Statistical parameters of time series, using only transits not rejected, see rejected_by_variability column in the VO Table epoch_photometry_url in gaia_source.
Note that NaN will be reported when the parameter value is missing or cannot be calculated.
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 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
A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id)
num_selected_g_fov : Total number of G FOV transits selected for variability analysis (int, Dimensionless[see description])
The number of processed observations for variability analyses of this source, using only transits not rejected, see rejected_by_variability column in the VO Table epoch_photometry_url in gaia_source.
mean_obs_time_g_fov : Mean observation time for G FoV transits (double, Time[Barycentric JD in TCB - 2455197.5 (day)])
Name: The mean observation time
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$. The mean $\overline{t}$ is defined as
$$\overline{t}=\frac{1}{N}\sum _{i=1}^{N}{t}_{i}.$$ | (14.6) |
Name: The time duration of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The time duration of the time series is equal to ${t}_{N}-{t}_{1}$.
Name: The minimum value of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The minimum value of the time series is defined as:
$$min({y}_{i})\forall i\in (1,N)$$ | (14.7) |
Name: The maximum value of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The maximum value of the time series is defined as:
$$max({y}_{i})\forall i\in (1,N)$$ | (14.8) |
Name: The mean of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$. The mean $\overline{y}$ is defined as
$$\overline{y}=\frac{1}{N}\sum _{i=1}^{N}{y}_{i}.$$ | (14.9) |
Name: The median of the time series
Control parameters: None
Output: The 50th percentile unweighted value.
Let ${y}_{i}$ be a time series of size $N$ ordered such as ${y}_{(1)}\le {y}_{(2)}\le \mathrm{\cdots}\le {y}_{(N)}$. The $m$-th (per cent) percentile ${P}_{m}$ is defined for $$ as follows:
$$ | (14.10) |
range_mag_g_fov : Difference between the highest and lowest G FoV magnitudes (double, Magnitude[mag])
Name: The range of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series, ${y}_{\mathrm{max}}$ its largest element, and ${y}_{\mathrm{min}}$ its smallest element, then the range is defined as
$$R={y}_{\mathrm{max}}-{y}_{\mathrm{min}}$$ | (14.11) |
Name: The square root of the unbiased unweighted variance.
Output: Let ${y}_{i}$ be a time series of size $N$. The unweighted standard deviation $\widehat{\sigma}$ is defined as the square root of the sample-size unbiased unweighted variance:
$$\widehat{\sigma}=\sqrt{\frac{1}{N-1}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{2}}.$$ |
skewness_mag_g_fov : Standardized unweighted G FoV magnitude skewness (double, Dimensionless[see description])
Name: The standardised unbiased unweighted skewness.
Output: Let ${y}_{i}$ be a time series of size $N>2$. The sample-size unbiased unweighted skewness moment $\mathcal{E}$ is defined as:
$$\mathcal{E}=\frac{N}{(N-1)(N-2)}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{3}.$$ |
The standardized unbiased skewness $E$ is defined as:
$$E=\frac{\mathcal{E}}{{\widehat{\sigma}}^{3}}$$ |
where $\widehat{\sigma}$ is the square root of the unbiased unweighted variance around the unweighted mean. While $\mathcal{E}$ is an unbiased estimate of the population value, $E$ becomes unbiased in the limit of large $N$.
kurtosis_mag_g_fov : Standardized unweighted G FoV magnitude kurtosis (double, Dimensionless[see description])
Name: The standardised unbiased unweighted kurtosis.
Output: Let ${y}_{i}$ be a time series of size $N>3$. The sample-size unbiased unweighted kurtosis cumulant $\mathcal{K}$ is defined as:
$$\mathcal{K}=\frac{N(N+1)}{(N-1)(N-2)(N-3)}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{4}-\frac{3}{(N-2)(N-3)}{\left[\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{2}\right]}^{2}.$$ |
The standardized unbiased kurtosis $K$ is defined as:
$$K=\frac{\mathcal{K}}{{\widehat{\sigma}}^{4}}$$ |
where ${\widehat{\sigma}}^{2}$ is the unbiased unweighted variance around the unweighted mean. While $\mathcal{K}$ is an unbiased estimate of the population value, $K$ becomes unbiased in the limit of large $N$.
