[Paper Review] ALMA imaging of SDP.81 - I. A pixelated reconstruction of the far-infrared continuum emission

Matus Rybak, J. P. McKean+3 more|arXiv (Cornell University)|Mar 6, 2015

Galaxies: Formation, Evolution, Phenomena1 references4 citations

TL;DR

This study uses ALMA's high-resolution sub-continuum data and a novel Bayesian pixelated visibility-fitting technique to reconstruct the unlensed far-infrared emission of the gravitationally lensed starburst galaxy SDP.81 at z = 3.042. It reveals a 1.9 kpc-diameter, elongated disk with multiple star-forming regions, including a compact clump with a star-formation rate density of 190 ± 20 M⊙ yr⁻¹ kpc⁻², consistent with a sub-Eddington starburst and indicating no strong size-bias in lensed systems.

ABSTRACT

We present a sub-50 pc-scale analysis of the gravitational lens system SDP.81 at redshift 3.042 using Atacama Large Millimetre/submillimetre Array (ALMA) science verification data. We model both the mass distribution of the gravitational lensing galaxy and the pixelated surface brightness distribution of the background source using a novel Bayesian technique that fits the data directly in visibility space. We find the 1 and 1.3 mm dust emission to be magnified by a factor of u_tot = 17.6+/-0.4, giving an intrinsic total star-formation rate of 315+/-60 M_sol/yr and a dust mass of 6.4+/-1.5*10^8 M_sol. The reconstructed dust emission is found to be non-uniform, but composed of multiple regions that are heated by both diffuse and strongly clumped star-formation. The highest surface brightness region is a ~1.9*0.7 kpc disk-like structure, whose small extent is consistent with a potential size-bias in gravitationally lensed starbursts. Although surrounded by extended star formation, with a density of 20-30+/-10 M_sol/yr/kpc^2, the disk contains three compact regions with densities that peak between 120-190+/-20 M_sol/yr/kpc^2. Such star-formation rate densities are below what is expected for Eddington-limited star-formation by a radiation pressure supported starburst. There is also a tentative variation in the spectral slope of the different star-forming regions, which is likely due to a change in the dust temperature and/or opacity across the source.

Motivation & Objective

• To resolve the sub-50 pc-scale structure of the far-infrared dust emission in the gravitationally lensed starburst galaxy SDP.81 at z = 3.042.
• To overcome limitations of beam-smearing and differential magnification by modeling the source directly in visibility space.
• To map the spatially resolved star-formation rate density across the source and test for Eddington-limited starburst conditions.
• To investigate variations in dust spectral slope across different star-forming regions to infer physical differences in temperature or opacity.
• To assess whether lensed systems suffer from size-bias due to magnification effects by measuring the intrinsic size of the source.

Proposed method

• Utilizes ALMA science verification data at 1 and 1.3 mm (236 GHz and 290 GHz) in Bands 6 and 7 with high signal-to-noise ratio.
• Applies a Bayesian pixelated visibility-fitting lens modeling technique that reconstructs the source directly from visibility data, avoiding image-plane deconvolution.
• Simultaneously models the mass distribution of the foreground lensing galaxy and the unlensed surface brightness distribution of the background source.
• Employs a pixelated source reconstruction with a Markov Chain Monte Carlo (MCMC) approach to infer uncertainties and posterior distributions.
• Uses the reconstructed source to derive intrinsic star-formation rate, dust mass, and surface brightness, correcting for total magnification (μ_total = 17.6 ± 0.4).
• Analyzes spectral slope variations between 230 and 290 GHz across different clumps to infer local dust temperature and opacity differences.

Experimental results

Research questions

• RQ1 What is the intrinsic size and morphology of the star-forming region in SDP.81 after correcting for gravitational lensing?
• RQ2 What is the spatially resolved star-formation rate density across the source, and does it exceed the Eddington limit for radiation-pressure-supported starbursts?
• RQ3 Are there variations in the dust spectral slope across different clumps, indicating differences in dust temperature or opacity?
• RQ4 Does the observed compactness of the main emission region reflect a size-bias in gravitationally lensed starbursts?
• RQ5 Can visibility-space modeling with pixelated source reconstruction provide a more accurate and unbiased view of high-redshift star-forming galaxies than traditional imaging?

Key findings

• The unlensed source has a diameter of ~1.9 kpc and is elongated, consistent with a disk-like morphology hosting multiple star-forming regions.
• The total magnification of the dust emission is μ_total = 17.6 ± 0.4, leading to an intrinsic total star-formation rate of 315 ± 60 M⊙ yr⁻¹ and a dust mass of 6.4 ± 1.5 × 10⁸ M⊙.
• The star-formation rate density varies from ~20 to 190 ± 20 M⊙ yr⁻¹ kpc⁻² across the source, with the peak in a compact clump, and is below the Eddington limit (~1000 M⊙ yr⁻¹ kpc⁻²).
• The central dominant clump has a flux ratio of 0.51 ± 0.07 between 230 and 290 GHz, while northern and southern clumps show lower ratios (0.41 ± 0.03 and 0.45 ± 0.05), indicating a steeper spectral slope and potential differences in dust temperature or opacity.
• The spectral index α varies from ~2.8 (global) to ~3.9–4.3 across clumps, suggesting that global dust models are insufficient to describe multi-component star-forming regions.
• The source is resolved into two arcs on ~100 mas scales, but most emission is resolved out on 30 mas scales (baseline ~5 Mλ), confirming that the source is intrinsically small and consistent with a size-bias in lensed systems.