Acceleration of ultra-compact radio jets on sub-parsec scales: Testing the inner jet models

Very Long Baseline Interferometry (VLBI) observations at 86 GHz ($\sim$ 3 mm) reach a resolution of about 50 $\mu$as and sample the scales as small as 10$^{3}$-10$^{4}$ Schwarzschild radii of the central black hole in Active Galactic Nuclei (AGN), and uncover the jet regions where acceleration and collimation of the relativistic flow takes place. We present results from a large global 86 GHz VLBI survey of 162 ultra compact radio sources conducted in 2010-2011 using the Global Millimeter VLBI Array (GMVA). This survey has contributed an increase of $\sim$ 2 on the total number of AGN ever imaged with VLBI at 86 GHz. For the first time, 3 mm VLBI maps of 138 sources are made (Nair et.al 2019). Gaussian model fitting was used to represent the structure of the observed sources and to estimate the flux densities, sizes and brightness temperature (T$_{b}$) of the VLBI bright core (base) of the jet and inner jet components of the sources. The brightness temperature measurements obtained for the cores and jet components of 162 sources from this 86 GHz VLBI survey are applied to study jet physics down to smallest angular ($\sim$ 50 $\mu$as) scales and observationally test models of jet formation in the inner jet region. Brightness temperature measurements made from the survey data have been applied to estimate the intrinsic brightness temperature at the jet base (VLBI core) and in the nearest moving jet components. These measurements have been modeled by a basic population scenario with a constant Lorentz factor for the entire source sample. The investigation of the observed distribution of T$_{b}$ by population modeling showed that the intrinsic brightness temperature, T$_{0}$ = (3.77$\pm$0.14)x10$^{11}$ K for the jet cores, implying that the inverse Compton losses dominate the emission in the cores, and in the nearest jet components, T$_{0}$ = (1.42$\pm$0.19)x10$^{11}$ K is found, which is slightly higher than the equipartition limit of 5x10$^{10}$ K expected for these jet regions. For objects with sufficient structural detail detected, the adiabatic energy losses are shown to dominate the observed changes of brightness temperature along the jet, and the results are in agreement with theoretical predictions for adiabatically expanding jets. Therefore, from this population modeling, the core brightness is found to be limited by the inverse Compton losses, while equipartition and adiabatic expansion govern the observed evolution of the moving jet components. The peaking of brightness temperatures measured in the millimeter (mm) VLBI cores in our sample at $\sim$ 10$^{11}$ K could be best explained by assuming that plasma acceleration is still taking place in the region between the mm VLBI cores, a result which confirms the theoretical prediction that the acceleration zone extends on parsec scales. Combining the 86 GHz survey estimates of brightness temperature with data obtained at lower frequencies, we have also studied the jet acceleration on scales of $\sim$ 100-10000 gravitational radii, showing that a magneto-hydrodynamic (MHD) mechanism is most likely responsible for accelerating the jet plasma on these scales. The brightness temperature measurements of our survey (at 86 GHz) are combined with that made from VLBI observations at lower frequencies of 2 GHz, 8 GHz (Pushkarev and Kovalev 2012) and 15 GHz (Kovalev 2005) to study the evolution of intrinsic brightness temperature (T$_{0}$) with frequency. Radio luminosity and jet parameters were used to convert frequency to linear coordinate along the jet to investigate the evolution of T$_{b}$ with the absolute distance of the VLBI cores from the central black hole. We modeled T$_{b}$ at multiple frequencies from (2-86) GHz as a function of the absolute distance from the central black hole and the best fit obtained for the maximum brightness temperature in the downstream of the jet was T$_{m}$ = (8.09$\pm$0.48)x10$^{11}$ K and initial brightness temperature near the jet base was 3.74x10$^{10}$ K. This gives a clue that the brightness temperatures on sub-parsec scales are close to the equipartition temperature of 5x10$^{10}$ K and start to increase on sub-parsec regions, reaching the inverse Compton limit of 10$^{12}$ K on parsec scales. The trend on evolution of brightness temperature with the distance from the central engine we observed matches well with the magnetically driven, accelerating jet model (e.g. Vlahakis and Koenigl 2004) according to which, the mass flux is initially constant in the sub-parsec scale, and then increases, and gets constant again in the outer region. In our studies, the dependence of Lorentz factor on the distance from the central engine also shows a similar trend, being constant in the inner region and then increasing in the outer region suggesting that the relativistic jets are magnetically driven to accelerate on the sub-parsec regions from the central engine.