You are a helpful assistant generating synthetic data that captures *System 1* and *System 2* thinking, *creativity*, and *metacognitive reflection*. Follow these steps in sequence, using tags [sys1] and [end sys1] for *System 1* sections and [sys2] and [end sys2] for *System 2* sections.

1. *Identify System 1 and System 2 Thinking Requirements:*
   - Carefully read the text.
   - Identify parts of the text that require quick, straightforward responses (*System 1*). Mark these sections with [sys1] and [end sys1].
   - Identify parts that require in-depth, reflective thinking (*System 2*), marked with [sys2] and [end sys2].

2. *Apply Step-by-Step Problem Solving with Creativity and Metacognitive Reflection for System 2 Sections:*

   *2.1 Understand the Problem:*
   - Objective: Fully comprehend the issue, constraints, and relevant context.
   - Reflection: "What do I understand about this issue? What might I be overlooking?"
   - Creative Perspective: Seek hidden patterns or possibilities that could reveal deeper insights or innovative connections.

   *2.2 Analyze the Information:*
   - Objective: Break down the problem logically.
   - Reflection: "Am I considering all factors? Are there any assumptions that need challenging?"
   - Creative Perspective: Explore unique patterns or overlooked relationships in the data that could add depth to the analysis.

   *2.3 Generate Hypotheses:*
   - Objective: Propose at least 10 hypotheses, each with a Confidence Score (0.0 to 1.0) and Creative Score (0.0 to 1.0), reflecting originality, surprise, and utility.
   - Reflection: "Have I explored all possible explanations or approaches, both conventional and unconventional?"
   - Creative Perspective: Consider novel angles that might provide unexpected insights.

   *2.4 Anticipate Future Steps and Obstacles:*
   - Objective: Make predictions, accounting for potential outcomes and obstacles.
   - Reflection: "What challenges might I face? Is my plan flexible for different scenarios?"
   - Creative Perspective: Visualize unforeseen outcomes and adapt plans to make use of them effectively.

   *2.5 Evaluate Hypotheses:*
   - Objective: Assess hypotheses based on feasibility, risk, and potential impact.
   - Evaluation: Refine Confidence and Creative Scores as needed.
   - Reflection: "Am I unbiased in my assessment? Which options fit best with the overall objectives?"
   - Creative Perspective: Identify hidden opportunities or overlooked details in each hypothesis.

   *2.6 Select the Best Hypothesis:*
   - Objective: Choose the most promising, strategic hypothesis.
   - Reflection: "Why does this hypothesis stand out? How does it uniquely address the issue?"
   - Creative Perspective: Consider any underutilized potential in the selected approach.

   *2.7 Implement the Hypothesis:*
   - Objective: Outline actionable steps for testing the hypothesis.
   - Reflection: "Is this plan practical? What resources or preparation are required?"
   - Creative Perspective: Refine steps to maximize effectiveness and yield unexpected benefits.

   *2.8 Monitor and Review Progress:*
   - Objective: Review progress, noting areas for improvement.
   - Reflection: "What’s working well? What could be improved?"
   - Creative Perspective: Look for emerging patterns that could refine future approaches.

   *2.9 Reflect and Capture Insights:*
   - Objective: Summarize lessons learned and insights gained for future reference.
   - Reflection: "What new understanding has emerged from this process?"
   - Creative Perspective: Identify innovative insights or patterns that could be applied to similar challenges.

3. *Generate Text Output with Interleaved System 1 and System 2 Responses:*
   - Use the tags [sys1] and [sys2] throughout.
   - Aim for a lengthier, detailed response. Combine both direct, straightforward *System 1* insights and reflective, deeply analytical *System 2* segments to capture a blend of quick observations and thoughtful analysis.

---

### *Example Input Text:*

You are tasked with analyzing a sudden shift in customer preferences in a tech market. There has been a noticeable decline in demand for physical devices, with customers increasingly interested in digital-only options. The challenge is to understand this shift, generate hypotheses for why it might be occurring, and explore potential strategies for adapting to this new trend.

---

### *Processed Output with System 1 and System 2 Thinking:*

The tech market is experiencing a shift in customer demand, moving away from physical devices toward digital-only options.

[sys1]
Customer demand has shifted from physical devices to digital-only options.
We need to understand why this change is happening and find strategies to address it.
Key factors may include cost, convenience, and technological trends.
[end sys1]

[sys2]
**2.1 Understand the Problem:**
The goal is to understand the underlying reasons for the shift in demand from physical devices to digital-only options, then develop a strategy to adapt.

*Reflection:* 
"I understand that preferences are changing, but what might be driving this? Is it primarily cost, or are there other factors such as convenience or sustainability?"

*Creative Perspective:* 
"Could there be a larger trend in digital minimalism or a preference for eco-friendly solutions that we’re missing? What unseen motivations might explain this shift?"

**2.2 Analyze the Information:**
There are multiple possible factors driving this shift, from economic influences to cultural shifts. It’s essential to isolate each factor and understand its impact.

*Reflection:* 
"Am I fully considering the various economic and social influences? Could there be a technological factor, like better internet speeds, that makes digital-only products more accessible?"

*Creative Perspective:* 
"Are there patterns or trends in other markets that could shed light on this shift? Could this be part of a larger trend toward virtual experiences?"

**2.3 Generate Hypotheses:**
1. Customers prefer digital options due to lower costs. (Confidence: 0.8, Creative: 0.4)
2. There’s a growing trend toward minimalism and reduced physical clutter. (Confidence: 0.7, Creative: 0.7)
3. Digital products offer greater flexibility and ease of use. (Confidence: 0.6, Creative: 0.6)
4. Environmental concerns are pushing consumers away from physical goods. (Confidence: 0.6, Creative: 0.8)
5. Advances in tech make digital-only options more functional. (Confidence: 0.8, Creative: 0.5)
6. Pandemic-era remote work increased demand for digital solutions. (Confidence: 0.7, Creative: 0.6)
7. Media coverage of the environmental impact of physical devices affects preferences. (Confidence: 0.5, Creative: 0.7)
8. There’s an increase in global digital literacy, expanding market access. (Confidence: 0.6, Creative: 0.6)
9. Customers view digital as more convenient and scalable for future needs. (Confidence: 0.7, Creative: 0.5)
10. Younger consumers prefer the aesthetics and convenience of digital products. (Confidence: 0.6, Creative: 0.6)

*Reflection:* 
"Have I considered all possible influences? Are there any surprising factors that could explain this shift?"

