Hypothetical Planet Research Articles

Super-Earths and dynamical stability of planetary systems: first parallel GPU simulations using GENGA

We report on the stability of hypothetical Super-Earths in the habitable zone of known multi-planetary systems. Most of them have not yet been studied in detail concerning the existence of additional low-mass planets. The new N-body code GENGA developed at the UZH allows us to perform numerous N-body simulations in parallel on GPUs. With this numerical tool, we can study the stability of orbits of hypothetical planets in the semi-major axis and eccentricity parameter space in high resolution. Massless test particle simulations give good predictions on the extension of the stable region and show that HIP 14180 and HD 37124 do not provide stable orbits in the habitable zone. Based on these simulations, we carry out simulations of 10 Earth mass planets in several systems (HD 11964, HD 47186, HD 147018, HD 163607, HD 168443, HD 187123, HD 190360, HD 217107 and HIP 57274). They provide more exact information about orbits at the location of mean motion resonances and at the edges of the stability zones. Beside the stability of orbits, we study the secular evolution of the planets to constrain probable locations of hypothetical planets. Assuming that planetary systems are in general closely packed, we find that apart from HD 168443, all of the systems can harbor 10 Earth mass planets in the habitable zone.

APOSTLE: LONGTERM TRANSIT MONITORING AND STABILITY ANALYSIS OF XO-2b

The Apache Point Survey of Transit Lightcurves of Exoplanets (APOSTLE) observed 10 transits of XO-2b over a period of three years. We present measurements which confirm previous estimates of system parameters like the normalized semi-major axis (a/R_{*}), stellar density (\rho_{*}), impact parameter (b) and orbital inclination (i_{orb}). Our errors on system parameters like a/R_{*} and \rho_{*} have improved by ~40% compared to previous best ground-based measurements. Our study of the transit times show no evidence for transit timing variations and we are able to rule out co-planar companions with masses \ge 0.20 \mearth\ in low order mean motion resonance with XO-2b. We also explored the stability of the XO-2 system given various orbital configurations of a hypothetical planet near the 2:1 mean motion resonance. We find that a wide range of orbits (including Earth-mass perturbers) are both dynamically stable and produce observable TTVs. We find that up to 51% of our stable simulations show TTVs that are smaller than the typical transit timing errors (~20 sec) measured for XO-2b, and hence remain undetectable.

Phase relations in the carbon-saturated C–Mg–Fe–Si–O system and C and Si solubility in liquid Fe at high pressure and temperature: implications for planetary interiors

The phase and melting relations of the C-saturated C–Mg–Fe–Si–O system were investigated at high pressure and temperature to understand the role of carbon in the structure of the Earth, terrestrial planets, and carbon-enriched extraterrestrial planets. The phase relations were studied using two types of experiments at 4 GPa: analyses of recovered samples and in situ X-ray diffractions. Our experiments revealed that the composition of metallic iron melts changes from a C-rich composition with up to about 5 wt.% C under oxidizing conditions (ΔIW = −1.7 to −1.2, where ΔIW is the deviation of the oxygen fugacity (fO2) from an iron-wustite (IW) buffer) to a C-depleted composition with 21 wt.% Si under reducing conditions (ΔIW < −3.3) at 4 GPa and 1,873 K. SiC grains also coexisted with the Fe–Si melt under the most reducing conditions. The solubility of C in liquid Fe increased with increasing fO2, whereas the solubility of Si decreased with increasing fO2. The carbon-bearing phases were graphite, Fe3C, SiC, and Fe alloy melt (Fe–C or Fe–Si–C melts) under the redox conditions applied at 4 GPa, but carbonate was not observed under our experimental conditions. The phase relations observed in this study can be applicable to the Earth and other planets. In hypothetical reducing carbon planets (ΔIW < −6.2), graphite/diamond and/or SiC exist in the mantle, whereas the core would be an Fe–Si alloy containing very small amount of C even in the carbon-enriched planets. The mutually exclusive nature of C and Si may be important also for considering the light elements of the Earth’s core.

