arXiv subjects

Marek Wolf

Publications and source records attributed to Marek Wolf.

At least 37 records · Page 2Linked to original sources

arXiv2020

Yellow symbiotic star AG Draconis in the scope of the New Online Database of Symbiotic Variables

Symbiotic stars are strongly interacting binaries, consisting of a white dwarf and a cool giant, mainly of spectral type M. AG Draconis belongs to a less numerous group of the yellow symbiotic systems, as the cool component in this binary is of a spectral type earlier than K4. Recently, after seven years of quiescence, this symbiotic star exhibited a very unusual active stage with the four minor outbursts observed. Thanks to the excellent involvement of amateur astronomers and professional observatories, we can study the activity of AG Draconis in unprecedented details. In the present work, we discuss the activity and peculiarities of this interacting system within the entire group of symbiotic stars whose properties have recently been presented in our New Online Database of Symbiotic Variables.

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arXiv2020

Two arguments that the nontrivial zeros of the Riemann zeta function are irrational. II

We extend the results of our previous computer experiment performed on the first 2600 nontrivial zeros $γ_l$ of the Riemann zeta function calculated with 1000 digits accuracy to the set of 40000 first zeros given with 40000 decimal digits accuracy. We calculated the geometrical means of the denominators of continued fractions expansions of these zeros and for all cases we get values very close to the Khinchin's constant, which suggests that $γ_l$ are irrational. Next we have calculated the $n$-th square roots of the denominators $Q_n$ of the convergents of the continued fractions obtaining values very close to the Khinchin---L{é}vy constant, again supporting the common opinion that $γ_l$ are irrational.

math.NT↗

arXiv2019

The activity of the symbiotic binary Z Andromedae and its latest outburst

Z Andromedae is a prototype of classical symbiotic variable stars. It is characterized by alternating of quiescent and active stages, the later ones are accompanied by changes in both photometry and spectral characteristics of this object. The current activity of Z And began in 2000, and the last outburst was recorded at the turn of the years 2017 and 2018. An important source of information about the behaviour of this symbiotic binary during the ongoing active stage is photometric and spectroscopic observations obtained with small telescopes by amateur astronomers. In this paper, we present the results of analysis of these observations, with an emphasis on the significant similarity of the last outburst of Z And with the previous ones, during which jets from this symbiotic system were observed. The presented results point to the importance of long-term monitoring of symbiotic binaries.

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arXiv2019

6+infinity new expressions for the Euler-Mascheroni constant

In the first part we present results of four ``experimental'' determinations of the Euler-Mascheroni constant $γ$. Next we give new formulas expressing the $γ$ constant in terms of the Ramanujan-Soldner constant $μ$. Employing the cosine integral we obtain the infinity of formulas for $γ$.

math.NT↗

arXiv2018

Negative moments of the gaps between consecutive primes

We derive heuristically approximate formulas for the negative $k$--moments $M_{-k}(x)$ of the gaps between consecutive primes$<x $ represented directly by $π(x)$ --- the number of primes up to $x$. In particular we propose an analytical formula for the sum of reciprocals of gaps between consecutive primes $<x : ~ M_{-1}(x)\sim \frac{π^2(x)}{x-2π(x)}\log\Big(\frac{x}{2π(x)}\Big) \sim x \log \log(x)/\log^2(x)$. We illustrate obtained results by the enormous computer data up to $x=4\times 10^{18}$.

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arXiv2018

Repeated transient jets from a warped disk in the symbiotic prototype Z And: A link to the long-lasting active phase

Active phases of some symbiotic binaries survive for a long time from years to decades. The accretion process onto a white dwarf (WD) sustaining long-lasting activity, and sometimes leading to collimated ejection, is not well understood. We present the repeated emergence of highly collimated outflows (jets) from the symbiotic prototype Z And during its 2008 and 2009-10 outbursts and suggest their link to the current long-lasting (from 2000) active phase. We monitored Z And with the high-resolution spectroscopy, multicolor $UBVR_{\rm C}$ and high-time-resolution photometry. The well-pronounced bipolar jets were ejected again during the 2009-10 outburst together with the simultaneous emergence of the rapid photometric variability ($Δm \approx 0.06$ mag) on the timescale of hours, showing similar properties as those during the 2006 outburst. These phenomena and the measured disk-jets connection could be caused by the radiation-induced warping of the inner disk due to a significant increase of the burning WD luminosity. Ejection of transient jets by Z And around outburst maxima signals a transient accretion at rates above the upper limit of the stable hydrogen burning on the WD surface. The enhanced accretion through the disk warping, supplemented by the accretion from the giant's wind, can keep a high luminosity of the WD for a long time, until depletion of the disk. In this way, the jets provide a link to long-lasting active phases of Z And.

