2.1.12 vari_rad_vel_statistics

Statistical parameters of radial velocity time series using only transits retained and not rejected (see the relevant rejection flag in the epoch radial velocity variability table).
Note that NaN will be reported when the parameter value is missing or cannot be calculated.

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 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

source_id : Unique source identifier (long)

A unique single numerical identifier of the source obtained from the Gaia DR3 main source catalogue (for a detailed description see gaiadr3.gaia_source.source_id).

num_selected_rv : Total number of radial velocity transits selected for variability analysis (short)

The number of processed observations for variability analyses of this source, using only transits not rejected, see rejected_by_variability column in vari_epoch_radial_velocity.

mean_obs_time_rv : Mean observation time for radial velocity transits (double, Time[Barycentric JD in TCB $-$ 2 455 197.5 (day)])

Name: The mean observation time

Output: Let $y_i$ be a time series of size $N$ at times $t_i$. The mean $\overline{t}$ is defined as

$$\overline{t}=\frac{1}{N}\sum _{i=1}^N{t}_i.$$

time_duration_rv : Time duration of the time series for radial velocity transits (float, Time[day])

Name: The time duration of the time series

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 $t_N-t_1$.

min_rv : Minimum radial velocity (float, Velocity[km s${}^{-1}$])

Name: The minimum value of the time series

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:

$$min(y_i)\forall i\in (1,N)$$

max_rv : Maximum radial velocity (float, Velocity[km s${}^{-1}$])

Name: The maximum value of the time series

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:

$$max(y_i)\forall i\in (1,N)$$

mean_rv : Mean radial velocity (float, Velocity[km s${}^{-1}$])

Name: The mean of the time series

Output: Let $y_i$ be a time series of size $N$. The mean $\overline{y}$ is defined as

$$\overline{y}=\frac{1}{N}\sum _{i=1}^N{y}_i.$$

median_rv : Median radial velocity (float, Velocity[km s${}^{-1}$])

Name: The median of the time series

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:

range_rv : Difference between the highest and lowest radial velocity transits (float, Velocity[km s${}^{-1}$])

Name: The range of the time series

Output: Let $y_i$ be a time series, $y_{\max }$ its largest element, and $y_{\min }$ its smallest element, then the range is defined as

$$R=y_{\max }-y_{\min }$$

std_dev_rv : Square root of the unweighted radial velocity variance (float, Velocity[km s${}^{-1}$])

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_rv : Standardized unweighted radial velocity skewness (float)

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 $ℰ$ is defined as:

$$ℰ=\frac{N}{(N-1)(N-2)}\sum _{i=1}^N{(y_i-\overline{y})}^3.$$

The standardized unbiased skewness $E$ is defined as:

$$E=\frac{ℰ}{{\widehat{\sigma }}^3}$$

where $\widehat{\sigma }$ is the square root of the unbiased unweighted variance around the unweighted mean. While $ℰ$ is an unbiased estimate of the population value, $E$ becomes unbiased in the limit of large $N$.

kurtosis_rv : Standardized unweighted radial velocity kurtosis (float)

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 $𝒦$ is defined as:

$$𝒦=\frac{N(N+1)}{(N-1)(N-2)(N-3)}\sum _{i=1}^N{(y_i-\overline{y})}^4-\frac{3}{(N-2)(N-3)}{\left[\sum _{i=1}^N{(y_i-\overline{y})}^2\right]}^2.$$

The standardized unbiased kurtosis $K$ is defined as:

$$K=\frac{𝒦}{{\widehat{\sigma }}^4}$$

where ${\widehat{\sigma }}^2$ is the unbiased unweighted variance around the unweighted mean. While $𝒦$ is an unbiased estimate of the population value, $K$ becomes unbiased in the limit of large $N$.

mad_rv : Median Absolute Deviation (MAD) for radial velocity transits (float, Velocity[km s${}^{-1}$])

Name: The Median Absolute Deviation (MAD)

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:

$$\text{MAD}=1.4826\text{median}\{|y_i-\text{median}\{y_j,\forall j\in (1,N)\}|,\forall i\in (1,N)\}.$$

abbe_rv : Abbe value for radial velocity transits (float)

Name: The Abbe value

Output: Let $\{t_i,y_i\}$ be a time-sorted time series of size $N$, such that for all . The Abbe value $𝒜$ is defined as

$$𝒜=\frac{{\sum }_{i=1}^{N-1}{(y_{i+1}-y_i)}^2}{2{\sum }_{i=1}^N{(y_i-\overline{y})}^2}$$

where $\overline{y}$ is the unweighted mean.

iqr_rv : Interquartile range for radial velocity transits (float, Velocity[km s${}^{-1}$])

Name: The Interquartile Range (IQR)

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: