradient
over the surface of Vega, which results in small departures from a pure A0V
color at 1 $-$ 2.5 $\mu$m (Rieke et al., 2008). Further departures result from
the hot excess emission in the near infrared (Absil et al., 2006). Small
adjustments are needed at J, H, and K to compensate both of these effects. To
determine these adjustments, we start with the intrinsic $H-K_{S}$ and
$J-K_{S}$ for Vega (i.e., including the effect of the temperature gradient),
taken as 0.0021 and 0.011, respectively, from Bessell & Brett (1988),
Koornneef (1983), Mamajek (2018), and Kidger & Martín-Luis (2003). We assume
that the hot excess adds 1.3% both at K and around 3.5 $\mu$m and adds 0.7% at
$H$ (Bohlin, 2014).

We also need to link the longer wavelengths out to $\sim$ 5 $\mu$m to $K_{S}$.
We first determine the magnitude difference between $K_{S}$ and the bands near
3.5 $\mu$m (W1, L, and IRAC Band 1) (we expect all of these bands to have the
same magnitude on an A0V-based system). To base the comparison on A stars that
are not rapid rotators, we use the compilation of Am and Ap stars in Renson &
Manfroid (2009), which should be dominated by slowly rotating stars (Royer et
al., 2002). We fitted the values of $J-K_{S}$ from 2MASS vs. the quoted
stellar temperatures (McDonald et al., 2012) with a fourth power polynomial
and rejected all stars deviating from the fit by 0.07 magnitudes or more (30
of 499). This step rejected stars with anomalous $J$ or $K$ photometry, and
any with strong extinction. We then calculated $K_{S}$ \- W1, rejecting all
cases with indicated errors in this color $>$ 0.1 mag ($\sim$ 20%), and fitted
a linear relation to $J-K_{S}$ vs. $K_{S}$ \- W1. This fit gives us a zero
point ($K_{S}-W1$ for $J-K_{S}$ = 0) of 0.022 mag. We set the fit to zero for
A0V by subtracting this value from the fit. The color of a star 2/3 of the way
from A0V to A1V (i.e., $V-K_{S}$ = 0.041, as should be roughly appropriate for
Vega as shown below) is then $K_{S}-W1=0.0010\pm 0.0020$.

We made an independent determination by estimating $K-L$ based on linear fits
on the values from A0V through F0V from a number of standard infrared color
compilations, with the A0V colors forced to zero. The results are 0.0024,
0.0017, and 0.0013 respectively from Bessell & Brett (1988), Koornneef (1983),
and Mamajek (2018). The slightly higher values are consistent with there being
a number of rapid rotators among the average A stars for which these colors
pertain, resulting in a “cooler” SED than implied by the optical spectrum.

We adopt a value of 0.002 for the observed intrinsic $K_{S}$ \- W1 color of
Vega. We used this value along with those for $H-K_{S}$ and $J-K_{S}$ derived
above to correct the values for J, H, and K to the equivalent values
normalized to the 3.5 $\mu$m region. The adjusted measurements of Vega
relative to Sirius are the ones given in Table 3.

The agreement for all the comparisons in Table 3 is excellent with an rms
scatter of only 0.015 mag. However, the summary also shows that the results
from Cohen et al. (1992) may be smaller by about 0.005 mag than the rest, as
also suggested by Bohlin (2014). This difference is within the errors but
suggests caution in interpreting these results. Another issue is that the
Cohen et al. (1992) values represent the comparison of theoretical SEDs
normalized to a smaller number of absolutely calibrated measurements. To avoid
over-weighting them in the average, we give them the weight of two
measurements (given that there are two filter sets) although nine values are
reported. We then find an average value of 1.370 magnitudes for the difference
between the two stars near 3.5 $\mu$m. This value depends on the assumed $K-L$
color, since it offsets the values at the shorter wavelengths. However, given
the weighting we have been using, adopting the difference between the observed
value and the one from SED models affects the derived difference by only
$\sim$ 0.001 mag.

Table 3: Comparison of Vega and Sirius in the Near Infrared BandaaOnly bands that do not extend past 11 $\mu$m are included, to avoid any excess around Vega. Specifically, the MSX $A$ band is not significantly affected by the far infrared excess component (Su et al., 2013). | Vega $F_{\nu}$ (Jy) | Sirius $F_{\nu}$ (Jy) | differencebb$J$ band difference is reduced by 0.026 mag, $H$ band by 0.011 mag, and $K_{S}$ by 0.002 mag to account for the temperature gradient over the surface of Vega and the hot dust excess.  (mag.) | reference
---|---|---|---|---
$J_{n}$ccNarrowband filters centered roughly on the indicated standard bands. See Selby et al. (1988); Cohen et al. (1992). | 1575.3 | 5688.3 | 1.368 | Cohen et al. (1992)
$K_{n}$ccNarrowband filters centered roughly on the indicated standard bands. See Selby et al. (1988); Cohen et al. (1992). | 640.1 | 2262.1 | 1.369 | Cohen et al. (1992)
$L_{n}$ccNarrowband filters centered roughly on the indicated standard bands. See Selby et al. (1988); Cohen et al. (1992). | 246.0 | 860.9 | 1.360 | Cohen et al. (1992)
$J$ | 1631.0 | 5896.4 | 1.369 | Cohen et al. (1992)
$H$ | 1049.7 | 3730.6 | 1.366 | Cohen et al. (1992)
$K$ | 655.0 | 2315.2 | 1.369 | Cohen et al. (1992)
$L$ | 276.4 | 967.8 | 1.359 | Cohen et al. (1992)
$L^{\prime}$ | 248.1 | 868.4 | 1.361 | Cohen et al. (1992)
$M$ | 159.7 | 557.5 | 1.357 | Cohen et al. (1992)
$[3.6]$ | – | – | 1.38 | Marengo et al. (2009)
$[4.5]$ | – | – | 1.38 | Marengo et al. (2009)
$[5.8]$ | – | – | 1.38 | Marengo et al. (2009)
MSX $B1$ | – | – | 1.342 | Price et al. (2004)
MSX $B2$ | – | — | 1.363 | Price et al. (2004)
MSX $A$ | – | — | 1.358 | Price et al. (2004)
DIRBEddBecause of the relatively large errors quoted for the DIRBE results, we show the weighted average of the three 2.2 - 4.9$\mu$m measurements; it has an indicated rms eror of 0.16 mag and is dominated by the 2.2 $\mu$m measurement. | – | – | 1.395 | Smith et al. (2004)
averageaaOnly bands that do not extend past 11 $\mu$m are included, to avoid any excess around Vega. Specifically, the MSX $A$ band is not significantly affected by the far infrared excess component (Su et al., 2013). | – | – | 1.370 | —
rms scatter | – | – | 0.012 | –

####  3.3.2 Determining the $K_{S}$ Magnitude of Vega

The photometry listed by Johnson et al. (1966) includes 178 measurements of
Vega at $K$, but with some significant outliers. We have obtained a “best”
value by averaging the results of two calculations. In the first, we fitted a
Gaussian to the full distribution, obtaining a centroid at $-$ 0.0178. The
width of the gaussian implies a 1-$\sigma$ error of 0.035 per measurement, so
the nominal error is $<$ 0.003. In the second, we rejected high and low
outliers that fell more than 0.07 away from the mean (i.e., 2 $\sigma$ from
the Gaussian fit), and averaged the remaining measurements to obtain $-$0.0161
with an rms scatter of 0.032, i.e., implying an uncertainty in the average $<$
0.003. We adopt $-0.017\pm 0.004$. This becomes a $K_{S}$-band magnitude of
$-$0.024 on the transformed 2MASS scale (using the transformation in Appendix
A). This value is equivalent within the errors to the finding by Maíz
Apellániz & Pantaleoni González (2018) that the Vega-based (Cohen et al.,
2003) $K_{S}$ zero point in 2MASS is $-0.015\pm 0.005$.

A total $K_{S}$ of -0.024, of which 0.013 mag is contributed by hot dust
(Absil et al., 2006, 2008), is consistent with other parameters of the star.
The intrinsic $K_{S}$ magnitude of Vega (i.e., without the hot dust excess) is
-0.011 and its intrinsic $V-K_{S}$ = 0.041. This color puts it 2/3 of the way
from A0V to A1V, where we compare with the colors tabulated by Mamajek (2018)
but force zero color for A0V stars by subtracting the values quoted for them
from the rest. These values are consistent with expectations for the color
with the temperature gradient over the surface of the star, lending
credibility to the $K_{S}$ magnitude.

