Simulating Systematic Errors in Exoplanetary Transits for the James Webb Space Telescope

University of Central Florida Honors Undergraduate Thesis

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David Wright
April 9, 2021

Overview

Motivation
Literature Review and Relevant Work
Methodology & Results - Adding JWST Features to ExoSim, Validation, and Comparisons
Future Work and Closing Remarks

Motivation

Background Information

The upcoming™ James Webb Space Telescope (JWST) offers multiple observation modes tailored specifically for transit observation

Figure 1: Artist render of JWST

Need

The community needs simulation tools that create realistic simulations including instrument systematic errors and noise

Literature Review and Relevant Work

Exoplanet Transits

In 1999, HD 209458 b was discovered via photometric transit observations [CH00]

Figure 2: Hot Jupiters. Image Credit: ESA

Exoplanet Transits

Figure 3: Animation of exoplanet transit. Animation credit: NASA

Total flux of the star+planet system has a fractional decrease of \(\approx \left(\frac{R_P}{R_S}\right)^2 \), often called the transit depth

Exoplanet Transits

Figure 4: Animation of exoplanet transit. Animation credit: NASA

The planet’s radius is \(R_P = R_S \sqrt{\textrm{Depth}}\)
This is a small ratio, usually ~1-2% for a typical hot Jupiter

Exoplanet Transits

Figure 5: HD 209458 b light curve fit with a Mandel and Agol model. Image Credit: Kathleen McIntyre

In practice, this ratio is found by fitting model light curves to the data, such as the model described by Mandel and Agol [MA02]

Exoplanet Transits

Spectroscopic observations yield more information on exoplanet atmospheres

Figure 6: HD 209458 b light curves from \(0.29-1.04 \mu\textrm{m}\). Image Credit: Heather Knutson

Exoplanet Transits

The \(\left(\frac{R_P}{R_S}\right)^2 \) ratio at different wavelengths, \(\left(\frac{R_P(\lambda)}{R_S}\right)^2 \), is coined the “transmission spectrum”

Figure 7: WASP-39b light curves from \(0.3-5.0 \mu\textrm{m}\). Image Credit: Wakeford et al. 2017 [WA17]

Exoplanet Transits

Transiting planets on circular orbits also pass behind their host star, known as an eclipse or secondary transit

Figure 8: Exoplanet phase curve. Image Credit: Deming & Knutson 2020 [DK20]

Exoplanet Transits

As the planet passes behind its star, the observed flux decreased by \( \left(\frac{R_P}{R_S}\right)^2 \frac{ F_{\lambda,P} }{ F_{\lambda,S} } \) with \(F_\lambda\) being the emergent flux density of the planet or star

Figure 9: WASP-39b light curves from \(0.3-5.0 \mu\textrm{m}\). Image Credit: Wakeford et al. 2017 [WA17]

The James Webb Space Telescope (JWST)

JWST has exoplanet science as one of its main goals
JWST will observe the 0.6–28\(\mu \textrm{m}\) range with detectors that are capable of greater than 100 parts per million (ppm) precision over time periods from hours to days [BE14]

Figure 10: Artist render of JWST

Figure 11: JWST wavelength coverage compared to Hubble and Spitzer

The James Webb Space Telescope (JWST)

JWST has a 25\(\textrm{m}^2\) primary mirror, the largest of any space telescope to date
It will orbit the Earth-Sun L2 point, providing extremely stable observations over long time periods

Figure 12: JWST orbit at Earth-Sun L2 point. Image credit: NASA

The James Webb Space Telescope (JWST)

Webb carries four instruments on board:
- The Near-InfraRed Camera (NIRCam, [BE12])
- The Near-InfraRed Spectrograph (NIRSpec, [FE12])
- The Near Infrared Imager and Slitless Spectrograph (NIRISS, [DO12])
- The Mid-Infrared Instrument (MIRI, [KE15])

