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16 pages, 9561 KiB  
Article
Classification of Planetary Motion around Super-Jupiters and Brown Dwarfs
by Euaggelos E. Zotos, Eman M. Moneer and Tobias C. Hinse
Universe 2024, 10(3), 138; https://doi.org/10.3390/universe10030138 - 13 Mar 2024
Viewed by 1422
Abstract
We investigate the orbital dynamics of an exosystem consisting of a solar-mass host star, a transiting body, and an Earth-size exoplanet within the framework of the generalized three-body problem. Depending on its mass, the transiting body can either be a super-Jupiter or a [...] Read more.
We investigate the orbital dynamics of an exosystem consisting of a solar-mass host star, a transiting body, and an Earth-size exoplanet within the framework of the generalized three-body problem. Depending on its mass, the transiting body can either be a super-Jupiter or a brown dwarf. To determine the final states of the Earth-size exoplanet, we conduct a systematic and detailed classification of the available phase space trajectories. Our classification scheme distinguishes between the bounded, escape, and collisional motions of the Earth-size exoplanet. Additionally, for cases of ordered (regular) motion, we further categorize the associated initial conditions based on the geometry of their respective trajectories. These bounded regular trajectories hold significant importance as they provide insights into the regions of phase space where the motion of the Earth-size exoplanet can be dynamically stable. Of particular interest is the identification of initial conditions that result in a bounded exomoon-like orbit of the Earth-size exoplanet around the transiting body. Full article
(This article belongs to the Special Issue Formation and Evolution of Exoplanets)
Show Figures

Figure 1

Figure 1
<p>Distribution of masses and radii for currently known super-Jupiter exoplanets. The mean mass and radius are represented by a five-pointed red star. For further information, please refer to <a href="https://exoplanetarchive.ipac.caltech.edu/" target="_blank">https://exoplanetarchive.ipac.caltech.edu/</a> (accessed on 5 May 2023).</p>
Full article ">Figure 2
<p>Schematic representations illustrating characteristic examples of orbit classification for regular orbits of <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math>, which refers to an exoplanet of Earth-size. Each panel provides a depiction of distinct orbit types, including: (<b>a</b>) a circumstellar orbit, (<b>b</b>) a circumbinary orbit, (<b>c</b>) a circumplanetary orbit, and (<b>d</b>) an intersecting orbit.</p>
Full article ">Figure 3
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math>. The dashed black lines denote a fixed radius measured from <math display="inline"><semantics> <msub> <mi>m</mi> <mn>1</mn> </msub> </semantics></math> (star) in which the aphelion and perihelion distances are equal to 0.05 AU. The mass of the transiting body changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math> = 5 <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math> = 15 <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math> = 30 <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math> = 45 <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math> = 60 <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math> = 70 <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>.</p>
Full article ">Figure 4
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> and also when <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>. The initial eccentricity <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.2, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.4, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.5, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.6, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.8.</p>
Full article ">Figure 5
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> and also when <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>70</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>. The initial eccentricity <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.2, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.4, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.5, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.6, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.8.</p>
Full article ">Figure 6
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> and also when <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>. The initial value (in AU) of the semi-major axis <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.02, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.04, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.06, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.08, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.10, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.12.</p>
Full article ">Figure 7
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> and also when <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>70</mn> </mrow> </semantics></math> <math display="inline"><semantics> <msub> <mi>M</mi> <mi>J</mi> </msub> </semantics></math>. The initial value (in AU) of the semi-major axis <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.02, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.04, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.06, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.08, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.10, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>a</mi> <mn>3</mn> </msub> </semantics></math> = 0.12.</p>
Full article ">Figure 8
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math>. The initial value of the eccentricity <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.2, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.4, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.5, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.6, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.8.</p>
Full article ">Figure 9
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math>, when <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. All the initial conditions are inside the Hill sphere of the transiting body with mass <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math>. The initial value of the eccentricity <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.2, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.4, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.5, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.6, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.8.</p>
Full article ">Figure 10
<p>Classification maps for <math display="inline"><semantics> <msub> <mi>m</mi> <mn>3</mn> </msub> </semantics></math> (Earth-size exoplanet), using different values of <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math>, when <math display="inline"><semantics> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <msub> <mi>M</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>180</mn> <mo>°</mo> </mrow> </semantics></math>. All the initial conditions are inside the Hill sphere of the transiting body with mass <math display="inline"><semantics> <msub> <mi>m</mi> <mn>2</mn> </msub> </semantics></math>. The initial value of the eccentricity <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> changes as follows: (<b>a</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0, (<b>b</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.2, (<b>c</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.4, (<b>d</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.5, (<b>e</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.6, and (<b>f</b>): <math display="inline"><semantics> <msub> <mi>e</mi> <mn>3</mn> </msub> </semantics></math> = 0.8.</p>
Full article ">
19 pages, 8301 KiB  
Article
Revealing Coupled Periodicities in Sunspot Time Series Using Bispectrum—An Inverse Problem
by Styliani Tassiopoulou, Georgia Koukiou and Vassilis Anastassopoulos
Appl. Sci. 2024, 14(3), 1318; https://doi.org/10.3390/app14031318 - 5 Feb 2024
Cited by 1 | Viewed by 1088
Abstract
Sunspot daily time series have been available for almost two centuries providing vast and complicated information about the behavior of our star and especially the interaction of the motion of the planets and other possible interstellar phenomena and their effects on the surface [...] Read more.
