The Accelerating Pace of Star Formation
MMNRAS , 1–7 (2017) Preprint 22 September 2018 Compiled using MNRAS L A TEX style file v3.0
The Accelerating Pace of Star Formation
Spencer Caldwell (cid:63) and Philip Chang Department of Physics, University of Wisconsin-Milwaukee, 3135 North Maryland Ave., Milwaukee, Wisconsin 53211, USA
22 September 2018
ABSTRACT
We study the temporal and spatial distribution of star formation rates in four well-studied star-forming regions in local molecular clouds(MCs): Taurus, Perseus, ρ Ophi-uchi, and Orion A. Using published mass and age estimates for young stellar objectsin each system, we show that the rate of star formation over the last 10 Myrs hasbeen accelerating and is (roughly) consistent with a t power law. This is in line withprevious studies of the star formation history of molecular clouds and with recent the-oretical studies. We further study the clustering of star formation in the Orion NebulaCluster(ONC). We examine the distribution of young stellar objects as a function oftheir age by computing an effective half-light radius for these young stars subdividedinto age bins. We show that the distribution of young stellar objects is broadly consis-tent with the star formation being entirely localized within the central region. We alsofind a slow radial expansion of the newly formed stars at a velocity of v = .
17 km s − ,which is roughly the sound speed of the cold molecular gas. This strongly suggests thedense structures that form stars persist much longer than the local dynamical time.We argue that this structure is quasi-static in nature and is likely the result of thedensity profile approaching an attractor solution as suggested by recent analytic andnumerical analysis. Key words: galaxies: star clusters: general – galaxies: star clusters: individual –galaxies: star formation – stars: formation
Per free-fall time, the mean star formation efficiency (SFE),the total mass of stars formed, in galaxies is of the orderof a few percent and follows from the well characterizedKennicutt-Schmidt (KS) relations (Kennicutt 1989, 1998)on galactic disk scales: (cid:219) Σ ∗ = η ΩΣ gas , (1)where (cid:219) Σ ∗ is the surface density of star formation, Σ gas is thetotal surface density of gas, Ω = v c / R d is the disk dynamicaltime, and η ≈ . is a dimensionless parameter that hasan observationally determined value.On smaller scales, ranging from ∼ (Schruba et al.2010) in nearby galaxies, to ∼
100 pc in the Milky Way(Mooney & Solomon 1988; Mead et al. 1990; Evans 1991;Lada et al. 2010; Murray 2011; Lee et al. 2016), the simpleKS relation breaks down. Here, these studies find relationssimilar in form to Equation (1), but the dispersion of η ap-pears to vary with the scale on which the star formation isprobed: measured values range from η < − to η ≈ . .What is responsible for the overall low efficiency of star (cid:63) E-mail: [email protected] formation on large scales and the large dispersion in η onsmall scales? Theoretical explanations for the low rate ofstar formation either invoke small scale physics, includingmagnetic fields (Mouschovias 1976; Shu 1983) or supersonicturbulence (Padoan 1995; Krumholz & McKee 2005), or in-voke large scale effects, including energy and momentumfeedback from massive stars (Murray et al. 2010). The vari-ation of the star formation rate then arises from variationsin the properties of molecular clouds, but it is presumedthat equation (1) continues to hold, i.e., the star formationefficiency is linear in time.Recent theoretical (Hartmann et al. 2012; Zamora-Avil´es et al. 2012; Myers et al. 2014; Gong & Ostriker2015; Lee et al. 2015; Murray & Chang 2015; Murray et al.2017b,a) work of the physics of star formation in turbulentmolecular clouds suggests that the KS relation (eq.