Astrophysical Distance Scale The JAGB Method: I. Calibration and a First Application

J-Branch Asymptotic Giant Branch (JAGB) stars are a photometrically well-defined population of extremely red, intermediate-age AGB stars that are found to have tightly-constrained luminosities in the near-infrared. Based on JK photometry of some 3,300 JAGB stars in the bar of the Large Magellanic Cloud (LMC) we find that these very red AGB stars have a constant absolute magnitude of= -6.22 mag, adopting the Detached Eclipsing Binary (DEB) distance to the LMC of 18.477 +/- 0.004 (stat) +/- 0.026 (sys). Undertaking a second, independent calibration in the SMC, which also has a DEB geometric distance, we find= -6.18 +/- $ 0.01 (stat) +/- 0.05~(sys) mag. The scatter is +/-0.27 mag for single-epoch observations, (falling to +/-0.15~mag for multiple observations averaged over a window of more than one year). We provisionally adopt= -6.20 mag +/- 0.01 (stat) +/- 0.04 (sys) mag for the mean absolute magnitude of JAGB stars. Applying this calibration to JAGB stars recently observed in the galaxy NGC 253, we determine a distance modulus of 27.66 +/- 0.01(stat) +/- 0.04 mag (sys), corresponding to a distance of 3.40 +/- 0.06 Mpc (stat). This is in excellent agreement with the averaged TRGB distance modulus of 27.68 +/- 0.05 mag, assuming M_I = -4.05 mag for the TRGB zero point.


INTRODUCTION
J-Type Asymptotic Giant Branch (JAGB) stars were first isolated as a distinct class of objects by Weinberg & Nikolaev (2001). Figure 1 reproduces their K vs (J − K) color-magnitude diagram defining eleven distinct sequences of stars, as seen in the 2MASS data for the Large Magellanic Cloud. JAGB stars are high-luminosity asymptotic giant branch (AGB) stars, whose colors are very red and whose intrinsic luminosities are well defined, and restricted to a narrow color range. JAGB stars almost certainly contain a subset of the spectroscopically classified "carbon-rich" population of intermediate-age, intermediate-mass stars in galaxies. And they also overlap with a subset of Mira variables in specific, and with Long-Period Variables (LPV) more generally, with those stars being sub-classified as such by their variability, amplitudes, colors and periods, etc. Within the context of this work on the extragalactic distance scale and within the following series of papers, JAGB stars are being defined and identified in terms of purely single-epoch photometric criteria. Their overlap with carbon stars and LPVs will play an interesting, but background role in understanding the JAGB stars' evolutionary status, and in optimizing their practical use as extragalactic distance indicators; but, we emphasize from the outset that we do not rely either on spectral data nor on time-domain information to make efficient use of JAGB stars as high-precision and accurate extragalactic distance indicators.
In a companion paper (Freedman & Madore 2020) we discuss the historical context and empirical evidence for JAGB stars being high-precision distance indicators. Based on previously published near-infrared data, we extend our application of this method to a sample of 14 galaxies, both within the Local Group and out to a distance of 4 Mpc. With this sample we can assess the accuracy and current precision of the JAGB method by making a comparison with published distances that are based on the tip of the red giant branch (TRGB) method.
In this contribution we use three galaxies to build, calibrate and then test this new parallel path in the establishing the extragalactic distance scale. The LMC and SMC are used to establish the zeropoint of the JAGB method, and the galaxy NGC 253 is used as an extreme-case system, having been observed at the current distance limit, for ground-based telescopes, of about 4 Mpc. Published, nearinfrared color-magnitude diagrams (CMDs) show that JAGB stars have been found in abundance and easily measured in all three galaxies.
We conclude that the JAGB method can take its place shoulder-to-shoulder with the Leavitt Law for Population I Cepheids and the TRGB method for Population II red giant branch stars. Taken as a whole, we refer to this tripartite ensemble of stellar distance indicators as forming the basis of the Astrophysical Distance Scale.

