20.14.8 vari_spurious_signals
Several statistics computed for all sources with published photometric time series which can help in the identification of sources that are affected by calibration issues resulting in, for example, spurious variability signals.
The table has a row for every source with gaia_source.has_epoch_photometry set to TRUE and is described in detail in Holl et al. (2023a).
Columns description:
A unique single numerical identifier of the source obtained from gaia_source (for a detailed description see gaia_source.source_id).
Flag indicating if variability was identified in the photometric data:

•
‘NOT_AVAILABLE’: source not processed and/or exported to catalogue;

•
‘CONSTANT’: Source not identified as variable;

•
‘VARIABLE’: source identified and processed as variable, see variability tables and Chapter 10.
Note that for this data release only a subset of (variable) sources was processed and/or exported, so for many (known) variable sources this flag is set to ‘NOT AVAILABLE’. No ‘CONSTANT’ sources were exported either.
This field is identical to gaia_source.phot_variable_flag.
in_andromeda_survey : Flag indicating that the source is present in the Gaia Andromeda Photometric Survey (GAPS) (boolean)
This flag indicates that the source is present in the Gaia Andromeda Photometric Survey (or GAPS), and as such that photometric light curves are provided for this source. GAPS contains all the sources contained in a 5.5 deg radius field centred on the Andromeda galaxy (Evans et al. 2023); brief details of GAPS are given also in Section 5.8.1.
This field is identical to gaia_source.in_andromeda_survey.
num_obs_common_all_bands : Number of observations in common for G, BP and RP bands, used in computation of the Spearman correlation excess factor fields (short)
Number of photometric FoV observations in which all of the $G$, ${G}_{\mathrm{BP}}$ and ${G}_{\mathrm{RP}}$ were available. Note that it includes only observations that were not rejected by the variability analysis, i.e., those with rejected_by_variability flag FALSE in the epoch photometry time series data.
The observations counted in this field are used in the computations of the fields spearman_corr_exf_g_fov, spearman_corr_exf_bp and spearman_corr_exf_rp.
num_obs_g_fov : Number of selected observations of G FoV transits, used in the frequency fields (short)
Number of photometric FoV observations in the $G$band. Note that it includes only observations that were not rejected by the variability analysis, i.e., those with rejected_by_variability flag FALSE in the epoch photometry time series data.
The observations counted in this field are used in the computations of the fields gls_freq_g_fov, gls_freq_ampl_g_fov, gls_freq_sde_g_fov, gls_freq_fap_g_fov, nhm_fund_freq_g_fov, and nhm_fund_freq_error_g_fov.
This field is identical to vari_summary.num_selected_g_fov.
gls_freq_g_fov : Frequency identified by Generalised Least Squares period search on G FoV timeseries (double, Frequency[day${}^{1}$])
Using the selected $G$band FoV observations counted in num_obs_g_fov an unweighted periodogram is made using Generalised LeastSquares (Heck et al. 1985; Cumming et al. 1999; Zechmeister and Kürster 2009). This is an extension of the Fourier periodogram on uneven sampled data that is independent of the mean of the data. The periodogram is computed between 25 cycles day${}^{1}$ (about 1 h) and $7\cdot {10}^{4}$ cycles day${}^{1}$ (1700 d), with a step size of typically ${10}^{5}$ cycles day${}^{1}$.
Value is null when $$.
gls_freq_ampl_g_fov : Normalised amplitude of the frequency identified by Generalised Least Squares period search on G FoV timeseries (float)
The normalised amplitude associated with gls_freq_g_fov.
Value is null when $$.
gls_freq_sde_g_fov : Signal Detection Efficiency (SDE) of the frequency identified by Generalised Least Squares period search on G FoV timeseries (float)
The signal detection efficiency (SDE, see Alcock et al. 2000b; Kovács et al. 2002) associated with gls_freq_g_fov.
Value is null when $$.
gls_freq_fap_g_fov : False Alarm Probability (FAP) of the frequency identified by Generalised Least Squares period search on G FoV timeseries (double)
The Baluev false alarm probability (FAP, see Alcock et al. 2000b; Kovács et al. 2002) associated with gls_freq_g_fov.