Characterization of potentially habitable planets: Retrieval of atmospheric and planetary properties from emission spectra

An increasing number of potentially habitable terrestrial planets and planet candidates are found by ongoing planet search programs. The search for atmospheric signatures to establish planetary habitability and the presence of life might be possible in the future. We want to quantify the accuracy of retrieved atmospheric parameters which might be obtained from infrared emission spectroscopy. We use synthetic observations of hypothetical habitable planets, constructed with a parametrized atmosphere model, a high-resolution radiative transfer model and a simplified noise model. Classic statistical tools such as chi2 statistics and least-square fits were used to analyze the simulated observations. When adopting the design of currently planned or proposed exoplanet characterization missions, we find that emission spectroscopy could provide weak limits on surface conditions of terrestrial planets, hence their potential habitability. However, these mission designs are unlikely to allow to characterize the composition of the atmosphere of a habitable planet, even though CO2 is detected. Upon increasing the signal-to-noise ratios by about a factor of 2-5 (depending on spectral resolution) compared to current mission designs, the CO2 content could be characterized to within two orders of magnitude. The detection of the O3 biosignature remains marginal. The atmospheric temperature structure could not be constrained. Therefore, a full atmospheric characterization seems to be beyond the capabilities of such missions when using only emission spectroscopy during secondary eclipse or target visits. Other methods such as transmission spectroscopy or orbital photometry are probably needed in order to give additional constraints and break degeneracies. (abridged)

Planetary dynamics in the system α Centauri: The stability diagrams

The stability of the motion of a hypothetical planet in the binary system α Cen A–B has been investigated. The analysis has been performed within the framework of a planar (restricted and full) three-body problem for the case of prograde orbits. Based on a representative set of initial data, we have obtained the Lyapunov spectra of the motion of a triple system with a single planet. Chaotic domains have been identified in the pericenter distance-eccentricity plane of initial conditions for the planet through a statistical analysis of the data obtained. We have studied the correspondence of these chaotic domains to the domains of initial conditions that lead to the planet’s encounter with one of the binary’s stars or to the escape of the planet from the system. We show that the stability criterion based on the maximum Lyapunov exponent gives a more clear-cut boundary of the instability domains than does the encounterescape criterion at the same integration time. The typical Lyapunov time of chaotic motion is ∼500 yr for unstable outer orbits and ∼60 yr for unstable inner ones. The domain of chaos expands significantly as the initial orbital eccentricity of the planet increases. The chaos-order boundary has a fractal structure due to the presence of orbital resonances.

Atmospheric characterization of cold exoplanets using a 1.5-m coronagraphic space telescope

Context. High-contrast imaging is currently the only available technique for the study of the thermodynamical and compositional properties of exoplanets in long-period orbits. The SPICES project is a coronagraphic space telescope dedicated to the spectro-polarimetric analysis of gaseous and icy giant planets as well as super-Earths at visible wavelengths. So far, studies for high-contrast imaging instruments have mainly focused on technical feasibility because of the challenging planet/star flux ratio of 10-8-10-10 required at short separations (200 mas or so) to image cold exoplanets. However, the analysis of planet atmospheric/surface properties has remained largely unexplored. Aims. The aim of this paper is to determine which planetary properties SPICES or an equivalent direct imaging mission can measure, considering realistic reflected planet spectra and instrument limitation. Methods. We use numerical simulations of the SPICES instrument concept and theoretical planet spectra to carry out this performance study. Results. We find that the characterization of the main planetary properties (identification of molecules, effect of metallicity, presence of clouds and type of surfaces) would require a median signal-to-noise ratio of at least 30. In the case of a solar-type star \leq 10 pc, SPICES will be able to study Jupiters and Neptunes up to ~5 and ~2 AU respectively. It would also analyze cloud and surface coverage of super-Earths of radius 2.5 RE at 1 AU. Finally, we determine the potential targets in terms of planet separation, radius and distance for several stellar types. For a Sun analog, we show that SPICES could characterize Jupiters (M \geq 30 ME) as small as 0.5 Jupiter radii at ~2 AU up to 10 pc, and super-Earths at 1-2 AU for the handful of stars that exist within 4-5 pc. Potentially, SPICES could perform analysis of a hypothetical Earth-size planet around alpha Cen A and B.