[1]) thatis applicable on galactic scales is not merely scaled down forsmall scales. Here rather than a linearly increasing SFE withtime, the SFE appears to accelerate in time. This accelera-tion has been explained either by global collapse of the cloud(Hartmann et al. 2012; Zamora-Avil´es et al. 2012; V´azquez-Semadeni et al. 2017) or is the result of self-gravitationalcollapse of turbulent gas where the action of gravitationalcollapse feeds back on the turbulence providing some lim- © a r X i v : . [ a s t r o - ph . GA ] N ov Caldwell & Chang ited turbulent support against collapse (Murray & Chang2015; Murray et al. 2017b,a). In particular, Murray & Chang(2015) showed that the density in collapsing turbulent gasapproaches a fixed asymptotic profile while the velocity pro-file assumes a Keplerian profile, i.e., v ∝ M / r − / near thestar giving rise to a mass accretion rate that scales like t and hence a SFE that scales like t . By suggesting an accel-erating rate of star formation, these results echo an earlierobservational result by Palla & Stahler (1999, 2000, 2002).In this paper, we re-examine the results of Palla &Stahler (1999, 2000, 2002) in light of recent theoretical re-sults (Lee et al. 2015; Murray & Chang 2015). We examineknown stellar populations of Orion A, Taurus, ρ Ophiuchi,and Perseus. These four were chosen because of their well-studied stellar populations and availability of high qualityobservations.We organize the paper as follows. We briefly describeour methodology in § § § § § We focus on four star-forming complexes in this work: OrionA, ρ Ophiuchi, Taurus, and Perseus. Published values of themasses and ages of young stellar objects in these complexeswere obtained and analyzed to study the temporal and spa-tial distribution of star formation. The ages of stars weredetermined from the fitting of the observed luminosity andtemperature to pre-main sequence models, but this fittingis subject to uncertainties. For instance, deuterium abun-dance, accretion rate, and accretion geometry influence the”birth line” on the H-R diagram Tan et al. (2006). Fortu-nately the birth-line mostly affects just < Myr ages, anddoes not alter the results dramatically. The free-fall timeused to determine the dynamical time of these complexeswas obtained through the work done by Lada et al. (2010).This estimate of the density assumes that the clouds arespherical and may be an overestimate because not all cloudsare spherical (Krumholz et al. 2012).
We first focus on the temporal distribution of star forma-tion in Orion, Taurus-Auriga, Perseus, and ρ Ophiuchi. TheOrion A molecular cloud is a substantial source of stellaractivity due to the number of nebulae contributing to starformation; the most well-studied being the Orion NebulaCluster. Orion A is approximately 400 pc away Schlafly et al.(2014) and has a diameter of roughly 40 pc Da Rio et al.(2016). Orion A has a large stellar density of × / pc Palla & Stahler (1999). The total mass of the molecular gasin the cloud is 67,714 M (cid:12) Lada et al. (2010).Da Rio et al. (2016) obtained data on 2691 stars inthe Orion A Molecular Cloud. We matched the data withconfirmed members from da Rio et al. (2016), yielding 2092
Table 1.
Parameters and Power Law Fit indices of Orion A,Taurus, ρ Ophiuchi, and Perseus.Name t ff (Myr) α a α b α c ReferencesOrion A 9.07 1.79 2.31 3.31 [1]Taurus 6.22 1.19 1.94 1.31 [2] ρ Ophiuchi 6.13 1.09 2.55 1.52 [3]Perseus 6.55 1.31 2.11 3.96 [4] a t = t ff , b t = t ff , c t = t ff [1] Da Rio et al. (2016) [2] K¨u¸c¨uk & Akkaya (2010)[3] Erickson et al. (2011) [4] Azimlu et al. (2015) stars. Using the published mass and ages of these stars (DaRio et al. 2016) that were obtained using the evolutionarymodel of Siess et al. (2000), we plot the SFE in the ONC asa function of time in Figure 1(a) and find a power-law fit of t . .K¨u¸c¨uk & Akkaya (2010) provided mass and age esti-mations on 78 young, low-mass stellar objects (class 1 toclass 3 sources) that were used to determine the star for-mation rate in the Taurus-Auriga complex. Taurus is ap-proximately 140 pc away Ungerechts & Thaddeus (1987)and has roughly a 30 pc diameter Palla & Stahler (2002).The cumulative mass of the molecular cloud constituents is14,964 M (cid:12) Lada et al. (2010). Far-infrared observations ofthese stars provided their spectral properties used for ouranalysis. The mass and age of the 78 young stellar objectsmembers were calculated using the evolutionary model ofK¨u¸c¨uk et al. (1998). The mass and age estimates predictedby this evolutionary model