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Lt is instead in excellent agreement with the 1.9 Gyr ound by CC€O94. who used the same distance mocdulus ancl "acdova tracks adopted here. | It is instead in excellent agreement with the 1.9 Gyr found by CC94, who used the same distance modulus and Padova tracks adopted here. |
c) Iteddening: it strongly depends on the metallicity of he models. but. varies from 0 to 0.07. in good. agreement with the 0.05 value found by AICTE. | c) Reddening: it strongly depends on the metallicity of the models, but varies from 0 to 0.07, in good agreement with the 0.05 value found by MCTF. |
d) Moetallicitv: we have obtained excellent. ts using he sets of models with metal content lower than solar. in agreement with the spectroscopic value. | d) Metallicity: we have obtained excellent fits using the sets of models with metal content lower than solar, in agreement with the spectroscopic value. |
However. in one case (Padova mocdels). we have also reached. satisfving results with the solar metallicity set. | However, in one case (Padova models), we have also reached satisfying results with the solar metallicity set. |
This is because a tight determination of the metallicity cannot be done on the basis of the photometry alone. | This is because a tight determination of the metallicity cannot be done on the basis of the photometry alone. |
While spectroscopic. values: are to be preferred. in general. we remind that the 0.52 found by Friel Janes (1993) is based. on. mecdium-low resolution spectra. calibrated against a metallicity scale. | While spectroscopic values are to be preferred in general, we remind that the [Fe/H]=--0.52 found by Friel Janes (1993) is based on medium-low resolution spectra, calibrated against a metallicity scale. |
Ligh resolution direct. spectroscopy will be able to put a more stringent limit on metallicitv. and our Vo4 values could be used. to derive input temperatures for the mocel fitting analysis. | High resolution direct spectroscopy will be able to put a more stringent limit on metallicity, and our $V-I$ values could be used to derive input temperatures for the model fitting analysis. |
As a by-procuct of our theoretical simulations. we can also provide a lower limit to the initial mass of the cluster within the examined region: that is the minimum mass of the stars that must have formed there to account for the current stellar content. | As a by-product of our theoretical simulations, we can also provide a lower limit to the initial mass of the cluster within the examined region; that is the minimum mass of the stars that must have formed there to account for the current stellar content. |
This value turns out to be «M; >2.610ML. (ranging from 1.6 to 3.0 depending on the adopted evolutionary tracks) and is a lower limit to the actual initial mass of the cluster region. since it does not take into account 10. possible effect of subsequent. stellar evaporation. | This value turns out to be $<$ $_i>\simeq2.6\times10^{3}$ $_{\odot}$ (ranging from 1.6 to 3.0 depending on the adopted evolutionary tracks) and is a lower limit to the actual initial mass of the cluster region, since it does not take into account the possible effect of subsequent stellar evaporation. |
The age dillerences presented at. point b) show. in our opinion. how much safer it is to date the clusters with the synthetic CMDs rather than with isochrone fitting. | The age differences presented at point b) show, in our opinion, how much safer it is to date the clusters with the synthetic CMDs rather than with isochrone fitting. |
Both methods provide results dependent on the adopted. stellar evolution mocels. | Both methods provide results dependent on the adopted stellar evolution models. |
However. the synthetic ςMDs. on the one mane. are independent of any other parameter and. on the other. are constrained by the many morphological features (c.g. shape of the MS. SG. and BG. branches. position of he chump. of the TO. of the AIS gaps) bv the stellar distributions with magnitude and colour in the diagram. and by the proportion between stars in dillerent evolutionary johases. | However, the synthetic CMDs, on the one hand, are independent of any other parameter and, on the other, are constrained by the many morphological features (e.g., shape of the MS, SG and RG branches, position of the clump, of the TO, of the MS gaps), by the stellar distributions with magnitude and colour in the diagram, and by the proportion between stars in different evolutionary phases. |
Isochrone dating is strongly allectecl by the choice of he AIS turn-oll (which can be quite subjective) ancl has no urther constraint aside from the average stellar clistribution in the CALD. | Isochrone dating is strongly affected by the choice of the MS turn-off (which can be quite subjective) and has no further constraint aside from the average stellar distribution in the CMD. |
