POPULATION SYNTHESIS OF CATACLYSMIC VARIABLES:
I. INCLUSION OF DETAILED NUCLEAR EVOLUTION

Goliasch & Nelson 2014

Figures associated with our publication are available for download below. We also provide two versions of the paper in .pdf format: one with high resolution figures and one with low resolution figures (for quicker download, viewing, and printing).

Published Figures

Fig01.jpg (1.1MB)
Fig. 1. Evolution of the mass-transfer rate (M_dot ) with orbital period (Porb) for representative evolutionary tracks. The initial values of MWD (in M ), Mdonor (in M ), and Xc0, respectively are: 0:40; 0:40; 0:7 (dotted [blue] curve); 0:60; 1:20; 0:7 (solid [black] curve); 1:00; 1:40; 0:7 (dashed [red] curve); 1:00; 1:80; 0:1 (dash-dot [green] curve). The dashed track illustrates the `canonical' CV evolution curve with a period gap from 2.8 hr to 2.2 hr. The solid line illustrates the evolution of a CV that is marginally stable with mass-transfer rates reaching ≈10-6.5 M /yr. In contrast, the track of a hydrogen depleted system (dash-dot line) exhibits significantly lower mass-transfer rates and has no discernable period gap. 

Fig02.jpg (1.6MB)

Fig. 2. PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the Porb - M_dot plane. M_dot is the mass-transfer rate and Porb is the orbital period of the system. The probability density for a given combination of the two observables has been arbitrarily normalized and the vertical color bar on the right-hand side illustrates that probability on a logarithmic scale. Hence the color of a particular Porb - M_dot pixel represents a relative measure of the probability that a PDCV has the properties defined by those two variables. Panels a) and b) each comprise 1000 horizontal cells covering an orbital period of 12 hours and 1000 vertical cells corresponding to six orders of magnitude in the mass-transfer rate. The upper panel denotes the intrinsic population while the lower panel has been scaled by M_dot to approximately take into account observational selection effects (selected population).

Fig03.jpg (2.7MB)
PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the Porb - M_dot plane. The population is divided into two distinct subsets and shown in separate panels. The unevolved group is shown in panels a) and c) and is composed of relatively young donors (<50% of their respective TAMS ages) while the evolved group is shown in panels b) and d) and is composed of systems in which the donors have already undergone significant chemical evolution (50% of their respective TAMS ages). Combined the two groups make up the full PDCV population shown in Figure 2. The probability density for a given combination of the two observables has been arbitrarily normalized and the vertical color bar on the right-hand side illustrates that probability on a logarithmic scale. The upper panels, a) and c), correspond to the intrinsic population while the lower panels, b) and d), show the respective probabilities for the selected population.

Fig04.jpg (2.2MB)

PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the Porb - M2 plane (panels a) and b)) and in the Porb - R2 plane (panels c) and d)). M2 and R2 are the mass and radius of the donor, and Porb is the orbital period of the system. The probability densities for a given combination of Porb and M2 (or Porb and R2) have been arbitrarily normalized and the vertical color bar on the right-hand side illustrates that probability on a logarithmic scale. Panels b) and d) show the respective probabilities for the selected
population.

Fig05.jpg (1.8MB)
PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the Porb - L plane (panels a) and b)) and in the Porb - Teff plane (panels c) and d)). L and Teff are the luminosity and effective temperature of the donor, and Porb is the orbital period of the system. The probability densities for a given combination of Porb and L (or Porb and Teff ) have been arbitrarily normalized
and the vertical color bar on the right-hand side illustrates that probability on a logarithmic scale. Panels b) and d) show the respective probabilities for the selected population.

Fig06.jpg (2.9MB)
PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the Porb - M2/MWD plane (panels a) and b)) and in the Porb - M20 plane (panels c) and d)). M2/MWD is the mass ratio q of the donor mass divided by the accretor mass, M20 is the initial mass of the donor when the system first comes into contact, and Porb is the orbital period of the system. The probability densities for a given combination of Porb and M2/MWD (or Porb and M20) have been arbitrarily normalized and the vertical color bar on the right-hand side illustrates that probability on a logarithmic scale. Panels b) and d) show the respective probabilities for the selected population.

Fig07.jpg (2.1MB)
Frequency histogram (Wm) for all PDCVs as a function of the orbital period corresponding to our standard case (Case 1, see Table 1). Panel a) shows the logarithm of the bin count of PDCVs while the lower panel (Figure 7 b)) has been weighted by M_dot in order to approximately take into account observational selection effects. In both panels the diagonally-hatched bins contain all CV systems at the present epoch, while the cross-hatched bins and
the gray-shaded bins only contain systems in which the donor star had an age of at least 50% and 80% (respectively) of its terminal age MS lifetime when the system  first came into contact. The bin width is 0.012 hr in both panels.

Fig08.jpg (1.3MB)
Present Day (PD) orbital period distribution corresponding to our standard case (Case 1, see Table 1) of systems that are detached (in the period gap) and do not experience any mass transfer. The count in each bin represents the logarithm of the number of PDCVs to be expected in that particular period
interval. The shading key for this figure is the same as for Figure 7. The bin width is 0.012 hr.

Fig09.jpg (1.4MB)
PDCV orbital period distribution of short-period CVs corresponding to our standard case (Case 1, see Table 1). The details for this gure are the same as for Figure 7 except that the bin width is 0.002 hr.

Fig10.jpg (1.5MB)
PDCV orbital period distribution for various cases (differentiated by color). The Case numbers in the legend correspond to those in Table 1. Panel a) shows the logarithm of the bin count of PDCVs while the lower panel (Figure 7 b)) has been weighted by M_dot in order to approximately take into account observational selection effects. The bin width is 0.012 hr in both panels.

Additional Figures

PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in presented for various observable quantities (see figure captions).

In the figures our population is divided into two distinct subsets and shown in separate panels. The unevolved group is shown in panels a) and c) and is composed of relatively young donors (<50% of their respective TAMS ages) while the evolved group is shown in panels b) and d) and is composed of systems in which the donors have already undergone significant chemical evolution (50% of their respective TAMS ages). Combined the two groups make up the full PDCV population shown in Figure 2 of the paper. The probability density for a given combination of the two observables has been arbitrarily normalized and the vertical color bar on the right-hand side illustrates that probability on a logarithmic scale. The upper panels, a) and c), correspond to the intrinsic population while the lower panels, b) and d), show the respective probabilities for the selected population.

01_Mdot.jpg (2.7MB)
Porb − M plane

02_M2.jpg (3MB)
Porb − M2 plane

03_R2.jpg (1.8MB)
Porb − R2 plane

04_Lum.jpg (1.9MB)
Porb − L plane

05_Te.jpg (1.9MB)
Porb − Teff plane

06_Mratio.jpg (3.5MB)
Porb − M2/MWD plane

07_M2_nod.jpg (3.4MB)
Porb − M20

Paper in pdf

High resolution figures (33.2MB)

Low resolution figures (2.2MB)