# 20.13.15 vari_rotation_modulation

This table describes the solar-like stars with rotational modulation.

Columns description:

All Gaia data processed by the Data Processing and Analysis Consortium comes tagged with a solution identifier. This is a numeric field attached to each table row that can be used to unequivocally identify the version of all the subsystems that were used in the generation of the data as well as the input data used. It is mainly for internal DPAC use but is included in the published data releases to enable end users to examine the provenance of processed data products. To decode a given solution ID visit https://gaia.esac.esa.int/decoder/solnDecoder.jsp

A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id).

This is the number of time intervals (segments) in which the magnitude and colour time-series are splitted. The segmentation of time-series is needed because the spots due to the stellar magnetic activity have a life-time shorter than the whole Gaia time-series. The rotational modulation induced by spots can therefore be detected only in segments whose duration is comparable with the spots life-time.

segments_start_time : Times at which segments start (double[num_segments] array, Time[Barycentric JD in TCB $-$ 2 455 197.5 (day)])

An array filled with the starting times of segments.

segments_end_time : Times at which segments end (double[num_segments] array, Time[Barycentric JD in TCB $-$ 2 455 197.5 (day)])

An array filled with the ending times of segments.

A robust linear regression is applied to the points (${G}_{\mathrm{BP}}$-${G}_{\mathrm{RP}}$, $G$) in each segment. This array is filled with the intercepts given by the fitting procedure in the different segments.

segments_colour_mag_intercept_error : Colour-Magnitude Intercept uncertainty in segments (float[num_segments] array)

This array is filled with the uncertainties associated with the intercepts given by the fitting procedure.

A robust linear regression is applied to the points (${G}_{\mathrm{BP}}$-${G}_{\mathrm{RP}}$, $G$) in each segment. This array is filled with the slopes given by the fitting procedure in the different segments.

segments_colour_mag_slope_error : Colour-Magnitude Slope uncertainty in segments (float[num_segments] array)

This array is filled with the uncertainties associated with the slopes given by the fitting procedure.

The Pearson correlation coefficient $r$ between ${G}_{\mathrm{BP}}$-${G}_{\mathrm{RP}}$ and $G$ is computed in each segment. The higher is the Pearson coefficient the higher is the probability that the stellar variability is due to rotational modulation. This array is filled with the Pearson coefficients obtained in the different segments.

segments_correlation_significance : Correlation coefficient significance in segments (float[num_segments] array)

This array is filled with the statistical significances associated with the Pearson coefficients computed in the different segments. The significance p associated with a given $r={r}_{0}$ gives the probability $P(r\ge {r}_{0}$) that two sets of uncorrelated measurements have a Pearson coefficient $\ge {r}_{0}$.

The number of outliers detected by the robust linear regression procedure.

outliers_time : Times at which outliers occurs (double[num_outliers] array, Time[Barycentric JD in TCB $-$ 2 455 197.5 (day)])

Times at which the detected outliers occurred.

A period search algorithm is applied to the different time-series segments. If the star is a solar-like variable the detected period is a measure of the stellar rotation period. This array is filled with the periods detected in the different segments (for each segment the period with the highest statistical significance is stored).

segments_rotation_period_error : Rotation period uncertainty in segment (float[num_segments] array, Time[day])

This array is filled with the errors associated with the periods found in the different segments.

False Alarm Probability = Probability that that a white noise sequence produces a peak similar or higher than the computed one; i.e., small FAP = little probability of noise, high FAP = noise is an acceptable explanation for the peak.

This field is the best estimate of the stellar rotation period and is obtained by taking the mode of the segments_rotation_period distribution. The distribution is built only with the periods, whose associated FAP is less than 0.05. See Section 10.13 of the release documentation for further details.

Error on the best rotation period.

In a given segment the $G$ magnitude corresponding to the unspotted state is estimated by taking the minimum $G$ value in the segment.

segments_g_unspotted_error : The unspotted G mag uncertainties in segment (float[num_segments] array, Magnitude[mag])

This array stores the errors associated with the unspotted $G$ values registered in the different segments.

