1. Create software to simulate the aperture synthesis for a radio

interferometer in orbit

2. Add realistic thermal noise to the simulation

3. Add realistic phase noise corresponding to the positional

uncertainty inherent in orbiting spacecraft

4. Simulate how well Relic can reconstruct a given model image of a

DRAGN over time

5. Simulate SunRISE to identify if it can indeed localize transient

radio hotspots with minimal integration time

Constellations of small spacecraft could be used to realize a low-

frequency phased array for either heliophysics or astrophysics

observations. However, there are issues that arise with an orbiting array

that do not occur on the ground, thus rendering much of the existing radio

astronomy software inadequate for data analysis and simulation. In this

work we address these issues and consider the performance 2 different

array concepts. One is Relic, a 32-spacecraft constellation for

astrophysical observations, whose goal would be to observe Double

Radio-source Associated with a Galactic Nucleus sources (DRAGNs) at

low frequencies impossible to see on Earth due to Ionospheric cutoff. The

other is SunRISE, a 6 spacecraft array whose science goal would be to

clarify the basic physics of Coronal Mass Ejections (CMEs) by localizing

radio emission on CMEs to within ¼ of their width.

• Radio imaging uses Interferometry, which yields 1 sample in the

Fourier plane per pair of spacecraft, 496 for Relic, 15 for SunRISE

• Where the sample is depends on the projected distance between 2

receivers, as seen from the source

• Adapted the APSYNSIM software [1] to orbiting arrays, recalculating

the projected difference every time step, using a orbital prediction file

that describes the location of the spacecraft in the EME2000 frame.

• Add thermal noise corresponding to Galactic Temperature at observing

wavelength [2]

• Add phase noise from various sources of uncertainty, can measure in

seconds, causes phase error of 2πντ for uncertainty τ seconds

Uncertainty = positional uncertainty + clock uncertainty

τ = 𝑑𝑧

𝑐 + 𝑑𝑡

This work began at the NASA Jet Propulsion Laboratory Deep Space

Tracking Division, California Institute of Technology while I spent the

summer of 2016 there on fellowship. Sonia Hernandez at JPL supplied

me with the files describing orbits of Relic for me to test.

[1] Marti-Vidal, Ivan 2015, https://launchpad.net/apsynsim

[2] Perley, R., et al. 1989, Astronomical Society of the Pacific

[3] Leblanc, Y., et al. 1998, Solar Physics, 183

[4] McMullin, J. P., et al. 2007, Astronomical Data Analysis Software and Systems XVI, 127

Simulating 3D Spacecraft Constellations for Low Frequency

Radio Imaging Alexander Hegedus1, Nikta Amiri2, Joseph Lazio2, Konstantin Belov2, Justin Kasper1

1Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI 2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA

Introduction

Objectives

Methods

Simulating Relic

Acknowledgements

References

Figure 2: SOHO image of a

CME

Figure 3: Example of how 3

dimensional structures like this

shape or a cloud of spacecraft

can have different projections

relative to the source of light

Figure 4: Columns of output from Orbital-APSYNSIM simulating the

response of the Relic Array after 1, 30, and 60 minutes on an idealized

DRAGN at 10 MHz with peak intensity 500 Jy, positional uncertainty of 3m

per spacecraft, 5 ns of clock bias error, a thermal noise corresponding to a

galactic temperature of ~300000K, and a noise rms of ~60 Jy. The right

most column is with integration times 12:00 – 12:29 & 17:00-17:29,

showcasing the code’s ability to combine non-contiguous chunks of time,

useful for systems engineers scheduling the operations of the spacecraft.

The upper right graph shows the error between the input and recovered

image with various sources of noise added.

Simulating SunRISE

Science Goal: Localize Radio Emission on CMEs

• Why? CMEs can potentially cause large blackouts; understanding

their basic physics helps with Space Weather prediction

• CMEs evolve quickly, so SunRISE must localize emission with quick

snapshots. No need for Orbital-APSYNSIM for integration, use

industry standard CASA [4]

Conclusions

Future Work

Relic & Orbital-APSYNSIM

• Orbital-APSYNSIM can realistically simulate the response of a Space

Based Interferometer with a particular orbit on a given science target

• It is useful for fine tuning orbits and scheduling system operations

• Can identify point of diminishing returns for integration time, e.g. for

Relic observing a 500 Jy DRAGN it is about 10-15 minutes

SunRISE

• SunRISE can only take ~25 degrees of phase error (equivalent

distance depends on observing wavelength) before shifting the

apparent location of the hotspot to a sidelobe

• With expected noise values, SunRISE can complete its goal of

localizing radio emission to within ¼ the CME’s width

VLBA Applications

Figure 1: Radio image of Cygnus A, one

of the brightest DRAGNs in the sky.

Photo courtesy of the NRAO

Science Goal: Image DRAGNs

• Why? Observing in this new frequency range helps constrain

models of black holes and shock processes that form DRAGNs

• Long Integration Time, needs new software to do Aperture Synthesis

• Created Orbital-APSYNSIM to simulate 3D orbiting array

• How well can Relic reconstruct a model image?

Figure 6: Left: Idealized Radio Hotspot, size informed by electron

density models & observing frequency [3].

Right: Reconstruction by SunRISE with no noise. Requires data

from multiple frequency bands since there are so few spacecraft.

Figure 7: Left: Noiseless reconstructions of hotspots

Right: Noisy reconstructions, top right has positional uncertainty

corresponding to a 20 degree error in phase, bottom right has 40

degree phase error, enough to lose the true position of the hotspot.

Figure 8: Histogram of

difference in degrees

between 100 different

truth Gaussians and the

SunRISE recovered

Gaussians with realistic

noise.

Orbital-APSYNSIM may also be used to conduct Very Long Baseline Array

(VLBA) observations, where antennae are spread across North America,

as well as in GEO. This is usually hard because the antenna do not lie on

a 2D plane. The vast separation enables high resolution images.

Improving & Using Orbital-APSYNSIM

• Add mode to Orbital-APSYNSIM integrating VINT (VLBI in the near-filed

toolkit ) for close range VLBA targets

• Do side by side analysis of ground based data between CASA and

APSYNSIM

• Find ways to tie the codes together, combine useful routines from CASA

in APSYNSIM, e.g. w-projection for large images

• Use Orbital APSYNSIM to fill out the trade space of building space

interferometers using created metrics for complexity, science value, and

cost over number of spacecraft & their proposed capabilities

• Make plots of Complexity vs Science Value & Cost vs Science Value

and look for ‘knees’, those are sweet spots for future missions

SunRISE Analysis

• Repeat analysis on SunRISE with more realistic CME truth models from

MHD simulations

• Define regression problem to describe likelihood that we can identify

CME hotspot given observations over time and frequency

• Use UVMULTIFIT to reconstruct models from simulations of the

baselines we would expect to see at all frequencies simultaneously

Figure 5: 10 VLBA antennae with 2 GEO satellites working together to

form an image.

Download Orbital-APSYNSIM Download this Poster https://github.com/alexhege/Orbital-APSYNSIM