# CVsyn

## 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

Evolution of the mass-transfer rate ($\dot{M}$) with orbital period ($P_{orb}$) for representative evolutionary tracks. The initial values of $M_{WD}$ (in $M_\odot$), $M_{donor}$ (in $M_\odot$), and $X_{c0}$, 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 $\approx$$10^{-6.5} M_\odot$/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

\caption{PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the \noindent $P_{orb} – \dot M$ plane. $\dot M$ is the mass-transfer rate and $P_{orb}$ is the orbital period of the system. The probability

density for a given combination of the two observables has been normalized ($\Delta Q$) and the vertical color bar on the right-hand side illustrates that probability on a logarithmic scale. Hence the color of a particular $ P_{orb} – \dot M $ 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 $\dot M$ to crudely take into account observational selection effects (selected population). }

\label{Mdot_Pcolor}

Fig03.jpg

PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the $P_{orb} – \dot M$ 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) and 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 ($\geq$ 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 normalized ($\Delta Q$) 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

PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the $P_{orb} – M_{2}$ plane (panels a) and b)) and in the $P_{orb} – R_{2}$ plane (panels c) and d)). $M_{2}$ and $R_{2}$ are the mass and radius of the donor, and $P_{orb}$ is the orbital period of the system. The probability densities for a given combination of $P_{orb}$ and $M_{2}$ (or $P_{orb}$ and $R_{2}$) have been normalized ($\Delta Q$) 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

PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the $P_{orb}$ – $L$ plane (panels a) and b)) and in the $P_{orb} – T_{eff}$ plane (panels c) and d)). $L$ and $T_{eff}$ are the luminosity and effective temperature of the donor, and $P_{orb}$ is the orbital period of the system. The probability densities for a given combination of $P_{orb}$ and $L$ (or $P_{orb}$ and $T_{eff}$) have been normalized ($\Delta Q$) 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

PS for PDCVs corresponding to our standard case (Case 1, see Table 1) in the $P_{orb}$ – $M_{2}/M_{WD}$ plane (panels a) and b)) and in the $P_{orb} – M_{2 \mathrm{0}}$ plane (panels c) and d)). $M_{2}/M_{WD}$ is the mass ratio $q$ of the donor mass divided by the accretor mass, $M_{2 \mathrm{0} }$ is the initial mass of the donor when the system first comes into contact, and $P_{orb}$ is the orbital period of the system. The probability densities for a given combination of $P_{orb}$ and $M_{2}/M_{WD}$ (or $P_{orb}$ and $M_{2 \mathrm{0}}$) have been normalized ($\Delta Q$) 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

PDCV orbital period distribution corresponding to our standard case (Case 1, see Table 1). In panel a) the count in each bin represents the logarithm of the actual total number of systems to be expected in that particular period interval at the current epoch. Each count in the bins of panel b) was weighted by $\dot M$ 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 $50\%$ 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

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 actual total number of systems to be expected in that particular period interval at the current epoch. The shading key for this figure is the same as for Figure 6. The bin width is 0.012 hr.

Fig09.jpg

PDCV orbital period distribution corresponding to our standard case (Case 1, see Table 1). The details for this figure are the same as for Figure 6 except that the bin width is 0.002 hr.

Fig10.jpg

PDCV orbital period distribution for various cases (differentiated by color).

### 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) and 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 ($\geq$ 50 \% of their respective TAMS ages). Combined the two groups make up the full PDCV population. The probability density for a given combination of the two observables has been normalized ($\Delta Q$) 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.

$P_{orb} – \dot M$ plane

$P_{orb} – M_{2}$ plane

$P_{orb} – R_{2}$ plane

$P_{orb}$ – $L$ plane

$P_{orb} – T_{eff}$ plane

$P_{orb}$ – $M_{2}/M_{WD}$ plane

$P_{orb} – M_{2 \mathrm{0}}$

### Paper in PDF