THE LMC
Near-infrared JHK data used here for the LMC calibration of the JAGB method were taken from Macri et al. (2015). These observations are to be preferred over previously-available 2M ASS data (as used by Weinberg & Nikolaev 2001) for a number of reasons: the Macri photometry is of higher precision and of better spatial resolution (alleviating crowding), and most importantly these data are temporally averaged. The Macri data, which are all on the 2MASS photometric system, were collected over 13 months, resulting in an average of 16 epochs being obtained for each star in the survey. The cadence and window over which the observations were made were chosen so as to be able to identify known Cepheids and to discover new long-period variables in order to determine their periods, amplitudes phases and mean magnitudes in the near infrared. The Cepheids are treated in Macri et al., while the Miras are discussed in Yuan et al (2017).
It is also important to note that the Macri sample is confined to the bar of the LMC. This region is co-located with the Detached Eclipsing Binary (DEB) stars, used for a geometric determination of the distance to the LMC, were observed by Pietrzynski et al. (2019). Having the DEBs and JAGB stars located co-spatially minimizes concern that the two populations might be at different mean distances due to inclination effects and/or the generic back-to-front geometry of the LMC (e.g., Welch et al. 1987, Weinberg & Nikolaev, 2011, Scowcroft et al. 2011. For the LMC bar and for our Figure 1. A near-infrared CMD for stars observed by Macri et al. (2015) in the bar of the Large Magellanic Cloud. We draw attention to the narrowly defined feature in the center of the plot, labeled as Region J, and highlight this region in the expanded plot to the right. This is the defining plot for our JAGB stars. Extreme carbon stars (having developed strong winds and probably producing dust in them) sparsely occupy Region K, redward of the JAGB population. Interested readers are referred to the originating paper for details on the other branches and populations delimited in this figure, noting that all other populations are blueward of the JAGB stars studied here.
JAGB stars we adopt a true distance modulus of µ o = 18.477 mag, carrying a systematic error of ±0.026 mag, as attributed to the DEB population by Pietrzynski et al. Figure 2 shows the J − (J − K) time-averaged, near-infrared CMD for the 3.5 million LMC stars published in Macri et al. (2015). The dominant population of red stars, rising vertically from J ∼ 14.5 mag at around (J − K) = 1.0 mag consists of the Population II red giant branch (RGB), continuing up to its "tip" at J ∼ 13.5 mag (Hoyt et al. 2018). This is followed (almost without  Macri et al. (2015). The AGB population, as marked, is seen to be constant in luminosity as a function of color within the color range 1.30 ≤ (J − K) ≤ 2.00 mag. In the right-hand panel the smoothed luminosity function of stars within that same color range is shown.
interruption in this high-density plot) by the "oxygen-rich" AGB plume (marked midway at J ∼ 12.5 mag). This feature continues up another several magnitudes to J ∼ 10.5 mag in this diagram. It is important to note that both of these red populations, and almost all of the other dominant stellar populations in the near-infrared CMD are confined to colors that are bluer than (J − K) ∼ 1.3 mag. Redward of this limit there is only one noteworthy population, that being the object of this study, i.e., the population of JAGB stars.
Operationally, we simply define JAGB stars to have near-infrared colors between 1.30 < (J − K) < 2.00 mag. The red limit eliminates the possibility of low level contamination from extreme carbon stars that fall in magnitude and continue out to (J − K) > 4.5 mag, constituting what Weinberg & Nikolaev (2001) have independently designated as constituting a separate population, the "K Branch" (see Figure 1).