In a given segment the ${G}_{\mathrm{BP}}$ magnitude corresponding to the unspotted state is estimated by taking the ${G}_{\mathrm{BP}}$ magnitude occurring at the same time of the unspotted $G$. If the ${G}_{\mathrm{BP}}$ transit corresponding to segment’s unspotted $G$ transit is not available, a NaN value is provided.

segments_bp_unspotted_error : The unspotted BP mag uncertainties in segment (float[num_segments] array, Magnitude[mag])

This array stores the errors associated with the unspotted ${G}_{\mathrm{BP}}$ values registered in the different segments.

In a given segment the ${G}_{\mathrm{RP}}$ magnitude corresponding to the unspotted state is estimated by taking the ${G}_{\mathrm{RP}}$ magnitude occurring at the same time of the unspotted $G$. If the ${G}_{\mathrm{RP}}$ transit corresponding to segment’s unspotted $G$ transit is not available, a NaN value is provided.

segments_rp_unspotted_error : The unspotted RP mag uncertainties in segment (float[num_segments] array, Magnitude[mag])

This array stores the errors associated with the unspotted ${G}_{\mathrm{RP}}$ values registered in the different segments.

Final estimate of the $G$ magnitude corresponding to the unspotted state. It is computed by taking the minimum $G$ magnitude in the whole time-series.

This field stores the photometric error associated with g_unspotted.

Final estimate of the ${G}_{\mathrm{BP}}$ magnitude corresponding to the unspotted state. It is estimated by taking the ${G}_{\mathrm{BP}}$ magnitude occurring at the same time in which the minimum $G$ magnitude has been measured. If the ${G}_{\mathrm{BP}}$ transit corresponding to unspotted $G$ transit is not available, a Null value is provided.

Error associated with the bp_unspotted value.

Final estimate of the ${G}_{\mathrm{RP}}$ magnitude corresponding to the unspotted state. It is estimated by taking the ${G}_{\mathrm{RP}}$ magnitude occurring at the same time in which the minimum $G$ magnitude has been measured. If the ${G}_{\mathrm{RP}}$ transit corresponding to unspotted $G$ transit is not available, a Null value is provided.

Error associated with the rp_unspotted value.

segments_g_cos_term : Coefficient of cosine term of linear fit in segment in the G band (float[num_segments] array, Magnitude[mag])

If a significative period ${T}_{0}$ is detected in a time-series segment, then the points of the time-series segment are fitted with the function

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.46) |

This array stores the A terms obtained by the fitting procedure in the different segments in the $G$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_g_cos_term_error : Errors on cosine terms in the G band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the A terms obtained from the fitting procedure in the different segments in the $G$ band.

segments_g_sin_term : Coefficient of sine term of linear fit in segment in the G band (float[num_segments] array, Magnitude[mag])

If a significative period ${T}_{0}$ is detected in a time-series segment, then the points of the time-series segment are fitted with the function

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.47) |

This array stores the B terms obtained by the fitting procedure in the different segments in the $G$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_g_sin_term_error : Errors on sine terms in the G band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the B terms obtained from the fitting procedure in the different segments in the $G$ band.

segments_g_a0_term : Constant term (A0) of linear fit in segment in the G band (float[num_segments] array, Magnitude[mag])

If a significative period ${T}_{0}$ is detected in a time-series segment, then the points of the time-series segment are fitted with the function

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.48) |

This array stores the $ma{g}_{0}$ terms obtained by the fitting procedure in the different segments in the $G$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_g_a0_term_error : Errors on constant terms in the G band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the $ma{g}_{0}$ terms obtained from the fitting procedure in the different segments in the $G$ band.

segments_bp_cos_term : Coefficient of cosine term of linear fit in segment in the BP band (float[num_segments] array, Magnitude[mag])

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.49) |

This array stores the A terms obtained by the fitting procedure in the different segments in the ${G}_{\mathrm{BP}}$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_bp_cos_term_error : Errors on cosine terms in the BP band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the A terms obtained from the fitting procedure in the different segments in the ${G}_{\mathrm{BP}}$ band.

