CaHK-band Photometry: Methods & Applications

• CaHK-band photometry is a method that measures the Ca II H and K spectral lines using narrow-band filters to capture metallicity-sensitive signals.
• It integrates narrow-band measurements with broad-band colors to control temperature effects and calibrates through systems like Gaia DR3 and neural networks.
• Advanced calibration techniques reduce systematic errors to ~0.01 mag, enabling precise metallicity determinations in both individual stars and integrated stellar populations.

CaHK-band photometry denotes photometric measurements of the spectral region containing the Ca II H and K resonance lines, usually with a narrow-band filter centered near $395\,\mathrm{nm}$ or $3955\,\text{\AA}$. In contemporary stellar-population work, the method is used primarily as a metallicity-sensitive observable: at fixed broad-band color, metal-poor stars have weaker Ca H&K absorption and therefore transmit more flux through the CaHK band, making their CaHK magnitudes brighter relative to continuum bands. The same spectral region is also used in integrated light for old stellar systems, in chromospheric activity diagnostics, and in solar Ca II K imaging, although the physical interpretation differs across those domains (Martin et al., 2023, Heumen et al., 18 Aug 2025, Chatzistergos et al., 2017).

1. Spectral basis and diagnostic content

The CaHK band is anchored to the Ca II K and H lines at $393.37\,\mathrm{nm}$ and $396.85\,\mathrm{nm}$, or equivalently $3933.66$ and $3968.47\,\text{\AA}$, depending on the convention used in a given study. In the Pristine framework the filter is described as a narrow-band, metallicity-sensitive CaHK filter centered near $395\,\mathrm{nm}$ with a near-top-hat transmission curve. In the DECam MAGIC survey the analogous filter, N395, is specified as having $\mathrm{CWL} = 3951.90~\text{\AA}$ and $\mathrm{FWHM} = 100.10~\text{\AA}$, with a design deliberately close to the Pristine CaHK filter (Martin et al., 2023, Chiti et al., 26 May 2026).

In stellar metallicity work, CaHK photometry is not interpreted in isolation. The narrow-band measurement is combined with broad-band colors that act as temperature proxies. Several color constructions are in active use. In the Pristine–Gaia system, the metallicity-sensitive plane is built from $(G_{\rm BP}-G_{\rm RP})_0$ and $3955\,\text{\AA}$0. In Sagittarius II and Draco II, the practical diagnostic is $3955\,\text{\AA}$1 versus $3955\,\text{\AA}$2. In MAGIC, the canonical color combination is $3955\,\text{\AA}$3 versus $3955\,\text{\AA}$4. In each case the broad-band color controls the temperature dependence and the CaHK residual carries the metallicity information (Martin et al., 2023, Longeard et al., 2019, Longeard et al., 2018, Chiti et al., 26 May 2026).

In integrated-light work the same logic is applied to unresolved old stellar systems. The M31 globular-cluster study used the dereddened colors $3955\,\text{\AA}$5 and $3955\,\text{\AA}$6, with the broad-band filter serving as a local continuum measure on either side of the CaHK bandpass. Because old globular clusters are dominated by late-type stars and are nearly mono-metallic, the Ca II H&K region remains useful even when broad-band colors have begun to lose metallicity sensitivity in the very metal-poor regime (Heumen et al., 18 Aug 2025).

Outside metallicity studies, the same spectral region traces different physics. In active late-type stars, Ca II H&K line-core emission is a chromospheric diagnostic. In solar Ca II K spectroheliograms, the line is used to map plage, network, and long-term chromospheric magnetic variability. A plausible implication is that “CaHK-band photometry” is best understood as a family of passband measurements whose meaning depends on whether the dominant signal is photospheric absorption, chromospheric core emission, or image contrast relative to the quiet Sun (Marvin et al., 2023, Chatzistergos et al., 2017, Özdarcan et al., 2018).

2. Filter systems, surveys, and calibration frameworks

The best-developed wide-field CaHK program in the northern sky is Pristine, which uses the MegaCam CaHK narrow-band filter on CFHT. The filter was procured in 2014 for MegaCam, and by the first public data release the survey had obtained $3955\,\text{\AA}$7 images covering more than $3955\,\text{\AA}$8. Since 2016B, typical observing has been a single $3955\,\text{\AA}$9 exposure per field. Pristine data are preprocessed by Elixir, and astrometry plus aperture photometry are performed with the CASU pipeline (Martin et al., 2023).

