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Table 1.
Important variables used in this paper.
| Number of GCs | ||
|---|---|---|
 : with binary fraction data in the l-reference |
||
 : with spectrum data in the l′-reference |
||
 : matched between binary fraction and spectrum data |
||
| in the l′-reference | ||
 : the sum of  for all references |
||
| Number of spectra | ||
| Nspe(l′) : in the l′-reference | ||
 : matched with binary fraction data in the l′-reference |
||
 : the sum of  for all references |
||
| Number of bins for binary fraction data, to determine the | ||
| binary fraction profile (Eq. (3)), used in Eqs. (4)–(7) | ||
| nlbin(l): in the l-reference | ||
| nbin : for all references | ||
| Number of bins for spectrum data, to calculate fdev, used in Eq. (8) | ||
 : in the l′-reference |
||
 : for all reference |
||
| Number of matched spectra for the i-GC | ||
 : in the l′-reference |
||
 : for all reference |
||
| Radius in common use | ||
| RC : core radius | ||
| RHL: half-light radius | ||
| RHM: half-mass radius | ||
| RT : tidal radius | ||
| Radius related to binary fraction data | ||
| RWFC: HST’s ACS/WFC radius | ||
| RWFV: J15’s whole field of view | ||
| R1, 2, 3: J15’s the 1st to 3rd radius | ||
| Radius related to calculations in Eqs. (4)–(6) | ||
| Rl(i, j): the lower radius for the i-GC and j-bin | ||
| Ru(i, j): the upper radius for the i-GC and j-bin | ||
| Radius related to spectrum data, to calculate fdev, used in Eq. (8) | ||
| RS, equ(i, j′): equivalent radius for the i-GC and j′-bin | ||
| Binary-fraction type | ||
| f(q > x) : binary fraction by using a mass-ratio of 0.5,0.6,0.7 | ||
| f(qH) : binary fraction by using a high mass-ratio | ||
| f(tot) : the total value | ||
| f(tot)qf : f(tot) by using a q distribution of Fisher et al. (2005) | ||
| f(tot)qr : f(tot) by using a q distribution of random associations | ||
| f(tot)mc : f(tot) by using the counting method | ||
| f(tot)mf : f(tot) by using the fitting method | ||
| f(tot)min: the minimum of f(tot) | ||
| f(tot)max: the maximum of f(tot) | ||
| Analytic binary fraction | ||
| fa(i, j, kf, kff): for the i-GC, j-bin, kf-type binary fraction, | ||
| kff-fitting function | ||
| Binary-fraction to calculate χ2 | ||
| fav(i, j, kf, kff): the value of fa(i, j, kf, kff) after fitting calculation | ||
| f(i, j, kf) : the observed value for the i-GC, j-bin, | ||
| kf-type binary fraction | ||
| Binary-fraction derived | ||
| fder(i, j′,kf): for the i-GC, j′-bin, kf-type binary fraction | ||
| Binary-fraction derived in three cases | ||
| fder(q > 0.5) : in the case of f(q > 0.5) | ||
| fder(tot)mc : in the case of f(tot)mc | ||
| fder(tot)mf : in the case of f(tot)mf | ||
Notes. In each part, the first line is the common meaning and purpose for the variables in each part. The second to the last lines give the variables and their meaning.
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