JWST Simulation Tools

Instrument Specific

NIRSpec - N. Batalha [BA15]
NIRISS - D. Louie [LO18]
MIRI - P. Klaasen [KL20]
NIRCam - J. Leisenring [LEPr]

General JWST

JexoSim - S. Sarkar [SA20]
PandExo - N. Batalha [BA17]

Methodology & Results

A Brief Overview of ExoSim

Figure 14: Overview of ExoSim Algorithm. Image credit: Enzo Pascale

ExoSim is a modular, time-domain simulator of exoplanet transits
ExoSim simulates the full light curve, including instrument noise and systematic errors
An ExoSim simulation is configured using a user-supplied XML file containing the parameters for the instrument(s) and observation and paths to relevant reference data (see reference files on diagram).
Users can specify parameters such as which noise sources to include, whether to simulate a transit or eclipse, phase curve effects, and the planet to observe
The Channel object is instantiate to hold channel specific parameters
Astroscene
- After reading in the XML configuration file, the ExoSim algorithm moves on to the Astroscene module
- In this module, the Star and Planet object classes are instantiated
  - PHOENIX stellar model or black body
  - Open Exoplanet Catalogue (OEC) for planet and star parameters (distance, temperatures, orbital inclination, etc. )
- The flux density at the telescope aperture is calculated using the generated stellar model and the parameters taken from the OEC
The background flux density at the telescope is calculated immediately following the astroscene module
Instrument
- The power per unit wavelength at the telescope aperture is calculated
- The incoming signal is
  - modulated by the optical elements of the telescope
  - placed on an oversampled focal plane using the given wavelength-pixel relation
  - convolved with a point-spread function
  - converted to photoelectrons using the given quantum efficiency of the detector
  - convolved with an intra-pixel response function to give a final, digitized focal plane
Timeline
- Using the input timing parameters, the timeline module sets up the 3D data cube that contains the time series data of the observation
- The full light curve is computed
- For computation reasons, the light curve is actually applied in the Noise module
Noise
- Read noise, shot noise, dark current, jitter noise, and inter-pixel variations
- Read and shot noise are generated by respectively sampling a normal and poisson distribution
- Dark current value is given in the configuration file, and value*time is added to each pixel in a frame
- Jitter noise is modeled using a user-supplied power spectral density (PSD) file
- ExoSim uses this file to generate random shifts in the x and y directions over small time scales (less than a frame time)
  - Each small time scale focal plane is coadded to result in the final frame
Output
- ExoSim outputs FITS files, much like a real observation
- Extra FITS HDUs with useful information, like the detector dispersion relation, are appended after the simulated image HDUs
- The FITS headers contain other information, like the target star and planet and the detector readout noise
- No post processing is done on these images, so they are very close to the results of a real observation

Adding New Features to ExoSim

In order to simulate JWST, ExoSim requires the following additional capabilities
1. Simulation of curved spectral traces
2. Simulation of multiple-ordered spectral traces
3. Use instrument specific PSFs
4. Support JWST detector readout patterns
5. Parallelization

Curved Spectral Traces

Allow a 2D wavelength-pixel relation, \(\lambda(x,y)\)

Figure 15: NIRISS SOSS. Three orders cover a wavelength range of \(0.6-2.8\mu\textrm{m}\). Image Credit: STScI

Multiple-Ordered Spectral Traces

Simulate a focal plane for each spectral order and coadd

Figure 16: NIRISS SOSS. Three orders cover a wavelength range of \(0.6-2.8\mu\textrm{m}\). Image Credit: STScI

JWST Readout Patterns

Figure 17: General structure of detector readout scheme used by all JWST detectors. Image Credit: STScI

Readout	N\(_{frames}\)	N\(_{skip}\)
NISRAPID	1	0
NIS	4	0
NRSRAPIDD1	2	1
SHALLOW4	5	1

Instrument Specific PSFs

Figure 18: Example PSFs from each JWST instrument and the fine guidance sensor.

Parallelization

Parallelization gives nearly an exact proportional decrease in run time for number of parallel processes

Figure 19: Dask parallel computing library task graph built during ExoSim execution.

