A Deep ALMA Survey of the Redshift Distribution of Dusty Star-forming Galaxies

This paper presents a deep ALMA spectroscopic survey of 870 $\mu$m-selected dusty star-forming galaxies in the GOODS-S field, achieving 97% spectroscopic completeness at fluxes above 2.5 mJy to reveal that fewer than 10% of these massive galaxies exist at redshifts greater than 4, while also demonstrating that current photometric redshift methods significantly overestimate high-redshift populations.

The Gist

Imagine the universe as a giant, dusty attic filled with billions of old, glowing lanterns. These aren't your average lanterns; they are Dusty Star-Forming Galaxies (DSFGs). They are cosmic factories churning out stars at a furious pace, but they are wrapped in thick blankets of cosmic dust. This dust blocks their visible light, making them invisible to regular telescopes, but it glows brightly in "submillimeter" light (a type of invisible radiation), like a campfire seen through a thick fog.

For decades, astronomers have been trying to answer a simple but tricky question: How old are these galaxies? In astronomy, "age" is measured by redshift (how much the light has stretched as the universe expands). The higher the redshift, the further away and older the galaxy is.

Here is a simple breakdown of what this new paper did, using some everyday analogies.

1. The Mission: Finding the IDs of the "Ghost" Galaxies

The researchers focused on a specific patch of sky called GOODS-S. They had a list of 75 of these dusty galaxies, identified because they were bright in submillimeter light. However, for most of them, they only had a "photometric redshift" (a photo-z).

• The Analogy: Think of a photo-z like guessing someone's age just by looking at a blurry, black-and-white photo. You might guess they are 30, but they could actually be 25 or 45. It's a best guess based on how bright they look.
• The Problem: For these dusty galaxies, the "guessing game" is notoriously bad. The dust confuses the cameras, and the guesses are often way off.
• The Solution: The team used the ALMA telescope (the world's most powerful radio telescope) to take a "spectral scan" of these galaxies. This is like taking a fingerprint or a voice recording of the galaxy. By listening to the specific "hum" of gas molecules (like Carbon Monoxide) inside the galaxy, they could determine the exact redshift. This is a spectroscopic redshift (spec-z).

2. The Results: A High-Definition Census

The team successfully identified or confirmed the exact "age" (redshift) for 20 of these galaxies using ALMA. When they combined this with previous data from other telescopes (including the new JWST space telescope), they now have exact redshifts for 69% of their entire sample of 75 galaxies.

• The Analogy: Imagine you have a class of 75 students, and you only know the names of a few. You want to know the average age of the class. In the past, you'd have to guess the ages of the rest based on their height (which is often wrong). Now, you've managed to ask 69 of them their exact birthdates. You can finally calculate the true average age with high confidence.

Key Finding: For the brighter galaxies (the "loud" ones), they achieved 97% completeness. They know almost exactly where these galaxies are in the timeline of the universe.

3. The "Guessing Game" Failed (Again)

The researchers used their new, exact data to test the "guessing" methods (photo-zs) that astronomers usually rely on.

• The Result: The guessing methods were surprisingly bad. Even the most advanced software, using data from the powerful JWST telescope, got the age wrong by a huge margin more than 20% of the time.
• The Analogy: It's like a weather forecast that says "It will be sunny" 80% of the time, but when it actually rains, the forecasters are completely shocked. The software tends to overestimate the age, thinking these galaxies are much older (further away) than they really are.
• The Consequence: Because the software thinks the galaxies are older, it creates a false picture of the universe having more ancient, massive galaxies than actually exist.

4. The High-Redshift Mystery: Are There Ancient Giants?

A major debate in astronomy is: Are there massive, dusty galaxies existing very early in the universe (less than 1.5 billion years after the Big Bang)?

• The Old Guess: Because the "guessing" software kept overestimating ages, many astronomers thought there was a hidden population of these ancient giants.
• The New Reality: With their exact data, the authors found that very few of these galaxies are actually that old.
  • Less than 10% are older than 4 billion years.
  • Less than 2% are older than 5 billion years.
• The Analogy: Imagine a party where everyone is guessing how many people are over 50. The guesses say "Half the room!" But when you actually check IDs, you find out it's only one or two people. The "ancient" giants are rare. The universe didn't build massive, dusty galaxies as quickly as we thought.

