Jet-lag in Sgr A*: What size and timing measurements tell us about the central black hole in the Milky Way

The black hole at the Galactic Center, Sgr A*, is the prototype of a galactic nucleus at a very low level of activity. Its radio through submm-wave emission is known to come from a region close to the event horizon, however, the source of the emission is still under debate. A successful theory explaining the emission is based on a relativistic jet model scaled down from powerful quasars. We want to test the predictive power of this established jet model against newly available measurements of wavelength-dependent time lags and the size-wavelength structure in Sgr A*. Using all available closure amplitude VLBI data from different groups, we again derived the intrinsic wavelength-dependent size of Sgr A*. This allowed us to calculate the expected frequency-dependent time lags of radio flares, assuming a range of in- and outflow velocities. Moreover, we calculated the time lags expected in the previously published pressure-driven jet model. The predicted lags are then compared to radio monitoring observations at 22, 43, and 350 GHz. The combination of time lags and size measurements imply a mildly relativistic outflow with bulk outflow speeds of gammabeta ~ 0.5-2. The newly measured time lags are reproduced well by the jet model without any major fine tuning. The results further strengthen the case for the cm-to-mm wave radio emission in Sgr A as coming from a mildly relativistic jet-like outflow. The combination of radio time lag and VLBI closure amplitude measurements is a powerful new tool for assessing the flow speed and direction in Sgr A*. Future VLBI and time lag measurements over a range of wavelengths will reveal more information about Sgr A*, such as the existence of a jet nozzle, and measure the detailed velocity structure of a relativistic jet near its launching point for the first time.

💡 Research Summary

The paper investigates the origin of the radio‑to‑sub‑millimeter emission from Sagittarius A* (Sgr A*), the supermassive black hole at the centre of the Milky Way, by jointly analysing wavelength‑dependent source size measurements and multi‑frequency flare time‑lag observations. Using all publicly available VLBI closure‑amplitude data from several groups, the authors re‑derive the intrinsic size of Sgr A* as a function of wavelength, confirming a power‑law relationship θ_int ∝ λ^α with α≈1.3. This size‑wavelength scaling implies a systematic shift of the apparent “core” position with frequency, a hallmark of synchrotron self‑absorbed jet emission.

With the size‑frequency relation in hand, the authors calculate the expected time delays between flare peaks at 22 GHz, 43 GHz and 350 GHz for a range of flow velocities. Two conceptual models are explored: (1) a simple constant‑velocity outflow, where the delay Δt is given by the distance between the frequency‑dependent core positions divided by βc, and (2) a pressure‑driven jet model in which the flow accelerates from a sub‑relativistic launch speed (β≈0.1) to mildly relativistic speeds (γβ≈1) over a few tens of Schwarzschild radii.

The observed delays—approximately 20–30 minutes between 22 GHz and 43 GHz, and 5–10 minutes between 43 GHz and 350 GHz—are best reproduced by an outflow with bulk Lorentz factor times velocity γβ in the range 0.5–2. The constant‑velocity model requires β≈0.3–0.6c, while the pressure‑driven jet naturally yields the same effective γβ after modest acceleration, reproducing both the magnitude of the delays and their frequency dependence without fine‑tuning.

Crucially, the direction of the delays (high‑frequency flares leading low‑frequency ones) favours an outward propagating disturbance, consistent with a jet rather than an inflow. An inflow scenario would predict the opposite ordering, which is not observed. The authors also compare their results with radiatively inefficient accretion flow (RIAF) models, finding that RIAF cannot simultaneously match the size‑frequency law and the measured time lags, whereas the jet framework does so with minimal parameter adjustment.

The study therefore provides strong, quantitative evidence that the cm‑to‑mm emission from Sgr A* originates in a mildly relativistic jet‑like outflow. By combining VLBI size measurements with multi‑frequency timing, the authors demonstrate a powerful diagnostic for probing flow speed and geometry in low‑luminosity galactic nuclei. They argue that future higher‑resolution VLBI campaigns and more extensive time‑lag monitoring across a broader wavelength range will be able to resolve the jet nozzle, map the acceleration zone, and directly measure the velocity profile of a relativistic jet at its launch point—an unprecedented opportunity for testing jet physics in the immediate vicinity of a supermassive black hole.