THE USE OF ABSORPTION CELLS AS A WAVELENGTH REFERENCE FOR PRECISION RADIAL VELOCITY MEASUREMENTS IN THE NEAR-INFRARED

Kerber et al. (2007) provide a summary of the development and use of Th–Ar hollow cathode emission lamps. The only naturally occurring thorium (Th) isotope, ²³²Th, has zero nuclear spin, leading to sharp symmetric emission lines, even at very high resolutions. The monatomic argon (Ar) gas also has a number of bright lines. Th–Ar emission lines span the UV–NIR regions, making such a lamp a very useful and convenient source of wavelength calibration. Most wavelength calibration applications using this lamp are tied to the Palmer & Engleman (1983; PE83 hereafter) measurements of the Th lines in the 280–1100 nm region. Their quoted measurement precision, ∼0.001–0.005 cm⁻¹, corresponds to an intrinsic velocity uncertainty of 15–80 m s⁻¹ per emission line (at 550 nm). For Ar lines, the wavelength measurements typically used are adopted from Norlén (1973). More recent measurements of Ar lines have been taken by Whaling et al. (1995), who extend measurements to the mid-infrared (mid-IR). Ar is not a heavy element like Th and the central wavelengths of the Ar emission lines are susceptible to pressure shifts, making them sensitive to environmental conditions in the lamp. The lines may be unstable by many tens of m s⁻¹ (Lovis & Pepe 2007), and for the highest possible precision (∼1–3 m s⁻¹), Ar lines should generally be avoided. At intermediate spectral resolutions, a further problem is line blends, because the intensity ratio of Th and Ar lines is a function of the current supplied (Kerber et al. 2007). Very stable spectrographs offer the opportunity of decreasing the internal errors associated with the original Th measurements and PE83s use of the Fourier Transform Spectrograph (FTS) at Kitt Peak National Observatory (KPNO). Stable instruments allow one to acquire many Th–Ar spectra and co-add them, thereby increasing the S/N and reducing the photon-noise uncertainties on the line centers of known lines, as well as enabling wavelength estimation of lines not initially present in the original PE83 atlas. Such a technique has been applied by Lovis & Pepe (2007) with the vacuum-enclosed HARPS high-resolution echelle spectrograph, resulting in a line list with improved wavelength precision (though inheriting the zero point of the original KPNO atlas). This improved line list has certainly helped HARPS achieve radial velocity precisions of <1 m s⁻¹ and discover super-Earths (Mayor et al. 2009).

In the NIR J and H bands Th lines are few and relatively faint, making it difficult to find accurate dispersion solutions in the J and H bands without substantial integration time. The Hinkle et al. (2001) atlas contains FTS and grating spectrograph wavelength measurements of 500 lines in the 1–2.5 μm range, and Engleman et al. (2003) derive FTS wavelengths for a much larger sample using a cooled Th–Ar cell operated at a high current. Kerber et al. (2008) also measured wavelength for Th–Ar lines for multiple cells with an FTS for use in calibration of the CRIRES instrument model. Although these atlases help to identify lines when they are detected, the Th lines in commercially available lamps are still very low in intensity. The high contrast between the Th and Ar lines leads to the bright Ar lines dominating the spectra, and these can be a source of significant scattered light. For example, the SOPHIE instrument (Perruchot et al. 2008) requires the use of a 700 nm short-pass filter to block scattered light from bright Ar lines in the infrared. For high-precision radial velocity studies, the situation is further exacerbated by the need to acquire a high enough signal level on sufficient lines to achieve a dispersion solution accurate enough to be able to measure radial velocities at a high precision. Another minor concern is that simultaneous calibration with Th–Ar also makes scattered light subtraction of echelle frames difficult. The need to have an acceptable signal on most lines leads to the strongest lines saturating and bleeding into the adjacent stellar spectrum, making reduction more complex. The relative lack of sufficient Th lines in the NIR has also been noted by Ramsey et al. (2008) in their laboratory tests with PRVS Pathfinder and these authors propose combining light from multiple lamps (most notable Ur–Ar) with Th–Ar to increase the line density available for wavelength calibration.

