Документ взят из кэша поисковой машины. Адрес оригинального документа : http://hea-www.harvard.edu/~pgreen/figs/xraydefs.pdf Дата изменения: Tue Jan 24 01:00:27 2006 Дата индексирования: Tue Oct 2 00:33:40 2012 Кодировка: Поисковые слова: http www.astronomy.com

SORTING OUT and for X-RAYS
Take a power-law in frequency f ( ) = f0 expressed usually in erg cm-2 s
-1

Hz-1 . Here,

f0 is just a constant, defined to be the monochromatic flux at some reference frequency 0 . Since E = h , we can also reframe this as fE (E ) = fE0 E , expressed usually in erg cm-2 s
-1

keV-1 .
-1

The broadband flux between energies E1 and E2 in erg cm-2 s
E
2

is

F=
E
1

fE dE =
(1+)

E (1+) (1 + ) E2
(1+)

E E

2 1

fE

0

=

E2

(1+)

- E1 (1 + )

fE0 =

- E1 (1 + )E

(1+)

fE
-1

So the monochromatic flux at any desired energy E in erg cm-2 s fE = To convert to erg cm-2 s
-1 -1

keV-1 is

(1 + )E E2
1 Hz (1+)



- E1

(1+)

F
18

Hz

use

=

1 keV keV Hz

=

h keV

where h = 4.138 в 10-

is

Planck's constant in keV sec. Therefore, the monochromatic flux at any desired energy E in erg cm-2 s
-1

Hz

-1

is f = h(1 + )E F E2
(1+)

- E1

(1+)

Now, the power law can also be expressed in terms of photons rather than energy units, that is NE (E ) = N
E
0

E = N E0 E E

(-1)

This allows a popular but confusing redefinition of the photon number index so that NE (E ) = NE0 E
-

whereby we see that since = (1 - ).

P.S. If further confusion is desired, in a standard X-ray definition, people unfortunately also use fE (E ) = fE0 E
-
X