Step-by-Step ETC Guide for NIRCam Grism Time-Series of GJ 436b

A walk-through of the JWST ETC for the NIRCam Grism Time-Series Example Science Program is provided, demonstrating how to select exposure parameters for this observing program.

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Main articles: NIRCam Grism Time-SeriesJWST Exposure Time Calculator Overview
See also: Video Tutorials

The 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 modes.

For the "NIRCam Grism Time-Series Observations of GJ 436b" Example Science Program, we focus on selecting the exposure parameters for NIRCam Grism Time-Series.

We start by defining a scene relevant to this science case. We show how to run ETC calculations to achieve the desired SNR for a single integration and how to convert this to the SNR over the secondary eclipse observation and assess how it will be detected. 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., number 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.

The ETC workbook associated with this Example Science Program is called "#30: NIRCam Grism Time-Series Observations of GJ 436b" and can be selected from the Get a Copy of an Example Science Program dropdown on the ETC Workbooks page to get the read only version. The nomenclature and reported SNR values in this article are based on ETC v.1.5. There may subtle differences if using a different version of ETC.



Define Source and Scene in the ETC

Main article: JWST ETC Scenes and Sources Page Overview
See also: 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 Editor" box, there are tabs for setting the source continuum, shape, and flux normalization. Below are the specification for this case. We renamed the Scene "Target".


Table 1. Input Source Parameters

SourceContinuumNormalizationShape
GJ 436Phoenix Stellar Models: M2VK (Johnson) = 6.1 (Vega mag)point source

Select NIRCam Grism Time-Series Calculation

Main article: JWST ETC Creating a New Calculation
See also: NIRCam Grism Time-SeriesJWST ETC Backgrounds

In APT, the NIRCam Grism Time-Series template, include both the short-wavelength (SW) and long-wavelength (LW) detector setups. In ETC, however, this is split in two modes: SW Time-Series and LW Grism Time-Series. Hence, we need to setup two different calculations for the SW and LW with the same parameters (i.e., same subarray, readout pattern, number of groups per integration, etc.). 

After selecting "LW Grism Time Series" from the NIRCam pull-down menu (Calculation #1), we specified the background parameters. The observatory background is very low for these observations (~ 1 e- / s / pixel in F322W2 + grism and F444W + grism).  In the "Backgrounds" tab, we can specify the position RA Dec = 11:42:11.09 +26:42:23.66 (J2000) and select "Low", which corresponds to the 10th percentile of the sky background. 



Select Instrument Parameters

Main article: NIRCam Time-Series Observation Recommended Strategies
See also: NIRCam Detector SubarraysNIRCam Detector Readout Patterns

For this example, we observed the target GJ346 using two LW filters (F332W2 and F444W), hence we need to create two different calculations. We entered the following parameter for the NIRCam Grism Time-Series Calculation #1:

  • "Instrument Setup" tab -
    • GRISMR is the only permitted Grism option
    • We selected the filter F322W2
  • "Detector Setup" tab -
    • subarray is set to SUBGRISM4.
    • we choose the RAPID readout pattern for which there is no averaging of reads into groups.
    • The ETC shows that the onset of saturation occurs in some pixel when the number of “groups per integration” is set to 9. We chose to set the number of “groups per integration” to 5 to stay below saturation and achieve about 50% full-well. This is to provide a recommended (i.e. NGroupssat/2 rounding up) margin of protection against the non-linear regime of the infrared detectors (see note below).
  • "Strategy" tab -
    • We selected the "centered on source" option for "Aperture location" from the drop-down menu, so that the SNR is calculated for the source. 
    • "Aperture Half-Height" is set to 0.15" and we sample the background in the regions 0.8" - 1.6" (~ 13 - 25 pixels) above and below the target spectrum.

For Calculation #2, we changed the LW filter and the number of "groups per integration;" the other parameters remained in the same. In detail, the updates are:

  • "Instrument Setup" tab -
    • we selected the filter F444W
  • "Detector Setup" tab -
    • The ETC shows that the onset of saturation occurs in some pixel when the number of "groups per integration" is set to 14. For the reason explained above, we set the number of "groups per integration" to 10.


Due to the intrinsic non-linearity in JWST’s infrared detectors, uncertainties in gain, and precise measurements needed by time-series observations, saturation for NIRCam Time-Series science modes is set to a “full-well” threshold of 70% in the ETC.

Details for the SW observation in Calculation #4:

  • "Instrument Setup" tab -
    • "LW Pairing" is set to LW Grism Time Series
    • "SW Pupil" is set to CLEAR 
    • "SW Filter" is set to WLP4 (F212N2)
  • "Detector Setup" tab - 
    • subarray is set to SUBGRISM64
    • we chose the RAPID readout pattern
    • "Groups per integration" is set to 5 to match the NIRCam Grism Time Series F332W2 observation.

  • "Strategy" tab -
    • We selected the "centered on source" option for "Aperture location" from the drop-down menu, so that the SNR is calculated for the source. 
    • "Aperture Half-Height" is set to 0.1" and we sample the background in the regions 0.22" - 0.4" (~ 7 - 13 pixels) above and below the target spectrum.


Note that in the ETC workbook associated with this Example Science Program, we created only 1 calculation for the SW observation (Calculation #4), since for both LW Grism Time-Series calculations we use the same filter (WLP4). We set the parameters for the SW calculation in order to match the LW calculation for filter F332W2. If the users want to calculate the SNR for the SW channel, when paired with filter F444W, they need to modify the number of "groups per integrations" accordingly (i.e., set "groups per integration" to 10).  



