Evolution of the infrared luminosity function and its corresponding dust-obscured star formation rate density out to z~6

This paper presents a new determination of the evolving far-infrared galaxy luminosity function and dust-obscured star formation rate density out to redshift z~6 by combining ALMA follow-up data with stacked optical/near-infrared samples, revealing that the characteristic luminosity increases monotonically with redshift while dust-obscured activity contributes less than 25% to the total star formation rate density by z~6.

The Gist

Imagine the universe as a giant, bustling city that has been growing and changing for 13.8 billion years. For a long time, astronomers have been trying to count how many "people" (stars) are being born in this city every year. This is called the Star Formation Rate.

However, there's a catch: in many parts of this cosmic city, the newborn stars are wrapped in thick, cosmic blankets of dust. These blankets are so thick that they hide the stars from our eyes (which see visible light) but glow brightly in the dark, infrared heat that our special telescopes can see.

This paper is like a new, high-tech census report that tries to count both the visible stars and the dusty, hidden ones, all the way back to when the universe was very young (about 1 billion years old).

Here is the story of their discovery, broken down into simple concepts:

1. The Two Ways to Count Stars

To get the full picture, the astronomers had to use two different counting strategies, like using a flashlight for one group and a thermal camera for another.

• The "Flashlight" Method (The Bright Stars): They used a powerful telescope called ALMA to look at the "celebrities" of the galaxy world: the massive, super-bright, dusty galaxies. These are the easy ones to spot because they shine like beacons. This gave them the count of the "bright end" of the population.
• The "Thermal Camera" Method (The Faint Stars): The tricky part was counting the millions of smaller, dimmer galaxies. They were too faint to see directly. So, the astronomers used a clever trick called stacking. Imagine trying to hear a whisper in a noisy room. If you listen to one person, you hear nothing. But if you gather 1,000 people whispering the same thing at the same time, the sound adds up and becomes clear.
  • They took thousands of normal, dusty galaxies, grouped them by how heavy they were (their "stellar mass"), and stacked their signals together in the infrared maps. This allowed them to "hear" the collective glow of the faint, hidden population.

2. The Cosmic Timeline: What They Found

By combining these two methods, they created a movie of how star formation changed over time, from the "Cosmic Noon" (when the universe was about 3 billion years old and star formation was at its peak) to the "Cosmic Dawn" (when the universe was less than 1 billion years old).

Here are the three main plot points of their movie:

A. The "Downsizing" Trend

They found that the "big stars" (the most massive, bright galaxies) were born early in the universe's history. As time went on, the universe started making smaller, dimmer stars instead.

• Analogy: Think of a construction company. In the beginning, they only built massive skyscrapers. Later on, they switched to building small cottages. The "average" building got smaller over time.

B. The Dusty Peak and the Fading

At "Cosmic Noon" (around 3 billion years after the Big Bang), the universe was a dusty, chaotic place. Most stars were being born inside thick dust clouds.

• The Finding: At this time, the dusty, hidden stars were responsible for the majority of all new stars being born.
• The Twist: As the universe got older and older (moving toward redshift 4, 5, and 6), the dusty galaxies started to disappear. The "dust blankets" weren't forming as quickly as the stars themselves. By the time we look at the very early universe (z > 4), the dusty, hidden stars became rare. The "visible" stars (those not hidden by dust) took over as the main producers of new stars.

C. The "Dust-Poor" Early Universe

For a long time, scientists debated: Was the early universe a dusty, chaotic mess (a "Dust-Rich" scenario), or was it a clear, dusty-free place (a "Dust-Poor" scenario)?

• The Verdict: This paper says the early universe was Dust-Poor.
• Analogy: Imagine a party. The "Dust-Rich" theory says the party was so crowded and smoky that you couldn't see anyone. The "Dust-Poor" theory says the air was clear. This study shows that in the very early days, the air was actually quite clear. The thick, dusty blankets hadn't had enough time to form yet.

