Luminosity profiles

The classical models of spiral galaxies were constructed using rotation velocities. In contrast, the models of elliptical galaxies were found from luminosity profiles and calibrated using central velocity dispersions or motions of companion galaxies. An overview of classical methods to construct models of galaxies is given by Perek (1962). 

The radial luminosity profiles of disks in spiral galaxies csin be described by an exponential law and are thus characterized by two parameters, the central stnface brightness (/uo) and the scalelength (h). Freeman (1970) foimd /to to be nearly constant in his sample of galaxies observed in the B band. This Freeman law has of course serious implications for theories on galaxy formation and evolution. 

Luminosity profile decomposition has been applied to the optical continuum images eind the NIR J, H and E images of NGC 5252. A multicomponent model that takes into account the contribution of a point source, the bulge and the disk has been used for fitting the observed luminosity profiles. Details of the fitting technique are given in Kotilainen et al. (1992). 

FIGURE 8.15 Typical temperature profiles along the centerline of laminar hydrocarbon fuel jets diluted with N2 to the point of no luminosity when burning in overventilated air streams. H is the height of the flame Zis the distance from jet exit along the centerline. 

Fig. 5.2. Internal structure of the Sun. The top four graphs show the density, temperature, chemical composition and luminosity as a function of distance from the centre. Such profiles can be buUt up for each stage of the star s evolution. The figure shows the general regions of radiative transfer and convection in the bulk of the Sun. The bottom graph shows the gradual increase in radius, temperature and luminosity from birth.

It was found during studies that side views of unconfined cylindrical chges of high d (1.6g/cc) Tetryl obtd during deton by the image-converter camera with exposure time of 0.2 microsec or less showed practically no outward luminosity in the region of the deton zone. Since it is known that the deton front has a curved profile somewhat as shown in Fig 3 it was decided that the luminosity was hidden by the protruding rim of unexploded material. To overcome this obstruction a strip of transparent polymethyl... 

We assume stationarity and radiative equilibrium for the energy balance because the radiative timescales are short in respect to the hydrodynamic timescales soon after the initial increase in luminosity. Spherical symmetry is assumed. According to detailed numerical models (Falk and Arnett, 1977 Muller, personal communication, 1987 Nompto, 1987 Nomoto et aL, 1987) and also analytical solutions for strong shock waves in spherical expanding enveloped (Sedov, 1959) density profiles are taken which are given by the self-similar expansion of an initial structure i.e. 

The spectrum in both the optical and the ultraviolet at about two days is fairly well represented by a hydrogen envelope with a power law density profile (p r11) of one-quarter solar metaiiiclty in LTE. Theoretical spectra at this early epoch tend to favor luminosities on the high side of observational estimates in order to ionize Ca II and prevent excessively strong lines at H and K and the infrared triplet, with some ramifications for distance estimates. 

Many of the models demand that the temperature at some mass cut above the helium core be in excess of the ignition temperature of hydrogen, Th, and hence, the structure is self-inconsistent. For a helium core mass of 4 M , models with total mass in the range 4.05 to 14 M , are excluded. This conclusion does not depend sensitively on the specific value adopted for Th, since the temperature profiles tend to rise so steeply in the excluded range. Similar conclusions follow for models with larger luminosities and... 

Ha line profile. The blue edge of the feature, which samples the highest velocity matter, is distinctly rounded in the observations. The brightest models reproduce this aspect rather well, whereas the dimmer models give sharper, abrupt blue edges. Other features sensitive to the luminosity are the Ca II lines, at H and K and the infrared triplet. These are not observed at two days, but appear in many of the theoretical spectra which are sufficiently dim or extended that appreciable Ca II exists. Satisfactory models must have the Ca II ionized away at this epoch. 

Figure 5. Three model atmospheres are given corresponding to a density profile of r 11, with p = 1.5 x 10 14 gm/cm3 at 20,000 km/s at two days. The three curves correspond to luminosities of 4.9,3.9, and 3.2 x 10 41 erg/s, from top to bottom, respectively. The lower curves are optical spectra from Cerro Tololo provided by Mark Phillips and UV spectra provided by Bob Kirshner. Note the diminishing Ca II features with increasing luminosity, and the strong UV deficit which is unprecedented in a Type II supernova.

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