Select NIRCam Target Acquisition Calculation

Main articles: NIRCam Grism Time-Series Target AcquisitionJWST ETC NIRCam Target Acquisition

All NIRCam TSOs require target acquisition (TA) to place the target at the appropriate pointing location. It is recommended that the TA achieves a SNR ≥ 30, which enables a centroid accuracy < 0.15 pixel. For very bright targets, a small number of saturated pixels can be tolerated for TA; users are advised to read the dedicated page on this


We selected "Target Acquisition" in the NIRCam pull-down menu to determine the exposure parameters we need to specify in order to achieve the desired SNR. For Calculation #1, we set the following parameters:

  • "Backgrounds" tab -  we entered the coordinates of GJ 436b (11:42:11.09, +26:42:23.66) and selected "Low" for "Background configuration," which corresponds to the 10th percentile background.
  • "Instrument Setup" tab:
    • Filter (F335M) is fixed  for NIRCam Target Acquisition. 
  • "Detector Setup" tab:
    • Subarray (Sub32 Time Series TA) is fixed for NIRCam Target Acquisition.
    • we choose the RAPID readout pattern due to the brightness of the source.
    • among the possible choice, the number of "groups per integration" is set to 3 (minimum number of group allowed).

The calculation output shows that GJ 436 b images saturate in 1 pixel at the end of the first group and in 4 pixels at the end of the ramp with these settings. Ideally a fainter nearby star should be used for target acquisition, but there are no suitable star within the 35″ visit splitting distance of GJ 436. Analysis has shown that this number of saturated pixels can still give good centroiding results, so we can go forward with these settings.



Adjust Exposure Parameters to Obtain Desired Signal-to-Noise Ratio

The grim time series calculation with the F322W2 filter shows a SNR of ~217 per pixel for a single integration with NGROUPS = 5 in RAPID mode with the SUBGRISM64 subarray (Calculation #1). Similarly, the calculation through the F444W filter (for the same subarray and readout mode) shows that the SNR per pixel is ~222 for NGROUPS = 10 (Calculation #2).

Determining Number of Integrations

We plan to observe GJ 436 for enough time to allow for sufficient detector settling time (currently estimated to be ~30 minutes), and to observe the secondary eclipse and twice the eclipse duration before and after the secondary eclipse to reduce photon noise (see Noise Sources for Time-Series Observations). We also allow for some margin if the observations do not start exactly when expected or if the secondary eclipse occurs at a slightly different time than predicted.

We use the dwell time (Tdwell) to calculate this exposure time: Tdwell ~ 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 GJ 436, T14 is 1.02 hours which gives us a total exposure time of 4.77 hours.

From inputting 5 Groups into the Astronomer's Proposal Tool, with the RAPID Readout Pattern and SUBGRISM64 Subarray, we find that 1 integration corresponds to 2.049 seconds for the observation in the F332W2 filter. We thus need 8381 integrations to cover the exposure window with this filter.

For the F444W filter, we found 10 Groups/Int to be the optimal integration ramp length, again with the RAPID Readout Pattern and SUBGRISM64 subarray. APT shows us that this combination corresponds to an exposure time of 3.752 s for 1 Groups/Int, such that we need 4577 integrations to cover the exposure window.

Interpreting SNR Results

Main article: 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.

Our goal in this example is to achieve a relative precision < 20 parts per million (ppm) on the transit depth per "spectral bin" or "channel," after subtracting the primary transit from the out-of-transit data (e.g., Greene et al. 2015). 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, without losing the spectral features in which we are interested in measuring. For the case of GJ 436, in particular, a spectral bin of 20 pixels (which decreases the NIRCam Grism resolution from ~1600 to ~80), would be enough to resolve the predicted spectral features in the atmosphere of this planet. 

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

Precision_{depth} \sim Precision_{point} \times \sqrt{1/N_{out} + 1/N_{in}} = \sqrt{1/N_{out} + 1/N_{in}}/SNR_{point}

where Precisionpoint is the photometric precision per data point, Nout is the number of datapoints (integrations) out-of-transit, Nin is the number of datapoints (integrations) in-transit, and SNRpoint is the SNR in one integration.

The time spent out-of-transit is 3.75 hours and the time spent in-transit is 1.02 hours. For our example science program and this observational setup (NGroups = 5, RAPID readout, and SUBGRISM64 subarray), these times correspond to  Nout = 6589 integrations and Nin = 1792 integrations. From the ETC, we found SNRpoint = 217 , such that Precisiondepth is ~ 0.000123 = 123 ppm, prior to binning. When binning by a factor of 20, our Precisiondepth lowers by a factor of √20, such that we achieve a precision of ~28 ppm. If we assume that the noise for this observation is Poissonian dominated, we thus need 3 exposures (i.e., 28 ppm /√3 ≈ 16 ppm) for this program.

We can repeat the same calculation as for F322W2 filter to assess the achievable precision and required number of epochs for the F444W filter. 

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

See the Step-by-Step APT guide to complete the proposal preparation for this example science program, where we will input the exposure parameters we derived here.



References 

Greene, T. P., Line M. R., Montera, C., et al. 2016, ApJ, 817, 1 ( (arXiv)
Characterizing transiting exoplanet atmospheres with JWST




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