were then plotted to show anincreasing rate of star formation with a t . power law asseen in Figure 1(b).Azimlu et al. (2015) gave age and mass estimates for 341stars in Perseus, which is located around 300 pc from the sunAzimlu et al. (2015) and has a cloud diameter of roughly 50pc Bally et al. (2008). The total mass of the cloud is approx-imately 18,438 M (cid:12) Lada et al. (2010). A WISE(Wide-FieldInfrared Survey Explorer) survey was performed to identifyyoung stellar objects in the Perseus complex and they alsocross-matched the candidates with the SIMBAD database toobtain known young stellar objects Azimlu et al. (2015). Theages and masses were given using the evolutionary model ofSiess et al. (2000). The star formation is accelerating with a t . power law shown in Figure 1(c).Erickson et al. (2011) offered mass and age estimates for132 members of the stellar population of ρ Ophiuchi, whichis approximately a distance 130 pc from the sun Ericksonet al. (2011) making it one of the closest star-forming MCsin our solar system. The total mass of the cloud was found tobe approximately 14,165 M (cid:12) Lada et al. (2010). The multi-fiber spectrograph Hydra was utilized in obtaining spectrafor the various members. R- and I-band photometry wereobtained with the 0.6m Curtis-Schmidt telescope to deriveeffective temperatures and bolometric luminosities for thestellar members. The data obtained was compared with theevolutionary model of D’Antona & Mazzitelli (1997) to ob-tain the mass and age estimates seen in Figure 1(d). Theplot shows that the evolution in the ρ Ophiuchi cloud isproducing stars at a rate of t . .For the four molecular clouds discussed above, the SFEis superlinear as seen in Figure 1. This is the case for both MNRAS , 1–7 (2017) he Accelerating Pace of Star Formation log ( t − t ) l og ( M ∗ ) , l og ( N ∗ ) N ∗ M ∗ t α , α = 2 . (a) Orion A log ( t − t ) l og ( M ∗ ) , l og ( N ∗ ) N ∗ M ∗ t α , α = 1 . (b) Taurus log ( t − t ) l og ( M ∗ ) , l og ( N ∗ ) N ∗ M ∗ t α , α = 2 . (c) Perseus log ( t − t ) l og ( M ∗ ) , l og ( N ∗ ) N ∗ M ∗ t α , α = 2 . (d) ρ Ophiuchi
Figure 1.
Total young stellar mass (red solid lines) and number of stars (blue dashed lines) formed since t in Orion A (a), Taurus (b),Perseus (c), and ρ Ophiuchi (d). Here t = t ff in these plots. Power law fits with time, t , are shown as a thin green dotted line and arefitted over the entire age range with the index given by α , which ranges from ∼ − . . Table 2.
Effective half-light radii of young stars in the ONC ofvarious age binsAge range(Myr) r eff (pc) Number of Stars t age < < t age < < t age < < t age < number (dashed line) and total mass (solid line) of stars.The fit of the SFE from the t = t points is consistent witha power law of ∼ t . This is suggestive of the observed t SFE in numerical simulations (Myers et al. 2014; Lee et al.2015; Gong & Ostriker 2015; Murray et al. 2017b,a) andfound in analytic models of turbulent collapse (Murray &Chang 2015). This is in line with previous work by Palla &Stahler (2000), who found that star formation in the ONCand other molecular clouds such as Taurus-Auriga, Lupus,Chamaeleon, ρ Ophiuchi, Upper Scorpius, IC 348, and NGC 2264 have been accelerating with time, though they did notattempt to deduce the rate of acceleration. Notably they ar-gued that the collapse of dense independent clusters wouldnot produce the observed SFE. They instead argued thatthis acceleration can only be the result of a global process,which they attributed to global collapse. Our quantificationof this collapse and its association with a t power law sug-gests that the turbulent (global) collapse of gas onto smallstar-forming regions is responsible for the observed acceler-ation. Having examined the history of star formation in these MCs,we now examine the spatial distribution of star formation.Of the four star-forming regions that we studied, only theONC provides the combination of sufficient statistics andcompactness to make definitive statements. The other star-forming regions that we have studied have low statistics by
MNRAS , 1–7 (2017)
Caldwell & Chang
Distance x (pc) D i s t a n c e y ( p c ) % % % Figure 2.