Besicks. it cannot account for the colour and magnitude spread due to photometric errors or for the cllect of incompleteness on the relative number of stars in the various phases. | Besides, it cannot account for the colour and magnitude spread due to photometric errors or for the effect of incompleteness on the relative number of stars in the various phases. |
Our study of open clusters is. aimed. at better understanding the chemical anc dynamical evolution. of the Galaxy: as stated in the Introduction. their ages (ancl distances) are among the soundest derived. lor the disc population. | Our study of open clusters is aimed at better understanding the chemical and dynamical evolution of the Galaxy; as stated in the Introduction, their ages (and distances) are among the soundest derived for the disc population. |
Nevertheless. homogeneity in. dating them. is fundamental if one wishes to preserve a meanineful. age ranking. | Nevertheless, homogeneity in dating them is fundamental if one wishes to preserve a meaningful age ranking. |
In this respect. the effort. made by CCO4. who re- ten well observed: clusters and. defined a relation between a measurable index. (AV) and age. dis. very important. | In this respect, the effort made by CC94, who re-analyzed ten well observed clusters and defined a relation between a measurable index $\Delta$ V) and age, is very important. |
Carraro Chiosi defined AV as the dillerence in magnitude between the TO and the red clump (like the OV used by JP94). but taking into account the possible misplacement of the PO duc to the binary sequence by adding an extra 0.25 mag to the value found from the CΔΙ). | Carraro Chiosi defined $\Delta$ V as the difference in magnitude between the TO and the red clump (like the $\delta$ V used by JP94), but taking into account the possible misplacement of the TO due to the binary sequence by adding an extra 0.25 mag to the value found from the CMD. |
Thev have then derived the age of the ten clusters with the synthetic CMD method ancl obtained a linear fit between Log(age) and V. They have then applied this relation to derive. ages for a sample of 26 clusters with reliable photometry published. | They have then derived the age of the ten clusters with the synthetic CMD method and obtained a linear fit between Log(age) and $\Delta$ V. They have then applied this relation to derive ages for a sample of 26 clusters with reliable photometry published. |
JP94 used a similar approach. | JP94 used a similar approach. |
TFhev used literature values for ages (stressing the [act that in doing so they lacked. the homogeneity one would have wished for). and chose the 7 more reliable open clusters. | They used literature values for ages (stressing the fact that in doing so they lacked the homogeneity one would have wished for), and chose the 7 more reliable open clusters. |
They. derived. a non-linear relation between oV. ancl Log(age). using also values for Globular clusters. | They derived a non-linear relation between $\delta$ V and Log(age), using also values for Globular clusters. |
In this wav their relation is quite sound for high &Y values. and furthermore. these are | In this way their relation is quite sound for high $\delta$ V values, and furthermore, these are |
electromagnetic wave in terms of the four Stokes parameters 7.Q.U. aud V: — so that the the transfer equation that desribes its evolution takes the form = /)H | electromagnetic wave in terms of the four Stokes parameters $I, Q, U$, and $V$ : = so that the the transfer equation that desribes its evolution takes the form ) = ). |
O) Iu this equation. 7;; is the trausfer matrix that describes the transition from one polarization to the other as well the absorption aud outscatteriug of radiation. whereas 5,4ο is tlie source matrix that describes emission aud iuscatteriug processes. | In this equation, $T_{\alpha\beta}$ is the transfer matrix that describes the transition from one polarization to the other as well the absorption and outscattering of radiation, whereas $S_{\alpha\beta}$ is the source matrix that describes emission and inscattering processes. |
In tlie basis of eigeuvectors of the trausler matrix (which correspoud to the normal modes of propagation). the trausler equation becomes οSij. where 2;; aud οἱ are the projections of the correlation and source matrices onto the eigenvectors aud Here. &; is the stun of the absorption aud scattering coefficients. w is the photon Irequency. auc i; is the refractive index of the ith mode. | In the basis of eigenvectors of the transfer matrix (which correspond to the normal modes of propagation), the transfer equation becomes ), where $R_{ij}$ and $S_{ij}$ are the projections of the correlation and source matrices onto the eigenvectors and = Here, $\kappa_i$ is the sum of the absorption and scattering coefficients, $\omega$ is the photon frequency, and $n_i$ is the refractive index of the $i$ th mode. |
