High Significance Detection of the Dark Substructure in Gravitational Lens SDSS J0946+1006 by Image Pixel Supersampling

Abstract Recent studies have shown that the dark substructure reported in the gravitational lens SDSS J0946+1006 has a high central density, which is in apparent tension with the flat cold dark matter (ΛCDM) paradigm. However, its detection significance has been found in D. J. Ballard et al. to be sensitive to prior assumptions about the smoothness of the source galaxy. Here we show that the detection significance of the substructure is higher than previously reported (log-Bayes factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo mathvariant="normal">Δ</mml:mo> <mml:mi>ln</mml:mi> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">E</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>143</mml:mn> </mml:math> , equivalent to a ∼17 σ detection) by approximating the integration of light over each pixel via ray tracing and averaging over many subpixels—a technique known as supersampling—and this result is insensitive to the assumed prior on the source galaxy smoothness. Assuming a dark matter subhalo, the combination of supersampling and modeling both sets of lensed arcs also tightens the subhalo constraints: we find the subhalo’s projected mass within 1 kpc lies in the range (2.2–3.4) × 10 9 M ⊙ at 95% confidence in our highest evidence model, while the log-slope of the subhalo’s projected density at 1 kpc is steeper than −1.75 at the 95% confidence level, further establishing it as an outlier compared to expectations from CDM. We also identify a systematic that has biased the slope of the primary lensing galaxy’s density profile in prior studies, which we speculate might be due to the presence of dust or an imperfect foreground subtraction. Our analysis places the existence of the substructure on firmer ground, and should motivate deeper follow-up observations to better constrain its properties and clarify its apparent tension with ΛCDM.