ABSOLUTE CALIBRATION
As we proceed in the calibration of the absolute magnitude of the JAGB method we begin by reviewing the conclusions reached earlier by Weinberg & Nikolaev (2001). They found a tight correlation between the (J − K) color and the K−band luminosity of the "J-branch" stars as delimited and separated out in Figure 1. A luminosity-color fit to their 2MASS data in the J Branch gave where D o is the K-band zero point of this particular "color-magnitude" relation. What Weinberg & Nikolaev did not comment on was that, by (not unreasonably) adopting a unit slope for the color term, their relation becomes which, upon transposing the color term, becomes Simply stated, in the near-infrared J-band, JAGB stars have a constant mean magnitude, independent of color. Weinberg & Nikolaev (2000) measured the scatter in their single-epoch data to be on the order of σ JAGB = ±0.33 mag. However, in the presence of known variability in the JAGB star population, the question naturally arises as to what the intrinsic (i.e., the time-averaged) scatter is for these stars. If we assume that the average amplitude of these stars is 0.7 mag (which corresponds to an equivalent sigma of ±0.22 mag) then subtracting this in quadrature from the observed (single-epoch) scatter ±0.33 mag gives an upper limit of σ o = ±0.25 mag for the intrinsic scatter of the JAGB method. The observed, time-averaged scatter seen in the JAGB LMC-bar sample (Macri et al.) is found to be ±0.15 mag. Given the possibility of additional, currently unaccounted for, sources of scatter (residual depth effects, crowding and photometric errors, etc.) we take this, already small, value for the intrinsic dispersion to still be an upper limit on the method. 1 .

The Large Magellanic Cloud (LMC)
By adopting a true distance modulus to the LMC bar of µ o = 18.477 mag and an apparent mean magnitude of J =12.31 ± 0.01 mag for the 3,341 JAGB stars studied here (also in the bar), we find that the mean absolute J-band zero point of the JAGB method (corrected for A J = 0.053 mag of foreground extinction, NED) is M Jo (LM C) = -6.22 mag ± 0.01 (stat) ± 0.03 (syst).
1 Indeed, some Mira are known to have amplitudes up to 10 mag (peak-to-peak) in the blue. However, most of what is (residually) seen in the NIR is the sinusoidal variation of the radius, giving K-band amplitudes of less than 0.5 mag according to Weinberg & Nikolaev. Similarly, Smith et al. (2002) cite average J-band amplitudes of 0.5 mag. On the other hand Huang et al. (2018) find H-band amplitudes of LMC Miras typically fall in the range of 0.4 to 1.3 mag, with an average amplitude of about 0.8 mag. Here we have adopted a provisional value of 0.7 mag for the average J-band amplitude). Weinberg & Nikolaev (2000) give a detailed break down of the various additional terms contributing to their single-phase observed scatter of ±0.33 mag. Those factors include back-to-front depth, photometric errors, differential extinction, and intrinsic scatter in their J Branch mean stellar magnitudes, and in their own words, they conclude that "This is direct evidence that our color-selected sources are standard candles at least as good as σ ∼ 0.2 mag. In fact, they are even better ..."

The Small Magellanic Cloud (SMC)
The SMC may not seem to be an ideal object for testing the JAGB method, given that it is well known to be highly disturbed and tidally extended on the sky (e.g., Scowcroft et al 2017, and references therein), presumably because of interactions with both the LMC and the Milky Way. But, one can select a sub-sample of JAGB stars found in a one-degree-radius circular region centered on the main body of the SMC, which may arguably be less dispersed along that particular line of sight, when compared to the tidal tails, far from the main body (see Scowcroft et al.). The JHK photometry for that subset of 116,298 SMC stars was extracted from the 2MASS on-line version of that survey, available through IRSA. The CMD and luminosity function for the JAGB stars in the SMC are each shown in Figure 3. 3,405 JAGB stars contributed to the color-selected luminosity function, yielding a mean apparent magnitude of J = 12.81±0.01 mag. The DEB distance modulus to the SMC is µ o = 18.965 mag, as published by Graczyk et al. (2014). Those DEB stars are centered on this same region of the SMC, making it not unreasonable to assume that their mean distance is the same as the average distance of the selected JAGB stars. Applying a foreground Galactic extinction correction of A J = 0.026 mag to the apparent magnitude of the JAGB stars, and correcting for distance yields M Jo (SM C)= -6.18 mag ± 0.01 (stat) ± 0.05 (syst).