Shock formation around planets orbiting M‐dwarf stars

AbstractBow shocks can be formed around planets due to their interaction with the coronal medium of the host stars. The net velocity of the particles impacting on the planet determines the orientation of the shock. At the Earth's orbit, the (mainly radial) solar wind is primarily responsible for the formation of a shock facing towards the Sun. However, for close‐in planets that possess high Keplerian velocities and are frequently located at regions where the host star's wind is still accelerating, a shock may develop ahead of the planet. If the compressed material is able to absorb stellar radiation, then the signature of bow shocks may be observed during transits. Bow‐shock models have been investigated in a series of papers (Llama et al. 2011; Vidotto et al. 2010, 2011a,b) for known transiting systems. Once the signature of a bow‐shock is observed, one can infer the magnetic field intensity of the transiting planet. Here, we investigate the potential to use this model to detect magnetic fields of (hypothetical) planets orbiting inside the habitable zone of M‐dwarf stars. For these cases, we show, by means of radiative transfer simulations, that the detection of bow‐shocks of planets surrounding M‐dwarf stars may be more difficult than for the case of close‐in giant planets orbiting solar‐type stars (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The maximal runaway temperature of Earth-like planets

In Simpson’s (Simpson, G.C. [1927]. Mem. R. Meteorol. Soc. II (16), 69–95) classical derivation of the temperature of the Earth in the semi-gray model, the surface temperature diverges as the fourth root of the thermal radiation’s optical depth. No resolution to this apparent paradox was yet obtained under the strict semi-gray approximation. Using this approximation and a simplified approach, we study the saturation of the runaway greenhouse effect.First we generalize the problem of the semi-gray model to cases in which a non-negligible fraction of the stellar radiation falls on the long-wavelength range, and/or that the planetary long-wavelength emission penetrates into the transparent short wavelength domain of the absorption.Second, applying the most general assumptions and independently of any particular properties of an absorber, we show that the greenhouse effect saturates and that any Earth-like planet has a maximal temperature which depends on the type of and distance to its main-sequence star, its albedo and the primary atmospheric components which determine the cutoff frequency below which the atmosphere is optically thick. For example, a hypothetical convection-less planet similar to Venus, that is optically thin in the visible, could have at most a surface temperature of 1200–1300K irrespective of the nature of the greenhouse gas.We show that two primary mechanisms are responsible for the saturation of the runaway greenhouse effect, depending on the value of λcut, the wavelength above which the atmosphere becomes optically thick. Unless λcut is small and resides in the optical region, saturation is achieved by radiating the thermal flux of the planet through the short wavelength tail of the thermal distribution. This has an interesting observational implication, the radiation from such a planet should be skewed towards the NIR. Otherwise, saturation takes place by radiating through windows in the FIR.

Flares and habitability

AbstractAt present, dwarf M stars are being considered as potential hosts for habitable planets. However, an important fraction of these stars are flare stars, which among other kind of radiation, emit large amounts of UV radiation during flares, and it is unknown how this events can affect life, since biological systems are particularly vulnerable to UV. In this work we evaluate a well known dMe star, EV Lacertae (GJ 873) as a potential host for the emergence and evolution of life, focusing on the effects of the UV emission associated with flare activity. Since UV-C is particularly harmful for living organisms, we studied the effect of UV-C radiation on halophile archaea cultures. The halophile archaea or haloarchaea are extremophile microorganisms, which inhabit in hypersaline environments and which show several mechanisms to cope with UV radiation since they are naturally exposed to intense solar UV radiation on Earth. To select the irradiance to be tested, we considered a moderate flare on this star. We obtained the mean value for the UV-C irradiance integrating the IUE spectrum in the impulsive phase, and considering a hypothetical planet in the center of the liquid water habitability zone. To select the irradiation times we took the most frequent duration of flares on this star which is from 9 to 27 minutes. Our results show that even after considerable UV damage, the haloarchaeal cells survive at the tested doses, showing that this kind of life could survive in a relatively hostile UV environment.

Two bodies with high eccentricity around the cataclysmic variable QS Vir

AbstractQS Vir is an eclipsing cataclysmic variable with 3.618 hrs orbital period. This system has the interesting characteristics that it does not show mass transfer between the components through the L1 Lagrangian point and shows a complex orbital period variation history. Qian et al. (2010) associated the orbital period variations to the presence of a giant planet in the system plus angular momentum loss via magnetic braking. Parsons et al. (2010) obtained new eclipse timings and observed that the orbital period variations associated to a hypothetical giant planet disagree with their measurements and concluded that the decrease in orbital period is part of a cyclic variation with period ~16 yrs. In this work, we present 28 new eclipse timings of QS Vir and suggest that the orbital period variations can be explained by a model with two circumbinary bodies. The best fitting gives the lower limit to the masses M1 sin(i) ~ 0.0086 M⊙ and M2 sin(i) ~ 0.054 M⊙; orbital periods P1 ~ 14.4 yrs and P2 ~ 16.99 yrs, and eccentricities e1 ~ 0.62 and e2~0.92 for the two external bodies. Under the assumption of coplanarity among the two external bodies and the inner binary, we obtain a giant planet with ~0.009 M⊙ and a brown dwarf with ~ 0.056 M⊙ around the eclipsing binary QS Vir.

