## Table 4

HARPS-N systemic radial velocities and jitter terms, Gaussian process hyper-parameters, and linear accelerations from the DE-MCMC radial-velocity modeling.

System | γ_{HN−1} [m s^{−1}] |
γ_{HN−2} [m s^{−1}] |
σ_{jit,HN−l} [m s^{−1}] |
σ_{jit,HN−2} [m s^{−2}] |
h [m s^{−1}] |
λ_{1} [day] |
λ_{2} – |
P_{rot} [day] |
[m s^{−1} day^{−1}] |
ΔBIC > 10 | Comment |
---|---|---|---|---|---|---|---|---|---|---|---|

Kepler-10 | −98 737.12 ± 0.47 | 0.09 ± 0.17^{(1)} |
2.13 ±0.15 | – | – | – | – | −2.7 E-04 ± 1.6 e-04 | – | ||

Kepler-19 | −10 614.72 ± 1.31 | – | – | – | – | 1.7 E-03 ± 0.9 E-03 | – | ||||

Kepler-20 | – | −21 070.23 ± 0.95 | – | – | – | – | – | 0.7 E-03 ± 1.2 E-03 | – | ||

Kepler-21 | – | – | 2.61 ± 0.44 | – | |||||||

Kepler-22 | −4221.01 ± 0.99 | – | – | – | – | 1.8 E-04 ± 8.0 E-04 | – | ||||

Kepler-37 | – | −30820.12 + 0.56 | – | – | – | – | – | 6.9 E-04 ± 7.4 E-04 | – | ||

Kepler-68 | – | – | 1.81 ±0.17 | – | – | – | – | – | 2 CJs (ro) | ||

Kepler-78 | – | −3530.11 ±3.21 | – | 1.65 ±0.33 | 12.92 ±0.12 | −1.6 E-03 ±3.2 E-03 | – | ||||

Kepler-93 | – | – | 1.25 ±0.16 | – | – | 3.92 E-02 ± 0.11 E-02 |
y | BD/LMS | |||

Kepler-102 | −28 152.22 ± 1.50 | −28 163.26 ±1.06 | < 2.20 | < 0.72 | −7.3 E-04 ± 7.0 E-04 | – | |||||

Kepler-103 | – | −28 609.58 ±0.71 | – | – | – | – | – | −−2.3 E-03 ± 1.8 E-03 | – | ||

Kepler-107 | – | 5536.53 ± 0.87 | – | < 2.34 | – | – | – | – | −1.2 E-03 ±1.4 E-03 | – | |

Kepler-109 | – | −37 129.88 ±1.53 | – | – | – | – | – | −2.9 E-03 ±2.0 E-03 | – | ||

Kepler-323 | – | – | < 2.86 | – | – | – | – | 3.2 E-03 ±1.4 E-03 | – | ||

Kepler-409 | – | −28 541.49 ±0.57 | – | – | – | – | – | 0.0 E-03 ± 0.4 E-03 | – | ||

Kepler-454 | – | – | – | – | – | – | y | CJ/BD/LMS + 2 CJs (ro) | |||

Kepler-538 | – | – | – | – | – | – | −0.2 E-03 ± 1.1 E-03 | – | |||

Kepler-1655 | – | −40769.17 ±0.64 | – | < 0.91 | – | – | – | – | 1.8 E-03 ±1.0 E-03 | – | |

Kepler-1876 | – | 7681.39 ±0.45 | – | – | – | – | – | 7.8 E-03 ±3.2 E-03 | – | ||

