Smadar Naoz

Hot Jupiters from secular planet-planet interactions

About 25 per cent of ‘hot Jupiters’ (extrasolar Jovian-mass planets with close-in orbits) are actually orbiting counter to the spin direction of the star. Perturbations from a distant binary star companion can produce high inclinations, but cannot explain orbits that are retrograde with respect to the total angular momentum of the system. Such orbits in a stellar context can be produced through secular (that is, long term) perturbations in hierarchical triple-star systems. Here we report a similar analysis of planetary bodies, including both octupole-order effects and tidal friction, and find that we can produce hot Jupiters in orbits that are retrograde with respect to the total angular momentum. With distant stellar mass perturbers, such an outcome is not possible. With planetary perturbers, the inner orbits angular momentum component parallel to the total angular momentum need not be constant. In fact, as we show here, it can even change sign, leading to a retrograde orbit. A brief excursion to very high eccentricity during the chaotic evolution of the inner orbit allows planet–star tidal interactions to rapidly circularize that orbit, decoupling the planets and forming a retrograde hot Jupiter.

Secular dynamics in hierarchical three-body systems

The secular approximation for the evolution of hierarchical triple configurations has proven to be very useful in many astrophysical contexts, from planetary to triple-star systems. In this approximation the orbits may change shape and orientation, on time scales longer than the orbital time scales, but the semi major axes are constant. For example, for highly inclined triple systems, the Kozai-Lidov mechanism can produce large-amplitude oscillations of the eccentricities and inclinations. Here we revisit the secular dynamics of hierarchical triple systems. We derive the secular evolution equations to octupole order in Hamiltonian perturbation theory. Our derivation corrects an error in some previous treatments of the problem that implicitly assumed a conservation of the z-component of the angular momentum of the inner orbit (i.e., parallel to the total angular momentum of the system). Already to quadrupole order, our results show new behaviors including the possibility for a system to oscillate from prograde to retrograde orbits. At the octupole order, for an eccentric outer orbit, the inner orbit can reach extremely high eccentricities and undergo chaotic flips in its orientation. We discuss applications to a variety of astrophysical systems, from stellar triples to merging compact binaries and planetary systems. Our results agree with those of previous studies done to quadrupole order only in the limit in which one of the inner two bodies is a massless test particle and the outer orbit is circular;our results agree with previous studies at octupole order for the eccentricity evolution, but not for the inclination evolution.

On the Formation of Hot Jupiters in Stellar Binaries

We study the production of hot Jupiters (HJs) in stellar binaries. We show that the “eccentric Kozai–Lidov” (EKL) mechanism can play a key role in the dynamical evolution of a star–planet–star triple system. We run a large set of Monte Carlo simulations including the secular evolution of the orbits, general relativistic precession, and tides, and we determine the semimajor axis, eccentricity, inclination, and spin–orbit angle distributions of the HJs that are produced. We explore the effect of different tidal friction parameters on the results. We find that the efficiency of forming HJs when taking the EKL mechanism into account is higher then previously estimated. Accounting for the frequency of stellar binaries, we find that this production mechanism can account for about 30% of the observed HJ population. Current observations of spin–orbit angles are consistent with this mechanism producing ∼30% of all HJs, and up to 100% of the misaligned systems. Based on the properties of binaries without an HJ in our simulations, we predict the existence of many Jupiter-like planets with moderately eccentric and inclined orbits and semimajor axes of several AU.

The Eccentric Kozai Mechanism for a Test Particle

We study the dynamical evolution of a test particle that orbits a star in the presence of an exterior massive planet, considering octupole-order secular interactions. In the standard Kozai mechanism (SKM), the planets orbit is circular and so the particle conserves vertical angular momentum. As a result, the particles orbit oscillates periodically, exchanging eccentricity for inclination. However, when the planets orbit is eccentric, the particles vertical angular momentum varies and its Kozai oscillations are modulated on longer timescales—we call this the eccentric Kozai mechanism (EKM). The EKM can lead to behavior that is dramatically different from the SKM. In particular, the particles orbit can flip from prograde to retrograde and back again, and it can reach arbitrarily high eccentricities given enough time. We map out the conditions under which this dramatic behavior (flipping and extreme eccentricities) occurs and show that when the planets eccentricity is sufficiently high, it occurs quite generically. For example, when the planets eccentricity exceeds a few percent of the ratio of semimajor axes (outer to inner), around half of randomly oriented test particle orbits will flip and reach extreme eccentricities. The SKM has often been invoked for bringing pairs of astronomical bodies (star-star, planet-star, compact-object pairs) close together. Including the effect of the EKM will enhance the rate at which such matchmaking occurs.

Eccentricity growth and orbit flip in near-coplanar hierarchical three-body systems

The secular dynamical evolution of a hierarchical three-body system in which a distant third object orbits around a binary has been studied extensively, demonstrating that the inner orbit can undergo large eccentricity and inclination oscillations. It was shown before that starting with a circular inner orbit, large mutual inclination (40°-140°) can produce long timescale modulations that drive the eccentricity to extremely large values and can flip the orbit. Here, we demonstrate that starting with an almost coplanar configuration, for eccentric inner and outer orbits, the eccentricity of the inner orbit can still be excited to high values, and the orbit can flip by ~180°, rolling over its major axis. The ~180° flip criterion and the flip timescale are described by simple analytic expressions that depend on the initial orbital parameters. With tidal dissipation, this mechanism can produce counter-orbiting exoplanetary systems. In addition, we also show that this mechanism has the potential to enhance the tidal disruption or collision rates for different systems. Furthermore, we explore the entire e 1 and i 0 parameter space that can produce flips.

RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS

We study the secular, hierarchical three-body problem to first-order in a post-Newtonian expansion of general relativity (GR). We expand the first-order post-Newtonian Hamiltonian to leading-order in the ratio of the semi-major axis of the two orbits. In addition to the well-known terms that correspond to the GR precession of the inner and outer orbits, we find a new secular post-Newtonian interaction term that can affect the long-term evolution of the triple. We explore the parameter space for highly inclined and eccentric systems, where the Kozai-Lidov mechanism can produce large-amplitude oscillations in the eccentricities. The standard lore, i.e., that GR effects suppress eccentricity, is only consistent with the parts of phase space where the GR timescales are several orders of magnitude shorter than the secular Newtonian one. In other parts of phase space, however, post-Newtonian corrections combined with the three-body ones can excite eccentricities. In particular, for systems where the GR timescale is comparable to the secular Newtonian timescales, the three-body interactions give rise to a resonant-like eccentricity excitation. Furthermore, for triples with a comparable-mass inner binary, where the eccentric Kozai-Lidov mechanism is suppressed, post-Newtonian corrections can further increase the eccentricity and lead to orbital flips even when the timescale of the former is much longer than the timescale of the secular Kozai-Lidov quadrupole perturbations.

ENERGY FEEDBACK FROM X-RAY BINARIES IN THE EARLY UNIVERSE

X-ray photons, because of their long mean-free paths, can easily escape the galactic environments where they are produced, and interact at long distances with the intergalactic medium, potentially having a significant contribution to the heating and reionization of the early universe. The two most important sources of X-ray photons in the universe are active galactic nuclei (AGNs) and X-ray binaries (XRBs). In this Letter we use results from detailed, large scale population synthesis simulations to study the energy feedback of XRBs, from the first galaxies (z ∼ 20) until today. We estimate that X-ray emission from XRBs dominates over AGN at z ≳ 6-8. The shape of the spectral energy distribution of the emission from XRBs shows little change with redshift, in contrast to its normalization which evolves by ∼4 orders of magnitude, primarily due to the evolution of the cosmic star-formation rate. However, the metallicity and the mean stellar age of a given XRB population affect significantly its X-ray output. Specifically, the X-ray luminosity from high-mass XRBs per unit of star-formation rate varies an order of magnitude going from solar metallicity to less than 10% solar, and the X-ray luminosity from low-mass XRBs per unit of stellar mass peaks at an age of ∼300 Myr and then decreases gradually at later times, showing little variation for mean stellar ages ≳ 3 Gyr. Finally, we provide analytical and tabulated prescriptions for the energy output of XRBs, that can be directly incorporated in cosmological simulations.

The first stars in the Universe

Large telescopes have allowed astronomers to observe galaxies that formed as early as 850 million years after the big bang. We predict when the first star that astronomers can observe (i.e. in our past light cone) formed in the Universe, accounting for the first time for the size of the Universe and for three essential ingredients: the light travel-time from distant galaxies, Poisson and density fluctuations on all scales, and the effect of very early cosmic history on galaxy formation. We find that the first observable star is most likely to have formed 30 million years after the big bang (at redshift 65). Also, the first galaxy as massive as our own Milky Way likely formed when the Universe was only 400 Myr old (at redshift 11). We also show that significant modifications are required in current methods of numerically simulating the formation of galaxies at redshift 20 and above.

MERGERS AND OBLIQUITIES IN STELLAR TRIPLES

Many close stellar binaries are accompanied by a faraway star. The “eccentric Kozai-Lidov” (EKL) mechanism can cause dramatic inclination and eccentricity fluctuations, resulting in tidal tightening of inner binaries of triple stars. We run a large set of Monte Carlo simulations, including the secular evolution of the orbits, general relativistic precession, and tides, and we determine the semimajor axis, eccentricity, inclination, and spin-orbit angle distributions of the final configurations. We find that the efficiency of forming tight binaries (! 16 days) when taking the EKL mechanism into account is ∼21%, and about 4% of all simulated systems ended up in a merger event. These merger events can lead to the formation of blue stragglers. Furthermore, we find that the spin-orbit angle distribution of the inner binaries carries a signature of the initial setup of the system; thus, observations can be used to disentangle close binaries’ birth configuration. The resulting inner and outerfinal orbits’ period distributions and their estimated fraction suggest that secular dynamics may be a significant channel for the formation of close binaries in triples and even blue stragglers.

Growth of linear perturbations before the era of the first galaxies

We calculate the evolution of linear density and temperature perturbations in a universe with dark matter, baryons and radiation, from cosmic recombination until the epoch of the first galaxies. In addition to gravity, the perturbations are affected by electron scattering with the radiation, by radiation pressure and by gas pressure. We include the effect of spatial fluctuations in the baryonic sound speed and show that they induce a ≥ 10 per cent change in the baryonic density power spectrum on small scales, and a larger change on all scales in the power spectrum of gas temperature fluctuations. A precise calculation of the growth of linear perturbations is essential because they provide the initial conditions for the formation of galaxies and they can also be probed directly via cosmological 21-cm fluctuations. We also show that in general the thermal history of the cosmic gas can be measured from 21-cm fluctuations using a small-scale anisotropic cut-off due to the thermal width of the 21-cm line.