segments_bp_sin_term : Coefficient of sine term of linear fit in segment in the BP band (float[num_segments] array, Magnitude[mag])

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.50) |

This array stores the B terms obtained by the fitting procedure in the different segments in the ${G}_{\mathrm{BP}}$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_bp_sin_term_error : Errors on sine terms in the BP band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the B terms obtained from the fitting procedure in the different segments in the ${G}_{\mathrm{BP}}$ band.

segments_bp_a0_term : Constant term (A0) of linear fit in segment in the BP band (float[num_segments] array, Magnitude[mag])

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.51) |

This array stores the $ma{g}_{0}$ terms obtained by the fitting procedure in the different segments in the ${G}_{\mathrm{BP}}$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_bp_a0_term_error : Errors on constant terms in the BP band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the $ma{g}_{0}$ terms obtained from the fitting procedure in the different segments in the ${G}_{\mathrm{BP}}$ band.

segments_rp_cos_term : Coefficient of cosine term of linear fit in segment in the RP band (float[num_segments] array, Magnitude[mag])

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.52) |

This array stores the A terms obtained by the fitting procedure in the different segments in the ${G}_{\mathrm{RP}}$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_rp_cos_term_error : Errors on cosine terms in the RP band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the A terms obtained from the fitting procedure in the different segments in the ${G}_{\mathrm{RP}}$ band.

segments_rp_sin_term : Coefficient of sine term of linear fit in segment in the RP band (float[num_segments] array, Magnitude[mag])

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.53) |

This array stores the B terms obtained by the fitting procedure in the different segments in the ${G}_{\mathrm{RP}}$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_rp_sin_term_error : Errors on sine terms in the RP band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the B terms obtained from the fitting procedure in the different segments in the ${G}_{\mathrm{RP}}$ band.

segments_rp_a0_term : Constant term (A0) of linear fit in segment in the RP band (float[num_segments] array, Magnitude[mag])

$$mag(t)=ma{g}_{0}+A\mathrm{cos}(\frac{2\pi}{{T}_{0}}t)+B\mathrm{sin}(\frac{2\pi}{{T}_{0}}t)$$ | (20.54) |

This array stores the $ma{g}_{0}$ terms obtained by the fitting procedure in the different segments in the ${G}_{\mathrm{RP}}$ band.
The fit is computed only if the FAP associated with the period ${T}_{0}$ is less than 0.05.

segments_rp_a0_term_error : Errors on constant terms in the RP band (float[num_segments] array, Magnitude[mag])

This array is filled with the errors associated with the $ma{g}_{0}$ terms obtained from the fitting procedure in the different segments in the ${G}_{\mathrm{RP}}$ band.

segments_g_activity_index : Activity Index in segment (computed in G band) (float[num_segments] array, Magnitude[mag])

This array stores the activity indexes measured in the different segments in the $G$ band. In a given segment the amplitude of variability A is taken as an index of the magnetic activity level. The amplitude of variability is measured by means of the equation:

$$A=ma{g}_{95}-ma{g}_{5}$$ | (20.55) |

where $ma{g}_{95}$ and $ma{g}_{5}$ are the 95-th and the 5-th percentiles of the magnitude values.

segments_g_activity_index_error : error on Activity index in segment (computed in G band) (float[num_segments] array, Magnitude[mag])

This array stores the errors associated with the activity indexes in the $G$ band. In a given segment the error on the activity index A is computed by means of the equation:

$${\sigma}_{A}=\sqrt{{\sigma}_{mag95}^{2}+{\sigma}_{mag5}^{2}}$$ | (20.56) |

segments_bp_activity_index : Activity Index in segment (computed in BP band) (float[num_segments] array, Magnitude[mag])

This array stores the activity indexes measured in the different segments in the ${G}_{\mathrm{BP}}$ band. In a given segment the amplitude of variability A is taken as an index of the magnetic activity level. The amplitude of variability is measured by means of the equation:

$$A=ma{g}_{95}-ma{g}_{5}$$ | (20.57) |

where $ma{g}_{95}$ and $ma{g}_{5}$ are the 95-th and the 5-th percentiles of the magnitude values.

