Image Restoration of Crab Nebula Image Observed with ASTRO-H's Hard X-ray Telescope

Sep. 9, 2024 | GATEWAY to Academic Articles

MORII Mikio / Science Satellite Operation and Data Archive Unit, ISAS

We successfully developed a new image restoration technique to enhance the image resolution for the Crab Nebula observed by the Hard X-ray Telescope (HXT) of the Japanese X-ray astronomy satellite ASTRO-H.
The size of the Crab Nebula is the same as that of HXT’s angular resolution, and the Crab pulsar at the center is too bright, making it difficult to recover images of the Crab Nebula using conventional methods. By developing and applying our method to overcome this difficulty, we found that the size of the Crab Nebula becomes smaller at higher energies in the hard X-ray band. We also succeeded in recovering the torus and jet structures at low energy band. This method can be applied to nebular diffuse objects with bright point sources similar to the Crab Nebula, even if they are observed by other telescopes.

Research Summary

The Crab Nebula is a supernova remnant*1 in the direction of Taurus, approximately 6,500 light years from Earth. There is a rapidly rotating neutron star with a strong magnetic field (Crab pulsar) at the center of the Crab Nebula. The Crab Nebula is a pulsar-wind nebula that shines brightly due to electromagnetic waves emitted by high-energy particles accelerated in the pulsar's magnetosphere*2. The Crab Nebula is a well-known object to observe for telescope instrument calibration because of its brightness and stable luminosity. On the other hand, for the reasons described below, the images of the Crab Nebula taken by the Japanese X-ray Astronomy Satellite ASTRO-H are difficult to be processed into high resolution images using conventional image restoration techniques.

ASTRO-H is a Japanese X-ray astronomy satellite (telescope) jointly developed by JAXA and NASA (National Aeronautics and Space Administration) to observe high-energy phenomena on black holes, galaxy clusters etc. It is no longer in operation. ASTRO-H was equipped with the Hard X-ray Telescope (HXT), a telescope sensitive to the higher-energy “hard” X-ray band*3. It was the telescope with the highest light-accumulating power in the hard X-ray band and had high angular resolution*4 (about 1.6 arcminutes; Half-power Diameter: HPD*5). The NuSTAR satellite in the United States is the other hard X-ray sensitive telescope in operation, with an angular resolution comparable to that of ASTRO-H.

ASTRO-H observed the Crab Nebula in the early phase of its operation to calibrate its instruments. In this study, we developed a new algorithm to enhance the resolution of images of the Crab Nebula taken by the HXT using an image restoration technique called Image Deconvolution*6.
In the soft X-ray band, the Chandra X-ray satellite has achieved a high angular resolution of about 0.8 arcsec (HPD) and has observed beautiful images of the Crab Nebula. On the other hand, there has been no observation of the hard X-ray band with a telescope having a high angular resolution like HXT except for the NuSTAR satellite. The Crab Nebula is a difficult object to restore the high-resolution image because its size is comparable to the angular resolution of HXT, and the central Crab pulsar is far brighter than the Crab Nebula itself. Therefore, the high-resolution image of the Crab Nebula obtained in the hard X-ray band by this research is scientifically valuable.

Figure 1 shows the result of the Image Deconvolution for the Crab Nebula. From left to right, the images are for the low-energy (3.6-15 keV), intermediate-energy (15-30 keV), and high-energy (30-70 keV) bands. The upper panel of Figure 1 shows the observed image before image processing. The entire image is blurred and it is difficult to separate the Crab Nebula from the Crab Pulsar, which should exist in the center of the Crab Nebula. It is also difficult to grasp the structure of the Crab Nebula. On the other hand, the lower panel is the output result of Image Deconvolution, and the structure of the Crab Nebula can be seen.

The higher resolution image clearly shows that the size of the Crab Nebula decreases with increasing energy. This is an important observation result that restricts the radiative model of the Crab Nebula. This is something that could not be understood at all in the observation image before the deconvolution process (upper part of Figure 1).
To demonstrate that the Image Deconvolution method developed in this study works well, we show a soft X-ray band image of the Crab Nebula (Figure 2). The right image of the Crab Nebula taken with the Chandra X-ray satellite, which has a higher angular resolution than ASTRO-H, and can be considered a true image in this energy band. The image on the left is the image obtained by image deconvolution of the ASTRO-H HXT image (identical to the lower left panel of Figure 1). The left image also shows the torus and jet structure*7 of the Crab Nebula, which are identified in the Chandra X-ray satellite image. It shows that our image deconvolution can successfully recover the true image of the Crab Nebula.

