Using a new catalog of 824 solar and late-type stars with X-ray luminosities
and rotation periods we have studied the relationship between rotation and
stellar activity. From an unbiased subset of this sample the power law slope of
the unsaturated regime, $L_X/L_{bol}\propto Ro^\beta$, is fit as
$\beta=-2.70\pm0.13$. This is inconsistent with the canonical $\beta=-2$ slope
to a confidence of 5$\sigma$ and argues for an interface-type dynamo.
Super-saturation is observed for the fastest rotators in our sample and its
parametric dependencies are explored. Significant correlations are found with
both the corotation radius and the excess polar updraft, the latter theory
being supported by other observations. We also present a new X-ray population
synthesis model of the mature stellar component of our Galaxy and use it to
reproduce deep observations of a high Galactic latitude field. The model,
XStar, can be used to test models of stellar spin-down and dynamo decay, as
well as for estimating stellar X-ray contamination rates for non-stellar
studies.Comment: 4 pages, 4 figures. To appear in the proceedings of Cool Stars 17:
  17th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, AN 334,
  1-2, Eds Klaus Strassmeier and Mercedes Lopez-Morale

Drake, Jeremy J.

Henry, Gregory W.

Mamajek, Eric E.

Wright, Nicholas J.

Astronomische Nachrichten

English

arXiv

Using a new catalog of 824 solar and late-type stars with measured X-ray luminosities and rotation periods we have studied the relationship between rotation and stellar activity that is believed to be a probe of the underlying stellar dynamo. Using an unbiased subset of the sample we calculate the power law slope of the unsaturated regime of the activity-rotation relationship as LX/Lbol α Roβ, where β = –2.70 ± 0.13. Notably this is inconsistent with the canonical β = –2 slope to a confidence of 5σ are argues for an interface-type dynamo. Super-saturation is observed for the fastest rotators in our sample and its parametric dependencies are explored. Significant correlations are found with both the corotation radius and the excess polar updraft, the latter theory being preferred as it is supported by other observations. We also present a new X-ray population synthesis model of the mature stellar component of our Galaxy and use it to reproduce deep observations of a high Galactic latitude field. The model, XStar, can be used to test models of stellar spin-down and dynamo decay, as well as for estimating stellar X-ray contamination rates for non-stellar studies. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Wright, N.J.

Drake, J.J.

Mamajek, E.E.

Henry, G.W.

Keele Research Repository

The stellar activity-rotation relationship: The stellar activity-rotation relationship

N.J. Wright

J.J. Drake

E.E. Mamajek

G.W. Henry

Crossref

The stellar activity-rotation relationship

Wright, Nick J.