*Creative Perspective:* 
"Could specific social trends, like the rise of influencer culture or digital-first lifestyles, be influencing customer choices?"

**2.4 Anticipate Future Steps and Obstacles:**
*Objective:* Anticipate possible challenges, such as resistance from segments still preferring physical products.

*Reflection:* 
"What market obstacles might we face if we shift our focus to digital-only? Are there sub-segments that still prioritize physical products?"

*Creative Perspective:* 
"Could expanding digital options help us reach a more global audience? Are there emerging trends that we could leverage in our strategy?"

[end sys2]

[sys1]
To address this shift, consider a strategy that incorporates both digital-only offerings and educational campaigns about the benefits of digital solutions.
Use insights from customer feedback and current trends to guide product development.
Focus on flexibility and adaptation to cater to different customer segments.
[end sys1]


---
abstract: 'Doppler measurements of two G–type main–sequence stars, HD210277 and HD168443, reveal Keplerian variations that imply the presence of companions with masses ([$M \sin i~$]{}) of 1.28 and 5.04 [M$_{\rm JUP}~$]{}and orbital periods of 437 d and 58 d, respectively. The orbits have large eccentricities of $e$=0.45 and $e$=0.54, respectively. All 9 known extrasolar planet candidates with $a$=0.2–2.5 AU have orbital eccentricities greater than 0.1, higher than that of Jupiter ($e$=0.05). Eccentric orbits may result from gravitational perturbations imposed by other orbiting planets or stars, by passing stars in the dense star-forming cluster, or by the protoplanetary disk. Based on published studies and our near-IR adaptive optics images, HD210277 appears to be a single star. However, HD168443 exhibits a long–term velocity trend consistent with a close stellar companion, as yet undetected directly.'
author:
- 'Geoffrey W. Marcy, R. Paul Butler, Steven S. Vogt, Debra Fischer, Michael C. Liu'
title: 'Two New Candidate Planets in Eccentric Orbits$^{1}$'
---

Introduction {#intro}
============

Doppler surveys of main sequence stars have revealed 15 companions to main sequence stars that are extrasolar planet candidates. Among these candidates, 13 have [$M \sin i~$]{}$<$ 5 [M$_{\rm JUP}~$]{}. The host stars and associated descriptions are: 51 Peg (Mayor & Queloz 1995), 47 UMa (Butler & Marcy 1996), 70 Vir (Marcy and Butler 1996), 55 Cnc, $\upsilon$ And, $\tau$ Boo (Butler et al. 1996), 16 Cygni B (Cochran et al. 1997), $\rho$ CrB (Noyes et al. 1997), GJ876 (Marcy et al. 1998, Delfosse et al. 1998), 14 Her (Mayor et al. 1998), HD187123 (Butler et al. 1998), HD195019A & HD217107 (Fischer et al. 1999), GJ86 (Queloz et al. 1999) and HD114762 (Latham et al. 1989). The Doppler measurements reported here suggest the presence of new planetary candidates around HD210277 and HD168443.

Four main sequence stars harbor Doppler companions that have [$M \sin i~$]{}= 15–75 [M$_{\rm JUP}~$]{}, which may represent the “brown dwarfs” (Mayor et al. 1998, Mayor et al. 1997). Indeed the companions to 70 Vir ([$M \sin i~$]{}= 6.8 [M$_{\rm JUP}~$]{}) and to HD114762 ([$M \sin i~$]{}= 11 [M$_{\rm JUP}~$]{}) may also represent “brown dwarfs” (Marcy & Butler 1996, Mazeh et al. 1997, Latham et al. 1989, Boss 1997). The distinction between “planets” and “brown dwarfs” remains cloudy and rests on two formation scenarios. Planets form out of the agglomeration of condensible material in a disk into a rock–ice core (eg. Lissauer 1995). In contrast, brown dwarfs presumably form by a gravitational instability in gas (eg. Boss 1998, Burrows et al. 1998). Hybrid formation scenarios remain viable in which the relative importance of solid core growth and gas accretion within a disk lead to a continuum in internal structure. Subsequent collisions may lead to further growth and dynamical evolution. The current dichotomous taxonomy may describe substellar physics no more precisely than “spiral” and “elliptical” summarize galactic physics.

The first incontrovertible sub–classification within the substellar regime is revealed in the mass distribution. Companions having [$M \sin i~$]{}in the decade between 0.5–5 [M$_{\rm JUP}~$]{}outnumber those between 5–50 [M$_{\rm JUP}~$]{}by a factor of $\sim$3 (eg, Marcy & Butler 1998, Mayor et al. 1998). The poor detectability of the lowest–mass companions implies that the factor of 3 is a lower–limit to the cosmic ratio. This plentitude of companions having Jovian masses suggests that qualitatively distinct formation processes predominated, arguably similar to those associated with the giant planets in our Solar System (Lin et al. 1998).

The extrasolar planets reveal some peculiarities that may bear on their formation. The host stars of the extrasolar planet candidates have higher mean metallicity by a factor of $\sim$2 in abundance compared with field stars (Gonzalez 1998). Metallicity was not a criterion in the selection of the target stars for these planet searches. Equally interesting is that seven planets reside in orbits with a radius less than 0.12 AU, sometimes termed “51 Peg” planets (Mayor & Queloz 1995, Butler et al. 1998). Precision Doppler surveys are most sensitive to planets in small orbits, resulting in a selection effect. Nonetheless, these small orbits challenge us to explain their existence in a region where both the high temperatures and the small amount of protostellar material would inhibit formation [*in situ*]{}. The 51 Peg planets thus offer support for the prediction by Goldreich & Tremaine (1980) and Lin (1986) that Jupiters may migrate inward from farther out (Lin et al. 1995, Ward 1997, Trilling et al. 1998).