Note that the two equations for the for the diagonal terms of the correlation matrix 2;; correspond to the most general form of equation (11) of Lai Ho (2002). | Note that the two equations for the for the diagonal terms of the correlation matrix $R_{ii}$ correspond to the most general form of equation (14) of Lai Ho (2002). |
null | When |
The current explanation for the origin of the 30. Doradus nebula is that as the massive stars within the nebula evolve. their winds (especially during the Woll-Ravet phase) and subsequent supernova explosions generate swept-up shells of ionized gas (Meaburn.1988.1991). | The current explanation for the origin of the 30 Doradus nebula is that as the massive stars within the nebula evolve, their winds (especially during the Wolf-Rayet phase) and subsequent supernova explosions generate swept-up shells of ionized gas \citep{meaburn88,meaburn91}. |
. Phe shells are observed to have a hierarchy of sizes and velocities as one moves further into the halo of 30 Doradus. | The shells are observed to have a hierarchy of sizes and velocities as one moves further into the halo of 30 Doradus. |
In the dense centre. the shell sizes ancl velocities are 1pc and 1050kms1 respectively. while in the halo the sizes reach ~LOOpe with velocities of up to 100kms (sco 1). | In the dense centre, the shell sizes and velocities are $\sim 1~{\rm pc}$ and $\sim 10-50~{\rm km~s^{-1}}$ respectively, while in the halo the sizes reach $\sim 100~{\rm pc}$ with velocities of up to $100~{\rm km~s^{-1}}$ (see 1). |
The shells are prone to instabilities and can break up and. fragment. venting the interior pressure. | The shells are prone to instabilities and can break up and fragment, venting the interior pressure. |
For example a dense shell that is accelerating. (due to either a rapid drop in the external density or to a new supernova explosion within the shell) may break up via the Iavleish-Tavlor instability. | For example a dense shell that is accelerating (due to either a rapid drop in the external density or to a new supernova explosion within the shell) may break up via the Rayleigh-Taylor instability. |
Alternatively. dvnanmical overstabilites can also lead to a shell breaking up into fragments (MacLow&Norman 1993). | Alternatively, dynamical overstabilites can also lead to a shell breaking up into fragments \citep{maclow&norman93}. |
. In. both cases. the fragments. produced. will have sizes of the order of the shell thickness. | In both cases, the fragments produced will have sizes of the order of the shell thickness. |
In. general. the ido of 30 Doradus. into which the shells are expanding. is inhomogeneous. | In general, the halo of 30 Doradus, into which the shells are expanding, is inhomogeneous. |
This inhomogeneity. ancl the clisruptive ellects of nearby supernovae and winds from stars not within he original shell. will mean that a shell will not. remain coherent [or long. | This inhomogeneity, and the disruptive effects of nearby supernovae and winds from stars not within the original shell, will mean that a shell will not remain coherent for long. |
Lt is important to note that the LMC is thought to be lattened. and viewed. close to [ace-on. | It is important to note that the LMC is thought to be flattened and viewed close to face-on. |
The scale height of he IL rin the LMC disk was caleulatect by Ixim to be ~180pe so that it is likely that the structure 30 Doradus max. also be somewhat flattened. | The scale height of the H in the LMC disk was calculated by \citet{kim.et.al99} to be $\sim 180~{\rm pc}$ so that it is likely that the structure 30 Doradus may also be somewhat flattened. |
The scale-height imposes a limit on the sizes ofthe shells that can be formed. irrespective of how intense ancl coeval in time the massive star activity is. | The scale-height imposes a limit on the sizes of the shells that can be formed, irrespective of how intense and coeval in time the massive star activity is. |
As the shells erow. they become elongated in the direction of the density scale height. 1992).. leading to a break up of the shell in this direction and a blow-out of the hot interior gas into the ealactic halo. | As the shells grow, they become elongated in the direction of the density scale height \citep{koo&mckee92}, leading to a break up of the shell in this direction and a `blow-out' of the hot interior gas into the galactic halo. |
The remaining structure is known as a galactic chimney (Norman&IHkeuchi1989). and they have been observed in the Galaxy (Normancdeauctal.1996). and in the starburst galaxy. MS2 (Willsetal.1999). | The remaining structure is known as a galactic chimney \citep{norman&ikeuchi89} and they have been observed in the Galaxy \citep{normandeau.et.al96} and in the starburst galaxy M82 \citep{wills.et.al99}. |