Name: The Median Absolute Deviation (MAD)
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$. The MAD is defined as the median of the absolute deviations from the median of the data, scaled by a factor of $1/{\mathrm{\Phi}}^{-1}(3/4)\approx 1.4826$ (where ${\mathrm{\Phi}}^{-1}$ is the inverse of the cumulative distribution function for the standard normal distribution), so that the expectation of the scaled MAD at large $N$ equals the standard deviation of a normal distribution:
$$\text{MAD}=1.4826\text{median}\{|{y}_{i}-\text{median}\{{y}_{j},\forall j\in (1,N)\}|,\forall i\in (1,N)\}.$$ | (14.12) |
Name: The Abbe value
Control parameters: None
Output: Let $\{{t}_{i},{y}_{i}\}$ be a time-sorted time series of size $N$, such that $$ for all $$. The Abbe value $\mathcal{A}$ is defined as
$$\mathcal{A}=\frac{{\sum}_{i=1}^{N-1}{({y}_{i+1}-{y}_{i})}^{2}}{2{\sum}_{i=1}^{N}{({y}_{i}-\overline{y})}^{2}}$$ | (14.13) |
where $\overline{y}$ is the unweighted mean.
Name: The Interquartile Range (IQR)
Control parameters: None
Output: The difference between the (unweighted) 75th and 25th percentile values: IQR$={P}_{75}-{P}_{25}$.
Let ${y}_{i}$ be a time series of size $N$ ordered such as ${y}_{(1)}\le {y}_{(2)}\le \mathrm{\cdots}\le {y}_{(N)}$. The $m$-th (per cent) percentile ${P}_{m}$ is defined for $$ as follows:
$$ | (14.14) |
num_selected_bp : Total number of BP observations selected for variability analysis (int, Dimensionless[see description])
The number of processed observations for variability analyses of this source, using only transits not rejected, see rejected_by_variability column in the VO Table epoch_photometry_url in gaia_source.
mean_obs_time_bp : Mean observation time for BP observations (double, Time[Barycentric JD in TCB - 2455197.5 (day)])
Name: The mean observation time
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$. The mean $\overline{t}$ is defined as
$$\overline{t}=\frac{1}{N}\sum _{i=1}^{N}{t}_{i}.$$ | (14.15) |
Name: The time duration of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The time duration of the time series is equal to ${t}_{N}-{t}_{1}$.
Name: The minimum value of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The minimum value of the time series is defined as:
$$min({y}_{i})\forall i\in (1,N)$$ | (14.16) |
Name: The maximum value of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The maximum value of the time series is defined as:
$$max({y}_{i})\forall i\in (1,N)$$ | (14.17) |
Name: The mean of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$. The mean $\overline{y}$ is defined as
$$\overline{y}=\frac{1}{N}\sum _{i=1}^{N}{y}_{i}.$$ | (14.18) |
Name: The median of the time series
Control parameters: None
Output: The 50th unweighted percentile value.
Let ${y}_{i}$ be a time series of size $N$ ordered such as ${y}_{(1)}\le {y}_{(2)}\le \mathrm{\cdots}\le {y}_{(N)}$. The $m$-th (per cent) percentile ${P}_{m}$ is defined for $$ as follows:
$$ | (14.19) |
Name: The range of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series, ${y}_{\mathrm{max}}$ its largest element, and ${y}_{\mathrm{min}}$ its smallest element, then the range is defined as
$$R={y}_{\mathrm{max}}-{y}_{\mathrm{min}}$$ | (14.20) |
Name: The square root of the unbiased unweighted variance.
Output: Let ${y}_{i}$ be a time series of size $N$. The unweighted standard deviation $\widehat{\sigma}$ is defined as the square root of the sample-size unbiased unweighted variance:
$$\widehat{\sigma}=\sqrt{\frac{1}{N-1}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{2}}.$$ |
skewness_mag_bp : Standardized unweighted BP magnitude skewness (double, Dimensionless[see description])
Name: The standardised unbiased unweighted skewness.
Output: Let ${y}_{i}$ be a time series of size $N>2$. The sample-size unbiased unweighted skewness moment $\mathcal{E}$ is defined as:
$$\mathcal{E}=\frac{N}{(N-1)(N-2)}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{3}.$$ |
The standardized unbiased skewness $E$ is defined as:
$$E=\frac{\mathcal{E}}{{\widehat{\sigma}}^{3}}$$ |
where $\widehat{\sigma}$ is the square root of the unbiased unweighted variance around the unweighted mean. While $\mathcal{E}$ is an unbiased estimate of the population value, $E$ becomes unbiased in the limit of large $N$.
kurtosis_mag_bp : Standardized unweighted BP magnitude kurtosis (double, Dimensionless[see description])
Name: The standardised unbiased unweighted kurtosis.