Sunspot daily time series have been available for almost two centuries providing vast and complicated information about the behavior of our star and especially the interaction of the motion of the planets and other possible interstellar phenomena and their effects on the surface of the Sun. The main result obtained from the sunspot time series analysis is the imprint of various periodicities, such as the planets’ orbital periods and the planetary synodic periods on the sunspots signature. A detailed spectrum representation is achieved by means of a periodogram and a virtual extension of the time length segments with zeroed samples for longer representations. Furthermore, the dependence or coupling of these periodicities is explored by means of a bispectrum. We establish the exact interdependencies of the periodic phenomena on the sunspot time series. Specific couplings are explored that are proved to be the key issues for the coupled periodicities on the sunspot time series. In this work, contrary to what has been presented in the literature, all periodic phenomena are limited within the time period of an 11-year cycle as well as the periodicities of the orbits of the planets. The main findings are the observed strong coupling of the Mercury, Venus, and Mars periodicities, as well as synodic periodicities with all other periodicities that appear on the sunspot series. Simultaneously, the rotation of the Sun around itself (25.6 to 33.5 days) provides an extensive coupling of all recorded periodicities. Finally, there is strong evidence of the existence of a quadratic mechanism, which couples all the recorded periodicities, but in such a way that only frequency pairs that sum up to specific periods are coupled. The justification for this kind of coupling is left open to the scientific community. Full article
Show Figures

Figure 1

Figure 1
<p>The 11-year cycle of sunspot data starting from 1818. A pulse with a 4000 sample semi-period (10.95 years) seems to fit the data perfectly. The horizontal axis represents days.</p>
Full article ">Figure 2
<p>The 11-years cycle of sunspot data having been processed with a median filter length of 11 days. The horizontal axis represents days.</p>
Full article ">Figure 3
<p>The symmetrical structure of the bispectrum. The blue region is the space that we have to investigate in order to recognize the frequency coordinates that contribute to the formation of coupled components. Frequencies in both axes are normalized in the sampling frequency <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <mn>2</mn> <mi>π</mi> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>(<b>a</b>). The three harmonics that appear at positions 4, 16, and 20 (dc is at position 1). From the power spectrum, it is not possible to distinguish that the 20th harmonic is the result of coupling the other two. The 64th harmonic is at position 65, which coincides with half of the sampling frequency, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> or π. (<b>b</b>). Since (1,1) is the position of dc, the coupling edge is present at coordinates <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mn>5</mn> <mo>,</mo> <mn>17</mn> </mrow> </mfenced> </mrow> </semantics></math>, i.e., for coupled frequencies 4 and 16. The created 20th harmonic does not present any footprint in the region of the bispectrum, which is enclosed in the red line. On both axes, the 64th harmonic is at position 65, which coincides with half of the sampling frequency, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>.</mo> </mrow> </semantics></math></p>
Full article ">Figure 5
<p>(<b>a</b>). The three harmonics that appear at positions 4, 12, and 16 (dc is at position 1). From the power spectrum, it is not possible to distinguish the coupled harmonic. The 64th harmonic is at position 65, which coincides with half of the sampling frequency, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>.</mo> </mrow> </semantics></math> (<b>b</b>). Since (1,1) is the position of dc, the coupling edge is present at coordinates <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mn>5</mn> <mo>,</mo> <mn>13</mn> </mrow> </mfenced> </mrow> </semantics></math>, i.e., for coupled frequencies 4 and 12. The original 16th harmonic does not present any footprint in the region of the bispectrum, which is enclosed in the red line. On both axes, the 64th harmonic is at position 65, which coincides with half of the sampling frequency, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>F</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <mi>π</mi> <mo>.</mo> </mrow> </semantics></math></p>
Full article ">Figure 6
<p>The first 100 harmonics of the sunspot time series from a total of 16,001. Since at position 16,001 we have the harmonic that corresponds to 2 days, the harmonic at position 101 corresponds to 32,000/100 = 320 days. Six is the 6th periodic planetary movement presented in <a href="#applsci-14-01318-t001" class="html-table">Table 1</a>, which corresponds to Jupiter’s rotation. It lies at the 8th harmonic position, i.e., it corresponds to a 4000-day period (11-year cycle). Positions 4 and 5 are the synodic periods of Saturn and Uranus with Jupiter, respectively. Their strength is greater than the period of Jupiter.</p>
Full article ">Figure 7
<p>Spectrum of the sunspot time series with harmonics from 20 to 500 from a total of 16,001. Since at position 16,001 we have the harmonic that corresponds to 2 days, the harmonic at position 501 corresponds to 32,000/500 = 64 days. The numbers above the red circles correspond to the serial numbers in <a href="#applsci-14-01318-t001" class="html-table">Table 1</a>. Indicatively, number 12 is the orbital period of Mars and corresponds to the 48th harmonic. Eighteen corresponds to Earth’s orbital period, which is the 89th harmonic, while numbers 28 and 29 represent the positions of the 361 and 365 harmonics, which represent the synodic periods of Mercury and Jupiter, and the orbital period of Mercury correspondingly. All the relative information is presented in <a href="#applsci-14-01318-t001" class="html-table">Table 1</a>.</p>
Full article ">Figure 8
<p>Spectrum of the sunspot time series with harmonics from 500 to 1300 from a total of 16,001. Since at position 16,001 we have the harmonic that corresponds to 2 days, the harmonic at position 1301 corresponds to 32,000/1300 = 24.6 days. Harmonics 950 to 1250, in the circle indicated as 30 from the corresponding information in <a href="#applsci-14-01318-t001" class="html-table">Table 1</a>, represent the rotational behavior of the body of the Sun, as it rotates at different periods in its equator (25.6 days) from its mass near the poles (33.5 days).</p>
Full article ">Figure 9
<p>Bispectrum of the sunspot series containing the first 200 harmonics. On both axes, the 200th harmonic corresponds to 32,000/200 = 160 days. We obtained symmetry with respect to the diagonal line with an origin at (1,1). All frequency coupling edges that we are interested in lie in the orthogonal red triangle. The four elongated ellipses contain specially coupled groups of periodicities, as explained in the text.</p>
Full article ">Figure 10
<p>Bispectrum of the sunspot series containing the first 400 harmonics. On both axes, the 400th harmonic corresponds to 32,000/400 = 80 days. We achieve symmetry with respect to the diagonal line with its origin at (1,1).</p>
Full article ">Figure 11
<p>Bispectrum of the sunspot series containing the first 1300 harmonics. On both axes, the 1200th harmonic corresponds to 32,000/1200 = 26.7 days (rotation of the Sun at its equator). We achieve symmetry with respect to the diagonal line with its origin at (1,1).</p>
Full article ">
15 pages, 1181 KiB  
Article
Update on WASP-19
by Judith Korth and Hannu Parviainen
Universe 2024, 10(1), 12; https://doi.org/10.3390/universe10010012 - 27 Dec 2023
Cited by 3 | Viewed by 1755
Abstract
Tidal interaction between a star and a close-in massive exoplanet causes the planetary orbit to shrink and eventually leads to tidal disruption. Understanding orbital decay in exoplanetary systems is crucial for advancing our knowledge of planetary formation and evolution. Moreover, it sheds light [...] Read more.
Tidal interaction between a star and a close-in massive exoplanet causes the planetary orbit to shrink and eventually leads to tidal disruption. Understanding orbital decay in exoplanetary systems is crucial for advancing our knowledge of planetary formation and evolution. Moreover, it sheds light on the broader question of the long-term stability of planetary orbits and the intricate interplay of gravitational forces within stellar systems. Analyzing Transiting Exoplanet Survey Satellite (TESS) data for the ultra-short period gas giant WASP-19, we aim to measure orbital period variations and constrain the stellar tidal quality parameter. For this, we fitted the TESS observations together with two WASP-19 transits observed using the Las Cumbres Observatory Global Telescope (LCOGT) and searched for orbital decay in combination with previously published transit times. As a result, we find a deviation from the constant orbital period at the 7σ level. The orbital period changes at a rate of P˙=3.7±0.5msyear1, which translates into a tidal quality factor of Q=(7±1)×105. We additionally modeled WASP-19 b’s phase curve using the new TESS photometry and obtained updated values for the planet’s eclipse depth, dayside temperature, and geometric albedo. We estimate an eclipse depth of 520±60 ppm, which is slightly higher than previous estimates and corresponds to a dayside brightness temperature of 2400±60 K and geometric albedo of 0.20±0.04. Full article
(This article belongs to the Special Issue The Royal Road: Eclipsing Binaries and Transiting Exoplanets)
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<p>Posterior TTV model with blue points, crosses, and dots showing the individual transit center time values for archival data, fitted <span class="html-italic">TESS</span> observations, and fitted LCOGT observations, respectively. Black dots with error bars show the transit center times binned to two years, the solid black line shows the median posterior TTV model, and the orange shading shows the 68% central posterior limits.</p>
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<p>Posterior densities for <math display="inline"><semantics> <mover accent="true"> <mi>P</mi> <mo>˙</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mrow> <msubsup> <mi>Q</mi> <mo>★</mo> <mo>′</mo> </msubsup> </mrow> </semantics></math>. The derivation of these posteriors is detailed in <a href="#sec3dot2-universe-10-00012" class="html-sec">Section 3.2</a> and <a href="#sec3dot3-universe-10-00012" class="html-sec">Section 3.3</a>.</p>
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<p>Phase curve of WASP-19 b. The upper panel shows the full phase curve, including the transit, and the lower plot shows a zoomed view centered around the secondary eclipse. We have removed the median Gaussian Process baseline model from the photometry and phase-folded and binned it for visualization.</p>
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<p>The newly-fitted WASP-19 b transits observed with <span class="html-italic">TESS</span> and the LCOGT 1 m telescopes. We center the <span class="html-italic">TESS</span> transits for each Sector around their fitted transit center times and bin the centered photometry over five minutes for visualization, but show the LCOGT transits individually without binning. The blue dots show the <span class="html-italic">TESS</span> photometry with the GP baseline removed, and black points show the binned <span class="html-italic">TESS</span> photometry and the LCOGT photometry with the GP baseline removed; the black line shows the transit model; the dashed gray vertical line shows the expected transit center based on best-fit linear ephemeris; and the solid black vertical line marks <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>−</mo> <msub> <mi>T</mi> <mi mathvariant="normal">c</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
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17 pages, 1288 KiB  
Article
Secular Orbital Dynamics of the Possibly Habitable Planet K2-18 b with and without the Proposed Inner Companion
by Valeri V. Makarov and Alexey Goldin
Universe 2023, 9(11), 463; https://doi.org/10.3390/universe9110463 - 28 Oct 2023
Cited by 1 | Viewed by 1620
Abstract
The transiting planet K2-18 b is one of the best candidates for a relatively nearby world harboring biological life. The long-term orbital evolution of this planet is investigated using theoretical and purely numerical techniques for two possible configurations: A single planet orbiting the [...] Read more.