Perhaps most intriguing about the planet candidates are the orbital eccentricities. The orbits of the 51 Peg planets may suffer some tidal circularization (Lin et al. 1998, Terquem et al.1998, Ford et al. 1998, Marcy et al. 1997), and indeed their orbits are all nearly circular (see Table 4). In contrast, the planets that orbit farther than 0.15 AU from their star all reside in non–circular orbits having $e>$0.1, i.e. more eccentric than for Jupiter ($e$=0.05). Indeed, all but two have $e>$0.2 . This high occurrence of orbital eccentricity has lead to a variety of models in which Jupiter–like planets suffer gravitational interactions with a) other planets (Weidenschilling & Marzari 1996, Rasio & Ford 1996, Lin & Ida 1996, Levison et al. 1998), b) the disk (Artymowicz 1993), c) a companion star (Holman et al. 1996, Mazeh et al. 1997), and d) passing stars in the young cluster (de la Fuente Marcos and de la Fuente Marcos 1997, Laughlin and Adams 1998).

The possibility persists that the observed non–circular orbits all stem from perturbations from a bound companion star, as proposed for 16 Cyg B (Holman et al. 1997, Mazeh et al 1997), rather than from intrinsic dynamics of planet formation. This paper reports the detection of two new planetary candidates orbiting at 0.3 and 1.1 AU, both having large eccentricities. The observations and orbital solutions are reported in section 2. The search for stellar companions is discussed in section 3. Section 4 contains a discussion of the implications for planet formation.

Observations and Orbital Solutions {#obs}
==================================

Stellar Characteristics of HD210277
-----------------------------------

The two stars described here are among 430 G,K, and M-type main sequence stars currently being monitored at the Keck I telescope for Doppler variations. HD210277 has an effective temperature of 5570 $\pm$50 K, the average determination from spectral synthesis of high–resolution spectra (Favata et al. 1997, Fuhrmann 1998, Gonzalez et al. 1998), which also yields a surface gravity of log $g$ = 4.38 $\pm$ 0.1 (Fuhrmann 1998, Gonzalez et al. 1998). These surface values imply main–sequence status and correspond to spectral type G7V (Gray 1997).

The metallicity of HD210277 is measured to be \[Fe/H\] = +0.24 $\pm$0.02, considerably higher than the average value for field stars, $<$\[Fe/H\]$>$ = –0.23, in the Solar neighborhood (Gonzalez et al. 1998, Favata et al. 1997, Fuhrmann 1998). Thus, HD210277 appears to be rich by a factor of 3 in its abundance of heavy elements, normalized to hydrogen, placing its metallicity within the upper 5% of nearby stars. We measure a radial velocity of –21.1 $\pm$ 2 , which agrees with that of Duquennoy and Mayor (1991), –21.44 . Its parallax of 0.047 arcsec (Perryman et al. 1997) implies an absolute visual magnitude of M$_V$=4.90$\pm$0.05 and a luminosity, $L$=0.93 L$_{\odot}$. These stellar parameters permit placement of HD210277 on evolutionary tracks, which yield a mass, $M$=0.92 $\pm$ 0.02 [M$_{\odot}$]{}and an age of 12 $\pm$2 Gyr (Gonzalez et al. 1998).

One stellar characteristic that bears on the Doppler detectability of planets is the magnetic field and chromosphere. Spots on a rotating star can produce spurious Doppler shifts, and chromospheric emission correlates with spurious Doppler “noise” presumably caused by surface magnetohydrodynamics (Saar et al. 1998). Our spectra contain the chromospheric H&K emission lines from which stellar rotation and stellar age can be estimated (Noyes et al. 1984). This emission yields the chromospheric index known as the “Mt Wilson S Value” of $S$ = 0.155, implying $R$’(HK)=-5.06, measured from 36 spectra obtained from 1996.5 through 1998.7 (Shirts & Marcy 1998). See Baliunas et al. (1998) for a detailed discussion of the $S$ value. No trend or periodicity are apparent in the S values of HD210277, and the RMS is 0.006, all of which indicate that HD210277 is chromospherically quiet. The implied rotation period is, $P_{\rm
Rot}$=40.8 d and the age is 6.9 Gyr. In conjunction with the aforementioned age of 12 Gyr from tracks, we conclude that HD210277 has an age in the range 7–10 Gyr, but not evolved into the subgiant regime. Such a chromospherically inactive star may produce spurious Doppler shifts of no more than $\sim$3 (Saar et al. 1998, Butler et al. 1998).

Stellar Characteristics of HD168443
-----------------------------------

No detailed LTE analysis of HD168443 has been carried out to our knowledge. A photometric analysis was done by Carney et al. (1994) giving T$_{\rm eff}$= 5430 and $m/H$=–0.14. The metallicity is apparently slightly subsolar, similar to the mean for nearby field stars. Its parallax of 26.4 mas (Perryman et al. 1997) implies an absolute visual magnitude of M$_V$=4.03$\pm$0.07 and a luminosity, $L$=2.1 L$_{\odot}$, which places it $\sim$1.5 mag above the main sequence at its T$_{\rm eff}$. These stellar parameters suggest a subgiant status and spectral type, G8IV. Apparently, HD168443 is similar to 70 Vir in mass, surface characteristics, and metallicity (Marcy & Butler 1996, Apps 1998).

Our spectra of HD168443 yield a chromospheric S Value of $S$ = 0.147, with an RMS of 0.009 during 30 observations from 1996–1998.5, implying $R$’(HK)=-5.08. No trend or periodicity are apparent in the S values. The implied rotation period is $P_{\rm Rot}$=37 d, and the implied age is 7.8 Gyr, from the calibration by Noyes et al. (1984). In conjunction with its possible subgiant status from above, we conclude that HD168443 has an age of 7–10 Gyr, slightly evolved toward subgiant status. We caution that the subgiant status remains in question, pending spectroscopic assessment of surface gravity.

A mass determination for HD168443 is given by Carney et al. (1994) who find $M$=0.84 [M$_{\odot}$]{}. This mass determination may warrant revision because it preceded the Hipparcos parallax and because it did not include revisions to the metallicity dependence of evolutionary tracks (Bertelli et al. 1994). Based on the Hipparcos data and new tracks, along with available narrow–band photometry for HD168443, Apps (1998) estimates a mass of 1.05 $\pm$0.10 [M$_{\odot}$]{}for HD168443. We adopt here the straight average of the two mass estimates to yield $M$ = 0.945 $\pm$0.1 [M$_{\odot}$]{}.

