The ESPRESSO Redshift Drift Experiment III -- The Third Epoch of QSO J052915.80-435152.0

This paper reports the third epoch of ESPRESSO observations of quasar J052915.80-435152.0, yielding a null redshift drift measurement consistent with $\Lambda$CDM predictions and demonstrating that while current instrumentation requires century-long baselines for detection, a combined ESPRESSO and ANDES effort could achieve the first detection before 2080.

The Gist

Imagine the universe is like a giant, expanding balloon. For decades, astronomers have been trying to measure how fast this balloon is inflating. Usually, they look at "mile markers" (like distant supernovae) to guess the speed. But the Sandage-Loeb test is different. Instead of looking at a snapshot of the balloon, it tries to watch the balloon inflate in real-time.

This paper is the third chapter in a story about trying to catch the universe "in the act" of expanding. Here is the breakdown in plain English:

1. The Big Idea: The "Cosmic Slow-Motion"

Imagine you are watching a very slow-motion video of a tree growing. You can't see it grow in real-time, but if you take a photo today, and another photo 10 years later, you might see the branches have moved slightly.

In astronomy, we look at Quasars (super-bright, ancient beacons of light from the early universe). As light travels from a quasar to us, it gets stretched by the expanding universe, turning into a "redshift."

• The Goal: The scientists want to see if the color of that light changes right now compared to 10 years ago.
• The Catch: The change is incredibly tiny. It's like trying to measure the growth of a single blade of grass over the course of a human lifetime. The signal is about 1 centimeter per second per year. That is slower than a snail crawling on a wall.

2. The Tool: The "Ultra-Stable Ruler"

To measure something this small, you need a ruler that doesn't wiggle. The team used ESPRESSO, a super-precise spectrograph attached to the Very Large Telescope (VLT) in Chile.

• The Target: They focused on a specific, incredibly bright quasar named J052915.80-435152.0 (let's call it "SB2").
• The Method: They took three "snapshots" of this quasar's light over a period of about two years.
  • Snapshot 1: Taken in 2022/2023.
  • Snapshot 2: Taken in 2023/2024.
  • Snapshot 3 (This Paper): Taken in late 2024.

3. The Experiment: "Listening for the Drift"

The light from the quasar isn't a smooth beam; it's like a barcode with thousands of dark lines (called the Lyman-alpha forest). These lines are caused by clouds of gas the light passed through on its way to Earth.

The scientists built a digital model of what these lines should look like. Then, they compared their three snapshots against this model to see if the lines had shifted position.

• The Analogy: Imagine a choir singing a specific note. If the room expands while they are singing, the pitch might drop slightly. The scientists are trying to hear if the choir's pitch has dropped just a tiny bit over two years.

4. The Results: "No Drift Detected (Yet)"

After analyzing the data with two different mathematical methods, the result was a null result.

• What does that mean? They didn't see the light shift.
• Is that bad? No! It's actually a huge success. The amount of "drift" they expected to see (based on our standard theory of the universe, called $\Lambda$CDM) is so small that it is currently hidden by the "noise" of the measurement.
• The Verdict: Their measurement was $-3.5 \pm 3.6$ m/s/year. The expected value was roughly $-0.4$ m/s/year. Since the error bar (the uncertainty) is larger than the signal, they couldn't confirm the drift yet, but their result is perfectly consistent with the theory. They proved their tools are working and that no weird "systematic errors" (like a broken ruler) are messing things up.

5. The Future: "The Century-Long Race"

So, if they didn't see it, why keep going?

• The Timeline: The paper calculates that to see this "snail-speed" drift clearly, they need to keep watching for a long time.
  • With just the current telescope (ESPRESSO): It might take until the 22nd century (around the year 2100+) to get a definitive detection.
  • With the new giant telescope (ELT/ANDES): If they team up with the upcoming Extremely Large Telescope, they could detect it by 2080.
  • The "Radio" Boost: If they combine the optical telescopes with radio telescopes (like FAST) looking at hydrogen gas in the nearby universe, they could potentially crack the code by 2070.