The transiting planet K2-18 b is one of the best candidates for a relatively nearby world harboring biological life. The long-term orbital evolution of this planet is investigated using theoretical and purely numerical techniques for two possible configurations: A single planet orbiting the host star, and a two-planet system including the proposed inner planet close to the 4:1 mean motion rationalization. The emphasis is made on the secular changes of eccentricity and orbital inclination, which are important for the climate stability of the planet. It is demonstrated that the secular orbital dynamics of planet K2-18 b with an internal companion are accurately represented by the periodic eccentricity and inclination exchange on the time scales of a few Kyr. A single planet is not expected to experience fast orbital changes, with the much weaker tidal and rotation-driven perturbations mostly reflecting in a slow periastron and nodal precession. The tidal decay of the orbit is too insignificant on the time scale of the stellar age. However, the conditions for the habitability of a single K2-18 b planet are much improved if, like the Earth, it rotates faster than the mean motion and its rotation angle is tilted by a hypothetical moon. Milanković’s cycles of the habitable planet’s climate are discussed for both configurations. Full article
(This article belongs to the Section Planetary Sciences)
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<p>Secular evolution of K2-18 planets in a two-planet configuration. Numerical integration of orbital motion was performed for 30 Kyr with the initial conditions: <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mn>5</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>ω</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi mathvariant="sans-serif">Ω</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. The black curves show the actual output of the numerical simulations. The red curves show the best fits with the theoretical model (2). <b>Upper left</b> panel: inner planet K2-18 c eccentricity. <b>Upper right</b> panel: inner planet K2-18 c inclination in degrees. <b>Lower left</b> panel: outer planet K2-18 b eccentricity. <b>Lower right</b> panel: outer planet K2-18 b inclination in degrees.</p>
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<p>Secular evolution of K2-18 planets in a two-planet configuration. The numerical integration of orbital motion was performed for 30 Kyr with the initial conditions: <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mn>40</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>ω</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi mathvariant="sans-serif">Ω</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. The black curves show the actual output of the numerical simulations. The red curve show the best fits with the theoretical model (2). <b>Left</b> panel: outer planet K2-18 b eccentricity. <b>Right</b> panel: outer planet K2-18 b inclination in degrees.</p>
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<p>Temporal behavior of K2-18 planets’ nodes and apsides in a two-planet configuration. The numerical integration of orbital motion was performed for 30 Kyr with the initial conditions: <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>e</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mn>5</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>ω</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="sans-serif">Ω</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi mathvariant="sans-serif">Ω</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. <b>Left</b> panel: outer planet K2-18 b periastron argument after subtraction of a constant-rate precession of <math display="inline"><semantics> <mrow> <msup> <mn>0.0277</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>/yr. <b>Right</b> panel: outer planet K2-18 b longitude of the ascending node. Both angles are in radians.</p>
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<p>The paths of the orbital axes of K2-18 planets over 30 Kyr in the inertial <math display="inline"><semantics> <mrow> <mo>{</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>}</mo> </mrow> </semantics></math> plane. The red curve is for the inner planet 1 (K2-18 c), and the black curve is for the outer planet 2 (K2-18 b). The same initial conditions are used for numerical integration as in <a href="#universe-09-00463-f001" class="html-fig">Figure 1</a>.</p>
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<p>Transit time variations in days for planet K2-18 b computed from the same simulation of a two-planet system as shown in <a href="#universe-09-00463-f001" class="html-fig">Figure 1</a>.</p>
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<p>Transit time variations in minutes for planet K2-18 b computed from a special simulation of a two-planet system with the same initial parameters as in <a href="#universe-09-00463-f001" class="html-fig">Figure 1</a> for 30 Kyr with a state dump step of 1 yr. A small section of the data spanning 30 yr close to a minimum of the secular variation curve is shown.</p>
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16 pages, 3070 KiB  
Review
Transiting Circumbinary Planets in the Era of Space-Based Photometric Surveys
by Veselin B. Kostov
Universe 2023, 9(10), 455; https://doi.org/10.3390/universe9100455 - 21 Oct 2023
Cited by 1 | Viewed by 1698
Abstract
Planets orbiting binary stars—circumbinary planets—play a paramount role in our understanding of planetary and stellar formation and evolution, dynamical interactions in many-body systems, and the potential for habitable environments beyond the Solar System. Each new discovery holds immense value and inherent fascination both [...] Read more.