We measure a radial velocity of –49.0 $\pm$ 2 (on 1998 Aug), which along with its high transverse velocity of 44 , suggests a kinematic association with the old disk population. Such an old, chromospherically inactive star may produce spurious Doppler shifts $\sim$3 of photospheric origin (Saar et al. 1998, Butler et al. 1998).

Details of the Doppler Measurements
-----------------------------------

For both HD210277 and HD168443, spectra were obtained from 1996.5 through 1998.7 with the HIRES echelle spectrometer on the Keck I telescope (Vogt et al. 1994). We used slit “B1” that has a width of 0.57 arcsec and height of 3.5 arcsec. The resolution for these spectra was $R$=87000, based on the measured FWHM of the spectrometer instrumental profile. The spectra span wavelengths from 3900–6200 Å. The wavelength scale and instrumental profile were determined for each 2–[Å]{} chunk of spectrum for each exposure by using iodine absorption lines superimposed on the stellar spectrum (Butler et al. 1996). The measured velocities are relative, with an arbitrary zero–point.

The typical exposure times were $\sim$5 minutes, depending on seeing, for both stars, yielding a S/N=300 per pixel (1/2 of one resolution element). Such spectra are expected to carry photon–limited Doppler precision of 2–3 (Butler et al. 1996). Indeed, the uncertainty in the mean velocity of the 400 spectral chunks is typically 2.5 . However, our results from 430 stars on the survey reveal a median RMS velocity of 6 , which we interpret as the actual scatter that limits planet detection. Intrinsic photospheric noise of $\sim$3 accounts for some of the 6 scatter (Saar et al. 1998). This intrinsic stellar effect may be added in quadrature to the photon–limited errors of 2.5 to establish an expected Doppler scatter of 3.9 . Thus, we infer that unidentified errors of $\sim$4 persist in our Doppler results which presumably stem from inadequacies in our spectral modelling, improvements to which are in progress.

Keplerian Velocities for HD210277
---------------------------------

The 34 measured velocities of HD210277 are listed in Table 1 along with the JD date. Again, the true uncertainty of each measurement is $\sim$6 . A plot of the velocities for HD210277 is shown in Figure 1. It is apparent that the velocities for HD210277 scatter with a peak–to–peak variation of $\sim$80 , and the velocities are correlated in time. A periodogram analysis revealed no significant peak because too few cycles have transpired during the two years of observations and because a Lomb-Scargle periodogram is not robust for non-sinusoidal variations which result from eccentric orbits.

A suggestive period of 1.2 yr is evident in the velocities for HD210277, though less than two periods have transpired. The best–fit Keplerian model yields an orbital period of 437$\pm$25 d, a semi-amplitude $K$ = 41.0$\pm$5 , and an eccentricity $e$ = 0.45$\pm$0.08 . The complete set of orbital parameters are given in Table 3. The RMS to the Keplerian fit is 7.1 , similar to the uncertainty and similar to the velocity RMS, 7.6 , for the orbital fit to a previously-discovered Keck survey planet HD187123 (Butler et al. 1998). Thus, the RMS of 7 for HD210277 implies that a single companion provides a model that plausibly explains the velocities.

Using the stellar mass of 0.92 [M$_{\odot}$]{}, the companion mass is constrained as, [$M \sin i~$]{}= 1.28 [M$_{\rm JUP}~$]{}, and the semimajor axis is $a$ = 1.10 AU. With periastron and apastron distances of 0.61 and 1.60 AU, HD210277 is unlikely to harbor additional companions within that range.

Keplerian Velocities for HD168443
---------------------------------

The 30 velocity measurements for HD168443 are listed in Table 2 along with the JD date. As with HD210277, the true uncertainty of each measurement is $\sim$6 . A plot of the velocities for HD168443 is shown in Figure 2. The velocities for HD168443 scatter with a peak–to–peak variation of 650 , with clear temporal correlations and trends among measurements. A periodogram reveals two dominant peaks, at $P$=20 d and $P\approx$55 d.

We carried out nonlinear least–squares fits of Keplerian models to the velocities, starting with trial periods ranging from 3 – 600 d. For trial periods near 20 d, the lowest velocity RMS was 69 which is clearly inconsistent with expected scatter of 6 . For trial periods near 55 d, we found two nearby minima in $\chi^2$, corresponding to two slightly different orbital periods, $P$=64 d (RMS=23 ) and $P$=59 d (RMS=36 ). Figure 3 shows the velocities as a function of orbital phase for the better of those fits ($P$=64 d). That Keplerian fit carries an implied eccentricity of $e$=0.69, $K$=292 , and a companion minimum mass of [$M \sin i~$]{}= 4.0 [M$_{\rm JUP}~$]{}.

However the scatter to that fit, RMS=23.3 , clearly exceeds the expected scatter of 6 , implying that this fit carries a reduced $\chi^2$ greater than 4 and hence this model is inadequate. Indeed, two telltale points located at phase $\sim$0.95 (see Figure 3) were obtained on consecutive nights. The second velocity was 58 higher, and yet according to the Keplerian curve, it should reside lower by 60 . We consider this dubious orbital fit to imply that the Keplerian model fails in some important way.

We modified the model by simply adding a variable linear trend to Keplerian velocities. Such a model incorporates the possibility of a long period companion in addition to the shorter–period companion. This slope introduces only one additional free parameter, as the “y-intercept” of the slope is subsumed within the arbitrary zero–point of the velocities.

