# 14.3.6 vari_rotation_modulation

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

Columns description:

solution_id : Solution Identifier (long)

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 where 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

source_id : Unique source identifier (long)

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

num_segments : Number of segments (int, Dimensionless[see description])

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, Time[Barycentric JD in TCB - 2455197.5 (day)])

an array filled with the starting times of segments

segments_end_time : Times at which segments end (double, Time[Barycentric JD in TCB - 2455197.5 (day)])

an array filled with the ending times of segments

segments_colour_mag_intercept : Colour-Magnitude Intercept in segments (double, Misc[see description])

a robust linear regression is applied to the points (BP-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 (double, Misc[see description])

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

segments_colour_mag_slope : Colour-Magnitude Slope in segments (double, Misc[see description])

a robust linear regression is applied to the points (BP-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 (double, Misc[see description])

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

segments_correlation_coefficient : Correlation coefficient in segments (double, Dimensionless[see description])

The Pearson correlation coefficient $r$ between BP-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 (double, Dimensionless[see description])

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 $P(r\geq r_{0}$) that two sets of uncorrelated measurements have a Pearson coefficient $\geq r_{0}$

num_outliers : Number of outliers (int, Dimensionless[see description])

the number of outliers detected by the robust linear regression procedure

outliers_time : Times at which outliers occurs (double, Time[Barycentric JD in TCB - 2455197.5 (day)])

times at which the detected outliers occurred

segments_rotation_period : Rotation period in segment (double, Time[day])

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 (double, Time[day])

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

segments_rotation_period_fap : FAP on rotation period in segment (double, Dimensionless[percentage/100])

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.

segments_cos_term : Coefficient of cosine term of linear fit in segment (double, 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

 $mag(t)=mag_{0}+Acos(\frac{2\pi}{T_{0}}t)+Bsin(\frac{2*\pi}{T_{0}}t)$ (14.1)

This array stores the A terms obtained by the fitting procedure in the different segments.

segments_cos_term_error : Errors on cosin terms (double, Magnitude[mag])

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

segments_sin_term : Coefficient of sin term of linear fit in segment (double, 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

 $mag(t)=mag_{0}+Acos(\frac{2\pi}{T_{0}}t)+Bsin(\frac{2*\pi}{T_{0}}t)$ (14.2)

This array stores the B terms obtained by the fitting procedure in the different segments.

segments_sin_term_error : Errors on sine terms (double, Magnitude[mag])

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

segments_a0_term : Constant term (A0) of linear fit in segment (double, 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

 $mag(t)=A_{0}+Acos(\frac{2\pi}{T_{0}}t)+Bsin(\frac{2*\pi}{T_{0}}t)$ (14.3)

This array stores the $A_{0}$ terms obtained by the fitting procedure in the different segments.

segments_a0_term_error : Errors on constant terms (double, Magnitude[mag])

This array is filled with the errors associated with the $A_{0}$ terms obtained from the fitting procedure in the different segments

best_rotation_period : Best rotation period (double, Time[day])

this field is an estimate of the stellar rotation period and is obtained by averaging the periods obtained in the different segments

best_rotation_period_error : Error on best rotation period (double, Time[day])

error on the best rotation period

segments_activity_index : Activity Index in segment (double, Magnitude[mag])

this array stores the activity indexes measured in the different segments. 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:

 $A=mag_{95}-mag_{5}$ (14.4)

where $mag_{95}$ and $mag_{5}$ are the 95-th and the 5-th percentiles of the $G$-band magnitude values.

segments_activity_index_error : error on Activity index in segment (double, 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:

 $\sigma_{A}=\sqrt{\sigma_{mag95}^{2}+\sigma_{mag5}^{2}}$ (14.5)

where $\sigma_{mag95}$ and $\sigma_{mag5}$ are the uncertainties of the measurements associated with the 95th and 5th percentiles of the $G$-band magnitude values, respectively

max_activity_index : The maximum Activity Index (double, Magnitude[mag])

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

max_activity_index_error : Error on maximum activity index (double, Magnitude[mag])

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

segments_g_unspotted : The unspotted G mags in segment (double, Magnitude[mag])

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 (double, Magnitude[mag])

this array stores the errors associated to the unspotted G values registered in the different segments

segments_bp_unspotted : The unspotted BP mag in segment (double, Magnitude[mag])

in a given segment the BP magnitude corresponding to the unspotted state is estimated by taking the BP magnitude occurring at the same time of the unspotted G

segments_bp_unspotted_error : The unspotted BP mag uncertainties in segment (double, Magnitude[mag])

this array stores the errors associated to the unspotted BP values registered in the different segments

segments_rp_unspotted : The unspotted RP mag in segment (double, Magnitude[mag])

in a given segment the RP magnitude corresponding to the unspotted state is estimated by taking the RP magnitude occurring at the same time of the unspotted G

segments_rp_unspotted_error : The unspotted RP mag uncertainties in segment (double, Magnitude[mag])

this array stores the errors associated to the unspotted RP values registered in the different segments

g_unspotted : Unspotted G mag (double, Magnitude[mag])

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

g_unspotted_error : Unspotted G mag uncertainty (double, Magnitude[mag])

this field stores the photometric error associated with g_unspotted

bp_unspotted : Unspotted BP mag (double, Magnitude[mag])

final estimate of the BP magnitude corresponding to the unspotted state. It is estimated by taking the BP magnitude occurring at the same time in which the minim G magnitude has been measured.

bp_unspotted_error : Unspotted BP mag uncertainty (double, Magnitude[mag])

error associated with the bp_unspotted value

rp_unspotted : Unspotted RP mag (double, Magnitude[mag])

final estimate of the RP magnitude corresponding to the unspotted state. It is estimated by taking the RP magnitude occurring at the same time in which the minim G magnitude has been measured.

rp_unspotted_error : Unspotted RP mag uncertainty (double, Magnitude[mag])

error associated with the rp_unspotted value