A central development in CaHK calibration is the use of Gaia DR3 BP/RP spectro-photometry to synthesize Pristine-like CaHK magnitudes, $393.37\,\mathrm{nm}$0, with GaiaXPy. Synthetic magnitudes were computed for $393.37\,\mathrm{nm}$1 million Gaia DR3 sources with BP/RP coefficient information and then used as the absolute reference system for recalibrating Pristine photometry. The calibration model is

$393.37\,\mathrm{nm}$2

where $393.37\,\mathrm{nm}$3 is an image-specific zero point and $393.37\,\mathrm{nm}$4 is a run-dependent field-of-view correction. The implementation uses the neural-network model PhotCalib, with three fully connected layers of 200 neurons each. After recalibration, the mean residual between calibrated Pristine and Gaia synthetic CaHK is $393.37\,\mathrm{nm}$5, and repeat observations imply a final systematic uncertainty floor of $393.37\,\mathrm{nm}$6 (Martin et al., 2023).

In the southern sky, MAGIC extends the same basic concept to DECam. The survey is a 54-night NOIRLab Survey Program using a narrow-band filter covering Ca II H&K and centered at $393.37\,\mathrm{nm}$7. It is designed to cover $393.37\,\mathrm{nm}$8 and reaches a typical $393.37\,\mathrm{nm}$9 depth of $396.85\,\mathrm{nm}$0. Calibration is again tied to synthetic CaHK magnitudes from Gaia XP spectra, derived with GaiaXPy; each pointing is calibrated with a per-pointing zeropoint, using calibration stars with synthetic CaHK uncertainty $396.85\,\mathrm{nm}$1, and the typical number of calibrators per pointing is $396.85\,\mathrm{nm}$2. The adopted extinction coefficient is

$396.85\,\mathrm{nm}$3

The survey also notes that subtle second-order zeropoint corrections and/or UberCal-style global calibration may be needed in future processing (Chiti et al., 26 May 2026).

Calibration issues also appear in targeted studies. In the M31 globular-cluster imaging study, calibration used synthetic photometry from Gaia XP spectra via GaiaXPy, transformed to the MegaCam system where necessary. CaHK zero points were corrected for the known $396.85\,\mathrm{nm}$4 mag offset between Gaia synthetic and Pristine CaHK magnitudes, and field-of-view corrections were applied to $396.85\,\mathrm{nm}$5, $396.85\,\mathrm{nm}$6, and CaHK. The derived systematic uncertainties were

$396.85\,\mathrm{nm}$7

with the systematic terms dominating the error budget for most clusters (Heumen et al., 18 Aug 2025).

3. Resolved stellar populations and photometric metallicities

In dwarf-galaxy and halo applications, CaHK photometry is used both star-by-star and at the population level. Sagittarius II and Draco II provide clear examples. In Sagittarius II, the photometric metallicity of each star is estimated from $396.85\,\mathrm{nm}$8 using the Pristine model. The authors do not take the raw Pristine metallicities at face value at the lowest metallicities, but correct the known metal-poor bias empirically with the calibration sample of Starkenburg et al. Reliability cuts exclude stars with $396.85\,\mathrm{nm}$9, $3933.66$0, or $3933.66$1, and the CaHK metallicities are used only down to $3933.66$2 because the narrow-band data are shallower than the deep broad-band imaging (Longeard et al., 2019).

For the Sagittarius II metallicity distribution, the intrinsic system metallicity is modeled as a Gaussian broadened by the individual photometric uncertainties,

$3933.66$3

Using 206 stars within $3933.66$4, the inferred values are

$3933.66$5

Independent DEIMOS Ca II triplet spectroscopy yields

$3933.66$6

and the combined final estimate is

$3933.66$7

The CaHK data also serve as a hard contamination filter for spectroscopy, including rejection of one star in the velocity peak with $3933.66$8, deemed too metal-rich to be a likely Sagittarius II member (Longeard et al., 2019).

