Photo-ionization of planetary winds: case study HD209458b

2.6 MB·

by  E. M. Schneiter

MNRAS000,1–9(2015) PreprintJanuary12,2016 CompiledusingMNRASLATEXstylefilev3.0
Photo-ionization of planetary winds: case study HD
209458b
E. M. Schneiter,(cid:63)1,2,3 A. Esquivel,4 C. S. Villarreal D’Angelo,1
P. F. Vela´zquez,4 A. C. Raga4 and A. Costa1
1Instituto de Astronom´ıa Te´orica y Experimental, Universidad Nacional de Co´rdoba, C´ordoba, Argentina
2Departamento de Materiales y Tecnolog´ıa, UNC, C´ordoba, Argentina
3Departament of Astronomy, AlbaNova, Stockholm University, Sweden
4Instituto de Ciencias Nucleares, Universidad Nacional Auto´noma de M´exico, M´exico D. F. M´exico
6
1
0
2
Accepted.Received;inoriginalform

n
a
J
ABSTRACT

9 Close-in hot Jupiters are exposed to a tremendous photon flux that ionizes the neu-
tralescapingmaterialfromtheplanetleavinganobservableimprintthatmakesthem
]
an interesting laboratory for testing theoretical models. In this work we present 3D
P
hydrodynamic simulations with radiation transfer calculations of a close-in exoplanet
E
in a blow-off state. We calculate the Ly-α absorption and compare it with observa-
.
h tions of HD 209458b and previous simplified model results. Our results show that the
p hydrodynamic interaction together with a proper calculation of the photoionization
-
proccess are able to reproduce the main features of the observed Ly-α absorption, in
o
r particular at the blue-shifted wings of the line. We found that the ionizing stellar flux
t produce an almost linear effect on the amount of absorption in the wake. Varying the
s
a planetary mass loss rate and the radiation flux, we were able to reproduce the 10%
[ absorption observed at 100 km s 1.
− −

1 Key words: hydrodynamics – radiation mechanisms: general – methods : numerical
v
– planets and satellites: individual: HD 209458b
8
5
0
2
0 1 INTRODUCTION 2014;Bourrier&LecavelierdesEtangs2013).Vidal-Madjar
1. et al. (2008) evaluated the absorption seen during transit
ThediscoveryofthefirsthotJupitertransitingitshoststar
0 within the ‘blue’ and the ‘red’ sides (of the wavelength do-
HD 209458 took place more than a decade ago (see Char-
6 main defined in Ben-Jaffel 2007) finding a 9.8±1.8% and
bonneau et al. 2000; Henry et al. 2000). The analysis of
1 5.2±1.0% absorption, respectively.
data samples of the extra-solar planet transit HD 209458b
:
v obtained with the Space Telescope Imaging Spectrograph Vidal-Madjar et al. (2003) first interpreted the absorp-
Xi on board of the Hubble Space Telescope made by Vidal- tionashydrogenatomsintheexosphereundergoinghydro-
dynamic escape, accelerated by the stellar radiation pres-
Madjar et al. (2003) revealed the existence of an extended
r sure. Later, Schneiter et al. (2007) developed a 3D hydro-
a upper atmosphere, and opened a discussion on whether
dynamic model of the interaction between the stellar wind
the atmosphere is being lost (see Ben-Jaffel 2007, 2008).
and the gas escaping from the planet (HD 209458b). By
Vidal-Madjaretal.(2008)revisitedtheobservationsandthe
comparing the calculated Ly-α absorption with the obser-
theoretical-worksbasedonthepictureofanescapingatmo-
vations they were able to estimate an upper limit for the
sphere(e.g.Lammeretal.2003;LecavelierdesEtangsetal.
planetarymasslossrate(M˙ ).InVillarrealD’Angeloetal.
2004;Yelle2004,2006;Baraffeetal.2005;Tianetal.2005; p
(2014) the stellar wind conditions were improved by com-
Schneiteretal.2007;Garc´ıaMun˜oz2007)andconfirmedit.
prehensivelystudyingthestellarwindparameters.Thiswas
Sincethennumeroustheoreticalworkshavebeencarriedout
donebyusingapolytropicmodeltoestimatetheinitialcon-
shifting the discussion to the escaping mechanism, putting
ditions for the stellar wind at the radial distance (from the
the focus on trying to explain the absorption produced at
centre of the star) at which it was imposed. Several stel-
high velocities (see Holmstro¨m et al. 2008; Ekenb¨ack et al.
lar wind velocities where tested together with the coupled
2010; Tremblin & Chiang 2013; Villarreal D’Angelo et al.
stellar wind temperature (T ), finding a suitable range for
∗
M˙ ([3–5]×1010 g s−1). Schneiter et al. (2007) and Villar-
p
(cid:63) E-mail:[email protected] realD’Angeloetal.(2014),distinguishedtheplanetarywind
c 2015TheAuthors
(cid:13)
2 Schneiter et al.
from the stellar wind with the aid of a passive scalar, and The model, some details of the code, and the param-
calculated the Ly-α absorption assuming that all neutral eters employed are presented in Section 2. The results are
materialwithtemperaturesabove105 Kwasionized.These presented in Section 3 and discussed in Section 4. The con-
works were able to reproduce the velocity range of neutral cluding remarks are given in Section 5.
planetary atoms responsible for the observed absorption in
the Ly-α line.