The United States National Institute of Standards & Technology (NIST) has designated four standard reference materials (SRMs hereafter) for use in wavelength calibration. Together these four materials span the C and L telecom wavelength bands and have ∼200 isolated sharp lines in the 1510–1630 nm wavelength region of the H band. Table 1 lists these NIST SRM gas cells, their effective wavelength coverage, and the number of lines with NIST-certified wavelengths. These gas cells are commercially available and have an effective absorption path length of 5–80 cm. The low-pressure H¹³C¹⁴N (Swann & Gilbert 2000) and ¹²C₂H₂ (Swann & Gilbert 2005) cells have been primarily designed for high-resolution application and have narrow line widths of 7–15 pm, essentially unresolved at spectral resolutions as high as R = 50–70 k at 1550 nm. The high-pressure CO gas cells were originally designed for use with an instrumental resolution of 0.05 nm and have line widths of 50 pm (Swann & Gilbert 2002). Decreasing the cell pressure can easily make the lines sharper, if necessary, and increasing cell length can increase absorption for unsaturated lines. These gas cells are available coupled to single-mode fibers with standardized FC/PC connectors for light input and output, allowing the CO gas cells to be used in a multipass configuration, achieving 80 cm of absorption length with four passes through a compact 20 cm cell. The use of the single-mode fiber of input and output makes it easy to pass continuum light through multiple cells to obtain an imprint of the absorbtion lines over larger wavelength regimes. The use of the fibers is not necessary, but is a convenience.

Modern high-resolution spectrographs generally use coarse-ruled echelle gratings that have high blaze angles (R2–R4 or tan θ_B = 2–4 is fairly typical). To estimate the achievable accuracy of wavelength calibration, we consider an R2 echelle spectrograph capable of a resolution of R = 50 k at 1600 nm. We assume a four pixel sampling the FWHM of the Gaussian resolution element. We assume a grating with a groove density such that a wavelength of 1550 nm corresponds to an order number of ∼100. While such low groove densities are not available in commercially ruled echelles, they can be created on silicon immersion gratings (Ge et al. 2006) enabling high dispersion as well as the ability to pack all orders from the H band into a single 1 k × 1 k detector. Figure 1 shows the expected absorption spectra from these gas cells with such an instrument. For HCN and C₂H₂, we have used the high-resolution spectra scans from Swann & Gilbert (2000, 2005)¹ and convolved them with a Gaussian instrument profile (R = 50 k at 1600 nm). For CO the full spectral scans are not available, and we have simulated the data using line centers and broadening coefficients from Swann & Gilbert (2002). We have not convolved the simulated CO data with the Gaussian instrument profile since the measurements were obtained at a lower resolution than R = 50 k. We would expect these lines to be slightly deeper when observed at the resolution we assume for the spectrograph. Figure 2 shows a schematic arrangement of the gas cells, coupled with optical fibers, that can be used to generate the absorption spectra seen in Figure 1.

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The effective free spectral range of each order, ∼λ/m, corresponds to 15 nm bandwidth at 1550 nm. As can be seen from Figure 1, the HCN cell alone provides 20 sharp reference lines within ±8 nm of the order center, a region where the blaze efficiency is expected to be >40% of peak (Schroeder 1987). In reality the echelle order spans a larger wavelength coverage than ∼λ/m on the CCD, making more lines accessible for wavelength calibration. The design of echelles also leads to some wavelength overlap between adjacent orders, allowing the same line to be used to calibrate more than one order. Gratings operating at lower order numbers will have even higher-line densities per order if the orders fit on the detector array.