Digital Scholarship @ Tennessee State University

Tennessee State University Digital Scholarship @ Tennessee State University Information Systems and Engineering Management Research Publications Center of Excellence in Information Systems and Engineering Management 2-6-2013 The stellar activity-rotation relationship Nick J. Wright Harvard-Smithsonian Center for Astrophysics Jeremy J. Drake Harvard-Smithsonian Center for Astrophysics Eric E. Mamajek University of Rochester Gregory W. Henry Tennessee State University Follow this and additional works at: https://digitalscholarship.tnstate.edu/coe-research  Part of the Stars, Interstellar Medium and the Galaxy Commons Recommended Citation Wright, N., Drake, J., Mamajek, E. and Henry, G. (2013), The stellar activity-rotation relationship. Astron. Nachr., 334: 151-154. https://doi.org/10.1002/asna.201211764 This Article is brought to you for free and open access by the Center of Excellence in Information Systems and Engineering Management at Digital Scholarship @ Tennessee State University. It has been accepted for inclusion in Information Systems and Engineering Management Research Publications by an authorized administrator of Digital Scholarship @ Tennessee State University. For more information, please contact XGE@Tnstate.edu. Astron. Nachr. / AN 334, No. 1/2, 151 – 154 (2013) / DOI 10.1002/asna.201211764The stellar activity-rotation relationshipN.J. Wright1,, J.J. Drake1, E.E. Mamajek2, and G.W. Henry31 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA2 Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA3 Center of Excellence in Information Systems, Tennessee State University, Nashville, TN 37209, USAReceived 2012 Aug 15, accepted 2012 Dec 5Published online 2013 Feb 1Key words stars: activity – stars: coronae – stars: late-type – stars: magnetic fields – stars: rotation – X-rays: starsUsing a new catalog of 824 solar and late-type stars with measured X-ray luminosities and rotation periods we have studiedthe relationship between rotation and stellar activity that is believed to be a probe of the underlying stellar dynamo. Usingan unbiased subset of the sample we calculate the power law slope of the unsaturated regime of the activity-rotationrelationship as LX/Lbol ∝ Roβ , where β = −2.70± 0.13. Notably this is inconsistent with the canonical β = −2 slopeto a confidence of 5σ are argues for an interface-type dynamo. Super-saturation is observed for the fastest rotators in oursample and its parametric dependencies are explored. Significant correlations are found with both the corotation radius andthe excess polar updraft, the latter theory being preferred as it is supported by other observations. We also present a newX-ray population synthesis model of the mature stellar component of our Galaxy and use it to reproduce deep observationsof a high Galactic latitude field. The model, XStar, can be used to test models of stellar spin-down and dynamo decay, aswell as for estimating stellar X-ray contamination rates for non-stellar studies.c© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim1 IntroductionThe majority of stars emit X-rays with only a few excep-tions. In solar- and late-type stars the X-rays are believed tobe generated by a magnetically confined plasma known asa corona (Vaiana et al. 1981), which is thought to be heatedby the stellar magnetic dynamo. The dynamo itself is be-lieved to be driven by differential rotation in the stellar inte-rior (e.g., Parker 1955), most likely at the tachocline, a phe-nomenon that has been confirmed in the Sun through helio-seismology (Duvall et al. 1984). The observed decrease inX-ray emission between the pre-main sequence and the ageof the Galactic field population can therefore be attributedto the rotational spin-down of the star, driven by mass lossthrough a magnetized stellar wind (Skumanich 1972).The relationship between stellar rotation and tracers ofmagnetic activity is a vital probe of the stellar dynamo. A re-lationship between rotation and activity was first quantifiedby Pallavicini et al. (1981), who found that X-ray luminos-ity scaled as LX ∝ (v sin i)1.9, providing the first evidencefor the dynamo-induced nature of stellar coronal activity.For very fast rotators the relationship was found to breakdown with X-ray luminosity reaching a saturation level ofLX/Lbol ∼ 10−3 (Micela et al. 1985), independent of spec-tral type. This saturation level is reached at a rotation periodthat increases toward later spectral types (Pizzolato et al.2003), but it is unclear what causes this. Despite much workthere is yet to be a satisfactory dynamo theory that can ex-plain both the solar dynamo and that of rapidly rotating stars Corresponding author: nwright@cfa.harvard.eduand the continued lack of a sufficiently large and unbiasedsample has no doubt contributed to this.We have produced a new catalog of stars with stellar ro-tation periods and X-ray luminosities, the details of whichare presented in Wright et al. (2011). The catalog includes824 solar- and late-type stars, including 445 field stars and379 stars in nearby open clusters (ages 40–700 Myr). Thesample was homogenized by recalculating all X-ray lu-minosities and converting them all onto the ROSAT 0.1–2.4 keV band. To minimize biases we removed all sourcesknown to be X-ray variable, those that exhibit signs of ac-cretion, or those in close binary systems. The sample isapproximately equally distributed across the color rangeV −Ks = 1.5–5.0 (G2 to M4) with ∼ 30 stars per subtype,dropping to ∼10 stars per subtype outside of this, from F7to M6.Here we highlight some of the results derived from thissample, focussing attention on the regimes of low-activitydynamo decay and high-activity supersaturation. Details ofthese findings and further results and discussions from thissample can be found in Wright et al. (2011). Finally wepresent a new population synthesis model that can be usedto address similar problems in stellar activity.2 Dynamo efficiency in the linear regimeThe compiled catalog has been used to study the relation-ship between the level of X-ray activity, represented by theratio of X-ray to bolometric luminosity, RX = LX/Lbol andthe rotation period, parameterized by the spectral-type in-c© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim152 N.J. Wright et al.: The stellar activity-rotation relationshipFig. 