Are radio telescopes finding radio-dark Nebulas

Are radio telescopes finding radio-dark Nebulas

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Are there "dark nebula" spots in the sky for radio telescopes? By that I mean, are there portions in the sky where these telescopes do not receive any radio waves? If so, do they match the visual dark nebula spots.

Silence please! Why radio astronomers need things quiet in the middle of a WA desert

Kate Chow works for the Commonwealth Scientific and Industrial Research Organisation.


CSIRO provides funding as a founding partner of The Conversation AU.

The Conversation UK receives funding from these organisations

A remote outback station about 800km north of Perth in Western Australia is one of the best places in the world to operate telescopes that listen for radio signals from space.

It’s the site of CSIRO’s Murchison Radio-astronomy Observatory (MRO) and is home to three telescopes (and soon a fourth when half of the Square Kilometre Array, the world’s largest radio telescope, is built there).

But it’s important these telescopes don’t pick up any other radio signals generated here on Earth that could interfere with their observations.

That’s why the observatory was set up with strict rules on what can and can’t be used on site.

Me (left) and my colleague Carol Wilson at the signs marking the start of the Australian Radio Quiet Zone WA. CSIRO , Author provided

Radio telescopes could spot stars hidden in the galactic center

The center of our Milky Way galaxy is a mysterious place. Not only is it thousands of light-years away, it's also cloaked in so much dust that most stars within are rendered invisible. Harvard researchers are proposing a new way to clear the fog and spot stars hiding there. They suggest looking for radio waves coming from supersonic stars.

"There's a lot we don't know about the galactic center, and a lot we want to learn," says lead author Idan Ginsburg of the Harvard-Smithsonian Center for Astrophysics (CfA). "Using this technique, we think we can find stars that no one has seen before."

The long path from the center of our galaxy to Earth is so choked with dust that out of every trillion photons of visible light coming our way, only one photon will reach our telescopes. Radio waves, from a different part of the electromagnetic spectrum, have lower energies and longer wavelengths. They can pass through the dust unimpeded.

On their own, stars aren't bright enough in the radio for us to detect them at such distances. However, if a star is traveling through gas faster than the speed of sound, the situation changes. Material blowing off of the star as a stellar wind can plow into the interstellar gases and create a shock wave. And through a process called synchrotron radiation, electrons accelerated by that shock wave produce radio emission that we could potentially detect.

"In a sense, we're looking for the cosmic equivalent of a sonic boom from an airplane," explains Ginsburg.

To create a shock wave, the star would have to be moving at a speed of thousands of miles per second. This is possible in the galactic center since the stars there are influenced by the strong gravity of a supermassive black hole. When an orbiting star reaches its closest approach to the black hole, it can easily acquire the required speed.

The researchers suggest looking for this effect from one already known star called S2. This star, which is hot and bright enough to be seen in the infrared despite all the dust, will make its closest approach to the Galactic center in late 2017 or early 2018. When it does, radio astronomers can target it to look for radio emission from its shock wave.

"S2 will be our litmus test. If it's seen in the radio, then potentially we can use this method to find smaller and fainter stars -- stars that can't be seen any other way," says co-author Avi Loeb of the CfA.

Are radio telescopes finding radio-dark Nebulas - Astronomy

Observations of the entire Carina Nebula have been made in the radio continuum at 0.843 GHz using the Molonglo Observatory Synthesis Telescope (MOST), covering an area of 7 deg^2^ with an enhanced resolution of 30". The observations reveal both the detailed structure of Car I and Car II, and the filamentary nature of the surrounding emission. Car I consists of three bright features, two of which (Car I-E and Car I-W) are opposing arcs that form a ringlike structure of diameter 2', while a third structure (Car I-S) lies several arcminutes to the south. These three features lie within a broad plateau and are interpreted as ionization fronts at a dense dust/molecular Cloud to the west. The characteristics of the region are consistent with ionization by the Tr 14 cluster. In the Car II region, three ionization fronts are present (Car II-E, Car II-W, and Car II-N) that form a ring structure enveloping a small dense molecular cloud. Radio emission associated with the peculiar star n Car appears prominently in the observations. New resolution-enhanced IRAS images of the nebula at 60 microns are also presented, and these show a close correspondence with the radio in all parts of the nebula, except to the west of Car I where bright infrared emission arises from a radio dark channel. No evidence of nonthermal Galactic radio emission is found in the region. The new data suggest that the dust/molecular cloud lying in the dark lanes across the nebula has a low density and is intermixed with the ionized gas to the southeast of Car II, but increases significantly in density near Car I, where its eastern face lies in contact with the ionized material, before wrapping around the back of the nebula.

