Solar-like Systems Research Articles

Bound states of central force system in special relativity

In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a massive body. Then, the motion of a planet in a solar-like system where the gravitational potential is modified by adding a term that is proportional to the inverse of the square of the radial coordinate is discussed. Using perturbative method, we obtain the explicit orbital function. At the end, the orbital precession of the planet and its relation to the result from general relativity are also discussed.

Systematic simulations of FFP scattering by a star–planet pair

The increasing number of free-floating planets discovered in recent years confirms earlier theoretical predictions and leads us to believe that the possibility of such an object intruding an existing planetary system is not negligible, especially in dense clusters. We present a theoretical dynamical study on the interaction of a free-floating planet (hereafter FFP) with an initially bound star–planet pair consisting of a Jupiter-sized planet (hereafter BP) orbiting a Sun-like star. Our results could serve as a base for analytical, or semi-analytical, studies on the three-dimensional three-body scattering problem. In our three-dimensional models, thousands of different trajectories for an incoming FFP with initially parabolic velocity are integrated, in order to investigate the interaction between the objects. The study is based on two independent approaches, in order to corroborate the significance of the results. In the first approach, the FFP interacts with a Solar-like system (hereafter SlS) consisting of the Sun and Jupiter at $$5.2\,\mathrm{AU}$$. In the second, we compute the trajectories of a FFP interacting with a closely bound exoplanetary system (hereafter ES) with the Jupiter-sized planet at an orbit of $$1\,\mathrm{AU}$$ around its host, Sun-like star. For both approaches, the simulations have five free parameters, namely the initial phase of the BP, $$\phi _{BP}$$, the mass, $$m_{FFP}$$, the initial inclination, $$i_{FFP}$$, the orientation of the velocity vector of the FFP and the impact parameter $$d_{FFP}=d$$. We focus on three possible final states, namely “flyby,” “capture” and “exchange.” One can observe that the overall picture does not change between the two models used. We present a statistical analysis of the data and the probabilities for the different outcomes for both. Capture and flyby are dominant, in almost equal parts, while the probability for an exchange is rather low. A close look of the orbital elements in case of a capture of the FFP provides more information on the dynamical behavior of the two models, allowing us to draw more precise conclusions, when it comes to the similarities and differences between them. Different mass, as well as different orientation of the velocity vector of the incoming planet, does affect the final outcome quantitatively and qualitatively, in both cases.

Ingredients for solar-like systems: protostar IRAS 16293-2422 B versus comet 67P/Churyumov–Gerasimenko

ABSTRACT Our modern day Solar System has 4.6 × 109 yr of evolution behind it with just a few relics of its birth conditions remaining. Comets are thought to be some of the most pristine tracers of the initial ingredients that were combined to produce the Earth and the other planets. Other low-mass protostars may be analogous to our proto-Sun and hence, could be used to study the building blocks necessary to form Solar-like systems. This study tests this idea on the basis of new high sensitivity, high spatial resolution ALMA data on the protoplanetary disc-scales (∼70 au) of IRAS 16293-2422 and the bulk composition of comet 67P/Churyumov-Gerasimenko, as determined for the first time with the unique in situ monitoring carried out by Rosetta. The comparative analysis of the observations from the Protostellar Interferometric Line Survey (PILS) and the measurements made with Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) shows that the relative abundances of CHO-, N-, and S-bearing molecules correlate, with some scatter, between protostellar and cometary data. A tentative correlation is seen for the first time for P- and Cl-bearing compounds. The results imply that the volatile composition of cometesimals and planetesimals is partially inherited from the pre- and protostellar phases of evolution.

A primordial origin for molecular oxygen in comets: a chemical kinetics study of the formation and survival of O2ice from clouds to discs

