Detection limits with spectral differential imaging data

Context. Direct imaging of exoplanets is polluted by speckle noise that severely limits the achievable contrast. Angular and spectral differential imaging have been proposed to make use of the temporal and chromatic properties of the speckles. Both modes, associated with extreme adaptive-optics and coronagraphy, are at the core of the new generation of planet imagers SPHERE and GPI. Aims. We aim to illustrate and characterize the impact of the SDI and SDI+ADI (ASDI) data reduction on the detection of giant planets. We also propose an unbiased method to derive the detection limits from SDI/ASDI data. Methods. Observations of AB Dor B and β Pictoris made with VLT/NaCo were used to simulate and quantify the effects of SDI and ASDI. The novel method is compared to the traditional injection of artificial point sources. Results. The SDI reduction process creates a typical radial positive-negative pattern of any point-source. Its characteristics and its self-subtraction depend on the separation, but also on the spectral properties of the object. This work demonstrates that the self-subtraction cannot be reduced to a simple geometric effect. As a consequence, the detection performances of SDI observations cannot be expressed as a contrast in magnitude with the central star without the knowledge of the spectral properties of detectable companions. In addition, the residual noise cannot be converted into contrast and physical characteristics (mass, temperature) by standard calibration of flux losses. The proposed method takes the SDI bias into account to derive detection limits without the cost of massively injecting artificial sources into the data. Finally, the sensitivity of ASDI observations can be measured only with a control parameter on the algorithms that controls the minimum rotation that is necessary to build the reference image