Planets orbiting binary stars—circumbinary planets—play a paramount role in our understanding of planetary and stellar formation and evolution, dynamical interactions in many-body systems, and the potential for habitable environments beyond the Solar System. Each new discovery holds immense value and inherent fascination both for the astronomical community and for the general public. This is perhaps best demonstrated by the 1500+ citations of the discovery papers for the 14 known transiting circumbinary planets and the dozens of related press-releases in major news outlets. This article reviews the observational and theoretical aspects related to the detection and confirmation of transiting circumbinary planets around main-sequence binaries from space-based surveys, discusses the associated challenges, and highlights some of the recent results. Full article
(This article belongs to the Special Issue The Royal Road: Eclipsing Binaries and Transiting Exoplanets)
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<p><b>Upper panel</b>: Short-cadence TESS data for CM Dra. <b>Middle panel</b>: same as the upper panel but zoomed-in to highlight the expected transit depth for a Neptune-sized CBP (red dashed line) and a Jupiter-sized CBP (black dashed line). <b>Lower panel</b>: measured eclipse timing variations for the primary (red) and secondary (blue) eclipses. Both eclipses follow linear ephemeris. The vertical red and blue lines represent the typical per-point uncertainties.</p>
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<p>Taken from [<a href="#B86-universe-09-00455" class="html-bibr">86</a>]. Planet radius, orbital period and distance from the host binary star for the known transiting (filled orange, green, and gray symbols for the host binaries, and circles for their planets) and non-transiting (open symbols, detected through eclipse-timing variations) CBPs discovered from Kepler and TESS data. The horizontal bars in the right panel show, on a logarithmic scale, the eccentricity-modified orbital separation of the planets from the binary (bars at large distance) and of the binary itself (bars at smaller distance). The red crosses on the horizontal lines represent the respective stability limits.</p>
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<p>Taken from [<a href="#B85-universe-09-00455" class="html-bibr">85</a>]. To-scale orbital configuration of the Kepler-413 system highlighting the rapid orbital precession of the CBP (precession period of ∼11 years). The solid overlapping symbols in the lower right panel represent the configuration of the system during the last transit observed from Kepler, and the open circles represent a missed transit one CBP conjunction later.</p>
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<p>Taken from [<a href="#B92-universe-09-00455" class="html-bibr">92</a>]. <b>Left panel</b>: A section of the Kepler lightcurve (small dots) during a CBP syzygy with a stellar eclipse. The eclipse is the deep feature that falls below the x-axis as it is too deep to fit on the scale of the panel. The red symbols represent the in-transit data and the blue curve represents the transit model. <b>Right panel</b>: Corresponding configuration of the system as seen from Kepler.</p>
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<p>Taken from Kostov et al. (2021). Planet radius, orbital period, and insolation for transiting CBPs (diamond symbols), confirmed single-star planets (small dots), planets in S-type orbits in wide binary systems (circles) and wide higher-order systems (squares). The vertical green band represents the regime of the habitable zone.</p>
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<p>Comparison between the orbital period and eccentricity of all exoplanets known in 1998 and of all transiting CBPs known in 2023.</p>
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<p>Kepler lighturve of Kepler-16 phase folded on the best-fit period of the CBP (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">P</mi> <mi>CBP</mi> </msub> <mo>=</mo> <mn>228.776</mn> </mrow> </semantics></math> days). Folding the data on <math display="inline"><semantics> <msub> <mi mathvariant="normal">P</mi> <mi>CBP</mi> </msub> </semantics></math> smears the transits in phase space.</p>
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<p>Examples of CBP false positives detected by visual inspection of TESS EB lightcurves. <b>Upper panel</b>: Taken from [<a href="#B124-universe-09-00455" class="html-bibr">124</a>]. Normalized TESS <span class="html-small-caps">eleanor</span> data [<a href="#B125-universe-09-00455" class="html-bibr">125</a>] of the stellar quadruple candidate TIC 438226195 from Sectors 6 and 33. The vertical green bands highlight extra transit-like events in addition to the clear EB signal. Initially, only Sector 6 data were available, exhibiting a single extra transit-like event in the TESS <span class="html-small-caps">eleanor</span> data [<a href="#B125-universe-09-00455" class="html-bibr">125</a>]. Subsequent data from Sector 33 showed that the event is in fact an eclipse from a second EB, making TIC 438226195 an on-target CBP false positive. <b>Lower panel</b>: TESS <span class="html-small-caps">QLP</span> data [<a href="#B126-universe-09-00455" class="html-bibr">126</a>] of the CBP false positive TIC 92469903 from Sector 9 showing two extra transit-like events.</p>
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<p>CBP false positive TIC 92469903. <b>First and second panel</b>: Lightcurve and pixel-level analysis of TESS data showing that the source of both extra events is the nearby EB TIC 92469882. <b>Last panel</b>: <math display="inline"><semantics> <mrow> <mn>7</mn> <mo>×</mo> <mn>7</mn> </mrow> </semantics></math> pixels Skyview image of the field around TIC 92469903 highlighting the contaminator TIC 92469882.</p>
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<p>Likely CBP false positive TIC 150582131. <b>Upper panel</b>: TESS <span class="html-small-caps">eleanor</span> lightcurve of TIC 150582131 from Sector 25 showing one extra event. <b>Lower panel</b>: <math display="inline"><semantics> <mrow> <mn>7</mn> <mo>×</mo> <mn>7</mn> </mrow> </semantics></math> pixels Skyview image of the field around TIC 150582131 showing a resolved, closely-separated (0.4 arcsec) star (TIC 508200354). The separation between the two stars is too small to determine which of them is the source of the extra event based on the available data, and the magnitude difference is such that either can produce the extra event. This makes TIC 150582131 a likely CBP false positive.</p>
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15 pages, 595 KiB  
Article
Application of Manifold Corrections in Tidal Evolution of Exoplanetary Systems
by Qian-Qian Xiao, Ying Wang, Fu-Yao Liu, Chen Deng and Wei Sun
Symmetry 2023, 15(1), 253; https://doi.org/10.3390/sym15010253 - 16 Jan 2023
Viewed by 2189
Abstract
The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and [...] Read more.
The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and requires reliable numerical methods. The manifold correction method, which strictly satisfies the integrals dissipative quasiintegrals of the system, exhibits good numerical accuracy and stability in the quasi-Kepler problem. Different manifold correction methods adopt different integrals or integral invariant relations to correct the numerical solutions. We apply the uncorrected five- and six-order Runge–Kutta–Fehlberg algorithm [RKF5(6)], as well as corrected by the velocity scaling method and Fukushima’s linear transformation method to solve the tidal evolution of exoplanet systems. The results show that Fukushima’s linear transformation method exhibits the best performance in the accuracy of the semimajor axis and eccentricity. In addition, we predict the tidal timescale of several current close exoplanetary systems by using this method. Full article
(This article belongs to the Special Issue Symmetry in Gravity Research)
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<p>The error map of the semimajor axis of GJ486b in the process of planetary evolution. The algorithms involved in the figure are RKF5(6), Fukushima’s linear transformation method(M1), and velocity scaling method(M2). (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>22</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, only tidal effects exist; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>22</mn> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math>, tidal and deformation forces and torques exist at the same time.</p>
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<p>Eccentricity error map of GJ486 b during planetary evolution. The algorithms used are RKF5(6), Fukushima’s linear transformation method(M1), and velocity scaling(M2). (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>22</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, only tidal effects exist; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>22</mn> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math>, tidal and deformation forces and torques exist at the same time.</p>
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<p>Error map of the ratio of the angular rotation velocity to the mean motion of GJ486 b during planetary evolution. The algorithms used are RKF5(6), Fukushima’s linear transformation method(M1), and velocity scaling(M2). (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>22</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, only tidal effects exist; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>C</mi> <mn>22</mn> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> </semantics></math>, tidal and deformation forces and torques exist at the same time.</p>
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<p>Time variation of <math display="inline"><semantics> <mrow> <mi mathvariant="normal">Ω</mi> <mo>/</mo> <mi>n</mi> </mrow> </semantics></math> for GJ486 b. Different evolutions were observed, including capturing <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>1</mn> </mrow> </semantics></math> spin-orbit resonances. The dotted line corresponds to the presence of only the tidal effect, and the solid line corresponds to the coexistence of tidal and deformation forces and torques. These evolutionary results are calculated from M1.</p>
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<p>Evolution of the semimajor axis of GJ486 b over time. The variable rates of <span class="html-italic">a</span> are different when the rotation is trapped in different capture. These evolutionary results are calculated from M1.</p>
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<p>Eccentricity evolution of GJ486 b over time. The rate of change of <span class="html-italic">e</span> depends on the specific capture in which the spin is trapped. When the rotation is in resonance, the eccentricity changes rapidly. These evolutionary results are calculated from M1.</p>
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38 pages, 3885 KiB  
Review
Interstellar Propulsion Using Laser-Driven Inertial Confinement Fusion Physics
by Kelvin F. Long
Universe 2022, 8(8), 421; https://doi.org/10.3390/universe8080421 - 15 Aug 2022
Cited by 8 | Viewed by 4370
Abstract
To transport a spacecraft to distances far beyond the solar heliosphere and around the planets of other stars will require advanced space propulsion systems that go beyond the existing technological state of the art. The release of fusion energy from the interaction of [...] Read more.