. The giant shells of 30. Doradus are likely to be he maximum sized. spherical momentum conserving shell structures. since. the scale height of the LMC is comparable o their diameters. | The giant shells of 30 Doradus are likely to be the maximum sized spherical momentum conserving shell structures, since the scale height of the LMC is comparable to their diameters. |
Phe supergiant shells [ar exceed. this scale height and may be collections of fossil chimneys viewed ace-on and also the result. of propagating star formation (sce AleCray&Walatos 1987)) that is constrained to oceed in the plane of the galaxy. resulting in a ring shape supergiant shell. | The supergiant shells far exceed this scale height and may be collections of fossil chimneys viewed face-on and also the result of propagating star formation (see \citealt{mccray&kafatos87}) ) that is constrained to proceed in the plane of the galaxy, resulting in a ring shape supergiant shell. |
Phe loss of driving pressure means they are expanding in a momentum conserving phase and surround a low density cavity. | The loss of driving pressure means they are expanding in a momentum conserving phase and surround a low density cavity. |
Such cavities are clearly seen in the IL cata of Iximetal.(1999). and Staveley-Smithetal.(2002). | Such cavities are clearly seen in the H data of \citet{kim.et.al99} and \citet{staveley-smith.et.al02}. |
. The hot gas that has escaped from the interior of the giant shells will enter the LMC halo. | The hot gas that has escaped from the interior of the giant shells will enter the LMC halo. |
Phere is strong evidence for such a halo in the LMC. | There is strong evidence for such a halo in the LMC. |
(Nakkeretal.1998). have used GURS/LIST observations to detect € absorption towards LAIC stars that do not to reside within a shell. | \citep{wakker.et.al98} have used GHRS/HST observations to detect C absorption towards LMC stars that do not to reside within a shell. |
Ες means the hot gas implied by these observations is not local to the star and is likely to reside in the halo (see also 199731. | This means the hot gas implied by these observations is not local to the star and is likely to reside in the halo (see also \citealt{savage.et.al97}) ). |
Lt would seem unlikely that the high speed. knots represen random gas clouds within 30 Dor since that would. require an explanation for both their hypersonic velocities anc the systematic way they are distributed. about the py arravs. | It would seem unlikely that the high speed knots represent random gas clouds within 30 Dor since that would require an explanation for both their hypersonic velocities and the systematic way they are distributed about the pv arrays. |
dn terms of the scenario discussed. above (section 3.1). a straight-Forward. interpretation of the kinematica features is as follows. | In terms of the scenario discussed above (section 3.1), a straight-forward interpretation of the kinematical features is as follows. |
The largest scale features represen old giant shells that have broken up via Rayleigh-Taylor (RV) instabilities. | The largest scale features represent old giant shells that have broken up via Rayleigh-Taylor (RT) instabilities. |
An instability is generated as the shel is accelerated by its interior pressure through a decreasing ambient clensity. | An instability is generated as the shell is accelerated by its interior pressure through a decreasing ambient density. |
“Phose portions of the shell that are expanding in the plane of the LAIC are less prone to disruption. | Those portions of the shell that are expanding in the plane of the LMC are less prone to disruption. |
Phe fragments that used to be part of the shel wave continued to coast at the pre-break up velocity. anc ogether these remain as a coherent velocity feature. | The fragments that used to be part of the shell have continued to coast at the pre-break up velocity and together these remain as a coherent velocity feature. |
For the VE instability. the characteristic knot size at the break up of he shell will be of the order of the thickness of the shell. | For the RT instability, the characteristic knot size at the break up of the shell will be of the order of the thickness of the shell. |
Phe sizes implied. by this pieture seem reasonable - the old shel will have a dimension of up to a hundred. parsees towards he outer regions of the nebulosity while the shell wall wil mve had a thickness of a few parsees. | The sizes implied by this picture seem reasonable - the old shell will have a dimension of up to a hundred parsecs towards the outer regions of the nebulosity while the shell wall will have had a thickness of a few parsecs. |
“Phese estimates are in accord with measurements of intact shells observed: within he halo of 30 Doradus and elsewhere in the LMC Oev1996). | These estimates are in accord with measurements of intact shells observed within the halo of 30 Doradus and elsewhere in the LMC \citealt{oey96}) ). |