Radio Telescopes Reveal Youngest Stellar Corpse

Astronomers using a global combination of radio telescopes to study a stellar explosion some 30 million light-years from Earth have likely discovered either the youngest black hole or the youngest neutron star known in the Universe. Their discovery also marks the first time that a black hole or neutron star has been found associated with a supernova that has been seen to explode since the invention of the telescope nearly 400 years ago.

Galaxy and Supernova (47K)
A VLA image (left) of the galaxy NGC 891,
showing the bright supernova explosion below
the galaxy's center. At right, a closer view of
the supernova, made with a global array of radio
CREDIT: Miguel A. Perez-Torres, Antxon Alberdi and
Lucas Lara, Instituto de Astrofisica de
Andalucia - CSIC, Spain, Jon Marcaide and
Jose C. Guirado, Universidad de Valencia,
Spain Franco Mantovani, IRA-CNR, Italy,
Eduardo Ros, MPIfR, Germany, and Kurt W.
Weiler, Naval Research Laboratory, USA

Multi-Frequency Closeup View (201K)
Blue and white area shows the nebula surrounding the
black hole or neutron star lurking in the center of the
supernova. This nebula is apparent at a higher radio
frequency (15 GHz). The red and also the contours show the
distorted, expanding shell of material thrown off in the
supernova explosion. This shell is seen at a lower radio
frequency (5 GHz).
CREDIT: Michael F. Bietenholz and Norbert Bartel,
York University, Michael Rupen, NRAO, NRAO/AUI/NSF

A supernova is the explosion of a massive star after it exhausts its supply of nuclear fuel and collapses violently, rebounding in a cataclysmic blast that spews most of its material into interstellar space. What remains is either a neutron star, with its material compressed to the density of an atomic nucleus, or a black hole, with its matter compressed so tightly that its gravitational pull is so strong that not even light can escape it.

A team of scientists studied a supernova called SN 1986J in a galaxy known as NGC 891. The supernova was discovered in 1986, but astronomers believe the explosion actually occurred about three years before. Using the National Science Foundation's Very Long Baseline Array (VLBA), Robert C. Byrd Green Bank Telescope (GBT), and Very Large Array (VLA), along with radio telescopes from the European VLBI Network, they made images that showed fine details of how the explosion evolves over time.

"SN 1986J has shown a brightly-emitting object at its center that only became visible recently. This is the first time such a thing has been seen in any supernova," said Michael Bietenholz, of York University in Toronto, Ontario. Bietenholz worked with Norbert Bartel, also of York University, and Michael Rupen of the National Radio Astronomy Observatory (NRAO) in Socorro, New Mexico, on the project. The scientists reported their findings in the June 10 edition of Science Express.

"A supernova is likely the most energetic single event in the Universe after the Big Bang. It is just fascinating to see how the smoke from the explosion is blown away and how now after all these years the fiery center is unveiled. It is a textbook story, now witnessed for the first time," Bartel said.

Analysis of the bright central object shows that its characteristics are different from the outer shell of explosion debris in the supernova.

"We can't yet tell if this bright object at the center is caused by material being sucked into a black hole or if it results from the action of a young pulsar, or neutron star," said Rupen.

"It's very exciting because it's either the youngest black hole or the youngest neutron star anybody has ever seen," Rupen said. The youngest pulsar found to date is 822 years old.

Finding the young object is only the beginning of the scientific excitement, the astronomers say.

"We'll be watching it over the coming years. First, we hope to find out whether it's a black hole or a neutron star. Next, whichever it is, it's going to give us a whole new view of how these things start and develop over time," Rupen said.

For example, Rupen explained, if the object is a young pulsar, learning the rate at which it is spinning and the strength of its magnetic field would be extremely important for understanding the physics of pulsars.

The scientists point out that it will be important to observe SN 1986J at many wavelengths, not just radio, but also in visible light, infrared and others.

