New formula to help estimate the mass of Black Hole

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A new study has suggested a formula that can help probe black holes. Black holes (BH) cannot be observed directly, but their presence can be detected by the huge amount of energy that is liberated through temporary accumulation of matter outside the BH, before it dives into the BH, a process called accretion.



  • Scientists have found the formula that can assess the spectrum emitted from the accretion discs around black holes. Spectra of accretion discs can help estimate the mass of the black hole. 
  • Accretion flow around BH is composed of ionised plasma, which is a soup of bare electrons and protons. Since electrons are more prone to radiative losses than the protons, it is expected that around a BH, electrons and protons would settle down into two separate temperature distributions. 
  • Therefore, the two-temperature equations are generally solved to obtain the emitted spectrum from the electron temperature distribution. This is known as two-temperature modeling of accretion flows.
  • Scientists from Aryabhatta Research Institute of Observational Sciences (ARIES), an autonomous institute under the Department of Science and Technology (DST), Govt. of India, investigated the nature of these two-temperature flows.
  • The research led by Shilpa Sarkar and Indranil Chattopadhyay from ARIES along with Philippe Laurent from IRFU / Service d’ Astrophysique and Laboratoire Astroparticule et Cosmologie, which has been recently accepted for publication in the journal Astronomy & Astrophysics (A&A), found that the number of unknown variables in the two-temperature regime exceeds the number of equations present. Hence, we get multiple solutions for the same set of constants of motion, like total energy or mass-inflow rate.
  • Using this formula, they found that with the increase of the mass supply to the central BH, the accretion disc becomes brighter and more high energy photons are emitted. With the increase of mass of the BH, luminosity increases, and the bandwidth of the emitted spectrum, both in the high energy and low energy range, increases, but the spectral shape does not change. In other words, matter around a massive BH will produce a lot of photons in the low energy and high energy band, but around a smaller BH, it will emit predominantly in the X-rays.
  • According to the ARIES team, this is the first time any approach of removing degeneracy from two-temperature theory has been proposed. It is necessary to obtain a correct solution, and hence a correct spectrum for any accretion flow around BH as any arbitrary choice of solution would give us a wrong picture of the system. The results could contribute in the understanding of physical processes around extreme objects like BHs.


About Aryabhatta Research Institute of Observational Sciences (ARIES) or Devasthal telescope

  • It is the largest optical telescope of its kind in Asia.
  • It will be used to study star structures and magnetic field structures of stars.
  • India produced this telescope in collaboration with a Belgian company called AMOS (Advanced Mechanical and Optical Systems) to build and install the mirrors in 2007
  • The telescope with a 3.6-metre-wide primary mirror will collect light from its field of view and focus it onto a 0.9-m secondary mirror from where it will be diverted to various detectors for analysis. This arrangement, called the Ritchey-Chrétien design.
  • It is located in a relatively advantageous position at a peak 2.5 km high in the Western Himalaya and 50 kilometers west of Nainital.
  • It will be able to log the physical and chemical properties of stars and star clusters; high-energy radiation emanating from sources like black holes; and the formation and properties of exo-planets.
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