Isolated Millimeter Flares of Cyg X-3

Cygnus X-3 (Cyg X-3) is a well-known microquasar with relativistic jets. Cyg X-3 is especially famous for its giant radio outbursts, which have been observed once every few years since their first discovery. Each giant outburst presumably consists of a series of short-duration flares. The physical parameters of the flares in the giant outbursts are difficult to derive because the successive flares overlap. Here, we report isolated flares in the quiescent phase of Cyg X-3, as observed at 23, 43, and 86 GHz with the 45-m radio telescope at Nobeyama Radio Observatory. The observed flares have small amplitude (0.5–2 Jy) and short duration (1–2 h). The millimeter fluxes rapidly increase and then exponentially decay. The lifetime of the decay is shorter at higher frequency. The radio spectrum of Cyg X-3 during the flares is flat or inverted around the peak flux density. After that, the spectrum gradually becomes steeper. The observed characteristics are consistent with those of adiabatic expanding plasma. The brightness temperature of the plasma at the peak is estimated to be $T_B\gtrsim 1 \times 10^{11}$ K. The magnetic field in the plasma is calculated to be $0.2 \lesssim H \lesssim 30$ G.

💡 Research Summary

This paper presents the discovery and detailed analysis of two isolated millimeter‑wave flares from the microquasar Cygnus X‑3 during its quiescent state, observed with the 45‑m Nobeyama Radio Observatory telescope at 23, 43, and 86 GHz. Over 20 days of monitoring between 2006 and 2010, the authors identified two clean events (MJD 53809 in March 2006 and MJD 54972 in May 2009) that were not contaminated by overlapping activity. Both flares exhibited modest amplitudes (0.5–2 Jy) and very short durations of 1–2 hours. The light curves show a rapid rise followed by an exponential decay; the e‑folding rise times are ≤ 7 min at 43 GHz and ≤ 6 min at 86 GHz, while the decay time constants τ decrease with frequency (τ≈0.17 d at 23 GHz, 0.10 d at 43 GHz, and 0.03 d at 86 GHz). No measurable time lag is seen between 43 and 86 GHz during the rise, indicating that the emission is initially optically thick across this band.

Spectral analysis reveals an inverted spectrum (α≈−0.5, where Sν∝ν⁻ᵅ) at the flux peak, transitioning to a flatter, slightly steepening spectrum (α≈+0.5) during the decay. This behavior is consistent with a synchrotron‑self‑absorbed plasma blob that expands adiabatically: as the blob grows, the magnetic field weakens, the optical depth drops, and higher‑frequency emission fades more quickly.

From the rise time the source size is constrained to r < c tₑ/2 ≈ 0.4 AU. Assuming a distance of 9 kpc, the brightness temperature at the peak exceeds 1.5 × 10¹¹ K, well above the inverse‑Compton limit for a non‑beamed source, implying a highly relativistic plasma. Using the turnover frequency (≈80 GHz, where the spectrum changes from inverted to flat) and the standard synchrotron self‑absorption relation νₛ≈42 H⊥¹·⁵ GHz, the magnetic field strength at the peak is estimated to be H≈30 G. An equipartition calculation yields a comparable field of ≈10 G, supporting the plausibility of near‑equipartition conditions.

The minimum total energy required to produce the observed synchrotron emission is E_min≈2 × 10⁴⁰ erg. Dividing by the rise time gives a minimum power supplied to the electrons of P_min≈5 × 10³⁷ erg s⁻¹, comparable to powers inferred from longer‑timescale, lower‑frequency flares. Electron cooling timescales, dominated by synchrotron losses (t_c≈12 c₁₂ H⁻³·² ≈ 14 h for H≈30 G), are much longer than the observed decay, indicating that the exponential fading is driven primarily by the decreasing magnetic field rather than radiative losses.

The authors also evaluate the ratio of inverse‑Compton to synchrotron losses (R = u_rad/u_mag) and find that to keep R≤1 the magnetic field must be at least ≈0.2 G, consistent with the derived values. This ensures that the relativistic electrons survive long enough to emit the observed millimeter radiation.

In summary, the study demonstrates that even during quiescence Cyg X‑3 can produce short, high‑brightness millimeter flares that are well described by an expanding synchrotron‑emitting plasma blob. By isolating individual events, the authors obtain direct constraints on source size, magnetic field, electron energy content, and expansion dynamics—parameters that are otherwise inaccessible in the crowded giant outbursts. The work highlights the importance of high‑time‑resolution, multi‑frequency millimeter monitoring for probing the microphysics of jet ejection in microquasars and sets the stage for future very‑long‑baseline interferometric imaging of such rapid events.