Summary Analogy

Think of this experiment like trying to hear a whisper in a hurricane.

1. The Whisper: The universe expanding (the redshift drift).
2. The Hurricane: The noise in the data and the limitations of our instruments.
3. The Paper: The team built a better microphone (ESPRESSO), listened for two years, and confirmed that the whisper is there (or at least, it's not contradicting our theories), but the hurricane is still too loud to hear it clearly.
4. The Plan: They are building a bigger, quieter room (the ELT and radio telescopes) and will keep listening for another few decades until the whisper becomes a shout.

The Bottom Line: This paper is a "check-in" report. It says, "We are on the right track, our tools are precise, the universe is behaving as we think it should, but we need to keep watching for a few more decades to catch the cosmic expansion in the act."

Technical Summary

1. Problem and Scientific Context

The Sandage-Loeb (SL) test is a unique, model-independent probe of cosmic dynamics. It aims to measure the redshift drift ($\dot{z}$), which is the slow temporal change in the redshift of distant sources due to the expansion of the Universe.

• The Challenge: The expected signal is extremely small ($\dot{z} \sim 10^{-11} \text{ yr}^{-1}$, or $\dot{v} \sim 0.5 \text{ cm s}^{-1} \text{ yr}^{-1}$). Detecting this requires ultra-stable, high-resolution spectrographs and long temporal baselines.
• Current Status: Previous geometric probes (Type Ia supernovae, BAO, CMB) rely on standard candles/rulers. The SL test offers a direct empirical measurement of the expansion rate without these assumptions.
• Objective: This paper (Paper III) reports the third observational epoch of the quasar J052915.80-435152.0 (SB2), extending the temporal baseline to $\sim 2$ years. The goal is to assess current instrumental capabilities, refine measurement procedures, diagnose systematics, and provide the tightest constraints on redshift drift to date.

2. Methodology

Data Acquisition

• Instrument: ESPRESSO on the Very Large Telescope (VLT) in single Unit Telescope (UT) mode.
• Target: Quasar SB2 ($z_{em} = 3.962$, $i = 16.071$ mag).
• Observations: 9.5 hours of new data acquired in December 2024 (Period P114), complementing 12 hours from two previous epochs (2022–2023).
• Setup: Resolving power $R \sim 135,000$. A $4\times2$detector binning was used to enhance Signal-to-Noise (S/N) in the Lyman-$\alpha$ forest.
• Calibration: Two calibration sources were used:
  1. FP+ThAr: Fabry-Pérot etalon + Thorium-Argon lamp (primary dataset).
  2. LFC: Laser Frequency Comb (used for systematic cross-checks, though LFC faced technical issues during the run).
• Data Reduction: Standard ESPRESSO DRS pipeline. Spectra were barycentrically corrected, flat-fielded, and flux-calibrated. Three independent epoch spectra and one combined spectrum were generated.

Analysis Techniques

The analysis focused on the Lyman-$\alpha$ forest region (509–603 nm). The team employed two independent methods to measure velocity shifts ($\delta v$) between epochs:

1. Pixel-by-Pixel Method:

   • A transmission model ($\bar{S}$) of the Lyman-$\alpha$ forest was created using 500 independent spline functions, calibrated on hydrodynamical simulations (Sherwood suite).
   • The observed flux ($F_{k,i}$) was compared to the model to derive velocity shifts based on first-order perturbations.
   • Weights were assigned based on flux errors and model derivatives.

2. Model Likelihood Correlation:

   • A maximum likelihood approach was used to find the rigid velocity shift ($\delta v$) that best aligns the model with the observed spectrum.
   • This method avoids weighting pixels based on derivatives (which can underestimate uncertainties) and relies on a robust statistical estimator.