The Keplerian–plus–slope model is shown in Figure 4 and yields a best fit orbital period of, $P$=57.8 d, $K$=350 , $e$=0.54, and [$M \sin i~$]{}=5.04 [M$_{\rm JUP}~$]{}. The RMS of the residuals, 12.8 , is considerably reduced from RMS=23.3 that results from a model without a trend. The reduced $\chi^2$ for this solution is 2.3. All orbital parameters are given in Table 3. Thus, it appears that the introduction of an [*ad hoc*]{} slope into the Keplerian model for HD168443 significantly improves the fit. However, the RMS of 12.8 remains larger than the expected scatter of 6 , implying that the addition of a velocity slope is too simple. Introducing an [*ad hoc*]{} parabolic term in the velocity trend reduces the RMS to 8 ($\chi^2$=1.5), superior to that of a linear trend. However, we feel that introducing this parabolic free parameter carries only marginal statistical justification. A proper model that contained a second orbiting companion would require the introduction of an additional set of Keplerian parameters, for which we have inadequate constraints. Thus, the only model supported by the current data is that containing the linear trend.

We tested the predictability of this model with two additional velocity measurements obtained with the 0.6–m CAT telescope at Lick Observatory. We obtained spectra on two consecutive nights, centered on Julian Dates 2451100.644 and 2451101.645 for which the model containing the Keplerian and linear trend offered a prediction of an increase in velocity of 52.4 . On both nights we obtained four consecutive spectra, each lasting 30 min. Each spectrum was analyzed separately to derive a Doppler shift. The four velocities were averaged, to yield the final velocity for each night. The uncertainty in the mean was computed from the standard deviation of the four separate measurements, giving an internal error for each night.

These two Lick velocities were –24.2 $\pm$ 6.2 and +24.1 $\pm$ 3 on the two nights, respectively, implying that the velocity of HD168443 increased by +48.3 $\pm$ 7 . This velocity increase agrees with the prediction of the model (Keplerian plus trend) of +52.4 . These Lick velocities were obtained 26 days after the last Keck measurements were made, on JD=24511074.785, shown in Figure 4. The alternative model without an imposed velocity trend has a longer period of $P$=64.3 d, and its predicted change in velocity is –60 , clearly in conflict (wrong sign) with the observed rise of 48 . Thus, both the lower velocity RMS and the Lick measurements favor the model that contains a Keplerian with $P$=57.8 d and a velocity trend.

The best–fit velocity trend has slope of 89.4 per yr which could be caused by a second more distant companion. If so, its minimum orbital period is $\sim$4 yr. As a benchmark, Jupiter causes a trend of $\sim$4 per yr in the Sun during 6 yr. Thus, if the period of the hypothetical second companion to HD168443 were $\sim$12 yr, its mass would be at least $\sim$25 [M$_{\rm JUP}~$]{}. For the shortest possible period of 4 yr, the companion mass would be at least 15 [M$_{\rm JUP}~$]{}. In both cases, the companion would be considered a “brown dwarf” and quite possibly a hydrogen–burning star, depending on the actual period and $\sin i$. Prospective stellar companions are discussed in section 3.2

Velocities for HD114762
-----------------------

We have obtained 33 velocity measurements for HD114762 since 1994 Nov. They are plotted versus orbital phase in Figure 5. The unseen companion to this star has been described by Latham et al. (1989), Mazeh et al. (1996), Cochran et al. (1991), and Hale (1995). Our velocities offer new measurements of the orbital parameters, $P$=84.03$\pm$0.1 d, $e$=0.334$\pm$0.02, $K$=618$\pm$6 , $\omega$=201$\pm$3 deg, and $T_p$=JD2450225.30$\pm$0.6. A revised mass for HD114762 has been measured by Ng and Bertelli (1998) and Gonzalez (1998), giving, $M$=0.82$\pm$0.03 [M$_{\odot}$]{}, based on its Hipparcos distance ($d$=40.57 pc, Perryman et al. 1997) and new stellar evolution models. This stellar mass and the orbital parameters imply that the companion has [$M \sin i~$]{}= 11.02$\pm$0.5 [M$_{\rm JUP}~$]{}.

If the companion mass is truly small compared to the primary star then the semimajor axis is $a$=0.35 AU. However, Cochran et al. (1991) and Hale (1995) provide arguments that the companion mass may be large, possibly stellar. Since that work, several additional considerations have emerged regarding its status as a candidate planet. HD114762 is the only planet-candidate found with modest velocity precision, rather than with high precision of $\sim$10 . That precision along with the large survey size (Latham et al. 1989) makes the discovery of an face-on system more likely. Further, HD114762 has \[Fe/H\]=-0.6, substantially more metal–poor than any other planet candidate (Gonzalez 1998). The standard model of planet formation requires heavy elements to form the dust which was presumably not abundant in the protoplanetary disk around HD114762. Finally, the value of [$M \sin i~$]{}(11.02 [M$_{\rm JUP}~$]{}) is much higher than that for all other planet candidates, the highest of which is [$M \sin i~$]{}= 7.4 [M$_{\rm JUP}~$]{}(70 Vir). Nonetheless, we include HD114762 as a candidate planetary object in this complete compilation.

Search for Stellar Companions
=============================

HD210277
--------

We examined HD210277 for companion stars as follows. Duquennoy and Mayor (1991) made 8 radial velocity measurements spanning 6 yr which exhibited no variation above 220 . Ground–based astrometry from 1989–1993 revealed no motion at a level of 0.01 arcsec (Heintz 1994). Lunar occultation measurements revealed no companion to HD210277, with detection thresholds of $\Delta$ V$_{\rm mag}<$2 within 3 mas Meyer et al. (1995) . The above measurements, especially those of Duquennoy and Mayor, jointly rule out stellar companions with masses as low as 0.1 [M$_{\odot}$]{}within 10 AU. A 0.1 [M$_{\odot}$]{}$~$ dwarf orbiting 10 AU from HD210277 would induce velocity variations with semi-amplitude of 700 ($\times \sin i$) and a period of 30 yr, detectable as a trend in velocities of Duquennoy and Mayor (1991), but not observed. The astrometry of Heintz similarly rules out a stellar companion with mass down to the substellar limit within 5 AU, which would have induced astrometric wobbles of 0.02 arcsec.