To transport a spacecraft to distances far beyond the solar heliosphere and around the planets of other stars will require advanced space propulsion systems that go beyond the existing technological state of the art. The release of fusion energy from the interaction of two low mass atomic nuclei that are able to overcome the Coulomb barrier offers the potential for ∼1011J/g specific energy release and implies that robotic missions to the nearby stars to distances of ∼5–10 ly may be possible in trip durations of the order of ∼50–100 years, travelling at cruise speeds of the order of ∼0.05–0.15 c. Such missions would be characterised with ∼kN-MN thrust levels, ∼GW-TW jet powers, ∼kW/kg-MW/kg specific powers. One of the innovative methods by which fusion reactions can be ignited is via the impingement of laser beams onto an inertial confinement fusion capsule, imploding it to a thermonuclear state. This paper gives an overview of the physics of inertial confinement fusion and the interaction of a laser beam with a capsule to include the simulation of a 1D particle-in-cell code calculation to illustrate the effects. In the application to deep space missions, various spacecraft concepts from the literature are discussed, and the range of values assumed for the pulse frequency, burn fraction and areal density appropriate for the mission are presented. It is concluded that advanced space propulsion via inertial confinement fusion is a plausible part of our future, provided that experimental validation of ignition is on the horizon and numerical models for feasibility concepts are developed to high fidelity and on a consistent basis. Full article
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Figure 1
<p>Illustration of engine reaction chamber. (<b>a</b>) Capsule target is accelerated onto central axis, (<b>b</b>) energy drivers target the capsule for a symmetry implosion, (<b>c</b>) some form of hot spot thermonuclear ignition occurs, (<b>d</b>) a self-sustaining burn wave is initiated with alpha-particle deposition to ignite surrounding fuel, (<b>e</b>) plasma expansion into the reaction chamber with neutron and x-ray deposition into structure and space, and with the charged plasma debris exhausted for the purposes of thrust generation.</p>
Full article ">Figure 2
<p>Illustration of a typical ICF physical model for the National Ignition Facility.</p>
Full article ">Figure 3
<p>Example of the electric field <math display="inline"><semantics> <mi mathvariant="bold-italic">E</mi> </semantics></math>y(x) in a 1D PIC code laser–plasma calculation, shown at 0.16 ps to simulate the interaction of a laser beam with the surface of an ICF capsule.</p>
Full article ">Figure 4
<p>Reaction chamber of fusion engines: (<b>a</b>) open hemispherical shell, (<b>b</b>) internal geometry of target chamber, (<b>c</b>) closed system.</p>
Full article ">Figure 5
<p>Illustration of an ICF spacecraft and its engine power cycle.</p>
Full article ">Figure 6
<p>Propulsion pulse frequency as a function of capsule burn fraction performance for an assumed constant thrust and capsule mass.</p>
Full article ">Figure 7
<p>The Daedalus spacecraft concept design.</p>
Full article ">Figure 8
<p>Illustration of non-aneutronic effects of deuterium–deuterium self-burn reactions within a deuterium–helium-3 dominant thermonuclear fuel.</p>
Full article ">Figure 9
<p>The Vista spacecraft concept design.</p>
Full article ">Figure 10
<p>Concept vehicle design schematic for Icarus resolution interstellar flyby probe propelled by an ICF propulsion engine.</p>
Full article ">Figure 11
<p>The Resolution spacecraft concept design.</p>
Full article ">
24 pages, 2360 KiB  
Article
Radial Oscillations of Quark Stars Admixed with Dark Matter
by José C. Jiménez and Eduardo S. Fraga
Universe 2022, 8(1), 34; https://doi.org/10.3390/universe8010034 - 5 Jan 2022
Cited by 24 | Viewed by 1811
Abstract
We investigated compact stars consisting of cold quark matter and fermionic dark matter treated as two admixed fluids. We computed the stellar structures and fundamental radial oscillation frequencies of different masses of the dark fermion in the cases of weak and strong self-interacting [...] Read more.
We investigated compact stars consisting of cold quark matter and fermionic dark matter treated as two admixed fluids. We computed the stellar structures and fundamental radial oscillation frequencies of different masses of the dark fermion in the cases of weak and strong self-interacting dark matter. We found that the fundamental frequency can be dramatically modified and, in some cases, stable dark strange planets and dark strangelets with very low masses and radii can be formed. Full article
(This article belongs to the Special Issue Properties and Dynamics of Neutron Stars and Proto-Neutron Stars)
Show Figures

Figure 1

Figure 1
<p>Each pair of panels with the same color for the plots displays the mass–radius relation and the mass as a function of the energy density for quark matter cores, i.e., <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>QM</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>QM</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, with different amounts of weakly (<math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>) interacting dark matter (<span class="html-italic">w</span>DM) for dark fermion masses of <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>50</mn> <mo>,</mo> <mn>100</mn> <mo>,</mo> <mn>200</mn> <mo>,</mo> <mn>500</mn> </mrow> </semantics></math> GeV.</p>
Full article ">Figure 1 Cont.
<p>Each pair of panels with the same color for the plots displays the mass–radius relation and the mass as a function of the energy density for quark matter cores, i.e., <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>QM</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>QM</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, with different amounts of weakly (<math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>) interacting dark matter (<span class="html-italic">w</span>DM) for dark fermion masses of <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>50</mn> <mo>,</mo> <mn>100</mn> <mo>,</mo> <mn>200</mn> <mo>,</mo> <mn>500</mn> </mrow> </semantics></math> GeV.</p>
Full article ">Figure 1 Cont.
<p>Each pair of panels with the same color for the plots displays the mass–radius relation and the mass as a function of the energy density for quark matter cores, i.e., <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>QM</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>QM</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, with different amounts of weakly (<math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>) interacting dark matter (<span class="html-italic">w</span>DM) for dark fermion masses of <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>50</mn> <mo>,</mo> <mn>100</mn> <mo>,</mo> <mn>200</mn> <mo>,</mo> <mn>500</mn> </mrow> </semantics></math> GeV.</p>
Full article ">Figure 2
<p>Same notation as in <a href="#universe-08-00034-f001" class="html-fig">Figure 1</a> but now for dark matter cores satisfying <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>DM</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>DM</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 2 Cont.
