SEARCHING FOR EVIDENCE OF PLANET ACCRETION IN RAPIDLY ROTATING K GIANT STARS

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1 SEARCHING FOR EVIDENCE OF PLANET ACCRETION IN RAPIDLY ROTATING K GIANT STARS Joleen K. Miller 1 Advisor: Steven R. Majewski 1 1 Department of Astronomy, University of Virginia, Charlottesville, VA jkm9n@virginia.edu ABSTRACT Rapid rotation in red giant stars may signify a violent past if the unusually large angular momentum was gained through the engulfment of a planetary companion; we explore the feasibility of this spin-up mechanism both theoretically and observationally. By modeling the tidal interaction of known extrasolar planets and their host stars, we have found that many of these exoplanets will indeed be engulfed during future stellar evolution. Furthermore, the orbital angular momentum of these accreted planets is, in some cases, sufficient to cause red giant rapid rotation. Planets accreted during the red giant phase should leave behind a chemical signature in the form of unusual abundance patterns in the host red giant s atmosphere. Proposed signatures of planet accretion include the enhancement of Li and 12 C (which are both depleted in giant stars atmospheres) and a preferential enhancement of elements with higher condensation temperatures (which are thought to be enhanced in planets themselves). We are performing a chemical abundance analysis of both rapidly rotating and normally rotating red giant stars to look for these expected chemical signatures. Our preliminary results show evidence for an enhancement of the average Li abundance in the rapid rotators when compared to the slower rotators. Introduction The inspiration to look for signatures of planet accretion in rapidly rotating K 1 giant stars stems from asking two questions: why is it that a small fraction of red giant stars exhibit large rotational velocities (v sin i>10 km s 1 ) the so-called rapid rotators and what are the consequences for stars that will engulf hot Jupiter companions during the stellar red giant phase? These questions are hardly unconnected because the orbital angular momentum of an orbiting planet, particularly a hot Jupiter, provides a source for extra angular momentum that can be deposited in the stellar envelope. Rapidly rotating red giant stars are an anomaly. Gray (1989) found that the average v sin i for giant stars cooler than G0 is significantly smaller than the v sin i of hotter giants. Gray postulated that these slow rotations were likely the result of efficient magnetic braking in the cooler giants (Gray 1981, 1982). Later work by de Medeiros et al. (1996a) confirms that 1 The spectral designations OBAFGKM indicate temperature from hottest to coolest. Note that the coolest stars (K and M) appear red to the eye, and for reference, the sun s designation is G2. cool giants are slow rotators having a mean v sin i of 2 km s 1, and less than 5% of these stars have v sin i greater than 5 km s 1 (de Medeiros et al. 1996b). Even before the first extrasolar planets were discovered, astronomers recognized that expanding giants could engulf planets and transfer the planet s orbital angular momentum to the stellar envelope (Peterson et al. 1983). The discovery of hot Jupiters lent credence to this hypothesis because they have small enough orbits to be engulfed but are massive enough to be large sources of angular momentum. Using numerical simulations of planet accretion events, Siess & Livio (1999) were the first to list potential observational signatures for such an event, including replenishment of light elements in the stellar atmosphere, IR and X-ray signatures, and increased stellar rotation. The prediction that planet accretion could replenish light elements in giants is significant because there is another group of unusual giant stars that are lithium rich. Lithium and other light elements are destroyed early in the giant phase of stellar evolution, and yet a small fraction of red giants have lithium abundances (specifically, the most common isotope 7 Li) that are Miller 1

2 times the average. Attempts have been made to correlate excess lithium and rapid rotation in red giants, with the idea that planet accretion is the common link between these two unusual phenomena. However, while rapid rotators are more likely to be lithium rich than slow rotators (Drake et al. 2002), it is not a simple 1:1 correlation. Some rapid rotators have normal lithium abundances, and some slow rotators have excessive lithium. Additional evidence is needed to make a case for or against the role of planet accretion in these stars. One way to test planet accretion is to link excess lithium in rapid rotators with an excess of another light element that is normally destroyed in giants, such as B, Be, or 6 Li. Previous work by Reddy et al. (2002) and Balachandran et al. (2000) searched for and found no 6 Li and Castilho et al. (1999) found an underabundance of Be in their respective samples of lithium rich giants. However, it is worth noting that in each of these studies the samples included only 1 or 2 stars. This project differs from these earlier analyses of rapidly rotating and/or lithium rich red giants