With the combination of large detectors, oversampling of the focal plane, long observation times, and the changes made to accommodate multiple ordered traces, run time drastically increased for certain configurations
NIRISS SOSS took nearly two hours when simulating all three orders
I used the Dask Python parallel computing library to parallelize sections of ExoSim
I was able to drop NIRISS SOSS run time from two hours to 7 minutes with 20 threads
Dask basics
- It has two main parts:
  - Distributed data structures that are similar to NumPy and Pandas
  - A task scheduler
- Dask, for most things, is a drop in replacement for scipy, numpy, and pandas that is parallelized
- Users can specify how many threads they’d like to use, and how much memory is allowed per thread
  - Dask calls these units “workers”
- Dask builds up a “task graph” whenever its functions are called, but it doesn’t actually evaluate anything
- When the user asks for the results, Dask determines what can be run in parallel and schedules tasks to the available workers
- The end result is a normal numpy array
- An interesting thing about Dask is that it can work nicely with other job schedulers, such as SLURM or PBS
- In the code I wrote, Dask is configured to see the local computer as a “cluster” of workers
- By changing this configuration, which is only 5 lines of code, one could actually run ExoSim in parallel on a normal university cluster
- This could be extremely useful if one were to simulate a very large detector
- It can also interface with AWS and Kubernetes for cloud computing

Example NIRISS SOSS Simulation

Figure 20: NIRISS SOSS simulation from ExoSim.

Validation

Validating the Focal Plane Signal

A simulated black body was compared to an analytic expression

Figure 21: Flat spectral trace

Figure 22: Curved spectral trace

A simulation without noise was performed for an out-of-transit observation of the star 55 Cancri.
The star was modeled as a black body with an effective temperature of 5172K.
In this test, the PSFs were represented as a series of delta functions, i.e., all of the signal fell directly on a pixel and there was no convolution with a PSF.
The focal plane was saved to disk in the Instrument module.
The columns of the focal plane were summed over, and the resulting signal was compared to the predicted value given by \[Q(x) = \pi B_{\lambda(x)} (5192K) \left(\frac{R_S}{D}\right)^2 A_{Tel}\eta_{Ch}(\lambda(x))QE(x)\Delta \lambda(x) \frac{\lambda(x)}{hc}.\]
In order to validate the implementation of multiple order traces, a noiseless simulation of two orders was performed separately and together for a total of three images.
The out-of-transit, black body system described previously was used in these simulations.
The two individual simulated images were summed and compared to the simulation of the orders on the same detector.

Comparison to Original ExoSim

To ensure no unforeseen changes were made to the noise models, I ran identical simulations in my modified version of ExoSim and the original version.

Comparison to PandExo

Table 1: Configuration for each instrument simulated (cont. next slide)
Parameter	NIRSpec BOTS	NIRCam F444W/Grism-R
Subarray	SUB512	SUBGRISM64
Size	\(32\ \times\ 512\)	\(64\ \times\ 2048\)
W\(_{slit}\)(pix)(pix)	16	N/A
\(\Delta_{pix}(\mu\textrm{m})\)	18	18
PS\((^\circ \times10^{-5}/\Delta_{pix})\)	2.78	1.75
T(K)	40	40

JexoSim and PandExo are the two tools mentioned which are comparable to my modified version of ExoSim.
JexoSim is not publicly available, so comparisons between simulations are only possible with PandExo.
Simulations of all four instruments configured for exoplanet transit observations were compared.
In these simulations, all noise sources were disabled except for shot noise.
Reference data from Pandeia was used for each simulation
NIRSpec was set to observe 55 Cancri out-of-transit, and the star was modeled as a black body.
The next instrument to be compared was NIRISS in its SOSS mode.
55 Cancri proved to be too bright of a target for NIRISS SOSS, so GJ 1214 was used instead.
This observation was also out of transit, and the star was modeled as a black body.
The same observation scene was used for MIRI in its low-resolution spectroscopy (LRS) mode and NIRCam in its grism time-series mode.
The measured signal was calculated for each simulation using the last-minus-first procedure
- Also known as correlated double sampling
- Final readout in integration minus first
Extracted spectra using JOSE (uses Horne’s algorithm) except for NIRISS (had issues with curved trace)
I used PandExo’s binning tools to bin the results spectra down to a common wavelength grid