####  3.3.3 Putting Sirius on the 2MASS Scale

The conversion of the magnitude difference between Vega and Sirius to a
magnitude for the latter star is influenced by the $1.26\pm 0.27\pm 0.06$%
excess for Vega from emission by hot dust (Absil et al., 2006, 2008), where
the first error describes the statistical uncertainty and the second is a
possible systematic error due to uncertainties in the stellar photospheric
model. The inability to detect this excess at 10 $\mu$m (Liu et al., 2004;
Ertel et al., 2018) might suggest that it is variable. However, the uniformity
of the results listed in Table 3 argues against this possibility. We have
assumed that the excess is constant over the time of the measurements listed
in this table. Our comparison has also assumed that the fractional excess
above the photospheric emission is wavelength-independent from 2 to 7 $\mu$m.
Models for the emission of the hot dust for two suggested compositions, carbon
and FeO (Rieke et al., 2016; Kirchschlager et al., 2017), indicate that this
assumption is probably justified, although carbon dust might produce a
spectrum somewhat redder than Rayleigh Jeans and FeO somewhat bluer. The
variability and color behavior of the emission by the hot dust adds to the
uncertainty in the final Sirius magnitude.

We found that Sirius is 1.370 mag brighter than Vega, which in turn is at
$K_{S}$ = -0.024, or -0.026 at IRAC Band 1, applying our nominal correction
for the temperature gradient on Vega. We therefore deduce a magnitude of
$-1.396\pm 0.010$ for Sirius at IRAC Band 1 and the same value at $K_{S}$ on
the basis that the magnitude should be wavelength-independent.

###  3.4 Use of Spitzer Photometry on Bright Field Stars

Yet another approach is to use the photometry from Su et al. (2021) of
selected field stars relative to Sirius in the IRAC Band 1, see row 4 of
Figure 1. The approach is summarized in Table 4. It proceeds by using a
standard color difference for the spectral type of the star to correct the
2MASS $K_{S}$ magnitude444That is, the value obtained from transformation of
heritage photometry. to the magnitude at IRAC Band 1, and then applying the
magnitude difference from Sirius to obtain an estimate of the magnitude of the
latter star. Since we are assuming that Sirius has zero color difference in
$K_{S}$ \- IRAC1, the same value applies at $K_{S}$.

The foundation of the approach in this section is that photometry of 1%
accuracy can be obtained using the wings of the Spitzer PSF (Marengo et al.,
2009). The accuracy of the PSF wing-fitting photometry is uniquely possible
with Spitzer because of its extremely stable beryllium optics, stemming from
operation in an isothermal environment at a temperature where the coefficient
of expansion for beryllium is virtually zero. The IRAC instrument has also
proven to be very stable (Carey et al., 2008, 2012; Lowrance et al., 2014).
However, the complex faint structures of the IRAC PSF are very sensitive to
the dither pattern in which the data were taken. We therefore designed
specific observations to utilize this technique. In an accompanying paper, Su
et al. (2021) reduce and discuss this photometry, including tests that support
the achievement of measurements with errors $\lesssim$ 1%. They tabulate
average values for the magnitude difference of each star relative to Sirius;
we use these values in our analysis.

We have to apply the $K_{S}$ \- IRAC1 color difference appropriate for the
spectral type to convert these measurements to $K_{S}$. We have derived these
color differences for main sequence stars (hence not for the K0III star
$\beta$ Gem) as described in Appendix B, finding

$K_{S}-IRAC1=-0.001228\times x^{4}+0.014382\times x^{3}-0.042158\times
x^{2}+0.057587\times x,$ $None$

where $x$ = $V-K_{S}$. To obtain IRAC Band 1 magnitudes for comparison with
the saturated photometry with Spitzer, we have applied this term to the
transformed $K_{S}$ magnitudes for all of the stars measured by Su et al.
(2021) except HD 19476555The two available K-band measurements for this star
differ by 0.06 mag; a review suggests that the measurement by Alonso et al.
(1994) is correct, but since it is a single measurement it does not deserve
equal weight with the others. We show in Su et al. (2021) that its $K_{S}$ is
nonetheless consistent with the results for the other, higher-weight stars.,
which we exclude because only a single measurement is available to determine
its $K_{S}$ magnitude. Averaging the results for all the other stars, we
obtain an estimate of the $K_{S}$ magnitude of Sirius of -1.394.

As discussed in Appendix B, there are two possible small biases to this
result, the offset of $0.0014\pm 0.0021$ magnitudes in comparing the
transformed $K_{S}$ magnitudes with the 2MASS ones, and a similar possible
offset due to extinction of the stars used to determine equation (1). Both of
these biases work to result in making our magnitude for Sirius being too
negative, perhaps by as much as 0.004 if we apply both. This full possible
offset would affect our final value for Sirius combining all of our approaches
by $\lesssim$ 0.001 mag.

Table 4: $K_{S}$ magnitude of Sirius Using Spitzer Photometric Transfer Star | Spec. | Vaafrom Stassun et al. (2019) | $K_{S}$ | refs.bb1 Johnson et al. (1966); 2 Kidger & Martín-Luis (2003); 3 Selby et al. (1988); 4 this work (relative to $K_{S}$ for HD 165459, with color correction as in Appendix B); 5 Aumann & Probst (1991); 6 Glass (1974); 7 Casagrande et al. (2014); 8 UKIRT (2018); 9 Smith et al. (2004); 10 Alonso et al. (1994); 11 Milone & Young (2005); 12 Alonso et al. (1998).  |  $K_{S}$- | IRAC1 | Sirius | Sirius
---|---|---|---|---|---|---|---|---
| Type |  | mag |  | IRAC1ccBased on $K_{S}$ magnitude and expected color difference from equation (1) (see also Appendix A), except for $\beta$ Gem = HD 62509, where we have taken the color difference from Tokunaga (2000).  | mag | Transfer | mag
HD 19373 | G0V | 4.05 | 2.650 | 1,2,3,4 | 0.033 | 2.617 | 4.001 | -1.384
HD 30652 | F6V | 3.19 | 2.076 | 1,4,5,6,7 | 0.030 | 2.046 | 3.440 | -1.394
HD 61421 | F5IV | 0.37 | -0.677 | 1,4,6,8,9 | 0.029 | -0.706 | 0.671 | -1.377
HD 62509 | K0III | 1.14 | -1.118 | 1,3,4,8,9 | 0.07 | -1.188 | 0.202 | -1.390
HD 102870 | F9V | 3.60 | 2.293 | 1,7,5,10 | 0.032 | 2.261 | 3.652 | -1.391
HD 126660 | F7V | 4.05 | 2.808 | 4,5,11 | 0.031 | 2.777 | 4.184 | -1.407
HD 142860 | F6V | 3.84 | 2.623 | 1,4,5,7 | 0.031 | 2.592 | 3.991 | -1.399
HD 173667 | F5.5IV-V | 4.19 | 3.039 | 3,4,5,7 | 0.030 | 3.009 | 4.410 | -1.401
HD 215648 | F6V | 4.20 | 2.900ddThere is a star 11$\farcs$1 from HD 215648 (Raghavan et al., 2010) with a $K_{S}$ magnitude from 2MASS of 7.30. This star would have been outside the photometric aperture for references 3 and 12, but would have been included in reference 4. The $K_{S}$ magnitude tabulated here is corrected for the influence of this additional star. For the transfer to Sirius, however, we have added the contribution of the nearby star (0.019 mag) to the brightness of HD 215648, since both stars would have been measured together. The combined magnitude is listed in column 7 as the “IRAC1 mag.”  | 3,4,12 | 0.032 | 2.849ddThere is a star 11$\farcs$1 from HD 215648 (Raghavan et al., 2010) with a $K_{S}$ magnitude from 2MASS of 7.30. This star would have been outside the photometric aperture for references 3 and 12, but would have been included in reference 4. The $K_{S}$ magnitude tabulated here is corrected for the influence of this additional star. For the transfer to Sirius, however, we have added the contribution of the nearby star (0.019 mag) to the brightness of HD 215648, since both stars would have been measured together. The combined magnitude is listed in column 7 as the “IRAC1 mag.”  | 4.233 | -1.389
mean (average) |  |  |  |  |  |  |  | -1.393
rms scatter |  |  |  |  |  |  |  | 0.009
standard error |  |  |  |  |  |  |  |
of the mean |  |  |  |  |  |  |  |  $<$0.004

###  3.5 Direct Transfer between Sirius and HD 165459

The preceding section relied on a direct transfer from Sirius to stars with
accurate $K_{S}$ magnitudes transformed from other systems. We can also
utilize a direct transfer from Sirius to HD 165459, a star that is
exceptionally well measured with Spitzer and is within the range for
unsaturated 2MASS measurements. We show this approach in the extreme right
column of Figure 1; we will use HD 165459 as a transfer standard from a suite
of 2MASS A-star measurements to Sirius. This allows a determination of the
$K_{S}$ magnitude of Sirius without the need to transform any photometry into
the 2MASS system.

