A walk through of the JWST PandExo (Pandeia-ETC for Exoplanets) for the NIRISS SOSS Science Use Case is provided, demonstrating how to select exposure parameters for this observing program.
PandExo is the "ETC ('Pandeia') for Exoplanets" which performs signal-to-noise (SNR) calculations for the JWST time series observing modes. The calculations from the JWST Exposure Time Calculator (ETC, which uses "Pandeia") are considered to be conservative (and averaged over wavelengths) SNR estimates for the exoplanet transit/eclipse depths or brown dwarf rotation amplitudes.
The ETC includes an error term for residual flat field errors which affects long exposures, and significantly underestimates the SNR for exoplanet transit spectroscopy where we take relative measurements. For exposures longer than ~10,000 s, 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. The Step-by-Step ETC Guide for NIRISS SOSS Science Use Case provides a conservative, average estimate, but using the JWST ETC to compute a full exposure with ~2000 integrations is not possible for time series observations (TSOs).
For the "NIRISS SOSS Time-Series Observations of HAT-P-1" Science Use Case, we focus on selecting stellar, planetary, and exposure parameters to detect the exoplanet transit at the desired signal-to-noise ratio (SNR), for each wavelength. We start by defining the stellar, planetary, observational, and instrument modes specific to the proposal observations. The result of these calculations will be both the expected SNR on the host star and exoplanetary atmospheres, as well as necessary parameters to input into the Astronomer's Proposal Tool (APT) observation template, which is used to specify an observing program and submit proposals.
Observing goals of time series observations
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 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 (33,667.199 s), which is three times the transit duration + 1 hour – for "detector settling" (see Noise Sources for Time-Series Observations).
After opening the PandExo website, select "New Calculation" under the picture of "James Webb Space Telescope".
At the top of the next page, it is useful to set the name of the target in the "Name" text box. This will become relevant on the next page, which will have a list of all recent calculations from the current computer.
Setting stellar parameters in PandExo
The set the stellar parameters for HAT-P-1, we will use is the "Phoenix Model Grid," setting:
Figure 2 shows a screenshot of the stellar parameters input page in PandExo.
Setting planetary parameters in PandExo
To supply the exoplanetary parameters for HAT-P-1b, we will use the "Select From Grid" under "Planet Model" option, setting:
Figure 3 shows a screenshot of the planetary parameters input page in PandExo.
Setting transit observational parameters in PandExo
We need to supply the observational parameters for HAT-P-1b and encompass the entire transit and necessary out of transit time to make the relative measurement. For this, we need to set the following parameters (Figure 4):
Set instrument (SOSS) parameters in PandExo
To supply the instrumetnal parameters for NIRISS SOSS, we will select the NIRISS SOSS option and sub-array selections as follows (Figure 5)
To compute all of the necessary – and useful – values for planning and proposing for JWST TSO observations, select the "Submit" button at the end of the page. This operation could take a few minutes. The following page will provide a rotating symbol and the label "Running" if the calculations are ongoing. Moreover, the buttons to the right (a box and an eye) will be grey and unusable.
After the calculation has finished processing on STScI server, the rotating dial will stop and the label "Running" will change to "Finished". Moreover, the buttons to the right are now useful.
Select the EYE symbol (), to view the JWST TSO planning and proposing calculations.
After selecting the EYE symbol , the first image that we can see is the raw, unbinned planetary spectrum as it would be resolved by fitting a transit model (see Kreidberg 2015) to the synthetic JWST-NIRISS simulated observations, which include photon noise, background noise, and read noise as is expected from both Pandeia and field testing of the instruments (Figure 6).
There are two dials to this plot, as well as the standad Bokeh interaction functions (e.g., move, zoom, etc): "binning" and "Num trans". The units of "binning" selection are given in the log10(min(wavelengths per bin)); the default is at the native resolution for NIRISS (R ~ 700), such that log10 (0.625/700) = -3.049. The scientific measurement for an exoplanet transit is the "transit depth" or "eclipse depth", which is a temporal measurement. The spectroscopic result is therefore a relative comparison between a contiguous sequence of time-series measurement i.e., transit/eclipse depth over wavelength. It is equivalent to measuring variations in the stellar spectrum over time.
The native resolution can provide a useful transmission/emission spectrum, if the atmospheric signal is large enough to overcome the intrinsic, temporal noise, which is dominated by the photon noise and read noise. It is much more common to "bin" the native spectrum into what are called "channels", which are higher SNR sets of pixels that improve the SNR on the temporal signal. In our case, we will bin 10 pixels together to form ~200 "channels" (i.e., 2048 pixels/10 (pixels per bin), which results in a binned resolution of R ~ 70. Sliding the dial to -2.049 (= log10(0.625/70)), is equivalent to binning by 10 pixels per channel. The plot itself will update to reveal what this binning should look like from our synthetic observation. This dial allows the user to visually determine ithe theoretical spectrum (here: clear, equilibrium chemistry) with the precise stellar model for the HAT-P-1 system.
