Table Of ContentCONTRIBUTEDARTICLE 1
StellaR: a Package to Manage Stellar
Evolution Tracks and Isochrones
byMatteoDell’Omodarme,andGiadaValle Get stellar evolutionary data
Abstract We present the R package stellaR, The Pisa low-mass database contains computations
whichisdesignedtoaccessandmanipulatepub- classified according to four parameters: the metal-
licly available stellar evolutionary tracks and licity z of the star, its initial helium value y, the
isochrones from the Pisa low-mass database. value of α-enhancement of the heavy elements mix-
The procedures of the extraction of impor- ture with respect to the reference mixture and the
tant stages in the evolution of a star from the mixinglengthparameterαml usedtomodelexternal
database, of the isochrones construction from convection efficiency. The values of the parameters
3 stellar tracks and of the interpolation among availableinthedatabasecanbedisplayedusingthe
1 tracksarediscussedanddemonstrated. functionshowComposition():
0
> showComposition()
2
Mixing-length values:
n Due to the advance in the instrumentation, nowa-
1.7, 1.8, 1.9
a days astronomers can deal with a huge amount of
J
high-quality observational data. In the last decade
6 impressiveimprovementsofspectroscopicandpho- alpha-enhancement values:
1 0, 1 (i.e. [alpha/Fe] = 0.0
tometric observational capabilities made available
[alpha/Fe] = 0.3)
data which stimulated the research in the globu-
]
R lar clusters field. The theoretical effort of recov-
Chemical compositions:
S ering the evolutionary history of the cluster bene-
z y.1 y.2 y.3 y.4 y.5 y.6
. fits by the computation of extensive databases of
h
1e-04 0.249 0.25 0.27 0.33 0.38 0.42
p stellar tracks and isochrones, such as Pietrinferni
2e-04 0.249 0.25 0.27 0.33 0.38 0.42
- etal.(2006);Dotteretal.(2008);Bertellietal.(2008).
o 3e-04 0.249 0.25 0.27 0.33 0.38 0.42
We recently computed a large data set of stellar
r 4e-04 0.249 0.25 0.27 0.33 0.38 0.42
t tracksandisochrones,“ThePisalow-massdatabase”
s 5e-04 0.250 0.25 0.27 0.33 0.38 0.42
a (Dell’Omodarme et al., 2012), with up to date phys-
[ ical and chemical inputs, and made available all 6e-04 0.250 0.25 0.27 0.33 0.38 0.42
1 the calculations to the astrophysical community at 7e-04 0.250 0.25 0.27 0.33 0.38 0.42
8e-04 0.250 0.25 0.27 0.33 0.38 0.42
v theCentredeDonnéesastronomiquesdeStrasbourg
9e-04 0.250 0.25 0.27 0.33 0.38 0.42
5 (CDS)1,adatacenterdedicatedtothecollectionand
9 1e-03 0.250 0.25 0.27 0.33 0.38 0.42
worldwidedistributionofastronomicaldata.
6 2e-03 0.252 0.25 0.27 0.33 0.38 0.42
In most databases, the management of the in-
3 3e-03 0.254 0.25 0.27 0.33 0.38 0.42
. formation and the extraction of the relevant evolu-
1 4e-03 0.256 0.25 0.27 0.33 0.38 0.42
tionary properties from libraries of tracks and/or
0 5e-03 0.258 0.25 0.27 0.33 0.38 0.42
3 isochrones is the responsibility of the end users.
6e-03 0.260 0.25 0.27 0.33 0.38 0.42
1 Due to its extensive capabilities of data manipula-
7e-03 0.262 0.25 0.27 0.33 0.38 0.42
: tion and analysis, however, R is an ideal choice for
v 8e-03 0.264 0.25 0.27 0.33 0.38 0.42
i these tasks. Nevertheless R is not yet well known
X 9e-03 0.266 0.25 0.27 0.33 0.38 0.42
inastrophysics;uptoDecember2012onlysevenas-
1e-02 0.268 0.25 0.27 0.33 0.38 0.42
r tronomical or astrophysical-oriented packages have
a
beenpublishedonCRAN(seethetaskviewChemo- Thetableofchemicalcompositionpresentsallthe y
metricsandComputationalPhysics). values available for a given z. For a set of parame-
The package stellaR (Dell’Omodarme and Valle, ters,thetracksfilesareidentifiedspecifyingthemass
2012) is an effort to make available to the astro- of the desired model (in the range [0.30, 1.10] M(cid:12)
physicalcommunityabasictool-setwiththefollow- (M(cid:12) =1.99·1033 g is the mass of the Sun), step of
ing capabilities: retrieve the required calculations 0.05 M(cid:12)),whiletheage(intherange[8.0-15.0]Gyr,
from CDS; plot the information in a suitable form; stepof0.5Gyr)isrequiredfortheisochrones.