HD165459 has been classified as a A3V star (Grenier et al., 1999) and to have
a $T_{eff}\sim 8565$K (Bohlin et al., 2017), also corresponding to a spectral
type of A3V. The IRAC data demonstrate that the star shows no variability, as
is expected for a main sequence A-star. Its 2MASS survey $K_{S}$ magnitude is
6.584 $\pm$ 0.027, and its V magnitude (converted from Tycho) is 6.86, i.e., V
$-$ KS = 0.28 $\pm$ 0.03, very similar to the intrinsic color for A3V, 0.25
(Pecaut & Mamajek, 2013; Mamajek, 2018), indicating it is only very lightly
reddened (although reddening is not important for our use of it as a transfer
standard). In confirmation, a value of $E(B-V)=0.021-0.023$ was found by
Bohlin et al. (2017). It has a debris disk infrared excess, by a factor of
$\sim$ 1.5 at 24$\mu$m and of 14 relative to the stellar photosphere at
70$\mu$m (Su et al., 2006), but again this will have no effect on our use of
it as a transfer standard in the IRAC band 1 at 3.6 $\mu$m, or even as a
primary standard at wavelengths short of $\sim$ 5 $\mu$m.

First, we consider the saturated Spitzer photometry of HD 165459. If we take
all six numbers for IRAC Band 1 from Su et al. (2021), that is all SNRs and
means and medians and average we get a ratio of 1552, rms scatter of 4. If we
do the same with Band 2, the average factor is 1564 $\pm$ 4, and if we take
all eight determinations (both bands) and average all of them we get 1558
$\pm$ 7\. This corresponds to 7.981 mag as the difference between the two
stars.

We discuss our derivation of an accurate $K_{S}$ magnitude for HD 165459 in
Section 4. The resulting average determination of the $K_{S}$ magnitude is
6.588 $\pm$ 0.007. This value agrees nearly perfectly with the 2MASS
measurement of 6.584 $\pm$ 0.027, but with a much smaller error. Applying the
transfer to Sirius, we obtain a $K_{S}$ magnitude for it of -1.389 based on
the IRAC Band 1 transfer. If we go through the same steps with the IRAC Band 2
photometry from Su et al., we find a magnitude for Sirius of -1.398, and if we
average both determinations we obtain the best value from this approach of
-1.393. This value is virtually identical to the final average of all the
determinations (see next section).Thus, if we eliminate it from the average,
we obtain the nearly the same estimate of the magnitude of HD 165459, 6.586,
this time utilizing the measurements of Sirius that are independent of HD
165459 and the Spitzer transfer from Sirius to HD 165459. The two
determinations, one from using the Spiter photometry to determine a high
accuracy $K_{S}$ magnitude and the other to transfer directly from Sirius, are
virtually identical. Since the are completely independent, we will adopt their
average, 6.587.

###  3.6 Summary, Final Value for $K_{S}$ of Sirius

Table 5 collects the five determinations of the magnitude of Sirius. They are
in excellent agreement, indicating that there is no significant systematic
error for any of them. We can therefore average them to obtain a “best”
estimate of the magnitude of the star, -1.395. To estimate the error, we took
all the individual measurements within each of the five approaches and
computed the rms scatter among the 46 such measurements. The value is 0.009
mag, again indicative of high accuracy throughout this study. A reasonable
final error is the $\pm$ peak-to-peak error, i.e., half of the full peak-to-
peak error. That is 0.005 mag.

Table 5: Summary, 2MASS $K_{S}$ Magnitude of Sirius Approach |  $K_{S}$ (2MASS)
---|---
transformed heritage photometry | -1.3944
using DIRBE photometry | -1.4018
via comparison with Vega | -1.394
direct transfer to field stars | -1.3934
direct transfer Sirius to HD 165459 | -1.3915
average | -1.3950
rms scatter | 0.009aaThis scatter is the standard deviation for all the individual determinations within each method, a total of 46.
indicated error of average |  $<$ 0.005bbWe assume an upper limit to the error to be half of the peak-to-peak range of the five results.

##  4 Transferring to Fainter Stars

In this section, we transfer the result for Sirius to fainter stars, starting
with all the A-stars from Krick et al. (2021). We then emphasize two stars
that have been used extensively for previous standard star networks: (1) BD
+60 1753 is a well-behaved 9.6th magnitude A1V star that, despite its distance
of $\sim$ 500 pc (Gaia DR2), is very lightly reddened (Bohlin et al., 2017) –
it was a primary standard for Spitzer and hence has more than 400 measurements
in IRAC Bands 1 and 2 extending throughout the cold and warm missions; (2)
2MASS J16313382+3008465 = GSPC P330-E was used as the primary solar-type
calibrator for NICMOS and has about 60 measurements with Spitzer in IRAC Bands
1 and 2 – it is of type G2V and has about 0.1 $-$ 0.15 magnitudes of
extinction ($A_{V}$) (Bohlin et al., 2017).

###  4.1 Accurate $K_{S}$ magnitudes for A-Stars

Krick et al. (2021) published accurate Spitzer photometry for 18 stars with
types between B9IV and A6V, providing the opportunity to derive very accurate
$K_{S}$ magnitudes for this list. To obtain an estimate of the $K_{S}$
magnitude of a target star independent of the actual 2MASS measurement of that
star, we proceed as follows. We select another of the A-type stars, calculate
its magnitude difference to the target star in IRAC Band 1 corrected for the
expected $K_{S}$ $-$ IRAC1 color difference from equation (1), and adjust the
$K_{S}$ observed by 2MASS for this star by this amount. We repeat this for all
the other A-type stars that are not significantly obscured (see next
paragraph) and average all of the resulting estimates of the $K_{S}$ magnitude
of the target star to get a much more accurate value. These values can be
found in Table 6. The scatter in the individual magnitudes for a given target
star is 2.2%, consistent with the expected scatter in the 2MASS magnitudes
(i.e., the normalization according to the IRAC measurements has not added
significant error). The indicated net uncertainty for the average for a given
target star is $\sim$ 0.7%.

An issue for this approach is that equation (1) is only applicable for
unobscured or very lightly obscured stars. For four of the stars, comparison
of the V $-$ $K_{S}$ color with expectations for their spectral type suggests
$A_{V}>$ 0.2: HD 2811, HD 163466, 2MJ17571324+6703409, and
2MJ18120957+6329423. As discussed further in Appendix B, in these cases
equation (1) will not return a highly accurate result. Given the uncertainties
in the spectral types, it is not feasible to separate the stellar color and
the extinction accurately, so we have left these four stars out of the
determinations of averaged accurate $K_{S}$ magnitudes. Of course, this is not
an obstacle in determining such magnitudes for them.

Table 6: Accurate $K_{S}$ Magnitudes for Calibration Sample A-Stars Star | Type | referenceaaReferences for spectral types: (1) Houk (1978); (2) Reach et al. (2005); (3) Houk & Cowley (1975); (4) Fehrenbach (1966); (5) Grenier et al. (1999); (6) Abt (1995); (7) Bohlin et al. (2017) |  $\left<K_{S}\right>$bbHigh precision magnitude (see text); indicated error 0.007 mag |  $K_{S}$ (2MASS)
---|---|---|---|---
HD 2811 | A3V | 1 | 7.056 | 7.057 $\pm$ 0.024
HD 14943 | A5V | 1 | 5.434 | 5.439 $\pm$ 0.018
HD 37725 | A3V | 2 | 7.913 | 7.902 $\pm$ 0.018
eta01Dor | A0V | 3 | 5.764 | 5.751 $\pm$ 0.024
HD 55677 | A2V | 4 | 9.161 | 9.156 $\pm$ 0.021
HD 116405 | B9IV | 5 | 8.489 | 8.476 $\pm$ 0.020
HR 5467 | A1V | 6 | 5.811 | 5.756 $\pm$ 0.018
BD 60 1753 | A1V | 7 | 9.639 | 9.645 $\pm$ 0.015
HD 158485 | A3V | 6 | 6.134 | 6.145 $\pm$ 0.023
HD 166205 | A0V | 6 | 4.239 | 4.258 $\pm$ 0.029
2MJ17325264+7104431 | A4V | 7 | 12.246 | 12.254 $\pm$ 0.030
HD 163466 | A5V | 7 | 6.346 | 6.339 $\pm$ 0.018
2MJ17571324+6703409 | A4V | 7 | 11.163 | 11.155 $\pm$ 0.023
2MJ18022716+6043356 | A2V | 7 | 11.854 | 11.832 $\pm$ 0.018
HD 165459 | A3V | 5 | 6.588 | 6.584 $\pm$ 0.027
2MJ18083474+6927286 | A6V | 7 | 11.584 | 11.532 $\pm$ 0.019
2MJ18120957+6329423 | A3V | 2 | 11.277 | 11.286 $\pm$ 0.019
HD 180609 | A0V | 2 | 9.103 | 9.117 $\pm$ 0.019

###  4.2 Transfer from HD 165459 to BD +60 1753 and GSPC P330-E

As already pointed out, our direct transfer from Sirius to HD 165459 yields a
nearly identical $K_{S}$ magnitude for the latter star as we obtain for the
high-precision $K_{S}$ magnitude in Table 6. We averaged the results of these
two approaches to derive a magnitude of $K_{S}$ = 6.587, which we use as the
reference for transferring Sirius to fainter stars. We now obtain brightnesses
relative to HD 165459 for fainter stars to continue this process.