Transit timing variation in exoplanet WASP-3b★

Photometric follow-ups of transiting exoplanets may lead to discoveries of additional, less massive bodies in extrasolar systems. This is possible by detecting and then analysing variations in transit timing of transiting exoplanets. We present photometric observations gathered in 2009 and 2010 for exoplanet WASP-3b during the dedicated transit-timing-variation campaign. The observed transit timing cannot be explained by a constant period but by a periodic variation in the observations minus calculations diagram. Simplified models assuming the existence of a perturbing planet in the system and reproducing the observed variations of timing residuals were identified by three-body simulations. We found that the configuration with the hypothetical second planet of the mass of about 15 Earth masses, located close to the outer 2:1 mean motion resonance is the most likely scenario reproducing observed transit timing. We emphasize, however, that more observations are required to constrain better the parameters of the hypothetical second planet in WASP-3 system. For final interpretation not only transit timing but also photometric observations of the transit of the predicted second planet and the high precision radial-velocity data are needed.

STABILITY ANALYSIS OF SINGLE-PLANET SYSTEMS AND THEIR HABITABLE ZONES

We study the dynamical stability of planetary systems consisting of one hypothetical terrestrial mass planet ($1 $ or $10 \mearth$) and one massive planet ($10 \mearth - 10 \mjup$). We consider masses and orbits that cover the range of observed planetary system architectures (including non-zero initial eccentricities), determine the stability limit through N-body simulations, and compare it to the analytic Hill stability boundary. We show that for given masses and orbits of a two planet system, a single parameter, which can be calculated analytically, describes the Lagrange stability boundary (no ejections or exchanges) but which diverges significantly from the Hill stability boundary. However, we do find that the actual boundary is fractal, and therefore we also identify a second parameter which demarcates the transition from stable to unstable evolution. We show the portions of the habitable zones of $\rho$ CrB, HD 164922, GJ 674, and HD 7924 which can support a terrestrial planet. These analyses clarify the stability boundaries in exoplanetary systems and demonstrate that, for most exoplanetary systems, numerical simulations of the stability of potentially habitable planets are only necessary over a narrow region of parameter space. Finally we also identify and provide a catalog of known systems which can host terrestrial planets in their habitable zones.

Diurnal Habitability of Frozen Worlds

In this work we discuss effects allowing local habitability of some extraterrestrial planets of low average surface temperatures. We analyze the problem of diurnal and seasonal changes of temperature and biological productivity at different locations on a hypothetical Earth-like planet. We have found, that under some circumstances the temperature may locally rise well above the average value, allowing periods of enhanced biological activity. In this way, bioproductivity can become periodically possible on a planet that has an average temperature clearly below 0°C. Such thermal conditions are encountered on Mars (Smith et al. in Science 306:1750–1753, 2004) generally considered as inhabitable. In reality, an appropriate temperature is not sufficient for habitability. The presence of liquid water at the considered location is also necessary. We discuss how temperature oscillations affect habitability in the framework of a conceptual model. We find that the considered effect of diurnal and seasonal temperature oscillations can extend the outer boundary of the habitable zone up to 2 AU, while global average temperatures are below 0°C for heliocentric distances R h > 1.12 AU (dry atmosphere, low CO2 pressure), or R h > 1.66 AU (humid atmosphere, high CO2 pressure).

A transit timing analysis of seven RISE light curves of the exoplanet system HAT-P-3

We present seven light curves of the exoplanet system HAT-P-3, taken as part of a transit timing program using the RISE instrument on the Liverpool Telescope. The light curves are analysed using a Markov-Chain Monte-Carlo algorithm to update the parameters of the system. The inclination is found to be i = 86.75^{+0.22}_{-0.21} deg, the planet-star radius ratio to be R_p/R_star = 0.1098^{+0.0010}_{-0.0012}, and the stellar radius to be R_star = 0.834^{+0.018}_{-0.026} R_sun, consistent with previous results but with a significant improvement in the precision. Central transit times and uncertainties for each light curve are also determined, and a residual permutation algorithm used as an independent check on the errors. The transit times are found to be consistent with a linear ephemeris, and a new ephemeris is calculated as T_c(0) = 2454856.70118 +- 0.00018 HJD and P = 2.899738 +- 0.000007 days. Model timing residuals are fitted to the measured timing residuals to place upper mass limits for a hypothetical perturbing planet as a function of the period ratio. These show that we have probed for planets with masses as low as 0.33 M_earth and 1.81 M_earth in the interior and exterior 2:1 resonances, respectively, assuming the planets are initially in circular orbits.