3. Systematic Checks:

   • Model Variance: Assessed by analyzing the variance among the 500 spline realizations.
   • Single Exposure Analysis: Measurements were performed on individual exposures (23 total) rather than just combined epochs to check for spurious drifts.
   • Calibration Comparison: Results from FP+ThAr and LFC calibrations were compared to identify wavelength solution instabilities.

3. Key Contributions

• Extended Baseline: Successfully extended the experiment to a third epoch, increasing the total integration time and S/N (combined S/N $\approx 113$ per pixel).
• Refined Modeling: Improved the Lyman-$\alpha$ forest modeling by re-calibrating the spline internodal distance ($A \approx 7.34 \text{ km s}^{-1}$) based on the higher S/N of the current dataset.
• Dual-Method Validation: Demonstrated consistency between two distinct statistical approaches (Pixel-by-pixel and Likelihood), strengthening the reliability of the null result.
• Systematic Characterization: Quantified that systematic effects (model variance, calibration differences) are currently subdominant to statistical noise.
• Forecasting: Provided detailed extrapolations for future detection timelines using ESPRESSO, the upcoming ANDES instrument on the ELT, and radio facilities (FAST).

4. Results

Measurement of Redshift Drift

Both methods yielded a consistent null result (no statistically significant detection of drift), which is in agreement with $\Lambda$CDM expectations (where the expected drift is $\sim -0.41 \text{ cm s}^{-1} \text{ yr}^{-1}$, well below the current noise floor).

• Pixel-by-pixel result: $\dot{v} = -3.43 \pm 3.56 \text{ m s}^{-1} \text{ yr}^{-1}$
• Likelihood correlation result: $\dot{v} = -3.63 \pm 3.65 \text{ m s}^{-1} \text{ yr}^{-1}$
• Combined constraint: $\dot{v} \approx -3.5 \pm 3.6 \text{ m s}^{-1} \text{ yr}^{-1}$ (or $\dot{z} \approx (-5.3 \pm 5.6) \times 10^{-8} \text{ yr}^{-1}$).

Systematics Analysis

• Model Variance: Contributed less than 2% to the total uncertainty.
• Calibration: The difference between FP+ThAr and LFC calibrations was $\Delta \dot{v} \approx 0.9 \text{ m s}^{-1} \text{ yr}^{-1}$, which is subdominant to the statistical uncertainty.
• Single Exposures: Analysis of individual exposures confirmed that no single exposure introduced significant spurious drifts.

Future Projections

• ESPRESSO Only: A 3$\sigma$ detection of the signal would require $\sim 470$ years with 10 hours/year integration, or $\sim 100$ years with 1000 hours/year.
• ESPRESSO + ANDES (ELT): Combining VLT and ELT data could achieve a first detection (3$\sigma$) before 2080.
• Radio Synergy: Adding low-redshift H I 21 cm absorption line observations (e.g., with the FAST telescope) could reduce the timeline to $\sim 2070$ for a 68% confidence detection.

5. Significance

• Validation of Methodology: This paper confirms that the observational strategy and data reduction pipelines for the SL test are robust and capable of handling the extreme precision required (cm/s level).
• Benchmarking: It establishes the current state-of-the-art limits on redshift drift measurements, showing that while the signal is not yet detectable, the noise levels are approaching the regime where systematic effects (rather than photon noise) will become the limiting factor.
• Roadmap for Detection: The study provides a concrete roadmap for the next two decades, highlighting the necessity of:
  1. Long-term monitoring of the "Golden Sample" of bright quasars.
  2. The transition to the ELT/ANDES instrument for increased collecting area.
  3. Synergy with radio astronomy (21 cm lines) to accelerate detection.
• Cosmological Impact: While the current result is a null detection, it serves as a crucial step toward a direct, model-independent measurement of cosmic acceleration, which will eventually allow for stringent tests of General Relativity and dark energy models.

In conclusion, Paper III demonstrates that while the redshift drift signal remains elusive with current single-target data, the experimental framework is sound. The path to detection lies in multi-decadal campaigns combining optical (ESPRESSO/ANDES) and radio (FAST/SKA) facilities.