Fundamental properties of solar-like oscillating stars from frequencies of minimum Δν\Delta \nu : II. Model computations for different chemical compositions and mass

The large separations between the oscillation frequencies of solar-like stars are measures of stellar mean density. The separations have been thought to be mostly constant in the observed range of frequencies. However, detailed investigation shows that they are not constant, and their variations are not random but have very strong diagnostic potential for our understanding of stellar structure and evolution. In this regard, frequencies of the minimum large separation are very useful tools. From these frequencies, in addition to the large separation and frequency of maximum amplitude, Y\i ld\i z et al. recently have developed new methods to find almost all the fundamental stellar properties. In the present study, we aim to find metallicity and helium abundances from the frequencies, and generalize the relations given by Y\i ld\i z et al. for a wider stellar mass range and arbitrary metallicity ($Z$) and helium abundance ($Y$). We show that the effect of metallicity is { significant} for most of the fundamental parameters. For stellar mass, for example, the expression must be multiplied by (Z/Z_{\sun})^{0.12}. For arbitrary helium abundance, M \propto (Y/Y_{\sun})^{0.25} . Methods for determination of $Z$ and $Y$ from pure asteroseismic quantities are based on amplitudes (differences between maximum and minimum values of \Dnu) in the oscillatory component in the spacing of oscillation frequencies. Additionally, we demonstrate that the difference between the first maximum and the second minimum is very sensitive to $Z$. It also depends on $\nu_{\rm min1}/\nu_{\rm max}$ and small separation between the frequencies. Such a dependence leads us to develop a method to find $Z$ (and $Y$) from oscillation frequencies. The maximum difference between the estimated and model $Z$ values is about 14 per cent. It is 10 per cent for $Y$.Comment: 8 pages, 13 figures; published in MNRAS (2015

Comparison of Gaia and asteroseismic distances

Asteroseismology provides fundamental properties (mass, radius and effective temperature) of solar-like oscillating stars using so-called scaling relations. These properties allow the computation of the asteroseismic distance of stars. We compare the asteroseismic distances with the recently released Gaia distances for 74 stars studied in Y{\i}ld{\i}z et al. There is a very good agreement between these two distances; for 64 of these stars, the difference is less than 10 per cent. However, a systematic difference is seen if we use the effective temperature obtained by spectroscopic methods; the Gaia distances are about 5 per cent greater than the asteroseismic distances.Comment: 4 pages, 4 figures, accepted by MNRA

On the structure and evolution of planets and their host stars −- effects of various heating mechanisms on the size of giant gas planets

It is already stated in the previous studies that the radius of the giant planets is affected by stellar irradiation. The confirmed relation between radius and incident flux depends on planetary mass intervals. In this study, we show that there is a single relation between radius and irradiated energy per gram per second ($l_-$), for all mass intervals. There is an extra increase in radius of planets if $l_-$ is higher than 1100 times energy received by the Earth ($l_\oplus$). This is likely due to dissociation of molecules. The tidal interaction as a heating mechanism is also considered and found that its maximum effect on the inflation of planets is about 15 per cent. We also compute age and heavy element abundances from the properties of host stars, given in the TEPCat catalogue (Southworth 2011). The metallicity given in the literature is as [Fe/H]. However, the most abundant element is oxygen, and there is a reverse relation between the observed abundances [Fe/H] and [O/Fe]. Therefore, we first compute [O/H] from [Fe/H] by using observed abundances, and then find heavy element abundance from [O/H]. We also develop a new method for age determination. Using the ages we find, we analyse variation of both radius and mass of the planets with respect to time, and estimate the initial mass of the planets from the relation we derive for the first time. According to our results, the highly irradiated gas giants lose 5 per cent of their mass in every 1 Gyr.Comment: 15 pages, 13 figures, 3 tables. Accepted by MNRA

Asteroseismic Investigation of 20 Planet and Planet-Candidate Host Stars

Planets and planet candidates are subjected to great investigation in recent years. In this study, we analyse 20 planet and planet-candidate host stars at different evolutionary phases. We construct stellar interior models of the host stars with the MESA evolution code and obtain their fundamental parameters under influence of observational asteroseismic and non-asteroseismic constraints. Model mass range of the host stars is 0.74-1.55 ${\rm M}_\odot$. The mean value of the so-called large separation between oscillation frequencies and its variation about the minima show the diagnostic potential of asteroseismic properties. Comparison of variations of model and observed large separations versus the oscillation frequencies leads to inference of fundamental parameters of the host stars. Using these parameters, we revise orbital and fundamental parameters of 34 planets and four planet candidates. According to our findings, radius range of the planets is 0.35-16.50 $\mathrm{R}_{\oplus}$. The maximum difference between the transit and revised radii occurs for Kepler-444b-f is about 25 per cent.Comment: 9 pages, 7 figures, 6 table