X-rays from celestial objects (Crab Nebula) pass through a telescope (HXT) and are observed by a pixel detector located at the focal plane. The image of the Crab Nebula is represented as a collection of point sources. The image of the Crab Nebula can be estimated by using the Point Spread Function (PSF), which is the distribution of X-rays emitted from each point source and detected on the pixel detector after they pass through the HXT. This problem of estimating the original image is called the “inverse problem.” In this research, we developed an algorithm to solve this inverse problem.

Pixel detectors can acquire the number of counts of X-ray photons. It is known that the counts follow a probability distribution called the Poisson distribution. In conventional image deconvolution, the object shape is basically estimated by maximum likelihood estimation*8 using this probability distribution. In the case of the Crab Nebula observed by HXT, however, the amount of data was not sufficient for this method, resulting in noisy restored images and unsatisfactory results.

In the proposed new method, a prior distribution with smooth constraints is set and the original image is estimated using the framework of Bayesian estimation*9. If a simple smooth constraint is applied, the Crab Nebula would be obscured by the Crab Pulsar because it is orders of magnitude brighter than the Crab Nebula. This problem was solved by representing the original image as a two-component model of the Crab Pulsar and Crab Nebula, and applying smooth constraints only to the Crab Nebula component. An iterative method called the “EM algorithm” (Figure 3) was used to maximize the posterior probability.
There are many nebular diffuse objects with bright point sources similar to the Crab Nebula. This method can be used for such objects. It can also be applied to telescopes other than ASTRO-H.

Terminologies

• ^*1 Supernova remnant: A nebula-like object left behind after a supernova explosion.
• ^*2 Pulsar’s magnetoshere: A region strongly affected by the magnetic field of a neutron star (pulsar).
• ^*3 Hard X-ray band: X-rays with energies above about 10 keV are called hard X-rays, and those below that are called soft X-rays.
• ^*4 Angular resolution: The smallest angle at which two nearby objects can be identified.
• ^*5 Half-power Diameter (HPD): It represents the angular resolution of a telescope. The diameter of the circle containing half of the incident X-ray photons.
• ^*6 Image deconvolution: A computational image processing technique used to restore an image taken with optical system (telescope, microscope) by correcting distortions and blurring caused by the optical system.
• ^*7 Torus and jet structure: The Crab Nebula is circularly distributed around the axis of rotation of a fast-rotating neutron star (Crab Pulsar) located at its center. In the direction of the axis of rotation, jets of plasma flow out.
• ^*8 Maximum likelihood estimation: The image of the Crab Nebula is estimated by calculating the parameters of the probability distribution (luminosity of the image of the Crab Nebula) that maximizes the probability (likelihood) of obtaining observed data.
• ^*9 Bayesian estimation: The image of the Crab Nebula is estimated by calculating parameters that maximize the posterior probability, which is obtained by multiplying the likelihood obtained from the observed data to the prior probability based on prior knowledge that the distribution of the Crab Nebula is smooth.

Information

Author

MORII Mikio
March 1999: B.S., Department of Physics, Tokyo Institute of Technology
March 2001: M.S., Department of Physics, Tokyo Institute of Technology
March 2004: Ph.D., Department of Physics, Tokyo Institute of Technology
April 2004-September 2006: Aerospace Project Researcher, ISS Science Project Office, Japan Aerospace Exploration Agency
October 2006-December 2008: Post-Doctoral Fellow, Research Center for Measurement in Advanced Science, Rikkyo University
January 2009-March 2013: Global COE Researcher, Department of Physics, Tokyo Institute of Technology
April 2013-March 2015: Affiliated Scientist, MAXI team, RIKEN
April 2015-March 2016: Project Researcher, Research Center for Statistical Machine Learning, The Institute of Statistical Mathematics
April 2016-June 2019: Project Assistant Professor, Research Center for Statistical Machine Learning, The Institute of Statistical Mathematics
July 2019-March 2022: Data Analyst, DATUM STUDIO Co., Ltd.
April 2022-Present: Associate Senior Researcher, Science Satellite Operation and Data Archive Unit, Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, on secondment from DATUM STUDIO Co., Ltd.