K2-2/HIP 116454 | – | −3299.73 ±0.61^{(2)} |
– | 0.97 ± 0.45 | – | – | 0.2 E-03 ±1.4 E-03 | – | |||

K2-3 | – | −0.06 ± 0.55^{(3)} |
– | −0.4 E-03 ±1.7 E-03 | – | ||||||

K2-12 | – | 17 000.18 ±0.99 | – | – | – | – | – | 1.884 E-02 ± 0.096 E-02 |
y | CJ/BD/LMS | |

K2-36 | – | 13 625.38 ±4.25 | – | 2.64 ± 1.06 | 3.7 E-03 ±7.3 E-03 | – | |||||

K2-38 | – | −36040.15 ±0.56 | – | 2.07 ± 0.67 | – | – | – | – | −8.2 E-03 ±3.1 E-03 | – | |

K2-79 | – | −10314.99 ±0.76 | – | < 1.74 | – | – | – | – | 1.8 E-03 ± 1.3 E-03 | – | |

K2-96/HD3167 | – | 19 371.36 ±0.24 | – | – | – | – | – | y | Activity | ||

K2-106 | – | −15735.71 ± 1.12 | – | < 1.17 | – | – | – | – | −1.4 E-03 ±2.1 E-03 | – | |

K2-110 | – | −21 798.17 ±0.93 | – | < 1.91 | – | – | – | – | 0.7 E-03 ± 1.5 E-03 | – | |

K2-111 | – | −16291.29 ±0.26 | – | < 0.93 | – | – | – | – | −1.8 E-03 ±0.5 E-03 | N | |

K2-131 | – | 6855.45 ± 6.17 | – | < 1.59 | 0.435 ± 0.074 | 9.194 ±0.065 | 3.8 E-02 ±3.3 E-02 | – | |||

K2-135/GI9827 | – | – | < 0.95 | −0.6 E-03 ± 1.3 E-03 | – | ||||||

K2-141 | – | −3408.80 ± 4.92 | – | < 1.17 | – | ||||||

K2-167 | – | −17 550.44 ±0.50 | – | – | – | – | – | 1.2 E-03 ±0.6 E-03 | – | ||

K2-222 | – | 1681.65 ±0.46 | – | – | – | – | – | 5.8 E-04 ±7.1 E-04 | – | ||

K2-262/Wolf 503 | – | −46781.43 ±0.46 | – | – | – | – | – | 6.6 E-03 ± 1.0 E-03 |
y | Activity | |

K2-263 | – | 29 837.72 ±0.29 | – | 1.50 ±0.37 | – | – | – | – | 4.1 E-04 ±4.9 E-04 | – | |

K2-312/HD80653 | – | – | 0.64 ± 0.30 | 0.0 ± 1.4 | – | 1 CJ (ro) | |||||

K2-418 /EPIC-229004835 | – | −31487.88 ±0.30 | – | 2.48 ± 0.24 | – | – | – | – | −2.5 E-03 ± 1.1 E-03 | – |

**Notes.** From left to right, the columns report the name of the system, the systemic radial velocity (*γ*), the jitter terms (*γ*_{jit}), the Gaussian process hyper-parameters – namely radial-velocity semi-amplitude (*h*), exponential decay time (*γ*_{1}), inverse harmonic complexity term (*γ*_{2}), and rotation period (*P*_{rot}) –, the linear acceleration () and the ABIC in favor of the model with acceleration. Even though, for simplicity, *γ* and *γ*_{jit} are reported for the HARPS-N spectrograph only, the DE-MCMC radial-velocity modeling was carried out by including the data gathered with other spectrographs, when available. Accelerations evaluated as significant, from both a confidence level higher than 3*γ* and an odds ratio greater than 10 from the ΔBIC, are highlighted in boldface. HN-1 and HN-2 refer to the HARPS-N data collected before and after September 2012, respectively. The last column reports comments about the origin of the detected trends, such as possible cold Jupiter (CI), brown dwarf (BD), or low-mass star (LMS) companions or stellar magnetic activity, and about the presence of cold Jupiters in resolved orbits (ro), which were modeled with Keplerians and are thus not responsible for the trends. ^{(1)}The radial-velocity zero point is close to zero because the radial velocities were extracted with the Yarara-v2 tool (Cretignier et al. 2022) from the HARPS-N spectra reduced with the DRS-v2.3.5 (see Bonomo et al., in prep.). ^{(2)}The last observing season was fitted as an independent dataset for the presence of an offset in the RVs of very likely activity origin. The systemic velocity and jitter of this season were found to be and . ^{(3)}The radial-velocity zero point is close to zero because the radial velocities were extracted with the TERRA software (see text for details). The systemic velocity is (Damasso et al. 2018).

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