5. Why is JWST not doing all the work?

The James Webb Space Telescope (JWST) is the new superstar of astronomy. You might think it could solve this problem alone.

• The Catch: While JWST is amazing at getting exact redshifts for the galaxies it targets, it has only managed to target about 29% of this specific dusty sample.
• The Analogy: JWST is like a super-sleuth who can solve a crime perfectly if they are assigned the case. But they are so busy and the list of suspects is so long that they haven't been assigned to most of the cases yet. We still need the "ground teams" (like ALMA) to help cover the rest.

Summary: What Does This Mean for Us?

1. We have a better map: We now have the most accurate map yet of where these dusty galaxies sit in the history of the universe.
2. The "Guessing" is broken: We can't rely on computer estimates for these dusty objects anymore; we need to measure them directly.
3. The Universe is younger than we thought: The "ancient" massive galaxies are much rarer than previous models suggested. The universe took a bit longer to build its biggest, dustiest structures than we hoped.

In short, this paper is like finally getting a roll call for a group of mysterious guests at a cosmic party. We found out that while we thought there were many ancient elders in the room, most of them are actually middle-aged, and our previous guesses were just too optimistic!

Technical Summary

1. Problem Statement

Dusty Star-Forming Galaxies (DSFGs) represent a critical phase in galaxy evolution, contributing significantly to the cosmic star formation rate density at $z \sim 2.5$. However, determining their true redshift distribution has been historically challenging due to:

• Spectroscopic Incompleteness: Previous surveys of DSFGs often suffered from low spectroscopic completeness (typically 5–40%), relying heavily on photometric redshifts (photo-zs) which are prone to catastrophic failures for dusty sources.
• Bias in High-Redshift Estimates: Existing photo-z methods tend to overestimate redshifts for DSFGs, leading to an overestimation of the population at $z > 4$ and $z > 5$.
• Lack of Unbiased Samples: Fully spectroscopically complete samples previously existed only at the very bright end (strongly lensed) or the very faint end (ASPECS), leaving a gap in the "classical" submillimeter galaxy (SMG) population ($f_{870\mu m} \sim 2–10$ mJy).

The authors aim to provide a highly complete, unbiased spectroscopic census of DSFGs in the GOODS-S field to accurately model their redshift distribution and test the efficacy of current photo-z and JWST spectroscopic capabilities.

2. Methodology

The study focuses on a sample of 75 DSFGs in the GOODS-S field, originally identified via JCMT/SCUBA-2 850 $\mu$m imaging and followed up with ALMA 870 $\mu$m continuum observations (the "SG-ALMA" sample). The sample is flux-complete down to $f_{870\mu m} \approx 2.25$ mJy.

• ALMA Spectroscopic Follow-up:
  • Two ALMA programs were executed to perform spectral scans in Bands 3, 4, and 6.
  • Program 1 (2021): Targeted 51 sources ($f_{870\mu m} > 2.25$ mJy) with moderate sensitivity.
  • Program 2 (2024): A deeper follow-up ($\sim 2.5\times$ deeper) targeting 24 sources that lacked multiple line detections in the first program.
  • Detection Strategy: A matched-filtering algorithm (similar to LineSeeker) was used to search for CO and [C I] emission lines across multiple spectral windows. A significance threshold of $4.5\sigma$ was adopted to minimize false positives.
• Redshift Assembly:
  • New ALMA detections were combined with existing literature spectroscopic redshifts (spec-zs) from ground-based telescopes and JWST/NIRSpec catalogs (DJA v4).
  • Redshifts were categorized by confidence: "Secure" (two or more lines or confirmation of previous spec-z) and "Tentative" (single line supported by photo-zs).
• Photo-z Evaluation:
  • The authors tested four photo-z methods against the new spec-zs:
    1. EAZY: Using optical/NIR data from ZFOURGE (S16) and JADES (E26).
    2. FIR Methods: MMPZ and mbb (modified blackbody fitting) using submillimeter data.
    3. MAGPHYS: Full SED fitting from UV to radio.
  • Performance metrics included Normalized Median Absolute Deviation ($\sigma_{NMAD}$), outlier fraction ($\eta$), and bias.