We have used four approaches to obtain an accurate transfer from HD 165459 to
BD +60 1753, summarized in Table 7. Since the two stars are both of early
A-type and with low levels of extinction, we have ignored color terms and
extinction corrections given that we are working reasonably far into the
infrared. The first two entries in the table are just based on the flux ratios
in Krick et al. (2021); in Figure 1, the two bands are merged into a single
item in row 6. The third entry, row 7 in Figure 1, is from the high-precision
$K_{S}$ magnitudes in Table 6.

The fourth entry, in the right-hand column in Figure 1, is based on an
automated pipeline comparing the measurements of HD 165459 to BD +60 1753
directly, as discussed in Section 2. Based on this reduction, we compared HD
165459 and BD +60 1753 in two ways. In the first, we fitted the signal for
each star with a linear dependence with time (to allow for the slow decrease
in sensitivity, see, e.g., Krick et al. (2021)), rejecting a few obvious
outliers, and calculated the average of the ratio of the fits. This approach
makes use of all the data. In the second, we took the ratio of the signals
from the two stars whenever they were both measured within a 24 hour interval,
so time variations in sensitivity are irrelevant. This method uses about 70%
of the data. The two determinations agree well, indicating a magnitude
difference of 3.049 in IRAC Band 1. The value for Band 2 is identical to
within $\sim$ 0.2%. Although in principle the error in this difference should
be very small, there is about a 0.7% difference in the value between cold and
warm Spitzer missions (perhaps due to residual errors in the linearity
corrections), so we assign an error of 0.005 for our measurements that combine
in roughly equal measure data from the cold and warm mission segments. We base
this estimate on the measurements that the nonlinearities for both mission
segments were corrected to better than 1% up to saturation (Lowrance et al.,
2014).

Table 7: $K_{S}$ Magnitudes of BD +60 1753 and GSPC P330-E Approach | HD 165459 to | BD +60 1753 | BD to P330 | P330-E
---|---|---|---|---
| BD +60 1753 difference |  $K_{S}$ magnitude | difference |  $K_{S}$ magnitude
| magnitudes |  | magnitudes |
Krick et al. (2021) I1 | 3.043 | 9.630aaApplying IRAC magnitude difference to high precision $K_{S}$ from Table 6 | 1.771bbIRAC1 value. Corrected for P330-E magnitude by 0.035 for $K_{S}$ \- IRAC1 color and 0.006 for extinction (Gordon et al., 2021). | 11.441
Krick et al. (2021) I2 | 3.046 | 9.633aaApplying IRAC magnitude difference to high precision $K_{S}$ from Table 6 | –ccNot used for P330-E because of uncertainty in depth of CO fundamental. | –
high precision $K_{S}$ (Table 6) | 3.051ddNot used for magnitude of BD +60 1753, but tabulated for completeness. | 9.638 | – | –
Direct IRAC comparison | 3.049 | 9.636aaApplying IRAC magnitude difference to high precision $K_{S}$ from Table 6 | – | –
NEOWISE W1 | – | – | 1.783eeRelative to average for BD +60 1753, 9.632. Corrected for P330-E magnitude by 0.014 for $K_{S}$ \- W1 color and 0.004 for extinction. | 11.433
CALSPEC | – | – | 1.855ffDifference in CALSPEC values at $H$-band, relative to average for BD +60 1753, 9.632.  | 11.424ggCorrected for P330-E by 0.056 for H $-$ $K_{S}$ color and 0.007 for extinction.
2MASS cal star | – | – | – | 11.424
Persson et al. (1998) | – | – | – | 11.418
Leggett et al. (2006) | – | – | – | 11.430
averages | – | 9.634 | – | 11.428
rms scatter | – | 0.004 | – | 0.009

We now turn to the G2V calibration star, GSPC P330-E, as shown in the bottom
four rows in Figure 1 and again with results summarized in Table 7. One route
to estimate the $K_{S}$ magnitude of GSPC P330-E is to use the NEOWISE post-
cryogenic mission (Mainzer et al., 2011) data (unfortunately, HD 165459 is
above the saturation limit for NEOWISE, so its photometry is compromised) and
apply the difference between BD +60 1753 and HD 165459 derived above. There
are about 150 measurements of GSPC P330-E and nearly 400 of BD +60 1753 in the
NEOWISE single-frame photometry at the Infrared Science Archive (IRSA). We
have rejected the high and low outliers (1 $-$ 2% of the total measurements)
and then computed mean magnitudes finding a difference of $1.783\pm 0.003$
magnitudes.

For a second estimate, we obtained a magnitude difference at H-band for BD +60
1753 and GSPC P330-E from the Wide Field Camera 3 (WFC3) IR grism spectra in
Bohlin et al. (2019). To do so, we averaged the ratio of the spectra of BD +60
1753 and GSPC P330-E from 1.59 to 1.72 $\mu$m (i.e., to the cutoff long
wavelength of the grism spectra and from a short wavelength limit so the ratio
is centered on the effective wavelength of the H band). The result is entered
in column 4 of Table 7. To convert it to a value at $K_{S}$, we took the H $-$
$K_{S}$ value (0.076) for a G2V star from Casagrande et al. (2012) but
corrected this value by 0.020 mag for the zero point offset for 2MASS H $-$
$K_{S}$. This correction is based on determinations of 0.019 mag (Rieke et
al., 2008), 0.026 (Cutri, cited in Rieke et al. (2008)) and 0.019 (Maíz
Apellániz & Pantaleoni González, 2018).

P-330E was a prime 2MASS calibration star (Skrutskie et al., 2006) and thus
was observed many times during the course of the survey. These results provide
a third estimate of its $K_{S}$ magnitude. The result is entered into Table 7;
it should have a very small nominal error.

Finally, Persson et al. (1998) conducted a campaign of high accuracy
photometry of solar-type stars in support of the calibration of NICMOS on HST.
They obtained two measurements of GSPC P330-E in slightly different K bands,
$K(Persson)=11.419\pm 0.007$ and $K_{S}(Persson)=11.429\pm 0.006$. However,
these measurements were made when the 2MASS calibration was still in a
formative stage. We use the 2MASS measurements of the entire set measured by
Persson et al. (1998) to derive linear transformations as a function of $J-K$
to obtain corrections of $K(Persson)-K_{S}(2MASS)$ = 0.003 and
$K_{S}(Persson)-K_{S}(2MASS)$ = 0.010, yielding values of $K_{S}$ of 11.416
and 11.419 for GSPC P330-E respectively; we adopt 11.418. Leggett et al.
(2006) also report accurate groundbased photometry of the star, obtaining a
$K_{MKO}$ magnitude of 11.419, which converts to a $K_{S}$ magnitude of 11.430
using the transformation given in that paper.

###  4.3 Comparison with CALSPEC

The good behavior of BD +60 1753 in the models of Bohlin et al. (2017) is
encouraging that an independent infrared calibration can be derived from the
CALSPEC models, which are normalized in the visible. To do so, we carried out
synthetic photometry in the 2MASS $K_{S}$ band for all the CALSPEC stars, with
the relative spectral response in the $K_{S}$ band from Cohen et al. (2003)
and on the system with the zero point determined in that work. We find $K_{S}$
magnitudes of -1.383 and 9.637 respectively for Sirius and BD +60 1753. The
value relative to Sirius when it is assigned $K_{S}$ = -1.395 (thus consistent
with our definitions) is 9.625 for BD +60 1753, within 1% of the value we have
derived in Table 7. This agreement shows that the infrared- and optically-
based calibrations are in reasonable agreement. This comparison will be
discussed further in a later paper in this series where we review the infrared
absolute calibration data.

##  5 Extending an accurate calibration over the entire sky

As always, extending an accurate calibration over the entire sky is a
challenge. The 2MASS survey is one option. A signal to noise ratio of $\sim$
100 (as needed for a 1% calibration reference) was achieved for sources
brighter than $K_{S}\sim$ 12 but “For 8.5 $<K_{s}<$ 13 default uncertainties
are consistently in the range 0.02 $-$ 0.03 mag. This limiting profile-fit
uncertainty is attributable to PSF mismatch in the profile-fit algorithm,
driven by undersampling due to the coarse 2$\farcs$0 pixel size.” - Skrutskie
et al. (2006). In addition, there are possibly large-scale non-uniformities up
to the 2% level, see Figure 18 of Skrutskie et al. (2006). Many of these
issues are mitigated for the 35 2MASS “tracer” fields (Nikolaev et al., 2000),
which include many of the stars in the Persson et al. (1998) list and by
association on the sky, fainter field stars. Leggett et al. (2020) provide a
listing of 81 equatorial standards that are much fainter (median $K_{S}$ =
17.5), and whose magnitudes are traceable to the 2MASS system through the
UKIRT Infrared Deep Sky Survey (UKIDSS) (Hodgkin et al., 2009) and Visible and
Infrared Survey Telescope for Astronomy (VISTA) (González-Fernández et al.,
2018) parent surveys.