Value is null when $$.
nhm_fund_freq_g_fov : Fundamental frequency identified by nonlinear harmonic modelling on G FoV timeseries, initialised by the Generalised Least Squares frequency (double, Frequency[day${}^{1}$])
This a refinement of the generalised least squares frequency provided in gls_freq_g_fov. It uses an unweighted multiharmonic modelling and a final nonlinear optimisation of all the fitted parameters. Only the fundamental frequency (and uncertainty) of this multiharmonic model are provided in this table. Generally the refined fundamental frequency is very close to the gls_freq_g_fov, though sometimes it settled in another (local) minimima of the parameter space. The latter mainly happens when the source is not (strictly) periodic.
Value is null when $$ or when the nonlinear harmonic modelling failed.
nhm_fund_freq_error_g_fov : Uncertainty of the fundamental frequency identified by nonlinear harmonic modelling on G FoV timeseries (float, Frequency[day${}^{1}$])
The uncertainty estimate of nhm_fund_freq_g_fov.
Value is null when $$ or when the nonlinear harmonic modelling failed.
spearman_corr_exf_g_fov : Gband FoV photometry Spearman correlation with corrected flux excess factor (float)
Correlation statistic based on the Spearman correlation between the $G$band magnitude and excess flux ${C}^{*}$ introduced in Distefano et al. (2023):
$$\mathrm{\U0001d69c\U0001d699\U0001d68e\U0001d68a\U0001d69b\U0001d696\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68c\U0001d698\U0001d69b\U0001d69b}\mathrm{\_}\mathrm{\U0001d68e\U0001d6a1\U0001d68f}\mathrm{\_}\U0001d690\mathrm{\_}\mathrm{\U0001d68f\U0001d698\U0001d69f}={f}_{\text{SpearmanCorr}}\left(\{G\text{[mag]}(i),{C}^{*}(i)i\in 1,\mathrm{\dots},N\}\right)$$ 
using the corrected excess flux ${C}^{*}$ from Riello et al. (2021):
$${C}^{*}=Cf({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$$ 
where $C=({I}_{BP}+{I}_{RP})/{I}_{G}$ is the excess flux factor, ${I}_{BP}$, ${I}_{RP}$ and ${I}_{G}$ are the cumulative fluxes in the ${G}_{\mathrm{BP}}$, ${G}_{\mathrm{RP}}$ and $G$ bands, and $f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$ is a correction function defined in table 2 of Riello et al. (2021).
Values close to 1 can be due to a variety of intrinsic, extrinsic and calibration reasons as further detailed in Distefano et al. (2023):

•
the star has strong emission lines whose intensity is correlated with $G$;

•
the star is a partially resolved binary;

•
the star has some calibration issue, e.g., due to the transition from a windowgate configuration to another.
Values around 0 can be considered ‘wellbehaved’ in terms of excess flux.
Because of the dependency on availability of transit flux from all three ${G}_{\mathrm{BP}}$, ${G}_{\mathrm{RP}}$ and $G$ bands, only transits for which all three were available are used in the computation of spearman_corr_exf_g_fov. This number of used observations $N$ (listed in num_obs_common_all_bands) is occasionally quite low, i.e., less than ten. Empirically we see that correlations computed on at least 11 points could be useful, see Holl et al. (2023a) for further details.
The value is null when $$.
num_obs_excl_epsl_g_fov : Number of Gband FoV photometry observations excluding EPSL, used for the IPD correlation and scan angle modelling in the G band (short)
Number of $G$band FoV photometric observations excluding EPSL, here defined as all observation after BJD 1693.14 (offset by 2455197.5). Note that we included only observations that were not rejected by the variability analysis, i.e., those with rejected_by_variability flag FALSE in the epoch photometry time series data.
The IPD GoF model ${M}_{\text{ipd}}(\psi )$ as detailed in the description of the parameter gaia_source.ipd_gof_harmonic_amplitude provides information about the phase and amplitude of a potential scanangle dependent signal in the data. In order to quantify how much the derived $G$band photometry is in reality affected by a scanangle dependent signal, we can assess how much the photometry correlates in phase with this IPD model. To do so we compute the Spearman correlation between the $G$band time series and the IPD GoF model sampled at the scan angles of the time series observations:
$$\mathrm{\U0001d69c\U0001d699\U0001d68e\U0001d68a\U0001d69b\U0001d696\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68c\U0001d698\U0001d69b\U0001d69b}\mathrm{\_}\mathrm{\U0001d692\U0001d699\U0001d68d}\mathrm{\_}\U0001d690\mathrm{\_}\mathrm{\U0001d68f\U0001d698\U0001d69f}={f}_{\text{SpearmanCorr}}\left(\{{G}_{i}\text{[flux]}({\psi}_{i}),{M}_{\text{ipd}}({\psi}_{i})i\in 1,\mathrm{\dots},N\}\right)$$  (20.62) 
with $i$ being the observation index in the time series of a source having a total of $N$ observations (excluding observations during the EPSL), as listed in num_obs_excl_epsl_g_fov. ${\psi}_{i}$ is the associated scan angle, which can be found in table commanded_scan_law for the time and FoV associated with each observation. Note that when using photometry expressed in magnitude instead of flux, the sign of the correlation should be flipped to produce the exact same spearman_corr_ipd_g_fov.