because it selects large samples of both rapid rotators and slow rotators (as a control sample) to look for multiple signatures of planet accretion simultaneously. In addition to a lithium enhancement, we are looking for evidence of enhancements of 12 C and refractory elements in the atmospheres of rapid rotators, which should also be indicative of planet accretion. Interpretation of these signatures will likely be open for debate for any individual star; however, trends that differ significantly between the two main samples (whose only a priori difference is rotational velocity) should make a much stronger case to either defend or refute the proposition that rapid rotators gain their angular momentum from a former planet. Finally, we have also approached the idea of planet accretion as the mechanism for creating rapid rotators from a theoretical standpoint. We used the database of known extrasolar planets to model the future evolution of their host stars. The goal was to see how many of these stars would accrete their planets during future evolution and become rapid rotators during the red giant phase. The results from this modeling will provide an additional level of context for interpreting the results of the chemical abundance work. This paper is organized as follows in the next section we describe the exoplanet host star modeling together with the results. The following section details the observational side of this project; we describe the selection of the K giant samples and give a more detailed presentation of the chemical signatures of planet accretion. Included are any preliminary results of the chemical signature analysis. Finally we describe our future work and conclusions. Theoretical Modeling This section is a summary of the method and results of the work presented in a paper submitted for publication (Miller et al. 2009) To study the question of future rapid rotator giants, we followed the stellar evolution and star-planet interactions of known exoplanet systems. Stars undergo drastic changes in their physical structure as they evolve; Girardi et al. (2000) provides theoretical evolution tracks of these changes for stars of a given initial mass and metallicity. With these tracks, one can predict the star-planet interactions, which mainly take the form of tidal decay of the planets orbits. Tidal interactions will pull a planet closer to the star as long as the orbital frequency of the planet is greater than the stellar rotation frequency, i.e. Ω p > Ω s. (For Ω p < Ω s, tidal interactions will push the planet outward). The larger orbital frequency of the planet means that tides raised on the star will lag behind the line connecting the centers of the star and planet. Because an alignment of the bulge with the planet is the equilibrium position, the lagging bulge experiences a torque that acts to increase the rotation frequency of the star. However, turbulent friction in the stellar atmosphere resists the torque; energy lost from the friction allows an exchange of angular momentum. As angular momentum is drained from the planet s orbit, the planet moves closer, and the star is spun up. The dissipation rate of energy dictates how quickly angular momentum is exchanged, and we adopt the Zahn (1977) model for turbulent dissipation. Combining this model with tidal orbital decay equations in Verbunt & Phinney (1995) and Zahn (1977) allows us to derive an expression for the radius around the star for which all planets have been accreted, r in. This radius, in units of solar radii, is given by the following equation: r in = ( (1 + 23e2 ) ( M M p M 2 ) I(t)) 1/8 (1) In this equation, M, M p, and M are the masses of the sun, the star, and the planet, respectively, and e is the eccentricity of the planet s orbit. The term I(t) is the integral of time-dependent stellar properties that affect the tidal evolution; it is described by equation (5) of Verbunt & Phinney (1995). The exoplanets are accreted by the host star in our models when r in reaches the semi-major axis of the planet, a p. Figure 1 shows how the accretion radius expands as the star evolves for stellar masses between 0.8 and 1.6 M. Two important evolutionary stages are marked: when Miller 2

3 Extrapolating these numbers to predict the expected fraction of red giant rapid rotators, we find that it still falls short of the fraction observed among present day red giants. In a strict statistical sense, planet accretion can only account for 10-30% of the observed rapid rotators. However, most of the exoplanet host stars that become rapid rotators in our model did so on the lower red giant branch, or in the earliest stages of being a red giant. Combined with the fact that angular momentum dredge-up does not work on the lower red giant branch, this evolution stage is an ideal location to look for planet accretion signatures. Additional details of this work can be found in Miller et al. (2009). Fig. 1. Evolution of r in for stars with masses ranging from M. Yellow points indicate when the star leaves the main sequence, and the red points indicate the base of the red giant branch. the stars leave the main sequence and the beginning of red giant branch evolution. We