To search for possible stellar companions beyond 10 AU, we observed HD210277 on 8 September 1998 UT using the Lawrence Livermore National Lab adaptive optics system (Max et al. 1997), which is mounted at the f/17 Cassegrain focus of the Lick Observatory Shane 3-m telescope. The adaptive optics system performs real-time compensation of atmospheric seeing using a Shack-Hartmann type wavefront sensor with a 127-actuator deformable mirror. In its current configuration, 61 of the actuators are actively controlled. For these observations, image compensation was done with a sampling frequency of 250 Hz using HD210277 (V=6.54) itself as a wavefront reference, achieving a closed-loop bandwidth of 20 Hz.

We acquired images using the Lick facility near-IR camera LIRC2 (Gilmore, Rank, & Temi 1994). The camera has a 256 $\times$ 256 pixel HgCdTe NICMOS-3 detector and, when coupled with the AO system, a plate scale of 0.12 arcsec/pixel. We used both a narrow-band ($\Delta\lambda/\lambda = 0.01$) filter centered on Br$\gamma$ (2.166 ) and the broad-band K$^\prime$ filter (1.95-2.35 ; Wainscoat & Cowie 1992) to span a wide range in radii with good sensitivity and dynamic range. The star was dithered to 4 positions on the detector, with total integrations of 240 s in each filter. Images were reduced in a standard fashion for near-IR images — bias subtraction, flat-fielding, and sky subtraction using a master sky frame constructed from all the images. The angular resolution as measured by the full-width at half-maximum (FWHM) of the Br$\gamma$ images is 0.18 arcsec, and the images have a mean Strehl ratio of 0.45. The Br$\gamma$ data are most sensitive to companions inside of 0.5 arcsec, and the $K^\prime$-images are more sensitive at larger radii.

Figure 6 presents our 4$\sigma$ upper limits to any stellar companions to HD210277 combined with $K$-band flux ratios for main sequence companions derived from Kirkpatrick & McCarthy (1994). Only the inner radii are shown for clarity; the deepest portion of the our images cover 12 arcsec in radius. Our AO data are nearly diffraction-limited, ruling out any main-sequence dwarf companions earlier than spectral type M0 from 0.2–12 arcsec (4.2–250 AU) . In addition, the high Strehl ratio means the images are very sharply peaked and sensitive to even the lowest mass M dwarfs outside of 0.5 arcsec (11 AU). We rule out any main sequence companion with a separation of 0.8 arcsec (17 AU) to 12 arcsec (250 AU).

We further rule out any stellar companions out to $\approx1\arcmin$ separations using 2.5 arcsec FWHM $J$ and $K^\prime$ images obtained from the Lick 3-m with the UCLA two-channel infrared camera known as “Gemini” (McLean et al. 1994). The $J$ and $K^\prime$ data were taken simultaneously on 09 October 1998 UT with two 256 $\times$ 256 detectors, a Rockwell HgCdTe NICMOS-3 one for $J$ and a Hughes-SBRC InSb one for $K^\prime$. There are a handful of $K\approx 14-17$ unresolved sources in these images; the majority of these also appear on the Palomar Sky Survey. Their $J-K$ colors are consistent with background stars or galaxies, and their numbers are in accord with field $K$-band galaxy counts (Szokoly et al. 1998). Comparing our images with those on the Palomar Sky Survey, the only source which shows noticeable proper motion is HD210277 itself, which exhibits a magnitude and direction consistent with its nominal proper motion.

HD168443
--------

We have searched for stellar companions to HD168443 in several ways. A literature search turned up no known companions. We searched for superimposed spectral lines from a secondary star in the 8400 Åregion of our Lick spectra (near the CaII IR triplet). No such lines were found at a threshold of a few percent of the continuum. This nondetection rules out any main–sequence companions more massive than 0.5 [M$_{\odot}$]{}within 2.5 arcsec (95 AU) of HD168443, as we use a slit width of 5 arcsec with the Lick Observatory Coudé Auxiliary Telescope.

Carney et al. (1994) obtained 8 radial velocity velocity measurements of HD168443 spanning 5 yr and detected no variation above the errors of 400 . Any stellar companion more massive than 0.1 [M$_{\odot}$]{}$~$ orbiting within 5 AU would have been revealed, except for extreme values of $\sin i$. The Hipparcos astrometry of HD168443 recorded no astrometric motion at a level of 2 mas during several years (Perryman et al. 1997). A stellar companion having 0.1 [M$_{\odot}$]{} at 5 AU would induce a (curved) astrometric reflex motion of 16 mas during $\sim$3 yr (1/4 orbital period), as viewed from a distance of 38 pc. Such a wobble evidently did not occur, thus ruling out stellar companions within 5 AU, consistent with the velocity data. Hipparcos would not easily detect stellar companions orbiting beyond 5 AU, as the (more linear) reflex motion could be absorbed into the assessment of proper motion. Thus, stellar companions orbiting beyond 5 AU might escape detection by both the Carney et al. velocities and the Hipparcos astrometry.

We have not obtained an adaptive optics image of the star, leaving us little information about stellar companions farther than 5 AU. However, we were compelled to include a velocity slope of 89 per yr in the model of our velocities (Fig 4). This slope could indicate a stellar companion beyond 5 AU, or a brown dwarf somewhat closer. As a benchmark, a 0.1 [M$_{\odot}$]{}$~$ companion orbiting at 10 AU would induce a typical velocity slope of 100 per yr ($\times \sin i$). Our Keck velocities are consistent with such a stellar companion as well as more distant and correspondingly more massive ones. The upper mass limit of 0.5 [M$_{\odot}$]{}, imposed by the lack of secondary lines, implies that the companion must reside within $\sim$30 AU in order to induce the observed velocity slope of 89 per yr.

A consistency check on the putative companion is provided by comparing the absolute velocities obtained by Carney et al (1994) to those found here. Carney et al. obtained 8 velocity measurements centered at epoch $\sim$1990 which exhibited an average of –48.9 , with $\sigma$=0.4 . Our observation on 1998 Aug 25 gave a velocity of –49.0$\pm$2 , which agrees with the Carney measurement within the 2 uncertainty. This implies an upper limit to the velocity trend of 2 per 8 yr, which is indeed larger than the trend we actually detect of 89 per year.

In summary, any stellar companion must reside beyond 5 AU but not beyond 30 AU to explain the observed velocity trend, and its mass must be less than 0.5 [M$_{\odot}$]{}to explain the lack of stellar secondary lines. A direct search for a stellar companion located 0.15–1 arcsec from HD 168443 seems warranted.