An interesting alternative utilizes the NEOWISE data as obtained from the
CatWISE2020(Eisenhardt et al., 2020) catalog (Marocco et al., 2021). We have
used the Spitzer photometry from Krick et al. (2021) to perform a test. We
used the measurements of stars with IRAC Band 1 flux densities from 3.56 to
192.51 mJy, corresponding to W1 magnitudes of 12.24 to 7.95. The signal to
noise and ability to identify background sources that might compromise the
photometry both dictate the fainter limit, and the brighter one corresponds to
the CatWISE W1 saturation limit. The stars for this test are listed in Table
8. We compared their magnitudes with those from Krick et al. (2021) by taking
the following steps. First, we averaged the magnitudes in W1 and W2 (for GSPC
P330-E, we made a 0.04 mag color correction in W2 before averaging). We
assigned this average magnitude to a pseudo-IRAC 1 Band (which is intermediate
in wavelength) and ratioed the actual IRAC Band 1 flux to the flux in the
pseudo-band, adjusting the zero point of the pseudo-band to set the average of
all the ratios to 1. The resulting zero point, 282.9 Jy, is in good agreement
with that from Reach et al. (2005), 280.0 $\pm$ 4.1 Jy for the real IRAC band.
Because the CatWISE2020 values are based on a huge number of measurements of
each star, our hope was that the resulting magnitudes would have small
internal errors (any overall offset due to calibration differences is removed
by our adjustment of the zero point). In fact, Table 8 shows that the results
agree with the IRAC Band 1 measurements to within about 1%. In making use of
the CatWISE2020 data to this degree of accuracy, one should check the images
to be sure that there are no potentially confusing sources, even to very faint
levels, and we found two cases where this was a possibility. Removing them
reduces the rms scatter to just below 1%. Although the sample size is small,
these results suggest that the CatWISE2020 data have substantial potential as
an all-sky standard network.

Applying this network to the conventional $K$ band requires a color difference
correction; however, we have found that there are significant discrepancies
among different estimates for these corrections, particularly outside the
$0.7<V-K_{S}<1.7$ range. We have compared three color difference studies: (1)
the tabulation of standard colors from Pecaut & Mamajek (2013)666available at
http://www.pas.rochester.edu/$∼$emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt;
(2) the photometric colors derived by Jian et al. (2017); Deng et al. (2020);
and (3) colors based on SDSS-classified stars by Davenport et al. (2014). As
shown in Figure 2, expressed as a function of $V-K_{S}$ color, there are
discrepancies of 1 $-$ 2% (with a limited range of better agreement between
the values of Pecaut & Mamajek (2013) and Jian et al. (2017) for $0.7\leq
V-K_{S}\leq 1.7$). However, for 1 $\lesssim$ $V-K_{S}$ $<\lesssim$ 2, the
slopes of the corrections are in reasonably good agreement, indicating that
the primary cause of the discrepancies at least for this range is the
normalization. Although the all-sky CatWISE photometry is promising for many
applications, it appears that to exploit it to high accuracy requires more
accurate transformations to other photometric systems. Fortunately, the
CatWISE measurements can still be used to full accuracy in applications where
such transfers are not necessary (e.g., in our applications in this paper).

Figure 2: Comparison of proposed color difference $K_{S}-W1$ as a function of $V-K_{S}$ for main sequence stars. The dashed line is from Mamajek (2018), the solid one from Jian et al. (2017); Deng et al. (2020), and the dash-dot one from Davenport et al. (2014).  Table 8: Test of CatWISE2020 Photometry Star | IRAC1 (mJy) | Average WISE magnitude | Flux Density (mJy) | Ratio
---|---|---|---|---
|  |  | for WISE average magaaAssuming a zero point of 282.9 Jy for this pseudo-band. | IRAC1/$<$W1+W2$>$
HD 37725 | 192.51 | 7.934 | 189.68 | 1.0149
HD 55677 | 61.03 | 9.162 | 61.21 | 0.9970
HD 116405 | 113.31 | 8.500 | 112.57 | 1.0066
P330-E | 7.74 | 11.387 | 7.886 | 0.9815bbIncludes allowance for W1 - W2 = -0.04
BD +60 1753 | 39.56 | 9.643 | 39.304 | 1.0065
2M J17325264+7104431 | 3.56 | 12.250 | 3.560 | 1.00004
2M J17571324+6703409 | 9.65 | 11.176 | 9.577 | 1.0076ccFrame image shows nearby clutter, photometry may have larger than typical errors
2M J18022716+6043356 | 5.11 | 11.866 | 5.075 | 1.0069
2M J18083474+6927286 | 6.55 | 11.565 | 6.696 | 0.9782ccFrame image shows nearby clutter, photometry may have larger than typical errors
2M J18120957+6329423 | 8.69 | 11.281 | 8.694 | 0.9995
HD 180609 | 64.38 | 9.109 | 64.244 | 1.0021
rms scatterddFor all the stars | – | – | – | 0.0112
rms scatter outliers rejectedeeWith 2M J17571324+6703409 and 2M J18083474+6927286 eliminated  | – | – | – | 0.0092

##  6 Summary

We have used multiple approaches to determine an accurate $K_{S}$ magnitude
for Sirius (-1.395), HD 165459 (6.587), BD +60 1753 (9.634), and GSPC P330-E
(11.428) on the 2MASS scale. This work will improve the transfer of the
accurate physical calibration of Sirius (e.g., Price et al. (2004), to be
reviewed in a future paper) to the other two stars, which are widely used
standard calibration stars and are central to the absolute calibration of
JWST. In turn, the absolute calibration can be transferred to much fainter
$K_{S}$ measurements (e.g., Leggett et al., 2020), or possibly over the entire
sky using either $K_{S}$ measurements or NEOWISE ones.

##  7 Acknowledgements

We thank Micaela Bagley and Rafia Bushra for extensive work on data reduction
and analysis. Ralph Bohlin provided very helpful comments. The paper is based
on observations made with the Spitzer Space Telescope, which was operated by
the Jet Propulsion Laboratory, California Institute of Technology. This
publication also makes use of data products from the NearEarth Object Wide-
field Infrared Survey Explorer (NEOWISE), which is a project of the Jet
Propulsion Laboratory/California Institute of Technology. NEOWISE is funded by
the National Aeronautics and Space Administration. We used data from the Two
Micron All Sky Survey (2MASS), a joint project of the University of
Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology, funded by the National Aeronautics and Space
Administration and the National Science Foundation. This work was supported by
NASA grants NNX13AD82G and 1255094.

