We present precise values of the eccentricity and periastron angle of 529 detached, eccentric, eclipsing stars from the Kepler Eclipsing Binary catalog that were determined by modeling their long cadence data. The temperatures and relative radii of their components as well as their mass ratios were calculated based on approximate values of the empirical relations of MS stars. Around one-third of the secondary components were revealed to be very late dwarfs, some of them possible brown dwarf candidates. Most of our targets fall below the envelope P(1 − e 2)3/2 = 5 days. The (e, P) distribution of the known eccentric binaries exhibits a rough trend of increasing eccentricity with the period. The prolonged and continuous Kepler observations allowed us to identify 60 new highly eccentric targets with e > 0.5.

We carried out light curve solutions of ten detached eclipsing eccentric binaries observed by Kepler. The formal errors of the derived parameters from the light curve solutions are below 1%. Our results give indications that the components of the eccentric binaries (especially those with mass ratios below 0.5) do not follow precisely the empirical relations between the stellar parameters derived from the study of circular-orbit binaries. We found the following peculiarities of the targets: (a) the components of KIC 9474969 have almost the same temperatures while their radii and masses differ by a factor around 2.5; (b) KIC 6949550 reveals semi-regular light variations with an amplitude of 0.004 and a period around 7 d which are modulated by long-term variations; (c) KIC 6220470, KIC 11071207, and KIC 9474969 exhibit tidally induced 'hump' around the periastron. These are the targets with the biggest relative radii of our sample. We derived the dependence of the hump amplitude on the relative stellar radii, eccentricity, and mass ratio of eccentric binary consisting of MS stars.

Photometric observations in V and I bands and low-dispersion spectra of ten ultrashort-period binaries (NSVS 2175434, NSVS 2607629, NSVS 5038135, NSVS 8040227, NSVS 9747584, NSVS 4876238, ASAS 071829-0336.7, SWASP 074658.62+224448.5, NSVS 2729229, NSVS 10632802) are presented. One of them, NSVS 2729229, is newly discovered target. The results from modeling and analysis of our observations revealed that: (i) Eight targets have overcontact configurations with considerable fillout factor (up to 0.5) while NSVS 4876238 and ASAS 0718-03 have almost contact configurations; (ii) NSVS 4876238 is rare ultrashortperiod binary of detached type; (iii) all stellar components are late dwarfs; (iv) the temperature difference of the components of each target does not exceed 400 K; (v) NSVS 2175434 and SWASP 074658.62+224448.5 exhibit total eclipses and their parameters could be assumed as well-determined; (v) NSVS 2729229 shows emission in the Hα line. Masses, radii and luminosities of the stellar components were estimated by the empirical relation "period, orbital axis" for short-and ultrashort-period binaries. We found linear relations mass-luminosity and mass-radius for the stellar components of our targets.

The paper presents light curve solutions of our observations of four new ultrashort-period eclipsing binaries with MS components. Two of them have periods almost at the upper limit (0.22 days) of the ultrashort-period binaries, while the periods of around 0.18 days of CSS J171508.5+350658 and CSS J214633.8+120016 are amongst the shortest known orbital periods. CSS J171410.0+ 445850, CSS J214633.8+120016 and CSS J224326.0+154532 are overcontact binaries with fillout factors around 0.25 while CSS J171508.5+350658 is a semidetached system. The two targets with shortest periods consist of M dwarfs.

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