Comparison to PandExo

Table 2: Configuration for each instrument simulated
Parameter	NIRISS SOSS	MIRI LRS
Subarray	SUBSTRIP256	SLITLESSPRISM
Size	\(256\ \times\ 2048\)	\(72\ \times\ 416\)
W\(_{slit}\)(pix)	N/A	N/A
\(\Delta_{pix}(\mu\textrm{m})\)	18	25
PS\((^\circ \times10^{-5}/\Delta_{pix})\)	1.81	3.06
T(K)	40	7

JexoSim and PandExo are the two tools mentioned which are comparable to my modified version of ExoSim.
JexoSim is not publicly available, so comparisons between simulations are only possible with PandExo.
Simulations of all four instruments configured for exoplanet transit observations were compared.
In these simulations, all noise sources were disabled except for shot noise.
Reference data from Pandeia was used for each simulation
NIRSpec was set to observe 55 Cancri out-of-transit, and the star was modeled as a black body.
The next instrument to be compared was NIRISS in its SOSS mode.
55 Cancri proved to be too bright of a target for NIRISS SOSS, so GJ 1214 was used instead.
This observation was also out of transit, and the star was modeled as a black body.
The same observation scene was used for MIRI in its low-resolution spectroscopy (LRS) mode and NIRCam in its grism time-series mode.
The measured signal was calculated for each simulation using the last-minus-first procedure
- Also known as correlated double sampling
- Final readout in integration minus first
Extracted spectra using JOSE (uses Horne’s algorithm) except for NIRISS (had issues with curved trace)
I used PandExo’s binning tools to bin the results spectra down to a common wavelength grid

Comparisons to PandExo - NIRSpec

Figure 23: Comparison of PandExo and ExoSim simulation of NIRSpec. Average percent difference of \(+1.53 \pm 1.63\)%.

Comparisons to PandExo - NIRCam

Figure 24: Comparison of PandExo and ExoSim simulation of NIRCam. Average percent difference of \(+2.18 \pm 1.08\)%.

Comparisons to PandExo - MIRI

Figure 25: Comparison of PandExo and ExoSim simulation of MIRI. Average percent difference of \(+3.0 \pm 2.2\)%.

Comparisons to PandExo - NIRISS

Figure 26: Comparison of PandExo and ExoSim simulation of NIRISS. Average percent difference of \(+4.54 \pm 1.37\)%.

Future Work and Closing Remarks

Future Work

Write bridge between ExoSim and Pandeia
Find cause of discrepancy between simulations
Combine ExoSim, Py-JOSE, and BART for an end-to-end simulation and retrieval

Two of the most time consuming tasks when working with ExoSim are sourcing reference files and configuring the instruments.
It would be beneficial to write code to bridge ExoSim and the Pandeia reference data directly.
Users would be able to simply specify the name of the filter, disperser, etc. and ExoSim would find and use the correct reference data.
An in depth study of PandExo and Pandeia is needed to find the cause of the differences observed in this thesis. This study could also be done in tandem with the previous future work mentioned.
Outside of future work to be done to ExoSim, using ExoSim to simulate known exoplanet spectra and then running atmospheric retrieval code on the simulated spectra is an interesting prospect.
This end-to-end simulation and retrieval would allow astronomers to benchmark the performance of instruments in regards to specific exoplanet observations or specific observational goals, such as detecting C/O ratios in an exoplanet’s atmosphere.

Closing Remarks

In summary, I’ve described the development and validation of a time-domain simulator of exoplanet transits and systematic errors JWST.

This tool is open-source and available to the community with the hope that it is used to further our understanding of the effects of systematic noise on exoplanet transits and to prepare for observations of exoplanet transits with the James Webb Space Telescope.

