Solar-mass Stars Research Articles

Sensitivity of the Roman Coronagraph Instrument to Exozodiacal Dust

Exozodiacal dust, warm debris from comets and asteroids in and near the habitable zone of stellar systems, reveals the physical processes that shape planetary systems. Scattered light from this dust is also a source of background flux which must be overcome by future missions to image Earthlike planets. This study quantifies the sensitivity of the Nancy Grace Roman Space Telescope Coronagraph to light scattered by exozodi, the zodiacal dust around other stars. Using a sample of 149 nearby stars, previously selected for optimum detection of habitable exoplanets by space observatories, we find the maximum number of exozodiacal disks with observable inner habitable zone boundaries is six and the number of observable outer habitable boundaries is 74. One zodi was defined as the visible-light surface brightness of 22 m V arcsec−2 around a solar-mass star, approximating the scattered light brightness in visible light at the Earth-equivalent insolation. In the speckle limited case, where the signal-to-noise ratio is limited by speckle temporal stability rather than shot noise, the median 5σ sensitivity to habitable zone exozodi is 12 zodi per resolution element. This estimate is calculated at the inner-working angle of the coronagraph, for the current best estimate performance, neglecting margins on the uncertainty in instrument performance and including a post-processing speckle suppression factor. For an log-norm distribution of exozodi levels with a median exozodi of 3× the solar zodi, we find that the Roman Coronagraph would be able to make 5σ detections of exozodiacal disks in scattered light from 13 systems with a 95% confidence interval spanning 7–20 systems. This sensitivity allows Roman Coronagraph to complement ground-based measurements of exozodiacal thermal emission and constrain dust albedos. Optimized post-processing and detection of extended sources in multiple resolution elements is expected to further improve this unprecedented sensitivity to light scattered by exozodiacal dust.

Monte Carlo simulations of evolving rotational distributions of low-mass stars in young open clusters. Testing the influence of initial conditions

ABSTRACT The rotational evolution of a young stellar population can give informations about the rotation pattern of more evolved clusters. Combined with rotational period values of thousands of young stars and theoretical propositions about the redistribution and loss of stellar angular momentum, it allows us to trace the rotational history of stars according to their mass. We want to investigate how internal and environmental changes on single stars can change the rotational evolution of a young stellar population. We run Monte Carlo simulations of a young cluster composed by solar mass stars of 0.5, 0.8 and 1.0 M⊙ from 1 to 550 Myr taking into account observational and theoretical parameters. In order to compare our results with the observations we run Kolmogorov-Smirnov tests. Our standard model is able to reproduce some clusters younger than h Per and marginally M37, which is 550 Myr old. Varying the disk fraction or the initial period distribution did not improve the results. However, when we run a model with a finer mass grid the Pleiades can be also reproduced. Changing the initial mass distribution to be similar to the empirical ONC mass function also gives good results. Modeling the evolution of a young synthetic cluster from pre-main sequence to early main sequence considering physical mechanisms of extraction and exchange of angular momentum can not be achieved successfully for all clusters for which we have enough rotational data. Clusters of about the same age present different rotational behaviors due perhaps to differences in their initial conditions.