chose the population of almost 100 main sequence planet-hosting stars as a proxy sample of rapid rotator progenitors (RRPs) and followed the predicted stellar evolution of these stars and the tidal decay of their planets orbits using Equations (1). We find that 90% of the stars will accrete one or more planets, and 36% of the stars will become rapid rotators for at least part of the red giant lifetime. These latter stars are therefore RRPs. Figure 2 shows M p and a p for the exoplanets included in our study. The different symbols encode whether the planet is accreted or survives and whether the host star is a RRP. Fig. 2. The masses and semi-major axes of exoplanets that survive (squares), that are accreted (triangles), and that orbit a RRP (circles). Because some planets are in multiple systems, a planet that will survive might still orbit a RRP. Chemical Abundance Analysis In the last section, we described how the accretion of planets can provide enough angular momentum to spin-up giant stars. In this section, we describe our observational experiment to look for remnant chemical abundance anomalies of rapid rotator giants that would indicate the past accretion of a planet. Light elements such as Li, B, and Be are normally destroyed by stellar evolution as are certain isotopes of heavier elements. For example, 12 C is preferentially destroyed over 13 C. Accretion of planets can replenish the elements that were destroyed, and the latter can be observed as a change in the isotopic ratio in the stellar atmosphere. In addition, the relative abundance of elements in a planet are affected by the planet forming environment giving planets a distinctive abundance pattern called chemical fractionation, which may be detectable in the surface abundances of a star that accreted a planet. In the following subsections, we describe the creation and observation of a sample of K giant stars, and we give a more detailed description of the three chemical abundance signatures lithium enhancement, enhanced carbon ratio, and chemical fractionation we will look for in the K giant sample. The K Giant Sample The chemical signatures we intend to measure require having high signal-to-noise (S/N) spectra at high resolution, and we required a priori knowledge of the rotational velocities of the stars. Therefore, we began the sample selection by first measuring rotational velocities of K giants in the database of giant candidates for the Astrometric Grid of NASA s Space Interferometry Mission (SIM). The Astrometric Grid candidate stars include both K giants from the Tycho catalog and K giants identified with the Grid Giant Star Survey (GGSS), a partially-filled all-sky survey dedicated to finding suitable Astrometric Grid candidates (Patterson et al. 2001). Stellar parameters for these stars are given by Miller 3

4 Bizyaev et al. (2006), and Bizyaev provided us with the reduced echelle 2 spectra of these stars. Using the high-resolution Arcturus spectrum of Hinkle et al. (2000) as a template, we cross-correlated each echelle order of the base sample spectra with the template and analyzed the widths of the cross-correlation peaks to get a measure of the stellar projected rotational velocity. Using all the echelle orders for each star gives independent measurements of v sin i and thus a measure of the uncertainty. Stars with a large standard deviation in the mean of v sin i or for which the crosscorrelation indicated a significant mismatch between the object and template (see description of Tonry- Davis Ratio; Tonry & Davis 1979) were flagged as being possibly unreliable. Rapid rotators in this sample were defined to be those stars with v sin i>10 km s 1. The results of this analysis are presented in Figure 3, which shows the derived rotational velocity of the Astrometric Grid stars as a function of the stellar temperature measured from photometry. Fig. 3. Projected rotational velocity as a function of temperature for the Astrometric Grid Stars. Points, squares, and x s represent slow rotators (v sin i < 10 km s 1 ), rapid rotators (v sin i 10 km s 1 ), and flagged stars, respectively. Arrows indicate upper limits. Out of the 1297 stars in the sample, 28 were identified as rapid rotators; an additional 48 stars meet the v sin i requirement, but where flagged. All rapid rotators and a matched set of control stars, i.e., slow rotators with the same range of temperature and metallicity, were selected for follow-up observations with. 2 Echelle spectrograph configurations use a cross-disperser to stack adjacent orders, or segments of the stellar spectra, on the CCD chip. The result is that the 2-D CCD chip records a stack of orders with roughly continuous wavelength coverage; the beginning wavelength of one order is roughly at the ending wavelength of the previous order. Additional known rapid rotators and control stars were added from the literature to increase the sample size. These stars are generally brighter and were selected from a catalog of giant stars of de Medeiros et al. (2006), which lists the measured rotational velocity, spectral type, luminosity class, and whether the star is a suspected binary. All de Medeiros et al. (2006) rapid