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arXiv2018

Some heuristics on the gaps between consecutive primes

We propose the formula for the number of pairs of consecutive primes $p_n, p_{n+1}<x$ separated by gap $d=p_{n+1}-p_n$ expressed directly by the number of all primes $<x$, i.e. by $π(x)$. As the application of this formula we formulate 7 conjectures, among others for the maximal gap between two consecutive primes smaller than $x$, for the generalized Brun's constants and the first occurrence of a given gap $d$. Also the leading term $\log \log(x)$ in the prime harmonic sum is reproduced from our guesses correctly. These conjectures are supported by the computer data.

math.NT↗

arXiv2017

Photometric study of fourteen low-mass binaries

New CCD photometric observations of fourteen short-period low-mass eclipsing binaries (LMB) in the photometric filters I, R and V were used for the light curve analysis. There still exists a discrepancy between radii as observed and those derived from the theoretical modelling for LMB in general. Mass calibration of all observed LMB was done using only the photometric indices. The light curve modelling of these selected systems were performed, yielding the new derived masses and radii for both components. We compared these systems with the compilation of other known double-lined LMB systems with uncertainties of masses and radii less then 5 \%, which includes 66 components of binaries where both spectroscopy and photometry were combined together. All of our systems are circular short-period binaries, and for some of them the photospheric spots were also used. A purely photometric study of the light curves without spectroscopy seems unable to achieve high enough precision and accuracy in the masses and radii to provide for a meaningful test of the M-R relation for low-mass stars.

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arXiv2017

The quadruple-lined, doubly-eclipsing system V482 Persei

We report spectroscopic and differential photometric observations of the A-type system V482 Per that reveal it to be a rare hierarchical quadruple system containing two eclipsing binaries. One has the previously known orbital period of 2.4 days and a circular orbit, and the other a period of 6 days, a slightly eccentric orbit (e = 0.11), and shallow eclipses only 2.3% deep. The two binaries revolve around their common center of mass in a highly elongated orbit (e = 0.85) with a period of 16.67 yr. Radial velocities are measured for all components from our quadruple-lined spectra, and are combined with the light curves and with measurements of times of minimum light for the 2.4 day binary to solve for the elements of the inner and outer orbits simultaneously. The line-of-sight inclination angles of the three orbits are similar, suggesting they may be close to coplanar. The available observations appear to indicate that the 6 day binary experiences significant retrograde apsidal motion in the amount of about 60 degrees per century. We derive absolute masses for the four stars good to better than 1.5%, along with radii with formal errors of 1.1% and 3.5% for the 2.4 day binary and about 9% for the 6 day binary. A comparison of these and other physical properties with current stellar evolution models gives excellent agreement for a metallicity of [Fe/H] = -0.15 and an age of 360 Myr.

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arXiv2017

On the moments of the gaps between consecutive primes

We derive heuristically formula for the $k$--moments $M_k(x)$ of the gaps between consecutive primes$<x $ represented directly by $x$$π(x)$ --- the number of primes up to: $M_k(x)= Γ(k+1)x^k/π^{k-1}(x)+\mathcal{O}(x)$, We illustrate obtained results by computer data.

math.NT↗

arXiv2015

Will a physicist prove the Riemann Hypothesis?

In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix Theory, relation with the Lee--Yang theorem on the zeros of the partition function, random walks, billiards etc.

math-ph↗

arXiv2015

The Physical Nature and Orbital Behavior of the Eclipsing System DK Cygni

New CCD photometry is presented for the hot overcontact binary DK Cyg, together with reasonable explanations for the light and period variations. Historical light and velocity curves from 1962 to 2012 were simultaneously analyzed with the Wilson-Devinney (W-D) synthesis code. The brightness disturbances were satisfactorily modeled by applying a magnetic cool spot on the primary star. Based on 261 times of minimum light including 116 new timings and spanning more than 87 yrs, a period study reveals that the orbital period has varied due to a periodic oscillation superposed on an upward parabola. The period and semi-amplitude of the modulation are about 78.1 yrs and 0.0037 d, respectively. This detail is interpreted as a light-travel-time effect due to a circumbinary companion with a minimum mass of $M_3$=0.065 $M_\odot$, within the theoretical limit of $\sim$0.07 M$_\odot$ for a brown dwarf star. The observed period increase at a fractional rate of $+$2.74 $\times $10$^{-10}$ is in excellent agreement with that calculated from our W-D synthesis. Mass transfer from the secondary to the primary component is mainly responsible for the secular period change. We examined the evolutionary status of the DK Cyg system from the absolute dimensions.