Convective blueshift strengths of 810 F to M solar-type stars

Context. The detection of Earth-mass exoplanets in the habitable zone around solar-mass stars using the radial velocity technique requires extremely high precision, on the order of 10 cm s−1. This puts the required noise floor below the intrinsic variability of even relatively inactive stars, such as the Sun. One such variable is convective blueshift varying temporally, spatially, and between spectral lines. Aims. We develop a new approach for measuring convective blueshift and determine the strength of convective blueshift for 810 stars observed by the HARPS spectrograph, spanning spectral types late-F, G, K, and early-M. We derive a model for infering blueshift velocity for lines of any depth in later-type stars of any effective temperature. Methods. Using a custom list of spectral lines, covering a wide range of absorption depths, we create a model for the line-core shift as a function of line depth, commonly known as the third signature of granulation. For this we utilize an extremely-high-resolution solar spectrum (R ~ 1 000 000) to empirically account for the nonlinear nature of the third signature. The solar third signature is then scaled to all 810 stars. Through this we obtain a measure of the convective blueshift relative to the Sun as a function of stellar effective temperature. Results. We confirm the general correlation of increasing convective blueshift with effective temperature and establish a tight, cubic relation between the two that strongly increases for stars above ~5800 K. For stars between ~4100 and ~4700 K we show, for the first time, a plateau in convective shift and a possible onset of a plateau for stars above 6000 K. Stars below ~4000 K show neither blueshift nor redshift. We provide a table that lists expected blueshift velocities for each spectral subtype in the data set to quickly access the intrinsic noise floor through convective blueshift for the radial velocity technique.

Global simulations of tidal disruption event disc formation via stream injection in GRRMHD

ABSTRACT We use the general relativistic radiation magnetohydrodynamics code KORAL to simulate the accretion disc formation resulting from the tidal disruption of a solar mass star around a supermassive black hole (BH) of mass 106 M⊙. We simulate the disruption of artificially more bound stars with orbital eccentricity e ≤ 0.99 (compared to the more realistic case of parabolic orbits with e = 1) on close orbits with impact parameter β ≥ 3. We use a novel method of injecting the tidal stream into the domain, and we begin the stream injection at the peak fallback rate in this study. For two simulations, we choose e = 0.99 and inject mass at a rate that is similar to parabolic TDEs. We find that the disc only becomes mildly circularized with eccentricity e ≈ 0.6 within the 3.5 d that we simulate. The rate of circularization is faster for pericenter radii that come closer to the BH. The emitted radiation is mildly super-Eddington with $L_{\rm {bol}}\approx 3{-}5\, L_{\rm {Edd}}$ and the photosphere is highly asymmetric with the photosphere being significantly closer to the inner accretion disc for viewing angles near pericenter. We find that soft X-ray radiation with Trad ≈ 3–5 × 105 K may be visible for chance viewing angles. Our simulations suggest that TDEs should be radiatively inefficient with η ≈ 0.009–0.014.

A search for transiting companions in the J1407 (V1400 Cen) system

Context. In 2007, the young star 1SWASP J140747.93-394 542.6 (V1400 Cen) underwent a complex series of deep eclipses over 56 days. This was attributed to the transit of a ring system filling a large fraction of the Hill sphere of an unseen substellar companion. Subsequent photometric monitoring has not found any other deep transits from this candidate ring system, but if there are more substellar companions and if they are coplanar with the potential ring system, there is a chance that they will transit the star as well. This young star is active, and the light curves show a 5% modulation in amplitude with a dominant rotation period of 3.2 days due to starspots rotating into and out of view. Aims. We model and remove the rotational modulation of the J1407 light curve and search for additional transit signatures of substellar companions orbiting around J1407. Methods. We combine the photometry of J1407 from several observatories, spanning a 19 yr baseline. We remove the rotational modulation by modeling the variability as a periodic signal, whose periodicity changes slowly with time over several years due to the activity cycle of the star. A transit least squares (TLS) analysis is used to search for any periodic transiting signals within the cleaned light curve. Results. We identify an activity cycle of J1407 with a period of 5.4 yr. A TLS search does not find any plausible periodic eclipses in the light curve, from 1.2% amplitude at 5 days up to 1.9% at 20 days. This sensitivity is confirmed by injecting artificial transits into the light curve and determining the recovery fraction as a function of transit depth and orbital period. Conclusions. J1407 is confirmed as a young active star with an activity cycle consistent with a rapidly rotating solar mass star. With the rotational modulation removed, the TLS analysis reaches down to planetary mass radii for young exoplanets, ruling out transiting companions with radii larger than about 1 RJup.