construct by interpolation tracks or isochrones of Uponspecificationoftheaforementionedparam-
compositions different to the ones available in the eters,thestellaRpackagecanimportdatafromCDS
database; construct isochrones for age not included (via anonymous ftp) from an active Internet con-
inthedatabase; extractrelevantevolutionarypoints nection. The CDS data are stored in ASCII format,
fromtracksorisochrones. andincludeaheaderwithcalculationmetadata,such
1viaanonymousftptocdsarc.u-strasbg.fr,orviahttp://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/540/A26
TheRJournalVol. X/Y,Month,Year ISSN2073-4859
CONTRIBUTEDARTICLE 2
as the metallicity, the inital helium abundance, the The function getTrk() returns an object of class
mixing-length. Theimportisdoneviaaread.table "trk", which is a list containing the track meta-
call,skippingtheheaderofthefiles. data, i.e. as the star mass, the metallicity, the ini-
The following data objects can be downloaded tial He abundance, the mixing-length and the α-
fromthedatabasesite: enhancement, and the computed data in the data
framedata.Trackdatacontainsthevaluesof15vari-
• Stellar track: a stellar evolutionary track com-
ables:
puted starting from Pre-Main Sequence (PMS)
and ending at the onset of helium flash (for > names(track$data)
masses M ≥0.55 M(cid:12)) or at the exhaustion of [1] "mod" "time" "logL" "logTe"
centralhydrogen(for0.30M(cid:12)≤M≤0.50M(cid:12)). "mass" "Hc" "logTc" "logRHOc"
The functions getTrk() and getTrkSet() can "MHEc" "Lpp" "LCNO" "L3a"
be used to access such data; they respectively "Lg" "radius" "logg"
returnobjectsofclasses"trk"and"trkset".
The included variables are: mod the progressive
modelnumber; timethelogarithmofthestellarage
• Stellar ZAHB: Zero-Age Horizontal-Branch
models. The functions getZahb() can be used (in yr); logL the logarithm of the surface luminos-
ity(inunitofsolarluminosity);logTethelogarithm
toaccesssuchdata;itreturnsanobjectofclass
"zahb". of the effective temperature (in K); mass the stellar
mass(inunitofsolarmass);Hcthecentralhydrogen
• HBmodels:computedfromZAHBtotheonset abundance (after hydrogen exhaustion: central he-
of thermal pulses. The functions getHb() and liumabundance); logTcthelogarithmofthecentral
getHbgrid() can be used to access such data; temperature(inK);logRHOcthelogarithmofthecen-
theyrespectivelyreturnobjectsofclasses"hb" traldensity(ing/cm3); MHEcthemassofthehelium
and"hbgrid". core (in units of solar mass); Lpp the luminosity of
ppchain(inunitsofsurfaceluminosity);LCNOthelu-
• Stellar isochrones: computed in the age range
minosityofCNOchain(inunitsofsurfaceluminos-
[8 - 15] Gyr. The functions getIso() and ity); L3a the luminosity of triple-α burning (in units
getIsoSet() can be used to access such data; of surface luminosity); Lg luminosity of the gravita-
theyrespectivelyreturnobjectsofclasses"iso" tionalenergy(inunitsofsurfaceluminosity);radius
and"isoset". the stellar radius (in units of solar radius); logg the
logarithmofsurfacegravity(incm/s2).
