A million-solar-mass object detected at cosmological distance using gravitational imaging

TL;DR

The paper demonstrates the feasibility of detecting and measuring a million-solar-mass object at cosmological distance using gravitational imaging of a strongly lensed arc with milli-arcsecond-resolution VLBI. By combining a visibility-plane Bayesian forward-modeling approach with non-parametric gravitational imaging and independent parametric modeling, the authors identify a compact low-mass perturber V with a mass within 80 pc of about $m_{80} \approx 1.13 \times 10^6$ and an extremely strong detection significance (26σ). The inferred position is measured with sub-mas precision, and the mass is robust across modeling choices for a nearby perturber A, underscoring the robustness of the GI detection. This work establishes VLBI-based strong lensing as a powerful tool to probe the $10^6$ M_sun regime at cosmological distances, enabling tests of dark matter models and subhalo populations across cosmic time.

Abstract

Structure on sub-galactic scales provides important tests of galaxy formation models and the nature of dark matter. However, such objects are typically too faint to provide robust mass constraints. Here, we report the discovery of an extremely low-mass object detected via its gravitational perturbation to a thin lensed arc observed with milli-arcsecond-resolution very long baseline interferometry (VLBI). The object was identified using a non-parametric gravitational imaging technique and confirmed using independent parametric modelling. It contains a mass of $m_{\rm 80}=(1.13 \pm 0.04)\times 10^6{M_\odot}$ within a projected radius of 80 parsecs at an assumed redshift of 0.881. This detection is extremely robust and precise, with a statistical significance of 26$σ$, a 3.3 per cent fractional uncertainty on $m_{\rm 80}$, and an astrometric uncertainty of 194 $μ$as. This is the lowest-mass object known to us, by two orders of magnitude, to be detected at a cosmological distance by its gravitational effect. This work demonstrates the observational feasibility of using gravitational imaging to probe the million-solar-mass regime far beyond our local Universe.

Figures (9)

• Figure 1: The strong gravitational lens system JVAS B1938+666. Left: Our best model of the 1.7 GHz global VLBI observation used here, which has been re-convolved with the main lobe of the interferometer's PSF and added to the residuals (34 $\mu$Jy/beam RMS). For reference, red contours show a 2.1 $\mu$m observation from the W. M. Keck Observatory adaptive optics system lagattuta2012. The positions of two low-mass perturbers are marked with black X's. The $2\times10^8~\mathrm{M_\odot}$ object first detected by vegetti2012 is labeled $\mathcal{A}$, while the $1.13\times 10^6~\mathrm{M_\odot}$ detection reported here is labeled $\mathcal{V}$. The zoomed-in region shown in the right two panels is indicated by the black square, which has a side length of 60 milli-arcseconds. Top right: Detail of the bright arc around $\mathcal{V}$, with the colour scale modified to emphasize the gap in the arc produced by $\mathcal{V}$'s gravitational perturbation. Bottom right: Gravitational imaging (GI) corrections to the lensing convergence (expressed in units of lens-plane surface mass density), showing a compact, positive feature whose position and mass are consistent with the independent parametric modeling results for $\mathcal{V}$. The dashed black circle has a radius of 80 pc, and the lensed emission are indicated by the black contours.
• Figure 1: Non-parametric gravitational imaging (GI) corrections to the lensing convergence (expressed in units of lens-plane surface mass density), for six different combinations of regularization type and grid resolution $N_\mathrm{GI}$. The discontinuities in the intensities of the colour scales indicate the $3\sigma_\mathrm{GI}$ thresholds used to identify features of interest in the convergence corrections. In all six GI runs, we recover compact, positive convergence features in the same location along the bright arc. These positions are consistent with the independent parametric modeling results for detection $\mathcal{V}$, whose location is shown by the black X's. The dashed black circles in the inset panels have a radius of 80 pc. The lensed images are indicated by the black contours.
• Figure 2: Visual comparison of models without and with perturber $\mathcal{V}$. Top row: Pixellated source surface brightness maps. In the model without $\mathcal{V}$ , the source model attempts to fit the gap in the bright lensed arc, resulting in a sharp discontinuity in the surface brightness along the lensing caustic (left column). The gravitational effect of $\mathcal{V}$ folds the caustic over onto the bright radio lobe, correcting this discontinuity and recovering a smooth, contiguous image (right column). The inset region around the bright, quadruply-imaged source component has a side length of 4 milli-arcseconds. Also note the presence of a much fainter, doubly-imaged source component $\sim50~\mathrm{mas}$ to the north of the bright component. Middle row: Lens-plane surface brightness maps (re-convolved with the main lobe of the PSF). Note that the gap in the arc is still present in the model without $\mathcal{V}$; in this case the source has attempted to absorb the discontinuity. Bottom row: Residuals, which have been normalized in the visibility plane and Fourier-transformed into the image plane for ease of visualization. The inclusion of $\mathcal{V}$ corrects a $>5\sigma$ peak in the residuals (corresponding to a $2$ percent change in surface brightness) near the intersection between the critical curve and the lensed arc. The zoomed-in region in the middle and bottom rows is the same as the inset region in Figure \ref{['fig:deconvolved']}.
• Figure 2: Significance map for gravitational imaging (GI) corrections to the lensing convergence, expressed in units of $\sigma_\mathrm{GI}$. While features above the $3\sigma_\mathrm{GI}$ threshold appear at various locations in some of the runs, only the feature associated with detection $\mathcal{V}$ (black X's) is robust and consistent across all six different combinations of regularization type and grid resolution $N_\mathrm{GI}$. See Supplemental Figure \ref{['fig:px']} for GI maps in units of surface mass density.
• Figure 3: Comparison of mass profiles of detection $\mathcal{V}$, in terms of cylindrical enclosed mass $M_\mathrm{cyl}(<r)$, for both gravitational imaging and parametric modeling procedures. For the gravitational imaging models, we compare three different regularization types (penalizing the convergence, gradient of convergence, or curvature of convergence) and two different grid resolutions ($N_\mathrm{GI}=512$ and $N_\mathrm{GI}=1024$, corresponding to pixel sizes of $3.5~\mathrm{mas}$ and $1.8~\mathrm{mas}$, respectively). The profiles are consistent to within $\sim 50$ percent at a radius of 80 pc (vertical dashed line). The discrete steps in the GI curves are due to the pixellated nature of the convergence corrections. Shaded regions denote the $1\sigma$ uncertainties in the enclosed mass profiles..