Output: Let ${y}_{i}$ be a time series of size $N>3$. The sample-size unbiased unweighted kurtosis cumulant $\mathcal{K}$ is defined as:
$$\mathcal{K}=\frac{N(N+1)}{(N-1)(N-2)(N-3)}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{4}-\frac{3}{(N-2)(N-3)}{\left[\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{2}\right]}^{2}.$$ |
The standardized unbiased kurtosis $K$ is defined as:
$$K=\frac{\mathcal{K}}{{\widehat{\sigma}}^{4}}$$ |
where ${\widehat{\sigma}}^{2}$ is the unbiased unweighted variance around the unweighted mean. While $\mathcal{K}$ is an unbiased estimate of the population value, $K$ becomes unbiased in the limit of large $N$.
Name: The Median Absolute Deviation (MAD)
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$. The MAD is defined as the median of the absolute deviations from the median of the data, scaled by a factor of $1/{\mathrm{\Phi}}^{-1}(3/4)\approx 1.4826$ (where ${\mathrm{\Phi}}^{-1}$ is the inverse of the cumulative distribution function for the standard normal distribution), so that the expectation of the scaled MAD at large $N$ equals the standard deviation of a normal distribution:
$$\text{MAD}=1.4826\text{median}\{|{y}_{i}-\text{median}\{{y}_{j},\forall j\in (1,N)\}|,\forall i\in (1,N)\}.$$ | (14.21) |
Name: The Abbe value
Control parameters: None
Output: Let $\{{t}_{i},{y}_{i}\}$ be a time-sorted time series of size $N$, such that $$ for all $$. The Abbe value $\mathcal{A}$ is defined as
$$\mathcal{A}=\frac{{\sum}_{i=1}^{N-1}{({y}_{i+1}-{y}_{i})}^{2}}{2{\sum}_{i=1}^{N}{({y}_{i}-\overline{y})}^{2}}$$ | (14.22) |
where $\overline{y}$ is the unweighted mean.
Name: The Interquartile Range (IQR)
Control parameters: None
Output: The difference between the (unweighted) 75th and 25th percentile values: IQR$={P}_{75}-{P}_{25}$.
Let ${y}_{i}$ be a time series of size $N$ ordered such as ${y}_{(1)}\le {y}_{(2)}\le \mathrm{\cdots}\le {y}_{(N)}$. The $m$-th (per cent) percentile ${P}_{m}$ is defined for $$ as follows:
$$ | (14.23) |
num_selected_rp : Total number of RP observations selected for variability analysis (int, Dimensionless[see description])
The number of processed observations for variability analyses of this source, using only transits not rejected, see rejected_by_variability column in the VO Table epoch_photometry_url in gaia_source.
mean_obs_time_rp : Mean observation time for RP observations (double, Time[Barycentric JD in TCB - 2455197.5 (day)])
Name: The mean observation time
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$. The mean $\overline{t}$ is defined as
$$\overline{t}=\frac{1}{N}\sum _{i=1}^{N}{t}_{i}.$$ | (14.24) |
Name: The time duration of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The time duration of the time series is equal to ${t}_{N}-{t}_{1}$.
Name: The minimum value of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The minimum value of the time series is defined as:
$$min({y}_{i})\forall i\in (1,N)$$ | (14.25) |
Name: The maximum value of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$ at times ${t}_{i}$, with $i=1$ to $N$. The maximum value of the time series is defined as:
$$max({y}_{i})\forall i\in (1,N)$$ | (14.26) |
Name: The mean of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$. The mean $\overline{y}$ is defined as
$$\overline{y}=\frac{1}{N}\sum _{i=1}^{N}{y}_{i}.$$ | (14.27) |
Name: The median of the time series
Control parameters: None
Output: The 50th unweighted percentile value.