Readers interested in details about the computa-
SimilarlythepartofthetrackstartingfromZAHB
tion procedure are referred to Dell’Omodarme et al.
and ending at the onset of thermal pulses can be
(2012). The data gathered from CDS are organized
downloadedbythecall:
into objects of appropriate classes. The package in-
cludes print and plot S3 methods for the classes > hbtk <- getHb(m = 0.80, z = 0.001,
"trk","trkset","hb","zahb","hbgrid","iso",and y = 0.25, ml = 1.90, afe = 0)
"isoset". > hbtk
Asanexample,weillustratetherecoveringofthe Stellar track from ZAHB
stellartrackforamodelofmassM=0.80M(cid:12),metal-
licity z = 0.001, initial helium abundance y = 0.25, Mass = 0.8 Msun
mixing-length α = 1.90, α-enhancement [α/Fe] = Mass RGB = 0.8 Msun
ml
0.0. Z = 0.001 , Y = 0.25
Mixing length = 1.9
> track <- getTrk(m = 0.80, z = 0.001,
[alpha/Fe] = 0
y = 0.25, ml = 1.90, afe = 0)
> track
> names(hbtk)
Stellar track
[1] "mass" "massRGB" "z" "y"
"ml" "alpha.enh" "data"
Mass = 0.8 Msun
Z = 0.001 , Y = 0.25
> class(hbtk)
Mixing length = 1.9
[1] "hb" "stellar"
[alpha/Fe] = 0
which returns an object of class "hb", which differs
> names(track) fromanobjectofclass"trk"onlyforthepresenceof
[1] "mass" "z" "y" "ml" thevariablemassRGB,i.e.theRed-GiantBranch(RGB)
"alpha.enh" "data" progenitormass.
Usually a set of tracks with different mass
> class(track) and/ormetallicityareneededforcomputations.The
[1] "trk" "stellar" package stellaR provides the function getTrkSet(),
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CONTRIBUTEDARTICLE 3
which can download a set of tracks with differ- > plot(trks, lty = 1:2)
ent values of mass, metallicity, helium and mixing-
TheoutputofthefunctionisshowninFigure1. The
length. Asanexamplethewholesetofmasses(from
plotisproducedbyacalltothefunctionplotAstro()
0.30 to 1.10 M(cid:12), step of 0.05 M(cid:12)), for metallicity
whichallowstheusertocustomizeseveralaspectsof
z=0.001,initialheliumabundancey=0.25,mixing-
theplot,suchastheaxeslabel,thenumberofminor
lengthα =1.90,α-enhancement[α/Fe]=0.0canbe
ml
ticksbetweentwomajorticks,thelimitsoftheaxes,
downloadedasfollows:
thecolorandtypeofthelines(asintheexample),the
> mass <- seq(0.3, 1.1, by = 0.05) typeoftheplot(lines,points,both,...).
> trks <- getTrkSet(m = mass, z = 0.001, The use of plot() function is further demon-
y = 0.25, ml = 1.90, afe = 0) stratedinFigure2,where,forz=0.001,y=0.25,αml
> trks = 1.90, [α/Fe] = 0.0, are displayed the evolutionary
[[1]] trackfor M=0.80 M(cid:12) fromPMS toHe flash(black
Stellar track line)andfromZAHBtothermalpulses(greenline).
Thefigureisobtainedasfollows:
Mass = 0.3 Msun
> plot(track)
Z = 0.001 , Y = 0.25
> plot(hbtk, add = TRUE, col = "green")
Mixing length = 1.9
[alpha/Fe] = 0
5
3.
[[2]]
0
Stellar track 3.
5
Mass = 0.35 Msun 2.
Z = 0.001 , Y = 0.25 0
Mixing length = 1.9 un 2.
s
[alpha/Fe] = 0 L 5
L 1.
g
o
... l 0
1.
5
0.
4
0
0.
3 5
0.
−
3.85 3.80 3.75 3.70 3.65 3.60 3.55
2 log T
eff
n
u
s
L
L 1 Figure 2: (black line): evolutionary tracks for mass
g
lo M=0.80 M(cid:12),z=0.001,y=0.25,αml=1.90,[α/Fe]=
0.0. fromPMStoHeflash. (greenline): evolutionary
0
trackfromZAHBtothermalpulses.