TheworkdoneinHolmstro¨metal.(2008)anditsfollow
2 THE MODEL
upEkenba¨cketal.(2010)reproducetheabsorptionobserved
at Doppler shift −100 km s−1. They simulated the produc- We used the radiation-hydrodynamics code guacho (Es-
tion of energetic neutral hydrogen (ENAs) through charge quivel et al. 2009; Esquivel & Raga 2013) to produce syn-
exchange between stellar wind protons and exospheric hy- theticLy-αabsorptionmapsofahot-Jupiteraroundasolar
drogen,assumingstellarwindconditionssimilartothoseat type star (i.e. the HD 209458 system).
anequivalentdistanceinourSun.Tremblin&Chiang(2013)
further explored the charge-exchange scenario by means of
2.1 The hydrodynamics core
a2Dhydrodynamicmodel,makingemphasisonthemixing
layer between both winds. The code solves the ideal hydrodynamics equations, along
Bourrier&LecavelierdesEtangs(2013)presenteda3D with gravity and radiative gains and losses, in a Cartesian
Monte-Carlo numerical particle model developed to simu- grid:
late the escaping gas of an exoplanet. In their model the
∂ρ
focuswassetontheradiationpressure,takingintoaccount +∇·(ρu)=0, (1)
∂t
the ionization, the self-shielding, and the stellar wind in-
teraction. The charge-exchange process was included as an
impulse given by the incoming stellar wind proton, aiming, ∂(ρu)
+∇·(ρuu+IP)=ρg, (2)
this way, to explain the blue-shifted absorption. ∂t
Eventhoughmostofthesemodelsemploydifferentac-
celerationmechanismfortheneutralparticles,theyallhave ∂E
+∇·[u(E+P)]=G −L +ρ(g·u), (3)
been capable of reproducing the global structure of the up- ∂t rad rad
per atmosphere of exoplanets undergoing mass loss due to
where ρ, u, P, and E are the mass density, velocity, ther-
Rochelobeoverflow,predictingplanetarymasslossratesin
mal pressure and energy density, respectively. I is the iden-
therange109–1011gs−1,leavingthequestionofwhichparti-
titymatrix,gistheaccelerationduetogravitationalforces,
cleaccelerationmechanismisresponsiblefortheabsorption
while G and L the gains and losses due to radiation.
at high Doppler shift, still open. rad rad
The total energy density and thermal pressure are related
Recentprogresshasbeenmadetomodeltheplanetary
by an ideal gas equation of state E =ρ|u|2/2+P/(γ−1),
masslossrateincludingtheeffectofmagneticfieldsinboth
where γ =5/3 is the ratio between specific heat capacities.
thestarandtheplanet.Ithasbeenshownforinstancethat
The hydrodynamics equations (left hand side of Equa-
spaceweatherevents(suchasCME)ortheparametersofthe
tions 1–3), are advanced with a second order Godunov
planetary system itself, can have an influence on the mass
method with an approximate Riemann solver (HLLC, Toro
loss from the planet (see for example Cohen et al. 2011a,b;
1999),andalinearreconstructionoftheprimitivevariables
Owen & Adams 2014; Trammell et al. 2014; Adams 2011;
using the minmod slope limiter to ensure stability.
Matsakosetal.2015).Owen&Adams(2014)find,through
a number of numerical simulations that include the stellar
UVflux,thatthepresenceofmagneticfields,canreducethe 2.2 Source terms
amountofplanetarymasslossratebyaproximatelyanorder
of magnitude if the planet can sustain moderate magnetic Ateverytime-step,thehydrodynamicvariablesareupdated,
fields values (B > 1 G). Finally, as mentioned in Cohen withtheupdatesvaluesthesourceterms(righthandsideof
p
et al. (2011a,b) and in Owen & Adams (2014), the inter- Equations 1–3) are computed and added to the solution in
actionoftheplanetarymagnetospherewiththemagnetized a semi-implicit scheme.
stellar wind is expected to be highly dynamic and change
withtimeaccordingtotheparametersoftheplanetarysys-
2.2.1 Gravity
tem.