Positions of all the young stars within 2 pc (projected)of the center of the ONC, smooth density map, and contours thatenclose 25%. 50%, and 75% of the total light from the ONC.Note the central concentration of the stars as evident from theirposition, peak of the smoothed intensity map, and contours. comparison or have a star formation spread over a large area.We will discuss these other regions in § t age < . (plot a), . < t age < (plot b), < t age < (plot c), and < t age < (plot d), where the ages are in Myrs. It is clearthat younger stars are more concentrated toward the center.To quantify this, we note that the 50% contour defines aregion that contains half of the light. We compute the areaenclosed by this 50% contour, A , and define an effectivehalf-light radius, r eff , by π r = A , (2)and list them in Table 2. The results of Figure 3 and theeffective radii computed in Table 2 show that younger starsare more centrally concentrated. In addition, the differentage bins all share a common center. This is consistent withstars forming in the center of the ONC, which then migrateoutward as they age. Moreover, this centralized star forma-tion region has persisted for at least Myrs, which is overan order of magnitude longer than the central free-fall timeof . Myrs (Tan et al. 2006). This strongly suggests that,at least for the ONC, stars form in structures that persistover many local free-fall times.In addition, stars appear to move outward as they age.We can estimate the rate of this motion from the rate atwhich the effective radius moves outward. This outward mo-tion can be due to diffusion or the stars having some initial velocity. The effect of diffusion is expected to be small as therelaxation time (Binney & Tremaine 2008) is much longerthan the timescale of interest, i.e., t relax ≈ . N stars ln Γ t cross ≈ (cid:18) N stars (cid:19) (cid:18) t cross . (cid:19) Myrs , (3)where N stars is the number of stars in the cluster, t cross is thecrossing time, and ln Γ is the Coulomb logarithm, which istaken to be order unity. Here, we take N stars to be the numberof stars in the central region, i.e., the centrally concentratedstars with t age < . Myrs. We use the Tan et al. (2006) valuefor the crossing time of t dyn of × yrs for the ONC, i.e.,twice the free fall time.In Figure 4, we plot the effective half-light radius r eff asa function of time, t , for the mean ages of the the stars ineach bin as in Figure 3. We fit r eff ( t ) with a linear expansionof the form, r eff = r + v eff t , (4)where r is the initial radius of the star cluster and v eff is theeffective expansion velocity. The fits reveal that r = . pcand the expansion velocity is 0.17 km s − . Equation (4) andFigure 4 implies that the stars that form in the ONC overthe past 2.5 Myrs formed around a common center and ifthis region of formation was fixed with an initial size of r that the stars that form there are migrating outward withan average speed of v eff . This velocity is much lower thanthe typical turbulent velocity ( v ∼ − ), which suggeststhat star formation occurs in a region of converging flowsand forms dynamically cold stars. Coupled with the factthat the region that forms these stars over 2.5 Myrs is thesame, it also suggests that structure that formed these starsis quasi-static. The results of this paper is summarized as follows:(i) Star formation is accelerating in MCs. This is in linewith an older observational result (Palla & Stahler 1999,2000, 2002) and with more recent theoretical results (Myerset al. 2014; Lee et al. 2015; Murray & Chang 2015; Mur-ray et al. 2017b,a). Other groups have also argued for somesort of acceleration to explain the large spread in protostel-lar ages (Hartmann et al. 2012; Zamora-Avil´es et al. 2012;V´azquez-Semadeni et al. 2017).(ii) The SFE is superlinear. For t (cid:38) t ff , a superlinearSFE is evident. There is some evidence that it follows a t power law, but this depends on how the initial time t isdefined.(iii) The star formation in the ONC over the last 5 Myrsis centrally concentrated. When the stars are divided up intodifferent age bins, they are all concentrated to within about0.5 pc. Moreover, when distribution of stars broaden withgreater age, they can be modeled as a linear expansion withan effective velocity of 0.17 km s − .The global acceleration of star formation (point i) mustbe attributed to a global process. Previously, Palla & Stahler(2000) argued for global collapse, but such a process wouldproduce stars everywhere as the dense pockets that collapseand form stars would vanish in one local dynamical time. MNRAS , 1–7 (2017) he Accelerating Pace of Star Formation Distance x (pc) D i s t a n c e y ( p c ) % % % (a) t age < Distance x (pc) D i s t a n c e y ( p c ) % % % (b) 0.5 < t age < Distance x (pc) D i s t a n c e y ( p c ) % % % (c) 1.0 < t age < Distance x (pc) D i s t a n c e y ( p c ) % % % (d) 2.0 < t age < Figure 3.