rotators visible from the northern hemisphere that were not suspected binaries and had a spectral type of G9- K9 III were added to the sample. Our sample is confined to K giant spectral types mainly because of the availability of a large database of the K giant spectroscopy taken for the SIM program from which we identified rapid rotators. This selection, however, also has scientific merit because constraining the spectral type simultaneously constrains physical stellar parameters, which will lessen the uncertainties of comparing stars at different evolutionary stages. The original echelle spectra from which rotational velocities were derived had low enough S/N to render them unsuitable for detailed chemical abundance work. We therefore obtained high-resolution, high S/N (> 100 per pixel) spectra for over 100 stars in our K giant sample covering a wide range in rotation speed (v sin i 1-31 km s 1 ) using the echelle spectrographs on the Kitt Peak 4-m Mayall and the Apache Point 3.5- m telescopes; these spectrographs have resolutions of 43,000 and 31,500, respectively. The sample observed with these instruments includes 33 rapid rotators, 19 stars with enhanced rotation (v sin i between 7 and 10 km s 1 ), 49 control stars, 10 giant stars with known planetary companions, and 17 standard stars. The standard star group is a sample of stars with published values of, for example, the Li or 12 C/ 13 C abundances with which we can compare our measurements as a check. Lithium Enhancement One well known consequence of stellar evolution is the destruction of light elements that occurs when the convective envelope of the star deepens during the first dredge-up. In the literature, an abundance of log ɛ(li) 1.5 is considered an excess in giant stars. Ingested planets could replenish the surface lithium abundance. In spectra from our March 2007 Kitt Peak observing run, a deep lithium absorption line can often be seen by eye, and this occurs mainly in rapid rotators. Using the stellar line analysis program MOOG (Sneden 1973), we derived the lithium abundance, N(Li), in the stars from this run. Figure 4 is a plot of N(Li) as a function of v sin i for both the stars observed by us in 2007 and a selection of slow rotators and rapid rotators from the literature as indicated by the different symbols. Although there is significant variation in Miller 4

5 Fig. 4. A measure of the lithium abundance (N(Li)) as a function of rotational velocity for two samples: K giants observed in 2007 for this work and a sample garnered from the literature (de Medeiros et al. 2000; Drake et al. 2002). The vertical line denotes the canonical separation between rapid rotators and slow rotators. The horizontal lines indicate the average lithium abundances for the slow rotators (dashed) and rapid rotators (dot dashed). the lithium abundances, there are two intriguing differences between the rapid and slow rotators. First, the average lithium abundance in the slow rotator sample is smaller than the average in the rapid rotator samples. Second, there almost no rapid rotators with lithium abundances less than the average value of the slow rotators. These results hint to global enhancement of lithium in rapid rotators compared to slow rotators. However, we consider these results preliminary because we used estimates of the stellar parameters instead of deriving them ourselves. The discrepancies of the [Fe/H] estimates compared to the iron abundance needed to fit the iron line near the lithium line was enough of a concern to dissuade us from formally publishing these intriguing results. We intend to improve these measurements by self-consistently deriving the iron abundance. Adding the rest of the stars from our observing runs should solidify the apparent trend. Lithium enhancement in rapid rotators, however, is not necessarily indicative of planet accretion. Sackmann & Boothroyd (1999) argue that lithium can be regenerated in giant stars by an entirely different process. During the later stages of red giant branch evolution, lithium may be regenerated via the Cameron- Fowler mechanism, shown in Eqs. 2-4, 3 He + 4 He 7 Be + γ (2) 7 Be + e 7 Li + ν (3) 7 Li + 1 H 4 He + 4 He (4) Fig. 5. Illustration of the increase in 12 C/ 13 C as a function of accreted planet mass for a 1M star with an initial surface carbon ratio of 20. The planet s carbon ratio is 90 and has a composition similar to Jupiter. The colored lines indicate different envelope mass fractions ranging from 0.1 (reddest) to 0.9 (bluest) in steps of 0.1. However, appropriate conditions for this nuclear chain only exist beyond the red bump stage the stage where the hydrogen burning shell reaches the mean molecular weight discontinuity left behind at the deepest point reached by the convective envelope during first dredge-up. Therefore, accurate stellar parameters combined with stellar evolution codes are needed to determine which stars in the sample have evolved beyond this point to distinguish excess lithium consistent with only planet accretion from those also consistent with lithium reproduction. Also, the Cameron-Fowler mechanism only replenishes the most common isotope of lithium, 7 Li. In stars bright