Acknowledgements

Thanks to Dr. Joseph Harrington, Dr. Enzo Pascale, Dr. Ryan Challener, and Kathleen McIntyre for their support and guidance

Bibliography

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[BA17] Batalha, Mandell, Pontoppidan, , Stevenson, Lewis, Kalirai, Jason, Earl, Greene, Albert, & Nielsen, PandExo: A Community Tool for Transiting Exoplanet Science withJWST&HST, Publications of the Astronomical Society of the Pacific 129(976), 064501 (2017). https://doi.org/10.1088BA17.pdf1538-3873BA17.pdfaa65b0
[BE12] Beichman, Rieke, Eisenstein, Daniel, Greene, Krist, McCarthy, , Meyer & Stansberry, Science opportunities with the near-IR camera (NIRCam) on the James Webb Space Telescope (JWST), in: Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, 2012. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/8442/84422N/Science-opportunities-with-the-near-IR-camera-NIRCam-on-the/10.1117/12.925447.short
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[FE12] Ferruit, Bagnasco, Barho, , Birkmann, Böker, Marchi, , Dorner, Ehrenwinkler, Falcolini, , Giardino, Gnata, Honnen, , Jakobsen, Jensen, Kolm, Maier, Hans-Ulrich, Maurer, Melf, Mosner, Peter, Rumler, Salvignol, , Sirianni, Strada, Plate, & Wettemann, The JWST near-infrared spectrograph NIRSpec: status, in: Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, 2012. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/8442/84422O/The-JWST-near-infrared-spectrograph-NIRSpec-status/10.1117/12.925810.short
[KE15] Kendrew, Scheithauer, Bouchet, , Amiaux, Azzollini, Bouwman, , Chen, Dubreuil, Fischer, , Glasse, Greene, Lagage, , Lahuis, Ronayette, Wright, & Wright, The Mid-Infrared Instrument for the James Webb Space Telescope, IV: The Low-Resolution Spectrometer, Publications of the Astronomical Society of the Pacific 127(953), 623 (2015). https://iopscience.iop.org/article/10.1086/682255/meta
[KL20] Klaassen, Geers, Beard, , O'Brien, Cossou, Gastaud, Coulais, , Schreiber, Kavanagh, Topinka, , Azzollini, De Meester, Bouwman, Glasse, , Glauser, Law, Cracraft, , Murray, Sargent, Jones, Wright & , MIRISim: A Simulator for the Mid-Infrared Instrument on JWST, Monthly Notices of the Royal Astronomical Society 500(3), 2813-2821 (2020). http://arxiv.org/abs/2010.15710
[LEPr] pyNRC:, , .
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Simulating Systematic Errors in Exoplanetary Transits for the James Webb Space Telescope

Overview

Motivation

Background Information

Need

Literature Review and Relevant Work

Exoplanet Transits

Exoplanet Transits

Exoplanet Transits

Exoplanet Transits

Exoplanet Transits

Exoplanet Transits

Exoplanet Transits

Exoplanet Transits

The James Webb Space Telescope (JWST)

The James Webb Space Telescope (JWST)

The James Webb Space Telescope (JWST)

The James Webb Space Telescope (JWST)

JWST Simulation Tools

Instrument Specific

General JWST

Methodology & Results

A Brief Overview of ExoSim

Adding New Features to ExoSim

Curved Spectral Traces

Multiple-Ordered Spectral Traces

JWST Readout Patterns

Instrument Specific PSFs

Parallelization

Example NIRISS SOSS Simulation

Validation

Validating the Focal Plane Signal

Comparison to Original ExoSim

Comparison to PandExo

Comparison to PandExo

Comparisons to PandExo - NIRSpec

Comparisons to PandExo - NIRCam

Comparisons to PandExo - MIRI

Comparisons to PandExo - NIRISS

Future Work and Closing Remarks

Future Work

Closing Remarks

Acknowledgements

Links

Bibliography