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Quasi-periodic eruptions (QPEs) are an extreme X-ray variability phenomenon associated with low-mass supermassive black holes. First discovered in the nucleus of the galaxy GSN 069, they have been so far securely detected in five other galaxies, including RX J1301.9+2747. When detected, the out-of-QPE emission (quiescence) is consistent with the high-energy tail of thermal emission from an accretion disk. We present the X-ray and radio properties of RX J1301.9+2747, both in quiescence and during QPEs. We analyse X-ray data taken during five XMM-Newton observations between 2000 and 2022. The last three observations were taken in coordination with radio observations with the Karl G. Jansky Very Large Array. We also make use of EXOSAT, ROSAT, and Chandra archival observations taken between 1983 and 2009. XMM-Newton detected 34 QPEs of which 8 have significantly lower amplitudes than the others. No correlated radio/X-ray variability was observed during QPEs. In terms of timing properties, the QPEs in RX J1301.9+2747 do not exhibit the striking regularity observed in the discovery source GSN 069. In fact there is no clear repetition pattern between QPEs: the average time separation between their peaks is about four hours, but it can be as short as one, and as long as six hours. The QPE spectral properties of RX J1301.9+2747 as a function of energy are however very similar to those of GSN 069 and of other QPE sources. The quiescent emission of RX J1301.9+2747 is more complex than that of GSN 069, as it requires a soft X-ray excess-like component in addition to the thermal emission from the accretion disk. Its long-term X-ray quiescent flux variations are of low-amplitude and not strictly monotonic, with a general decay over $\sim 22$ years. We discuss our observational results in terms of some of the ideas and models that have been proposed so far for the physical origin of QPEs., Comment: Accepted for publication in Astronomy & Astrophysics. 22 pages and 17 figures in the main text; 11 pages, 5 tables, and 4 figures in the Appendix. Abstract shortened to comply with arXiv requirements

We report on two epochs of simultaneous near-infrared (IR) and X-ray observations with a sub-second time resolution of the low mass X-ray binary black hole candidate Swift J1753.5--0127 during its long 2005--2016 outburst. Data were collected strictly simultaneously with VLT/ISAAC (K$_{S}$ band, 2.2 $\mu m$) and RXTE (2-15 keV) or \textit{XMM-Newton} (0.7-10 keV). A clear correlation between the X-ray and the IR variable emission is found during both epochs but with very different properties. In the first epoch, the near-IR variability leads the X-ray by $ \sim 130 \, ms$. This is the opposite of what is usually observed in similar systems. The correlation is more complex in the second epoch, with both anti-correlation and correlations at negative and positive lags. Frequency-resolved Fourier analysis allows us to identify two main components in the complex structure of the phase lags: the first component, characterised by a few seconds near-IR lag at low frequencies, is consistent with a combination of disc reprocessing and a magnetised hot flow; the second component is identified at high frequencies by a near-IR lag of $\approx$0.7 s. Given the similarities of this second component with the well-known constant optical/near-IR jet lag observed in other black hole transients, we tentatively interpret this feature as a signature of a longer-than-usual jet lag. We discuss the possible implications of measuring such a long jet lag in a radio-quiet black hole transient., Comment: 10 pages, 7 figures, accepted for publication in A&A