Molecular oxygen has been confirmed as the fourth most abundant molecule in cometary material O$_2$/H$_2$O $\sim 4$ %) and is thought to have a primordial nature, i.e., coming from the interstellar cloud from which our solar system was formed. However, interstellar O$_2$ gas is notoriously difficult to detect and has only been observed in one potential precursor of a solar-like system. Here, the chemical and physical origin of O$_2$ in comets is investigated using sophisticated astrochemical models. Three origins are considered: i) in dark clouds, ii) during forming protostellar disks, and iii) during luminosity outbursts in disks. The dark cloud models show that reproduction of the observed abundance of O$_2$ and related species in comet 67P/C-G requires a low H/O ratio facilitated by a high total density ($\geq 10^5$ cm$^{-3}$), and a moderate cosmic ray ionisation rate ($\leq 10^{-16}$ s$^{-1}$) while a temperature of 20 K, slightly higher than the typical temperatures found in dark clouds, also enhances the production of O$_2$. Disk models show that O$_2$ can only be formed in the gas phase in intermediate disk layers, and cannot explain the strong correlation between O$_2$ and H$_2$O in comet 67P/C-G together with the weak correlation between other volatiles and H$_2$O. However, primordial O$_2$ ice can survive transport into the comet-forming regions of disks. Taken together, these models favour a dark cloud (or "primordial") origin for O$_2$ in comets, albeit for dark clouds which are warmer and denser than those usually considered as solar system progenitors.

CCD PHOTOMETRIC STUDY AND PERIOD INVESTIGATION OF AH TAURI

In this paper, we present new CCD photometric observations of AH Tauri in the R band observed in 2006 at the Yunnan Observatory. Two new times of light minima were derived from these observations. We modeled the light curves using the 2003 version of the Wilson–Devinney program. The results show that the variations of the light curves can be expained by a cool spot on the primary star. The fill-out factor is about 6.6%, indicating that AH Tauri is a shallow-contact system. The mass ratio was determined to be about 0.505. In addition, the orbital period variations of AH Tauri were investigated based on all of the photoelectric and CCD light minimum times, including our two new data. It was found that the orbital period exhibits a possible periodic variation with a period of years and a secular period decrease of . Since AH Tauri is an overcontact solar-like system, we discuss three mechanisms of the mass transfer, the light-time effect of the third body, and magnetic activity responsible for the orbital period changes.

Forming different planetary systems

With the increasing number of detected exoplanet samples, the statistical properties of planetary systems have become much clearer. In this review, we summarize the major statistical results that have been revealed mainly by radial velocity and transiting observations, and try to interpret them within the scope of the classical core-accretion scenario of planet formation, especially in the formation of different orbital architectures for planetary systems around main sequence stars. Based on the different possible formation routes for different planet systems, we tentatively classify them into three major catalogs: hot Jupiter systems, standard systems and distant giant planet systems. The standard system can be further categorized into three sub-types under different circumstances: solar-like systems, hot Super-Earth systems, and subgiant planet systems. We also review the theory of planet detection and formation in binary systems as well as planets in star clusters.

Reducing star leakage with a nuller coronagraph

Aims. Our objective is to test the improvement of the detection capabilities of a nuller coronagraph when it is coupled to an apodizer. We call this instrument an apodized nuller coronagraph (ANC). Methods. With the usual Fourier optics formalism we first derive the analytical expression of the intensity distribution for an off-axis point-like source in the aperture and the focal plane of an ANC. Then the star leakage is obtained by integration of this response over the angular extension of the star. In this process are included the star’s angular diameter, the apodization strength and the diameter of the telescope. Eventually we consider an application to the specific case of Sonine apodization. Results. From this analytical approach we obtain expressions of the contrast and signal-to-noise ratio for the direct detection of an exoplanet. These expressions involving instrumental parameters allow one to optimize the required minimum telescope’s diameter and apodization strength with respect to the detection of a given target in spite of star leakage. We show that the direct detection of an exoplanet in a solar-like system can be obtained with a nuller coronagraph as soon as the aperture is sufficiently apodized, although the energy throughput of the system is reduced. For a system at 10 pc, an 8-m class telescope appears necessary to detect an exo-Earth, while no larger than a 2-m class telescope is required for an exo-Jupiter.

FREQUENCY OF SOLAR-LIKE SYSTEMS AND OF ICE AND GAS GIANTS BEYOND THE SNOW LINE FROM HIGH-MAGNIFICATION MICROLENSING EVENTS IN 2005-2008