Herewepresenta3Dnumericalmodelofthehydrody- For the gravitational force we add to each cell on the grid
namicinteractionbetweenthewindsthatincludesinaself- the acceleration due to two point masses, the mass of the
consistent manner the calculation of the photo-ionization, planet(whosepositionchangesasitorbitsaroundthestar),
and we focus in the effects of varying the ionizing flux, the and the mass of star. The mass of the star is reduced to
stellarwindparametersandthemasslossrateoftheplanet. 1/3 of the actual value for the computation of the gravi-
SimilarsimulationshaverecentlybeenpresentedbyTripathi tational acceleration, to emulate the effect of the radiation
et al. (2015), where the evaporation of the exoplanet atmo- pressureforcethatactsinoppositiontogravity(seeforex-
sphere is modeled with radiation hydrodynamics. In such ample Vidal-Madjar et al. 2003).
work,anasymmetricplanetarywindisproducedbyaplane A more detailed calculation of the radiation pressure
parallelradiativefieldandstellarwind.However,theirfocus is possible. For instance, Bourrier & Lecavelier des Etangs
isinthemasslossfromtheplanet,andnotontheextended (2013); Bourrier et al. (2015), calculated the ratio of the
wake. radiation pressure to gravitational forces (the β parameter
MNRAS000,1–9(2015)
Photo-ionization of planetary winds 3
in their models, which is proportional to the Ly-α flux) to is then included in the energy term (Eq. 3) after each hy-
model the evaporation of the atmospheres of HD 209458b drodynamical timestep. The energy gain per ionization is
and HD 189733b. Such calculation involves the knowledge assumed to be E = 13 eV. The cooling rate at low tem-
0
of the Ly-α emission as seen by each cell, which is beyond peratures (< 3×104 K), is due to collisional ionization of
the scope of the present paper. We plan to pursue this re- oxygen, assuming that the ionization of Oii follows that of
finement in a future study. Hii (obtained from Eq. 4). This is a good approximation
due to the efficient charge exchange between H and O, see
Hartigan & Raymond 1993. At higher temperatures, when
2.2.2 Heating, cooling, and radiative transfer oxygenisexpectedtobemorethansinglyionized,thecool-
ing is switched to a coronal equilibrium cooling curve.
InordertoconsiderthephotoionizationofH,togetherwith
thegas-dynamicequationsweintegrateanadditionalequa-
tion for neutral hydrogen of the form: 2.3 Parameters of the simulations
∂nHI +∇.(n u)=(n−n )2α(T) Thestar/planetsystemismodeledastheinteractionoftwo
∂t HI HI (4) isotropic wind sources in orbit. There are many physical
−(n−nHI)nHIc(T)−nHIφ, processes that could lead to an anisotropic planetary wind.
Forinstance,atidallylockedplanetwouldleadtothesame
whereα(T)istherecombinationcoefficient,c(T)isthecol-
hemispherefacingthehoststar,and,unlessthereareatmo-
lisional ionization coefficient of hydrogen, and φ the pho-
spheric flows that transport heat efficiently (see Batygin &
toionization rate. In Equation (4) we have assummed that
Stanley 2014; Showman et al. 2008, for a discussion on in-
the electron density is equal to that of ionized hydrogen
ternal flows) that are capable of thermalising the whole at-
n =n =n−n , where n and n are the neutral and
e HII HI HI mosphere,thewindswillbeassymetric.Thiseffecthasbeen
total hydrogen density, respectively.
studiedbeforeinVillarrealD’Angeloetal.(2014)bymeans
The hydrogen photoionization rate (φ), due to the UV
of a few toy models. In that work, inspite of the simplic-
photons emitted by the star is given by:
ity of the models, only a minor effect in the wake structure
(cid:90) ∞ 4πJ that produced most of the Ly-α absorption was found. Re-
φ= ν0a dν (5)
hν ν cently, a more detailed calculation of the photoevaporation
ν0
of the planet atmosphere was presented in Tripathi et al.
where J is the solid angle averaged intensity of the ion-
ν0 (2015). They used 3D radiation-hydrodynamics and arrive
izing radiative field, ν0 is the Lyman limit frequency, h is tothesamevalueofM˙ thatweadopt(2×1010g s−1).For
p
Plank’sconstantanda isthephotoionizationcrosssection
ν simplicity, and left to a future work, we assume isotropic
ofH.Tocomputethephotoionizationratewehaveusedthe
planetary and stellar winds.
standard ‘grey approximation’ in which the frequency de-
Weplacethesourcethatcorrespondstothestaratthe
pendence of the cross section is not considered, and all the
center of the computational domain, which coincides with
photons are assumed to be at the Lyman limit, with a con-
the origin of a Cartesian grid. The planet orbits the star
stant photoionization cross section a =6.3×10−18 cm−2.
0 in the xz-plane in an anti-clockwise direction. Both winds
Toincludethephoto-ionizingradiationofthehoststar
are reimposed at every time-step with the planet position
we modified the ray tracing method described in Esquivel
updated according to its orbital period (τ = 3.52 days).
orb
& Raga (2013). In the version used here we divide the
The orbit is assumed circular with a radius of 0.047 AU.