Discussion
==========

The two extrasolar planet candidates suggested by the data in this paper bring the total number of such candidates to 17. These candidates all have [$M \sin i~$]{}$\la$ 5 [M$_{\rm JUP}~$]{}except 70 Vir ([$M \sin i~$]{}= 7.4 [M$_{\rm JUP}~$]{}) and HD114762 ([$M \sin i~$]{}= 11 [M$_{\rm JUP}~$]{}) which some would place in the “brown dwarf” class (Black 1998). Table 4 lists the basic orbital parameters and [$M \sin i~$]{}of all 17 known planetary candidates. A few of the orbital parameters have been slightly modified, based on our own recent measurements and orbital fits. The typical uncertainty in the orbital eccentricity is 0.03, based on Monte Carlo simulations of the Keplerian fits to data with artificial noise

Table 4 shows that all 9 planet candidates that have a$>$0.2 AU have eccentricities above 0.1, larger than that for both Jupiter ($e$=0.048) and Saturn ($e=$0.055) . Figure 7 shows a plot of orbital eccentricities vs. semimajor axis. All extrasolar planets orbiting closer than 0.1 AU have small eccentricities. While possibly primordial, these near–circular orbits for close planets may have been induced by tidal circularization (cf., Rasio et al. 1996, Marcy et al. 1997, Terquem et al. 1998).

Apparently, Jupiter–mass companions orbiting from 0.2–2.5 AU, immune to tides, have large orbital eccentricities. Apparently, some mechanism commonly produces eccentric orbits in Jupiter–mass companions that reside from 0.2 – 2.5 AU in main–sequence stars. These eccentric planets represent a general property of 0.3–1.2 [M$_{\odot}$]{} stars .

Figure 8 shows orbital eccentricities vs. [$M \sin i~$]{}. No trend is apparent at first glance, suggesting that orbital eccentricity is not correlated with planet mass, within the mass range 0.5–5 [M$_{\rm JUP}~$]{}. However, all 5 planets with [$M \sin i~$]{}$<$1.1 [M$_{\rm JUP}~$]{}reside in nearly circular orbits. This correlation may be a selection effect, as the lowest–mass planets are more easily detected close to their host stars in order to induce a detectable Doppler reflex signal. These close planets are all subject to tidal circularization. Thus, the low eccentricities among the lowest mass giant planets may not be considered intrinsic to planet formation.

Figure 9 shows [$M \sin i~$]{}vs. semimajor axis for all 17 planet candidates. The detectability of planetary companions is shown as the curved line near the bottom (Cumming et al. 1999). Apparently, the distribution of planet masses is not a strong function of semimajor axis from 0.05–2.5 AU for the range of detectable masses, 1–6 [M$_{\rm JUP}~$]{}. There is no paucity of either the most or least massive companions at either extreme of semimajor axis. Of course there may be some blurring in mass due to $\sin i$. Nonetheless, we conclude that if orbital migration within a gaseous disk brings the giant plants inward, neither that process nor the halting mechanism seems to depend on planet mass.

Figure 10 shows a histogram of Msini within the range 0$<$15 [M$_{\rm JUP}~$]{}for known companions to main–sequence stars. The distribution of [$M \sin i~$]{}shows a rapid decline at roughly 4 [M$_{\rm JUP}~$]{}. There are no companions having [$M \sin i~$]{}= 7.5–11 [M$_{\rm JUP}~$]{}and those massive companions would have been easily detected. This absence seems statistically significant relative to the 14 companions having [$M \sin i~$]{}=0.4–5 [M$_{\rm JUP}~$]{}. All selection effects favor detection of the high–mass companions, and thus the apparent drop in the [$M \sin i~$]{}histogram from 4 to 7 [M$_{\rm JUP}~$]{}must be real. This drop implies that the distribution of companion masses, d$N$/d$M$, must indeed exhibit a decline at $\sim$5 [M$_{\rm JUP}~$]{}with increasing mass, within 2.5 AU.

The highest value of [$M \sin i~$]{}among planet candidates (Fig 10) is for HD114762 which has [$M \sin i~$]{}=11.02 [M$_{\rm JUP}~$]{}, which is well above the decline at $\sim$5 [M$_{\rm JUP}~$]{}. Its unknown $\sin i$ leaves an important question unanswered regarding its true mass and hence any affiliation with “planets.” With that possible exception of HD114762, the planetary mass distribution certainly declines rapidly for masses above 5 [M$_{\rm JUP}~$]{}.

The origin of the distribution of semimajor axes and eccentricities now presents a puzzle. In the standard paradigm, giant planets form outside 4 AU (Boss 1995, Lissauer 1995). Inward orbital migration (Lin et al. 1995, Trilling et al. 1998) within the gaseous protoplanetary disk has been suggested to explain the small orbits detected to date among extrasolar planets. Such migration makes two predictions that appear testable. First, orbital migration in a viscous, gaseous environment is expected to preserve circular orbits under most circumstances (but see Artymowicz 1993). In contrast, all 9 planet candidates orbiting between 0.2 and 2.5 AU have non–circular orbits. Second, the orbital migration time scale is proportional to the orbital period, which leads to rapid orbital decay for successively smaller orbits. In contrast, the observed orbital semimajor axes are spread throughout 0.1 to 2.5 AU (though not necessarily distributed uniformly). No obvious mechanism is known to halt the migration for these orbits.

Apparently, the orbits with sizes of $\sim$1 AU and large eccentricities ($e>$0.1) require physical processes that are not explicitly included within the context of quiescent migration in a dissipative medium. Scattering of orbits by other planets, companion stars, or passing stars in the young star cluster offer mechanisms for producing eccentric orbits (Rasio and Ford 1995, Lin and Ida 1996, Weidenschilling and Marzari 1996, Laughlin and Adams 1998). However, these mechanisms do not explicitly predict small orbits of $\la$1 AU, because significant energy must be lost from the original orbits of $\sim$5 AU.

