Kepler-408 is one of the 33 planet-hosting Kepler stars for which asteroseismology has been used to investigate the orientation of the stellar rotation axis relative to the planetary orbital plane. ...The transiting hot Earth, Kepler-408b, has an orbital period of 2.5 days and a radius of 0.86 R⊕, making it much smaller than the planets for which spin-orbit alignment has been studied using the Rossiter-McLaughlin effect. Because conflicting asteroseismic results have been reported in the literature, we undertake a thorough re-appraisal of this system and perform numerous checks for consistency and robustness. We find that the conflicting results are due to the different models for the low-frequency noise in the power spectrum. A careful treatment of the background noise resolves these conflicts, and shows that the stellar inclination is degrees. Kepler-408b is, by far, the smallest planet known to have a significantly misaligned orbit.
A number of ongoing surveys are likely to discover star-black hole binaries in our Galaxy in the near future. A fraction of them may be triple systems comprising an inner binary, instead of a single ...black hole, which might be progenitors of binary black holes (BBHs) routinely discovered now from the gravitational wave. We extend our previous proposal to locate inner BBHs from the short-term radial-velocity (RV) variation of a tertiary star in coplanar triples, and we consider noncoplanar triples and their long-term RV variations as well. Specifically, we assume coplanar and noncoplanar triples with an inner BBH of total mass 20 M , whose outer and inner orbital periods are 80 days and 10 days, respectively. We perform a series of N-body simulations and compare the results with analytic approximate solutions based on quadrupole perturbation theory. For coplanar triples, the pericenter shift of the outer star can be used to detect the hidden inner BBH. For noncoplanar triples, the total RV semiamplitude of the outer star is modulated periodically on the order of 100 km s−1, due to its precession over roughly the Kozai-Lidov oscillation timescale. Such long-term modulations would be detectable within a decade, independent of the short-term RV variations on the order of 100 m s−1 at roughly twice the orbital frequency of the inner binary. Thus the RV monitoring of future star-black hole binary candidates offers a promising method for searching for their inner hidden BBHs in optical bands.
Abstract
While there have been many studies examining the stability of hierarchical triple systems, the meaning of “stability” is somewhat vague and has been interpreted differently in previous ...literatures. The present paper focuses on “Lagrange stability,” which roughly refers to the stability against the escape of a body from the system, or “disruption” of the triple system, in contrast to “Lyapunov-like stability,” which is related to the chaotic nature of the system dynamics. We compute the evolution of triple systems using direct
N
-body simulations up to 10
7
P
out
, which is significantly longer than previous studies (with
P
out
being the initial orbital period of the outer body). We obtain the resulting disruption timescale
T
d
as a function of the triple orbital parameters with particular attention to the dependence on the mutual inclination between the inner and outer orbits,
i
mut
. By doing so, we have clarified explicitly the difference between Lagrange and Lyapunov stabilities in astronomical triples. Furthermore, we find that the von Zeipel–Kozai–Lidov oscillations significantly destabilize inclined triples (roughly with 60° <
i
mut
< 150°) relative to those with
i
mut
= 0°. On the other hand, retrograde triples with
i
mut
> 160° become strongly stabilized with much longer disruption timescales. We show the sensitivity of the normalized disruption timescale
T
d
/
P
out
to the orbital parameters of triple system. The resulting
T
d
/
P
out
distribution is practically more useful in a broad range of astronomical applications than the stability criterion based on the Lyapunov divergence.
Abstract
Nearly a hundred binary black holes (BBHs) have been discovered with gravitational-wave signals emitted at their merging events. Thus, it is quite natural to expect that significantly more ...abundant BBHs with wider separations remain undetected in the Universe or even in our Galaxy. We consider a possibility that star–BH binary candidates may indeed host an inner BBH instead of a single BH. We present a detailed feasibility study of constraining the binarity of the currently available two targets, Gaia BH1 and Gaia BH2. Specifically, we examine three types of radial velocity (RV) modulations of a tertiary star in star–BBH triple systems; short-term RV modulations induced by the inner BBH, long-term RV modulations induced by the nodal precession, and long-term RV modulations induced by the von Zeipel-Kozai–Lidov oscillations. Direct three-body simulations combined with approximate analytic models reveal that the Gaia BH1 system may exhibit observable signatures of the hidden inner BBH if it exists at all. The methodology that we examine here is quite generic and is expected to be readily applicable to future star–BH binary candidates in a straightforward manner.
Abstract
We present an analytic model of the light-curve variation for stars with non-evolving starspots on a differentially rotating surface. The Fourier coefficients of the harmonics of the ...rotation period are expressed in terms of the latitude of the spot, ℓs, and the observer’s line-of-sight direction, ℓo, including the limb-darkening effect. We generate different realizations of multi-spots according to the model, and perform mock observations of the resulting light-curve modulations. We discuss to what extent one can recover the properties of the spots and the parameters for the differential rotation law from the periodogram analysis. Although our analytical model neglects the evolution of spots on the stellar surface (dynamical motion, creation, and annihilation), it provides a basic framework to interpret the photometric variation of stars, in particular from the existing Kepler data and the future space-born mission. It is also applicable to photometric modulations induced by rotation of various astronomical objects.
There are several ongoing projects to search for stars orbiting around an invisible companion. A fraction of such candidates may be a triple, instead of a binary, consisting of an inner binary black ...hole (BBH) and an outer orbiting star. In this paper, we propose a methodology to search for a signature of such an inner BBH, possibly a progenitor of gravitational-wave sources discovered by LIGO, from the precise radial velocity (RV) follow-up of the outer star. We first describe a methodology using an existing approximate RV formula for coplanar circular triples. We apply this method and constrain the parameters of a possible inner binary object in 2M05215658+4359220, which consists of a red giant and an unseen companion. Next we consider coplanar but non-circular triples. We compute numerically the RV variation of a tertiary star orbiting around an inner BBH, generate mock RV curves, and examine the feasibility of detection of the BBH for our fiducial models. We conclude that short-cadence RV monitoring of a star-BH binary provides an interesting and realistic method to constrain and/or search for possible inner BBHs. Indeed a recent discovery of the star-BH binary system LB-1 may imply that there are a large number of such unknown objects in our Galaxy, which are ideal targets for the methodology proposed here.
We measure the rotation periods of 19 stars in the Kepler transiting planetary systems, Prot,astero from asteroseismology and Prot,phot from the photometric variation of their light curves. Two stars ...exhibit two clear peaks in the Lomb-Scargle periodogram, neither of which agrees with the seismic rotation period. Other four systems do not show any clear peak, whose stellar rotation period is impossible to estimate reliably from the photometric variation; their stellar equators may be significantly inclined with respect to the planetary orbital plane. For the remaining 13 systems, Prot,astero and agree within 30%. Interestingly, 3 out of the 13 systems are in the spin-orbit resonant state in which with Porb,b being the orbital period of the innermost planet of each system. The corresponding chance probability is (0.2-4.7)% based on the photometric rotation period data for 464 Kepler transiting planetary systems. While further analysis of stars with reliable rotation periods is required to examine the statistical significance, the spin-orbit resonance between the star and planets, if confirmed, has important implications for the star-planet tidal interaction, in addition to the origin of the spin-orbit (mis-)alignment of transiting planetary systems.
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