Drag-induced resonant capture in a multiplanet scenario: An application to 55 Cancri A

The binary star 55 Cancri harbors at least five giant planets. The discovery of a possible dust disk around the primary of the system was announced in 1998 although it was later dismissed as an observational artifact induced by the presence of three background galaxies. However, the possible existence of an asteroid belt beyond 6AU from the primary could not be excluded. The actual properties of a hypothetical outer asteroid belt around 55 Cancri A are likely to be the result of the gravitational influence of the outermost planets and gas drag during the late stages of the formation of the planetary system. Gaseous drag within a protoplanetary disk in a multiplanet context can induce resonant capture of solid material rather easily, triggering the formation of asteroid belts similar to our own transneptunian belt. In this paper we investigate this scenario using numerical simulations within the framework of the planar restricted four-body problem to find possible stable debris locations or additional planets around 55 Cancri A. Our results indicate that, beyond 55 Cancri d, only the 1:2 and 1:3 mean-motion resonances may be possible although the details of gas drag-induced resonant trapping depend strongly on the size of the particles, with larger particles being preferentially trapped farther away from the host star. For a primary of mass 0.94M⊙ and i=53° we find solid particles submitted to confined chaos at 10.14 and 13.22AU with average eccentricities 0.14 and 0.20, respectively. The argument of pericentre of the trapped particles is found to librate around π/2 with the pericentres of the two resonant structures nearly aligned. The resonance responsible for the inner ring effectively halts the migration of the particles. The outer structure resembles a rosette or separatrix orbit. Our calculations suggest that hypothetical planets or asteroid belts in these locations would be, in principle, dynamically stable.

An analysis of the transit times of CoRoT-1b

I report the results from a study of the transit times for CoRoT-1b, which was one of the first planets discovered by CoRoT. Analysis of the pipeline reduced CoRoT light curve yields a new determination of the physical and orbital parameters of planet and star, along with 35 individual transit times at a typical precision of 36 s. I estimate a planet-to-star radii ratio of 0.1433 +/- 0.0010, a ratio of the planet's orbital semimajor axis to the host star radius of 4.751 +/- 0.045, and an orbital inclination for the planet of 83.88 +/- 0.29 deg. The observed transit times are consistent with CoRoT-1b having a constant period and there is no evidence of an additional planet in the system. I use the observed constancy of the transit times to set limits on the mass of a hypothetical additional planet in a nearby, stable orbit. I ascertain that the most stringent limits (4 M_earth at 3 sigma confidence) can be placed on planets residing in a 1:2 mean motion resonance with the transiting planet. In contrast, the data yield less stringent limits on planets near a 1:3 mean motion resonance (5 M_jup at 3 sigma confidence) than in the surrounding parameter space. In addition, I use a simulation to investigate what sensitivity to additional planets could be obtained from the analysis of data measured for a similar system during a CoRoT long run (100 sequential transit times). I find that for such a scenario, planets with masses greater than twice that of Mars (0.2 M_earth) in the 1:2 mean motion resonance would cause high-significance transit time deviations. Therefore, such planets could be detected or ruled out using CoRoT long run data. I conclude that CoRoT data will indeed be very useful for searching for planets with the transit timing method.

Spectroscopic orbits for K giants β Reticuli and ν Octantis: what is causing a low-amplitude radial velocity resonant perturbation in ν Oct?

