Step by step ETC calculation instructions for the JWST NIRSpec BOTS mode observation of WASP-79b are presented and discussed in this article.

See also: NIRSpec Bright Object Time-Series Spectroscopy, JWST Exposure Time Calculator Overview, Proposal Planning Video Tutorials

The JWST Exposure Time Calculator (ETC) performs signal-to-noise ratio (SNR) calculations for the JWST observing modes. Sources of interest are defined by the user and assigned to scenes and are used by the ETC to run calculations for the requested observing mode.

The "NIRSpec BOTS observations of WASP-79b" Example Science Program focuses on selecting exposure parameters to detect the exoplanet transit at the desired SNR. An accompanying ETC workbook on which this tutorial is based can be downloaded as a sample workbook from the ETC user interface.

The optimal exposure specifications (e.g., numbers of groups and integrations) are the input needed for the Astronomer's Proposal Tool (APT) observation template, which is used to specify an observing program and submit proposals.

---

Define Source and Scene in the ETC

See also: JWST ETC Scenes and Sources Page Overview, JWST ETC Defining a New Source, JWST ETC Source Spectral Energy Distribution

In the "Scene and Sources" tab, you can edit the sources within your scene. In the Scene box, there are tabs for setting the source continuum, shape, and flux normalization. Below is the specification for this case. The scene was renamed "WASP-79b scene".

Table 1. Source specifications for Gliese 1214 in the JWST ETC.

---

Select NIRSpec BOTS calculation

See also: JWST ETC Creating a New Calculation, NIRSpec Bright Object Time-Series Spectroscopy, NIRSpec BOTS Operations, NIRSpec Detector Recommended Strategies, JWST ETC Backgrounds

In the ETC, calculations for the NIRSpec BOTS mode are selected via the option Bright Object Time Series from the NIRSpec drop-down menu. 

In the Background tab, enter the target coordinates that were fetched from the Gaia DR2 archive (RA = 04:25:29.0167, Dec = -30:36:01.5669) and select the Low background setting, which corresponds to the 10th percentile of the sky background. This option can be toggled to examine the influence of the background on the observations.

---

Select instrument parameters

See also: NIRSpec Dispersers and Filters, NIRSpec Fixed Slits, NIRSpec BOTS Wavelength Ranges and Gaps

In the Instrument Setup panel, enter the required filter/grating settings and the aperture in the NIRSpec focal plane. For BOTS, all observations use the S1600A1 aperture, a 1.6" square-shaped aperture. As you are aiming to observe between 3–5 µm, select the G395H/F290LP grating/filter pair. This provides coverage from 2.87 to 5.17 µm with a resolving power of ~2,700.  The plot in the Instrument Setup panel shows the system throughput over the selected band; this plot is useful for verifying that the wavelength coverage is as expected.

---

Adjust exposure parameters

See also: NIRSpec Detector Recommended Strategies, JWST Time-Series Observations TSO Saturation, NIRSpec Detector Readout Modes and Patterns, NIRSpec Detector Subarrays

In the Detector Setup panel, select the appropriate subarray, the readout pattern, number of groups, integrations and exposures. Note that time-series observations (TSOs) are recommended to be executed in a single exposure for optimal stability and efficiency. As the number of integrations is determined by the length of the transit or eclipse event that you want to observe (with each integration treated as an individual observation in the time series), perform the calculation for Integrations per Exposure = 1.

The recommended subarray for BOTS observations using gratings is SUB2048, which is selected from the Subarray drop-down list. If the target is so bright that it will saturate in < 3 groups, a smaller subarray should be selected (SUB1024A or B); for WASP-79b this is not the case. As the target is bright, choose the fastest readout pattern and do not average frames into groups, NRSRAPID. Select the wavelength of interest to be 4.5 µm in the Strategy panel; both the SNR and Reports pane numbers will be returned for this value. Also in Strategy, set the Aperture Full-Height, over which the flux will be co-added, to 0.30 arcsec. 

As the main concern is to avoid saturation, you can run an initial calculation (Calculation #1) with NGroups = 10 (integration time of 9.94 s). From the Reports pane, you'll see that the maximum number of groups before saturation occurs at NGroups = 41. Note that reporting of saturation in the ETC assumes 80% of full well, i.e., includes some safety margin.

From the output image labeled "Detector", you'll see a maximum count rate of ~1800 e^-/s. If you aim to fill the brightest pixels to 50% of their full well capacity (approx. 65,000 e^-), your integration time should be 65,000/2/1800 ≈ 18.1 s, or 19 groups. This produces SNR at 4.5 µm of ~101. 

Determining number of integrations

You're planning to observe WASP-79b for enough time to allow for sufficient detector settling time (currently estimated to be ~30 minutes; see JWST Time-Series Observations Noise Sources). You'll also allow for some margin if the observations do not start exactly when expected or if the eclipse occurs at a slightly different time than predicted.Use the dwell time (T_dwell) to calculate this exposure time: T_dwell ~ 0.75 hr + MAX(1 hr, T₁₄/2)(before transit) + T₁₄ (eclipse) + MAX(1 hr, T₁₄/2)(after transit) + 1 hr (timing window), where T₁₄ is the transit duration.

For WASP-79b, T₁₄ is 1.0152 hours (60.91 minutes¹), giving a total exposure time of 4.7652 hours.

