Detection of lensing substructure using ALMA observations of the dusty galaxy SDP.81

Abstract: We study the abundance of substructure in the matter density near galaxies using ALMA Science Verification observations of the strong lensing system SDP.81. We present a method to measure the abundance of subhalos around galaxies using interferometric observations of gravitational lenses. Using simulated ALMA observations, we explore the effects of various systematics, including antenna phase errors and source priors, and show how such errors may be measured or marginalized. We apply our formalism to ALMA observations of SDP.81. We find evidence for the presence of a $M=10^{8.96\pm 0.12} M_{\odot}$ subhalo near one of the images, with a significance of $6.9\sigma$ in a joint fit to data from bands 6 and 7; the effect of the subhalo is also detected in both bands individually. We also derive constraints on the abundance of dark matter subhalos down to $M\sim 2\times 10^7 M_{\odot}$, pushing down to the mass regime of the smallest detected satellites in the Local Group, where there are significant discrepancies between the observed population of luminous galaxies and predicted dark matter subhalos. We find hints of additional substructure, warranting further study using the full SDP.81 dataset (including, for example, the spectroscopic imaging of the lensed carbon monoxide emission). We compare the results of this search to the predictions of $\Lambda$CDM halos, and find that given current uncertainties in the host halo properties of SDP.81, our measurements of substructure are consistent with theoretical expectations. Observations of larger samples of gravitational lenses with ALMA should be able to improve the constraints on the abundance of galactic substructure.

Analysis of Substructure Detection via ALMA Observations in Gravitational Lensing

This paper presents a sophisticated methodological framework for detecting dark matter (DM) substructure using data from the Atacama Large Millimeter/submillimeter Array (ALMA). The focus is on the lensed galaxy SDP.81 to probe the hierarchical structure formation as predicted by the ΛCDM model. The gravitational lensing technique enables the detection of subhalos that might be devoid of baryons, making it an effective tool for examining the small-scale challenges faced by the cold dark matter (CDM) paradigm, notably the "Missing Satellite Problem."

Methodological Approach

Hezaveh et al. utilize interferometric data, specifically targeting submillimeter observations with ALMA, to model mass distributions via strong gravitational lensing. A pivotal part of their method is the development of a linearized approach to identify potential substructures by mapping deviations in the observed visibilities against expectations from a smooth lens model. This process leverages the perturbative nature of low-mass subhalos: the deflection fields they generate are small and localized but discernible within the precision-framework provided by ALMA's extensive uv-coverage.

The analysis is divided into phases of identifying and modeling subhalos, inflating computational tractability through visibility binning, employing efficient algorithms for handling large and dense visibility matrices, and statistically assessing detection significances. The theoretical framework detailed emphasizes analytic marginalization over source and nuisance parameters like antenna phase errors, a necessary step to achieve unbiased subhalo detections.

Results and Discussion

The ALMA observations indicate the presence of a subhalo of mass (M \approx 10^{8.96} M_{\odot}) near SDP.81, with a detection significance of (6.9\sigma) confirmed across multiple frequency bands. The analyses suggest substructure constraints that align with simulations predicting a significant halo-to-halo scatter in DM subhalo properties. These results provide direct empirical support for the existence and detectability of DM substructure, reinforcing theoretical predictions from ΛCDM simulations concerning the abundance and distribution of subhalos.

On a broader scale, the results have implications for precision cosmology, especially in resolving small-scale structures in the ΛCDM framework. By extending the analysis to additional gravitational lenses and utilizing line emission data, future research could substantially refine the empirical characterization of the subhalo mass function, probing distinctions between CDM and alternative DM models like warm dark matter (WDM).

Implications and Future Directions

The approach highlights ALMA's potential to revolutionize our understanding of dark matter at scales previously difficult to probe. These findings underline the need for methodological rigor and careful treatment of systematics in substructure analyses, emphasizing the importance of working directly with unprocessed visibilities instead of composite images to mitigate errors stemming from instrumental uncertainties.

Future developments could harness the large catalog of strong lens systems being discovered in submillimeter surveys, expanding statistical power to constrain the subhalo mass function robustly. This, combined with joint analysis frameworks encompassing dark matter simulations, will enhance the fidelity of forecasts about cosmic structure formation processes, providing deeper insights into the nature of dark matter itself.

Overall, the investigation serves as a roadmap for applying sophisticated analytical frameworks to tackle essential questions in astrophysics and cosmology, particularly about dark matter's elusive small-scale properties.