<p>Same notation as in <a href="#universe-08-00034-f001" class="html-fig">Figure 1</a> but now for dark matter cores satisfying <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>DM</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>DM</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>Fundamental-mode frequencies, <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> </semantics></math>, versus gravitational masses, <span class="html-italic">M</span>, and central energy densities, <math display="inline"><semantics> <msub> <mi>ϵ</mi> <mi>c</mi> </msub> </semantics></math>, all for the oscillating QM cores with different values of central wDM and dark fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>. Panels with the same color belong to the same class of admixed stars. Notice that the behavior in the planes <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is highly dependent on the value of <math display="inline"><semantics> <msubsup> <mi>ϵ</mi> <mi>c</mi> <mi>wDM</mi> </msubsup> </semantics></math>, especially for the low-mass QM cores. In a marked contrast, the changes are more modest in the <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>ϵ</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> planes.</p>
Full article ">Figure 3 Cont.
<p>Fundamental-mode frequencies, <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> </semantics></math>, versus gravitational masses, <span class="html-italic">M</span>, and central energy densities, <math display="inline"><semantics> <msub> <mi>ϵ</mi> <mi>c</mi> </msub> </semantics></math>, all for the oscillating QM cores with different values of central wDM and dark fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>. Panels with the same color belong to the same class of admixed stars. Notice that the behavior in the planes <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is highly dependent on the value of <math display="inline"><semantics> <msubsup> <mi>ϵ</mi> <mi>c</mi> <mi>wDM</mi> </msubsup> </semantics></math>, especially for the low-mass QM cores. In a marked contrast, the changes are more modest in the <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>ϵ</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> planes.</p>
Full article ">Figure 4
<p>Same notation as in <a href="#universe-08-00034-f003" class="html-fig">Figure 3</a> but now for oscillating wDM cores and different central QM energy densities. Notice that, although the frequencies still reach high values, e.g., ∼<math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>5</mn> </msup> </mrow> </semantics></math> KHz for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> GeV, the qualitative behavior in the <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>ϵ</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> planes is markedly different and characteristic of dominating wDM in the admixed star for any amount of central QM.</p>
Full article ">Figure 4 Cont.
<p>Same notation as in <a href="#universe-08-00034-f003" class="html-fig">Figure 3</a> but now for oscillating wDM cores and different central QM energy densities. Notice that, although the frequencies still reach high values, e.g., ∼<math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mn>5</mn> </msup> </mrow> </semantics></math> KHz for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> GeV, the qualitative behavior in the <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>M</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>ϵ</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> </mrow> </semantics></math> planes is markedly different and characteristic of dominating wDM in the admixed star for any amount of central QM.</p>
Full article ">Figure 5
<p>Mass–radius and mass–energy density relationships for QM cores with different amounts of strongly (<math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>) interacting dark matter (<span class="html-italic">s</span>DM) at the center of the admixed stars. Different values for the dark fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> are considered and results characterized by the same color. Notice that the effects of <span class="html-italic">s</span>DM are mainly for high-mass stars and especially marked for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> GeV.</p>
Full article ">Figure 5 Cont.
<p>Mass–radius and mass–energy density relationships for QM cores with different amounts of strongly (<math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>) interacting dark matter (<span class="html-italic">s</span>DM) at the center of the admixed stars. Different values for the dark fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> are considered and results characterized by the same color. Notice that the effects of <span class="html-italic">s</span>DM are mainly for high-mass stars and especially marked for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> GeV.</p>
Full article ">Figure 5 Cont.
<p>Mass–radius and mass–energy density relationships for QM cores with different amounts of strongly (<math display="inline"><semantics> <mrow> <mi>y</mi> <mo>=</mo> <msup> <mn>10</mn> <mn>3</mn> </msup> </mrow> </semantics></math>) interacting dark matter (<span class="html-italic">s</span>DM) at the center of the admixed stars. Different values for the dark fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> are considered and results characterized by the same color. Notice that the effects of <span class="html-italic">s</span>DM are mainly for high-mass stars and especially marked for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> GeV.</p>
Full article ">Figure 6
<p>Mass–radius and mass–energy density relations obtained for <span class="html-italic">s</span>DM cores for different fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> (indicated by different colors) with increasing amounts of QM at the centers of the admixed stars. Notice that the competition between <span class="html-italic">s</span>DM and QM densities in some cases allows for the presence of very small stars, which are not present in the one-fluid case, producing qualitatively different behavior in the mass–radius relations of <span class="html-italic">s</span>DM stars, especially for low <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>.</p>
Full article ">Figure 6 Cont.
<p>Mass–radius and mass–energy density relations obtained for <span class="html-italic">s</span>DM cores for different fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> (indicated by different colors) with increasing amounts of QM at the centers of the admixed stars. Notice that the competition between <span class="html-italic">s</span>DM and QM densities in some cases allows for the presence of very small stars, which are not present in the one-fluid case, producing qualitatively different behavior in the mass–radius relations of <span class="html-italic">s</span>DM stars, especially for low <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>.</p>
Full article ">Figure 6 Cont.
<p>Mass–radius and mass–energy density relations obtained for <span class="html-italic">s</span>DM cores for different fermion masses <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> (indicated by different colors) with increasing amounts of QM at the centers of the admixed stars. Notice that the competition between <span class="html-italic">s</span>DM and QM densities in some cases allows for the presence of very small stars, which are not present in the one-fluid case, producing qualitatively different behavior in the mass–radius relations of <span class="html-italic">s</span>DM stars, especially for low <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>.</p>
Full article ">Figure 7
<p>Fundamental-mode frequency, <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> </semantics></math>, versus QM core masses and central energy densities with different amounts of <span class="html-italic">s</span>DM for increasing values of the dark fermion masses, <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, denoted by different colors. It can be seen that the densities of <span class="html-italic">s</span>DM for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> GeV have almost no effect on the stability of the corresponding QM cores. Nevertheless, as one increases <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, the stable QM core masses are reduced to lower and lower values and require higher QM central densities.</p>
Full article ">Figure 7 Cont.
<p>Fundamental-mode frequency, <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> </semantics></math>, versus QM core masses and central energy densities with different amounts of <span class="html-italic">s</span>DM for increasing values of the dark fermion masses, <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, denoted by different colors. It can be seen that the densities of <span class="html-italic">s</span>DM for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> GeV have almost no effect on the stability of the corresponding QM cores. Nevertheless, as one increases <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, the stable QM core masses are reduced to lower and lower values and require higher QM central densities.</p>
Full article ">Figure 7 Cont.
<p>Fundamental-mode frequency, <math display="inline"><semantics> <msub> <mi>f</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </msub> </semantics></math>, versus QM core masses and central energy densities with different amounts of <span class="html-italic">s</span>DM for increasing values of the dark fermion masses, <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, denoted by different colors. It can be seen that the densities of <span class="html-italic">s</span>DM for <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> GeV have almost no effect on the stability of the corresponding QM cores. Nevertheless, as one increases <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, the stable QM core masses are reduced to lower and lower values and require higher QM central densities.</p>
Full article ">Figure 8
<p>Same notation as in <a href="#universe-08-00034-f007" class="html-fig">Figure 7</a>, but now for the oscillating core composed of <span class="html-italic">s</span>DM corresponding to increasing <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> (with different colors) and increasing values of central QM densities. Notice the changing qualitative behavior when QM densities dominate over <span class="html-italic">s</span>DM for low <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> </mrow> </semantics></math> GeV but the opposite happening for larger <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, where QM only allows for more stable <span class="html-italic">s</span>DM cores.</p>
Full article ">Figure 8 Cont.