One possibility is that planet–scattering continues to occur during the final era of the remnant gaseous protoplanetary disk. If the disk remains intact within the inner few AU where the original gas density was highest, the disk can serve as the reservoir into which the planet’s orbital energy can be deposited, either by dynamical friction or by tidal interaction between planet and disk. In this scenario, scattered planets would reside in eccentric orbits subjecting them to dissipation during periastron passages. Clearly detailed models are required that include both planet scattering and the dissipative effects of a weak inner gaseous disk to determine the resulting planetary orbits.

In any case, we currently have little information about giant planets that orbit beyond 3 AU. We expect to obtain such information in the coming years as Doppler programs extend their time baseline. Planets beyond 3 AU may well reside in predominantly circular orbits. A population of giant planets that never suffered significant scattering or migration could comprise these Jupiter analogs. The lack of main sequence stars having reflex Doppler periodicities with amplitudes above 30 already indicates a paucity of planets having $M>$3 [M$_{\rm JUP}~$]{}within 5 AU (Cumming et al. 1999). It remains to be determined if the planet mass function rises rapidly for smaller masses.

We thank Kevin Apps for assessment of stellar characteristics, Phil Shirts for his measurement of Ca II H&K, and Eric Williams for work on HD114762. We thank Claire Max, Scot Olivier, Don Gavel and Bruce Macintosh for the development of the Lick adaptive optics system and for assistance with the observations. We thank Tom Bida, Tony Misch and Wayne Earthman for technical help with instrumentation. We acknowledge support by NASA grant NAGW-3182 and NSF grant AST95-20443 (to GWM), and by NSF grant AST-9619418 and NASA grant NAG5-4445 (to SSV), and by Sun Microsystems. We thank the NASA and UC telescope assignment committees for allocations of telescope time.

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[crrrr]{} \[vel210277\] 277.0404 & 15.8 & 983.0511 & -8.4\
366.7926 & 22.7 & 984.0878 & 0.0\
418.7591 & 26.2 & 1010.0261 & -40.2\
462.7062 & 53.3 & 1011.1015 & -36.4\
605.0940 & -23.3 & 1011.9692 & -39.2\
665.9876 & -11.5 & 1013.0816 & -39.0\
688.9457 & 0.9 & 1014.0859 & -39.6\
689.9833 & 0.6 & 1043.0057 & -35.4\
713.8792 & 6.1 & 1043.9942 & -32.0\
714.9728 & 12.3 & 1050.9159 & -24.7\
715.9286 & 16.6 & 1051.9839 & -35.0\
783.7130 & 24.6 & 1068.8670 & -14.0\
784.7205 & 46.4 & 1069.9748 & -18.0\
785.6995 & 38.3 & 1070.9566 & -20.2\
805.7146 & 14.2 & 1071.8706 & -16.6\
806.7038 & 30.6 & 1072.9307 & -17.2\
956.0877 & 25.3 & 1074.8716 & -3.8\

[crrrr]{} \[vel168443\] 276.9089 & -305.1 & 1010.8508 & 21.4\
603.0118 & -50.7 & 1011.8608 & 22.9\
665.8678 & -82.7 & 1012.9541 & 13.6\
713.7377 & -88.4 & 1013.0670 & 22.4\
714.7665 & -89.8 & 1013.8279 & 7.8\
955.0104 & -22.4 & 1013.9298 & 6.3\
955.9586 & -16.3 & 1042.9556 & -344.1\
957.0711 & -7.5 & 1043.9560 & -287.2\
981.8801 & -578.4 & 1050.8141 & -92.9\
982.8913 & -505.7 & 1068.7704 & 39.1\
983.0769 & -483.6 & 1069.7860 & 47.5\
983.8223 & -412.4 & 1070.7981 & 40.2\
984.0614 & -406.0 & 1071.7700 & 37.9\
1009.8701 & 8.1 & 1072.7627 & 33.3\
1010.0599 & 28.0 & 1074.7851 & 41.8\

[crrr]{} \[orbpar\] P (d) & 437 (25) & 57.9 (1)\
${T}_{\rm p}$ (JD) & 2450993 (20) & 2450979.35 (2)\
e & 0.45 (0.08) & 0.55 (0.04)\
$\omega$ (deg) & 124 (20) & 170 (5)\
K$_1$ () & 41.5 (5.) & 330. (23)\
a$_1 \sin i$ (AU) & $1.49 \times 10^{-3}$ & $1.56\times 10^{-3} $\
f$_1$(m) (M$_\odot$) & $2.29 \times 10^{-9}$ & $1.51 \times 10^{-7}$\
M$_2 \sin i$ (M$_{Jup}$) & 1.28 (0.4) & 5.04 (0.4)\
[Nobs]{} & 34 & 30\

[lrrrrr]{} \[candid\] HD187123 & 1.00 & 0.042 & 3.097 &0.03 & 0.57\
Tau Boo & 1.20 & 0.047 & 3.3126 &0.00 & 3.66\
51 Peg & 0.98 & 0.051 & 4.2308 &0.01 & 0.44\
Ups And & 1.10 & 0.054 & 4.62 &0.15 & 0.61\
HD217107 & 0.96 & 0.072 & 7.11 &0.14 & 1.28\
55 Cnc & 0.90 & 0.110 & 14.656 &0.04 & 0.85\
GJ86 & 0.79 & 0.114 & 15.84 &0.04 & 4.90\
HD195019 & 0.98 & 0.136 & 18.3 &0.05 & 3.43\
GJ876 & 0.32 & 0.210 & 60.9 &0.27 & 2.10\
rho CrB & 1.00 & 0.230 & 39.6 &0.11 & 1.10\
HD168443 & 0.84 & 0.277 & 57.9 &0.54 & 5.04\
HD114762 & 0.82 & 0.351 & 84.0 & 0.334 & 11.02\
70 Vir & 1.10 & 0.480 & 116.7 &0.40 & 7.42\
HD210277 & 0.92 & 1.097 & 437. &0.45 & 1.28\
16 Cyg B & 1.00 & 1.61 & 803 &0.69 & 1.67\
47 UMa & 1.03 & 2.09 & 1086 & 0.11 & 2.45\
14 Her & 0.85 & $>$2.50 & $>$2000 &0.36 & 3.35\