In addition, the astronomers also now want to look for simiilar objects elsewhere in the Universe.

Copyright © 2009 Associated Universities, Inc.
The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Using an RTL-SDR to Measure the Basis for the Dark Matter Hypothesis

From calculations depending on the distribution of visible star mass in our galaxy, a certain galactic rotational velocity vs distance from center curve is expected. However, when scientists actually measure the galactic rotation, another curve is found - a curve which should result in the galaxy flying apart. This mismatch in expected vs measured data has given rise to the theory of "dark matter". The theory essentially states that in order to get the measured curve, the galaxy must have more mass, and that this mass must come from non-luminous matter scattered amongst the galaxy which is difficult or impossible to observe.

In the past we have posted about Job Geheniau's radio astronomy projects a few times on this blog. So far he has used an RTL-SDR and radio telescope dish to generate a full radio image of the galaxy at the Hydrogen Line frequency of 1.42 GHz. This project worked by pointing the telescope at one section of the galaxy, measuring the total Hydrogen line power with the RTL-SDR over a number of minutes, then moving the telescope to the next section.

Job's Radio Telescope + Laptop and RTL-SDR Setup

Using the same hardware and techniques to observe the Hydrogen Line frequency, he was now able to measure the rotational curve of our galaxy. When the telescope points to different arms of the galaxy, the Hydrogen line measurement will be doppler shifted differently. The measured doppler shift can be used to figure out the rotational velocity of that particular arm of the galaxy. By measuring the rotational velocity from the center of the galaxy to the outer edges, a curve is created. Job's measured curve matches that seen by professional radio astronomers, confirming the mismatch in expected vs measured data.

Job's Measured vs Expected Curve

If you'd like to get started with Hydrogen line radio astronomy with an RTL-SDR, we have a tutorial over here.

Why radio astronomers need things quiet in the middle of a Western Australia desert

Panorama of the spectacular night sky over some of the ASKAP antennas at the MRO. Credit: Alex Cherney/CSIRO, Author provided

A remote outback station about 800km north of Perth in Western Australia is one of the best places in the world to operate telescopes that listen for radio signals from space.

It's the site of CSIRO's Murchison Radio-astronomy Observatory (MRO) and is home to three telescopes (and soon a fourth when half of the Square Kilometre Array, the world's largest radio telescope, is built there).

But it's important these telescopes don't pick up any other radio signals generated here on Earth that could interfere with their observations.

That's why the observatory was set up with strict rules on what can and can't be used on site.

One of the radio telescopes is the Australian Square Kilometre Array Pathfinder (ASKAP) operated by CSIRO. It's actually an array of 36 individual antennas that work together as one large telescope.

ASKAP can capture high-quality images and scan the whole sky, a bit like a wide-angle lens allowing you to see more through a single viewpoint. It has already found a niche as a finder and localiser of fast radio bursts. These are flashes of radio waves in space that last just milliseconds.

The MRO site also hosts the Curtin University-led Murchison Widefield Array (MWA) telescope, which has been peering into the universe's "dark ages" and finding no trace of aliens.

Antennas of the Murchison Widefield Array (MWA) low-frequency radio telescope. Credit: Dragonfly Media, Author provided

The other radio telescope is Arizona State University's EDGES, which is looking for signals from the formation of stars and galaxies early in the universe.

These internationally recognized instruments detect mere whispers from space—radio waves that have traveled for billions of light-years before reaching Earth.

But their sensitivity exposes them to sources of unwanted radio frequency interference, known as RFI.

RFI can be caused by radio transmitters, such as mobile phones, CB radios or even wi-fi devices. Electrical equipment such as power tools can also be a problem.

Way outback and beyond

What makes the Murchison region an ideal operating environment for limiting RFI is the location has minimal human activity or occupancy. The Murchison Shire is the size of a small country but with a population of only 100 people.

The Shire covers an area of 49,500km²—roughly the size of the Netherlands in Europe.

With the help of the Commonwealth and Western Australia governments, significant regulatory protection has been established to protect the site.

For example, the Australian Radio Quiet Zone Western Australia (ARQZWA), established by the Australian Communications and Media Authority, created a fixed zone around the MRO site to protect the telescopes from interference. Other groups intending to use transmitting equipment must seek permission first and follow any guidelines given.