Axion spectra and the associated x-ray spectra of low-mass stars

For the first time, we predict the axion spectra and their associated luminosities for several low-mass stars -- one and two solar masses stars in the main sequence and post-main sequence stages of evolution. Equally, we also compute the x-ray excess emission resulting from the conversion of axions back to photons in the presence of a strong magnetic field in the envelope of these stars. Hence, a given star will have a unique axion spectrum and $L_a$ axion luminosity. And if such star has a strong magnetic field in its stellar envelope, it will also show a characteristic x-ray spectrum and $L_{a\gamma}$ x-ray luminosity. Such radiation will add up to the x-ray electromagnetic spectrum and $L_X$ luminosity of the star. The present study focuses on axion models with an axion-photon coupling constant, $5\;10^{-11} {\rm GeV}^{-1}$, a value just below the most recent upper limit of $6.6\;10^{-11} {\rm GeV}^{-1}$ found by CAST and IAXO helioscopes. The range of axion parameters discussed here spans many axion models' parameter space, including the DFSZ and KSVZ models. We found that axions with a mass in the range $10^{-7}$ to $10^{-5}\; {\rm eV}$ and an axion-photon coupling constant of $5\;10^{-11} {\rm GeV}^{-1}$ produce an axion emission spectra with an averaged axion energy that varies from 1 to 5 KeV, and an $L_{a}$ ranging from $10^{-6} $ to $7\;10^{-3} \;L_\odot$. We also predict that $L_{a\gamma}$ varies from $5\;10^{-8}$ to $10^{-5} \;L_\odot$ for stars with an averaged magnetic field of $3 \;10^{4}\;{\rm G}$ in their atmospheres. Most of these $L_{a\gamma}$ predictions are larger than the $L_X$ observed in some stars. Therefore, such preliminary results show the potential of the next generation of stellar x-ray missions to constrain several classes of axion models.

X-Ray Superflares from Pre-main-sequence Stars: Flare Energetics and Frequency

Abstract Solar-type stars exhibit their highest levels of magnetic activity during their early convective pre-main-sequence (PMS) phase of evolution. The most powerful PMS flares, superflares and megaflares, have peak X-ray luminosities of log ( L X ) = 30.5 – 34.0 erg s−1 and total energies log ( E X ) = 34 – 38 erg. Among >24,000 X-ray-selected young (t ≲ 5 Myr) members of 40 nearby star-forming regions from our earlier Chandra MYStIX and SFiNCs surveys, we identify and analyze a well-defined sample of 1086 X-ray superflares and megaflares, the largest sample ever studied. Most are considerably more powerful than optical/X-ray superflares detected on main-sequence stars. This study presents energy estimates of these X-ray flares and the properties of their host stars. These events are produced by young stars of all masses over evolutionary stages ranging from protostars to diskless stars, with the occurrence rate positively correlated with stellar mass. Flare properties are indistinguishable for disk-bearing and diskless stars indicating star–disk magnetic fields are not involved. A slope of α ≃ 2 in the flare energy distributions dN / dE X ∝ E X − α is consistent with that of optical/X-ray flaring from older stars and the Sun. Megaflares ( log ( E X ) > 36.2 erg) from solar-mass stars have an occurrence rate of 1.7 − 0.6 + 1.0 flares/star/year and contribute at least 10%–20% to the total PMS X-ray energetics. These explosive events may have important astrophysical effects on protoplanetary disk photoevaporation, ionization of disk gas, production of spallogenic radionuclides in disk solids, and hydrodynamic escape of young planetary atmospheres. Our following paper details plasma and magnetic loop modeling of the >50 brightest X-ray megaflares.