enough to obtain very high S/N spectra (S/N > 400), the component of lithium lines due to the less abundant 6 Li is theoretically measurable. The presence of 6 Li at any point of red giant evolution is indicative of an outside source of replenishment, such as planet ingestion. Enhanced Carbon Ratio In addition to lithium destruction, the deep mixing of first dredge-up also preferentially destroys 12 C causing the surface carbon ratio, 12 C/ 13 C, to drop from the meteoritic value of 90 down to Planets have a carbon ratio of 90 and, for accreted planets larger than 10M Jup, can raise the surface abundance of the star by a considerable degree. Figure 5 shows the effect that different planet masses have on the stellar surface carbon ratio as a function of accreted planetary mass. The colored lines indicate different mass fractions of the stellar envelope ranging from 0.1 (red) to Miller 5

6 0.9 (blue). Planets more massive than 10M Jup will raise the ratio by 10% or more regardless of the envelope mass. For stars with smaller envelopes, planets with masses a few times that of Jupiter can also have a measurable effect. The carbon ratio in the stellar sample will be measured from the lines in the rotational bands of 12 CN and 13 CN between Å. Recently, Eggleton et al. (2007) published the predicted carbon ratio of low mass giant stars for different initial metallicities. These models will help determine the predicted ratio for each star. Chemical Fractionation Planets form in an environment that is irradiated by the light of the developing parent proto-star. In the inner disk, temperatures are hot enough to evaporate volatile elements leaving behind proportionally larger abundances of refractory elements elements with higher condensation (and hence evaporation) temperatures. Material that shows a trend of increased abundance with an increase in condensation temperature is known as chemically fractionated, and the slope of this trend is referred to as the T c -slope. Planets that form from chemically fractionated material will likewise show this trend. Figure 6 shows a plot of the abundances of a range of elements for the star HD19994 as a function of the elements condensation temperatures (data from Smith et al. 2001) to illustrate how one measures the T c -slope. Previous studies (Smith et al. 2001; Edvardsson et al. 1993; Gonzalez et al. 2001) have examined the trend of T c -slope as a function of stellar metallicity, and they have identified a baseline trend of T c -slope vs. [Fe/H] that is mainly due to the increase of [O/Fe] over successive episodes of chemical enrichment from the stellar life-death cycle. If an accreted planet is massive enough, the chemical fractionation trend should be visible on top of the baseline galactic abundance trend. We will measure the T c -slope for each star in my sample and plot the slope as a function of [Fe/H] and compare it to the galactic trend. If rapid rotators did indeed accrete planets, we expect them to lie higher than the galactic trend while the control stars should lie on the trend. Future Work & Conclusions The chemical abundances analysis is presently at the stage where stellar parameters are being measured. These parameters include the effective temperature, surface gravity, metallicity, and microturbulence of the stellar atmosphere. Deriving these parameters with high precision is time intensive but essential to the Fig. 6. An example of measuring T c -slope with data for the star HD19994 (Smith et al. 2001). Each point is an individual element. The dashed line is a linear fit to the trend and is the T c -slope for this star. project. First, it allows us to estimate the evolutionary stage of the stars. Next, accurate temperatures and gravities are needed for an accurate conversion from strengths of spectral lines to the abundance of the elements responsible for those lines. Once stellar parameters are measured, we will begin measuring abundances of the various elements required for the three chemical tests described in this paper. In conclusion, this study was motivated by the question of whether the phenomenon of rapidly rotating red giant stars can be explained solely by spin-up from the accretion of planets. We approach this question from both a theoretical and observational standpoint. Using main sequence planet-hosting stars as a proxy sample of red giant rapid rotator progenitors, we predicted that rapid rotators can indeed to be created by the accretion of a planetary companion. However, the expected frequency of rapid rotators from these models falls short of the frequency of rapid rotation seen in present day giants. To further study the role of planet accretion, we have observed a sample of rapidly rotating and slow rotating giants with the aim of finding chemical abundance signatures that point to planet accretion in the rapid rotators. REFERENCES Balachandran, S. C., Fekel, F. C., Henry, G. W., & Uitenbroek, H. 2000, ApJ, 542, 978 Bizyaev, D., Smith, V. V., Arenas, J., Geisler, D., Majewski, S. R., Patterson, R. J., Cunha, K., Del Pardo, C., Suntzeff, N. B., & Gieren, W. 2006, AJ, 131, 1784 Miller 6

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