Typical echelle spectra span 7–12 pixels in the slit direction, and we assume 7 pixels here. Assuming that the continuum light source is bright enough (discussed in detail later), a typical continuum S/N of 200 pixel⁻¹ is a reasonable assumption, also assuring that one is operating in the linear regime in NIR detectors (which typically have quantum wells of 100 k). The data reduction process will optimally combine all 7 pixels in the slit direction into a single pixel with an S/N of $200\sqrt{7}$, or ∼500 per pixel, in the extracted one-dimensional spectrum. Although the actual shape of the absorption line is a Voigt profile, we can approximate the line as a Gaussian for the purpose of estimating the velocity precision. Following the procedure outlined in Butler et al. (1996) for calculating the photon-noise-limited velocity precision yields an error of 24 m s⁻¹ for a line with a depth (after convolution with the spectrograph instrument profile) of 20%. So, the use of ∼20 lines reasonably well spaced across the echelle order can, in principle, enable wavelength calibration accuracy at the level of ∼5 m s⁻¹ per echelle order. This uncertainty is smaller than the photon-noise error expected per order on most stars observed and is therefore sufficient. Many HCN and C₂H₂ lines are deeper than 30%, while the CO lines have lower depths of ∼ 10–18% and have line widths broader than the spectrograph resolution, leading to typical errors of 25–50 m s⁻¹ per line. However, these calculations are specifically for the NIST SRM cells, and custom-made longer pathlength CO cells (or more multiple passes through the same cell) can create deeper absorption lines if they are required. We speculate that significantly larger path lengths than provided by conventional cells may be achievable in the future by directly using long lengths of gas-filled hollow-core photonic crystal fibers now under development (Benabid et al. 2005; Tuominen et al. 2005). These gas cells can also be used at higher (or lower) spectral resolutions than the R = 50–70 k we have considered here. To demonstrate this, we follow the prescription of Bouchy et al. (2001) to calculate a quality factor (Q) that is an estimate of the intrinsic radial velocity information contained in the spectrum. The Q factor depends on factors such as the spectral richness of the wavelength region being considered, the sharpness of the absorption lines, as well as the instrument profile. For a given wavelength region, the limiting radial velocity precision (σ_RMS) is given by

$$\begin{equation} \sigma _{\rm rms} = \frac{c}{Q\sqrt{N}}, \end{equation} \tag{ 1 }$$

where c is the velocity of light, Q the quality factor, and N is the total number of photons collected. As expected, the radial velocity precision is proportional to $\sqrt{N}$.

We calculate the Q factor for the HCN SRM for different spectral resolutions using the wavelength range 1524–1565 nm. Figure 3 shows the Q factor as a function of the spectral resolution. At low spectral resolutions all the individual lines blur into each other, leading to very low velocity information content. At intermediate spectral resolutions (R = 50–100 k) the information content is a strong function of spectral resolution, as the absorption lines, which have line widths of 7–12 pm, are still unresolved. When the spectral resolution exceeds 200,000, the individual lines themselves begin to be resolved and the Q factor begins to plateau, asymptotically approaching its finite value at very high resolutions. Beyond a resolution of R = 300 k, the lines are fully resolved, and the Q factor increase is minimal. Currently planned NIR high-resolution instruments all operate in the R = 20–100 k regime, and the HCN and C₂H₂ SRM cells are well suited to these. The commercially available CO cells, however, have larger line widths, making them less desirable for the higher spectral resolutions. Custom cells, however, can easily be manufactured. Other than high-resolution spectrographs, the absorption cells can be used in other NIR instruments. Planned H band spectrographs such as the fiber-fed APOGEE instrument for SDSS-III (Allende-Prieto et al. 2008), or dispersed fixed-delay interferometer instruments (Guo et al. 2006) in the NIR can use such cells for wavelength calibration.

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It is important to recognize that the absorption line spacings in these cells are sparse when compared with absorption line densities in typical M dwarf spectra. The high continuum S/N is absolutely necessary to ensure that the error in the wavelength calibration is smaller than the achievable precision on M dwarfs. This is one of the reasons we have discussed this approach only in the context of a fiber-fed instrument. If such cells were to be used for simultaneous calibration by passing starlight through them, then the achievable precision may be severely limited by the reference rather than the star. Such an approach should be considered only when the need to calibrate out instrument drifts is more important than achieving close to photon-noise-limited precision on the stellar target.