Star-planet interactions

Context. Tidal interactions and planetary evaporation processes impact the evolution of close-in star–planet systems. Aims. We study the impact of stellar rotation on these processes. Methods. We compute the time evolution of star–planet systems consisting of a planet with an initial mass between 0.02 and 2.5 MJup (6 and 800 MEarth) in a quasi-circular orbit with an initial orbital distance between 0.01 and 0.10 au, around a solar-type star evolving from the pre-main-sequence (PMS) phase until the end of the main-sequence phase. We account for the evolution of: the stellar structure, the stellar angular momentum due to tides and magnetic braking, the tidal interactions (equilibrium and dynamical tides in stellar convective zones), the mass evaporation of the planet, and the secular evolution of the planetary orbit. We consider that at the beginning of the evolution, the proto-planetary disk has fully dissipated and planet formation is complete. Results. We find that both a rapid initial stellar rotation and a more efficient angular momentum transport inside the star, in general, contribute to the enlargement of the domain that is devoid of planets after the PMS phase, in the plane of planet mass versus orbital distance. Comparisons with the observed distribution of exoplanets orbiting solar mass stars, in the plane of planet mass versus orbital distance (addressing the “Neptunian desert” feature), show an encouraging agreement with the present simulations, especially since no attempts have been made to fine-tune the initial parameters of the models to fit the observations. We also obtain an upper limit for the orbital period of bare-core planets that agrees with observations of the “radius valley” feature in the plane of planetary radius versus the orbital period. Conclusions. The two effects, namely, tides and planetary evaporation, should be accounted for simultaneously and in a consistent way, with a detailed model for the evolution of the star.

The active lives of stars: A complete description of the rotation and XUV evolution of F, G, K, and M dwarfs

Aims. We study the evolution of the rotation and the high energy X-ray, extreme ultraviolet (EUV), and Ly-α emission for F, G, K, and M dwarfs, with masses between 0.1 and 1.2 M⊙, and provide a freely available set of evolutionary tracks for use in planetary atmosphere studies. Methods. We develop a physical rotational evolution model constrained by observed rotation distributions in young stellar clusters. Using rotation, X-ray, EUV, and Ly-α measurements, we derive empirical relations for the dependences of high energy emission on stellar parameters. Our description of X-ray evolution is validated using measurements of X-ray distributions in young clusters. Results. A star’s X-ray, EUV, and Ly-α evolution is determined by its mass and initial rotation rate, with initial rotation being less important for lower mass stars. At all ages, solar mass stars are significantly more X-ray luminous than lower mass stars and stars that are born as rapid rotators remain highly active longer than those born as slow rotators. At all evolutionary stages, habitable zone planets receive higher X-ray and EUV fluxes when orbiting lower mass stars due to their longer evolutionary timescales. The rates of flares follow similar evolutionary trends with higher mass stars flaring more often than lower mass stars at all ages, though habitable zone planets are likely influenced by flares more when orbiting lower mass stars. Conclusions. Our results show that single decay laws are insufficient to describe stellar activity evolution and highlight the need for a more comprehensive description based on the evolution of rotation that also includes the effects of short-term variability. Planets at similar orbital distances from their host stars receive significantly more X-ray and EUV energy over their lifetimes when orbiting higher mass stars. The common belief that M dwarfs are more X-ray and EUV active than G dwarfs is justified only when considering the fluxes received by planets with similar effective temperatures, such as those in the habitable zone.

New ^{59}Fe Stellar Decay Rate with Implications for the ^{60}Fe Radioactivity in Massive Stars.

The discrepancy between observations from γ-ray astronomy of the ^{60}Fe/^{26}Al γ-ray flux ratio and recent calculations is an unresolved puzzle in nuclear astrophysics. The stellar β-decay rate of ^{59}Fe is one of the major nuclear uncertainties impeding us from a precise prediction. The important Gamow-Teller strengths from the low-lying states in ^{59}Fe to the ^{59}Co ground state are measured for the first time using the exclusive measurement of the ^{59}Co(t,^{3}He+γ)^{59}Fe charge-exchange reaction. The new stellar decay rate of ^{59}Fe is a factor of 3.5±1.1 larger than the currently adopted rate at T=1.2 GK. Stellar evolution calculations show that the ^{60}Fe production yield of an 18 solar mass star is decreased significantly by 40% when using the new rate. Our result eliminates one of the major nuclear uncertainties in the predicted yield of ^{60}Fe and alleviates the existing discrepancy of the ^{60}Fe/^{26}Al ratio.