3. Key Contributions

• Highest Completeness to Date: This study achieves the highest spectroscopic completeness for an unbiased, flux-limited DSFG sample at this flux limit.
  • 69% of the total 75 sources have secure or tentative spec-zs.
  • At $f_{870\mu m} > 2.5$ mJy, completeness reaches 97% (including tentative) and 72% (secure).
• JWST/NIRSpec Efficiency Test: The paper provides a comprehensive assessment of JWST's success rate for DSFGs, noting that while nearly all targeted sources were successfully identified, coverage remains low ($\sim 29\%$) due to target selection difficulties.
• Photo-z Benchmarking: A rigorous evaluation of photo-z codes specifically for dusty galaxies, highlighting systematic overestimation of redshifts at high-$z$.

4. Key Results

A. Redshift Distribution

• Median Redshift: The median redshift of the flux-complete sample ($f_{870\mu m} \ge 2.25$ mJy) is $\langle z \rangle = 2.57^{+0.13}_{-0.24}$.
• Distribution Shape: The distribution is well-fit by a log-normal function with parameters $z_\mu = 2.65$ and $\sigma = 0.21$.
• Flux Dependence: There is no statistically significant correlation between redshift and 870 $\mu$m flux ($r=0.20, p=0.093$), though a weak trend ($z \propto f_{870\mu m}$) is consistent with previous studies.
• Overdensities: 50% of the confirmed spec-z sources align with known protocluster overdensities in GOODS-S at $z \approx 1.6, 2.3, 2.6, 3.5,$ and $3.7$.

B. High-Redshift Population ($z > 4$)

• Abundance: The study finds a steep decline in massive dusty galaxies at high redshift.
  • $z > 4$: $\lesssim 10\%$ (specifically $6.6^{+3.2}_{-5.8}\%$ based on log-normal fit; 4/75 sources).
  • $z > 5$: $\lesssim 2\%$ (specifically $0.8^{+1.0}_{-0.8}\%$; 0/75 confirmed sources).
• Implication: This reflects a rapid decline in the abundance of massive dusty galaxies within the first 1.5 Gyr of the universe's history.

C. Photo-z Performance

• Outlier Fractions: All tested photo-z methods exhibit outlier fractions ($|\Delta z|/(1+z) > 0.15$) of $> 20\%$.
• Systematic Bias: Nearly all methods tend to overshoot redshifts, leading to an artificial excess of sources at $z > 4$.
  • EAZY (Optical/NIR): Performs best among optical methods ($\sigma_{NMAD} \approx 0.05$) but fails for $K_s$-dark sources and blends.
  • FIR Methods (MMPZ/mbb): Suffer from higher scatter ($\sigma_{NMAD} \approx 0.12-0.14$) and bias.
  • MAGPHYS: Including FIR data reduces the outlier fraction compared to optical-only fits but still results in $\sim 22\%$ outliers.
• Conclusion: Photo-zs alone are insufficient for precise redshift determination of DSFGs; deep spectroscopy is required.

D. JWST Spectroscopic Coverage

• Success Rate: Nearly 100% of the 20 DSFGs targeted with JWST/NIRSpec were successfully identified (mostly using PRISM mode).
• Coverage Gap: Despite high success, only 29% of the total sample has JWST spec-zs. Coverage is lower for fainter ($K_s > 23$) and fainter submillimeter sources, largely due to the low space density of DSFGs making efficient MSA targeting difficult.

5. Significance

• Cosmological Constraints: The results provide a robust, unbiased constraint on the high-redshift tail of the DSFG population, correcting previous overestimates derived from photo-zs. This suggests that the "peak" of dusty star formation is tightly confined to $z \sim 1.5–3.5$.
• Simulation Benchmarking: The derived log-normal redshift distribution serves as a critical benchmark for cosmological simulations attempting to reproduce the DSFG population.
• Future Survey Strategy: The study highlights that while JWST is powerful for individual targets, it is not yet a complete solution for large DSFG surveys due to targeting inefficiencies. Future efforts must combine ALMA Wideband Sensitivity Upgrade (WSU) capabilities with more efficient proxy selections or joint ALMA/JWST strategies to reach the faint end of the luminosity function.
• Methodological Validation: The paper demonstrates that even with deep JWST photometry, photo-zs for dusty galaxies remain unreliable without spectroscopic confirmation, reinforcing the need for continued investment in millimeter spectroscopy.