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The Forefront of Space Science

Do “medium-sized black holes” exist?
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Calculating a black hole’s mass through X-ray observation

Star-sized and huge black holes are frequently observed as strong X-ray sources. By analyzing X-ray observational data, it is possible to know the black hole’s mass and the physical conditions around them. Today, based on such data, we can even discuss whether black holes rotate or not.

ISAS’s X-ray astronomical satellites, “TENMA,” “GINGA” and “ASCA,” have greatly contributed to the advancement of black-hole research with X-ray observations. One of GINGA’s significant achievements was its demonstration that an estimate of star-sized black holes’ mass is possible with X-ray spectrum observations. The principle is simple. At first, with X-ray observation, we calculate the size of accretion disk of star-sized black holes. An accretion disk is formed when objects from a companion star flow in whirls and fall into a black hole. The disk’s size is then combined with the Schwarzschild radius. From observations by TENMA and GINGA, it was found that the X-ray energy spectra of accretion disks can be approximated to blackbody radiation (one like glowing coals). The energy spectrum of blackbody radiation, including coals, accretion disk, etc., is given only by its temperature, and the emitted heat amount is given only by its surface area. The temperature of accretion disks around star-sized black holes is around 10 million degree. The temperature is determined with an X-ray spectrum fit, and then the disk area, namely the inner boundary radius, is determined with observed flux.

The GINGA satellite found that, even if a disk’s temperature and flux change largely, its inner boundary radius does not change. From the general theory of relativity, we know that rotating objects around a black hole cannot come closer than three times the Schwarzschild radius. Therefore, the disk’s radius should be exactly and always three times the Schwarzschild radius. This is exactly what the GINGA satellite revealed. This beautiful result is cited in a recent textbook of high-energy astrophysics (Fig.1).

Figure 1
Figure 1. Temporal change of X-ray spectrum parameters of the star-sized black hole “LMC X-3” measured by GINGA satellite. Even with great changes in mass-accretion ratio, brightness and high-energy constituent, the inner boundary of the disk is constant. Based on this, the mass of black holes is given. The figures are excerpted from the author’s doctoral dissertation. These also appear in the textbook “High Energy Astrophysics” by Longair.

What is the real identity of the celestial body “ULX” shining brightly in X-rays?

Black holes possess another important nature: the heavier the black hole, the lower the temperature of accretion disks around them. Since accretion disks are close to blackbody radiation, their brightness is proportional to the product of surface area and quadruplicated temperature. Meanwhile, as stated below, the maximum brightness of black holes is proportional to their mass. Now, you will recall that the Schwarzschild radius is proportional to mass. Surface area of disks is proportional to the square of the Schwarzschild radius, namely the square of mass. As a result, as a black hole’s mass increases, the inner boundary of accretion disks becomes larger and their temperature becomes lower. In fact, accretion disks around star-sized black holes have been observed with around 1keV in the X-ray region, while disks around huge black holes are observed with far longer wavelength in the ultraviolet region.

When objects fall into black holes and shine with gravity energy release, the brightness cannot exceed the “Eddington limit of luminosity” which is determined by mass. This means that, supposing spherical symmetry, there is a limit where objects are repelled by strong pressure of light and balance with gravity and, therefore, further release of gravity energy cannot take place. The Eddington limit of luminosity is proportional to mass. For example, in the case of solar mass, it is 1038 erg/sec. This means that, with star-sized black holes, brightness cannot exceed around 10 times the value 1039 erg/sec. Nonetheless, since the 1980s when imaging X-ray observation became possible, we discovered celestial bodies that are off the center core of galaxies and are substantially bright, shinning at around 1040 erg/sec. If they are black holes with a mass 100 times that of the Sun, they would not exceed the Eddington limit of luminosity. Are these bodies really “medium-sized black holes?”

With the ASCA satellite launched in 1993, it became possible to measure precisely the energy spectra of the bodies known as “Ultra-Luminous X-ray sources (ULX).” We believed that if we applied the approach established for star-sized black holes by the GINGA satellite to the measurement results, we would be able to discern the ULX’s mass. The results obtained, however, were the opposite of our expectation. If the ULX were medium-sized mass black holes, their accretion-disk temperature should have been lower than the disks of star-sized black holes. The temperature of all observed accretion disks, however, was higher than disks of star-sized black holes. If we understand correctly what the results suggest, then ULX have smaller mass than star-sized black holes (e.g., neutron stars) and shine at tens of times the Eddington luminosity. But this is physically impossible! What exactly is happening in ULX?

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