The Experiment to Detect the Global EoR Signature (EDGES) instrument. Credit: CSIRO, Author provided

Switch off everything

When staff go out to the site for the first time they get training about RFI, health and safety and indigenous culture.

Mobile phones need to be turned off at all times (which is fine, because it's too far from any mobile towers to work anyway).

Bluetooth devices (wireless mice or fitness trackers) should be switched off or left behind, laptops should have Bluetooth and Wi-Fi switched off. The list goes on.

The MRO control building has a double RFI door to enter through—think airlock-style in any sci-fi movie.

The site has a hybrid power station with solar panels that deliver up to 40% of the observatory's power.

During the day, when the the clean energy system generates more power than the site requires, the excess energy is stored in a 2.5MWh lithium-ion battery, one of the largest in Australia.

The design specifications of the MRO power station ensure the facility contains the RFI generated by its own electronic systems.

The location of the MRO on Boolardy Station in WA. Credit: CSIRO, Author provided

You can't stop everything

Unfortunately, as with all Earth-based locations, the telescopes receive RFI from orbiting satellites, which fall under international jurisdiction. The site also receives signals from aircraft safety beacons on commercial flights over the region.

Astronomers have developed software to remove this RFI from data as it usually overwhelms any astronomical signals.

We've also had several recorded occasions (usually during summer) when radio signals from as far away as Perth have been detected, due to atmospheric ducting. This is where the atmosphere effectively "guides" the radio waves much further than they would normally travel, due to changes in the atmospheric layers. Fortunately this is very rare.

The MRO has been in existence for about ten years, one of the newest such observatories in the world, but the 3,450km² Boolardy pastoral station on which it stands was established back in the 1850s.

The traditional owners are the Wajarri Yamatji, who have lived in the region for tens of thousands of years. Together we negotiated an Indigenous Land Use Agreement (ILUA) in 2009 for the current telescopes, and we are negotiating a second one to allow the construction of the SKA.

Protection of the indigenous heritage is a significant component of this agreement and a major responsibility for the Australian government, CSIRO and the SKA organization.

We also work collaboratively with neighboring pastoralists to ensure they can carry on their daily work, including practices such as mustering, in a way that is compatible with radio astronomy.

Aerial view of the MRO power station, which has an array of 5,280 solar panels and battery with RFI shielding. Credit: CSIRO, Author provided

Visitors are not welcome

Due to the remoteness of the MRO and the radio quiet rules and regulations, even those involved with the projects are discouraged from visiting (I've only been to the site once).

Tourists are discouraged. We've distributed fact sheets to locals and visitor centers to explain this in more detail.

But you can visit the site remotely. We've created a cool techy replacement where you can take a virtual tour of this unique and wondrous place.

This article is republished from The Conversation under a Creative Commons license. Read the original article.


The radio telescope comprises 27 independent antennas in use at a given time plus one spare, each of which has a dish diameter of 25 meters (82 feet) and weighs 209 metric tons (230 short tons). [4] The antennas are distributed along the three arms of a track, shaped in a wye (or Y) -configuration, (each of which measures 21 kilometres (13 mi) long). Using the rail tracks that follow each of these arms—and that, at one point, intersect with U.S. Route 60 at a level crossing—and a specially designed lifting locomotive ("Hein's Trein"), [5] the antennas can be physically relocated to a number of prepared positions, allowing aperture synthesis interferometry with up to 351 independent baselines: in essence, the array acts as a single antenna with a variable diameter. The angular resolution that can be reached is between 0.2 and 0.04 arcseconds. [6]

There are four commonly used configurations, designated A (the largest) through D (the tightest, when all the dishes are within 600 metres (2,000 ft) of the center point). The observatory normally cycles through all the various possible configurations (including several hybrids) every 16 months the antennas are moved every three to four months. Moves to smaller configurations are done in two stages, first shortening the east and west arms and later shortening the north arm. This allows for a short period of improved imaging of extremely northerly or southerly sources. [ citation needed ]

The frequency coverage is 74 MHz to 50 GHz (400 cm to 0.7 cm). [7]

The Pete V. Domenici Science Operations Center (DSOC) for the VLA is located on the campus of the New Mexico Institute of Mining and Technology in Socorro, New Mexico. The DSOC also serves as the control center for the Very Long Baseline Array (VLBA), a VLBI array of ten 25-meter dishes located from Hawaii in the west to the U.S. Virgin Islands in the east that constitutes the world's largest dedicated, full-time astronomical instrument. [8]