Smoothed stellar density maps and contours for young stars in the ONC in different age bins. The density maps are producedusing a gaussian smoothing kernel of stellar distribution in different age bins. The contours are traced at 25%, 50% and 75% of the totallight. Note that the spatial distribution broadens as the stars age, a fact that is confirmed from calculating the effective half-light radiusfor the different bins. t age in Myrs. Hence, while most of the young stars would appear clustered,this would be attributed to having the most recent round ofcollapse produce most of the stars. The turbulent collapsemodel of Murray & Chang (2015) would naturally explainthe origin of SFE ∝ t (point ii), but as mentioned this issomewhat sensitive to the definition of t . Notably this is alsoa problem for simulations (Myers et al. 2014; Lee et al. 2015;Gong & Ostriker 2015; Murray & Chang 2015; Murray et al.2017b,a), but here the definition is easier as the formationof the first star in a simulation is a measurable quantity.We note that several other lines of observational ev-idence suggest that the star formation rate of molecularclouds accelerate in time. For instance, it has been noted byMooney & Solomon (1988) that there exists a large spread(by a factor of about 300) in the star formation rate amongmolecular clouds in our galaxy. This has been confirmed bymore recent measurements (Evans et al. 2009; Lada et al.2010; Murray 2011; Lee et al. 2016). Krumholz et al. (2012)attributed this disparity to variations in the local free-fall time in clouds, but Evans et al. (2014) found that a largedispersion in the star formation rate still exists even afteraccounting for the variation in local free-fall times.Murray & Chang (2012) suggested that a time vari-able, i.e., accelerating, star formation rate could account forthe observed scatter. This suggestion drove much of the nu-merical Myers et al. (2014); Lee et al. (2015); Murray et al.(2017b,a) and analytic Murray & Chang (2015) work on starformation in turbulent collapsing molecular clouds. Obser-vationally, Lee et al. (2016) cross-correlated the molecularcloud catalog produced by Miville-Deschˆenes et al. (2017)with the star-forming complexes catalog produced by Leeet al. (2012) and showed that the dispersion of the star for-mation rate varies over 3-4 orders of magnitude (much largerthan Mooney & Solomon 1988). More importantly, they ex-amined many different models to produce these large dis-persions and found that a star-forming efficiency of t (evenlarger than the t star-forming efficiencies found in simula-tions) best explains the large variation. MNRAS , 1–7 (2017)
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Stellar Bin Age (Myr) r e ff ( p c ) r = 0 . pc v eff = 0 . km/s Figure 4.
Effective half light radius (blue dots) as a functionof age bin for young stars in the ONC. Shown as a thin dottedline is a linear fit given by equation (4) with r = . pc and v eff = .
17 km s − which is similar to the sound speed and muchlower than the turbulent velocity. The observation that old and young star formation oc-curs in the same region in the ONC does bolster the tur-bulent collapse model. Here, the model of Murray & Chang(2015) predicts that as the density approaches an attractorsolution, dense collapsing regions in a turbulent medium canpersist for many local dynamical times. Hence all the starformation would occur in a concentrated well-defined regionas opposed to many different regions. By examining the clus-tering of stars as a function of age, we have shown that allthe stars are centrally concentrated to within about 0.5 pcand that this region is expanding slowly with an effectiveexpansion velocity similar to the cold gas sound speed. Notethat this is different from a global collapse model which doesnot prescribe how the forming stars are distributed in thethe molecular cloud. In this case, it would be expected thatdense star-forming regions do not persist for many local dy-namical times and so stars of different ages would clusterdifferently.We should note that point (ii) does not strictly en-dorse the model of Murray & Chang (2015). For instance,Tan et al. (2006) argued that the rate of star formation indense gas should be slow and thus this dense gas can persistfor many dynamical times. How these structures remain inquasi-equilibrium, however, is unclear in this case. Moreover,this picture would presume that the rate of star formationremains constant in contrast with the observed acceleration.However, coupling this quasi-equilibrium gas with some formof global collapse may provide the observed acceleration.Other models of time-varying star formationare also present in literature and fall either underthe aegis of global gravitational collapse (Hartmannet al. 2012; Zamora-Avil´es et al. 2012; V´azquez-Semadeni et al. 2017) or quasi-static evolution(Palla & Stahler 1999, 2000; Huff & Stahler 2006, 2007).For instance, Huff & Stahler (2006, 2007) explored asimplified quasi-equilibrium model of the ONC