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arXiv2014

Nearest neighbor spacing distribution of prime numbers and quantum chaos

We give heuristic arguments and computer results to support the hypothesis that, after appropriate rescaling, the statistics of spacings between adjacent prime numbers follows the Poisson distribution. The scaling transformation removes the oscillations in the NNSD of primes. These oscillations have the very profound period of length six. We also calculate the spectral rigidity $Δ_3$ for prime numbers by two methods. After suitable averaging one of these methods gives the Poisson dependence $Δ_3(L)=L/15$.

math.NT↗

arXiv2013

Absolute Properties of the Triple Star HP Aurigae

New photometric, spectroscopic, and eclipse timing observations of the eclipsing binary star HP Aur allow for very accurate orbital determinations, even in the presence of a third body and transient starspot activity. The eclipsing binary masses are determined to an accuracy of +/-0.4% and the radii to +/-0.6%. The masses are 0.9543 +/- 0.0041 and 0.8094 +/- 0.0036 solar masses, and the radii are 1.0278 +/- 0.0042 and 0.7758 +/- 0.0034 solar radii, respectively. The orbital period in the outer orbit is accurately known for the first time - 4.332 +/- 0.011 years. A comparison with current theories of stellar evolution show that the components absolute properties can be well-matched by the current models at an age of about 7 billion years.

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arXiv2011

Computer experiments with Mersenne primes

We have calculated on the computer the sum $\bar{\BB}_M$ of reciprocals of all 47 known Mersenne primes with the accuracy of over 12000000 decimal digits. Next we developed $\bar{\BB}_M$ into the continued fraction and calculated geometrical means of the partial denominators of the continued fraction expansion of $\bar{\BB}_M$. We get values converging to the Khinchin's constant. Next we calculated the $n$-th square roots of the denominators of the $n$-th convergents of these continued fractions obtaining values approaching the Khinchin-L{è}vy constant. These two results suggests that the sum of reciprocals of all Mersenne primes is irrational, supporting the common believe that there is an infinity of the Mersenne primes. For comparison we have done the same procedures with slightly modified set of 47 numbers obtaining quite different results. Next we investigated the continued fraction whose partial quotients are Mersenne primes and we argue that it should be transcendental.

math.NT↗

arXiv2011

The Skewes number for twin primes: counting sign changes of $π_2(x)-C_2 \Li_2(x)$

The results of the computer investigation of the sign changes of the difference between the number of twin primes $π_2(x)$ and the Hardy--Littlewood conjecture $C_2\Li_2(x)$ are reported. It turns out that $d_2(x)=π_2(x) - C_2\Li_2(x)$ changes the sign at unexpectedly low values of $x$ and for $x<2^{48}=2.81\...\times10^{14}$ there are 477118 sign changes of this difference. It is conjectured that the number of sign changes of $d_2(x)$ for $x\in (1, T)$ is given by $\sqrt T/\log(T)$. The running logarithmic densities of the sets for which $d_2(x)>0$ and $d_2(x)<0$ are plotted for $x$ up to $2^{48}$.

math.NT↗

arXiv2011

Spectral and photometric analysis of the eclipsing binary epsilon Aurigae prior to and during the 2009-2011 eclipse

A series of 353 red electronic spectra obtained between 1994 and 2010, and of 171 UBV photometric observations of the 2010 eclipse, were analyzed in an effort to better understand the eclipsing binary eps Aur. The main results follow. (1) We attempted to recover a spectrum of the companion by disentangling the observed spectra of the eps Aur binary failed, but we were able to disentangle the spectrum of telluric lines and obtain a mean spectrum of the F-type primary star. The latter was then compared to a grid of synthetic spectra for a number of plausible values of T(eff) and log(g), but a reasonably good match was not found. However, we conclude that the observed spectrum is that of a low-gravity star. (2) We examined changes in the complex H-alpha line profiles over the past 16 years, with particular emphasis on the 2009-2011 eclipse period, by subtracting a mean out-of-eclipse H-alpha profile (appropriately shifted in radial velocity) from the observed spectra. We find that the dark disk around the unseen companion has an extended 'atmosphere' that manifests itself via blueshifted and redshifted H-alpha 'shell' absorptions seen projected against the F star. Significantly, the H-alpha shell line first appeared three years before first contact of the optical eclipse when the system was not far past maximum separation. (3) Analyses of radial velocities and central intensities of several strong, unblended spectral lines, as well as UBV photometry, demonstrated that these observables showed apparent multiperiodic variability during eclipse. The dominant period of 66.21 was common to all the observables, but with different phase shifts between these variables. This result strongly supports our earlier suggestion that the photometric variability seen during eclipse is intrinsic to the F star, and therefore, the idea of a central brightening due to a hole in the disk should be abandoned.

astro-ph.SR↗

arXiv2011

Hydrodynamical and radiative modeling of temporal Hα emission V/R variations caused by a discontinuous mass transfer in binaries

Hα emission V/R variations caused by a discontinous mass transfer in interacting binaries with a rapidly rotating accreting star are modelled qualititatively for the first time. The program ZEUS-MP was used for a non-linear 3-D hydrodynamical modeling of a development of a blob of gaseous material injected into an orbit around a star. It resulted in the formation of an elongated disk with a slow prograde revolution. The LTE radiative transfer program SHELLSPEC was used to calculate the Hα profiles originating in the disk for several phases of its revolution. The profiles have the form of a double emission and exhibit V/R and radial velocity variations. However, these variations should be a temporal phenomenon since imposing a viscosity in given model would lead to a circularization of the disk and fading-out of given variations.

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