1
− Apart from the plots discussed before, it is easy
todisplayotherrelationbetweenthecomputedvari-
2 ables. In the following example we get the data for
−
two masses, namely 0.50 and 1.00 M(cid:12) and plot the
3.90 3.85 3.80 3.75 3.70 3.65 3.60 3.55
log T trend of the radius (in units of solar radius) versus
eff
thelogarithmoftheageforthefirst100models. The
resultingplotisdisplayedinFig.3.
Figure 1: The evolutionary tracks for masses from
M=0.30M(cid:12)toM=1.10M(cid:12)fromPMStoHeflash. > trkr <- getTrkSet(m = c(0.5, 1), z = 0.01,
Theparametersofthecalculationsare: z=0.001,y= y = 0.25, ml = 1.8, afe = 0)
0.25,α =1.90,[α/Fe]=0.0. > mydata <- do.call(rbind, lapply(trkr,
ml
"[[", "data"))
The function getTrkSet() returns an object of > D <- mydata[mydata$mod <= 100, ]
class "trkset", a list containing objects of class > key <- as.numeric(factor(D$mass))
"trk". The track set can be displayed in the usual > plotAstro(D$time, D$radius, type = "p",
(logTeff, logL/L(cid:12)) plane by a call of the function pch = key, ylab = "Radius (Rsun)",
plot(): xlab = "log age (yr)")
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CONTRIBUTEDARTICLE 4
> legend("topright", c("M=0.50", "M=1.00"), [1] "logL" "logTe" "mass" "radius" "logg"
pch = 1:2)
Thefunctionreturnsanobjectofclass"isoset",alist
containing objects of class "iso". These last objects
6 l M=0.50 arelistscontainingmetadata(age,metallicity,initial
M=1.00
He abundance, mixing-length, and α-enhanchment)
and the data frame data, which contains the com-
5
putedtheoreticalisochronesdata.Figure4showsthe
setofisochronesplottedwiththecommands:
4
n) > plot(isc, lty = 1:2)
u
us (Rs 3 l l lllllllllllll > legend(l"ttyop=le1f:t2"), c("9 Gyr", "12 Gyr"),
di l
a l
R 2 llll 4 9 Gyr
12 Gyr
l
l
1 lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll 3
0 2
4 5 6 7 8 9 un
s
L
log age (yr) 1
L
g
o
l
Figure3: Radiusversusthelogarithmoftheagefor
0
thefirst100modelsoftwostarswithdifferentmass
(M=0.50 M(cid:12),and M=1.00 M(cid:12))andidenticalcom-
1
position,z=0.01,y=0.25,α =1.8,[α/Fe]=0.0. −
ml
IsochronescanbeobtainedfromCDSandplotted 2
−
inasimilarway. Asanexample,letgetisochronesof
3.85 3.80 3.75 3.70 3.65 3.60 3.55
9and12Gyrforz=0.001,y=0.25,α =1.90,[α/Fe]
ml log T
=0.0: eff
> isc <- getIsoSet(age = c(9, 12), z = 0.001, Figure 4: Isochrones in the theoretical plane for 9
y = 0.25, ml = 1.90, afe = 0) and12Gyr. Calculationsperformedforz=0.001,y=
> isc 0.25,α =1.90,[α/Fe]=0.0.