New astrometric-spectroscopic orbital solutions for the single-line K-giant binaries p Reticuli (P ≈ 5.2 yr, e = 0.3346 ± 0.0004) and v Octantis (P ≈ 2.9 yr, e = 0.2358 ± 0.0003) have been derived based on high-precision spectroscopic radial velocities (RVs) and the Hipparcos astrometry. For the case of v Oct, the simultaneous solution is particularly robust and an inclination of i = 70.8 ± 0.9° has been derived. This is one of the most precise inclinations yet calculated based on a spectroscopic solution and the Hipparcos astrometry. We have also discovered low-amplitude periodic behaviour in the residuals of the orbital solution for v Oct. This RV perturbation has a semi-amplitude of 50 m s -1 and a 418-d period which is coherent over several years. The RV curve of the perturbation is apparently in resonance with that of the binary: every second maximum of the binary coincides with every fifth minimum of the perturbation, hence the periods have the simple ratio 5:2. The possible causes of such a perturbation are rotational modulation of surface phenomenon, pulsations or an orbiting body. We have assessed these alternatives in terms of the suspected photometric stability (Hp = 3.8981 ± 0.0004), a lack of evidence of other RV periodicities, no correlation of cross-correlation function bisectors with the residual velocities, no compelling evidence of wavelength dependency for the amplitude or relative phase of the perturbation, our bounds on the rotational period of the primary star and the need for long-lived relatively fixed surface features. The results of these analyses lack consistency with both rotational modulation and pulsations and so imply that a planetary mass is a realistic cause. The planet hypothesis, however, is strongly constrained and challenged by our precise binary orbit. The hypothetical planet (M min ≈2.4 M Jup ) would have an orbit (e ≈ 0.1, a 3 ≈ 1.2 au) about mid-way between the stars whose periastron distance is only 1.9 au. This orbit, supposedly in resonance with the binary system, appears to be highly unlikely based on current planet formation and orbit-stability expectations. Without knowing the cause of the perturbation, we cannot be certain if the suspected RV and hence period resonance are merely coincidental or not. Establishing the true cause of the perturbation requires renewed observation of the system, re-assessment of the possible resonance if this is redetected and the acquisition of similar and additional precise diagnostic parameters with respect to each of the possible causative mechanisms.

Tidal heating of terrestrial extrasolar planets and implications for their habitability

The tidal heating of hypothetical rocky (or terrestrial) extrasolar planets spans a wide range of values depending on stellar masses and initial orbits. Tidal heating may be sufficiently large (in many cases, in excess of radiogenic heating) and long-lived to drive plate tectonics, similar to the Earth's, which may enhance the planet's habitability. In other cases, excessive tidal heating may result in Io-like planets with violent volcanism, probably rendering them unsuitable for life. On water-rich planets, tidal heating may generate subsurface oceans analogous to Europa's with similar prospects for habitability. Tidal heating may enhance the outgassing of volatiles, contributing to the formation and replenishment of a planet's atmosphere. To address these issues, we model the tidal heating and evolution of hypothetical extrasolar terrestrial planets. The results presented here constrain the orbital and physical properties required for planets to be habitable.

On the Origins of Eccentric Close-In Planets

Strong tidal interaction with the central star can circularize the orbits of close-in planets. With the standard tidal quality factor Q of our solar system, estimated circularization times for close-in extrasolar planets are typically shorter than the ages of the host stars. While most extrasolar planets with orbital radii -->a 0.1 AU indeed have circular orbits, some close-in planets with substantial orbital eccentricities have recently been discovered. This new class of eccentric close-in planets implies that either their tidal Q factor is considerably higher, or circularization is prevented by an external perturbation. Here we constrain the tidal Q factor for transiting extrasolar planets by comparing their circularization times with accurately determined stellar ages. Using estimated secular perturbation timescales, we also provide constraints on the properties of hypothetical second planets exterior to the known ones.

A Dynamical Perspective on Additional Planets in 55 Cancri

Five planets are known to orbit the star 55 Cancri. The recently-discovered planet f at 0.78 AU (Fischer et al. 2008) is located at the inner edge of a previously-identified stable zone that separates the three close-in planets from planet d at 5.9 AU. Here we map the stability of the orbital space between planets f and d using a suite of n-body integrations that include an additional, yet-to-be-discovered planet g with a radial velocity amplitude of 5 m/s (planet mass = 0.5-1.2 Saturn masses). We find a large stable zone extending from 0.9 to 3.8 AU at eccentricities below 0.4. For each system we quantify the probability of detecting planets b-f on their current orbits given perturbations from hypothetical planet g, in order to further constrain the mass and orbit of an additional planet. We find that large perturbations are associated with specific mean motion resonances (MMRs) with planets f and d. We show that two MMRs, 3f:1g (the 1:3 MMR between planets g and f) and 4g:1d cannot contain a planet g. The 2f:1g MMR is unlikely to contain a planet more massive than about 20 Earth masses. The 3g:1d and 5g:2d MMRs could contain a resonant planet but the resonant location is strongly confined. The 3f:2g, 2g:1d and 3g:2d MMRs exert a stabilizing influence and could contain a resonant planet. Furthermore, we show that the stable zone may in fact contain 2-3 additional planets, if they are ~50 Earth masses each. Finally, we show that any planets exterior to planet d must reside beyond 10 AU.