Spectroscopy involves measuring the flux of an object over a range of wavelengths. This technique can yield information impossible to measure with photometry. Spec- troscopic observations are performed using a spectrograph. In a spectrograph the light is first passed through a slit, located at the focus of the telescope. The diver- gent beam is collimated by a collimator mirror (or lens) and sent to a dispersing element, usually a diffraction grating. The diffracted light is then sent to a camera which focuses it onto a detector (e.g a CCD).
Spectroscopy is a powerful tool for analysing stellar objects and vital for determining binary parameters. However, as with photometry, the data need to be properly calibrated and reduced before any analysis can be performed. The following
Figure 2.6: Raw image of a stellar spectrum taken using GMOS on the Gemini North Telescope. The star is the bright line across the centre, sky emission lines run perpendicular to it. The dark region x <35 is an overscan region and can be used to estimate the bias level. The sky level will be measured between the green lines whilst the star’s flux will be measured between the red lines.
sections outline the calibration steps for reducing spectroscopic data.
Bias and dark-current subtraction
Bias subtraction and dark current removal are performed in the same way as pho- tometric reduction. Most spectrographs have an extended region on the chip which is not exposed to light. This overscan region can be used to measure the bias level for each frame individually (Figure 2.6).
Flat-fielding
The concept of flat-fielding remains the same for spectroscopic data, although there are slight differences. Flat field spectra are usually obtained using a Tungsten lamp located inside the spectrograph. However, the Tungsten spectrum in not flat since it is modulated by its intrinsic, blackbody-like spectrum. Therefore, the flat field frame is collapsed along the spatial direction and the 1D spectrum is fitted with a polynomial. The 2D frame is then divided by the polynomial and applied to the science frames.
Spectrum extraction
Figure 2.6 shows a raw science image obtained with a spectrograph. The target’s spectrum runs across the centre of the CCD, although not precisely parallel to the rows due to a small tilt introduced by the optics. A low-order polynomial is fitted to the target spectrum to measure this tilt. Regions either side of the object spectrum are selected to use to measure the sky level (the green regions in Figure 2.6). For each
column a polynomial is fitted to the sky and interpolated in the region containing the target spectrum. A profile is fitted to the target region, this profile is used to assign weights to each pixel. Finally, the background is subtracted and the object extracted using the determined weights in the method outlined by Marsh (1989).
Wavelength calibration
In order to properly analyse the extracted spectrum we need to convert the x-axis from pixels to wavelength. This is achieved by extracting an arc spectrum. These are exposures of emission line lamps with numerous spectral lines with precisely known wavelengths. Examples are CuNe, CuAr or ThAr lamps. The position of each identified line is fitted and compared to the reference wavelength. A polynomial (usually of order 5-7) is fitted to determine the transformation between pixels and wavelength. This transformation is then applied to the science spectra.
Often the arcs will drift during the night, and can be affected by the position of the telescope. Common practice is to observe an arc spectrum both before and after the science exposure and interpolate in time between them for the science spectrum.
Flux calibration
Similar to photometry, the conversion from counts to flux units requires the obser- vation of a standard star. For spectroscopy these spectrophotometric standards are constant stellar sources with well known spectra, observed using a wide slit. The observed spectrum is compared to the template spectrum and the difference is fit- ted with a spline. The fit is then applied to the science spectra. This approach can remove the instrumental response fairly well. However, since most science spectra are taken with a narrow slit (to achieve the best resolution), some of the light from the target is lost on the slit. These slit losses, and variations in conditions, make absolute flux calibration of variable sources difficult.
One approach to improve the flux calibration of a variable source is to use its light curve. For example, if we fit models to flux calibrated light curves of a source in a number of different filters then we can predict what the flux should be over a range of wavelengths during the spectroscopic observations (if the source’s light curve is regular and periodic). Using the known filter profiles we can derive synthetic fluxes from the spectra for those filters and compare them with the photometric models. The difference between the synthetic and model fluxes can then be fitted with a low- order polynomial, which can be applied to the spectrum. This corrects for variable
Figure 2.7: A spectrum of the B7 starσAri, showing both real features (the hydro- gen Paschen series) and telluric absorption features.
extinction across the wavelength range, as well as variations in seeing.