Spitzer, WISE, 2MASS, COBE

## References

  * Absil et al. (2006) Absil, O., di Folco, E., Mérand, A. et al. 2006, A&A, 452, 237
  * Absil et al. (2008) Absil, O., Di Folco, E., Mérand, A. et al. 2008, A&A, 487, 1041
  * Abt (1995) Abt, H. A., & Morrell, N. I. 1995, ApJS, 99, 135
  * Allen & Cragg (1983) Allen, D. A. & Cragg, T. A. 1983, MNRAS, 203, 777
  * Alonso et al. (1994) Alonso, A., Arribas, S, & Martínez-Roger, C. 1994, A&A, 282, 684
  * Alonso et al. (1998) Alonso, A., Arribas, S, & Martínez-Roger, C. 1998, A&AS, 131, 209
  * Aufdenberg et al. (2006) Aufdenberg, J. P., Mérand, A., Coudé du Foresto, V. et al.et al. 2006, ApJ, 645, 664
  * Aumann et al. (1984) Aumann, H. H., Gillett, F. C., Beichman, C. A. et al. 1984, ApJL, 278, 23
  * Aumann & Probst (1991) Aumann, H. H., & Probst, R. G. 1991, AJ, 368, 264
  * Bessell & Brett (1988) Bessell, M. K., & Brett, J. M. 1988, PASP, 100, 1134
  * Bohlin et al. (2011) Bohlin, R. C., Gordon, K. D., Rieke, G. H. et al. 2011, AJ, 141, 173
  * Bohlin et al. (2014) Bohlin, R. C., Gordon, K. D., & Tremblay, P.-E. 2014, PASP, 126, 711
  * Bohlin (2014) Bohlin, R. C. 2014, AJ, 147, 127
  * Bohlin et al. (2014) Bohlin, R. C., Gordon K. D., & Tremblay, P.-E. 2014, PASP, 126, 711
  * Bohlin et al. (2017) Bohlin, R. D., Mészáros, S., Fleming, S. W. et al. 2017, AJ, 153, 234
  * Bohlin et al. (2019) Bohin, R. C., Deustua, S. E., & de Rosa, G. 2019, , 158, 211
  * Bohlin et al. (2020) Bohlin, R. C., Hubeny, I., & Rauch, T. 2020, AJ, 160, 21
  * Bouchet et al. (1991) Bouchet, P., Schmider, F. X., & Manfroid, J. 1991, A&AS, 91, 409
  * Carey et al. (2008) Carey, S., Surace, J., Lacy, M. et al. 2008, SPIE, 7010E..2V
  * Carey et al. (2012) Carey, S., Ingalls, J., Hora, J., et al. 2012, SPIE, 8442E..1Z
  * Carpenter (2001) Carpenter, J. M. 2001, AJ, 121, 2871
  * Carter (1990) Carter, B. S. 1990, MNRAS, 242, 1
  * Casagrande et al. (2012) Casagrande, L., Ramírez, I., Meléndez, J., & Asplund, M. 2012, ApJ, 761, 16
  * Casagrande et al. (2014) Casagrande, L., Portman, L., Glasse, I. S. et al. 2014, MNRAS, 439, 2060
  * Cohen et al. (1992) Cohen, Martin, Walker, R. G., Barlow, M. J., & Deacon, J. R. 1992, AJ, 104, 1650
  * Cohen et al. (2003) Cohen, M., Megeath, S. T., Hammersley, P. L., Martin-luis,F. & Stauffer, J. 2013, AJ, 125, 2645
  * Cutri et al. (2003) Cutri, R. M., Skrutskie, M. F., van Dyk, S. et al. 2003, “2MASS All Sky Catalog of point sources,” http://irsa.ipac.caltech.edu/applications/Gator/
  * Davenport et al. (2014) Davenport, J. R. A., Ivezic, A., Becker, A. C. et al. 2014, MNRAS, 440, 3430
  * Deng et al. (2020) Deng, D., Sun, Y., Jian, M., Jiang, B., & Yuan, H. 2020, AJ, 159, 208
  * Deustua et al. (2018) Deustua, S., Woodward, J. T., Rice, J. P. et al. 2018, AAS. 23134905
  * Eisenhardt et al. (2020) Eisenhardt, P. R. M., Marocco, F., Fowler, J. W. et al. 2020, ApJS, 247, 69
  * Engelke et al. (2006) Engelke, C. W., Price S. D., & Kraemer, K. E. 2006, AJ, 132, 1445
  * Engelke et al. (2010) Engelke, C. W., Price, S. D., & Kraemer, K. E. 2010, AJ, 140, 1919
  * Engels et al. (1981) Engels, D., Sherwood, W. A., Wamsteker, W., & Schultz, G. V. 1981, A&AS, 45, 5
  * Ertel et al. (2016) Ertel, S., Defrére, D., Absil, O. et al. 2016, A&A, 595A, 44
  * Ertel et al. (2018) Ertel, S., Defrére, D., Hinz, P. et al. 2018, AJ, 155, 194
  * Farihi (2016) Farihi, J. 2016, New Astronomy Reviews, 71, 9
  * Fazio et al. (2004) Fazio, G. G., Hora, J. L., Allen, L. E. et al. 2004, ApJS, 154, 10
  * Feast et al. (1990) Feast, M. W., Whitelock, P. A., & Carter, B. S. 1990, MNRAS, 247, 227
  * Fehrenbach (1966) Fehrenbach, C. 1966, Pub. Obs. Haute-Provence, 8, 25
  * Fluks et al. (1994) Fluks, M. A., Plez, B., The, P. S. et al. 1994, A&AS, 105, 311
  * Gehrz et al. (2007) Gehrz, R. D., Roellig, T. L., Werner, M. W. et al. 2007, Rev.Sci. Inst., 78a1302
  * Gentile Fusillo et al. (2020) Gentile Fusillo, N. P., Tremblay, P.-E., Bohlin, R. C., Deustua, S. E., & Kalirai, J. S. 2020, MNRAS, 491, 3613
  * Glass (1974) Glass, I. S. 1974, Mon. Not. S. African Ast. Soc., 33, 71
  * González-Fernández et al. (2018) González-Fernández, C., Hodgkin, S. T., Irwin, M. J. et al. 2018, MNRAS, 474, 5459
  * Gordon et al. (2021) Gordon, K. D., Misselt, K. A., Bouwman, J. 2021, ApJ, in press
  * Gray et al. (2003) Gray, R. O., Corbally, C. J., Garrison, R. F., McFadden, M. T., & Robinson, P. E. 2003, AJ, 126, 2048
  * Gray (2014) Gray, D. F. 2014, AJ, 147, 81
  * Grenier et al. (1999) Grenier, S., Baylac, M.-O., Rolland, L. et al. 1999, A&AS, 137, 451
  * Groote & Kaufmann (1983) Groote, D., & Kaufmann, J. P. 1083, A&AS, 53, 91
  * Hora et al. (2008) Hora, J. L., Carey, S., Surace, J. et al. 2008, PASP, 120, 1233
  * Hodgkin et al. (2009) Hodgkin, S. T., Irwin, M. J., Hewett, P. C., & Warren, S. J. 2009, MNRAS, 394, 675
  * Houk & Cowley (1975) Houk, N., & Cowley, A. P. 1975, Mich. Spect. Survey, Vol. 1
  * Houk (1978) Houk, N. 1978, Mich. Spect. Survey, Vol. 2
  * Jian et al. (2017) Jian, M., Gao, S., Zhao, H., & Jiang, B. 2017, AJ, 153, 5
  * Johnson & Morgan (1953) Johnson, H. L., & Morgan, W. W. 1953, ApJ, 117, 313
  * Johnson et al. (1966) Johnson, H. L., Mitchell, R. I., Iriarte, B., & Wisniewski, W. Z. 1966, Comm. Lun. & Plan. Lab., 4, 193
  * Kent et al. (2009) Kent, S., Kaiser, M. B., Deustra, S. E. et al. 2009, ”Photometric Calibrations for 21st Century Science,” for astro2010: The Astronomy and Astrophysics Decadal Survey, arXiv 0903.2788
  * Kervella et al. (2003) Kervella, P., Thévenin, F., Morel, P., Bordé, P., & Di Folco, E. 2003, A&A, 408, 681
  * Kidger & Martín-Luis (2003) Kidger, M. R., & Martín-Luis, F. 2003, AJ, 125, 3311
  * Kirchschlager et al. (2017) Kirchschlager, F., Wolf, S., Krivov, A. V. et al. 2017, MNRAS, 467, 1614
  * Koornneef (1983) Koornneef, J. 1983, A&A, 128, 84
  * Krick et al. (2021) Krick, J. E., Lowrance, P., Carey, S., et al. 2021, AJ, 161, 177
  * Krisciunas et al. (2017) Krisciunas, K., Suntzeff, N. B., Kelarek, B., Bonar, K., & Stenzel, J. 2017, PASP, 129, 054504
  * Koen et al. (2007) Koen, C., Marang, F., Kilkenny, D., & Jacobs, C. 2007, MNRAS, 380, 1433
  * Leggett et al. (2003) Leggett, S. K., Hawarden, T. G., Currie, M. J. et al. 2003, MNRAS, 345, 144
  * Leggett et al. (2006) Leggett, S. K., Currie, M. J., Varricatt, W.. P. et al. 2006, MNRAS, 373, 781
  * Leggett et al. (2020) Leggett, S. K., Cross, N. J., & Hambly, N. C. 2020, MNRAS, 493, 2568
  * Liu et al. (2004) Liu, W. M., Hinz, P. M., Hoffmann, W. F., et al. 2004, ApJL, 610, L125
  * Lowrance et al. (2014) Lowrance, P. J., Carey, S. J., Ingalls, J. G. et al. 2014, SPIE, 9143L..58
  * Lowrance et al. (2016) Lowrance, P. J., Carey, S. J., Surace, et al. 2016, SPIE, 9904, 99045Z
  * Marocco et al. (2021) Marocco, F., Eisenhardt, P. R. M., Fowler, J. W. et al. 2021, ApJS, 253, 8
  * Mainzer et al. (2011) Mainzer, A. K., Bauer, J., Grav, T et al. 2011, AJ, 731, 53
  * Maíz Apellániz & Pantaleoni González (2018) Maíz Appellániz, J. & Pantaleoni González 2018, A&A, 616, L7
  * Mamajek (2018) Mamajek, E. E. 2018, http://www.pas.rochester.edu/$∼$emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt
  * Marengo et al. (2009) Marengo, M., Stapelfeldt, K., Werner, M. W. t al. 2009, ApJ, 700, 1647
  * Mather et al. (1990) Mather, J. C., Cheng, E. S., Eplee, R. E. Jr., et al. 1990, ApJL, 354, L37
  * Mathys (2004) Mathys, G. 2004, Proc. IAU Symp. 215, ”Stellar Rotation,” ed. A. Maeder & P. Eenens, p. 270
  * McDonald et al. (2012) McDonald, I., Zijlstra, A. A., & Boyer, M. L. 2012, MNRAS, 427, 343
  * McGregor (1994) McGregor, P. J. 1991, PASP, 106, 508
  * Milone & Young (2005) Milone, E. F., & Young, A. T. 2005, PASP, 117, 485
  * Nikolaev et al. (2000) Nikolaev, S., Weinberg, M., Skrutskie, M. F. et al. 2000, AJ, 120, 3340
  * O’dell & Wen (1994) O’dell, C. R., & Wen, Zhang 1994, ApJ, 436, 194
  * Pecaut & Mamajek (2013) Pecaut, M. J. & Mamajek, E. E. 2013, ApJS, 208, 9
  * Persson et al. (1998) Persson, S. E., Murphy, D. C., Krzeminski, W., & Rieke, M. J. 1998, AJ, 116, 2475
  * Price et al. (1999) Price, S. D., Egan, M. P., & Shipman, R. F. 1999, in “Astrophysics with Infrared Surveys: A Prelude to SIRTF,” ASP Conf. Series, 1777, ed., M. D. Bicay, R. M. Cutri, B. F. Madore, page 394
  * Price et al. (2004) Price, S. D., Paxson, C., Engelke, C., & Murdock, T. L. 2004, AJ, 128, 889
  * Price et al. (2010) Price, S. D., Smith, B. J., Kuchar, T. A., Mizuno, D. R., & Kraemer, K. E. 2010, ApJS, 190, 203
  * Raghavan et al. (2010) Raghavan, D., McAlister, H. A., Henry, T. J. et al. 2010, ApJS, 190, 1
  * Reach et al. (2005) Reach, W. T., Megeath, S. T., Cohen, Martin, et al. 2005, PASP, 117, 978
  * Reis et al. (2011) Reis, W., Corradi, W., de Avillez, M. A., &Santos, F. F. 2012, ApJ, 734, 8
  * Renson & Manfroid (2009) Renson, P. & Manfroid, J. 2009, A&A, 498, 961
  * Rieke & Lebofsky (1985) Rieke, G. H. & Lebofsky, M. J. 1985, ApJ, 288, 618
  * Rieke et al. (2008) Rieke, G. H., Blalock, M., Decin, L. et al. 2008, AJ, 135, 2245
  * Rieke et al. (2016) Rieke, G. H., Gáspár, A., Ballering, N. P. 2016, ApJ, 816, 50
  * Royer et al. (2002) Royer, F., Gerbaldi, M., Faraggiana, R., & Goméz, A E. 2002, A&A, 381, 105
  * Selby et al. (1988) Selby, M. J., Hepburn, I., Blackwell, D. E. et al. 1988, A&AS, 74, 127
  * Silverberg et al. (1993) Silverberg, R. F., Hayser, M. G. Boggess, N. W. et al. 1993, Proc. SPIE, 2019, 180
  * Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R. et al. 2000, AJ, 131, 1163
  * Sloan et al. (2015) Sloan, G. C., Herter, T. L., Charmandaris, V. et al. 2015, AJ, 149, 11
  * Smith et al. (2004) Smith, B. J., Price, S. D., & Baker, R. I. 2004, ApJS, 154, 673
  * Stassun et al. (2019) Stassun, K. G., Oelkers, R. J., Paegert, M. et al. 2019, AJ, 158,138
  * Su et al. (2006) Su, K. Y. L., Rieke, G. H., Stansberry, J. A. et al. 2006, ApJ, 653, 675
  * Su et al. (2013) Su, K. Y. L., Rieke G. H., Malhotra, Renu et al. 2013, ApJ, 763, 118
  * Su et al. (2021) Su, K. Y. L., Rieke, G. H., & Marengo, M. 2021, AJ, in press.
  * Takeda (2020) Takeda, Y. 2020, MNRAS, 499, 1126
  * Thompson et al. (1998) Thompson, R. I., Rieke, M., Schneider, G., Hines, D. C., & Corbin, M. R. 1998, ApJL, 492, L95 C., & Mandel, H. 2003, Solar Phys., 214, 1
  * Tokunaga (2000) Tokunaga, A. T. 2000, in “Allen’s AstrophysicalQuantities,” 4th edition, ed: A. N. Cox, New Yokr: AIP/Springer
  * UKIRT (2018) UKIRT (2018) https://www.gemini.edu/sciops/instruments/near-ir-resources/nir-photometric-standard-stars/ukirt-bright-standards
  * van der Bliek et al. (1996) van der Bliek, N. S., Manfroid, J., & Bouchet, P. 1996, A&AS, 119, 547
  * Warren et al. (2007) Warren, S. J., Cross, N. J. G., Dye, S. et al. 2007, MNRAS, 375, 213
  * Werner et al. (2004) Werner, M. W., Roellig, T. L., Low, F. J. et al. 2004, ApJS, 154, 1