EUV stellar luminosity into 107 photon packets, which are The initial position of the planet is 25◦ ‘behind’ the x-axis
launchedinrandomdirections,fromrandompositionsatthe
toensurethatthewakeisformedbythetimeitreachesthe
surface of the star. 1 During the propagation, each photon-
z-axis, wich we have taken to be the line of sight (LOS),
package is decimated by factors of e−∆τ when travelling
unless otherwise stated.
through the intercepted cells (when neutral material is en-
We ran a total of 19 models, varying the stellar wind
countered, ∆τ =a n ∆l, where ∆l is the path-length tra-
0 HI temperature and velocity, the photoionizing rate and the
versed).Thephotoionizingrateisobtainedbyequatingthe
mass loss rate of the planet. For clarity we present the pa-
photon rate to the ionizations per unit time in each cell, as
rameters used in the simulations in two tables. In Table 1
the photon packets reach it
we show the star and planet parameters, and the symbols
S =n φdV. (6) we use for them. In this table we show the ranges of the
HI parametersthatwevaryaswellassomecommonquantities
Thecontributionsfromtheabsorbedphotonsareadded inthesimulations.InTable2weshowthedetailsofeachof
tothephotoionization(Eq.4),andheatingratesofeachcell the models.
in the computational grid. The resulting heating rate Thestellarwindisimposedfullyionizednearthesonic
point with the corresponding temperature and velocity, the
ψ=n φE , (7)
HI 0 density follows an ∝ r−2 profile, scaled to give the corre-
sponding mass loss rate. The temperature and velocity of
the winds were extrapolated from the surface of the star to
1 We have made a convergence test to ensure that this number
thelaunchpositionwiththeaidofapolytropicmodelwith
ofphotonpacketsissufficient.Werepeatedthesamecalculation
foramodel(B2b)with105,106,107and5 107photonpackets. index close 1.01 (see Villarreal D’Angelo et al. 2014).
We then computed the Ly-α absorption p×rofile. With 107 rays Theplanetarywindisimposedwithanionizationfrac-
theresultswerealmostindistinguishablefromthosewithalarger tion of 0.8, at 3 Rp (roughly the Hill radius). This choice is
number. based on the results obtained in Murray-Clay et al. (2009),
MNRAS000,1–9(2015)
4 Schneiter et al.
Table 1. Stellar and planetary winds parameters employed in
simulations
Stellar parameters Symbol Value
Radius R∗ 1.146R(cid:12)
Mass M∗ 1.148M(cid:12)
Windvelocity v∗ 130–372kms−1
Windlaunchradius Rw,∗ 3.5–6.9R∗
Windtemperature T∗ 1–3MK
Masslossrate M˙∗ 2.0M(cid:12) yr−1
Ionizingphotonrate S0 2.4 1038 s−1
×
Planetary parameters Symbol Value
Radius Rp 1.38RJup
Mass Mp 0.67MJup
Windvelocity vp 10kms−1
Windlaunchradius Rw,p 3Rp
Windtemperature Tp 1 104 K
Masslossrate M˙p (1×–2) 1010 gs−1
×
where a one-dimensional model for photoevaporative mass
loss from a hot Jupiter is constructed. They focus on the
Figure1.3Drenderingofthedensityofoneofthemodels(C1b,
escapeofhydrogenoriginatedonthesubstellarpointofthe
seeTable2),afteranintegrationtimeof3.8days.
planet, and assume that mass loss occurs in the form of
a steady, hydrodynamic, transonic wind. Their results pre-
dictthat20%ofthematerialremainsneutralat3R .This
p
value,however,dependsstronglyonthemodelassumptions.
For instance, Koskinen et al. (2013) predicts a transition
3 RESULTS
Hi/Hii at an altitude of 3.1R , implying that 50% of the
p
escapingmaterialremainsneutralatthisaltitude.Themass As explored in previous works, the interaction between the
loss rate adopted is also consistent with that obtained in stellar and planetary winds forms a wake structure similar
Tripathi et al. (2015), who presented 3D simulations of the to what is shown in Figure 1. The parameters we used for
photoevaporation near the planet atmosphere. the wind sources result in similar morphology in all cases,
In our models, the temperature and terminal velocity where the morphological differences lie in the details. For
aresetconstantatthebaseoftheplanetarywind,whilethe instance,arapidwindfromthestarresultsinalesscurved
density profile is scaled to give the desired mass loss rate. and more radial wake than a slow wind, or a higher mass
Based on luminosity estimated for HD 209458 in Sanz- loss rate of the planet produces a larger bow-shock. Figure
Forcada et al. (2011) (they find logL < 27.74 erg s−1) 2showsthedensitystratification,temperatureandionizing
EUV
we have chosen a S = 2.46 × 1038 s−1 for the ste- heatingrateforacutintheorbitalplaneafteranevolution
0
llar photon rate, which corresponds to a flux of F = time of t=2.9 days.