<p>Same notation as in <a href="#universe-08-00034-f007" class="html-fig">Figure 7</a>, but now for the oscillating core composed of <span class="html-italic">s</span>DM corresponding to increasing <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> (with different colors) and increasing values of central QM densities. Notice the changing qualitative behavior when QM densities dominate over <span class="html-italic">s</span>DM for low <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> </mrow> </semantics></math> GeV but the opposite happening for larger <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, where QM only allows for more stable <span class="html-italic">s</span>DM cores.</p>
Full article ">Figure 8 Cont.
<p>Same notation as in <a href="#universe-08-00034-f007" class="html-fig">Figure 7</a>, but now for the oscillating core composed of <span class="html-italic">s</span>DM corresponding to increasing <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math> (with different colors) and increasing values of central QM densities. Notice the changing qualitative behavior when QM densities dominate over <span class="html-italic">s</span>DM for low <math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>D</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>10</mn> </mrow> </semantics></math> GeV but the opposite happening for larger <math display="inline"><semantics> <msub> <mi>m</mi> <mi>D</mi> </msub> </semantics></math>, where QM only allows for more stable <span class="html-italic">s</span>DM cores.</p>
Full article ">
15 pages, 1363 KiB  
Article
ASASSN-13db 2014–2017 Eruption as an Intermediate Luminosity Optical Transient
by Amit Kashi, Amir M. Michaelis and Leon Feigin
Galaxies 2020, 8(1), 2; https://doi.org/10.3390/galaxies8010002 - 19 Dec 2019
Cited by 11 | Viewed by 2924
Abstract
The low mass star ASASSN-13db experienced an EXor outburst in 2013, which identified it as a Young Stellar Object (YSO). Then, from 2014 to 2017 it had another outburst, longer and more luminous than the earlier. We analyze the observations of the second [...] Read more.
The low mass star ASASSN-13db experienced an EXor outburst in 2013, which identified it as a Young Stellar Object (YSO). Then, from 2014 to 2017 it had another outburst, longer and more luminous than the earlier. We analyze the observations of the second outburst, and compare it to eruptions of Intermediate Luminosity Optical Transients (ILOTs). We show that the decline of the light curve is almost identical to that of the V838 Mon, a prototype of a type of ILOT known as Luminous Red Nova (LRN). This similarity becomes conspicuous when oscillations that are associated with rotation are filtered out from the light curve of ASASSN-13db. We suggest that the eruption was the result of accretion of a proto-planet of a few Earth masses. The proto-planet was shredded by tidal forces before it was accreted onto the YSO, releasing gravitational energy that powered the outburst for 800 days , and ended in a 55 days decline phase. When the accretion material started depleting the accretion rate lowered and the eruption light curve declined for almost two months. Then it exhausted completely, creating a sharp break in the light curve. Another possibility is that the mass was a result of an instability in the proto-planetary disk that lead to a large episode of accretion from an inner viscous disk. We find that the variation of the temperature of the outburst is consistent with the surface temperature expected from a depleted viscous accretion disk. The 2014–2017 outburst of ASASSN-13db may be the least energetic ILOT to have been discovered to date, with an energy budget of only 10 42 erg . Full article
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Figure 1

Figure 1
<p>(<b>a</b>) Comparing the <span class="html-italic">V</span>-band light curves of A13db1417 [<a href="#B47-galaxies-08-00002" class="html-bibr">47</a>] and V838 Mon (Bond et al. [<a href="#B2-galaxies-08-00002" class="html-bibr">2</a>], Starrfield et al. [<a href="#B39-galaxies-08-00002" class="html-bibr">39</a>], Sparks et al. [<a href="#B63-galaxies-08-00002" class="html-bibr">63</a>]). The magnitude scale is the apparent magnitude for A13db1417. The light curve of V838 Mon was shifted by <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>V</mi> <mrow> <mi mathvariant="normal">V</mi> <mn>838</mn> <mspace width="3.33333pt"/> <mi>Mon</mi> </mrow> </msub> <mo>=</mo> <mn>6.9</mn> </mrow> </semantics></math> mag to match the second peak before decline. The time axis focuses on the end of the <math display="inline"><semantics> <mrow> <mo>≈</mo> <mn>800</mn> <mspace width="3.33333pt"/> <mi>days</mi> </mrow> </semantics></math> duration of A13db1417 (see Sicilia Aguilar et al. [<a href="#B47-galaxies-08-00002" class="html-bibr">47</a>]) which is the <math display="inline"><semantics> <mrow> <mo>≃</mo> <mn>55</mn> <mspace width="3.33333pt"/> <mi>days</mi> </mrow> </semantics></math> decline phase. The peak at <math display="inline"><semantics> <mrow> <mi>JD</mi> <mo>≃</mo> </mrow> </semantics></math> 2,457,728 marks <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>. (<b>b</b>) Same us the upper panel, but the light curves were shifted to match the peak just before decline. In addition, the time axis of the light curve V838 Mon is scaled by a factor of 1.3 relative to the matched peak. This results in that the two light curves match for about 4 mag.</p>
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<p>The light curve of A13db1417, with the variability resulted by rotation of stellar spot filtered out, compared to the light curve of V838 Mon. This variability caused oscillations of <math display="inline"><semantics> <mrow> <mi>δ</mi> <mi>V</mi> <mo>≃</mo> <mn>1</mn> </mrow> </semantics></math> mag. By filtering out the effect of rotation, we isolate the component resulted from accretion. The filtered signal matches better the scaled light curve of V838 Mon.</p>
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<p>The light curve of A13db1417 compared to that of the FU Ori eruption of V1647 Ori [<a href="#B66-galaxies-08-00002" class="html-bibr">66</a>]. It can be seen that the two curves are very different and the decline does not follow the same slope. This suggest that this objects are different. Note that the LCOGT observation at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mo>−</mo> <mn>2</mn> <mspace width="3.33333pt"/> <mi>days</mi> </mrow> </semantics></math> may be an outlier.</p>
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<p>The effective temperature of A13db1417, obtained from different filters as indicated in the legend. The calculation was performed assuming black-body emission, which is apparently not the emitting spectrum, hence the differences between the estimated in different filter pairs. Nevertheless we can see that the effective temperature is declining from <math display="inline"><semantics> <mrow> <mo>≃</mo> <mn>4500</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">K</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>≃</mo> <mn>2000</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">K</mi> </mrow> </semantics></math> during the eruption. Over-plotted is the effective temperature from of V838 Mon, adopted from [<a href="#B67-galaxies-08-00002" class="html-bibr">67</a>]. It is evident that both objects have a similar decline.</p>
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<p>A focus on the fast increase in luminosity at the beginning of A13db1417. Observations are taken from [<a href="#B47-galaxies-08-00002" class="html-bibr">47</a>].</p>
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<p>An estimate to a classical accretion disk surface temperature, according to Equation (<a href="#FD7-galaxies-08-00002" class="html-disp-formula">7</a>). When the disk is depleted the mass accretion rate decreases and so does the surface temperature of the disk.</p>
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7 pages, 501 KiB  
Article
Jsolated Stars of Low Metallicity
by Efrat Sabach
Galaxies 2018, 6(3), 89; https://doi.org/10.3390/galaxies6030089 - 15 Aug 2018
Viewed by 3108
Abstract
We study the effects of a reduced mass-loss rate on the evolution of low metallicity Jsolated stars, following our earlier classification for angular momentum (J) isolated stars. By using the stellar evolution code MESA we study the evolution with different mass-loss rate efficiencies [...] Read more.