Values close to 1 generally show strong scanangle dependent signals and should thus be treated with most care. Values around 0 are uncorrelated with the IPD GoF scanangle model and thus should be free from any scanangle dependent signals. Values close to 1 would have an anticorrelation with IPD GoF model and should thus also be treated with care but do not appear systematically in the data.
The number of observations $N$ is occasionally quite low, i.e., less than ten. Empirically we see that correlations computed on at least 11 points could be useful. The value is set to null when $$.
For further details on this parameter and how to use it see Holl et al. (2023a).
scan_angle_model_offset_g_fov : Magnitude offset of the scan angle model fit to Gband FoV photometry (float, Magnitude[mag])
Strong scanangle dependent signals in $G$band photometry, e.g. those with spearman_corr_ipd_g_fov close to 1, are often relatively well characterized by the photometric bias model for small separation discussed in Holl et al. (2023a):
$G(\psi )$  $=$  ${c}_{0}+{c}_{2}\mathrm{cos}(2\psi )+{s}_{2}\mathrm{sin}(2\psi )$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d698\U0001d68f\U0001d68f\U0001d69c\U0001d68e\U0001d69d}\mathrm{\_}\U0001d690\mathrm{\_}\mathrm{\U0001d68f\U0001d698\U0001d69f}$  $=$  ${c}_{0}$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d68a\U0001d696\U0001d699\U0001d695}\mathrm{\_}\U0001d690\mathrm{\_}\mathrm{\U0001d68f\U0001d698\U0001d69f}$  $=$  $\sqrt{{c}_{2}^{2}+{s}_{2}^{2}}$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d699\U0001d691\U0001d68a\U0001d69c\U0001d68e}\mathrm{\_}\U0001d690\mathrm{\_}\mathrm{\U0001d68f\U0001d698\U0001d69f}$  $=$  $\frac{1}{2}}\mathrm{atan2}({s}_{2},{c}_{2})\mathit{\hspace{1em}}(+{180}^{\circ})$ 
with scan angle $\psi $ [rad], amplitude scan_angle_model_ampl_g_fov [mag], and phase scan_angle_model_phase_g_fov [deg]. Despite the parameterisation being identical to the IPD model (see the detailed description of the relevant field gaia_source.ipd_gof_harmonic_amplitude), the fitted phase here often will be offset by 90 deg with respect to the gaia_source.ipd_gof_harmonic_phase, as it is intended to model the position angle of an assumed smallangle separated binary.
The significance of the amplitude listed in field scan_angle_model_ampl_sig_g_fov, is computed from the fitted ${c}_{2}$ and ${s}_{2}$ and their correlation coefficient, by means of eq. 3 of Halbwachs et al. (2023).
The ${\chi}_{\text{red}}^{2}$ of the fit is provided in the scan_angle_model_red_chi2_g_fov field along with the goodnessoffit F2 parameter in the scan_angle_model_f2_g_fov field.
The total number of used observations is provided in num_obs_excl_epsl_g_fov and excludes observations during the EPSL and those rejected by the variability analyses (i.e., with rejected_by_variability set to TRUE in the epoch photometry).
For a source with nonsignificant scanangle dependent signals, e.g. with spearman_corr_ipd_g_fov close to 0, the above scan angle model can be an arbitrarily bad fit to the data, especially when the source has intrinsic variability (which is the case for the majority of sources in this table). The model parameters should thus be interpreted with appropriate care.
The model values are set to null when $$.
