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Roche lobe radius - mass relation for cataclysmic variables.
Using the orbital period and masses of components of systems listed in the
Catalogue of characteristics of cataclysmic variables
(http://minerva.uni-sw.gwdg.de/cvcat/tpp3.pl), we have determined the
barotropic radius of the secondary filling it's Roche lobe. All 3
characteristics have been determined for 90 systems, 7 from them show values
very distinct from the "main" relation.
For these 83 systems, the best linear fit in a double logarithmic scale
lg R_2=<lg R_2> + b(lg M_2-<lg M_2>) (in units of Solar radius and mass,
respectively)
is
lg R_2=-0.327 + 0.197(lg M_2+0.489)
+- 4 14
with a correlation coefficient r=0.848+-0.059. However, this sequence is
cut, so for two groups separated by the gap,
lg R_2=-0.420 + 0.023(lg M_2+0.918), r=0.102+-0.207, n=25, 0.058<M_2<0.185
+- 30 46
and
lg R_2=-0.288 + 0.169(lg M_2+0.304), r=0.574+-0.109, n=58, 0.25<M_2<1.10
+- 5 32
The residuals range from -0.06 to +0.04 and from -0.12 to 0.05, respectively.
Such dependencies significantly differ from that previously assumed
by Robinson (1976,ApJ, 203,485): lg R_2= lg0.93+lg M_2
and Echevarria (1983, RMAA, 8, 109).
Recent models of low-mass stars have been studied in a series of papers by
I.Baraffe, Y.Kolb, H.Ritter and J.Patterson.
Despite the individual values listed in the catalogue are affected by
rounding and observational errors,
the revised dependencies argue for different mass-radius laws for the stars
M_2<0.18 (no statistically significant dependence) and M_2>0.25
(r/\sigma_r=5.3), what is possibly connected with an absence of the radial
core in low-mass stars.
Ivan L.Andronov, Roman V.Kozelov
Department of Astronomy, Odessa National University, Odessa, Ukraine
Crimean Astrophysical Observatory, Odessa, Ukraine
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