segments_bp_activity_index_error : error on Activity index in segment (computed in BP band) (float[num_segments] array, Magnitude[mag])

This array stores the errors associated with the activity indexes in the ${G}_{\mathrm{BP}}$ band. In a given segment the error on the activity index A is computed by means of the equation:

$${\sigma}_{A}=\sqrt{{\sigma}_{mag95}^{2}+{\sigma}_{mag5}^{2}}$$ | (20.58) |

segments_rp_activity_index : Activity Index in segment (computed in RP band) (float[num_segments] array, Magnitude[mag])

This array stores the activity indexes measured in the different segments in the ${G}_{\mathrm{RP}}$ band. In a given segment the amplitude of variability A is taken as an index of the magnetic activity level. The amplitude of variability is measured by means of the equation:

$$A=ma{g}_{95}-ma{g}_{5}$$ | (20.59) |

where $ma{g}_{95}$ and $ma{g}_{5}$ are the 95-th and the 5-th percentiles of the magnitude values.

segments_rp_activity_index_error : error on Activity index in segment (computed in RP band) (float[num_segments] array, Magnitude[mag])

This array stores the errors associated with the activity indexes in the ${G}_{\mathrm{RP}}$ band. In a given segment the error on the activity index A is computed by means of the equation:

$${\sigma}_{A}=\sqrt{{\sigma}_{mag95}^{2}+{\sigma}_{mag5}^{2}}$$ | (20.60) |

This field is the maximum of measured the activity indexes in the $G$ band.

This field stores the error associated with the maximum activity index in the $G$ band.

segments_bp_rp_corr_coeff : Pearson coefficient between BP and RP in segment (float[num_segments] array)

For each segment, this parameter provides the Pearson coefficient of the transits in the (${G}_{\mathrm{BP}}$,${G}_{\mathrm{RP}}$) magnitude plane. This correlation coefficient can be used to infer properties of stellar spots and faculae.

segments_bp_rp_corr_signif : Significance associated with Pearson coefficient (float[num_segments] array)

For each segment, this parameter provides the statistical significance associated with the Pearson coefficient segments_bp_rp_corr_coeff.

segments_bp_rp_intercept : Intercept of regression fit of RP vs BP magnitudes in the segment (float[num_segments] array, Magnitude[mag])

This array provides the intercepts obtained for the line regression fit of the transits in the (${G}_{\mathrm{BP}}$,${G}_{\mathrm{RP}}$) magnitude plane in each segment.

segments_bp_rp_intercept_error : Error on intercept of regression fit of RP vs BP magnitudes in the segment (float[num_segments] array, Magnitude[mag])

This array stores the errors associated with the intercepts stored in segments_bp_rp_intercept.

segments_bp_rp_slope : Slope of regression fit of RP vs BP magnitudes in the segment (float[num_segments] array)

This array provides the slopes obtained for the line regression fit of the transits in the (${G}_{\mathrm{BP}}$,${G}_{\mathrm{RP}}$) magnitude plane in each segment.

segments_bp_rp_slope_error : Error on slope of regression fit of RP vs BP magnitudes in the segment (float[num_segments] array)

This array stores the errors associated with the slopes stored in segments_bp_rp_slope.

segments_model_reference_time : Time used as reference time for the period search procedure in the segment (double[num_segments] array, Time[Barycentric JD in TCB $-$ 2 455 197.5 (day)])

For each segment, this parameter provides the reference time used when the data points are fitted to the models represented by the equations in the definitions of segments_g_cos_term, segments_bp_cos_term, and segments_rp_cos_term.

Array of chisquares for linear models ($G$ band).

segments_bp_chi_square : Array of chisquares for linear models (BP band) (float[num_segments] array)

Array of chisquares for linear models (${G}_{\mathrm{BP}}$ band).

segments_rp_chi_square : Array of chisquares for linear models (RP band) (float[num_segments] array)

Array of chisquares for linear models (${G}_{\mathrm{RP}}$ band).