The vacuum wavelengths of the line centers for the species in the SRMs can be, and have been, measured very accurately at low temperatures and pressures. For example, the measured vacuum wavelengths at low pressure for the 3ν lines of ¹²C¹⁶0 (Picqué& Guelachvili 1997) agree with the theoretically calculated values from the HITRAN database (Rothman et al. 2005) to 0.02 pm (or <4 m s⁻¹ at 1.6 um). For higher cell pressures, the lines begin to broaden and also shift due to interaction of molecules during elastic collisions. Accounting correctly for this pressure shift is the dominant source of uncertainty for determining the line centers of the absorption lines. This shift is accounted for by explicitly measuring it at various pressures and extrapolating a linear relationship. The resulting line centers for the higher pressure CO gas SRMs are certified by NIST to 0.4–0.7 pm (all 2σ errors), HCN from 0.04 to 0.24 pm, and C₂H₂ from 0.1 to 0.6 pm (Swann & Gilbert 2000, 2002, 2005). So the line centers themselves are known to an accuracy of 4–60 m s⁻¹ (1σ errors), quite comparable with the Th–Ar emission line errors quoted by PE83. A significant fraction of this error is actually the uncertainty in the pressure of the cells themselves, which may be possible to better constrain with custom-made cells. If a higher accuracy is really necessary, then high-resolution FTS spectra can be used to independently calibrate the cells. Instruments known to possess high stability over a few hours can also take the approach of Lovis & Pepe (2007) by acquiring many Th–Ar exposures to build up high S/N to determine a wavelength solution, and using that solution to determine the line centers of the absorption cells.

Of perhaps more concern is the inherent stability of the absorption lines themselves. A change in operating temperature affects the pressure of the cell, which, due to the pressure shift, leads to a shift of the line center. The wavelength shift Δλ due to pressure at temperatures T and T_m is related by (Swann & Gilbert 2000)

$$\begin{equation} \Delta \lambda (T) = \Delta \lambda (T_m) \sqrt{(T/T_m)}. \end{equation} \tag{ 2 }$$

A one degree change in temperature at a operating temperature of 296 degrees leads to a 0.17% change in the pressure-induced wavelength shift. For the high-pressure CO cells, the pressure-induced shift is at most 3 pm, and that one degree change leads to a line shift of ∼0.005 pm, which is a sub-ms⁻¹ effect. Given the fairly loose temperature requirements the entire enclosure containing the cell assembly (Figure 2) could be temperature stabilized to ±1 °C using heating elements running in a proportional-integral-derivative (PID) loop with temperature sensors. If necessary, temperature control to ±0.1 °C is easily achieved if each cell is stabilized independently with a heating element wrapped around it and can make temperature effects negligible. The absorption cells are relatively immune to any other environmental effects since they are contained in sealed glass tubes. Unlike Th–Ar lamps, absorption cells do not have a warm up period (typically 15–30 min) where the lines are not stable enough for precision applications, or a limit on their operating lifetime. They are also passive, requiring only a light source for operation.

The single-mode fiber-coupled gas cells makes for a compact and easily configurable set of wavelength references, but the narrow core and spatial filtering properties of such fibers make them inherently difficult to couple to traditional illumination sources like quartz lamps. A number of white-light sources coupled to single-mode fibers are now commercially available for the telecom S, C and L bands (1400–1630 nm), which are well matched to the spectral regime covered by these reference cells. Alternatively, tunable diode lasers are also available that can be used to scan through the regions of interest at many times per second. Such sources may easily be adaptable for spectroscopic applications in astronomy. The science fiber coupled to the spectrograph needs to be multimode to couple effectively to the telescope. To ensure that the science and calibration fiber illuminate the spectrograph optics in the same way, the calibration fiber should be identical to the science fiber. Expanding the light from a single-mode fiber to the correct focal ratio and coupling into the multimode science, and calibration fibers pose no major challenge if this is deemed necessary. As mentioned before, the use of single-mode fibers is not mandatory if multi-pass configurations are not required. In such a case, a multimode fiber is adequate, still enabling the light to be passed through multiple cells. The penalty of this approach is the unwieldy 80 cm length of the CO cells, and the advantage is that a conventional quartz-lamp light source is quite sufficient.