We present the first measurement of planet frequency beyond the "snow line" for planet/star mass-ratios[-4.5<log q<-2]: d^2 N/dlog q/dlog s=(0.36+-0.15)/dex^2 at mean mass ratio q=5e-4, and consistent with being flat in log projected separation, s. Our result is based on a sample of 6 planets detected from intensive follow-up of high-mag (A>200) microlensing events during 2005-8. The sample host stars have typical mass M_host 0.5 Msun, and detection is sensitive to planets over a range of projected separations (R_E/s_max,R_E*s_max), where R_E 3.5 AU sqrt(M_host/Msun) is the Einstein radius and s_max (q/5e-5)^{2/3}, corresponding to deprojected separations ~3 times the "snow line". Though frenetic, the observations constitute a "controlled experiment", which permits measurement of absolute planet frequency. High-mag events are rare, but the high-mag channel is efficient: half of high-mag events were successfully monitored and half of these yielded planet detections. The planet frequency derived from microlensing is a factor 7 larger than from RV studies at factor ~25 smaller separations [2<P<2000 days]. However, this difference is basically consistent with the gradient derived from RV studies (when extrapolated well beyond the separations from which it is measured). This suggests a universal separation distribution across 2 dex in semi-major axis, 2 dex in mass ratio, and 0.3 dex in host mass. Finally, if all planetary systems were "analogs" of the Solar System, our sample would have yielded 18.2 planets (11.4 "Jupiters", 6.4 "Saturns", 0.3 "Uranuses", 0.2 "Neptunes") including 6.1 systems with 2 or more planet detections. This compares to 6 planets including one 2-planet system in the actual sample, implying a first estimate of 1/6 for the frequency of solar-like systems.

ARC: an Achromatic Rotation-shearing Coronagraph

Context. Because of the larger size of future telescopes, the star leakage effect due to the finite diameter of the stars will become a major problem for coronagraphs with very small inner working angles (IWA). Aims. To reduce this star leakage, we propose a new instrumental concept, the Achromatic Rotation-shearing Coronagraph (ARC), that provides a variable IWA that is easily tunable to ensure the observation of Solar-like systems with an extremely large telescope. Methods. The ARC belongs to the nuller class of coronagraphs. It takes advantage of the achromatic dark output of a Mach-Zehnder interferometer (MZI). Field rotators set in the arms of the MZI rotate the π-phase shifted images of the MZI by an angle ψ. An on-axis point source (the star) is nulled as twin-images of an off-axis point source (the planet) are formed. For ψ = π, the ARC is equivalent to the achromatic interfero-coronagraph. For small ψ, the twin images of the off-axis source are formed close to each another, and eventually nulled if too close. In this way, the ARC can get rid of star leakage while optimizing the transmission of the planet. We describe the compensation of polarization effects induced by field rotators. An application to diluted apertures is shortly presented. Results. We perform the mathematical analysis of the technique using Cartesian and polar coordinates, and assuming that the system is optically perfect. Analytic expressions are given for the leakage in both the focal and aperture planes. Simplified expressions for the contrast and signal-to-noise ratio (SNR) in the focal plane are given for a circular aperture, explicitly showing that the level of star leakage decreases as sin 2 (ψ/2), while the SNR increases as the inverse of sin(ψ/2). Conclusions. The ARC is appropriate for the detection of exoplanets and is not intended to provide images of the environment of stars.

A robotic approach to fault-tolerant, precision pointing

Future spaceborne optical interferometers and laser satellite communication systems are two space applications that require a precision pointing function in order to meet mission goals. Spaceborne interferometers provide a promising means to discover Earth-like planets in other solar-like systems. The laser communication systems provide a low-power, low-cost, lightweight means of data relay between ground and space and for deep-space communications to interplanetary probes. Both applications share the need to acquire and track a target. The interferometry application requires pointing errors to be submicroradian while the laser communication application requires microradian-level errors. In order to meet the precision pointing requirements found in these applications, a precision pointing strategy has been developed. The strategy employs a hexapod as the pointing platform to reject vibrations from a noisy spacecraft bus over all frequencies: at low frequency using 2- or 3-axis pointing and at high frequency using 6-axis vibration isolation. The benefits include broadband pointing stability without a high-bandwidth pointing sensor or destabilizing excitation of high-frequency structural modes, as well as tolerance to failures. This article outlines this approach to pointing.

Discovering planetary systems through gravitational microlenses

Planetary systems of Galactic disk stars can be detected as microlenses of stars in the Galactic bulge. Planets in a solar-like system positioned half-way to the Galactic center should leave a noticeable signature (magnification larger that 5%) on the light curve of a gravitationally lensed bulge star in ∼20% of the microlensing events. This high probability results from a coincidence between Jupiter's orbital radius and the solar Einstein radius at this distance. Typical planetary signals last for about 1 day, a small fraction of the approximately 1 month duration of the entire microlensing event