0
884 erg cm−2 s−1 at the orbital distance of HD 209458b. In the top panel we indicate by a solid circle the ex-
Otherworks,wherefocusissetontheescapeprocesswhich tent of HD 209458 (the photon packages are launched from
utilize the EUV and X-ray as energy input consider a this radius), and with a dashed circle the size of the region
rangeinluminosities/fluxes.Forinstance,Tianetal.(2005) in which the stellar wind is imposed. In addition, the top
use the current Solar luminosity value, yielding a flux of panel of this Figure includes the ionization fraction isocon-
F = 0.15 erg cm−2 s−1 at 1 AU (roughly a tenth of ours); toursat0.9(closetotheplanet),0.99and0.999levels.The
while Owen & Jackson (2012) adopt a larger photon rate ionizationstructureofthetailissignificantlydifferentfrom
(S = 1040 s−1). Murray-Clay et al. (2009) use the solar ourpreviousmodels,wherethephotoionizationwasnotcon-
∗
EUV flux of 450 erg s−1 at 0.05 AU, which corresponds to sidered,andafullyneutralplanetarywindwasimposed.In
a S =1.4×1037 s−1. Similar values have been adopted in Schneiter et al. (2007); Villarreal D’Angelo et al. (2014) we
∗
theworksofOwen&Adams(2014);Matsakosetal.(2015). assumedthatmaterialarisingfromtheplanetarywindwith
Toevaluatetheeffectoftheionizingphotonrateonthees- a temperature T < 105 K was neutral (and it was consid-
caping planetary material and somehow cover the range of ered to estimate the Ly-α absorption). In the models with
values discussed in the literature we use three different val- photoionizationwenowassumeanionizationfractionof0.8,
uesforthephotonfluxinoursimulations(0.2, 1.,5.)×S . which increases rapidly, implying that there is less material
0
Figure 1 shows the computational domain with a ren- available to absorb.
deringofthedensity.Thesystemhasreachedafullyquasi- Fromtheothertwopanels,temperatureandionization
stationarystatewithalongcurvedwakebehindtheplanet. heating rate stratification (b and c) it is clear how the im-
Theinitialconditionsareevolvedforanintegrationtimeof pingingphotonsheatupthetrailingplanetarymaterialand
3.8days,inwhichtheplanetcompletesanorbitaroundthe howtheplanetandthehighdensityinteractionregionshield
star. the outer part of escaping neutral atoms in the wake.
MNRAS000,1–9(2015)
Photo-ionization of planetary winds 5
Table 2.Parametersofallthesimulations.
Runs M˙p v∗ Grida T PhotonRate
( 1010 gs−1) (kms−1) (AU) ( 106 K) (s−1)
× ×
A1a 1 130 0.2 0.05 0.2 1 0.2 S0
× × ×
A1b 2 130 0.2 0.05 0.2 1 0.2 S0
× × ×
A2a 1 130 0.2 0.05 0.2 1 S0
× ×
A2b 2 130 0.2 0.05 0.2 1 S0
× ×
ANRb 2 130 0.2 0.05 0.2 1 NoRad
× ×
A3a 1 130 0.2 0.05 0.2 1 5 S0
× × ×
A3b 2 130 0.2 0.05 0.2 1 5 S0
× × ×
B1a 1 205 0.2 0.05 0.2 1.3 0.2 S0
× × ×
B1b 2 205 0.2 0.05 0.2 1.3 0.2 S0
× × ×
B2a 1 205 0.2 0.05 0.2 1.3 S0
× ×
B2b 2 205 0.2 0.05 0.2 1.3 S0
× ×
B3a 1 205 0.2 0.05 0.2 1.3 5 S0
× × ×
B3b 2 205 0.2 0.05 0.2 1.3 5 S0
× × ×
C1a 1 372 0.3 0.075 0.3 3 0.2 S0
× × ×
C1b 2 372 0.3 0.075 0.3 3 0.2 S0
× × ×
C2a 1 372 0.3 0.075 0.3 3 S0
× ×
C2b 2 372 0.3 0.075 0.3 3 S0
× ×
C3a 1 372 0.3 0.075 0.3 3 5 S0
× × ×
C3b 2 372 0.3 0.075 0.3 3 5 S0
× × ×
a All simulations have the same resolution, but to avoid neutral material
from the tail leaving the domain we had to increase the grid size in some of
theruns.
3.1 Ly-α absorption main reason is that the photoionization results in a smaller
neutral tail.
Tocalculatetheabsorptionproducedbytheescapinghydro-
Figure4showstheabsorptionofthestellaremissionas
gen we employed a similar post-processing procedure as in
afunctionoftime,firstfromthe+z direction(t<2.2days)
Schneiteretal.(2007)andVillarrealD’Angeloetal.(2014).
and the subsequent transit as would be measured from the
Foreachofthesimulationswecomputetheopticaldepthas
−z direction (see Figure 2) for all the models.
a function of velocity along the LOS
We have separated the models according to the stel-
(cid:90)
τ = n a ϕ(∆v )ds, (8) lar wind velocity. Panel (a) shows all the models with
vlos HI 0 los v =130km s−1,includingthereferencemodelANRbthat
∗
has the same parameters as A2b (see Table 2 for details)
whereϕ(∆v )isaGaussianline-profile.Theopticaldepth
los
but does not include the photoionization process. In this
is obtained projecting the velocity on a LOS that is almost
alignedwiththezand−z-axes,inclined3.41◦aroundthex- model the absorption was computed as in (Schneiter et al.