ml
[[1]]
Stellar isochrone
Tools for interpolating among data
Age = 9 Gyr structures
Z = 0.001 , Y = 0.25
Mixing length = 1.9 Even if the database provides a fine grid of mod-
[alpha/Fe] = 0 els it is possible that the specific model needed
for a comparison with observational data has not
[[2]] been calculated. To address this issue, the package
Stellar isochrone stellaR includes tools for construction of new sets
of isochrones. The simplest case is whenever one
Age = 12 Gyr desires an isochrone for ages not included in the
Z = 0.001 , Y = 0.25 database, but for a combination of metallicity, He
Mixing length = 1.9 abundance,mixing-lengthandα-enhanchmentexist-
[alpha/Fe] = 0 ing in the database. The function makeIso() is able
to compute the required isochrones by mean of in-
attr(,"class") terpolationonatracksset. Theinterpolationcanbe
[1] "isoset" "stellar" performedforageintherange[7-15]Gyr. Theuser
hasthechoicetoexplicitlyprovidetothefunctiona
> names(isc[[1]]) set of tracks, previously downloaded from CDS, or
[1] "age" "z" "y" "ml" to specify the required composition of the tracks to
"alpha.enh" "data" be downloaded for the interpolation. To show the
usage of the function we use the object trks down-
> names(isc[[1]]$data) loadedbeforetoobtainanisochroneofage9.7Gyr:
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CONTRIBUTEDARTICLE 5
> iso.ip <- makeIso(age = 9.7, tr = trks) rithmproceedsasfollows:
> iso.ip
Stellar isochrone 8sets 4sets 2sets 1sets
(cid:122) (cid:125)(cid:124) (cid:123) (cid:122) (cid:125)(cid:124) (cid:123) (cid:122) (cid:125)(cid:124) (cid:123) (cid:122) (cid:125)(cid:124) (cid:123)
Age = 9.7 Gyr Tz,y,αml(M)i→Tz,y,∗(M)i→Tz,∗,∗(M)i→T∗,∗,∗(M)i
Z = 0.001 , Y = 0.25 where the symbol ∗ means that interpolation oc-
Mixing length = 1.9 curred in the substituted variable. The selection
[alpha/Fe] = 0 of the tracks set which enter in the interpolation is
based upon the identification of the vertexes of the
the call produces a result identical to makeIso(age
cellofthe(z,y,α )spacecontainingthepointiden-
ml
= 9.7,z = 0.001,y = 0.25,ml = 1.9,afe = 0); in
tified by the required parameters. Then, for all the
thislastcasethedataaretakenfromCDSbeforethe
17 masses at the vertexes, the linear interpolation
interpolationprocedure.
described above is performed. In the worst case
The interpolation technique is based upon the scenario, whenever no one of the supplied parame-
fact that all the tracks contain the same number of tersvaluesexistinthedatabase,theinterpolationre-
points by construction, and that a given point cor- quires23=8setsof17masses.Thealgorithmishow-
responds to the same evolutionary phase on all the everabletoreducethedimensionalityoftheprocess
tracks. WedefineS(M)asthesetoftrackstobeused ifsomeofthevariablesvaluesexistinthedatabase.
for interpolation, parametrized by the value of the
Asademonstration,letuscomputeasetoftracks
mass M. Let ti(M) be the evolutionary time for the with mixing-length value α = 1.74, z = 0.002, y =
ml
ithpointonthetrackofmass M,and Abetheageof
0.25,[α/Fe]=0.0:
therequiredisochrone.Letkbethepointonthetrack
oflowermassofthesetS(M)forwhicht (M)≥ A. > ip.trk <- interpTrk(z = 0.002, y = 0.25,
k
For each point j≥k on the tracks in S(M), a linear ml = 1.74, afe = 0)
interpolationinageofthevaluesofmass,logarithm
oftheeffectivetemperatureandlogarithmofthelu- Sincethevaluesofzandyexistinthedatabase,only
minosity is performed among tracks. These points an interpolation on the mixing-length value is per-
define the required isochrone. A potential problem formedbythecode. Thesetoftrackscanbeusedfor
of this simple procedure will occur whenever mas- isochronesconstruction,likeastandardsetoftracks:
sivestarsdevelopaconvectivecoreduringtheMain
> ip.iso <- makeIso(age = 12, tr = ip.trk)
Sequence(MS).Inthiscase,asshownforexamplein
Mowlavietal.(2012),themonotonictrendoftheevo-
lutionarytime–thatdecreaseswithincreasingstellar
Keypoints extraction
massattheendoftheMS–invertsatthemiddleof
the MS. However the problem will be encountered
onlyforearly-timeisochrones,forwhichthemassat Importantstagesintheevolutionofastararedefined
theisochroneTurn-Offwillbeintheintervalduring as"keypoints",e.g.hydrogencoreexhuastion,Turn-
which the convective core develops. The procedure Offluminosity,RGBtipluminosity. Tosimplifytheir
outlined in this Section is adequate for construction extractionthepackagestellaRprovidesthefunction
of isochrones throughout the range allowed by the keypoints(), which operates on an object of class
function. "trk"or"iso".
