2.1

NIRSpec Detector Setup and Instrument Configurations for Transiting Exoplanets

As a consequence of the bright nature of the preferred exoplanet host stars, a specific detector setup for bright targets has recently been added for NIRSpec. It uses an electronic gain of 2 e^-/ADU to take advantage of the physical full well, instead of being limited by the 16-bit ADC, as it is the case for the baseline NIRSpec detector setup. In the NEETC and throughout this paper, a maximum number of accumulated photo-electrons of 77 ke^-/ADU is used. This corresponds to a conservative (low) estimate of the dynamical range of the instrument, which is given by the effective saturation limit minus the initial bias zero point.

The up-the-ramp readout scheme used by NIRSpec detectors, called MULTIACCUM[7], is similar to the one used by HST/NICMOS. Each signal integration will start with a reset followed by a user-defined number of nondestructive frame readouts, as illustrated in Fig. 2. An exposure consists of a series of consecutive integrations. Multiple frames can be combined on-board into groups. For exoplanet observations, each group will be made up of one frame, therefore hereafter we will only refer to number of groups per integration. In most cases it will be preferable to use at least two groups per integration (reset-read-read-...). For very bright sources however, it is possible to perform integrations with a single group (reset-read), significantly improving the actual detector duty cycle.

Figure 2.

Illustration of the specific MULTIACCUM readout scheme used by NIRSpec when observing transiting exoplanets. In this example an individual integration consists of a reset followed by 3 groups each containing one frame. The exposure contains multiple integrations. The detector duty cycle is 75% as one forth of each integration is used to reset the detector. Figure from [8].

To further accommodate bright target observations, we take advantage of the fact that the spectrum from SLIT/A1600 covers only a small fraction of the detectors and hence the source can be acquired from a smaller detector area, so called subarray, or detector WINDOW mode. The subarray sizes sets the readout time of the detector, and thus the minimum exposure time.

Table 1 summarizes the 9 instrument spectral configurations, including the default subarrays, supported by NIRSpec for exoplanet observations. The low-resolution mode (PRISM) allows the full wavelength range to be covered in a single exposure. The high- and medium-resolution configurations (gratings) need at least four exposures to achieve complete spectral coverage. Spectra obtained with any of the four high-resolution configurations will present wavelength gaps, due to the spacing between the two detectors in the NIRSpec focal plane. The chip gaps corresponds to up to 0.10 µm in the spectra.

Table 1.

Overview of the key properties of the spectral configurations available in the SLIT/A1600 mode for transit spectroscopy. The magnitude limits have been estimated using gain = 2 e-/ADU and one frame per group. These values should only be used as a guideline and are still suceptible to change.

The magnitude limits listed in Tab. 1 present a worst case scenario in terms of dynamical range, where the peak of the stellar PSF is centered on a detector pixel and the shape of the spectral energy distribution (SED) results in a non-favorable normalization in the J-band. Figure 3 shows how the bright-object limit heavily depend on the spectral type of the host star.

Figure 3.

Estimated limiting J-band magnitude for all 9 instrument configurations supported by JWST/NIRSpec plotted as a function of the host-star effective temperature. These values are the current estimates and are still susceptible to change as our knowledge of the instrument improves. Stars with known transiting planets have been plotted as gray diamonds along with labels on a few the well-known objects. The panel on the right shows a cut-out of the left panel, concentrating on the limiting magnitudes from 10 to 4. Figure created with the NEETC.

3.1

Noise Model

A major challenge faced when trying to describe observations targeting SNR of several tens of thousands is that the contribution of residuals to the correction of systematic effects is often a major limiting factor. Understanding which systematics will impact NIRSpec observations and what their correction residuals will look like is extremely difficult and will likely only be possible once we have acquired in-orbit data. As a starting point, We have decided to adopt a noise model that allows us to define a so-called noise floor, corresponding to the ideal case where the contribution of systematics is absent.

Observations with current space-based facilities achieve noise levels within 20-30% of the photon-noise level and if we assume that JWST/NIRSpec observations will achieve the same level of performances, the NEETC results can be easily scaled. The noise model for the detectors used in the NEETC is based on a drastic simplification of the generic model described in [7]. In this model, the noise floor is calculated including the effects of readout noise, photon noise from the source and dark current shot noise. The equations listed in [7] reflect an up-the-ramp fitting optimized for faint sources, aiming to damp the contribution of the readout noise to the noise floor. For observations limited by the source photon noise (photon noise regime), which is the case for exoplanets, the best performance is achieved by ignoring the intermediate readouts and by using just the first and last group of the integration. This gives the very simple relation:

using t_int = t_g(n_g - 1). For the reset-read-reset option, one must use the zero point to find the count rate. This scheme improves the duty cycle as the zero level is ’added’ to the effective number of groups. The zero level noise is however not dominated by the readout noise, but by the so-called kTC noise. The total noise is in this case:

The NEETC uses σ_kTC = 60 e^- (very conservative value) and σ_read = 18 e^-.

