How the super massive black hole have formed!!! 

That's remarkable news! As of my last knowledge update in September 2021, the James Webb Space Telescope (JWST) had not yet launched. However, if the information you provided is accurate, it signifies a significant achievement for astronomy and astrophysics.

       The James Webb Space Telescope is one of the most advanced space observatories ever constructed, designed to succeed the Hubble Space Telescope. It is specifically tailored to observe the universe in infrared light and is expected to revolutionize our understanding of the cosmos, including the study of supermassive black holes.

       The discovery of the most distant active supermassive black hole would mean that astronomers have detected a black hole with incredibly high mass and activity levels very far away from us in the universe. By observing such objects, scientists can gain insights into the early stages of galaxy formation, the co-evolution of galaxies and black holes, and the processes that govern their growth and activity.

       As this information is beyond my last update, I recommend checking the latest news from reliable sources in astronomy and space exploration to get more details on this exciting discovery made by the Webb Telescope.

       As of my last update in September 2021, the JWST had not yet launched, but it was highly anticipated in the scientific community for its potential to make groundbreaking discoveries. As an infrared space telescope, the JWST is particularly well-suited for observing distant and faint objects, including supermassive black holes.

       The detection of a supermassive black hole at such a vast distance suggests that researchers have managed to peer deep into the early universe and gain insights into its formation and evolution. Observing active black holes in the early cosmos allows scientists to study the conditions and processes that were prevalent billions of years ago, shedding light on how galaxies and black holes co-evolve over cosmic time.

       With this remarkable discovery, the JWST has already proven its value as a powerful tool for exploring the cosmos. I recommend keeping an eye on the latest scientific publications and updates from reputable sources to learn more about the specifics and implications of this fascinating discovery.

•  accelerate disc and emission:Massive black holes are often found at the centers of galaxies and can be actively accreting matter from their surroundings. As matter falls into the black hole, it forms an accretion disk around it. The intense gravitational forces and friction within the disk generate significant amounts of energy. This process emits electromagnetic radiation across the electromagnetic spectrum, from radio waves to X-rays and gamma rays.

• Radio Observation:Radio telescopes are used to detect the radio waves emitted from the accretion disks around massive black holes. The Very Long Baseline Interferometry (VLBI) technique, which combines signals from multiple radio telescopes across the world, helps achieve high-resolution images of these region.
• X-ray and Gamma-ray Observation:High-energy observatories like the Chandra X-ray Observatory and the Fermi Gamma-ray Space Telescope can detect X-rays and gamma rays emitted by the hot gas and particles near the black hole.
• Visible and Infrared observation:While the accretion disk emits high-energy radiation, the surrounding environment, such as the immediate vicinity of the black hole and the host galaxy, also emits visible and infrared light. These wavelengths can be observed with ground-based telescopes and space-based observatories.
• Doppler shift:As matter orbits the black hole, some of it may be ejected in powerful jets. These jets can emit radiation as well. By studying the Doppler shift of these emissions (how the wavelengths of light are stretched or compressed due to the motion of the source), astronomers can infer the velocity and direction of the outflowing material, providing clues about the presence of a black hole.
• Gravitational effect:The presence of a black hole can be inferred by observing the gravitational effects it has on nearby stars and gas. For example, if a star is seen to orbit an invisible companion with very high velocity, it could indicate the presence of a black hole.
• Quasars and active Galactic nuclei(AGN):Some of the most luminous objects in the universe are powered by massive black holes at their centers. Quasars and AGN are highly active and bright due to the accretion of matter into their black holes. Their intense emission makes them observable over vast distances.

Combining observations from different wavelengths and techniques helps astronomers build a comprehensive picture of these massive active black holes and understand their properties and behavior. Keep in mind that astronomical observations and technology may have advanced since my last update, so there might be new or more refined methods for detecting black holes beyond that point.