The Relationship Between X-ray Luminosity and Duty Cycle for Dwarf Novae and their Specific Frequency in the Inner Galaxy

TL;DR

This study establishes an empirical relation between X-ray luminosity and duty cycle in dwarf novae, and estimates their specific frequency in the Galactic Bulge, aiding future surveys like LSST.

Contribution

It provides the first quantitative relation between X-ray luminosity and duty cycle for dwarf novae and estimates their specific frequency in the inner Galaxy.

Findings

A new empirical relation: log DC = 0.63 * (log Lx - 31.3) - 0.95.

Estimated specific frequency of X-ray bright dwarf novae in the Galactic Bulge.

Derived space density of long-period CVs in the Solar neighborhood.

Abstract

We measure the duty cycles for an existing sample of well observed, nearby dwarf novae using data from AAVSO, and present a quantitative empirical relation between the duty cycle of dwarf novae outbursts and the X-ray luminosity of the system in quiescence. We have found that $\log DC=0.63(\pm0.21)\times(\log L_{X}({\rm erg\,s^{-1}})-31.3)-0.95(\pm0.1)$, where DC stands for duty cycle. We note that there is intrinsic scatter in this relation greater than what is expected from purely statistical errors. Using the dwarf nova X-ray luminosity functions from \citet{Pretorius12} and \citet{Byckling10}, we compare this relation to the number of dwarf novae in the Galactic Bulge Survey which were identified through optical outbursts during an 8-day long monitoring campaign. We find a specific frequency of X-ray bright ($L_{X}>10^{31}\,{\rm erg\,s^{-1}}$) Cataclysmic Variables undergoing Dwarf Novae outbursts in the direction of the Galactic Bulge of $6.6\pm4.7\times10^{-5}\,M_{\odot}^{-1}$. Such a specific frequency would give a Solar neighborhood space density of long period CVs of $\rho=5.6\pm3.9\times10^{-6}\,$pc$^{-3}$. We advocate the use of specific frequency in future work, given that projects like LSST will detect DNe well outside the distance range over which $\rho\approx{\textrm const}$.