For further details on this parameter and how to use it see Holl et al. (2023a).
scan_angle_model_ampl_g_fov : Amplitude of the scan angle model fit to Gband FoV photometry (float, Magnitude[mag])
See the detailed description of scan_angle_model_offset_g_fov for more details.
scan_angle_model_ampl_sig_g_fov : Significance of the amplitude of the scan angle model fit to Gband FoV photometry (float)
See the detailed description of scan_angle_model_offset_g_fov for more details.
scan_angle_model_phase_g_fov : Phase of the scan angle model fit to Gband FoV photometry (float, Angle[deg])
See the detailed description of scan_angle_model_offset_g_fov for more details.
scan_angle_model_red_chi2_g_fov : Reduced Chi2 of the scan angle model fit to Gband FoV photometry (float)
See the detailed description of scan_angle_model_offset_g_fov for more details.
scan_angle_model_f2_g_fov : F2 goodnessoffit of the scan angle model fit to Gband FoV photometry (float)
See the detailed description of scan_angle_model_offset_g_fov for more details.
spearman_corr_exf_bp : BPband photometry Spearman correlation with corrected flux excess factor (float)
Correlation statistic based on the Spearman correlation between the $BP$band magnitude and excess flux ${C}^{*}$ introduced in Holl et al. (2023a):
$$\mathrm{\U0001d69c\U0001d699\U0001d68e\U0001d68a\U0001d69b\U0001d696\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68c\U0001d698\U0001d69b\U0001d69b}\mathrm{\_}\mathrm{\U0001d68e\U0001d6a1\U0001d68f}\mathrm{\_}\mathrm{\U0001d68b\U0001d699}={f}_{\text{SpearmanCorr}}\left(\{{G}_{\mathrm{BP}}\text{[mag]}(i),{C}^{*}(i)i\in 1,\mathrm{\dots},N\}\right)$$ 
using the corrected excess flux ${C}^{*}$ from Riello et al. (2021):
$${C}^{*}=Cf({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$$ 
where $C=({I}_{BP}+{I}_{RP})/{I}_{G}$ is the excess flux factor, ${I}_{BP}$, ${I}_{RP}$ and ${I}_{G}$ are the cumulative fluxes in the ${G}_{\mathrm{BP}}$, ${G}_{\mathrm{RP}}$ and $G$ bands, and $f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$ is a correction function defined in table 2 of Riello et al. (2021).
The distribution has a single mode peaking around 0.78 as shown in Holl et al. (2023a).
Because of the dependency on availability of transit flux from all three ${G}_{\mathrm{BP}}$, ${G}_{\mathrm{RP}}$ and $G$ bands, only transits for which all three were available are used in the computation of spearman_corr_exf_bp. This number of used observations $N$ (listed in num_obs_common_all_bands) is occasionally quite low, i.e., less than ten. Empirically we see that correlations computed on at least 11 points could be useful, see Holl et al. (2023a) for further details.
The value is null when $$.
num_obs_excl_epsl_bp : Number of BPband photometry observations excluding EPSL, used for the IPD correlation and scan angle modelling in the BP band (short)
Number of ${G}_{\mathrm{BP}}$band photometric observations excluding EPSL, here defined as all observation after BJD 1693.14 (offset by 2455197.5). Note that we included only observations that were not rejected by the variability analysis, i.e., those with rejected_by_variability flag FALSE in the epoch photometry time series data.
The IPD GoF model ${M}_{\text{ipd}}(\psi )$ as detailed in the description of the parameter gaia_source.ipd_gof_harmonic_amplitude provides information about the phase and amplitude of a potential scanangle dependent signal in the data. In order to quantify how much the derived ${G}_{\mathrm{BP}}$band photometry is in reality affected by a scanangle dependent signal, we can assess how much the photometry correlates in phase with this IPD model. To do so we compute the Spearman correlation between the ${G}_{\mathrm{BP}}$band time series and the IPD GoF model sampled at the scan angles of the time series observations:
$$\mathrm{\U0001d69c\U0001d699\U0001d68e\U0001d68a\U0001d69b\U0001d696\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68c\U0001d698\U0001d69b\U0001d69b}\mathrm{\_}\mathrm{\U0001d692\U0001d699\U0001d68d}\mathrm{\_}\mathrm{\U0001d68b\U0001d699}={f}_{\text{SpearmanCorr}}\left(\{{G}_{\mathrm{BP},i}\text{[flux]}({\psi}_{i}),{M}_{\text{ipd}}({\psi}_{i})i\in 1,\mathrm{\dots},N\}\right)$$  (20.63) 
with $i$ being the observation index in the time series of a source having a total of $N$ observations (excluding observations during the EPSL), as listed in num_obs_excl_epsl_bp. ${\psi}_{i}$ is the associated scan angle, which can be found in table commanded_scan_law for the time and FoV associated with each observation. Note that when using photometry expressed in magnitude instead of flux, the sign of the correlation should be flipped to produce the exact same spearman_corr_ipd_bp.