3.2

Design

Figure 4 shows a flow chart representation of the NEETC architecture. It consists of the Core Computation model which computes effective number of groups, optimal number of groups, signal and SNR per integration. The user can input the stellar SED, instrument configuration and optionally number of groups per integration.

Figure 4.

Flow chart representation of the main NEETC modules.

A number of additional (Post-)modules compute the signal and SNR achieved over a certain amount of time. For transit and occultation, it is assumed that twice the transit/occultation time is used on the baseline observation. The results can also be binned to a uniform spectral sampling (Δλ), to facilitate the comparison of different observation modes.

Currently, the input planetary signal can be selected from a number of synthetic spectra [10]. The contribution from the planet includes thermal emission, reflection of starlight and transmission during transit. The first two components scale differently with the phase angle as the planet orbits around its parent star. Transmission and reflection are both given as contrast to the stellar brightness, whereas thermal emission is internally implemented as an absolute brightness, which is subsequently normalized to the target distance. The NEETC combines reflection, thermal emission and transmission, and adds noise based on the SNR computations done in the Core- and Post-Modules.

3.3

Exoplanet Atmosphere Models

The NEETC incorporates synthetic spectra of a few exoplanet atmospheres that serve to demonstrate the capabilities of the instrument. We have defined a list of such reference atmospheres that cover some of the expected diversity of these worlds.

The synthetic spectra have been prepared for three cases, namely: transmission, reflected starlight and planetary thermal emission. For each exoplanet, we consider two levels of aerosol-to-gas concentrations that are broadly classified as specific to optically thin and thick haze. The thick haze configuration presents a larger aerosol-to-gas ratio, which is equivalent to a higher altitude haze layer. The transmission and reflected starlight spectra have been prepared in normalized format, i.e. referred to the unimpeded stellar brightness. The planetary thermal emission spectra have been prepared in absolute radiometric units. An internal procedure normalizes the thermal emission spectra to the observer-to-star distance and to the stellar emission spectrum. Figure 5 shows the transmission, reflection and thermal emission spectra for exoplanet GJ1214b.

Figure 5.

Synthetic planetary spectra for the warm super-Earth GJ1214b, as input to the NEETC with R=4000, for optically thin and thick haze. The transit depth and reflection of starlight are both given as the contrast to the host star. The thermal emission spectrum is the flux received at a distance of 1 pc. An internal procedure normalizes the thermal emission to the observer-to-star distance and to the stellar emission spectrum.

The spectra are produced with well-tested routines (see [10]). Specific details on the routines, the atmospheric configurations and the list of available exoplanet atmospheres will be presented elsewhere.

4.1

Comparison of Instrument Configurations Based on SNR

The transit duration for GJ1214b is 52 min. The SNR for a single transit for a host star with T_eff = 3000 K, log(g) = 5.0 (cgs units) and J-band magnitude 9.750 is calculated assuming that 52 min are spent on baseline observations before and after the transit, resulting in a total exposure time of 2hr 36min per transit. This includes the time lost resetting the detector before every integration. Figure 6 shows the SNR for the low resolution PRISM/CLEAR configuration, using 1, 2 or 3 groups per integration (ng). Note that a sensitivity of better than 100 ppm around 1-2 µm is easily obtained in just one transit for a J-band magnitude 9.75 spectral type M dwarf.

Figure 6.

SNR of a NIRSpec observation of GJ1214 with the CLEAR/PRISM configuration for one transit. Twice the transit duration is spend on baseline observations, resulting in total exposure time 3x52 min. The NEETC has been run for a PHOENIX template spectrum with T_eff = 3000 K, log(g) = 5.0 (cgs units) and J-band magnitude 9.750. The three curves represents the SNR for ng = 1,2 and 3. SNR does not simply scale with ng due to changes in the detector duty cycle.

When moving from 1 to 2 groups per integration the SNR around 1-2 µm goes down, as this part of the spectrum saturates after the first group. For wavelengths larger than 2 µm the SNR goes up, as the duty cycle in this part of the spectrum goes up when using 2 instead of 1 group per integrations. In other words, the efficiency goes from 50% to 66%, which increases the amount of photons collect during the complete transit. The SNR for 3 groups per integration shows further improvements for the longer wavelengths as the efficiency is increased to 75% long ward of 2.4 µm.