Draco II shows the same dual use. After empirical low-metallicity bias correction, the CaHK metallicity distribution of stars within $3933.66$9 is modeled as a Dra II Gaussian plus an empirical background built from stars outside $3968.47\,\text{\AA}$0, with star-by-star broadening

$3968.47\,\text{\AA}$1

The inferred mean metallicity is

$3968.47\,\text{\AA}$2

with unresolved metallicity dispersion,

$3968.47\,\text{\AA}$3

In this study the CaHK metallicity is explicitly favored over the CMD-fit metallicity and over a Ca-triplet estimate from three faint low-RGB stars (Longeard et al., 2018).

The methodology has now been scaled to survey catalogs. The Pristine–Gaia DR3 release provides synthetic CaHK magnitudes for all Gaia DR3 BP/RP sources with coefficient information and more than $3968.47\,\text{\AA}$4 million photometric metallicities for high-S/N FGK stars. The resulting metallicity catalog is stated to be accurate down to $3968.47\,\text{\AA}$5 and particularly suited for $3968.47\,\text{\AA}$6. Combined, the synthetic and Pristine-based catalogs contain more than two million metal-poor candidates with $3968.47\,\text{\AA}$7, more than 200,000 with $3968.47\,\text{\AA}$8, and $3968.47\,\text{\AA}$9 with $395\,\mathrm{nm}$0. The recommended catalog-level cuts include

$395\,\mathrm{nm}$1

with stricter use often adopting $395\,\mathrm{nm}$2, $395\,\mathrm{nm}$3, $395\,\mathrm{nm}$4, and $395\,\mathrm{nm}$5 (Martin et al., 2023).

MAGIC adopts a different but closely related forward-modeling strategy. Synthetic spectra are generated with Turbospectrum, MARCS atmospheres, and VALD line lists over

$395\,\mathrm{nm}$6

with $395\,\mathrm{nm}$7 synthetic spectra in total. The photometric metallicity is inferred in the plane $395\,\mathrm{nm}$8, with gravity estimated from 12 Gyr Dartmouth isochrones and Gaia parallaxes or proper motions used to separate main-sequence from RGB solutions. The adopted systematic metallicity uncertainty floor is $395\,\mathrm{nm}$9. Against APOGEE DR17, the median offset is $\mathrm{CWL} = 3951.90~\text{\AA}$0 and the scatter is $\mathrm{CWL} = 3951.90~\text{\AA}$1. Initial follow-up further shows that among 28 stars with $\mathrm{CWL} = 3951.90~\text{\AA}$2, 25 have $\mathrm{CWL} = 3951.90~\text{\AA}$3, while among 22 stars with $\mathrm{CWL} = 3951.90~\text{\AA}$4, 13 have $\mathrm{CWL} = 3951.90~\text{\AA}$5 (Chiti et al., 26 May 2026).

4. Integrated-light CaHK photometry and globular clusters

Integrated-light CaHK photometry has been tested explicitly as a selection tool for massive globular clusters below the putative globular-cluster metallicity floor, $\mathrm{CWL} = 3951.90~\text{\AA}$6. The motivating case is the M31 cluster EXT8, which is both extremely metal poor, $\mathrm{CWL} = 3951.90~\text{\AA}$7, and very massive, $\mathrm{CWL} = 3951.90~\text{\AA}$8. The M31 study used CFHT MegaCam imaging in July 2022 for 126 globular clusters spanning $\mathrm{CWL} = 3951.90~\text{\AA}$9, including EXT8 and the additional very metal-poor candidates B157-G212 $\mathrm{FWHM} = 100.10~\text{\AA}$0 and B160-G214 $\mathrm{FWHM} = 100.10~\text{\AA}$1. The observing pattern was $\mathrm{FWHM} = 100.10~\text{\AA}$2 s in CaHK and $\mathrm{FWHM} = 100.10~\text{\AA}$3 s in each of $\mathrm{FWHM} = 100.10~\text{\AA}$4, $\mathrm{FWHM} = 100.10~\text{\AA}$5, and $\mathrm{FWHM} = 100.10~\text{\AA}$6, chosen to reach $\mathrm{FWHM} = 100.10~\text{\AA}$7 in CaHK for a typical M31 globular cluster (Heumen et al., 18 Aug 2025).

The integrated-light measurements were made with SourceExtractor on Elixir-preprocessed images, using a fixed circular aperture of diameter $\mathrm{FWHM} = 100.10~\text{\AA}$8. No aperture correction was applied, so the magnitudes were intended only for colors. The two central colors are $\mathrm{FWHM} = 100.10~\text{\AA}$9 and $(G_{\rm BP}-G_{\rm RP})_0$0. Their behavior with metallicity differs sharply. $(G_{\rm BP}-G_{\rm RP})_0$1 spans only about $(G_{\rm BP}-G_{\rm RP})_0$2 mag across the full metallicity range and is non-monotonic, with a maximum near $(G_{\rm BP}-G_{\rm RP})_0$3. The reported Spearman coefficients are

$(G_{\rm BP}-G_{\rm RP})_0$4

The explicit conclusion is that $(G_{\rm BP}-G_{\rm RP})_0$5 cannot be interpreted alone as a unique metallicity indicator and must be paired with another color to break the degeneracy (Heumen et al., 18 Aug 2025).

By contrast, $(G_{\rm BP}-G_{\rm RP})_0$6 is much cleaner. Over the full sample it has a strong positive correlation with metallicity,

$(G_{\rm BP}-G_{\rm RP})_0$7

and changes by about $(G_{\rm BP}-G_{\rm RP})_0$8 mag from $(G_{\rm BP}-G_{\rm RP})_0$9 at the metal-poor end to $3955\,\text{\AA}$00 near solar metallicity. The relation appears approximately bilinear, with a break around $3955\,\text{\AA}$01; above that break, $3955\,\text{\AA}$02, while below it $3955\,\text{\AA}$03. Even in the metal-poor regime, however, the color remains sufficiently monotonic for candidate selection (Heumen et al., 18 Aug 2025).

For clusters with $3955\,\text{\AA}$04, the fitted linear relations are

$3955\,\text{\AA}$05

and

$3955\,\text{\AA}$06

The slopes show that $3955\,\text{\AA}$07 is much more metallicity-sensitive than $3955\,\text{\AA}$08 in the metal-poor regime: $3955\,\text{\AA}$09 mag/dex versus $3955\,\text{\AA}$10 mag/dex. The RMS scatters are $3955\,\text{\AA}$11 mag for $3955\,\text{\AA}$12 and $3955\,\text{\AA}$13 mag for $3955\,\text{\AA}$14, and both imply roughly $3955\,\text{\AA}$15 dex uncertainty in metallicity at the $3955\,\text{\AA}$16 level. The practical preference nevertheless goes to $3955\,\text{\AA}$17, which gives the cleaner visual separation (Heumen et al., 18 Aug 2025).

EXT8 illustrates the difference. Its measured dereddened colors are

$3955\,\text{\AA}$18

In $3955\,\text{\AA}$19, EXT8 is the bluest object in the metal-poor sample and is separated by $3955\,\text{\AA}$20 mag from the nearest regular metal-poor globular cluster. In $3955\,\text{\AA}$21, the separation is only $3955\,\text{\AA}$22 mag. The candidate-selection thresholds proposed for clusters below the metallicity floor are

$3955\,\text{\AA}$23

Among these, the first is identified as the most useful single discriminator (Heumen et al., 18 Aug 2025).

Broad-band comparison reinforces the point. For the same metal-poor subsample, the fitted relations for $3955\,\text{\AA}$24 and $3955\,\text{\AA}$25 correspond to metallicity uncertainties of about $3955\,\text{\AA}$26 dex and $3955\,\text{\AA}$27 dex, respectively, both worse than the CaHK colors. Folding the fitted RMS scatter into Galactic and M31 globular-cluster metallicity distributions gives a false-positive rate of about $3955\,\text{\AA}$28 percent for ordinary globular clusters with $3955\,\text{\AA}$29 being misidentified as $3955\,\text{\AA}$30 by the CaHK colors. This is described as “a factor 2 better” than $3955\,\text{\AA}$31 and “a factor 3.8 better” than $3955\,\text{\AA}$32; the abstract and conclusion summarize the gain more conservatively as reducing false positives by at least a factor of 2 (Heumen et al., 18 Aug 2025).

Potential contamination from horizontal-branch morphology was also tested. The morphology indicator was the Simplified Mironov Index,

$3955\,\text{\AA}$33

where $3955\,\text{\AA}$34 and $3955\,\text{\AA}$35 are the numbers of HB stars bluer and redder than a threshold. The authors found no strong systematic shifts of the CaHK colors with HB morphology, either in the sparse M31 sample or in synthetic colors generated from WAGGS integrated spectra of Galactic globular clusters. They nevertheless stress the limitations: only 9 M31 clusters in the sample have HB measurements, most are effectively lower limits, the WAGGS spectra sample only a fraction of each cluster’s light and show UV stochasticity up to 12 percent, and neither dataset includes metal-poor red-HB clusters with $3955\,\text{\AA}$36 and $3955\,\text{\AA}$37 (Heumen et al., 18 Aug 2025).