Tracking Advanced Planetary Systems (TAPAS) with HARPS-N

Context. We present the current status of and new results from our search for exoplanets in a sample of solar-mass evolved stars observed with the HARPS-N and the 3.6 m Telescopio Nazionale Galileo (TNG), and the High-Resolution Spectrograph (HRS) and the 9.2 m Hobby-Eberly Telescope (HET). Aims. The aim of this project is to detect and characterize planetary-mass companions to solar-mass stars in a sample of 122 targets at various stages of evolution from the main sequence to the red giant branch, mostly subgiants and giants, selected from the Pennsylvania-Toruń Planet Search sample, and to use this sample to study relations between stellar properties, such as metallicity, luminosity, and the planet occurrence rate. Methods. This work is based on precise radial velocity (RV) measurements. We have observed the program stars for up to 14 yr with the HET/HRS and the TNG/HARPS-N. Results. We present the analysis of RV measurements with the HET/HRS and the TNG/HARPS-N of four solar-mass stars, HD 4760, HD 96992, BD+02 3313, and TYC 0434-04538-1. We found that HD 4760 hosts a companion with a minimum mass of 13.9 MJ (a = 1.14 au, e = 0.23); HD 96992 is a host to a m sin i = 1.14 MJ companion on an a = 1.24 au and e = 0.41 orbit, and TYC 0434-04538-1 hosts an m sin i = 6.1 MJ companion on an a = 0.66 au and e = 0.08 orbit. In the case of BD+02 3313 we found a correlation between the measured RVs and one of the stellar activity indicators, suggesting that the observed RV variations may either originate in stellar activity or be caused by the presence of an unresolved companion. We also discuss the current status of the project and a statistical analysis of the RV variations in our sample of target stars. Conclusions. In our sample of 122 solar-mass stars, 49 ± 5% of them appear to be single and 16 ± 3% spectroscopic binaries. The three giants hosting low-mass companions presented in this paper join the six previously identified giants in the sample.

MRI-active inner regions of protoplanetary discs. I. A detailed model of disc structure

ABSTRACT Short-period super-Earth-sized planets are common. Explaining how they form near their present orbits requires understanding the structure of the inner regions of protoplanetary discs. Previous studies have argued that the hot inner protoplanetary disc is unstable to the magnetorotational instability (MRI) due to thermal ionization of potassium, and that a local gas pressure maximum forms at the outer edge of this MRI-active zone. Here we present a steady-state model for inner discs accreting viscously, primarily due to the MRI. The structure and MRI-viscosity of the inner disc are fully coupled in our model; moreover, we account for many processes omitted in previous such models, including disc heating by both accretion and stellar irradiation, vertical energy transport, realistic dust opacities, dust effects on disc ionization, and non-thermal sources of ionization. For a disc around a solar-mass star with a standard gas accretion rate ($\dot{M}\, \sim \, 10^{-8}$ M⊙ yr−1) and small dust grains, we find that the inner disc is optically thick, and the accretion heat is primarily released near the mid-plane. As a result, both the disc mid-plane temperature and the location of the pressure maximum are only marginally affected by stellar irradiation, and the inner disc is also convectively unstable. As previously suggested, the inner disc is primarily ionized through thermionic and potassium ion emission from dust grains, which, at high temperatures, counteract adsorption of free charges on to grains. Our results show that the location of the pressure maximum is determined by the threshold temperature above which thermionic and ion emission become efficient.