Values close to 1 generally show strong scanangle dependent signals and should thus be treated with most care. Values around 0 are uncorrelated with the IPD GoF scanangle model and thus should be free from any scanangle dependent signals. Values close to 1 would have an anticorrelation with IPD GoF model and should thus also be treated with care but do not appear systematically in the data.
The number of observations $N$ is occasionally quite low, i.e., less than ten. Empirically we see that correlations computed on at least 11 points could be useful. The value is set to null when $$.
For further details on this parameter and how to use it see Holl et al. (2023a).
scan_angle_model_offset_bp : Magnitude offset of the scan angle model fit to BPband photometry (float, Magnitude[mag])
Strong scanangle dependent signals in $G$band photometry, e.g. those with spearman_corr_ipd_g_fov close to 1, are often relatively well characterized by the photometric bias model for small separation discussed in Holl et al. (2023a). For completeness we here also provide the model fit for the ${G}_{\mathrm{BP}}$band photometry, even though the associated spearman_corr_ipd_bp is generally close to zero, meaning that this model might in the vast majority of cases be not a good fit to the data:
${G}_{\mathrm{BP}}(\psi )$  $=$  ${c}_{0}+{c}_{2}\mathrm{cos}(2\psi )+{s}_{2}\mathrm{sin}(2\psi )$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d698\U0001d68f\U0001d68f\U0001d69c\U0001d68e\U0001d69d}\mathrm{\_}\mathrm{\U0001d68b\U0001d699}$  $=$  ${c}_{0}$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d68a\U0001d696\U0001d699\U0001d695}\mathrm{\_}\mathrm{\U0001d68b\U0001d699}$  $=$  $\sqrt{{c}_{2}^{2}+{s}_{2}^{2}}$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d699\U0001d691\U0001d68a\U0001d69c\U0001d68e}\mathrm{\_}\mathrm{\U0001d68b\U0001d699}$  $=$  $\frac{1}{2}}\mathrm{atan2}({s}_{2},{c}_{2})\mathit{\hspace{1em}}(+{180}^{\circ})$ 
with scan angle $\psi $ [rad], amplitude scan_angle_model_ampl_bp [mag], and phase scan_angle_model_phase_bp [deg].
The significance of the amplitude listed in field scan_angle_model_ampl_sig_bp, is computed from the fitted ${c}_{2}$ and ${s}_{2}$ and their correlation coefficient, by means of eq. 3 of Halbwachs et al. (2023).
The ${\chi}_{\text{red}}^{2}$ of the fit is provided in the scan_angle_model_red_chi2_bp field along with the goodnessoffit F2 parameter in the scan_angle_model_f2_bp field.
The total number of used observations is provided in num_obs_excl_epsl_bp and excludes observations during the EPSL and those rejected by the variability analyses (i.e., with rejected_by_variability set to TRUE in the epoch photometry).
For a source with nonsignificant scanangle dependent signals, e.g. with spearman_corr_ipd_bp close to 0, the above scan angle model can be an arbitrarily bad fit to the data, especially when the source has intrinsic variability (which is the case for the majority of sources in this table). The model parameters should thus be interpreted with appropriate care.
The model values are set to null when $$.
For further details on this parameter and how to use it see Holl et al. (2023a).
scan_angle_model_ampl_bp : Amplitude of the scan angle model fit to BPband photometry (float, Magnitude[mag])
See the detailed description of scan_angle_model_offset_bp for more details.
scan_angle_model_ampl_sig_bp : Significance of the amplitude of the scan angle model fit to BPband photometry (float)
See the detailed description of scan_angle_model_offset_bp for more details.
scan_angle_model_phase_bp : Phase of the scan angle model fit to BPband photometry (float, Angle[deg])
See the detailed description of scan_angle_model_offset_bp for more details.
scan_angle_model_red_chi2_bp : Reduced Chi2 of the scan angle model fit to BPband photometry (float)
See the detailed description of scan_angle_model_offset_bp for more details.