Thefunctionextractsfromthedatastoredinob-
jectsofclass"trk"therowsofthedataframerelative
Tracksinterpolation
tothefollowingevolutionarystages:
ThepackagestellaRprovidesalsoatoolforperform-
1. ZAMS. Zero-Age Main-Sequence, defined as
inga3Dinterpolationonthedatabasetoconstructa
the point for which the central H abundance
set of tracks for values of metallicity, helium abun-
dropsbelow99%ofitsinitialvalue.
danceandmixing-lengthnotincludedinthecompu-
tations available at CDS. The function interpTrk() 2. TO. Turn-Off, defined as the point for which
canbeusedforthisprocedure. Acalltothisfunction theeffectivetemperaturereachesitsmaximum
causes the download from CDS of the sets of tracks value. If multiple lines satisfy the constraint,
neededfortheinterpolation. thevaluesofalltherowsareaveraged.
The new set of tracks is computed by mean
of a linear interpolation. The metallicity is log- 3. BTO.BrighterTurn-Off,definedasthepointfor
transformedbeforetheinterpolationprocedure. Let which the effective temperature drops below
T (M) beithpointonthedatasetcontainingthe theoneoftheTOminus100K.Thepointscan
z,y,αml i
evolutionarytime,theeffectivetemperatureandthe notexistforlowmasses. Detailsontheadvan-
logarithmofsurfaceluminosityforthetrackofmass tagesofthisevolutionarypointwithrespectto
M, and given composition. The interpolation algo- theTOcanbefoundinChaboyeretal.(1996).
TheRJournalVol. X/Y,Month,Year ISSN2073-4859
CONTRIBUTEDARTICLE 6
4. exHc. Central H exhaustion, defined as the > xlab <- expression(italic(M) ~
point for which the central H abundance is (italic(M)[sun]))
zero. For low masses the point can coincide > ylab <- "log age (yr)"
withTO.Thisisthelastpointofthetrackswith > symbol <- as.numeric(factor(kpH$z))
masslowerorequalto0.50 M(cid:12). > plotAstro(kpH$M, kpH$time, type = "p",
pch = symbol, xi = 0.1, xlab = xlab,
5. Heflash. Helium flash, the last point of the ylab = ylab)
trackformasseshigherthan0.50 M(cid:12). lab <- levels(factor(format(kpH$z,
nsmall = 4, scientific = FALSE)))
When the function is called on an object of class
> legend("topright", lab, pch = 1:3)
"iso"itreturnsadataframecontainingonlyTOand
BTOphases.
In both cases the function inserts in the re-
turned data frame the columns relative to mass
(or age for isochrones), metallicity, initial He value,
mixing-length, α-enhancement, and evolutionary
phaseidentifier. 4 l TO
BTO
As a demonstration we extract the TO and BTO
points from the object isoc generated in a previous
3
example:
> kp <- keypoints(isoc)
2
> kp
n
u
logL logTe mass radius Ls
1
TO 0.4044723 3.816652 0.8396903 1.23558 L
g
BTO 0.5556971 3.809943 0.8561162 1.51671 lo ll
TO1 0.2917250 3.803611 0.7772973 1.15234 0
BTO1 0.4495597 3.796545 0.7909500 1.42768
logg age z y ml alpha.enh
1
TO 4.178911 9 0.001 0.25 1.9 0 −
BTO 4.009265 9 0.001 0.25 1.9 0
TO1 4.205965 12 0.001 0.25 1.9 0 −2
BTO1 4.027426 12 0.001 0.25 1.9 0
3.85 3.80 3.75 3.70 3.65 3.60 3.55
id log T
eff
TO 1
BTO 2 5
1. l 0.0001
TO1 1 1 0.0010
0.0100
BTO1 2
The points can be easily superimposed to the 0
isochronesinthetheoreticalplane. Thetoppanelof 11. l
Figure5isobtainedwiththefollowingcommands:
yr) l
> plot(isoc) e ( 5
> points(logL ~ logTe, data = kp, pch = id, ag 10. l
g
col = id) o
l
l
> legend("topleft", c("TO", "BTO"),
pch = 1:2, col = 1:2) 0.0 l
1
l
Asalastexampleweextractasetoftracksformasses
l
in the range [0.40 - 1.10] M(cid:12) and three metallicity z
=0.0001,0.001,0.01andwedisplay(bottompanelin 9.5 l
Figure5)thetimeofexhaustionofcentralhydrogen
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
asafunctionofthemassofthestar. M (M )
sun
> mT <- seq(0.4, 1.1, by = 0.1)
> zT <- c(0.0001, 0.001, 0.01) Figure5: Toppanel: sameasFigure4. Theposition
> tr <- getTrkSet(m = mT, z = zT, y = 0.25, of Turn-Off (TO) and Brighter TO (BTO) are shown.
