Luminosity Distributions

Reviews:

  1. Holmberg, E. in Galaxies and the Universe (Sandage, A., Sandage, M., & Kristian, J., eds.) = Stars and stellar Systems Vol. IX, Univ. Chicago Press (1975). p. 123.
  2. The World of Galaxies (H.C. Corwin Jr., & L. Bottinelli, eds.), Berlin, Springer (1989).
  3. The Magellanic Clouds (R. Haynes, & D. Milne, eds.), Int. Astron. Union Symp. 148, Dordrecht, Kluwer (1991).

Surface Photometry of Elliptical Systems

The radial surface-brightness distribution of the brighter elliptical galaxies (MV < -15 mag) and compact dwarf systems follows closely the empirical law.

  1. de Vaucouleurs, G. in Stellar Systems (Figure, S., ed.), Hdb. Physik 59, Springer, Berlin (1959). p. 311.
  2. de Vaucouleurs, G. Mon. Not. R. Astron. Soc. 113 (1953) 134.
  3. Kormendy, J., & Djorgovski, S., Annu. Rev. Astron. Astrophys. 27 (1989) 235.
See also:
  1. Nguyen, Q., Jackson, J.M., Henkel, C., Truony, B., & Mauersberger, R., Astrophys. J. 399 (1992) 521.
  2. Gallimore, J.F., Baum, S.A., O'Dea, C.P., Brinks, E., & Pedlar, A., Astrophys. J. 422 (1994) 13.

log I(varrho) = -3.33 (varrho1/4 - 1)   (1)

with rho = R / Re

Re = effective radius = radius (or major axis) of that isophote inside which half of the total light is emitted

I(rho) = surface brightness at distance rho from the center along the major axis.

The formula fails only in the innermost and in the outermost parts. Another representation is given by King's model [King, I.R. Astron. J. 71 (1966) 64].

The distribution is similar to an isothermal sphere. The similarity of I(rho) for all normal ellipticals means that they are all now in a fairly similar dynamical state.

For variation of the ellipticity of the isophotes within individual galaxies.

The specific intensity Ie at Re or the corresponding surface brightness µe in [mag per unit solid angle] is related to the average surface brightness µ'e within Re; for an rho1/4 distribution

µ'e = µe - 1.40 .   (2)

In the denser systems the rho1/4 law apparently applies right up to the center. Here, according to Eq. (1), the surface brightness should be 2.5 × 3.33 = 8.3 mag brighter than at Re, thus

µ0 = µe - 8.3 = µ'e - 6.9.   (3)

The range of µ'e in dense systems is from approx 19.5 to approx 21.5 mag(B)/arcsec2 (corresponding to about 1200...200 Lsun pc-2).

Supergiant elliptical systems show an elliptical-like core in an extended outer envelope.

Carter, D. [Mon. Not. R. Astron. Soc. 178 (1977) 137] investigated the optical extent of four giant elliptical and cD galaxies, and in two of them he found no indication of the convergence of the total luminosity of the galaxy.

Low-density dwarf spheroidal systems (MV > -15) do not obey the rho1/4 law. The light concentration is slight and the central core with radius R approx Re/2 has a nearly constant surface brightness. But the surface brightness drops off more rapidly in the outer parts than for giant systems. The Fornax system (dE) has µ'e = 24.8 mag/arcsec2 (approx 9 Lsun pc-2) or about 1% of the corresponding luminosity density in the compact dwarf E 2 system M 32. Preliminary photometries of Sculptor and other nearby dwarfs indicate even lower densities. Large numbers of dwarfs with such densities might remain undetectable by current techniques.

Galaxy Luminosity Classification: [Ohta, K., Sasaki, M., Yamada, T., Saito, M., & Nakai, N., Pub. Astron. Soc. Japan. 44 (1992) 585].

Spiral Systems:

Edge-on spirals and S0 galaxies clearly show two main structural components, a flat disk and a spherical bulge. The bulge varies in its relative importance from dominant to zero (see Fig. 3). Luminosity distribution of the bulge (characteristic for ellipticals, see above):

log I1 (rho) propto rho1/4,   (4)

luminosity distribution of the flat component (characteristic for disks of late spirals)

I2(R) = I0 e-alphaR   or   log I2(R) = const - alpha R   (5)

i.e. an exponential luminosity law. alpha is the inverse of the scale length Lambda; it is measured by the photometric gradient

G(R) = d(log I) / dR,   thus   Lambda = 0.4343 / G(R) .   (6)

For a purely exponential law: effective radius Re = 1.6785 Lambda. The relations corresponding to Eq. (3) are:

µ0 = µe - 1.82 = µ'e - 1.12 .   (7)

From an investigation of 36 exponential disks Freeman, K.C. [Astrophys. J. 160 (1970) 811] arrived at the following conclusions:

a) Lambda has a range of one order of magnitude from 0.5 to 5 kpc for types earlier than Sc.

b) For types later than Sc the maximum value of Lambda decreases from 5 kpc at Sc (morphological parameter t = 5) to 1 kpc at Im (t = 10), confirming earlier results on the dependence of galaxy diameters on Hubble type.

c) For 28 out of 36 spirals and S0 galaxies the exponential disks have nearly the same intensity scale: < µ0 > = 21.65 mag/arcsec2 with a very small standard deviation of 0m.3, in spite of a large range of 5M in absolute magnitudes and independent of morphological type from L-(t = -3) to Im (t = 10), Fig. 2. However, see critical comments in [Burstein, D. in Photometry, Kinematics and Dynamics of Galaxies (Evans, D.S., ed.), University of Texas (1979). p. 81].