scan_angle_model_f2_bp : F2 goodnessoffit of the scan angle model fit to BPband photometry (float)
See the detailed description of scan_angle_model_offset_bp for more details.
spearman_corr_exf_rp : RPband photometry Spearman correlation with corrected flux excess factor (float)
Correlation statistic based on the Spearman correlation between the $RP$band magnitude and excess flux ${C}^{*}$ introduced in Holl et al. (2023a):
$$\mathrm{\U0001d69c\U0001d699\U0001d68e\U0001d68a\U0001d69b\U0001d696\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68c\U0001d698\U0001d69b\U0001d69b}\mathrm{\_}\mathrm{\U0001d68e\U0001d6a1\U0001d68f}\mathrm{\_}\mathrm{\U0001d69b\U0001d699}={f}_{\text{SpearmanCorr}}\left(\{{G}_{\mathrm{RP}}\text{[mag]}(i),{C}^{*}(i)i\in 1,\mathrm{\dots},N\}\right)$$ 
using the corrected excess flux ${C}^{*}$ from Riello et al. (2021):
$${C}^{*}=Cf({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$$ 
where $C=({I}_{BP}+{I}_{RP})/{I}_{G}$ is the excess flux factor, ${I}_{BP}$, ${I}_{RP}$ and ${I}_{G}$ are the cumulative fluxes in the ${G}_{\mathrm{BP}}$, ${G}_{\mathrm{RP}}$ and $G$ bands, and $f({G}_{\mathrm{BP}}{G}_{\mathrm{RP}})$ is a correction function defined in table 2 of Riello et al. (2021).
The distribution has a single mode peaking around 0.75 as shown in Holl et al. (2023a).
Because of the dependency on availability of transit flux from all three ${G}_{\mathrm{BP}}$, ${G}_{\mathrm{RP}}$ and $G$ bands, only transits for which all three were available are used in the computation of spearman_corr_exf_rp. This number of used observations $N$ (listed in num_obs_common_all_bands) is occasionally quite low, i.e., less than ten. Empirically we see that correlations computed on at least 11 points could be useful, see Holl et al. (2023a) for further details.
The value is null when $$.
num_obs_excl_epsl_rp : Number of RPband photometry observations excluding EPSL, used for the IPD correlation and scan angle modelling in the RP band (short)
Number of ${G}_{\mathrm{RP}}$band photometric observations excluding EPSL, here defined as all observation after BJD 1693.14 (offset by 2455197.5). Note that we included only observations that were not rejected by the variability analysis, i.e., those with rejected_by_variability flag FALSE in the epoch photometry time series data.
The IPD GoF model ${M}_{\text{ipd}}(\psi )$ as detailed in the description of the parameter gaia_source.ipd_gof_harmonic_amplitude provides information about the phase and amplitude of a potential scanangle dependent signal in the data. In order to quantify how much the derived ${G}_{\mathrm{RP}}$band photometry is in reality affected by a scanangle dependent signal, we can assess how much the photometry correlates in phase with this IPD model. To do so we compute the Spearman correlation between the ${G}_{\mathrm{RP}}$band time series and the IPD GoF model sampled at the scan angles of the time series observations:
$$\mathrm{\U0001d69c\U0001d699\U0001d68e\U0001d68a\U0001d69b\U0001d696\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68c\U0001d698\U0001d69b\U0001d69b}\mathrm{\_}\mathrm{\U0001d692\U0001d699\U0001d68d}\mathrm{\_}\mathrm{\U0001d69b\U0001d699}={f}_{\text{SpearmanCorr}}\left(\{{G}_{\mathrm{RP},i}\text{[flux]}({\psi}_{i}),{M}_{\text{ipd}}({\psi}_{i})i\in 1,\mathrm{\dots},N\}\right)$$  (20.64) 
with $i$ being the observation index in the time series of a source having a total of $N$ observations (excluding observations during the EPSL), as listed in num_obs_excl_epsl_rp. ${\psi}_{i}$ is the associated scan angle, which can be found in table commanded_scan_law for the time and FoV associated with each observation. Note that when using photometry expressed in magnitude instead of flux, the sign of the correlation should be flipped to produce the exact same spearman_corr_ipd_rp.