3. Why This Matters

Before this study, there was a big disagreement in the scientific community. Some studies using different telescopes suggested that the early universe was full of dusty, hidden star factories. Others said it was mostly clear.

This paper acts as the referee. By using a method that counts both the "celebrities" (bright galaxies) and the "crowd" (faint galaxies) together, they found that:

1. Dusty star formation was huge at the peak of the universe's history.
2. But, as we go further back in time, the dusty galaxies become less important.
3. By the time the universe was very young, the "dusty" contribution dropped to less than 25% of the total star formation.

The Bottom Line

The universe started as a place where stars were born in the open, then it got dusty and chaotic (hiding most of the stars), and now, as we look back to the very beginning, it seems the dust hadn't fully formed yet, leaving the early stars relatively visible.

This paper helps us understand that the "dust" in the universe takes time to build up, and without it, the early universe was a very different, clearer place than we previously thought.

Technical Summary

1. Problem Statement

The primary goal of modern extragalactic astronomy is to map the evolution of star formation (SF) throughout cosmic history. While the unobscured (UV) star formation rate density ($\rho_{SFR}$) is well-constrained up to $z \sim 11$, the contribution of dust-obscured star formation remains highly uncertain at high redshifts ($z \gtrsim 4$).

• The Discrepancy: At low redshifts ($z < 3$), IR and UV studies generally agree. However, at $z \gtrsim 4$, derived values for the total $\rho_{SFR}$ differ by over an order of magnitude.
• The Challenge: Direct detection of faint, dusty galaxies at high redshifts is limited by the sensitivity of current telescopes. Previous studies relying on submillimeter (SMG) or Herschel-selected samples often suffer from:
  • Blending issues in low-resolution Herschel data.
  • Inhomogeneous samples in ALMA surveys (often targeting only the brightest sources).
  • Large extrapolations required to account for the faint-end of the luminosity function (LF), leading to inconsistent faint-end slopes ($\alpha$) ranging from -0.2 to -1.0.

The paper aims to resolve these uncertainties by deriving a robust, evolving IR Luminosity Function (LF) up to $z \sim 6$, explicitly constraining the faint-end slope without relying solely on direct detections of faint sources.

2. Methodology

The authors employed a hybrid approach, combining direct detections of bright sources with a stacking technique for faint sources to construct the full IR LF.

A. Data Sources

1. Bright End (Direct Detections):

   • Dataset: AS2UDS (ALMA follow-up of the JCMT SCUBA-2 Cosmology Legacy Survey in the UKIDSS UDS field).
   • Selection: 708 ALMA-identified submillimeter galaxies with $S_{870} > 4.3$ mJy.
   • Properties: Photometric redshifts and IR luminosities ($L_{IR}$) were adopted from Dudzevičiūtė et al. (2020), derived using magphys SED modeling.
   • Completeness: The sample is flux-complete ($>80\%$) for $S_{850} > 4$ mJy.

2. Faint End (Stacking Analysis):

   • Dataset: Optical/Near-IR mass-complete catalogs from the UKIDSS UDS and COSMOS fields (McLeod et al. 2021).
   • Technique: Stacking these optical sources in FIR maps (Herschel at 100–500 $\mu$m and JCMT at 850 $\mu$m).
   • Proxy: Stellar mass ($M_*$) was used as a proxy for $L_{IR}$, leveraging the tight correlation between $M_*$ and $L_{IR}$ for star-forming galaxies (the "Main Sequence").
   • Bins: Analysis was performed in redshift bins spanning $z \approx 1.2$ to $5.7$ and stellar mass bins.

B. Analysis Framework

• Luminosity Function Construction:
  • Faint End: Derived via the $1/V_{max}$method applied to the stacked$L_{IR}$ values.
  • Bright End: Derived via the $1/V_{max}$method applied to AS2UDS detections, corrected for completeness ($w_i$) and false detection rates (FDR).
• Functional Fitting:
  • The combined data were fitted with a Schechter function: $\Phi(L, z) = \Phi^* (L/L^*)^\alpha \exp(-L/L^*)$.
  • Faint-end slope ($\alpha$): Determined at two low-redshift bins ($1.2 \le z < 1.6$and$1.6 \le z < 2.2$). The more robust value ($\alpha = -0.26 \pm 0.11$) was fixed for all higher redshift bins to avoid extrapolation errors.
  • Evolutionary Parameters: The characteristic luminosity ($L^*$) and characteristic number density ($\Phi^*$) were modeled as functions of redshift.