1 RX = LX/Lbol plotted against Prot (left) and the Rossby number, Ro = Prot/τ (right), for all stars in our sample. Knownbinary stars are shown as plus symbols, and the Sun with a solar symbol. The best-fitting saturated and non-saturated activity-rotationrelations are shown as a dashed red line in the right-hand panel.dependent Rossby number, Ro = Prot/τ , the ratio of therotation period to the convective turnover time (Noyes etal. 1984). Figure 1 shows RX as a function of Prot andRo, illustrating that the use of the latter parameter greatlyreduces the scatter in the rotation–activity diagram, andhighlights the two main regimes of coronal activity: a lin-ear regime where activity increases with decreasing rota-tion period, and a saturated regime where the X-ray lumi-nosity ratio is constant with log RX = −3.13± 0.08. Thetransition between these two regimes is found to occur atRo = 0.13± 0.02 from a two-part power-law fit.The sample used here suffers from a number of biases,most importantly an X-ray luminosity bias due to the selec-tion only of sources with measured X-ray fluxes and pho-tometric rotation periods. To overcome this we used an X-ray unbiased subset of our sample, the 36 Mt. Wilson starswith measured rotation periods (Donahue et al. 1996), all ofwhich are detected in X-rays. While some biases may stillexist due to the ability to measure rotation periods, Don-ahue et al. (1996) conclude that any such biases are unlikelyto affect the rotation period distribution.A single-part power-law fit in the linear regime (whereRX ∝ Roβ) to this sample is shown in Fig. 2 with a fitof β = −2.70± 0.13. This is a steeper slope than fit us-ing the full sample and notably steeper than the canonicalvalue of β = −2 (Pallavicini et al. 1981), though their useof projected rotational velocities instead of rotation peri-ods represents a different relationship than that fitted here.Our slope is inconsistent with the canonical value to a con-fidence of 5σ, which argues against a distributed dynamooperating throughout the convection zone, the efficiency ofwhich scales as Ro−2 (Noyes et al. 1984), and instead ar-gues for an interface dynamo (e.g., Parker 1993), which hasa more complex dependency where β = −2.Fig. 2 RX = LX/Lbol versus Rossby number for an unbi-ased sample of 36 stars with unsaturated X-ray emission. The log-log ordinary least squares bisector fit, β = −2.70, is shown as adashed line alongside a fit with the canonical slope of β = −2.0.3 SupersaturationAt very high rotational velocities the fractional X-ray lu-minosity is observed to decrease below the saturation level(Randich et al. 1996), an effect dubbed supersaturation,the cause of which is still heavily debated. Figure 3 showsLX/Lbol for all stars with saturated X-ray emission as afunction of various quantities suggested as parameters ofsupersaturation. The first two panels show the effect of ro-tation period and Rossby number on the X-ray luminosityratio, neither of which show evidence for supersaturation(i.e. a decline in LX/Lbol) for either the fastest rotators orthe sources with the smallest Rossby numbers.Two theories suggested to explain the supersaturationeffect are coronal stripping and convective updrafts. In thec© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.an-journal.orgAstron. Nachr. / AN (2013) 153Fig. 3 (online colour at: www.an-journal.org) LX/Lbol for stars with saturated X-ray emission as a function of the rotation period(upper left), the Rossby number (upper right), the Keplerian co-rotation radius (lower left), and the excess polar updraft (lower right).Also shown are 25-star average luminosity ratios, with standard errors.theory of coronal stripping the star is spinning so fast thatcentrifugal forces strip away the outer layers of the corona,reducing the X-ray emitting volume (Jardine & Unruh 1999,James et al. 2000). This theory is parameterized by the coro-tation radius, RKepler, the radius at which centrifugal forcesbalance gravitational forces in the corona. In Fig. 3 it isclear that this parameter exhibits a correlation with the su-persaturation effect with the fastest rotators showing a dropto log RX = −3.41± 0.26.In the theory of convective updrafts, nonuniform heat-ing of the convective envelope (in accordance with the vonZeipel 1924 theorem for rapidly rotating stars) results in apoleward migration of active regions and a reduction in thefilling factor of active regions on the stellar surface (Stȩpieńet al. 2001). This can be quantified in terms of the excesspolar updraft at the bottom of the convective envelope andis also shown in Fig. 3, where the parameter also displaysa strong correlation with the supersaturation effect with thefastest rotators dropping to log RX = −3.45± 0.16.Based on this data it is difficult to distinguish betweenthese two theories, partly because they have similar depen-dencies in terms of stellar parameters. An