Values close to 1 generally show strong scanangle dependent signals and should thus be treated with most care. Values around 0 are uncorrelated with the IPD GoF scanangle model and thus should be free from any scanangle dependent signals. Values close to 1 would have an anticorrelation with IPD GoF model and should thus also be treated with care but do not appear systematically in the data.
The number of observations $N$ is occasionally quite low, i.e., less than ten. Empirically we see that correlations computed on at least 11 points could be useful. The value is set to null when $$.
For further details on this parameter and how to use it see Holl et al. (2023a).
scan_angle_model_offset_rp : Magnitude offset of the scan angle model fit to RPband photometry (float, Magnitude[mag])
Strong scanangle dependent signals in $G$band photometry, e.g. those with spearman_corr_ipd_g_fov close to 1, are often relatively well characterized by the photometric bias model for small separation discussed in Holl et al. (2023a). For completeness we here also provide the model fit for the ${G}_{\mathrm{RP}}$band photometry, even though the associated spearman_corr_ipd_rp is generally close to zero, meaning that this model might in the vast majority of cases be not a good fit to the data:
${G}_{\mathrm{RP}}(\psi )$  $=$  ${c}_{0}+{c}_{2}\mathrm{cos}(2\psi )+{s}_{2}\mathrm{sin}(2\psi )$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d698\U0001d68f\U0001d68f\U0001d69c\U0001d68e\U0001d69d}\mathrm{\_}\mathrm{\U0001d69b\U0001d699}$  $=$  ${c}_{0}$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d68a\U0001d696\U0001d699\U0001d695}\mathrm{\_}\mathrm{\U0001d69b\U0001d699}$  $=$  $\sqrt{{c}_{2}^{2}+{s}_{2}^{2}}$  
$\mathrm{\U0001d69c\U0001d68c\U0001d68a\U0001d697}\mathrm{\_}\mathrm{\U0001d68a\U0001d697\U0001d690\U0001d695\U0001d68e}\mathrm{\_}\mathrm{\U0001d696\U0001d698\U0001d68d\U0001d68e\U0001d695}\mathrm{\_}\mathrm{\U0001d699\U0001d691\U0001d68a\U0001d69c\U0001d68e}\mathrm{\_}\mathrm{\U0001d69b\U0001d699}$  $=$  $\frac{1}{2}}\mathrm{atan2}({s}_{2},{c}_{2})\mathit{\hspace{1em}}(+{180}^{\circ})$ 
with scan angle $\psi $ [rad], amplitude scan_angle_model_ampl_rp [mag], and phase scan_angle_model_phase_rp [deg].
The significance of the amplitude listed in field scan_angle_model_ampl_sig_rp, is computed from the fitted ${c}_{2}$ and ${s}_{2}$ and their correlation coefficient, by means of eq. 3 of Halbwachs et al. (2023).
The ${\chi}_{\text{red}}^{2}$ of the fit is provided in the scan_angle_model_red_chi2_rp field along with the goodnessoffit F2 parameter in the scan_angle_model_f2_rp field.
The total number of used observations is provided in num_obs_excl_epsl_rp and excludes observations during the EPSL and those rejected by the variability analyses (i.e., with rejected_by_variability set to TRUE in the epoch photometry).
For a source with nonsignificant scanangle dependent signals, e.g. with spearman_corr_ipd_rp close to 0, the above scan angle model can be an arbitrarily bad fit to the data, especially when the source has intrinsic variability (which is the case for the majority of sources in this table). The model parameters should thus be interpreted with appropriate care.
The model values are set to null when $$.
For further details on this parameter and how to use it see Holl et al. (2023a).
scan_angle_model_ampl_rp : Amplitude of the scan angle model fit to RPband photometry (float, Magnitude[mag])
See the detailed description of scan_angle_model_offset_rp for more details.
scan_angle_model_ampl_sig_rp : Significance of the amplitude of the scan angle model fit to RPband photometry (float)
See the detailed description of scan_angle_model_offset_rp for more details.
scan_angle_model_phase_rp : Phase of the scan angle model fit to RPband photometry (float, Angle[deg])
See the detailed description of scan_angle_model_offset_rp for more details.
scan_angle_model_red_chi2_rp : Reduced Chi2 of the scan angle model fit to RPband photometry (float)
See the detailed description of scan_angle_model_offset_rp for more details.
scan_angle_model_f2_rp : F2 goodnessoffit of the scan angle model fit to RPband photometry (float)
See the detailed description of scan_angle_model_offset_rp for more details.