5. Chromospheric and solar uses of the CaHK region

CaHK measurements are not restricted to metallicity. In chromospheric activity work, the Ca II H&K lines are classical diagnostics of magnetic heating and rotation. A recent extension of $3955\,\text{\AA}$38 to M dwarfs uses HARPS template spectra normalized to PHOENIX-ACES model atmospheres to measure absolute Ca II HK and H$3955\,\text{\AA}$39 fluxes for 110 stars. The Mount Wilson-compatible definition is

$3955\,\text{\AA}$40

with $3955\,\text{\AA}$41, while the chromospheric ratio is

$3955\,\text{\AA}$42

The paper derives new $3955\,\text{\AA}$43-based calibrations for the continuum-conversion factor $3955\,\text{\AA}$44 and the photospheric term $3955\,\text{\AA}$45 over $3955\,\text{\AA}$46 to $3955\,\text{\AA}$47 K, thereby extending the classical Noyes et al. framework beyond its original $3955\,\text{\AA}$48 validity range (Marvin et al., 2023).

The M-dwarf study also makes clear that CaHK activity calibration is strongly parameter-dependent. Across three adopted temperature scales, the mean $3955\,\text{\AA}$49 is $3955\,\text{\AA}$50 K overall; the mean $3955\,\text{\AA}$51 is $3955\,\text{\AA}$52 dex over the sample, but rises to $3955\,\text{\AA}$53 dex for stars with $3955\,\text{\AA}$54. The most extreme case, GJ 1002, has $3955\,\text{\AA}$55 K and $3955\,\text{\AA}$56 dex. The practical conclusion is that beyond about $3955\,\text{\AA}$57, accurate $3955\,\text{\AA}$58 cannot be made unless $3955\,\text{\AA}$59 is well constrained (Marvin et al., 2023).

An activity-oriented but non-photometric example is the study of four cool giants or subgiants with Ca II H&K emission. It uses medium-resolution optical spectroscopy plus long-term $3955\,\text{\AA}$60-band photometry, not a dedicated CaHK narrow-band filter, but it shows that Ca II H&K core emission can be very strong and time-variable. All four stars exhibit Ca II H&K emission; in BD+13 5000 and TYC 3557-919-1 the emission is described as very strong and exceeding the continuum. The line strengths vary between epochs and are interpreted as rotation-modulated. Long-term photometric cycles of $3955\,\text{\AA}$61 yr, $3955\,\text{\AA}$62 yr, and $3955\,\text{\AA}$63 yr are reported for three of the stars (Özdarcan et al., 2018).

Solar Ca II K imaging introduces a different photometric problem: calibration of full-disc historical spectroheliograms. The proposed solution is based on the assumption that the center-to-limb variation of intensity in quiet-Sun internetwork regions does not vary with time. The basic density definition is

$3955\,\text{\AA}$64

and density and intensity contrasts are defined by

$3955\,\text{\AA}$65

The historical quiet-Sun density CLV is fitted with a 5th-degree polynomial $3955\,\text{\AA}$66, matched to a modern reference CLV from Rome/PSPT CCD data, and used to derive a plate-specific calibration curve. On synthetic datasets, the method yields maximum relative errors generally $3955\,\text{\AA}$67 and average error $3955\,\text{\AA}$68; in the absence of strong artefacts, the recovered images differ from the ideal ones by $3955\,\text{\AA}$69 in any pixel. For feature photometry the validation uses the thresholds

$3955\,\text{\AA}$70

for plage and network (Chatzistergos et al., 2017).

6. Systematics, failure modes, and observational scope

Across applications, the first limitation is that CaHK photometry is usually not self-sufficient. In metallicity work it requires a temperature proxy from broad-band colors, and in many cases a gravity estimate as well. The Pristine–Gaia metallicity grids are restricted to FGK stars with

$3955\,\text{\AA}$71

corresponding roughly to $3955\,\text{\AA}$72, and the method is stated to perform best for $3955\,\text{\AA}$73. MAGIC similarly recommends

$3955\,\text{\AA}$74

and relies on Gaia parallaxes or proper motions to distinguish RGB from main-sequence solutions because the metallicity mapping is $3955\,\text{\AA}$75-dependent (Martin et al., 2023, Chiti et al., 26 May 2026).