Appendix A: Transformations and Standard Colors

This appendix summarizes the transformed (to 2MASS) magnitudes of the stars
used in our study, and indicates where the transformations were derived. Many
transformations were obtained from Carpenter (2001), which were used for the
photometry from Feast et al. (1990), Fluks et al. (1994), Bouchet et al.
(1991), Glass (1974)777Except for those used in the direct photometry of
Sirius, see Section 3.1., & UKIRT starred magnitudes. The photometry of
Casagrande et al. (2012) was transformed as in Koen et al. (2007).
Transformations were derived for this work for the remaining sets of
photometry. Doing so is challenging for the Johnson et al. (1966) photometry
because there is very little overlap between it and non-saturated 2MASS
photometry. We proceeded by transforming to intermediate sets of stars with
reasonable overlap with both the Johnson and 2MASS results, as summarized in
Table 9.

Table 9: Transformations from Johnson $K$ to 2MASS $K_{S}$ Magnitudes Method | Transformation | Numberaathe number of stars in common with those in Johnson et al. (1966) on which the transformation is based - virtually all these stars are main sequence A through K types
---|---|---
via ESO standardsbbBouchet et al. (1991) | $K_{S}\left(2MASS\right)=K\left(Johnson\right)-0.055+0.028(J-K)$ | 97
via SAAOccCarter (1990) | $K_{S}\left(2MASS\right)=K\left(Johnson\right)-0.038+0.025(J-K)$ | 82
via Kidger & Martín-LuisddKidger & Martín-Luis (2003) | $K_{S}\left(2MASS\right)=K\left(Johnson\right)-0.033+0.024(J-K)$ | 39
via UKIRT bright standardseeUKIRT (2018) | $K_{S}\left(2MASS\right)=K\left(Johnson\right)-0.038+0.022(J-K)$ | 54
adopted | $K_{S}\left(2MASS\right)=K\left(Johnson\right)-0.041+0.024(J-K)$ | –

The derivation of transformations for the photometry of Aumann & Probst
(1991), Alonso et al. (1998) (Telescopio Carlos Sánchez (TCS) system), Kidger
& Martín-Luis (2003) and Milone & Young (2005) was relatively straightforward
and they are shown in the equations below.

$J_{2MASS}=J_{TCS}-0.004+0.049\times(J-K)_{TCS}$
$H_{2MASS}=H_{TCS}+0.040-0.030\times(J-K)_{TCS}$
$K_{2MASS}=K_{TCS}+0.003-0.007\times(J-K)_{TCS}$

$J_{2MASS}=J_{Aumann}-0.039+0.069\times(J-K)_{Aumann}$
$H_{2MASS}=H_{Aumann}+0.015+0.001\times(J-K)_{Aumann}$
$K_{2MASS}=K_{Aumann}-0.019+0.001\times(J-K)_{Aumann}$
$J_{2MASS}=J_{Kidger}-0.0199+0.0483\times(J-K)_{Kidger}$
$H_{2MASS}=H_{Kidger}+0.01083-0.01563\times(J-K)_{Kidger}$
$K_{2MASS}=K_{Kidger}+0.00081+0.00257\times(J-K)_{Kidger}$
$K_{2MASS}=K_{Milone}-7.3398-0.0979\times(J-K)_{Milone}+0.2657\times(J-K)^{2}_{Milone}$

The magnitudes used in this work are the averages of all the available
photometry transformed into the 2MASS system. The values and references are
provided in the Table 10 below.