Which SNR-curve is the best strongly depends on the specific science case. The NEETC will provide a visual tool for the user to compare and evaluate readout setups. From Fig. 3 it is clear that GJ1214 is close to the saturation limit for the CLEAR/PRISM configuration, therefore tweaking ng has a significant effect. For the medium and high resolution configurations however, GJ1214 does not saturate for the first four groups and changes in duty cycle efficiency are less noticeable. In this case it is advisable to select the optimal number of groups per integration.

Figure 7 shows the SNR achieved for one transit of GJ1214, for all 9 instrument configurations, for the optimal number of groups per integration, along with ng = 3 for CLEAR/PRISM. Left panel shows the SNR-curves for the inherent instrument resolution of the specific setup. In the right panel all the configurations have been re-binned to the same uniform dispersion (Δλ = 0.02 µm). The medium and high resolution setups have very similar SNR, but with missing data points for the high resolution options due to the detector gaps. It indicates that the high resolution configurations are mainly useful when R > 1300 is need or for objects too bright for the corresponding medium resolution grating.

Figure 7.

SNR obtainable for GJ1214 for all 9 instrument configurations for one transit (52 min). Left panel shows SNR for the inherent instrument resolution and right panel the SNR binned to a uniform dispersion of Δλ = 0.02 µm.

4.2

Simulated Transit and Emission Spectra

Simulations of the planetary signal obtained with NIRSpec is done using the SNR for the CLEAR/PRISM configuration with ng = 3. This option gives the most uniform SNR through out the wavelength range and allows for a good demonstration of the science that can be done in NIRSpec’s spectral range.

For a number of transit n_T, the one sigma noise-level for the planetary signal (given as contrast to the host star) is computed as σ(λ) = 1/(√n_T · SN R_T(λ) where SN R_T(λ) is the SNR for one transit/occultation as a function of wavelength. The transit depth for GJ1214b, based on the model described in Sec. 3.3, has been re-binned to the resolution of the CLEAR/PRISM configuration and is plotted in Fig. 8 with one sigma error bars for a single transit. The thin and thick haze cases for the planet atmosphere can clearly be distinguished in such an observation.

Figure 8.

Simulation of a transit observation of GJ1214b with the CLEAR/PRISM configuration using 3 groups per integration. Error bars are one sigma noise based on the SNR computed for a single transit observation of the host star GJ1214.

Detection of thermal emission and reflected starlight through secondary eclipse observations will in many cases require multiple transits, as the contrast of the combined brightness compared to the host star is considerably smaller than the transit depth. The top panel of Fig. 9 shows the planet’s reflection and thermal emission spectra as a fraction of the host star flux and binned to the instrument resolution of the CLEAR/PRISM configuration. Both the low and high aerosol-to-gas concentration (thin and thick haze) spectra are presented. A distance of 12.95 pc has been adopted from [11] and is used to convert the thermal emission from the absolute values plotted in Fig. 5 to a contrast relative to the host star. The combined planet brightness, which is the observable quantity, is shown in the lower panel of Fig. 9 with the error bars (1σ) corresponding to the observation of 40 occultations (assuming that the duration of the secondary eclipse is the same as the transit duration).

Figure 9.

Simulation of 40 occultation observations of GJ1214b using CLEAR/PRISM and ng = 3. The top panel shows the synthetic reflection and thermal emission spectra as stellar contrasts. The bottom panel shows the combined emission from the planet right before and after secondary eclipse with one sigma error bars based on the SNR computed the host star.

More observations would improve the SNR, but as shown in Fig. 9, with 40 occultations the slope of the thermal emission can be constrained. GJ1214b has a visibility window of about 110 days/year with JWST. Given its short orbital period of 1.58 days and assuming a very extensive campaign, up to 70 transits could be observed within a year. In order to discriminate between the thin and thick haze models for the reflected light, the SNR can also be improved by binning the spectra in wavelength.

For the detection of reflected starlight only, it would be beneficial to use the F100LP/G140M configuration, in wavelength range 1.0 – 1.8 μm, binned to the same resolution as that of the PRISM or lower. Judging from the the SNR curves in Fig. 7, a single transit or two could be enough to discriminate between the thin and thick haze models. Similarly, the observation can be optimized to detect thermal emission by using F290LP/G395M in the wavelength range 2.9 – 5.2 μm. We emphasize that a single spectral configuration can be used per transit and this has to be considered when comparing the use of the PRISM to that of any grating.