In 2011, a decade-long upgrade project resulted in the VLA expanding its technical capacities by factors of up to 8,000. The 1970s-era electronics were replaced with state-of-the-art equipment. To reflect this increased capacity, VLA officials asked for input from both the scientific community and the public in coming up with a new name for the array, and in January 2012 it was announced that the array would be renamed the "Karl G. Jansky Very Large Array". [9] [10] [11] On March 31, 2012, the VLA was officially renamed in a ceremony inside the Antenna Assembly Building. [12]

The VLA is a multi-purpose instrument designed to allow investigations of many astronomical objects, including radio galaxies, quasars, pulsars, supernova remnants, gamma-ray bursts, radio-emitting stars, the sun and planets, astrophysical masers, black holes, and the hydrogen gas that constitutes a large portion of the Milky Way galaxy as well as external galaxies. In 1989 the VLA was used to receive radio communications from the Voyager 2 spacecraft as it flew by Neptune. [13] A search of the galaxies M31 and M32 was conducted in December 2014 through January 2015 with the intent of quickly searching trillions of systems for extremely powerful signals from advanced civilizations. [14]

It has been used to carry out several large surveys of radio sources, including the NRAO VLA Sky Survey and Faint Images of the Radio Sky at Twenty-Centimeters.

In September 2017 the VLA Sky Survey (VLASS) began. [15] This survey will cover the entire sky visible to the VLA (80% of the Earth's sky) in three full scans. [16] Astronomers expect to find about 10 million new objects with the survey — four times more than what is presently known. [16]

The driving force for the development of the VLA was David S. Heeschen. He is noted as having "sustained and guided the development of the best radio astronomy observatory in the world for sixteen years." [17] Congressional approval for the VLA project was given in August 1972, and construction began some six months later. The first antenna was put into place in September 1975 and the complex was formally inaugurated in 1980, after a total investment of US$78,500,000 (equivalent to $246,564,822 in 2020). [7] It was the largest configuration of radio telescopes in the world.

With a view to upgrading the venerable 1970s technology with which the VLA was built, the VLA has evolved into the Expanded Very Large Array (EVLA). The upgrade has enhanced the instrument's sensitivity, frequency range, and resolution with the installation of new hardware at the San Agustin site. A second phase of this upgrade may add up to eight additional dishes in other parts of the state of New Mexico, up to 190 miles (300 km) away, if funded. [18]

Magdalena Ridge Observatory is a new observatory under construction a few miles south of the VLA. It includes an optical interferometer and is run by VLA collaborator New Mexico Tech.

The VLA is located between the towns of Magdalena and Datil, about 50 miles (80 km) west of Socorro, New Mexico. U.S. Route 60 passes east–west through the complex. [ citation needed ]

The VLA site is open to visitors year round during daylight hours, and on every first and third Saturdays of the month, special guided and behind-the-scenes tours are offered. A visitor center houses a small museum, theater, and a gift shop. A self-guided walking tour is available, as the visitor center is not staffed continuously. Visitors unfamiliar with the area are warned that there is little food on site, or in the sparsely populated surroundings those unfamiliar with the high desert are warned that the weather is quite variable, and can remain cold into April. [3] For those who cannot travel to the site, the NRAO created a virtual tour of the VLA called the VLA Explorer. [19]

The VLA has appeared repeatedly in American popular culture since its construction.

Are radio telescopes finding radio-dark Nebulas - Astronomy

Why are major telescopes always built in the middle of nowhere, why not on large sky scrapers or university campuses?

This is a good question. I agree that it would be more convenient to have all our telescopes on the roof of the astronomy building, here on campus rather than having to fly all around to go observing (though perhaps not as much fun!).

There are two good reasons why telescopes are generally built "in the middle of nowhere":

1- Light pollution. Where there are people, there is light. And this light can interfere with astronomical observations. If you have tried to look at the sky during the night in a big city, you will have noticed that you are only able to see a handful of stars, even on a cloudless night. The glow of the lights makes the sky look bright and makes impossible good astronomical observations. For more details on light pollution, see this previously answered question, and have a look at this map of Earth, showing the regions affected by light pollution.