We study the effects of a reduced mass-loss rate on the evolution of low metallicity Jsolated stars, following our earlier classification for angular momentum (J) isolated stars. By using the stellar evolution code MESA we study the evolution with different mass-loss rate efficiencies for stars with low metallicities of Z = 0.001 and Z = 0.004 , and compare with the evolution with solar metallicity, Z = 0.02 . We further study the possibility for late asymptomatic giant branch (AGB)—planet interaction and its possible effects on the properties of the planetary nebula (PN). We find for all metallicities that only with a reduced mass-loss rate an interaction with a low mass companion might take place during the AGB phase of the star. The interaction will most likely shape an elliptical PN. The maximum post-AGB luminosities obtained, both for solar metallicity and low metallicities, reach high values corresponding to the enigmatic finding of the PN luminosity function. Full article
(This article belongs to the Special Issue Asymmetric Planetary Nebulae VII)
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Figure 1

Figure 1
<p>The evolution during the final <math display="inline"><semantics> <mrow> <mo>≃</mo> <mn>2.5</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>5</mn> </msup> <mrow> <mspace width="3.33333pt"/> <mi>yr</mi> </mrow> </mrow> </semantics></math> of the asymptotic giant branch (AGB) of stars of initial mass <math display="inline"><semantics> <mrow> <mn>0.9</mn> <mspace width="3.33333pt"/> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math> (<b>left plot</b>) and <math display="inline"><semantics> <mrow> <mn>1.2</mn> <mspace width="3.33333pt"/> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math> (<b>right plot</b>). The graphs are shifted so that at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> the envelope mass of the star is equal to <math display="inline"><semantics> <mrow> <mn>0.01</mn> <mspace width="3.33333pt"/> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math>. We present the evolution for 2 metallicities: <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math> (solar; dotted) and <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math> (old population; solid), and for three mass-loss rate efficiency parameters, <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> (the “traditional” commonly mass-loss rate efficiency; black), <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> (purple), and <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math> (red). The panels depict, from top to bottom: the mass of the star, the mass loss rate (logarithmic of the absolute value), the stellar radius, and the stellar luminosity.</p>
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<p>The summary of the evolution of a <math display="inline"><semantics> <mrow> <mn>0.9</mn> <mspace width="3.33333pt"/> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math> star (<b>left plot</b>) and a <math display="inline"><semantics> <mrow> <mn>1.2</mn> <mspace width="3.33333pt"/> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </semantics></math> star (<b>right plot</b>). For each star we studied the evolution from zero age main sequence until the formation of a white dwarf, for several mass-loss rate efficiency parameters, from <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> (the “traditional” commonly mass-loss rate) to as low as <math display="inline"><semantics> <mrow> <mi>η</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>. We present the evolution for 3 metallicities: <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math> (circles), <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mn>0.004</mn> </mrow> </semantics></math> (triangles) and Z = 0.001 (squares). The upper panels present the final white dwarf mass of each star. The middle panels present the maximum value of the stellar radius over the orbital separation, <math display="inline"><semantics> <msub> <mfenced separators="" open="(" close=")"> <mi>R</mi> <mo>/</mo> <mi>a</mi> </mfenced> <mi>max</mi> </msub> </semantics></math>, for both the red giant branch (RGB; blue) and the asymptotic giant branch (AGB; red). The companion mass is <math display="inline"><semantics> <mrow> <mn>10</mn> <mspace width="3.33333pt"/> <msub> <mi>M</mi> <mi>J</mi> </msub> </mrow> </semantics></math> and the initial orbital separation taken is <math display="inline"><semantics> <mrow> <mn>3</mn> <mspace width="3.33333pt"/> <mi>A</mi> <mi>U</mi> </mrow> </semantics></math>. The green horizontal line indicates the capture condition above which planet engulfment can take place (Equation (<a href="#FD2-galaxies-06-00089" class="html-disp-formula">2</a>)). The lower panels present the maximum value of the luminosity on the post-AGB, <math display="inline"><semantics> <msub> <mi>L</mi> <mrow> <mi>pAGB</mi> <mo>,</mo> <mspace width="0.277778em"/> <mi>max</mi> </mrow> </msub> </semantics></math>.</p>
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6 pages, 3706 KiB  
Article
Planets, Planetary Nebulae, and Intermediate Luminosity Optical Transients (ILOTs)
by Noam Soker
Galaxies 2018, 6(2), 58; https://doi.org/10.3390/galaxies6020058 - 28 May 2018
Cited by 6 | Viewed by 3158
Abstract
I review some aspects related to the influence of planets on the evolution of stars before and beyond the main sequence. Some processes include the tidal destruction of a planet on to a very young main sequence star, on to a low-mass main [...] Read more.
I review some aspects related to the influence of planets on the evolution of stars before and beyond the main sequence. Some processes include the tidal destruction of a planet on to a very young main sequence star, on to a low-mass main sequence star, and on to a brown dwarf. This process releases gravitational energy that might be observed as a faint intermediate luminosity optical transient (ILOT) event. I then summarize the view that some elliptical planetary nebulae are shaped by planets. When the planet interacts with a low-mass, upper asymptotic giant branch (AGB) star, it both enhances the mass-loss rate and shapes the wind to form an elliptical planetary nebula, mainly by spinning up the envelope and by exciting waves in the envelope. If no interaction with a companion, stellar or substellar, takes place beyond the main sequence, the star is termed a Jsolated star, and its mass-loss rates on the giant branches are likely to be much lower than what is traditionally assumed. Full article
(This article belongs to the Special Issue Asymmetric Planetary Nebulae VII)
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<p>Maximum radii stars reach on their RGB and AGB as function of their initial mass for traditional mass-loss rates (from [<a href="#B11-galaxies-06-00058" class="html-bibr">11</a>]).</p>
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<p>A schematic evolution of the radii and densities of planets and stars from the pre-main-sequence phase to the WD phase. <b>Upper panel</b>: the ratio of the planet density to the stellar density. If the ratio is above 1, the planet dives in to the envelope as one entity. If the density ratio is below 1, the planet is tidally destroyed and forms an accretion belt/disk around the star. <b>Lower panel</b>: The planet and stellar radii as function of time.</p>
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<p>Outcomes of planet–star interaction.</p>
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<p>Observed transient events on the energy–time diagram. Blue empty circles represent the total (radiated plus kinetic) energy of the observed transients as a function of the duration of their eruptions, i.e., usually the time for the visible luminosity to decrease by 3 magnitudes. The Optical Transient Stripe is populated by ILOT events that we [<a href="#B18-galaxies-06-00058" class="html-bibr">18</a>] suggest are powered by gravitational energy of complete merger events or vigorous mass-transfer events. For details of this figure, see <a href="http://phsites.technion.ac.il/soker/ilot-club/" target="_blank">http://phsites.technion.ac.il/soker/ilot-club/</a>.</p>
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<p>The evolutionary channels and the PN types that result from them (based on De Marco &amp; Soker 2011 [<a href="#B4-galaxies-06-00058" class="html-bibr">4</a>]).</p>
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