ml = 1.9, afe = 1) Bottom panel: time to exhaustion of central hydro-
> kp <- keypoints(tr) genasafunctionofthemassofthestar.Thesymbols
> kpH <- kp[kp$id == 4,] identifythevaluesofthemetallicityzform0.0001to
0.01.
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CONTRIBUTEDARTICLE 7
Summary
B.Chaboyer,P.Demarque,P.J.Kernan,L.M.Krauss,
and A. Sarajedini. An accurate relative age esti-
This paper demonstrated how the package stellaR matorforglobularclusters. MNRAS,283:683–689,
can be useful to the astrophysical community as 1996.
a tool to simplify the access to stellar tracks and
isochrones calculations available on-line. A set of M.Dell’OmodarmeandG.Valle.stellaR:stellarevolu-
tools to access, manipulate and plot data are in- tiontracksandisochrones,2012. URLhttp://CRAN.
cluded in the package and their usage was shown. R-project.org/package=stellaR. Rpackagever-
The interpolation functions included in the package sion0.3-1.
canbeusedtosafelyproducetracksorisochronesat
compositions not included in the database, without M.Dell’Omodarme, G.Valle, S.Degl’Innocenti, and
theneedthatusersdevelopsoftwareontheirown.A P. G. Prada Moroni. The Pisa Stellar Evolution
plannedextensionofthepackageisthemodification DataBaseforlow-massstars. A&A,540:A26,2012.
of the algorithm of isochrone construction to make
A. Dotter, B. Chaboyer, D. Jevremovic´, V. Kostov,
feasible the calculation of isochrone of young ages.
E.Baron,andJ.W.Ferguson. TheDartmouthStel-
This step can be useful in view of a possible exten-
larEvolutionDatabase. ApJS,178:89–101,2008.
sionofthePisadatabasetohighermasses,ortoma-
nipulationofdatastoredinotherdatabases. Infact,
N.Mowlavi,P.Eggenberger,G.Meynet,S.Ekström,
whilethepackageiscurrentlydevelopedforaccess-
C.Georgy,A.Maeder,C.Charbonnel,andL.Eyer.
ing data from Pisa low-mass database, other public
Stellar mass and age determinations . I. Grids of
databases can be in principle accessed in the same
stellar models from Z = 0.006 to 0.04 and M = 0.5
way. This step is however complicated by the fact
to3.5 M(cid:12). A&A,541:A41,2012.
thatnostandardforstellarmodeloutputexistsinthe
astrophysicalcommunity,requiringthepersonaliza-
A.Pietrinferni, S.Cassisi, M.Salaris, andF.Castelli.
tionoftheinterfacefunctionsforeachsetofdata.
A Large Stellar Evolution Database for Popu-
lation Synthesis Studies. II. Stellar Models and
Acknowledgments Isochrones for an α-enhanced Metal Distribution.
ApJ,642:797–812,2006.
Wearegratefultoouranonymousrefereesformany
stimulating suggestions that helped in clarify and
MatteoDell’Omodarme
improvethepaperandthepackage. WethankSteve
DipartimentodiFisica“EnricoFermi”,UniversitàdiPisa
Shore for a careful reading of the manuscript and
LargoPontecorvo3,PisaI-56127
manyusefulsuggestions.
Italy
[email protected]
Bibliography
GiadaValle
G.Bertelli,L.Girardi,P.Marigo,andE.Nasi. Scaled DipartimentodiFisica“EnricoFermi”,UniversitàdiPisa
solartracksandisochronesinalargeregionofthe LargoPontecorvo3,PisaI-56127
Z-Y plane. I. From the ZAMS to the TP-AGB end Italy
for0.15-2.5 M(cid:12) stars. A&A,484:815–830,2008. [email protected]
TheRJournalVol. X/Y,Month,Year ISSN2073-4859
