Spectroscopy

Spectroscopy is a fundamental tool for astronomy. By dispersing incident light we can measure the intensity of the light as a function of wavelength. The resolving

power of a spectrographR is given by

R= λ

∆λ (3.1)

Figure 3.1: Schematic of a diffraction grating, with the right plot showing a zoom in

on the left plot. Two light beams are incident at an angleα to the grating normal.

The light is then diffracted at an angleβ from the grating normal. The grooves are

separated by a distanced. The bold black lines in the right-hand zoom indicate the

extra path distance travelled by the second ray of light, whose lengths are given by

dsinα anddsinβ, respectively. Figure from Huitson (2013).

between two spectral lines of the same intensity that can be distinguished.

Maxima in the dispersed light occur when the path difference between two diffracted beams of light is equal to an integer number of wavelengths such that the

interference is constructive. These maxima are called the orders of the diffraction

pattern, and run from zero to n.

The setup of a diffraction grating is shown in Fig. 3.1. This figure can be used to yield the difference in path lengths travelled by two beams of light incident on a diffraction grating to give the grating equation

mλ=d(sinα+ sinβ) (3.2)

where m is the diffraction order, λ is the wavelength of incident light, d is

the groove spacing, α is the angle of incident light to the grating normal and β is

the angle of diffracted light to the grating normal, as described by Palmer & Loewen (2005).

The resolving power of a diffraction grating is related to the orderm of the

diffracted light and the total number of grooves illuminated on the surface of the

grating,N by

R=mN (3.3)

Figure 3.1 actually depicts ablazed diffraction grating whereby incident light

is diffracted by grooves in the grating instead of passing through slits. The angle

Figure 3.2: Figure indicating the blaze angle, θB of the grating. The angles of

incidence and diffraction are given by α and β respectively. GN is the grating

normal and FN is the facet normal. Figure from Palmer & Loewen (2005).

blaze wavelength λB (the wavelength of the maximum intensity for a given orderm)

through

λB= 2d

m sinθB (3.4)

The spectrographs used in this thesis employ agrism, which is a diffraction

grating on the hypotenuse side of a right-angled triangular prism. The prism acts to refract the light back into line for a central wavelength. This is useful as the same camera can be used for spectroscopy and imaging by removing the grism without having to move the detector.

The science results presented in Chapters 5 and 6 were based on long slit spectroscopic data. Long slit spectroscopy is performed with a single, long slit that is placed in the optical path, before the light is dispersed. The 27 arcsec slit used in Chapter 5 has a length of 6.8 arcmin (with a physical length of 90.5 mm) and the 40 arcsec slit used in Chapter 6 has a length of 7.6 arcmin (with a physical length of 101.1 mm). Long slit spectroscopy lends itself well to ground-based transmission spectroscopy since it allows for a comparison star to be observed simultaneously with the target. This is necessary to correct for changes due to observing conditions and the effects of observing through Earth’s atmosphere (telluric effects). It is also possible to request custom made slits which are much wider (tens of arcsec) than

standard (a few arcsec), thereby avoiding differential slit losses between the target and comparison. The disadvantages of wide slits, however, is that the spectral resolution varies with the seeing and the wavelength calibration varies with guiding errors.

The grism spectrographs used in this thesis provide low resolution spectra

(R _≈400) across the optical regime. We chose to use these spectrographs as they

are relatively simple in their optical design and they can observe a broad range of wavelengths simultaneously, which is particularly important when looking for Rayleigh scattering signatures in exoplanetary atmospheres (as described in Chapter 1).

While I employ long-slit spectroscopy with grism spectrographs in my re- search, other spectroscopy techniques and instruments exist.

Echellespectrographs have very high blaze angles and often very high diffrac-

tion orders are observed to increase the resolution of the spectrum. The incredibly successful planet hunting HARPS (Mayor et al., 2003) spectrograph on the Euro- pean Southern Observatory’s 3.6 metre telescope is an echelle spectrograph, with a resolution of 115,000.

Multi-object spectroscopy (MOS) allows the observer to place slits at the

locations of stars on the CCD without being restricted by a single slit. In this way MOS can extract spectra for many objects within a field of view, allowing for a greater number of comparison stars. MOS has been used on several occasions to study exoplanet atmospheres, such as the recent observation of clouds in the atmosphere of WASP-4b using the Gemini Multi-Object Spectrometers (Huitson et al., 2017).

Integral field units (IFUs) feed each pixel into a spectrograph so that each

pixel has an associated spectrum. This results in a datacube so that the 2D image has a third dimension corresponding to the individual pixels’ spectra. Recently,

Hoeijmakers et al. (2018) detected CO and H2O in the atmosphere of βPictoris b

using the SINFONI integral field spectrograph on the VLT.