The smaller chains of high-speed. knots could. be due o more localised disruptions of the giant shells due to. for example. a neighbouring supernova explosion. | The smaller chains of high-speed knots could be due to more localised disruptions of the giant shells due to, for example, a neighbouring supernova explosion. |
Εις latter scenario was proposed by Recimanetal.(1999). to explain he unique Honeycomb nebula. which lies in the halo of 30 Doradus. | This latter scenario was proposed by \citet{redman.et.al99b} to explain the unique Honeycomb nebula, which lies in the halo of 30 Doradus. |
They argued that its cellular structure is due to a shell that has begun to fragment by a IE instability being impacted by a blast wave from a nearby SN explosion. | They argued that its cellular structure is due to a shell that has begun to fragment by a RT instability being impacted by a blast wave from a nearby SN explosion. |
There jwe been approximately 40 supernova explosions within he halo of 30 Doradus in the last 107vr alone (Meaburn1901) (in comparison. in the starburst galaxy M82 there ive been 250 SNe in the last 2200vr: Aluxlowetal. 19943) | There have been approximately $\sim$ 40 supernova explosions within the halo of 30 Doradus in the last $10^4~{\rm yr}$ alone \citep{meaburn91} (in comparison, in the starburst galaxy M82 there have been $\simeq 50$ SNe in the last $\simeq 200~{\rm yr}$; \citealt{muxlow.et.al94}) ). |
In the 11 py array data ο "Stavelev-Smithetal.(2002).. he LMC and the Galaxy are well separated in velocity. | In the H pv array data of \citet{staveley-smith.et.al02}, the LMC and the Galaxy are well separated in velocity. |
In heir data. the Galaxy does ncX exhibit kinematical features witha Vu2100kms+ while the LMC docs not exhibit kinematical features with a Vue100kms.I. | In their data, the Galaxy does not exhibit kinematical features with a $V_{\rm HEL}\ga
100~{\rm~km~s^{-1}}$ while the LMC does not exhibit kinematical features with a $V_{\rm HEL}\la 100~{\rm~km~s^{-1}}$. |
In our data aint velocity features are seen from the Vue, of 30 Doradus down to a πει100kais+) | In our data faint velocity features are seen from the $V_{\rm HEL}$ of 30 Doradus down to a $V_{\rm HEL}\la 100~{\rm km~s^{-1}}$. |
However. it is unlikely that hese velocity features are associated with the Galaxy rather han the LMC for several reasons. | However, it is unlikely that these velocity features are associated with the Galaxy rather than the LMC for several reasons. |
Firstly. such features are not seen at slit positions offset from. 30 Doracus: secondly. many of the features can be traced back to the 30 Doraclus svstemic velocity: thirdly. there is no known Galactic rregion or ionizing source along the line of sight that could excite the eemitting gas and there is also no extensive background eemission in the galaxy (compare 7 and S here with ligure 9 of Stavelev-Smithetal. 2002)). | Firstly, such features are not seen at slit positions offset from 30 Doradus; secondly, many of the features can be traced back to the 30 Doradus systemic velocity; thirdly, there is no known Galactic region or ionizing source along the line of sight that could excite the emitting gas and there is also no extensive background emission in the galaxy (compare \ref{deep1} and \ref{deep2} here with figure 9 of \citealt{staveley-smith.et.al02}) ). |
Starburst activity can give rise to a "superwind. due to the intense radiation fields. winds and supernova explosions | Starburst activity can give rise to a `superwind' due to the intense radiation fields, winds and supernova explosions |
O-sturs are ejected near birth and a further 20% just. before exploding as supernovae and taking the time-integrated energy inputs from ionising radiation. winds and supernovae to be equal. a typical cluster may receive 17% less energy from O-star feedback than if it retained all of its O-stars. | O-stars are ejected near birth and a further $20\%$ just before exploding as supernovae and taking the time-integrated energy inputs from ionising radiation, winds and supernovae to be equal, a typical cluster may receive $17\%$ less energy from O-star feedback than if it retained all of its O-stars. |
This figure may often be an understimate since. as Hoogerwerf et al. ( | This figure may often be an understimate since, as Hoogerwerf et al. ( |
2001) point out. the interaction between AE Aurigae. u Columbae and the binary t Orionis removed ~70M. from the neighbourhood of the Trapezium cluster. comparable to the total mass of the Trapezium cluster itself. | 2001) point out, the interaction between AE Aurigae, $\mu$ Columbae and the binary $\iota$ Orionis removed $\sim70 \msun$ from the neighbourhood of the Trapezium cluster, comparable to the total mass of the Trapezium cluster itself. |
