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

This paper proposes extending the cosmic distance ladder by two orders of magnitude to $z\lesssim1$ by utilizing gravitational lensing to detect individual standard candles like Cepheids and RGB stars in background galaxies, a method that simultaneously offers a critical check on supernova distances and enables the mapping of dark matter substructures.

Original authors: J. M. Diego, S. P. Willner, J. M. Palencia, R. A. Windhorst

Published 2026-02-04

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CC BY 4.0

Original authors: J. M. Diego, S. P. Willner, J. M. Palencia, R. A. Windhorst

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, dark room where we are trying to measure how far away the furniture is. Astronomers usually use "standard candles"—stars that shine with a predictable brightness—to figure out distances. If you know how bright a candle should be, and you see how dim it looks to you, you can calculate how far away it is.

The problem is that the universe is expanding, and there is a disagreement among scientists about exactly how fast. One group of measurements says it's expanding at a "slow" pace, while another says it's "fast." This disagreement is a major puzzle in cosmology.

This paper proposes a clever way to solve this puzzle by using the universe's own "magnifying glasses."

The Cosmic Magnifying Glass

Galaxy clusters are massive groups of galaxies that act like giant lenses in space. They bend light, just like a magnifying glass bends sunlight. Usually, these lenses make background objects look bigger and brighter. But sometimes, right at the edge of these clusters (called "critical curves"), the magnification is extreme—making distant stars look thousands of times brighter than they really are.

Think of it like holding a magnifying glass over a tiny firefly in the distance. Suddenly, that tiny firefly looks as bright as a streetlamp.

The New "Candles"

For a long time, we could only use very bright explosions (Supernovae) as our candles for faraway places. But this paper suggests we can now use "non-explosive" stars that are usually too faint to see at such great distances. These include:

Cepheids: Stars that pulse like a heartbeat, changing brightness in a predictable rhythm.
Carbon AGB stars: Cool, red giants that are very bright in infrared light.
Red Giant Branch (TRGB) stars: The "tip" of the red giant branch, which is a very specific, consistent brightness level.

The authors simulate what would happen if we took a known galaxy (the Large Magellanic Cloud, which is our cosmic "neighbor") and placed it far away in a galaxy called the "Dragon Arc" (at a distance of 7.25 billion light-years). They then applied the "magnifying glass" effect of a galaxy cluster (A370) to it.

The Results: Seeing the Unseeable

The simulation shows that with the James Webb Space Telescope (JWST), we could detect over 1,000 of these individual stars in the Dragon Arc.

The "Knee" in the Graph: Imagine a graph showing how many stars there are at different brightness levels. Usually, the line goes up smoothly. But at a specific point (the "tip" of the red giants), there is a sharp "knee" or bend where the number of stars suddenly jumps. This paper argues that even with the distortion of the magnifying glass, this "knee" remains visible.
Solving the Speed Debate: The exact position of this "knee" depends on how fast the universe is expanding. If the universe is expanding at the "slow" rate, the knee appears at one brightness level. If it's "fast," it appears slightly dimmer. By finding this knee in the Dragon Arc, we can check which speed is correct.

The "Micro-Lenses" and Dark Matter

There is a second layer to this. Inside the galaxy cluster, there are smaller objects (like individual stars or invisible clumps of dark matter) that act as tiny, secondary magnifying glasses.

The Transient Effect: As these tiny lenses move, they cause the background stars to flicker or flare up suddenly. This is called a "microlensing event."
Mapping the Invisible: The paper suggests that the faintest stars (the red giants) will cluster tightly around the invisible "clumps" of dark matter. By watching where these stars light up, we can essentially draw a map of the invisible dark matter, revealing its structure down to very small scales.

Looking Even Further

The authors also looked at another galaxy called "Spock" (at 10 billion light-years). They found that the brightest, longest-pulsing Cepheid stars might be visible there too, especially if they get a lucky boost from a microlensing event. This could allow us to use these "heartbeat" stars as distance markers in a part of the universe we've never tested them in before.

Summary

In short, this paper claims that by using the extreme magnification of galaxy clusters, we can turn faint, ordinary stars into bright, visible beacons. This allows us to:

Measure cosmic distances with a new type of "ruler" (Cepheids and Red Giants) far beyond what was previously possible.
Check the speed of the universe's expansion to resolve the current disagreement between scientists.
Map the invisible skeleton of the universe (dark matter) by seeing where these magnified stars appear.

It's like using a cosmic telescope to turn a crowd of distant, dim fireflies into a bright, organized display that tells us exactly how big the room is and where the invisible furniture is hiding.