C. Star Formation Rate Density ($\rho_{SFR}$)

• Calculated by integrating the fitted Schechter functions over $8.0 < \log(L_{IR}/L_\odot) < 14.0$.
• Converted to $\rho_{SFR}$ using the Kennicutt (1998) relation with a Chabrier IMF correction factor (0.63).

3. Key Results

A. Evolution of the IR Luminosity Function

The study establishes the following evolutionary trends for the Schechter parameters:

1. Faint-end Slope ($\alpha$): Found to be $\alpha = -0.26 \pm 0.11$. This is a relatively shallow slope, indicating a lack of a steep rise in the number of faint dusty galaxies.
2. Characteristic Luminosity ($L^*$): Increases monotonically with redshift, following a power law:
   $$L^* \propto z^{1.38 \pm 0.07}$$
   This supports the "downsizing" scenario, where the most luminous (and massive) galaxies form earlier than their fainter counterparts.
3. Characteristic Number Density ($\Phi^*$):
   • Constant at $z < 2.24$.
   • Declines steeply at $z > 2.24$ following:
     $$\Phi^* \propto z^{-4.95 \pm 0.73}$$
   • This steep decline is consistent with "dust-poor" models of the early Universe.

B. Star Formation Rate Density ($\rho_{SFR}$)

• Peak: The dust-obscured $\rho_{SFR}$ peaks at $z \approx 2$ (Cosmic Noon).
• High-Redshift Decline: Beyond $z \sim 2$, the obscured $\rho_{SFR}$ declines rapidly.
• Dominance:
  • At $z \sim 2-3$, dust-obscured star formation dominates the total $\rho_{SFR}$.
  • At $z > 4$, UV-visible star formation becomes dominant.
  • By $z \sim 6$, dust-obscured activity contributes less than 25% to the total star formation rate density.

C. Comparison with Literature

• Agreement: Results align well with recent ALMA-based studies (Dunlop et al. 2017; Wang et al. 2019; Magnelli et al. 2024; Liu et al. 2025) that utilize stacking or deep individual detections.
• Discrepancies: The derived $\rho_{SFR}$ is significantly lower than results from Rowan-Robinson et al. (2016) and Gruppioni et al. (2020). The authors attribute these higher values in previous works to:
  • Blending in low-resolution Herschel data (overestimating flux).
  • Clustering biases in ALMA pointings targeting dense regions.
  • Inhomogeneous sample selection.

4. Significance and Conclusions

• Resolution of High-$z$ Uncertainty: By combining direct ALMA detections with a robust stacking method for the faint end, the paper provides a self-consistent IR LF up to $z \sim 6$, reducing the order-of-magnitude discrepancies seen in previous high-redshift studies.
• Dust-Poor Early Universe: The steep decline in $\Phi^*$ and the shallow faint-end slope support a "dust-poor" scenario for the early Universe. This suggests that the timescale for dust formation (driven by AGB stars and supernovae) is longer than the formation timescale of the first UV-bright galaxies. Consequently, the Universe at $z > 4$ is dominated by unobscured star formation.
• Methodological Advancement: The study demonstrates the efficacy of using stellar mass as a proxy for IR luminosity in stacking analyses to constrain the faint end of the LF, a technique that avoids the biases inherent in selecting only the brightest submillimeter sources.

In summary, the paper concludes that while dusty star-forming galaxies exist at the highest redshifts, their contribution to the cosmic star formation budget diminishes rapidly beyond $z \sim 4$, placing the early Universe firmly in a regime where UV-bright, dust-poor galaxies drive the majority of star formation.