A PROVISIONALLY ADOPTED JAGB ZERO POINT
Taking the two geometrically-calibrated zero points, based on DEB distances to the LMC and SMC we arrive at our first estimate of the J-band zero point of the JAGB distance scale: M Jo =-6.20 mag ± 0.01 (stat) ± 0.04 (syst).
For single-epoch observations, the scatter in the JAGB method is found by Weinberg & Nikolaev (2001) to be ±0.27 mag. For time-averaged observations, the scatter reduces to ±0.15 mag (Macri et al. 2015). In conservatively adopting the larger dispersion, a sample of 200 JAGB stars can deliver a distance that is statistically good to a precision of 1%. To put that sample size in perspective, even in the restricted bar region of the LMC (itself a relatively low-mass, low-luminosity galaxy) there are over 3,000 of these stars cataloged.
All galaxies with intermediate-age populations are now candidates for having high-precision distances determined by the JAGB method. In what follows, we make the first application of this method to the galaxy NGC 253 at 3.5 Mpc, some 70 times more distant than the LMC.

NGC 253: A FIRST TEST OF THE JAGB METHOD OUTSIDE OF THE LOCAL GROUP
For NGC 253 there are four modern HST detections of TRGB stars outside of the main disk of this nearly edge-on galaxy. Each determination has been standardized to an absolute I-band magnitude for tip of M I = -4.05 mag and uniformly corrected for the same foreground extinction of A I = 0.136 mag (NED). The homogenized distance moduli are 27.53 mag (Mouchine et al. 2005), 27.68 mag (Dalcanton et al. 2009), 27.67 mag (Rayburn-Smith et al. 2011) and 27.82 mag (Jacobs et al. 2009). The averaged TRGB distance modulus is found to be < µ o (T RGB) >= 27.68 mag ± 0.06 (scatter on the mean).
Ground-based Z and J band data, used for the JAGB detection, were published by Greggio et al. (2014) based on observations made as part of the V IST A science verification process. The CMD is shown in Figure 4. 3,169 JAGB stars in NGC 253 give an apparent distance modulus of µ J (JAGB) = 27.67 ± 0.006 mag. Correcting for a foreground extinction of A J = 0.013 mag (NED), the true JAGB distance modulus to NGC 253 then becomes µ o (JAGB) = 27.66 ± 0.01 mag (stat).
The agreement of these two determinations, made at the current limit of ground-based observing, is very encouraging, and foreshadows the confirming results of an inter-comparison of a significantly larger sample of JAGB and TRGB distances to nearby galaxies, given in Freedman & Madore (2020). But what can be said here is that the low-metallicity calibration made using the LMC [Z = 8.50] amd SMC [Z = 7.98] appears to apply equally well to the high-metallicity galaxy NGC 253 [Z = 8.99, (Zaritsky et al. 2000, which is almost identical to the metallicity of M 31, at Z = 8.98] whose JAGB distance is in exact agreement with its independently-determined TRGB distance. Before concluding this paper, we next give a short description of the physics behind the JAGB method, showing that current models can justifiably claim to describe most of the salient aspects of this promising, new distance indicator.