Blue-end signal-to-noise is a second generic constraint. In the Gaia synthetic catalog, the recommended cut is $3955\,\text{\AA}$76, typically reached around $3955\,\text{\AA}$77, with strong color dependence because redder stars have less blue flux. Pristine is much deeper, reaching $3955\,\text{\AA}$78 at approximately $3955\,\text{\AA}$79, again depending on color. In the dwarf-galaxy studies, reliable CaHK photometry with uncertainty below $3955\,\text{\AA}$80 extends to $3955\,\text{\AA}$81, still shallower than the deep broad-band photometry. The M31 globular-cluster experiment was designed to reach $3955\,\text{\AA}$82 in CaHK for a typical M31 globular cluster (Martin et al., 2023, Longeard et al., 2018, Longeard et al., 2019, Heumen et al., 18 Aug 2025).

Calibration at the lowest metallicities is another persistent issue. Both the Sagittarius II and Draco II analyses state that the original Pristine metallicity model is slightly biased low at the metal-poor end and therefore apply empirical corrections before scientific interpretation. In the Pristine–Gaia DR3 catalog, the model is hard-capped at $3955\,\text{\AA}$83, and the paper explicitly warns that strict rejection of edge-of-grid objects can exclude true ultra metal-poor stars. In MAGIC, values below $3955\,\text{\AA}$84 are treated cautiously because of the rarity of real stars in that regime and the presence of outliers (Longeard et al., 2019, Longeard et al., 2018, Martin et al., 2023, Chiti et al., 26 May 2026).

Astrophysical contaminants also matter. In the Pristine–Gaia metallicity catalog, carbon-enhanced stars bias metallicities to artificially higher values: for cool stars with $3955\,\text{\AA}$85 and $3955\,\text{\AA}$86, the mean metallicity overestimate is $3955\,\text{\AA}$87; for hotter stars with $3955\,\text{\AA}$88, it is $3955\,\text{\AA}$89. In MAGIC, dwarf/giant misclassification can shift $3955\,\text{\AA}$90 by more than $3955\,\text{\AA}$91, especially for $3955\,\text{\AA}$92 and $3955\,\text{\AA}$93. Nonstellar contaminants, unresolved galaxies, variable sources, quasars, blue HB stars, and blue stragglers therefore require explicit filtering (Martin et al., 2023, Chiti et al., 26 May 2026).

Reddening and crowding are particularly severe because the CaHK band lies in the blue. The Pristine–Gaia metallicity papers recommend caution for $3955\,\text{\AA}$94 and exclude $3955\,\text{\AA}$95 from the metallicity catalogs. MAGIC adopts the stricter working cut

$3955\,\text{\AA}$96

and excludes sources within $3955\,\text{\AA}$97 of the Magellanic Clouds for routine metal-poor mapping. Cluster centers and other crowded regions are also identified as problematic because both Gaia and narrow-band photometry degrade there (Martin et al., 2023, Chiti et al., 26 May 2026).

In integrated-light globular-cluster work, the main caveat is one of scientific role. The M31 study explicitly does not recommend CaHK photometry as a high-accuracy standalone metallicity estimator in the same sense as spectroscopy. The goal is effective preselection for spectroscopic follow-up, not replacing spectroscopy. The empirical precision of $3955\,\text{\AA}$98 dex is sufficient for triage, but not for definitive abundance work, especially given the sparse calibration at the lowest metallicities and the limited HB-morphology tests (Heumen et al., 18 Aug 2025).

Taken together, these studies define CaHK-band photometry as a mature but context-dependent technique. It is exceptionally effective when a strong Ca II H&K response survives where other low-resolution metallicity tracers have saturated, or when the Ca II core region is itself the chromospheric observable of interest. Its strongest implementations combine narrow-band CaHK measurements with carefully calibrated broad-band photometry, explicit treatment of extinction and stellar type, and an external reference system such as Gaia XP or spectroscopy (Martin et al., 2023, Chiti et al., 26 May 2026, Heumen et al., 18 Aug 2025).