Figure 7 shows a zoom-in of the binned spectrum using the Bokeh tools on the right side of the interactive plot.
1-D stellar and error spectra for HAT-P-1
Scrolling down on this page, we come to the 1-D stellar and error spectra for HAT-P-1. The first tab on the top figure defaults to "Total Flux" (Figure 8), which shows the integrated electrons per wavelength, integrated to form the 1-D stellar spectrum (top) and 2-D spectral image (bottom).
Selecting the SNR tab at the top of the upper figure reveals the SNR expected per wavelength along the stellar spectrum (Figure 9). Because our exoplanet host stars are nominally bright, the stellar spectrum is very nearly photon noise limited; the SNR figure is therefore precisely the √(1-D stellar spectrum) over wavelengths.
Transit/Eclipse depth uncertainty over wavelengths
The final tab to select on this figure is likely the most important. Select the "Error" tab to see the predicted ppm uncertainty as a function of wavelength (Figure 10).
Figure 10 shows that the smallest uncertainty predicted for HAT-P-11 in our observational parameters is ~100 ppm; the average is closer to 200 ppm. This estimate is for the native resolution (R ~ 700); because we are expecting to bin the 2-D image by 10 columns to form 200 channels from 2048 columns, we will state that we predict to achieve 200/√10 ~ 63 ppm uncertainty (on average) across the spectrum. Note that we sought to achieve <50 ppm uncertainty, on average, across the spectrum. To sustain this uncertainty, we would need to bin the spectrum by 16 pixels instead of 10; or observe the target for a second observation. Depending on the spectral resolution desired to detect specific atmospheric molecular signatures, either of these options is viable (see Figure 11).
Figure 11 (top) bins the native spectrum by 16 pixels per channel, with 1 visit. Figure 11 (bottom) bins the native spectrum by 10 pixels per channel, with two visits. Both panels show the "error spectrum" at the native resolution.
Determining number of groups and number of integrations
APT requires the user to enter the number of groups (NGroups) and number of integrations (NIntegrations) to define the length of the exposure. We want to observe a balanced number of groups per integration to maximize both temporal resolution and spectral precision. Previous experience has led the community to nominally fill the detector pixel wells to an average of half full. Because an H2RG pixel can hold ~65k e–, we nominally choose ~30k e– per pixel per integration. In the context of number of groups for JWST, PandExo derives the number of groups corresponding to the onset of saturation (NGroupssat) (we defined this at 80% well depth), and then selects the number of groups per integration to be NGroupssat/2 (rounding up).
After the "Table of Original Inputs"–which matches the values we entered at the beginning–there is a second table named "Timing Info" (Figure 12).
Both of these values will be entered in the APT NIRISS SOSS Observation template as described in the Step-by-Step APT Guide for NIRISS SOSS Science Use Case.
The final table provided by PandExo is named "Warnings" (Figure 13). If the target is not too bright for the minimum number of groups (NGroupsmin = 2), and the given instrument/detector setup, then all "values" should be listed as "All Good." If the any pixels on the detector are saturated, or experience strong non-linearity, then one of these warnings will list further information.
PandExo provides a "Download Data" button at the bottom of the results page, which allows the user to download a `pickle` file for the user to use Python to plot and interact with all of these figures. The follow code snippet would allow user to create the "Error Spectrum" figure above – with Python 3.6.1 :: Anaconda 4.4.0 (×86_64):
# To plot the error spectrum after downloading the PandExo results
from pylab import *; ion()
id = '2a348356-69f9-4a31-826f-5dbcaf075946e' # this `id` only applies for this test case; all users will have a different values for `id`
ppm = 1e6
num_bins_per_channel = 10
with open("ETC-calculation" +id+".p", "rb") as f:
hatp1 = pickle.load(f)
plot(hatp1['FinalSpectrum']['wave'], hatp1['FinalSpectrum']['error_w_floor']*ppm / sqrt(num_bins_per_channel))
# To print the average expected error across the entire spectrum
print(mean(hatp1['FinalSpectrum']['error_w_floor']*ppm / sqrt(num_bins_per_channel)))
PandExo does not yet comptue expectations for target acquisition (TA). Please see the "Target Acquisition" section of the Step-by-Step ETC Guide for NIRISS SOSS Science Use Case for guidance on how to select observing parameters to ensure a successful TA. Note that if a TA does not succeed, the observation can not be performed.