Extending the cosmic distance ladder two orders of magnitude with strongly lensed Cepheids, carbon AGB, and RGB stars

Gravitational lensing by galaxy clusters can create extreme magnification near the cluster caustics, thereby enabling detection of individual luminous stars in high-redshift background galaxies. Those stars can include non-explosive standard candles such as Cepheid variables, carbon stars in the asymptotic giant branch, and stars at the tip of the red-giant branch out to $z\lesssim1$. A large number of such detections, combined with modeling of the magnification affecting these stars (including microlensing), opens the door to extending the distance range of these standard candles by two orders of magnitude, thereby providing a check on the distances derived from supernovae. Practical measurement of a distance modulus depends on measuring the apparent magnitude of a ``knee feature’’ in the lensed luminosity function due to the great abundance of red-giant-branch stars just below the luminosity of the tip of the red-giant branch. As a bonus, strongly lensed stars detected in deep exposures also provide a robust method of mapping small dark-matter substructures, detections of which also cluster around the critical curves of small-scale dark matter halos.

💡 Research Summary

The manuscript investigates a novel way to push the cosmic distance ladder far beyond its traditional limits by exploiting the extreme magnification produced by galaxy‑cluster strong lensing together with microlensing by intracluster stars. The authors focus on three non‑explosive standard candles—classical Cepheid variables, carbon‑rich asymptotic‑giant‑branch (AGB) stars, and stars at the tip of the red‑giant branch (TRGB)—which are routinely used in the nearby Universe (tens of Mpc) but are far too faint to be seen at cosmological distances. They argue that when such stars lie in a background galaxy that is strongly lensed by a massive cluster, the macroscopic magnification (µ ≈ 10²–10⁴) near the critical curve can boost their apparent fluxes into the detection regime of JWST, while microlensing by individual intracluster stars can provide brief additional boosts (µ ≈ 10³–10⁴) that make even the faintest TRGB stars observable as transient events.

To quantify the feasibility, the authors construct a realistic stellar population by taking the 2MASS catalog of LMC stars, converting the observed J and H magnitudes to AB, and shifting them to the redshift of the “Dragon arc” (z = 0.725) behind the A370 cluster. They adopt the distance modulus of the LMC (18.5 mag) and that of the Dragon galaxy (≈ 43.12 mag for H₀ = 74 km s⁻¹ Mpc⁻¹), apply a simple (1 + z) bandwidth correction, and then multiply each star’s flux by a total magnification µ = µ_m × µ_micro. The macromodel magnification µ_m is drawn from a power‑law distribution P(µ_m) ∝ µ_m⁻³ with limits 50 < µ_m < 5000, reflecting the expected range of magnifications across the arc. The microlensing contribution µ_micro is sampled from probability density functions derived from inverse‑ray‑tracing simulations that incorporate the surface mass density of intracluster stars (Σ_* ≈ 30 M_⊙ pc⁻²) and the critical surface density at the relevant redshifts (Σ_crit ≈ 3640 M_⊙ pc⁻²). When Σ_eff = µ_m Σ_* approaches Σ_crit (i.e., µ_m ≳ 120), the microlensing regime becomes “optically thick” and the total magnification PDF transitions from a narrow peak with a µ⁻³ tail to a log‑normal shape.

Applying this framework, the simulated color‑magnitude diagram (Figure 3) shows that Cepheids, J‑region AGB stars, and TRGB stars are spread over several magnitudes, but their colors remain essentially unchanged because lensing is achromatic. Crucially, the TRGB “knee” in the luminosity function—where the number of stars rises sharply just below the tip—remains identifiable after magnification. For a typical total magnification of order 10³, a TRGB star at the Dragon’s distance would appear at AB ≈ 30.5 mag in JWST’s F200W filter, well within reach of a ∼ 4‑hour exposure (the authors quote a 30.6 mag 5σ limit for a 16.7‑hour exposure). The simulated number of stars brighter than this limit is ≈ 1 100, providing ample statistics to locate the knee with sub‑0.1 mag precision.

The authors compare their predictions with the 45 transient events reported by Fudamoto et al. (2024) in the Dragon arc. Those transients, detected in difference imaging at a 5σ limit of AB ≈ 28.75 mag, are interpreted as microlensing spikes of luminous stars. When the observed luminosity function of these events is normalized by the LMC stellar surface density, it matches the simulated LF both in slope and normalization, supporting the assumption that the Dragon’s stellar population resembles that of the LMC. The authors note that changing H₀ from 74 to 68 km s⁻¹ Mpc⁻¹ shifts the TRGB knee by ≈ 0.18 mag, a difference that can be distinguished given the sharpness of the feature.

Beyond distance measurement, the paper highlights a secondary benefit: the same microlensing events trace the small‑scale dark‑matter substructure in the cluster. Since microlensing probability depends on the local surface density of compact objects, the spatial clustering of transients around the critical curve can be used to map sub‑halo populations down to masses of 10⁶–10⁸ M_⊙.

The manuscript acknowledges several caveats. The magnification PDFs assume a stellar radius of 300 R_⊙; smaller stars (e.g., TRGB stars with R_* ≈ 100 R_⊙) can achieve higher peak magnifications during a micro‑caustic crossing, potentially altering the predicted detection rates. Uncertainties in the exact location of the cluster critical curve and in the macromodel parameter A (which sets µ_m = A/d) translate directly into systematic errors on the inferred distance modulus. Moreover, the analysis treats the high‑z stellar population as a scaled‑up LMC, neglecting possible metallicity or age differences that could shift the intrinsic colors and absolute magnitudes of the standard candles. Finally, the required JWST depth (AB ≈ 30.5 mag) and cadence to capture short microlensing spikes (hours to days) pose observational challenges.

In summary, the paper proposes a compelling strategy to extend the reach of Cepheids, AGB carbon stars, and TRGB stars by two orders of magnitude in distance, thereby providing an independent cross‑check on the Hubble‑constant tension. By combining macrolensing and microlensing statistics, the method yields a measurable “knee” in the lensed luminosity function that directly encodes the distance modulus. If realized with deep, multi‑epoch JWST observations, this approach could become a powerful new rung on the cosmic distance ladder and simultaneously offer a novel probe of dark‑matter substructure in galaxy clusters.