Let ${y}_{i}$ be a time series of size $N$ ordered such as ${y}_{(1)}\le {y}_{(2)}\le \mathrm{\cdots}\le {y}_{(N)}$. The $m$-th (per cent) percentile ${P}_{m}$ is defined for $$ as follows:
$$ | (14.28) |
Name: The range of the time series
Control parameters: None
Output: Let ${y}_{i}$ be a time series, ${y}_{\mathrm{max}}$ its largest element, and ${y}_{\mathrm{min}}$ its smallest element, then the range is defined as
$$R={y}_{\mathrm{max}}-{y}_{\mathrm{min}}$$ | (14.29) |
Name: The square root of the unbiased unweighted variance.
Output: Let ${y}_{i}$ be a time series of size $N$. The unweighted standard deviation $\widehat{\sigma}$ is defined as the square root of the sample-size unbiased unweighted variance:
$$\widehat{\sigma}=\sqrt{\frac{1}{N-1}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{2}}.$$ |
skewness_mag_rp : Standardized unweighted RP magnitude skewness (double, Dimensionless[see description])
Name: The standardised unbiased unweighted skewness.
Output: Let ${y}_{i}$ be a time series of size $N>2$. The sample-size unbiased unweighted skewness moment $\mathcal{E}$ is defined as:
$$\mathcal{E}=\frac{N}{(N-1)(N-2)}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{3}.$$ |
The standardized unbiased skewness $E$ is defined as:
$$E=\frac{\mathcal{E}}{{\widehat{\sigma}}^{3}}$$ |
where $\widehat{\sigma}$ is the square root of the unbiased unweighted variance around the unweighted mean. While $\mathcal{E}$ is an unbiased estimate of the population value, $E$ becomes unbiased in the limit of large $N$.
kurtosis_mag_rp : Standardized unweighted RP magnitude kurtosis (double, Dimensionless[see description])
Name: The standardised unbiased unweighted kurtosis.
Output: Let ${y}_{i}$ be a time series of size $N>3$. The sample-size unbiased unweighted kurtosis cumulant $\mathcal{K}$ is defined as:
$$\mathcal{K}=\frac{N(N+1)}{(N-1)(N-2)(N-3)}\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{4}-\frac{3}{(N-2)(N-3)}{\left[\sum _{i=1}^{N}{({y}_{i}-\overline{y})}^{2}\right]}^{2}.$$ |
The standardized unbiased kurtosis $K$ is defined as:
$$K=\frac{\mathcal{K}}{{\widehat{\sigma}}^{4}}$$ |
where ${\widehat{\sigma}}^{2}$ is the unbiased unweighted variance around the unweighted mean. While $\mathcal{K}$ is an unbiased estimate of the population value, $K$ becomes unbiased in the limit of large $N$.
Name: The Median Absolute Deviation (MAD)
Control parameters: None
Output: Let ${y}_{i}$ be a time series of size $N$. The MAD is defined as the median of the absolute deviations from the median of the data, scaled by a factor of $1/{\mathrm{\Phi}}^{-1}(3/4)\approx 1.4826$ (where ${\mathrm{\Phi}}^{-1}$ is the inverse of the cumulative distribution function for the standard normal distribution), so that the expectation of the scaled MAD at large $N$ equals the standard deviation of a normal distribution:
$$\text{MAD}=1.4826\text{median}\{|{y}_{i}-\text{median}\{{y}_{j},\forall j\in (1,N)\}|,\forall i\in (1,N)\}.$$ | (14.30) |
Name: The Abbe value
Control parameters: None
Output: Let $\{{t}_{i},{y}_{i}\}$ be a time-sorted time series of size $N$, such that $$ for all $$. The Abbe value $\mathcal{A}$ is defined as
$$\mathcal{A}=\frac{{\sum}_{i=1}^{N-1}{({y}_{i+1}-{y}_{i})}^{2}}{2{\sum}_{i=1}^{N}{({y}_{i}-\overline{y})}^{2}}$$ | (14.31) |
where $\overline{y}$ is the unweighted mean.
Name: The Interquartile Range (IQR)
Control parameters: None
Output: The difference between the (unweighted) 75th and 25th percentile values: IQR$={P}_{75}-{P}_{25}$.
Let ${y}_{i}$ be a time series of size $N$ ordered such as ${y}_{(1)}\le {y}_{(2)}\le \mathrm{\cdots}\le {y}_{(N)}$. The $m$-th (per cent) percentile ${P}_{m}$ is defined for $$ as follows:
$$ | (14.32) |