Extending a Grid of Hydrodynamic Planetary Upper Atmosphere Models

Abstract In this research note, we outline the extension of the grid of upper atmosphere models first presented in Kubyshkina et al. The original grid is based on a 1D hydrodynamic model and consists of about 7000 models covering planets of a size ranging from that of Earth to twice that of Neptune at orbits corresponding to equilibrium temperatures between 300 and 2000 K around solar-like (0.4 to 1.3 solar mass) stars. The extended and revised grid of models consists of 10,235 points and covers a planetary mass range of up to 109 Earth masses, which allows one to outline the transition between low- and high-gravity hot planets in in short period orbits. We prepared the interpolation tool allowing one to use the grid to define the mass-loss of a planet that falls into the parameter range of the grid. We provide a comparison of our results to common analytical models.

How does the mass and activity history of the host star affect the population of low-mass planets?

ABSTRACT The evolution of the atmospheres of low- and intermediate-mass planets is strongly connected to the physical properties of their host stars. The types and the past activities of planet-hosting stars can, therefore, affect the overall planetary population. In this paper, we perform a comparative study of sub-Neptune-like planets orbiting stars of different masses and different evolutionary histories. We discuss the general patterns of the evolved population as a function of parameters and environments of planets. As a model of the atmospheric evolution, we employ the own framework combining planetary evolution in Modules for Experiments in Stellar Astrophysics (mesa) with the realistic prescription of the escape of hydrogen-dominated atmospheres. We find that the final populations look qualitatively similar in terms of the atmospheres survival around different stars, but qualitatively different, with this difference accentuated for planets orbiting more massive stars. We show that a planet has larger chances of keeping its primordial atmosphere in the habitable zone of a solar-mass star compared to M or K dwarfs and if it starts the evolution having a relatively compact envelope. We also address the problem of the uncertain initial temperatures (luminosities) of planets and show that this issue is only of particular importance for planets exposed to extreme atmospheric mass losses.

Neutron stars within the Bogoliubov quark-meson coupling model

A quark-meson coupling model based on the quark model proposed by Bogoliubov for the description of the quark dynamics is developed and applied to the description of neutron stars. Starting from a su(3) symmetry approach, it is shown that this symmetry has to be broken in order to satisfy the constraints set by the hypernuclei and by neutron stars. The model is able to describe observations such as two solar mass stars or the radius of canonical neutron stars within the uncertainties presently accepted. If the optical potentials for $\Lambda$ and $\Xi$ hyperons in symmetric nuclear matter at saturation obtained from laboratory measurements of hypernuclei properties are imposed the model predicts no strangeness inside neutron stars.

Rapid formation of super-Earths around low-mass stars

ABSTRACT NASA’s TESS mission is expected to discover hundreds of M dwarf planets. However, few studies focus on how planets form around low-mass stars. We aim to better characterize the formation process of M dwarf planets to fill this gap and aid in the interpretation of TESS results. We use ten sets of N-body planet formation simulations that vary in whether a gas disc is present, initial range of embryo semimajor axes, and initial solid surface density profile. Each simulation begins with 147 equal-mass embryos around a 0.2 solar mass star and runs for 100 Myr. We find that planets form rapidly, with most collisions occurring within the first 1 Myr. The presence of a gas disc reduces the final number of planets relative to a gas-free environment and causes planets to migrate inward. We find that roughly a quarter of planetary systems experience their final giant impact inside the gas disc, suggesting that some super-Earths may be able to reaccrete an extended gaseous envelope after their final giant impact, though these may be affected by additional processes such as photoevaporation. In addition, we find that the final distribution of planets does not retain a memory of the slope of the initial surface density profile, regardless of whether or not a gas disc is present. Thus, our results suggest that present-day observations are unlikely to provide sufficient information to accurately reverse-engineer the initial distribution of solids.