Telluric correction
The Earth’s atmosphere is not completely transparent, even in the visual wavelength range. Figure 2.7 shows forests of lines appearing at∼6900˚A,∼7600˚A and∼9500˚A as well as other places throughout the spectrum. These are caused by oxygen and water vapour in the atmosphere and may need to be corrected for in some cases, this is particularly important for the sodium doublet at∼8200˚A.
Telluric standards are used to correct for these features. These are observa- tions of stars with relatively featureless spectra. The telluric spectrum is continuum normalised, using a spline fit or model spectrum, leaving just the telluric features. One problem is that many of the absorption features are saturated and hence their strength will not be linearly proportional to airmass. This can be somewhat cor- rected for by using a power law scaling, or trying to minimise the scatter in a well defined telluric region (e.g. the deep feature at ∼ 7600˚A). This only really works for low to medium resolution data. Applying a telluric correction can restore the original shape of the spectrum, but these regions are much noisier due to the lower number of original counts.
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Echelle spectroscopy
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Echelle spectrographs work on the same principles as normal slit-based spectro- graphs but have the advantage of large wavelength coverage and the potential to reach very high resolution. An ´echelle spectrograph works at very high diffraction orders (e.g. n ∼ 100) and introduces a cross-disperser to separate and stack the
Figure 2.8: A raw ´echelle spectrum taken using X-Shooter at the VLT. The object spectrum is the dark, highly curved lines in the centre of each order. There are 16 orders in total, with the shortest wavelengths at the bottom. Also visible are a num- ber of sky lines running perpendicular to the objects spectrum. This image covers the NIR region (1.0−2.5 microns) and the deepJ and H atmospheric absorption bands are visible in the 8th and 13th orders up.
orders. An example of a raw ´echelle spectrum taken using X-Shooter is shown in Figure 2.8. X-Shooter (D’Odorico et al., 2006) is a medium resolution spectrograph and works at diffraction orders ofn ∼20 (c.f. the high resolution ´echelle spectro- graph UVES (Dekker et al., 2000) which works at n ∼ 120). In Figure 2.8, the bottom order is in fact the highest order (n= 26) and contains the shortest wave- length information. The order above this (n= 25) contains longer wavelength data, but there is a region of wavelength overlap.
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Echelle spectroscopy requires two additional steps beyond those used for normal spectroscopy. Firstly, each order must be identified and traced. For the highly curved orders seen in X-Shooter this requires resampling each order. The transformation from pixels to wavelength and slit height must be calculated for each order. Secondly, the orders must be combined. A weighted average is usually used for those wavelengths in the overlap regions.
An ´echelle grating produces a spectrum that drops as one moves away from the blaze peak, this is known as the blaze function. The left hand panel of Figure 2.9 shows a non-flat fielded spectrum. The peaks are caused by the blaze and are much larger than the genuine stellar features. Applying a flat field correction essentially removes the blaze. However, this removal is not perfect and a residual ripple can
Figure 2.9: Left: a non-flat fielded ´echelle spectrum of a white dwarf. Right: the same spectrum but divided by the flat field frame. This demonstrates the importance of using a flat field frame to correct for the blaze function.
often be seen in the final spectrum (this is a particularly large problem for UVES data). We can attempt to remove this ripple by fitting it with a sinusoid of the form
B(λ) = a0+a1sin(2πφ) +a2λsin(2πφ) (2.2)
+a3cos(2πφ) +a4λcos(2πφ).
The phase (φ) can be calculated by identifying the central wavelength of each echelle order. Then using the relation
λn(O−n) =c, (2.3)
wherec and O are constants and λn is the central wavelength of order n, gives us
the phase. Since the phase is now known, Equation 2.2 reduces to a simple linear fit.