# Probing an X-ray flare pattern in Mrk 421 induced by multiple stationary shocks: a solution to the bulk Lorentz factor crisis

## TL;DR

This study analyzes 13 years of X-ray data from Mrk 421 to identify a specific variability pattern linked to stationary shocks in the jet, providing insights into jet dynamics and resolving the bulk Lorentz factor crisis.

## Contribution

It introduces a novel method to detect intrinsic variability patterns in blazar jets, linking radio stationary knots to high-energy emission and estimating jet perturbation properties without direct motion observation.

## Key findings

- Identified a significant variability pattern consistent with a shock crossing all radio knots.
- Estimated the jet perturbation's apparent speed at 45 c.
- Linked stationary radio knots to high-energy particle acceleration.

## Abstract

The common observations of multiple radio VLBI stationary knots in high-frequency-peaked BL Lacs (HBLs) can be interpreted as multiple recollimation shocks accelerating particles along jets. This approach can resolve the so-called "bulk Lorentz factor crisis" of sources with high Lorentz factor, deduced from maximum gamma-gamma opacity and fast variability, and apparently inconsistent slow/stationary radio knots. It also suggests that a unique pattern of the non-thermal emission variability should appear after each strong flare. Taking advantage of the 13 years of observation of the HBL Mrk 421 by the X-ray Telescope on the Neil Gehrels Swift Observatory Swift-XRT, we probe for such an intrinsic variability pattern. Its significance is then statistically estimated via comparisons with numerous similar simulated lightcurves. A suggested variability pattern is identified, consistent with a main flare emission zone located in the most upstream 15.3 GHz radio knot at 0.38 mas from the core. Subsequent flux excesses in the lightcurve are consistent with a perturbation crossing all the downstream radio knots with a constant apparent speed of 45 c. The significance of the observed variability pattern not arising from stochastic processes is found above 3 standard deviations, opening a promising path for further investigations in other blazars and with other energy bands. In addition to highlight the role of stationary radio knots as high-energy particle accelerators in jets, the developed method allows estimates of the apparent speed and size of a jet perturbation without the need to directly observe any motion in jets.