High Resolution Imaging of Exoplanets Using the Sun as a Lens

We will be able to take megapixel images of exoplanets by putting telescopes in zones that are 600 to 2000 times the distance of the Earth to the Sun. Getting to 600 times as far away from the Sun we can observe exoplanets in other solar systems when we go the exact opposite direction. We look back around the sun and there will be a ultra-high resolution donut image around the sun that is the image of part of the exoplanet.

Gravitational lensing of light is a well-known phenomenon that has been widely used to gather images of distant galaxies and measure the masses of the intervening lensing galaxy clusters. Gravitational lensing has also been used to detect and characterize exoplanets around distant stars, by the study of the transient amplification of light seen at Earth from background stars when the exoplanet and its host star passes directly in front of them. It is perhaps less well-known that the gravitational field of a star like the Sun produces a real image of distant exoplanets that could potentially be measured.

For an Earth-sized exoplanet located between one and ten parsecs away from the Sun and observed at about 1,000 au from the Sun, the image is kilometers in size and cannot be measured all at once by a meter-scale telescope.

The Einstein ring (donut like image) must be wider than the Sun to not be blocked by the Sun’s photosphere. This means getting out beyond 550 au and possibly a further so that the image is beyond the light effects of the sun. We will use coronagraphs to block out the sun, but getting more separation would make it easier to get rid of those light effects.

Creating a megapixel image requires at least one million separate measurements. For a typical photograph, each detector pixel within the camera is performing a separate measurement. This is not the case for exoplanet imaging at the SGL. Only the pixels in the telescope detector that image the Einstein ring are measuring the exoplanet, and the observed Einstein ring contains a blend of light from the entire exoplanet surface, due to the blur of the SGL, along with a large coronal foreground signal. Substantial deconvolution would be required to synthesize the exoplanet image.

Calculating Imaging Time

Consider a simple method to form a megapixel image of the exoplanet:
1. Divide the SGL image plane into a 1000×1000 grid that just contains the exoplanet in the ’directly imaged’ sense.
2. Position the telescope in the center of each pixel for a time T1 and measure the total combined power of the Einstein ring and solar corona.
3. Subtract the independently determined coronal power for each pixel to get the Einstein ring contribution at that pixel.
4. Multiply the vector of image pixels so obtained by a deconvolution matrix describing the SGL blur to obtain a vector of object pixels at the exoplanet

The time required to produce a 1000×1000 pixel image of an exo-Earth at the distance of Proxima Centauri with an SNR of 10 is by this formula the total time of 37 billion seconds, or 1,200 years. An exoplanet twice as far away will take four times as long to image.

Imaging time scales as the NxN image scales. Reducing the resolution to 500×500 reduces the measurement time by a factor of 16 to 75 years.

Reducing the resolution to 250×250 reduces the measurement time by a factor of 16 to 4.68 years.

Reducing the resolution to 125×125 reduces the measurement time by a factor of 16 to 3.5 months.

Reducing the resolution to 62×62 reduces the measurement time by a factor of 16 to 6.6 days.

Sending multiple telescopes reduces the time to form the images.
Ten one-meter telescopes to the same exoplanet image line would reduce the time by ten. This would reduce the 125X125 imaging time to about 10 days.
Twelve hundred one-meter telescopes would reduce the megapixel image time to 1 year.

If one could control the illumination of the exoplanet, a simple method to remove the blur is available. One could illuminate only one pixel on the exoplanet, gather the light for that pixel through the solar corona, and then illuminate the next pixel, and so on, until the whole exoplanet has been imaged. Because all regions contained in pixels other than the one being measured are dark, they cannot contribute light to the pixel of interest, so the blur need not be deconvolved away. The time to collect a megapixel image of an exo-Earth at Proxima Centauri would then
drop from 1,200 years to only 10 hours.

An exoplanet can only have as little as 10% of its surface illuminated as seen from Earth if its orbital plane is within 18 degrees of edge-on as viewed from Earth, which is relatively rare. Another is that the exoplanet would spend only a relatively small fraction of its orbit in such a crescent phase. If only 10% of the exoplanet’s surface is illuminated (g = 0.1), then the total measurement time is reduced by a factor of 100, or 12 years for the ’exo-Earth at Proxima Centauri’ case.

The observation strategy would be to capture many 15X15, 31X31 and 62X62 using a few dozen telescopes. Multiple observations would be used to understand the illumination phases and other characteristics that would impact how to observe the exoplanet. This could be used to make an observation plan.

SOURCES – Arxiv – Photometric Limits on the High Resolution Imaging of Exoplanets Using the Solar Gravity Lens,Phil A. Willems
Summary Written by Brian Wang, Nextbigfuture.com

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