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## Exposure Time Calculator See also: Video TutorialsThe JWST Exposure Time Calculator performs signal-to-noise (SNR) calculations for the JWST observing modes. Sources of interest are defined by the user and assigned to scenes which are used by the ETC to run calculations for the requested observing mode. For the "NIRISS SOSS Time-Series Observations of HAT-P-1" Science Use Case, we focus on selecting exposure parameters to detect the exoplanet transit at the desired signal-to-noise ratio (SNR). We start by defining a scene for the SOSS calculation and then describe how to run ETC calculations to determine the appropriate MULTIACCUM exposure parameter to input to the Astronomer's Proposal Tool (APT) observation template, which is used to specify an observing program and submit proposals. ## Define ETC scene
We first define a source in ETC that emulates the HAT-P-1 system. After creating and loading a new ETC workbook, open the "Scenes and Sources" tab, and click on the "default source" in the "Select a Source" pane so that we edit its properties. To emulate a source whose properties mimic HAT-P-1, we define the continuum to be a Phoenix Stellar model, choosing a star with spectral type G0V, in the "Continuum" tab in the Source Editor. We renormalize the source to a Vega magnitude of K = 8.858 in the Johnson filter (see Figure 1).
## Run ETC to determine exposure parameters for required SNR
## Observing goals of time series observationsThe 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. Our goal in this example is to achieve a relative precision of <50 parts per million (ppm) on the transit depth per "spectral bin" or "channel," after subtracting the primary transit from the out-of-transit data. Atmospheric models (see PandExo) predict that this should provide a useful signal-to-noise on the exoplanet atmospheric spectroscopic signal (~100-250 ppm). A "spectral bin" or "channel" is a set of pixels across the spectrum that we will combine ("bin") to maximize the temporal precision per spectroscopic channel. To maximize the relative precision between the in-transit and out-of-transit flux (over time), we need to observe the science target long enough to observe the transit, plus a window of time before and after the transit. For this source, the transit duration is 2.784 hours. We will therefore choose a transit window of 9.352 hours (33667.199 s), which is 3 times the transit duration + 1 hour – for "detector settling" (see Noise Sources for Time-Series Observations). ## Determining number of groups and number of integrations
To determine NGroups To determine the onset of saturation, update the "Number of Groups per integration" to 2, the lowest permissible number of groups in ETC (Figure 3). To efficiently repeat this calculation by only increasing the number of groups, use Batch Expansion: in the "Expand" drop-down menu, we select the "Expand Groups" option, set the starting number of groups to 3, and leave the step size and number of iterations at their default values of 1 and 5, respectively (Figure 4). Clicking "Submit" will initialize additional calculations for 3 ≤ NGroups ≤ 7.
_{sat} = 3. Our optimal number of groups (NGroups_{sat}/2, rounding up) is 2, corresponding to an exposure time of 16.48s, for a SNR per pixel of ~289. To fully cover the transit window of 9.352 hours (33667.199 s), we need 2042 integrations.
## Interpreting SNR results
To estimate the SNR for the desired exposure setup that covers the transit window, we use the Poissonian approximation: we multiply the SNR results above for NGroups = 2 and NIntegrations = 1 by the square root of the increase the exposure time. In NISRAPID mode, there is 1 frame per group, so the exposure time for 2042 integrations increases by a factor of 2042, and the SNR increases by √2042. The SNR for the full transit window is thus 293 × √2042 = 13240. Because we are making a relative measurement, we are comparing the "before/after" window with the window during the transit. The accuracy of the transit depth is defined as SNR We will bin the spectrum by 10 pixels, which increases the temporal precision by √10, which results in a precision of 34 ppm. This precision is high enough to measure the average exoplanetary atmosphere beyond the 3σ level. Note that the ETC includes an error term for residual flat field errors which affects long exposures. For exposures longer than ~10,00 0s, 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 we are making relative measurements on the same pixels for exoplanet transit spectroscopy, our precision is not affected by the "noise floor" imposed by the residual flat field errors. Thus, using the Poissonian approximation above provides a better estimate of the SNR than the ETC results for 2042 integrations. ## Target acquisition
A target acquisition (TA) must be performed when using a SOSS subarray so that the target is precisely positioned on the detector. A signal-to-noise ratio (SNR) ≥ 30 is recommended to achieve a successful TA, which achieves a centroid accuracy of ≤ 0.15 pixel. Increasing the SNR to 100 improves the centroiding accuracy up to ≤ 0.05 pixel. If the TA fails, the observation will not be performed. Only one integration and one exposure is allowed for a TA. The acquisition mode is either SOSSFAINT (for objects between 6.1 < M < 14.5, Vega) or SOSSBRIGHT (for objects between 3 < M < 6.1, Vega). To estimate the number of groups we need to perform a successful TA, we select "Target Acquisition" under the NIRISS pull-down menu in ETC. In the "Instrument Setup" tab, we select "SOSS or AMI Faint" in the "Acq Mode" pull-down menu, since the source is fainter than M ~ 6.1 (Figure 7). With 3 groups, the minimum allowed number, we achieve a SNR ~120, which ensures that the TA will succeed.
With the exposure parameters now determined for this program, we can populate the observation template in APT. See the Step-by-Step APT guide to complete the proposal preparation for this science use case. |

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