A map of the world, showing the extent of light pollution. The brighter a region is, the worse light pollution is for astronomical observations. Credit: P. Cinzano, F. Falchi (University of Padova), C. D. Elvidge (NOAA National Geophysical Data Center, Boulder). Copyright Royal Astronomical Society. Reproduced from the Monthly Notices of the RAS by permission of Blackwell Science.

The usual form of light pollution we are used to means that optical telescopes have a hard time seeing but radio telescopes suffer the same problems. Cell phones, wireless internet, GPS satellites, and even planes and cars can all be "seen" by radio telescopes. They also have to be built in remote locations away from transmitters or radio sources so that they can observe celestial radio waves directly.

2- Atmospheric conditions. We use space telescopes, like Hubble, because you gain a lot by getting rid of the atmosphere. For groundbased telescopes, the light from astronomical objects that they receive has to go through all of the atmosphere, which causes attenuation and distortion. Therefore, the less atmosphere and the more stable the atmosphere, the better. For some types of telescopes, humidity is also a problem, so the dryer the atmosphere the better. The sites in the world that fit these criteria are few and generally remote: the top of volcano Mauna Kea in Hawaii, the Atacama desert in Northern Chile (and other sites in altitude in Chile), Antarctica, the desert in Arizona, California and New Mexico (though this last places suffer more and more from light pollution as cities get bigger and bigger).

For a combination of all these reasons, astronomers end up having to travel around the world to visit telescopes that are located in prime locations. Though these days, it is getting more and more common for observations to be done remotely, thanks to the Internet. Some telescopes are now setup in a way that allows astronomers to control them by sending commands through the Internet, which requires only a telescope operator to be present on site. For example, while I am writing this answer to you, I am observing galaxies from the comfort of my office in Ithaca, NY, using the Arecibo telescope, a radio telescope located in Puerto Rico!

This page was last updated November 21, 2015.

About the Author

Amelie Saintonge

Amelie is working on ways to detect the signals of galaxies from radio maps.

4 Strange Objects Discovered in Deep Space Have Astronomers Baffled

Australian astronomers are puzzled by the discovery of 4 mystery objects discovered through the use of radio telescope.

Four unidentified objects have been discovered in deep space and astronomers have never seen anything like them. Australian astronomers know that the mysterious objects are round with bright outer edges. They apparently look like four "distant ring-shaped islands" and were discovered while astronomers were mapping the sky in radio frequencies. This is a part of a pilot survey for a new project called the Evolutionary Map of the Universe (EMU).

The four unidentified objects have been dubbed, odd radio circles, or ORC. According to the research team's findings, "None of the ORCs has obvious optical, infrared, or X-ray counterparts to the diffuse emission, although in two cases there is an optical galaxy near the center of the radio emission." They went on to note that the ORCs have "strong circular symmetry" and all had a diameter of around one arcminute. For comparison, the moon's diameter is 31 arcminutes. The astronomers have ruled out objects like supernovas, star-forming galaxies, planetary nebulas, and gravitational lensing.

One theory about the ORCs states that they could be shockwaves leftover from some "extragalactic event" or even possible activity from a radio galaxy. "While this is a theoretical possibility, such a shock has not yet been observed elsewhere," researchers say. With that being said, it sounds like this could very well be a pretty major discovery, which is all thanks to two different radio telescopes. The astronomers used two just to make sure they were not getting any imaging errors since they were blown away by what they discovered. Kaustubh Rajwade, from the Jodrell Bank Centre for Astrophysics, University of Manchester, U.K., who is not affiliated with the original study, had this to say about the discovery.

This is exciting for the world of astronomy, but may be a bit of a disappointment for those hoping that these were UFOs with Alien pilots. There's a lot going on out in space exploration at the moment and there's more to come. Chinese astronomers recently found a green gel-like substance on the dark side of the moon, which was very intriguing to everybody involved, though it turned out to be a mixture of melted moon rock, thanks to an alleged meteoroid crash.

The report has not been officiated by Nature Astronomy, though it has been submitted for peer review. From there, the scientists will more than likely get the green light to explore further using different wave lengths and possibly getting a budget to do so. Who knows what else is lurking out there in deep space? You can head over to the Arxiv website to read the research paper and form your own hypothesis as to what these ORCs really are.