Dark matter environments and safeguards for spacetime inference from horizon scale interferometry

Abstract

Horizon scale interferometry can test a black hole spacetime only when the data, source model, and numerical response are reliable. We study this requirement with the public 2017 M87* closure data, a frozen semi analytic emission model, explicit dark matter controls, and a rotating tidal charge deformation. We normalize NFW and Einasto halos, an adiabatic spike, a capture suppressed spike, and a heated crest for M87*. Even the intentionally optimistic rendered case, $M_{\rm DM}(<10M)/M_{\rm BH}=7.33\times10^{-5}$, changes the normalized image and visibility by only about $2.65\times10^{-6}$ and $4.9\times10^{-7}$. We then build an independent closure phase and log closure amplitude likelihood with covariance and three fixed high/low band correlation cases. Synthetic Kerr tests recover the expected statistic, coverage, and false positive rate. The real data give $\chi^2/N=1.7583$, $1.7206$, and $1.6873$, above the global adequacy limit of $1.5$; the worst band gives $2.0216$. Removing the most influential scan still leaves $\chi^2/N=1.6472$. If tidal charge is allowed anyway, the residual projects strongly onto it, but the preferred direction changes sign between image resolutions. Direct libraries at $N=192$, 224, and 256 also fail the differential response convergence tests. At a smoothing width of $0.5M$, the Kerr image changes by about $0.45\%$ between $N=192$ and 224, while the tidal charge response changes by about $49\%$. We therefore report no posterior or bound. Spacetime inference should remain closed until the adopted data and covariance are validated, the undeformed source passes an absolute adequacy test, and the differential metric response converges independently of the image.