J/AJ/81/807 Deprojection of the r1/4 law tables (Young, 1976)
Tables of functions for a spherical galaxy obeying the r1/4 law in projection
Young P.J.
<Astron. J. 81, 807 (1976)>
=1976AJ.....81..807Y 1976AJ.....81..807Y
ADC_Keywords: Models ; Galaxies, photometry; Photometry, surface
Abstract:
A spherical galaxy with reduced surface brightness, J=B(α)/Be,
obeying the r1/4 law, logJ=-3.3307 (α1/4-1), where α
is the reduced radius, α=r/re (re is the effective radius),
is deprojected to find the corresponding space density, mass, mean
density, force, potential, escape velocity, and potential energy at
each point in the galaxy. Numerical tabulations to five significant
figures are given for 124 points in the range 10-6≤R/re≤260. In
addition the projected surface brightness B(α) and integrated
luminosity within α are tabulated for the range
10-6≤α=r/re≤260. Conversion factors to cgs units and to
M☉, pc, km/s, L☉ units are given. Asymptotic expansions
for the space density ρ(s) in the ranges s=<10-4 and s≥10-1
are derived, and it is demonstrated that the projection of the
expansion for s≤10-1 is almost indistinguishable from the r1/4
law itself, apart from a small excess of luminosity in the central
regions. Formulae and numerical tables of the luminosity distribution
are given for use in galaxy photometry. Relations between the total
galactic mass MT, the effective radius re, the velocity dispersion
σv, the central density ρc and the mass MN and radius
RN of the nucleus are derived. Here the "nucleus" is defined as the
region within which stars having a velocity equal to the mean velocity
dispersion in space, σv.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table2.dat 117 124 Quantities in reduced units for spherical
galaxy obeying R1/4-law in projection
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Table 1: Conversion factors.
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Reduced quantity M_☉, pc, km/s, L_☉ cgs system
system
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total galaxy mass
MT*=1 MT in M☉ MT' in grams
projected effective radius
s=1 re in pc re' in centimeters
total luminosity
LT*=1 LT in L☉ (B system) LT' in erg/s (bolometric)
LT'' in erg/s (B band)
mass-to-luminosity ratio
K*=1 K=MT/LT (B system) K'=MT'/LT' (bolometric)
K''=MT'/LT'' (B band)
β index
β*=2.62175 β=1.1277x10-2 β'=2.62175 G=1.749x10-7
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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1- 7 E7.1 --- s/alpha *[1.0E-06,2.6E+02]+ Space/Plane radius
9- 18 E10.4 --- B*(alpha) *Reduced surface luminosity
(specific intensity)
20- 29 E10.4 --- f*(alpha) *Reduced luminosity enclosed within (circular)
isophote of radius α
31- 40 E10.4 mag Dm(alpha) *Magnitude difference
42- 51 E10.4 --- rho*(s) *Reduced space density
53- 62 E10.4 --- M*(s) *Reduced mass contained within sphere of
radius s
64- 73 E10.4 --- <rho*(s)> *Reduced mean space density within sphere of
radius s
75- 84 E10.4 --- F*(s) *Reduced force
86- 95 E10.4 --- psi*(s) *Reduced potential
(with psi*(0)=1 and psi*(infinity)=0)
97-106 E10.4 --- w*(s) *Reduced escape velocity
108-117 E10.4 --- OMEGA*(s) *Reduced potential energy contained
within radius s
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Note on s/alpha:
α = a/ae = reduced radius (semi-major axis) in projection
s = R/re = reduced radius in space
(s is in units of the effective radius re)
Note on B*(alpha):
B(r) = B*(alpha)MTK-1/re2 in L☉/pc2
B'(r')= B*(alpha)MT'K'-1/re'2 in erg/s/cm2
Note on f*(alpha):
f(alpha)= f*(alpha)MT/K in L☉
f'(r') = f*(alpha)MT'/K' in erg/s
Note on Dm(alpha):
Difference in magnitudes between luminosity enclosed within α
and the total luminosity
Note on rho*(s):
rho(R) = rho*(s)MT/re3 in M☉/pc3
rho'(R')= rho*(s)MT'/re'3 in g/cm3
Note on M*(s):
M(R) = M*(s)MT in M☉
M'(R')= M*(s)MT' in g
Note on <rho*(s)>:
(R) = *(s)MT/re3 in M☉/pc3
'(R')= *(s)MT'/re'3 in g/cm3
means rho{bar}
Note on F*(s):
F(R) = F*(s)βMT/re2 in (km/s)2/pc
F'(R')= F*(s)β'MT'/re'2 in dyn
Note on psi*(s):
psi(R) = psi*(R)βMT/re in (km/s)2
psi'(R')= psi*(R)β'MT'/re' in (cm/s)2
Note on w*(s):
w(R) = w*(s)[βMT/re]1/2 in km/s
w'(R')= w*(s)[β'MT'/re']1/2 in cm/s
Note on OMEGA*(s):
OMEGA(R) = OMEGA*(s)βMT2/re in (km/s)2
OMEGA'(R')= OMEGA*(s)β'MT'2/re' in g(cm/s)2
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History: Prepared via OCR at CDS.
(End) James Marcout, Patricia Bauer [CDS] 08-Jun-2000