From entering the SUB2048 Subarray and 19 Groups/Int with a Readout Pattern of NRSRAPID in the Astronomer's Proposal Tool, you'll see that the exposure time for 1 Integrations/Exp is 18.06 s with these exposure specifications. Thus, you'll need 950 Integrations/Exp to cover the exposure window.

Interpreting SNR results

See also: JWST ETC Residual Flat Field Errors 

The scientific measurement for an exoplanet transit is the "transit depth", which is a temporal measurement.  The spectroscopic result is therefore a relative comparison between a contiguous sequence of time-series measurements, i.e., transit depth over wavelength. It is equivalent to measuring variations in the stellar spectrum over time.

The goal in this example is to achieve a relative precision of ~120 parts per million (ppm) on the transit depth per "spectral bin" or "channel" around the CO+CO2 molecular bands at ~4.5 µm, after subtracting the primary transit from the out-of-transit data. A "spectral bin" or "channel" is a set of pixels across the spectrum that you will combine ("bin") to maximize the temporal precision per spectroscopic channel, without losing the spectral features in which you are interested in measuring. Since the molecular bands are relatively broad and high resolution capabilities are not required to detect these transitions, you'll bin by factor of 60 (degrading the spectral resolution from ~2700 to ~45).

If you assume a box-shaped transit, the transit depth precision (Precision_depth) can be approximated by:

$$//<![CDATA[ \begin{array}{l}\displaystyle Precision_{depth} \sim Precision_{point} \times \sqrt{1/N_{out} + 1/N_{in}} = \sqrt{1/N_{out} + 1/N_{in}}/SNR_{point}\end{array} //]]>$$

where Precision_point is the photometric precision per data point, N_out is the number of data points (integrations) out-of-transit, N_in is the number of data points (integrations) in-transit, and SNR_point is the SNR in one integration.

The time spent out-of-transit is 3.75 hours and the time spent in-transit is 1.0152 hours. For this example science program and this observational setup (Groups per integration = 19, NRSRAPID readout, and SUB2048 subarray), these times correspond to  N_out = 748 integrations and N_in = 202 integrations. From the ETC, you found SNR_point = 101, such that Precision_depth is ~ 0.000785 = 785 ppm. When binning by a factor of 60, Precision_depth improves to 785/√60 = 101 ppm.

Note that the ETC includes an error term for residual flat field errors which affects long exposures. For exposures longer than ~10,000s, ETC calculations have a "noise floor" above which an increase in exposure time no longer results in an increase in SNR that scales with the square root of the exposure time. Since you are making relative measurements on the same pixels for exoplanet transit spectroscopy, the precision is not affected by the "noise floor" imposed by the residual flat field errors. 

Note also that the ETC does not fully account for systematic errors that affect the real spectrophotometric precision.

---

Target acquisition

See also: JWST ETC NIRSpec Target Acquisition, NIRSpec Target Acquisition, NIRSpec Wide Aperture Target Acquisition, JWST Pointing Performance

Ideally, for time-series observations, the target should be accurately placed into the aperture or subarray, particularly when the transit event will be observed over multiple epochs. This allows for the best control of systematic errors in the pixels covered by the science target. For NIRSpec BOTS observations, the default target acquisition (TA) mode is the wide aperture target acquisition, or WATA. The user has a choice of filters and subarrays, but the TA image will always consist of a single integration using 3 groups. As the target WASP-79b is bright, select the narrowest available filter (F110W) with the smallest available subarray (SUB32).

In the ETC, these details can be entered in a new calculation from the "NIRSpec" menu, labelled "Target Acquisition". Select the same source, scene and background level as for the BOTS calculation, and enter the above selections in the relevant fields under Instrument Setup and Detector Setup. Running the calculation returns a warning regarding saturation: WASP-79b is in fact too bright for a target acquisition with WATA. Therefore, use a nearby source for the target acquisition.

From querying the 2MASS Point Source Catalog, you'll find a source with a J-band magnitude of 14.46 (Vega): 2MASX J04253078-3035541. Fetching the coordinates of this source from the Gaia DR2 catalog (RA = 04:25:30.7764, Dec = -30:35:53.8902), you'll find that it is ~24 arc seconds away from WASP-79b. This distance is under the visit splitting distance in APT, making the position for the source acceptable for a target acquisition.

From querying SIMBAD, you'll find that this source is a nearby galaxy rather than a star. STScI cautions that any structure within the galaxy on the scale of 0.1" could affect the fidelity of the target acquisition's performance in centering the galaxy in the WATA aperture. In such cases, blind pointing might be preferable over a target acquisition. In this case, this example proceeds with this source for the TA to illustrate the process of crafting a BOTS proposal with a target acquisition, noting this caveat for serious consideration for proposals to be submitted.

Create a source and scene for this offset source ("2MASX J04253078-3035541" and "W79-TA scene", respectively). Since you will use the F110W filter for the target acquisition, assume an SED shape of a flat continuum normalized to the 2MASS J band magnitude of 14.46 (Vega) in the Bessel system. You will find that with the F110W filter, the SUB32 subarray and the NRSRAPID readout pattern, you obtain a SNR > 30 on the TA (Calculation #2), ensuring the target acquisition will succeed (a SNR > 20 is recommended for target acquisitions).

---

Links

2MASS All-Sky Release Database

Simbad entry for 2MASX J04253078-3035541

Gaia DR2 catalog

---

---