... If we neglect Kcorrections, the flux from the lens is 2 L DOS rH / ; П 1ч Fј DOL DLS П1 Ч zl ч 4 D 2 П 1 Ч z l ч 2 OL where rH is the Hubble radius c/H0. ...
... 9 The observed background counts are also modeled as indepen dent Poisson random variables, B S # Poisson re S # S П ч; BH # Poisson re H # H П ч П6ч where # is scaled by a known correction factor r, to account for differences in source and background ...
... The soft color is defined as HR1 ј and the hard color as HR2 ј H юM ; SЧM ЧH П 3ч M юS SЧM ЧH П 2ч where S, M, and H are the counts in a soft (0.3 1.0 keV ), medium (1.0 2.1 keV ), and hard (2.1 8.0 keV ) energy bands, respectively. ...
... 2 correspond formally to a radius over distance ratio (angular size) of R1 =D 100 ј 4:12 # 0:68 km per 100 pc, where R1 ј R= 1# П 2GM=Rc 2 ч 1=2 is the `` radiation radius '' corresponding to the true radius R for a star of mass M, and the quoted uncer ...
... to explicitly include the neutral species ionization potential ) as n max $q IH In 1=2 qю1 1 Ч pffiffiffiffiffi 2q ю1=2 ; П 1ч where q is the ion charge, In is the ionization potential of the neutral species, and IH is the ionization potential of atomic H ...
... We use the simple Cravens (2000) model for neutral gas density within the astrosphere, n n r П ч ј n n0 e ## n =r , where n n0 is the neutral gas density far from the star (0.05 cm #3 ) and # n is the scale for neutral gas depletion. ...
... For the point sources falling within the D25 ellipse, we estimated an XLF that in differential form can be expressed as ю dN LX јk : П 1ч dLX 10 38 ergs sю1 To construct the XLF, we calculated fluxes and luminosities of the point sources in the 0.3Y8 keV ...
... Normal quasars and AGNs have 0:1 < fX =fV < 10; normal galaxies have only 10ю2 < fX =fV < 10ю1 ; while a high-luminosity cluster of galaxies (LX ј 1045 ergs sю1) would have a first-ranked elliptical with Lgal ј 10Lц Пј 1011:5 L ч giving fX =fV $ 8. ...