Optimal fitting of Gaussian-apodized or under-resolved emission lines in Fourier transform spectra providing new insights on the velocity structure of NGC 6720

Abstract

An analysis of the kinematics of NGC 6720 is performed on the commissioning data obtained with SITELLE, the Canada-France-Hawaii Telescope's new imaging Fourier transform spectrometer. In order to measure carefully the small broadening effect of a shell expansion on an unresolved emission line, we have determined a computationally robust implementation of the convolution of a Gaussian with a sinc instrumental line shape which avoids arithmetic overflows. This model can be used to measure line broadening of typically a few km s −1 even at low spectral resolution (R less than 5000). We have also designed the corresponding set of Gaussian apodizing functions that are now used by ORBS, the SITELLE's reduction pipeline. We have implemented this model in ORCS, a fitting engine for SITELLE's data, and used it to derive the [S ii] density map of the central part of the nebula. The study of the broadening of the [N ii] lines shows that the Main Ring and the Central Lobe are two different shells with different expansion velocities. We have also derived deep and spatially resolved velocity maps of the Halo in [N ii] and Hα and found that the brightest bubbles are originating from two bipolar structures with a velocity difference of more than 35 km s −1 lying at the poles of a possibly unique Halo shell expanding at a velocity of more than 15 km s −1 .tionally robust implementation for small broadening values which avoids arithmetic overflows. In Section 3, we provide the definition of a set of Gaussian apodizing functions with an adjustable broadening parameter that is perfectly suitable for this model. We then apply this new line model to a data cube of the planetary nebula NGC 6720 (the Ring nebula, M 57), which was SITELLE's first target during commissioning. This analysis provides new insights on its velocity structure which are then presented in section 4.

When does an old nova become a dwarf nova? Kinematics and age of the nova shell of the dwarf nova AT Cancri

“…The data were reduced using ORBS, SITELLE's dedicated data reduction software (Martin, Drissen & Joncas 2015;Martin, Prunet & Drissen 2016). Fig.…”

“…A fitting routine using the correct instrument line shape (essentially a convolution of a sinc function with a Gaussian) described in Martin et al (2016) was then applied to each spectrum, providing radial velocities and reliable uncertainties (Table 1, where blobs are listed in increasing order of radial velocity, from the most blueshifted to the most redshifted). In 51 cases, the fainter [N II] 6548 line was clearly detected and fitted.…”

SIGNALS: I. Survey description

“…As they come out of the reduction pipeline, datacubes have a pixel-to-pixel velocity error estimated to be of the order of 0.1 km s −1 at R = 5000. Additional correction is applied to the absolute wavelength calibration using the skylines centroid map as described in Martin et al (2018) resulting in an accuracy of ∼1 km s −1 on the measured relative velocities across the FOV (see appendix B of Martin et al 2016 for details).…”

“…The FWHM of the sinc function is known and fixed since it depends only on the sampling and the maximum optical path displacement of the interferogram scan (Martin et al 2016;Drissen et al 2019). As shown in the work of Martin et al (2016), when natural line broadening is observed, a sinc convolved with a Gaussian function can be used to properly recover the line parameters. If so, the line model has three varying parameters (amplitude, velocity, and broadening of the Gaussian).…”

3D optical spectroscopic study of NGC 3344 with SITELLE: I. Identification and confirmation of supernova remnants

“…The data reduction was performed with ORBS (v. 4.0-DR1beta; Martin et al 2015Martin et al , 2016. ORBS is an automatic data reduction software designed for iFTS data obtained with SITELLE freely available on the web 2 .…”