Figure 2

Figure 2. Corrected face-on central surface brightness µ0 for exponential disks versus the morphological type t (see [Freeman, K.C. in Galaxies and the Universe (Sandage, A., Sandage, M.; Kristian, J., eds.) = Stars and stellar Systems Vol. IX, Univ. Chicago Press (1975). p. 409]. µ0 is independent of the type, but some individual galaxies are aberrant. Full circles: type I luminosity profiles; open circles: type II luminosity profiles, as explained in Fig. 3.

Figure 3 shows the radial luminosity distribution for three galaxies with different ratios of spherical and exponential components, and for comparison a R1/4-distribution.

Figure 3

Figure 3. Radial luminosity distribution for NGC 4459 (type S0) M83 (Sc), and M33 (Scd). The R1/4 distribution is also shown [Freeman, K.C. in Galaxies and the Universe (Sandage, A., Sandage, M., & Kristian, J., eds.) = Stars and stellar Systems Vol. IX, Univ. Chicago Press (1975). p. 409].

Almost all disk galaxies including the Magellanic irregulars show the exponential disk. Thus in all these systems the outer parts, containing most of the angular momentum, have reached a similar dynamical state.

Magellanic Clouds: [Westerlund, B.E., Astron. Astrophys. Rev. 2 (1990) 29]. See also:

  1. Aalto, S., Booth, R.S., Black, J.H., Koribalski, B., & Wielebinski, R., Astron. Astrophys. 286 (1994) 365.
  2. Baan, W.A., Rhoads, J., & Haschick, A.D., Astrophys. J. 401 (1992) 508.

Inclination Effects and Internal Absorption in Spiral Galaxies:

  1. Kaneko, N., Morita, K., Fukui, Y., Takahashi, N., Sugitani, K., Nakai, N., & Morita, K., Publ. Astron. Soc. Japan. 44 (1992) 341.
  2. Peletier, R.F., & Willner, S.P., Astrophys. J. 418 (1993) 626.
  3. Gallimore, J.F., Baum, S.A., O'Dea, C.P., Brinks, E., & Pedlar, A., Astrophys. J. 422 (1994) 13.

Opacity of Spiral Disks:

The Opacity of Spiral Disks [J.I. Davies, & D. Burstein, eds., Dordrecht, Kluwer (1995)].

Some S0 galaxies show up clearly a third, flat, lens-like component.

The luminosity profiles of high surface-brightness disks dip below the projected exponential component, see for instance M83 in Fig. 3. Freeman [Freeman, K.C. in Freeman, K.C. Observational Determination of the Overall Features. In Freeman, K., Larson, R.B., Tinsley, B. Galaxies, Sixth advanced course of the Swiss Society of Astronomy and Astrophysics (Martinet, L., Mayor, M., eds.), Geneva Observatory (1976) p. 1] supposes that those M83-like galaxies are systems with a lens component: the dip is the result of adding a flat lens component to the bulge and exponential components, as schematically shown in Fig. 4.

Figure 4

Figure 4. Possible explanation of the "dip" (M83 type, see Fig.3) by superposition of bulge-, exponential- and lens components [Freeman, K.C. in Freeman, K.C. Observational determination of the overall features. In Freeman, K., Larson, R.B., Tinsley, B. Galaxies, Sixth advanced course of the Swiss Society of Astronomy and Astrophysics (Martinet, L., Mayor, M., eds.), Geneva Observatory (1976) p. 1].

More recent observations of luminosity distribution in 25 spiral systems are given in [Boroson, T. Astrophys. J. Suppl. 46 (1980) 177].

The local mass-to-luminosity ratio has been investigated in 6 spiral galaxies [Bosma, A., & van der Kruit, D.C. Astron. Astrophys. 79 (1979) 281] by combining 21 cm-line studies and optical surface photometry. In spite of the large uncertainties in the modeling procedures it is concluded that this ratio increases significantly in the outer parts. Local values of M/L may be of the order 102 ... 103.

Barred Spirals

Surface photometry of two barred spirals (NGC 7479 and NGC 7743) [Okamura, S. Publ. Astron. Soc. Japan 30 (1978) 91] shows four components: (1) central bulge, (2) bar, (3) spiral arms, (4) underlying disk. The luminosity distribution of the bar follows the R1/4 law.


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