# 6.3 Calibration models

In the processing for this release only two models were used, one for the general time series models and one for the specific object models used by the Cepheids and RR Lyrae studies. Only the main parameters of the Cepheids and RR Lyrae models are published in Gaia DR1.

## 6.3.1 General time series models

Author(s): Leanne Guy, Joris De Ridder, Jan Cuypers

The general model of variability that we fit to time series of Gaia observations is given by:

 $y=\sum_{n=1}^{N_{f}}\sum_{k=1}^{N_{h}(n)}A_{n,k}\cos(2\pi kf_{n}t+\psi_{n,k})+% \sum_{i=0}^{N_{p}}c_{i}t^{i}$ (6.1)

where we assume that the reference epoch $t_{\rm ref}$, the middle of the time series, has already been subtracted from the time points. $N_{p}\geq 0$ is the degree of the polynomial, $N_{f}\geq 0$ is the number of detected frequencies, and $N_{h}(n)\geq 1$ is the number of significant harmonics of frequency $f_{n}$. This multi-frequency harmonic model includes a low-order polynomial trend and n frequencies, each with k associated harmonics.

## 6.3.2 Time series models of Specific Objects

Author(s): Nami Mowlavi, Gisella Clementini

In Gaia DR1, only the Cepheids and RR Lyrae stars Specific Object Studies pipeline (SOS Cep&RRL) was run. Using a non-linear fitting algorithm their variability periods were refined and their light curves modelled with a truncated Fourier Series, as explained in section 2.1 of Clementini et al. (2016).