2007), that is, assuming that only material originally from
axis to have the same orientation as the HD 209548 system
seenfromEarth(anorbitalinclinationangleofi=86.59◦). the planet with temperatures below 105 K absorb the Ly-
α emission. Panels (b) and (c) show the absorption for the
Intheopticaldepthcalculationwehaveconsideredaveloc-
ity range of [−300,300] km s−1, covered with 250 velocity models with 205 and 372 km s−1, respectively. Notice that
thereareonlyminordifferencesinthefirstandsecondtran-
bins. By choosing the LOS close to z and −z we are able
sits,showingthatthequasi-stationarywakestructureforms
toobservetwotransitsinthesameorbit.Theopticaldepth
rapidly.TheabsorptioninFigure4wascalculatedexcluding
isonlycalculatedconsideringthematerialontheobserver’s
the velocity range between −40 and 40 km s−1, which for
side from the star.
Earthbasedobservationsiscontaminatedbythegeocoronal
The total absorption can be calculated by integrating
emission.
τ in velocity. The Ly-α emission from the star would be
vlos
absorbedbyafactor(1−e−τ),whereτ istheopticaldepth From the plots we can see that the maximum absorp-
integrated over all velocities. Figure 3 shows an example tionchangeswhendoublingM˙p.Thisisinaccordancewith
(samemodelshowninFigures1and2)ofthetotalabsorp- the results obtained in Schneiter et al. (2007)and Villarreal
tionfractioncalculatedfromthemodelsduringatransit,as D’Angeloetal.(2014).Atthesametimethetotalabsorption
it would be seen by an observer in the −z direction (with isgreatlyaffectedbythechangeinFEUV,producingappre-
the inclination of HD 209458b). ciable changes both in the maximum absorption as well as
After computing the Ly-α absorption as a function of in the tail of the wake (absorption after the transit of the
time, we found that the wake reaches a quasi-stationary planet),adenserandmoreextendedstructureisformedfor
state in only a fraction of the orbital period. This is some- low ionizing fluxes.
whatdifferentfromourpreviousmodels,whereatleasthalf From the detection made with the Space Telescope
a period was required to reach such a stationary state. The ImagingSpectrograph(STIS)onboardoftheHubbleSpace
MNRAS000,1–9(2015)
6 Schneiter et al.
(a)Density [email protected](intransit)
0.15 0.30
C1b@t=2.9days 106
0.02 0.27
0.10
0.24
105 0.01 0.21τe)−
0.05 −
(1
0.18n
z[AU] 00..0050 1043n[cm]−H y[AU] 0.00 00..1125bsorptionfractio
− a
103 −0.01 0.09αy
L
0.10 0.06
−
0.02 0.03
102 −
0.15
− 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.00
− − − x[AU] −0.02 −0.01 0.00 0.01 0.02
x[AU]
(b)Temperature
0.15
106 Figure 3. Map of Ly-α optical depth (integrated over all ve-
locities) for model C1b in transit as observed from the z-axis
−
(integrationtimeof2.9days).Themapshowediszoom-inofthe
0.10
entire domain. Both the star and the planet are shown in scale
bythewhitecircleandblackdisk,respectively.
0.05
Telescope (HST) in 2001 (see Vidal-Madjar et al. 2003) it
z[AU] 0.00 105T[K] is clear that the deepest absorption signatures are found in
thebluewingoftheLy-αline,inthevelocityrangebetween
−130and−40km s−1.WhereastheredsideoftheDoppler
0.05
− Shifted absorption, defined within the velocity range be-
tween 32 and 100 km s−1 is less significant. To study this
0.10 features,weshowinFigure5thestellaremissionasafunc-
−
tionofvelocity,forallthemodels,atthetimeofmaximum
absorption during the second transit (t=2.9 days).
−0.150.15 0.10 0.05 0.00 0.05 0.10 0.15 104 From Figure 5 we notice that the absorption depends
− − −
x[AU] strongly on the ionizing flux, especially on the blue side of
(c)Ionizationheatingrate the spectrum, contrary to what it is observed on the red
0.15
side, where all models show similar behaviour.
10−11
Itisexpectedthathigherionizingfluxesresultinalower
0.10 10−12 absorption,asphotoionizedmaterialbecomestransparentto
Ly-α.Inaddition,neutralmaterialinthewakeoftheplane-
10−13 tarywindacceleratesduetoitshydrodynamicalinteraction
0.05 with the stellar wind, as well as due to radiation pressure
10−141]− (modeled here as a deficit in the gravitational pull of the
s
AU] 0.00 3m− star).Theneutralwakethereforeacceleratestowardstheob-
z[ 10−15ψ[ergc sfreormverth(esesetaFrigpurroedu2)c,inagndthientperroamctisnewnitthbltuhee-sLhyif-tαedemabissosiropn-
−0.05 10−16 tion, whose maximum value shifts towards more negatives
velocities when the ionizing flux diminish.
10−17
To compare our results with the observations we took
0.10
− 10−18 theoriginaloff-transitdata(reproducedfromVidal-Madjar
etal.2003),andmultipliedthembythevelocitydependent
−0.150.15 0.10 0.05 0.00 0.05 0.10 0.15 10−19 absorptionfactorinourmodels.TheresultingLy-αprofiles
− − − x[AU] can be compared with the in-transit observations in Figure
6 (also reproduced from Vidal-Madjar et al. 2003).