It is possible for dynamical interactions in a small-N system to expel N-2 objects and to leave only a tight binary (e.g. Kiseleva et al. | It is possible for dynamical interactions in a small-N system to expel N-2 objects and to leave only a tight binary (e.g. Kiseleva et al. |
1998). | 1998). |
A star cluster born with a rich population of O-stars could in principle be left with only Decreasing the energy input from feedback into a stellar cluster has the obvious consequence that the cluster is less likely to become unbound Gf it was bound at formation). | A star cluster born with a rich population of O-stars could in principle be left with only Decreasing the energy input from feedback into a stellar cluster has the obvious consequence that the cluster is less likely to become unbound (if it was bound at formation). |
The efticiency of star formation will also be affected. although i is not clear whether it will be increased or decreased since feecback from massive stars can be both positive. in that it can induce or accelerate star formation locally. and negative. in that accretion onto existing stars can be halted and potentially-star-forming gas can be expelled from embedded stellar systems (e.g. Dale et al. | The efficiency of star formation will also be affected, although it is not clear whether it will be increased or decreased since feedback from massive stars can be both positive, in that it can induce or accelerate star formation locally, and negative, in that accretion onto existing stars can be halted and potentially-star-forming gas can be expelled from embedded stellar systems (e.g. Dale et al. |
LMD and JED are supported by the Leicester PPARC rolling grant for theoretical astrophysics. and RN by a PPARC Advanced Fellowship. | LMD and JED are supported by the Leicester PPARC rolling grant for theoretical astrophysics, and RN by a PPARC Advanced Fellowship. |
MEB acknowledges the support of a UKAFF fellowship. | MEB acknowledges the support of a UKAFF fellowship. |
ARK gratefully acknowledges a Royal Society Wolfson Research Merit Award. | ARK gratefully acknowledges a Royal Society Wolfson Research Merit Award. |
lately been used to measure A for several transiting exoplauet systems (0.2.Fabrveky&Winn2009.andreferences therein).. | lately been used to measure $\lambda$ for several transiting exoplanet systems \citep[e.g.][and references therein]{fab09}. |
Indeed. the latest RAL measurements described in Triaud et al. ( | Indeed, the latest RM measurements described in Triaud et al. ( |
2010. submitted) show that eight of the 26 svstems with RAD measurements are sienificautly spin-orbit iuisaligued in the plane of the sky. | 2010, submitted) show that eight of the 26 systems with RM measurements are significantly spin-orbit misaligned in the plane of the sky. |
Though ἐς is not constrained bv the RAL effect. if all of /,,. ἐκ. aud A are kuown. the calculation of the true deprojected angle c—arecostn,1.) betweeu n, aud n; is trivial. | Though $i_s$ is not constrained by the RM effect, if all of $i_p$, $i_s$, and $\lambda$ are known, the calculation of the true deprojected angle $\psi \equiv
\arccos(\mathbf{n}_p \cdot \mathbf{n}_s)$ between $\mathbf{n}_p$ and $\mathbf{n}_s$ is trivial. |
The inchnation ἐς to the line of sight of stellar spin is difficult to measure for individual stars. | The inclination $i_s$ to the line of sight of stellar spin is difficult to measure for individual stars. |
[Hf the rotation period of a star is kuown through photometric observations of starspots moving across its surface. and if the projected rotational velocity ¢sin/ has been ineasured. then /, is easy to compute (eg.Winnctal. 2007). | If the rotation period of a star is known through photometric observations of starspots moving across its surface, and if the projected rotational velocity $v\sin{i}$ has been measured, then $i_s$ is easy to compute \citep[e.g.][]{win07}. |
. Astrosicsimoloev imueasureiments of ἐν are also possible im special circumstances (Cüzou&Solanki 2003). | Astrosiesmology measurements of $i_s$ are also possible in special circumstances \citep{giz03}. |
. Unfortunately. period measuremeuts are resource-dntensive and require well-sampled and precise photometric time series. | Unfortunately, period measurements are resource-intensive and require well-sampled and precise photometric time series. |
They may also be biased toward stars with many starspots aud therefore biased toward more active and vounecr stars. | They may also be biased toward stars with many starspots and therefore biased toward more active and younger stars. |
Ou the other haud. the projection of stellar rotation velocity along the line of sight esinyg can be measured cheaply by examining the rotational broadening of absorption Ines in asinele high-resolution stellar spectrum. | On the other hand, the projection of stellar rotation velocity along the line of sight $v\sin{i}$ can be measured cheaply by examining the rotational broadening of absorption lines in a single high-resolution stellar spectrum. |