λ Andromedae: Driving a post-main sequence wind from a solar-mass star

λ Andromedae: Driving a post-main sequence wind from a solar-mass star

Feedback-limited accretion: variable luminosity from growing planets

ABSTRACT Planets form in discs of gas and dust around stars, and continue to grow by accretion of disc material while available. Massive planets clear a gap in their protoplanetary disc, but can still accrete gas through a circumplanetary disc. For high enough accretion rates, the planet should be detectable at infrared wavelengths. As the energy of the gas accreted on to the planet is released, the planet surroundings heat up in a feedback process. We aim to test how this planet feedback affects the gas in the coorbital region and the accretion rate itself. We modified the 2D code FARGO-AD to include a prescription for the accretion and feedback luminosity of the planet and use it to model giant planets on 10 au circular and eccentric orbits around a solar mass star. We find that this feedback reduces but does not halt the accretion on to the planet, although this result might depend on the near-coincident radial ranges where both recipes are implemented. Our simulations also show that the planet heating gives the accretion rate a stochastic variability with an amplitude $\Delta \dot{M}_p \sim 0.1 \dot{M}_p$. A planet on an eccentric orbit (e = 0.1) presents a similar variability amplitude, but concentrated on a well-defined periodicity of half the orbital period and weaker broad-band noise, potentially allowing observations to discriminate between both cases. Finally, we find that the heating of the co-orbital region by the planet feedback alters the gas dynamics, reducing the difference between its orbital velocity and the Keplerian motion at the edge of the gap, which can have important consequences for the formation of dust rings.

λ And: a post-main-sequence wind from a solar-mass star

ABSTRACT We investigate the wind of λ And, a solar-mass star that has evolved off the main sequence becoming a subgiant. We present spectropolarimetric observations and use them to reconstruct the surface magnetic field of λ And. Although much older than our Sun, this star exhibits a stronger (reaching up to 83 G) large-scale magnetic field, which is dominated by the poloidal component. To investigate the wind of λ And, we use the derived magnetic map to simulate two stellar wind scenarios, namely a ‘polytropic wind’ (thermally driven) and an ‘Alfven-wave-driven wind’ with turbulent dissipation. From our 3D magnetohydrodynamics simulations, we calculate the wind thermal emission and compare it to previously published radio observations and more recent Very Large Array observations, which we present here. These observations show a basal sub-mJy quiescent flux level at ∼5 GHz and, at epochs, a much larger flux density (>37 mJy), likely due to radio flares. By comparing our model results with the radio observations of λ And, we can constrain its mass-loss rate $\dot{M}$. There are two possible conclusions. (1) Assuming the quiescent radio emission originates from the stellar wind, we conclude that λ And has $\dot{M} \simeq 3 \times 10^{-9}$ M⊙ yr −1, which agrees with the evolving mass-loss rate trend for evolved solar-mass stars. (2) Alternatively, if the quiescent emission does not originate from the wind, our models can only place an upper limit on mass-loss rates, indicating that $\dot{M} \lesssim 3 \times 10^{-9}$ M⊙ yr −1.

Eccentricities and the stability of closely-spaced five-planet systems

Observations of exoplanets have revealed that systems with planets on closely-spaced orbits are common, which motivates the question “How closely can planets orbit to one another and still be dynamically-stable for very long times?”. To address this question, we investigate the stability of idealized planetary systems consisting of five planets, each equal in mass to the Earth, orbiting a one solar mass star. All planets orbit in the same plane and in the same direction, and the planets are uniformly spaced in units of mutual Hill Sphere radii. Most of the systems that we integrate begin with one or more planets on eccentric orbits, with eccentricities e as large as e=0.05 being considered. For a given initial orbital separation, larger initial eccentricity of a single planet generally leads to shorter system lifetime, with little systematic dependence of which planet is initially on an eccentric orbit. The approximate trend of instability times increasing exponentially with initial orbital separation of the planets found previously for planets with initially circular orbits is also present for systems with initially eccentric orbits. Mean motion resonances also tend to destabilize these systems, although the reductions in system lifetimes are not as large as for initially circular orbits. Systems with all planets having initial e=0.05 and aligned periapse angles typically survive far longer than systems with the same spacing in initial semi-major axis and one planet with e=0.05, but they have slightly shorter lifetimes than those with planets initially on circular orbits.