Figure 2. 2D cuts in the orbital plane (y = 0) of (a) density, The observations show absorption in both the blue
(b)temperature,and(c)ionizationheatingrate,att=2.9days part of the spectrum (in the velocity range from −130 to
formodelC1b.Inthetoppanel,weshowthesizeofthecentral −40km s−1),aswellasintheredpartofthespectrum(ve-
star(solidlinecircle)andthesizeoftheregionatwhichthewind
locity range from 32 to 100 km s−1) with an attenuation of
is imposed (dashed line circle). In the same panel we also show
∼10% and ∼5%, respectively.
ionizationfractioniso-contoursatvaluesof0.9(themostinterior
Most of the models reproduce the level of absorption
totheplanet),0.99,and0.999(themostexterior).
MNRAS000,1–9(2015)
Photo-ionization of planetary winds 7
(a)v∗T=im1e3(h0rk)ms−1 (b)v∗T=im2e0(h5rk)ms−1 (c)v∗T=im3e7(2hrk)ms−1
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
A1a A2a A3b B1a B2b B3b C1a C2b C3b
A1b A2b P.disctransit B1b B3a P.disctransit C1b C3a P.disctransit
ANRb A3a B2a C2a
101 101 101
Absorption(percent) Absorption(percent) Absorption(percent)
100 100 100
1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5 1.0 1.5 2.0 2.5 3.0 3.5
Time(days) Time(days) Time(days)
Figure4.Velocityaveragedtotalabsorptionasafunctionoftimecalculatedfromanobserversituatedinthe+z(firsttransitt<2.2days)
and-zdirections(secondtransit,t>2.2days).Themodelsaregroupedintopanelsaccordingtothestellarwindvelocity,asindicated
inthetitle.Thecolorcodingrepresentstheionizingflux:0.2S0 (orange),S0 (green),and5S0 (purple).Thedotsjoinedbydottedlines
correspondtoM˙p =2 1010 gs−1,andthesolidlinestoM˙p =1 1010 gs−1.Thegreenverticalstriperepresentsthetimeswhena
× ×
portionoftheplanetarydiscblocksthestar(i.e.theplanetisintransit).
1.0 (a)v∗=130kms−1 1.0 (b)v∗=205kms−1 1.0 (c)v∗=372kms−1
0.9 0.9 0.9
0.8 0.8 0.8
0.7 0.7 0.7
malizedFlux00..56 malizedFlux00..56 malizedFlux00..56
Nor Nor Nor
0.4 0.4 0.4
0.3 A1a ANRb 0.3 B1a B3a 0.3 C1a C3b
A1b A3a B1b B3b C1b C3a
0.2 A2a A3b 0.2 B2a Geo.abs. 0.2 C2a Geo.abs.
A2b Geo.abs. B2b C2b
0.1 0.1 0.1
−300 −200 −100 Velocity0[kms−1] 100 200 300 −300 −200 −100 Velocity0[kms−1] 100 200 300 −300 −200 −100 Velocity0[kms−1] 100 200 300
Figure 5.Normalizedstellaremissionatt=2.9daysasafunctionofLOSvelocity.Themodelsaregroupedinthesamemannerasin
Figure 4 Panel (a) includes the line profile for a simulations without radiation transfer (black line), calculated with the passive scalar
andtheaionizationtemperatureasinSchneiteretal.(2007);VillarrealD’Angeloetal.(2014).Theyellowstriperepresentsthepartof
thelinethatiscontaminatedwiththegeocoronalglowandwasomittedformthetotalabsorptioncalculation.
(a)v∗=130kms−1 (b)v∗=205kms−1 (c)v∗=372kms−1
3.5 Intransit(VM03) A2a A3a 3.5 Intransit(VM03) B1b B3a 3.5 Intransit(VM03) C1b C3a
Offtransit(VM03) A2b A3b Offtransit(VM03) B2a B3b Offtransit(VM03) C2a C3b
3.0 A1a ANRb Geo.abs. 3.0 B1a B2b Geo.abs. 3.0 C1a C2b Geo.abs.
A1b
˚A)2.5 ˚A)2.5 ˚A)2.5
21ms−−2.0 21ms−−2.0 21ms−−2.0
1410ergc×1.5 1410ergc×1.5 1410ergc×1.5
Flux(1.0 Flux(1.0 Flux(1.0
0.5 0.5 0.5
0.0 0.0 0.0
−300 −200 −100 Velocity0[kms−1] 100 200 300 −300 −200 −100 Velocity0[kms−1] 100 200 300 −300 −200 −100 Velocity0[kms−1] 100 200 300
Figure 6. Ly-α observations (reproduced from Vidal-Madjar et al. 2003), and the corresponding synthetic absorption calculated with
ourmodels.Thecolorandlinecodingisthesameasinpreviousfigures,anditisindicatedinthelabel.
in the blue wing (except models with low stellar flux that coronal emission in observations, thus it should not be con-
overestimate the absorption for all velocities), considering sidered when comparing our models with observations.
the large uncertainties in the observations. The red wing
absorption is generally underestimated, and only a couple
of models show very little absorption around 90 km s−1.