Technical Summary: Extending the Cosmic Distance Ladder with Strongly Lensed Stars

Problem Statement
The paper addresses the persistent tension in cosmology regarding the Hubble constant ( $H_0$ ), where measurements from the Cosmic Microwave Background ( $H_0 \approx 68$ km s $^{-1}$ Mpc $^{-1}$ ) disagree with those derived from the supernova (SN) distance ladder ( $H_0 \approx 74$ km s $^{-1}$ Mpc $^{-1}$ ). Current non-explosive standard candles (NESCs)—specifically Cepheid variables, Asymptotic Giant Branch (AGB) carbon stars, and the Tip of the Red-Giant Branch (TRGB)—are limited to distances of only a few tens of Megaparsecs due to their intrinsic low luminosity compared to Type Ia supernovae. This limitation prevents independent calibration of the distance ladder at the redshifts where the $H_0$ tension is most critical. While gravitational lensing by galaxy clusters can magnify background stars, previous detections of high-redshift stars (e.g., Icarus, Earendel) have focused on extremely luminous, rare objects, leaving the population of standard candles at cosmological distances ( $z \gtrsim 0.5$ ) unexplored.

Methodology
The authors investigate the feasibility of detecting NESCs in strongly lensed galaxies, specifically focusing on the "Dragon arc" (a $z=0.725$ galaxy magnified by the $z=0.375$ cluster A370) and the "Spock arc" ( $z=1.0054$ ). The methodology involves:

Stellar Population Simulation: Using real observations of stars in the Large Magellanic Cloud (LMC) from the 2MASS survey as a proxy for the stellar population in the Dragon galaxy. These stars are redshifted to $z=0.725$ and converted to AB magnitudes in JWST filters (F200W and F277W).
Magnification Modeling: The authors combine macromodel magnification ( $\mu_m$ ) from the galaxy cluster with microlensing effects from stars in the intracluster medium (ICM). They utilize the M_SMiLe code to generate probability distribution functions (PDFs) for total magnification ( $\mu$ ). The model accounts for the transition from an "optically thin" regime (where $\mu \approx \mu_m$ ) to an "optically thick" regime (where microlenses create a lognormal distribution of magnifications) near the cluster's critical curves (CC).
Luminosity Function (LF) Analysis: The simulated magnified magnitudes are used to construct a lensed luminosity function. The authors specifically analyze the "knee" feature in the LF caused by the abundance of TRGB stars, which serves as a distance indicator.
Cosmological Comparison: The simulations are run for two cosmological models ( $H_0 = 68$ and $H_0 = 74$ km s $^{-1}$ Mpc $^{-1}$ ) to determine if the position of the LF knee shifts sufficiently to distinguish between the two values.

Key Contributions and Results

Detection Feasibility: The study demonstrates that with deep JWST exposures (approx. 16.7 hours in F200W, reaching AB 30.6 mag), approximately 1,100 stars in the Dragon arc could be detected. This includes a significant population of NESCs: TRGB stars, J-region AGB (JAGB) stars, and long-period Cepheids.
The "Knee" Feature: The authors show that the sharp "knee" in the luminosity function, corresponding to the TRGB, survives the lensing process. The observed magnitude of this knee is sensitive to $H_0$ . For $H_0 = 68$ , the knee appears at a magnitude 0.18 mag fainter than for $H_0 = 74$ . This shift is distinct from changes in stellar surface density, offering a potential method to measure $H_0$ independently.
Cepheid Variability: The paper highlights that Cepheids can be identified via their light curves. While microlensing introduces perturbations, the timescale of Cepheid variability (days to weeks) is generally distinct from microlensing events (years), except during rare microcaustic crossings. The authors suggest that observing multiple Cepheids in close proximity can break the degeneracy between unknown macromagnification and distance modulus, as magnification scales predictably with distance from the critical curve ( $\mu_m \propto 1/d$ ).
Dark Matter Mapping: The spatial distribution of detected stars is predicted to trace the cluster's critical curves. Crucially, the faintest detected stars (such as TRGB and RGB stars) will concentrate around the critical curves of small-scale dark matter substructures, enabling the mapping of dark matter down to scales of $10^4 M_\odot$ .
Extension to Higher Redshifts: Simulations for the Spock arc ( $z \approx 1$ ) suggest that highly magnified long-period Cepheids could be detected with medium-depth observations, potentially extending the standard candle distance ladder by two orders of magnitude.

Significance and Claims
The paper claims that strongly lensed galaxies provide a unique laboratory to extend the cosmic distance ladder to redshifts ( $z \sim 0.7 - 1.0$ ) previously inaccessible to non-explosive standard candles. By leveraging the extreme magnification near cluster critical curves, the authors propose a method to:

Resolve the $H_0$ Tension: Provide an independent check on distances derived from supernovae by measuring the TRGB "knee" and Cepheid periods at high redshift.
Map Dark Matter: Use the spatial clustering of faint, lensed stars to probe the distribution of dark matter subhalos on small scales.
Validate Standard Candles: Confirm the utility of JAGB and TRGB stars as standard candles in environments dominated by strong lensing and microlensing.

The authors remain cautious, noting that practical measurement requires deep observations to detect the LF knee and that identifying Cepheids requires disentangling microlensing distortions from intrinsic variability. However, they conclude that the combination of high-magnification events and the statistical power of large stellar samples makes this a viable pathway for precision cosmology.