by modelingit as a collapsing isothermal sphere supported by turbulentpressure and applied the Schmidt law as their model for star formation. This quasi-equilibrium model does accountfor much of the observed acceleration and the balance be-tween turbulent pressure and self-gravity and can producequasi-equilibrium dense structures, but it assumes thatmolecular clouds begin in equilibrium, which is unclear ifthey do.Hartmann et al. (2012) have argued using numericalsimulations that the existence of > − Myr old stars innearby molecular clouds is consistent with rapid evolution(i.e., collapse) of a molecular cloud over a few Myrs. Simi-larly, Zamora-Avil´es et al. (2012) argue on a semi-analyticalbasis that the global collapse of molecular clouds sets aninitially slow star formation rate that accelerates in time.Murray & Chang (2015) is fully consistent with both state-ments as timescale of the collapse is set by the mean densityof the cloud. The difference is that our theory links the lo-cal density and structure velocity of collapsing regions withthe SFE and makes a somewhat different prediction for thetime dependence compared to Zamora-Avil´es et al. (2012).Although, in the regime for which comparison to numericalsimulations is possible, the predictions are similar. In addi-tion, the regions of star formation may not be constant, butrather can differ in different epochs, though if the cloud isnaturally centrally concentrated, the regions of star forma-tion would also be centrally concentrated (Hartmann et al.2012).In the case of the ONC discussed in § ρ Ophiuchi, and Tau-rus. In our maps (not shown) of Perseus and ρ Ophiuchi,the regions of star formation remain localized across dif-ferent age bins. For the case of Perseus, the regions of starformation are not centrally concentrated and are spread over ∼ pc. For ρ Ophiuchi, the regions of star formation areconcentrated in a regions of ∼ pc, but the statistics aremuch poorer than for the ONC. We studied the history of star formation in four MCs: Tau-rus, Perseus, Orion A, and ρ Ophiuchi. By using publishedmass and age estimates for each MC, we were able to recon-struct the history of star formation in each cloud in a mannersimilar to Palla & Stahler (1999, 2000, 2002). In agreementwith their results, we found that the star formation rate overthe last 10 Myrs has been accelerating. We also find that thestar-forming efficiency is broadly consistent with a superlin-ear star formation rate and some evidence that it followsa t (quadratic in time) power law in line with recent an-alytic and numerical studies (Myers et al. 2014; Lee et al.2015; Gong & Ostriker 2015; Murray & Chang 2015; Murrayet al. 2017b,a). In particular, the analytic turbulent collapsemodel of Murray & Chang (2015) naturally produces a t power law because the density profile around collapsing re-gions approach an attractor solution and the infall velocityis proportional to √ M ∗ , where M ∗ is the mass of the centralstar or star cluster.Because the density approaches an attractor solution,structures in collapsing regions can persist for far longerthan their local dynamical times (Murray & Chang 2015; MNRAS , 1–7 (2017) he Accelerating Pace of Star Formation see also the simulations of Murray et al. 2017b). To exam-ine this possibility, we then studied the spatial distributionof star formation in the ONC and found that the the stel-lar density of stars in different age bins all peak toward acommon center, but the distribution broadens with increas-ing age. The central region of star formation has persistedfor at least 5 Myrs, which is at least an order of magnitudelonger than the local free-fall time. We computed an effectivehalf-light radius, r eff , for each age bin and found that thisradii can be modeled as a linear expansion with time withan effective radial expansion velocity of v eff ≈ .
17 km s − ,which is roughly the sound speed of the cold molecular gas.The spatial distribution of the young stars suggest that theyare formed in centrally concentrated regions that persist formany local dynamical times.The global acceleration of the star formation rate hasbeen noted by a number of workers previously observation-ally (Palla & Stahler 2000; Lee et al. 2016). The fact thatthe star formation efficiency scales like t and appears tohave a common center for all the young stars independentof their ages suggests that some form of turbulent collapselike that proposed by Murray & Chang (2015) may be re-sponsible though as we noted competing models (Huff &Stahler 2006; Tan et al. 2006; Huff & Stahler 2007; Hart-mann et al. 2012; Zamora-Avil´es et al. 2012) may also beoperating. ACKNOWLEDGMENTS
We thank the anonymous reviewer for constructive com-ments. SC is supported in part by the Office of Undergradu-ate Research at the University of Wisconsin-Milwaukee. PCis supported in part by the NASA ATP program throughNASA grant NNX13AH43G, NSF grant AST-1255469, andthe University of Wisconsin-Milwaukee.
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