On the existence of a standard rod in the Universe

TL;DR

The paper argues that ultra-compact radio source cores observed with ground-based VLBI cannot serve as standard rods due to resolution limits and biases, challenging previous assumptions in cosmology.

Contribution

It demonstrates that the cores of ultra-compact radio sources are unsuitable as standard rods with current ground-based VLBI resolution, clarifying the origin of luminosity-size correlations.

Findings

VLBI cores cannot be used as standard rods with current resolution.

Luminosity-size correlation arises from resolution limits and biases.

Ground-based VLBI resolution is insufficient for reliable size measurements.

Abstract

Using standard cosmological model we show that the cores of ultra-compact radio sources observed with ground-based Very Long Baseline Interferometry (VLBI) on the angular scales of milliarcseconds cannot be used as a reasonable standard unit of linear size. "Luminosity - linear size" correlation obtained by many authors for ultra compact radio sources has different origin than that for the radio galaxies and quasars on the angular scales of arcminutes. It is just the manifestation of the fact that ground-based VLBI networks are unable to resolve VLBI-cores and the Malmquist bias presents. Thus, the cores of compact radio sources can't be used as "standard rods" at least with resolution offered by ground-based VLBI. This conclusion is illustrated on 15 GHz VLBA sample of radio sources.