alternative dis-tinguishing method is the underlying coronal structure thatthe two theories require to be effective. Coronal strippingwill occur if the loops are large, low density, and unstableto the centrifugal force. In Fig. 3 a decrease in X-ray lu-minosity begins at RKepler/R ∼ 3, suggesting that coronalloops are as large as two stellar radii in height. Alternativelycoronal loops may be compact, high density and influencedby the dynamics of surface flows where convective updraftsmay influence the surface activity level. The difference be-tween the two supersaturation theories is therefore the sizeand density of the coronal plasma. High-resolution X-rayspectroscopy can be used to infer coronal plasma densities(and therefore scale heights), but such data for supersatu-rated stars is rare. The only such observation to date is ofVW Cephei, for which coronal loop heights of 0.06–0.2Rhave been measured (Huenemoerder et al. 2006). The ro-www.an-journal.org c© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim154 N.J. Wright et al.: The stellar activity-rotation relationshipFig. 4 (online colour at: www.an-journal.org) Cumulativedistribution of X-ray fluxes for sources in the COSMOSfield compared to two predictions from the XStar model forβ = −2.0 and β = −2.7. The observations are complete tofX ∼ 2×10−15 erg s−1 cm−2.tational period of VW Cephei implies RKepler/R  1.75,significantly higher than the observed coronal loop heights,and suggesting that coronal stripping is unlikely to be re-sponsible for supersaturation.4 Modeling the decay of stellar dynamosStudies of the rotation – activity relation in the manner per-formed above are limited both by the sample size of starswith measured X-ray luminosities and rotation periods andalso by biases inherent in compiling such samples. A dif-ferent approach that allows one to overcome such problemsis to model the X-ray emission of a population of stars andcompare the number and properties of such stars with obser-vations. We have compiled such a model, XStar, combin-ing a Galactic population synthesis model with models ofrotational spin-down (e.g., Barnes 2003) and the activity–rotation framework outlined here. The results of this modelcan then be compared to X-ray observations that sample dif-ferent sight-lines in our Galaxy such as deep targeted obser-vations or wide-field, shallow surveys.An example of the model is shown in Fig. 4 wheretwo realizations of the model using β = −2.0 and β =−2.7 are compared to the cumulative flux distribution ofX-ray sources in the high Galactic latitude Chandra COS-MOS field (Wright, Drake & Civano 2010). The mod-els reproduce the observations very well down to the esti-mated observational completeness limit of fX ∼ 2×10−15erg s−1 cm−2, with similar forms and the brightest sourcesreproduced well. The β = −2.7 model provides the bet-ter fit, although various other parameters within the modelmust be fully tested before firm conclusions can be drawn.Nonetheless the code does well in reproducing the proper-ties (distances, spectral types, X-ray fluxes) of the observa-tions, and will therefore prove useful for studying the prop-erties of mature, X-ray emitting stellar populations as wellas for estimating stellar contamination rates for studies ofstar forming regions and extra-Galactic populations (e.g.,Brassington et al. 2012).5 SummaryA new catalog of stars with measured X-ray luminositiesand rotation periods is used to study the rotation-activity re-lation. The power-law slope of the unsaturated regime is fitas β = −2.7±0.13, inconsistent with the canonical β = −2value with a confidence of 5σ and arguing for an interface-type dynamo. Coronal supersaturation in ultra-fast rotatorsis shown to correlate well with both the corotation radiusand the excess polar updraft as the parameters of the coro-nal stripping and convective updrafts theories, though otherobservations support the latter theory. Finally a new popu-lation synthesis model of X-ray emitting stars in a Galacticsightline is introduced and tested successfully on deep ob-servations of the high Galactic latitude COSMOS field. Abetter fit is found for β = −2.7 than for β = −2, confirm-ing results with a fixed sample.ReferencesBarnes, S. A. 2003, ApJ, 586, 464Brassington, N. J., et al. 2012, ApJ, 755, 162Donahue, R. A., Saar, S. H., & Baliunas, S. L. 1996, ApJ, 466, 384Duvall, Jr., T. L., Dziembowski, W. A., Goode, P. R., et al. 1984,Nature, 310, 22Huenemoerder, D. P., Testa, P., & Buzasi, D. L. 2006, ApJ, 650,1119Jardine, M., & Unruh, Y. C. 1999, A&A, 346, 883James, D. J., Jardine, M. M., Jeffries, R. D., et al. 2000, MNRAS,318, 1217Micela, G., et al., 1985, ApJ, 292, 172Noyes, R. W., Hartmann, L. W., Baliunas, S. L., et al. 1984, ApJ,279, 763Pallavicini, R., Golub, L., Rosner, R., et al. 1981, ApJ, 248, 279Parker, E. N. 1955, ApJ, 122, 293Parker, E. N. 1993, ApJ, 408, 707Pizzolato, N., Maggio, A., Micela, G., et al. 2003, A&A, 397, 147Randich, S., Schmitt, J. H. M. M., Prosser, C. F., & Stauffer, J. R.1996, A&A, 305, 785Skumanich, A. 1972, ApJ, 171, 565Stȩpień, K., Schmitt, J. H. M. M., & Voges, W. 2001, A&A, 370,157Telleschi, A., Güdel, M., Briggs, K. R., et al. 2007, A&A, 468, 425Vaiana, G. S., et al. 1981, ApJ, 245, 163von Zeipel, H. 1924, MNRAS, 84, 665Wright, N. J., Drake, J. J., & Civano, F. 2010, ApJ, 725, 480Wright, N. J., Drake, J. J., Mamajek, E. E., & Henry, G. W. 2011,ApJ, 743, 48c© 2013 WILEY-VCH Verlag GmbH & Co. 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The Stellar Activity - Rotation Relationship

The Stellar Activity - Rotation Relationship

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