If the radius of the star is known from other iesus. it is easv to forward-inodel the observable quautity ¢sins from the stellar rotation period P. predicted from theoretical or enipirical models eiven a distribution for /. | If the radius of the star is known from other means, it is easy to forward-model the observable quantity $v\sin{i}$ from the stellar rotation period $P_{\ast}$ predicted from theoretical or empirical models given a distribution for $i$. |
Moute Carlo simulations can then derive the distribution of possible esin/ measurenients. | Monte Carlo simulations can then derive the distribution of possible $v\sin{i}$ measurements. |
That distribution can then be compared to observational data for trausiting exoplanct svstenus to determine if the observations are consisteut with the aligummeut of a transiting planets orbit with the spin of its host star. | That distribution can then be compared to observational data for transiting exoplanet systems to determine if the observations are consistent with the alignment of a transiting planet's orbit with the spin of its host star. |
Calculating the rotation period of Suu-like stars as a function. of mass and time is a tractable problem for stars older than about 650 Myr. | Calculating the rotation period of Sun-like stars as a function of mass and time is a tractable problem for stars older than about 650 Myr. |
First. the rotation period of isolated Sun-like stars monotonically slows down as they age (Ixraft1967). | First, the rotation period of isolated Sun-like stars monotonically slows down as they age \citep{kra67}. |
. Second. even though a population of Suu-like stars is formed with a broad distribution of periods P. (Attridge&Herbst1992:Choi&Ierbst 1996).. by the time that population is the age of the ILIvades and Pracsepe (about 650 My) the broad distribution has couvereed to a well-defined function of mass (Tassoul2000:bwin&Bouvier2009). | Second, even though a population of Sun-like stars is formed with a broad distribution of periods $P_{\ast}$ \citep{att92,cho96}, by the time that population is the age of the Hyades and Praesepe (about 650 Myr) the broad distribution has converged to a well-defined function of mass \citep{tas00,irw09}. |
. T3vo classes of plivsical models have been proposed to explain this earlv-tine behavior: magnetic breaking bw protostellar disks (e.g.I&oenigl1991:Shuetal.1991:CollierCamerouetal1995) aud accretiou-drivon stellar winds (e.g.Matt&Pudvitz 2005). | Two classes of physical models have been proposed to explain this early-time behavior: magnetic breaking by protostellar disks \citep[e.g.][]{koe91,shu94,col95}
and accretion-driven stellar winds \citep[e.g.][]{mat05}. |
Though the physical process that produces this effect iu the first ~650 Myr is nof vet known. the data (Radicketal.19587:Prosser1995:Scholz&Ejisloftel2007) aud theoretical mocels (IXeppeusetal.1995:Tassoul2000) are in agreemieut ou the rotational evolution of Sun-like stars after this time. | Though the physical process that produces this effect in the first $\sim 650$ Myr is not yet known, the data \citep{rad87,pro95,sch07} and theoretical models \citep{kep95,tas00} are in agreement on the rotational evolution of Sun-like stars after this time. |
Tudeed. Sun-ike stars likely lose augular mionienutuu through magnetized stellar winds (Weber&Davis1967:Alestel1968:Isawaler 1988).. aud their rotation slows as Pox£7, as described observationalle as esindxf.E? by κιαΙσ(1972). | Indeed, Sun-like stars likely lose angular momentum through magnetized stellar winds \citep{web67,mes68,kaw88}, and their rotation slows as $P_{\ast} \propto
t^{1/2}$, as described observationally as $v\sin{i} \propto t^{-1/2}$ by \citet{sku72}. |
. Tn this paper. IP use a simple enipirical model to calculate the rotation period of Sun-ike stars as a function of mass and age. | In this paper, I use a simple empirical model to calculate the rotation period of Sun-like stars as a function of mass and age. |
I combine that model with a Monte Carlo simulation to mareialize over the nucertain niasses, radi and ages of a control sample of S66 stars from the Spectroscopic Properties of Cool Stars (SPOCS) catalog of Valeuti&Fischer(2005). to determine the expected range of projected rotation esin/ or cach star in the control sample under the assuniptiou hat the inclination distribution of the SPOCS sample is isotropic. | I combine that model with a Monte Carlo simulation to marginalize over the uncertain masses, radii, and ages of a control sample of 866 stars from the Spectroscopic Properties of Cool Stars (SPOCS) catalog of \citet{val05}
to determine the expected range of projected rotation $v\sin{i}$ for each star in the control sample under the assumption that the inclination distribution of the SPOCS sample is isotropic. |
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