Luminosity functions

However, there are two sets of observations which indicate that AGB stars do indeed reach the AGB limit Mbol = -7.1. Firstly, the results of WBF and Reid, Glass and Catchpole (1987) for the LPVs show that such stars do reach the AGB limit. Secondly, a luminosity function for red stars in the bar of the LMC obtained by Hughes and Wood (1987) shows that AGB stars extend to Mbol = -7.1, although there is a steep fall-off with luminosity above Mboi = -6. One explanation for the rapid fall-off in the number of AGB stars above Mboi = -6 is provided by Wood and Faulkner (1986) who show that envelope ejection will occur at this point in all but the most massive AGB stars due to the luminosity of the star exceeding the Eddington limit at the base of the hydrogen-rich envelope during the surface luminosity peak of a helium shell flash. 

THE WHITE DWARF LUMINOSITY FUNCTION AND THE PHASE DIAGRAM OF THE CARBON-OXYGEN DENSE PLASMA... 

In Figure 1, we present the luminosity functions obtained with the assumptions of total miscibility (full line) and total separation (dashed line) for an age of the Galactic disk of 15 10 years. These luminosity functions take into account the increase of the vertical scale height over the plane of the disk with the age of the objects. This geometrical effect [2] nearly suppress the bump at L 10-4 Lq which would have been produced by the strong decrease of the cooling rate in the case of total separation [3]. 

It can be seen that the low luminosity cut-off of the luminosity function can be reproduced, even for a large age of the Galactic disk, if carbon and oxygen separate. 

The total separation we have considered may be however an extreme case and the time delay introduced by a partial separation would naturally be smaller. The uncertainty on the carbon-oxygen phase diagram then appears to be a main difficulty for a reliable determination of the age of the Galactic disk using the white dwarf luminosity function. 

The White Dwarf Luminosity Function and the Phase Diagram of the Carbon-Oxygen Dense Plasma... 

Figure 4.9 Calculated luminosity functions L(l/°p, Usp) for a sector CMA as described in [DFM87], The parameter S gives the width of the dispersion slit measured perpendicular to the principal ray (the length of this slit is 8 mm). The data refer to a photon beam of 0.5 mm diameter which results in an image width B of approximately 0.6 mm. Therefore, the three cases shown refer to the situations (a) B S, (b) B S, (c) B S. From [Ehr91],...

There is an additional difficulty in experimental design where one or both of the C.I.E. Luminosity Functions are used as a reference function. The Central Limit Theorem insures that any results obtained through the addition to or subtraction from these reference functions will contain all of the errors associated with these functions. 

Using these values and the resulting parameters from TABLE 5.5.10-1, the photopic and scotopic luminosity functions can be computed precisely (See Chapter 17). 

Figure 5.5.10-2 compares the typical putative spectrums based on such a linear analysis, (3, y, p compared to the actual chromophores, Rhodonines 5, 7 9 [with Rhodonine(l 1) shown for completeness. It is not significant in human vision except for aphakic patients.] Hunt describes the (3,y p spectrums as probable sensitivity curves of the three types of cones. He did not discuss any rod spectrum in his figure. The probable sensitivity curves appear to have been normalized individually. The peak in the p spectrum appears to be at a longer wavelength than frequently suggested. However, it is still at too short a wavelength to support the known spectral response of the human eye as illustrated by the Photopic Luminosity Function. 

Besides the nearby cluster detections (z O.l) that are using simple galaxy density criteria, the combination of such galaxy densities over the sky and of the shape of the galaxy luminosity function allows cluster detections up to 1... 

For a finite source volume the situation for the analyser transmission becomes much more complicated, because for each point within the source volume a different transmission T(r) exists, and the relevant quantity to be considered is the luminosity function L(U°P, Usp)... 

Figure 6-2 Spectral Energy Distribution of Light Sources A and C, the CIE, and Relative Luminosity Function y for the CIE Standard Observer...

H.-J. Grimm, M. Gilfanov, and R. Sunyaev (2001). The Milky Way in X-rays for an outside observer Log(N)-Log(S) and Luminosity Function of X-ray binaries from RXTE/ASM data Astronomy and Astrophysics , astro-ph/0109239. 

Dickinson, Persson 1994), the DLA counts would naturally be dominated by the far more numerous galaxies at the steep (a = —1.6) faint end of the luminosity function. 

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