Fundamental properties of Kepler and CoRoT targets -- IV. Masses and radii from frequencies of minimum Δν\Delta {\nu} and their implications

Recently, by analysing the oscillation frequencies of 90 stars, Yildiz, \c{C}elik Orhan & Kayhan have shown that the reference frequencies ($\nu_{\rm min0}$, $\nu_{\rm min1}$ and $\nu_{\rm min2}$) derived from glitches due to He {\scriptsize II} ionization zone have very strong diagnostic potential for the determination of their effective temperatures. In this study, we continue to analyse the same stars and compute their mass, radius and age from different scaling relations including relations based on $\nu_{\rm min0}$, $\nu_{\rm min1}$ and $\nu_{\rm min2}$. For most of the stars, the masses computed using $\nu_{\rm min0}$ and $\nu_{\rm min1}$ are very close to each other. For 38 stars, the difference between these masses is less than 0.024 ${\rm M}_\odot$. The radii of these stars from $\nu_{\rm min0}$ and $\nu_{\rm min1}$ are even closer, with differences of less than 0.007 ${\rm R}_\odot$. These stars may be the most well known solar-like oscillating stars and deserve to be studied in detail. The asteroseismic expressions we derive for mass and radius show slight dependence on metallicity. We therefore develop a new method for computing initial metallicity from this surface metallicity by taking into account the effect of microscopic diffusion. The time dependence of initial metallicity shows some very interesting features that may be important for our understanding of chemical enrichment of Galactic Disc. According to our findings, every epoch of the disc has its own lowest and highest values for metallicity. It seems that rotational velocity is inversely proportional to 1/2 power of age as given by the Skumanich relation.Comment: 19 pages, 12 figure

Morphometric and morphological evaluation of mastoid emissary canal using cone-beam computed tomography

Objectives: This study aimed to determine mastoid emissary canal’s (MEC) and mastoid foramen (MF) prevalence and morphometric characteristics on cone-beam computed tomography (CBCT) images to underline its clinical significance and discuss its surgical consequences. Methods: In the retrospective analysis, two oral and maxillofacial radiologists analyzed the CBCT images of 135 patients (270 sides). The biggest MF and MEC were measured in the images evaluated in MultiPlanar Reconstruction (MPR) views. The MF and MEC mean diameters were calculated. The mastoid foramina number was recorded. The prevalence of MF was studied according to gender and side of the patient. Results: The overall prevalence of MEC and MF was 119 (88.1%). The prevalence of MEC and MF is 55.5% in females and 44.5% in males. MEC and MF were identified as bilateral in 80 patients (67.20%) and unilateral in 39 patients (32.80%). The mean diameter of MF was 2.4 ± 0.9 mm. The mean height of MF was 2.3 ± 0.9. The mean diameter of the MEC was 2.1 ± 0.8, and the mean height of the MEC was 2.1 ± 0.8. There is a statistical difference between the genders (p = 0.043) in foramen diameter. Males had a significantly larger mean diameter of MF in comparison to females. Conclusion: MEC and MF must be evaluated thoroughly if the surgery is contemplated. Radiologists and surgeons should be aware of mastoid emissary canal morphology, variations, clinical relevance, and surgical consequences while operating in the suboccipital and mastoid areas to avoid unexpected and catastrophic complications. CBCT may be a reliable imaging diagnostic technique

Fundamental properties of solar-like oscillating stars from frequencies of minimum ??-I. Model computations for solar composition

Low amplitude is the defining characteristic of solar-like oscillations. The space projects Kepler and CoRoT give us a great opportunity to successfully detect such oscillations in numerous targets. Achievements of asteroseismology depend on new discoveries of connections between the oscillation frequencies and stellar properties. In the previous studies, the frequency of the maximum amplitude and the large separation between frequencies were used for this purpose. In the present study, we confirm that the large separation between the frequencies has two minima at two different frequency values. These are the signatures of the He II ionization zone, and as such have very strong diagnostic potential. We relate these minima to fundamental stellar properties such as mass, radius, luminosity, age and mass of convective zone. For mass, the relation is simply based on the ratio of the frequency of minimum ?? to the frequency of maximum amplitude. These frequency comparisons can be very precisely computed, and thus the mass and radius of a solar-like oscillating star can be determined to high precision. We also develop a new asteroseismic diagram which predicts structural and evolutionary properties of stars with such data. We derive expressions for mass, radius, effective temperature, luminosity and age in terms of purely asteroseismic quantities. For solar-like oscillating stars, we now will have five very important asteroseismic tools (two frequencies of minimum ??, the frequency of maximum amplitude, and the large and small separations between the oscillation frequencies) to decipher properties of stellar interior astrophysics. © 2014 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society