Table 10: Transformed PhotometryaaTable 10 is published in its entirety in machine-readable format. A portion is shown here for guidance regarding its form and content. star | V | IRAC1 | J | H | $K_{S}$ | Refs.bb1, 2MASS; 2, Su & Rieke, unpublished; 3, Allen & Cragg (1983); 4, Bouchet et al. (1991); 5, Alonso et al. (1998); 6, Kidger & Martín-Luis (2003); 7, Aumann & Probst (1991); 8, Carter (1990); 9, Glass (1974) ; 10, McGregor (1994); 11, Johnson et al. (1966); 12, Groote & Kaufmann (1983) | IRAC 1 | $K_{S}$
---|---|---|---|---|---|---|---|---
|  | (Jy) |  |  |  |  | (magccZero point taken to be 276.5 Jy to force zero color for V $-$ $K_{S}$ = 0.) | heritagedd$K_{S}$ magnitude based only on heritage photometry. The JHK magnitudes in the previous columns include 2MASS photometry as well as the transformed heritage photometry whenever unsaturated 2MASS photometry is available.
HD000142 | 5.700 | 4.630 | 4.757 | 4.533 | 4.464 | 1,2 | 4.440 | 4.453
HD000739 | 5.237 | 6.409 | 4.401 | 4.201 | 4.139 | 2 | 4.087 | 4.139
HD001835 | 6.383 | 3.222 | 5.231 | 4.950 | 4.856 | 1,3,4,5 | 4.834 | 4.856
HD003795 | 6.131 | 5.482 | 4.780 | 4.400 | 4.318 | 1,2 | 4.257 | 4.303
HD004307 | 6.147 | 4.022 | 4.981 | 4.723 | 4.610 | 1,6 | 4.593 | 4.599
HD003302 | 5.509 | 4.803 | 4.739 | 4.522 | 4.479 | 1,2 | 4.400 | 4.455

We also calculated specific transformations for the determination of the
magnitude of Sirius by conventional photometry, as discussed in Section 2.1:

$K_{2MASS}=K_{Glass}-0.0243-0.0057\times(J-K)_{Glass}$

This provided a magnitude of -1.375 for Sirius; if we had used the Carpenter
(2001) transformation, we would have obtained -1.373, indicating that our
caution in deriving a new transformation from the Glass (1974) photometry
itself made little difference. The transformation for the Engels et al. (1981)
photometry is

$K_{2MASS}=K_{Engels}-0.0396-0.0018\times(J-K)-0.0202\times(J-K)^{2}_{Engels}$

Appendix B: $K_{S}$ to IRAC Band 1 Color Behavior

Figure 3 compares the $K_{S}$ photometry transformed from heritage
measurements with the 2MASS photometry, based on the $K_{S}-IRAC1$ color as a
function of $V-K_{S}$. (The full set of transformed photometry is provided in
Table 10 and the IRAC Band 1 photometry in Table 11.) The underlying
assumption is that the IRAC photometry is stable, as found in multiple studies
(e.g., Krick et al., 2021). Although for best values, we merge

Table 11: Photometry in IRAC Band 1aaTable 11 is published in its entirety in machine-readable format. A portion is shown here for guidance regarding its form and content. star | Band 1 flux (Jy) | Error (Jy)
---|---|---
HD000319 | 1.817 | 0.050
HD001237 | 3.303 | 0.040
HD003302 | 4.803 | 0.049
HD003369 | 3.683 | 0.049
HD003823 | 4.498 | 0.052
HD004150 | 5.413 | 0.046
HD004277 | 0.866 | 0.029
HD004391 | 5.515 | 0.056
HD006569 | 0.338 | 0.005
HD006767 | 3.500 | 0.050
HD007590 | 2.424 | 0.032
HD008224 | 1.518 | 0.030
HD008556 | 3.149 | 0.049
Figure 3: Color-color plot showing $K_{S}-IRAC1$ vs. $V-K_{S}$ for stars from
Spitzer PID 70076 with $K_{S}$ measurements transformed from heritage $K$
photometry (red squares, 89 stars) compared with stars with only 2MASS $K_{S}$
measurements (small blue dots, 820 stars), over the range of $V-K_{S}$
represented by the former sample, $-0.5<V-K_{S}<2.5$. The blue line is a 4th
order polynomial fitted to the blue dots.

2MASS measurements when they are available with transformed data, in this case
we have separated the two and plot the results only for the heritage $K_{S}$
values. The figure also shows similar color-color measurements for 2MASS
measurements compared with IRAC Band 1. The blue line is a 4th order
polynomial fitted to the 2MASS-only values. We have adjusted the $K_{S}-IRAC1$
color to be zero at $V-K_{S}$ = 0 by making a small adjustment in the assumed
calibration of the IRAC photometry (this affects only a constant in the fit,
which is effectively set to zero). We assume an error for the IRAC
measurements of 1% (Hora et al., 2008) and for both the transformed and 2MASS-
only $K_{S}$ ones of 2%, in the former case as demonstrated in Appendix C and
in the latter, a typical value even for bright stars (Skrutskie et al., 2006).
These errors are combined quadratically and then reduced $\chi^{2}$ values
calculated for each of the heritage and 2MASS-only photometry. The values are
0.68 and 0.96 respectively for the transformed and native 2MASS sets of
measurements. The average offset in $K_{S}-IRAC1$ between the transformed
photometry and the line fitted to the 2MASS-only results is $0.0014\pm 0.0021$
magnitudes, where the error is the standard deviation.

As with Appendix C, this test confirms the accuracy of the transformed $K_{S}$
photometry, in this case on a different sample of (much fainter) stars. It
further demonstrates that the transformed values are accurately on the 2MASS
$K_{S}$ photometric system. Therefore, we merge the two sets of data and
determine an overall relation between $V-K_{S}$ and $K_{S}-IRAC1$:

$K_{S}-IRAC1=-0.001228\times x^{4}+0.014382\times x^{3}-0.042158\times
x^{2}+0.057587\times x,$ $None$

where $x$ = $V-K_{S}$.

The limiting faint $K_{S}$ magnitude for this sample is $\sim$ 6, except for a
small number of very red and low luminosity stars. Taking values of $M_{K}$
from Mamajek (2018), the stars of type A0V and later therefore lie within 100
pc, i.e., are within the Local Bubble. Similarly stars with $V-K_{S}>$ 1
(later than F4V) lie within 60 pc. Within 100 pc, the level of extinction is
uniformly very low, with $E(b-y)<0.03$ (Reis et al., 2011), i.e., $A_{V}<0.1$
and typically $\sim$ 0.04. Low levels of extinction move the points in Figure
3 diagonally, and values of $A_{V}<0.1$ (or $\sim$ 0.04)have very little
overall effect on the relation in equation (2) (based on the extinction
relations in Rieke & Lebofsky (1985) and Gordon et al. (2021) \- ($A_{V}$ =
0.04 corresponds to E($K_{S}-IRAC1)\sim 0.002$)). We can therefore use this
equation as a general conversion for IRAC Band 1 measurements to $K_{S}$ for
main-sequence stars.

Appendix C: Test of the Accuracy of GG and Transformed Groundbased Photometry

To test the accuracy of both the COBE DIRBE 2.2 $\mu$m photometry (converted
to K magnitudes with an assigned zero point) and our transformed heritage
photometry onto the 2MASS $K_{S}$ system, we have compared K-magnitudes for
all the stars brighter than 2nd magnitude. This gives us an initial sample of
507 stars, which we have trimmed to eliminate stars that are variable, or have
missing data or nearby stars bright enough to affect the DIRBE photometry. For
the fainter stars, the DIRBE photometry is not sufficiently sensitive to
eliminate variability to the level of 3%, which is the threshold we have
adopted. We therefore have also cut stars of types where variability is common
but the DIRBE data are not definitive in this regard. The overall statistics
are summarized in Table 12. We fitted a linear transformation in $J-K$ vs.
$2.2_{DIRBE}$ $-$ $K_{S}$ and corrected the DIRBE results to be equivalent to
the 2MASS system.

Table 12: Source Counts for Transformed and DIRBE Photometry

Total | DIRBE variablesaaAs determined by Smith et al. (2004). | Missing Data | Nearby StarsbbWhere the DIRBE data had inadequate signal to noise to probe variability to the 1$\sigma\sim$ 2% level, we rejected all stars of types S, C, and MIII since they have a relative high probability of being variable.  | C, S, or MIIIccfootnotemark:  | Final Sample
---|---|---|---|---|---
507 | 53 | 63 | 44 | 64 | 283

aafootnotetext: We rejected all cases where the 2MASS survey showed a star at
$K_{S}$ $\gtrsim$ 3% as bright as the target star within the DIRBE beam.

Table 13: Error Analysis of Transformed and DIRBE Photometry Error Source | rms | rms | rms | rms | rms | rms
---|---|---|---|---|---|---
DIRBE assumed | 0 | 0.005 | 0.010 | 0.015 | 0.020 | 0.022
2MASS derived | 0.022 | 0.0215 | 0.019 | 0.0155 | 0.008 | 0
2MASS 2$\sigma$ upper limit | 0.027 | 0.026 | 0.024 | 0.021 | 0.017 | –

We found that the rms scatter in $2.2_{DIRBE}$ $-$ $K_{S}$ for the 127 stars
brighter than 1st magnitude is 0.026 mag. The rms scatter for the full sample
is larger, 0.043 mag, reflecting the lower signal to noise in the DIRBE
measurements of the fainter stars. We therefore turned to a $\chi^{2}$
analysis of the full sample of 283 stars. We assumed that the uncertainty for
each star consisted of the $rms$ combination of $<$err$>$ tabulated for that
star in Smith et al. (2004), plus a value for additional DIRBE and transformed
2MASS photometry that we varied to understand the permissible tradeoffs. The
results are in Table 13. They show that the $rms$ errors in our transformed
photometry are no more than $\sim$ 2%, similar to the errors in the 2MASS
photometry of non-saturated stars (Skrutskie et al., 2006). From evaluating
the scatter in standard colors for the stars with transformed photometry, we
believe that the derived values significantly $<$ 2% are overly optimistic.
Thus, with care to eliminate stars in the DIRBE beam, this instrument can
deliver photometry at the 1% level, according to this study.