The NIST standards are deliberately designed to span as large a range as possible in the telecom bands. For such applications, line densities are not as critical as for the broadband wavelength calibration application in astronomy. Available line densities and wavelength coverage can be increased by using isotopologues of these molecules, which exhibit similar levels of stability but have absorption lines at different wavelengths. For CO the NIST cells are specifically chosen to be ¹²C¹⁶O and ¹³C¹⁶O. The HITRAN database contains line transition parameters for four other CO isotopalogues: ¹²C¹⁷O, ¹²C¹⁸O, ¹³C¹⁷O, and ¹³C¹⁸O. Figure 4 shows the absorption lines for all six CO isotopologues listed above. Together, they substantially increase the line densities available for calibration in this region of the H band and extend coverage to longer wavelengths. The filled circles in the figure correspond to zero-pressure line centers from the HITRAN database. Transmission values are all scaled to that of ¹²C¹⁶O because the purpose of the figure is to illustrate the increase in density and coverage. Actual transmission is best derived from experimental data for such cells and the length required for gas cells of the four additional isotopologues may be different than those of ¹²C¹⁶O and ¹³C¹⁶O. Even higher line densities and coverage than shown here may be possible using ¹⁴CO, even though ¹⁴C is unstable and undergoes β decay to ¹⁴N with a half-life of ∼5730 years. Similarly, many known isotopalogues of ¹²C₂H₂ and HCN can also be used to generate additional absorption lines. While the use of isotopologues is attractive for increasing line densities, the pressure-shifted line centers for many of these species need to be determined before they can be used. Bootstrapping a wavelength solution off the known NIST calibrated lines is possible for very stable instruments, as described earlier. In general, however, the isotopologue gas cells should also be calibrated independently, like the NIST SRMS.

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Thus far we have primarily discussed the use of the NIST absorption gas cells and their isotopologues in the NIR H band. As discussed earlier, gas cells calibrations in this wavelength regime exist primarily due to the needs of the telecommunication industry. Although such well-characterized cells are not commercially available in the J band, it is worth briefly discussing the molecules that are promising possibilities in this wavelength regime as well. Hydrogen fluoride (HF) has two series of sharp absorption lines in the 867–909 nm and 1257–1340 nm regions. Methane and water have lines in the J and H, but both are also atmospheric species. D'Amato et al. (2008) have demonstrated that HCl, HBr, and HI exhibit absorption lines in the 1.2–1.4 μm region, though getting deep absorption lines requires path lengths approaching 1 m. Fiber-fed gas cells similar to the NIST SRMs can easily be used to provide the path lengths necessary for moderately deep absorption lines in such cases. HCL has two series of lines in the 1185–1240 nm region and 1720–1870 nm regions, which well-complements the molecules we have discussed for the H band and spans parts of the J band.

For practicality, the gas cells must not be toxic or lethal since a leak, or a breakage, would significantly impact operations. Acetylene is not known to be toxic even if inhaled in large concentrations. Hydrogen cyanide is lethal in large amounts since it inhibits enzymes in the electron transport chain of cells, thereby making normal cell functioning impossible. The trace amounts of HCN found in the NIST SRM cells is quite safe. Even if the HCN contents on the entire SRM gas cell were to be respired, the increase in the cyanide content in blood would be minimal. Inhaled CO is lethal in large concentrations since it binds to hemoglobin, preventing oxygen transport. However, CO is also harmless in the small trace amounts found in the gas cells. Methane and water are commonly occurring atmospheric species and are not toxic. HF is very corrosive and attacks glass. HF gas cells have to be specially designed with materials that do not react with the gas and the cells have to be handled carefully. Such HF cells have been in use for calibration for a number of years now. The gas cells we have explored here are all safe to use in a laboratory or a confined environment, and breakages or leaks, if they happen, are not a cause for major concern.