A VERY BRIEF INTRODUCTION TO STELLAR EVOLUTION MODELS
Stellar evolution models have become sufficiently sophisticated of late that they can accommodate many of the details leading up to and including the transition producing carbon-rich AGB stars from their thermally-pulsing (TP) oxygen-rich precursors (see Habing & Olofsson 2004 for extensive reviews, and especially Marigo et al. 2008Marigo et al. , 2017 for more recent updates.) The intermediate-age, intermediate-metallicity TP-AGB stars, that are of interest to us here, as a whole have a narrowlydefined range of masses, going from 2 to 5 M . As Marigo et al. (2008) show (and as can be seen in Figure 5), these same stars (that have ages between 300 Myr and 1 Gyr) are also tightly constrained in luminosity at their latest stages, being funneled into a carbon-rich phase whose total range is only ∆log(L/L ) = 0.5 (i.e., σ = ±0.31 mag) at Z = 0.008. Those evolutionary tracks are shown in Figure 5 as a muted backdrop to a schematic of the RGB/AGB populations highlighted in color, and emphasizing a variety of interesting features: (1) the RGB population (in green) terminates at its so-called 'tip' (horizontally defined at log(L/L ) = 3.4) at a luminosity that is at least 3 magnitudes fainter than the upper limit of oxygen-rich AGB population, rising above the TRGB, at approximately the same color and effective temperature. Bold black arrows trace the evolutionary tracks within the oxygen-rich AGB phase, showing the focusing of those tracks on the carbon-rich phase at significantly lower effective temperatures, and within the aforementioned small range of luminosities.
It should be noted that the stellar interior physics, predicting the narrowly confined luminosities of carbon stars has been part of stellar evolution theory for nearly half a century. As for the reaction of the atmospheres, that situation is succinctly summarized by Marigo (2008) wherein "... the main physical effects driving the appearance of the red tail of C stars, are the cool effective temperatures, caused by changes in molecular opacities, as the third dredge-up events increase the C/O ratio." The reasons for the upper and lower cut-offs to the oxygen-rich AGB evolution towards the red have also been known and understood for decades. The sole reason for these advanced-evolutionary-phase stars becoming as red as some of them do is because of carbon being transferred from the interior out into the envelope (and then into the atmosphere). The "dredge-up" episodes (number 3 and beyond), that penetrate deep enough into the interior to reach the carbon-rich, helium-burning shell, are only effective in bringing carbon to the surface for masses in excess of 1.2-1.3 M (Groenewegan & Marigo 2004). Below that critical mass AGB stars cannot, and do not, develop carbon-rich atmospheres. This leads to a lower bound on carbon star luminosities (Iben & Renzini 1983). At the other extreme, an upper limit on carbon star masses (and luminosities) comes from the destruction of carbon at the base of the convective zone. This occurs when the temperature in the carbon-rich interior region becomes so hot that carbon itself burns, leaving none of it left to be convected to the surface. This phase transition to "Hot-Bottom Burning" turns on for AGB stellar masses in excess of 3.5 M (Iben 1973, Sackmann et al. 1974, and it may be cutting in at 2M for very low metallicity stars (Siess et al. 2002). Finally, Karakas (2014), in her Figure 3, shows that the distribution functions of the C/O ratio as a function of initial mass, all come to a maximum within the narrow mass range of 3.0 to 3.6 M , for the three metallicities she considers (those being Z = 0.007, 0.014 & 0.030). Her models also indicate that C/O ratios on the surface exceed unity predominantly in the mass range from 2.0 to 4.5 M .  Marigo et al. (2008) are plotted in the logT ef f versus logL plane, showing the final phases of asymptotic giant branch evolution leading to the carbon-rich JAGB stars. The first-ascent RGB stars are highlighted in green, and the oxygen-rich AGB stars are shown in blue.
The region containing the carbon-rich JAG stars is highlighted in red. The funneling effect is the result of (1) "Hot-Bottom Burning", at high luminosities, destroying the carbon before it can be brought to the surface, and then (2) at lower luminosities and lower masses, "the third dredge-up phenomenon" no longer occurs, and the earlier two dredging events do not reach deep enough to touch the shell-burning carbon-rich region. These two cut-off regions are marked and named above and below the "Carbon Rich" JAGB region.
JAGB stars are easily identified in the near infrared by their extremely red colors. They are also very luminous and have a well-defined mean magnitude in the J band that is constant with color. Based on a sample of 3,300 JAGB stars in the bar of the LMC, and a similar number of JAGB stars in the main body of the SMC, we have calibrated the mean absolute magnitude of JAGB stars in the near-infrared J band. Using the detached eclipsing binary (DEB) distance modulus of 18.477 mag to the LMC and an SMC DEB distance modulus of 18.965 mag, we provisionally find the mean J-band absolute magnitude of the JAGB stars to be M Jo = -6.20 ± 0.01 (stat) ± 0.04 (sys) mag.
A more extensive application of the JAGB method to galaxies within and beyond the Local Group, extending out to 4 Mpc is presented in a companion paper (Freedman & Madore 2020).

ACKNOWLEDGEMENTS
We thank the it University of Chicago and Observatories of the Carnegie Institution for Science and the University of Chicago for their support of our long-term research into the calibration and determination of the expansion rate of the Universe. Support for this work was also provided in part by NASA through grant number HST-GO-13691.003-A from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. This research would simply not have been possible without the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.