In Figures 5 and 6 the region shaded in yellow corre-
sponds to the part of the spectrum contaminated by geo-
MNRAS000,1–9(2015)
8 Schneiter et al.
4 DISCUSSION atmosphere of HD 209458b.
Itwouldbeimportanttohavesomeobservationalconstraint
The models presented here are closer to a self-consistent
tothevalueofη,asmentionedEhrenreich&D´esert(2011).
studyofthestellar-planetarywindinteractionthanthetwo
Thiscouldshedsomelightintotheatmosphericcomposition
previous works (Schneiter et al. 2007; Villarreal D’Angelo
of exoplanets.
etal.2014),whereaproperphotoionizatingphotonfluxwas
When comparing our models with the observations,
not included.
in particular focusing on the Doppler blue-shifted part of
Focusing on the the outer part of the planetary atmo-
the curve (Figure 6) we see that the v = 130 km s−1
sphere (r (cid:38)3R ), and adjusting the hydrodynamic param- ∗
p peak is better fitted with the S photon rate, whereas a
eters according the results in Schneiter et al. (2007); Vil- 0
lower absolute velocity part of the spectrum (between −40
larreal D’Angelo et al. (2014), we have done a study of the
to −75 km s−1) is better fitted with a larger photon rate
influence of the high energy photon flux on the escaping
(5×S ) flux. The same trend is observed for larger wind
partoftheatmosphere.Themaximumabsorptionisshown 0
velocity.Certainlywithamorefineparametercoverageone
in Figure 4 (the portion shaded in green which corresponds
couldreproducetheabsorptioninmoredetail,howeverthis
to the planet transit), where a strong almost linear depen-
is beyond the scope of this paper.
dence on the high ionizing flux is found. The importance of
In a recent work, Tremblin & Chiang (2013) study the
the planetary mass loss rate becomes less obvious (almost
effect of charge exchange in the mixing region of the two
negligible) within the accepted range estimated in previous
winds. With their choice of parameters they are able to re-
works(Schneiteretal.2007;VillarrealD’Angeloetal.2014).
produce an asymmetric absorption (also favouring the blue
At the same time, M˙ does affect the absorption in the tail
p wing),in particularthe∼10%absorption at−100km s−1.
(after the planetary transit). This result is not surprising,
Their parameters are similar to our model A1b, but with
since most of the neutral material is swept, by the stellar
the inclusion of a treatment for charge exchange between
wind, to produce the tail which, due to the orbital motion,
the stellar and planetary winds.
andgravitationalpull,itbecomescurvedgettingexposedto
IncontrasttothestudiesofTremblin&Chiang(2013);
the photoionizing flux incoming from the star (see Figures
Holmstro¨m et al. (2008), our simulations did not inlude
1 and 2).
charge exchange but where still able to produce absorption
The stellar EUV flux in our models ranges between ∼
at high blue Doppler-shift velocities, but due to the pure
[1 × 102 − 4 × 103] erg cm−2 s−1. This implies that the
hydrodynamic interaction, along with the global radiation
planetary evaporation for HD 209458b will be driven by an
pressure2. It is clear that both effects are expected to be
energy limited mechanism (see Murray-Clay et al. 2009).
present, and charge exchange in models as ours would en-
Under this paradigm we can estimate the planetary mass
hance the absorption in the blue. An assessment of their
loss rate from the simple equation (Yelle 2004; Penz et al.
relative (or collective) contribution is left for a follow up
2008)
study.
πR3F The inclusion of the radiation transfer calculation also
M˙p =ηrad GpMEUV (9) showsthatthepreviousestimatesoftheplanetarymassloss
p rates where a bit low. It is clear from Figure 4 that the
where η is the heating efficiency and F is the EUV samehydrodynamicalparametersresultinaoverestimation
rad EUV
flux at the position of the planet. M , R are the mass and of the absorption respect to the models that do include the
p p
the planetary radius and G is the gravitational constant. photionization of the tail. Therefore, to reach a similar ab-
This formula does not take into account the correction for sorptionwiththephotonionizationincludedrequiresalarger
the Roche lobe effects that acording to Penz et al. (2008); masslossrate.Howeverthemasslossratesusedinthiswork
Erkaevetal.(2007),canchangethevalueofM˙ inafactor are compatible to previous estimates.
p
of ∼1.5 for HD 209458b.
In our simulations, we fix the mass loss rate of the planet
and the stellar flux for each model. This implies, according 5 CONCLUSIONS
to the Eq. 9, to assume a certain value for the heating effi-
Weusedthe3DnumericalhydrodynamiccodeGuacho,to
ciencyatthepositionwheretheplanetarywindislaunched.
simulate the interaction of the wind escaping a hot-Jupiter
Hence, in our models, the heating efficiency varies from 2%
(with parameters resembling HD 209458b) and a photo-
to100%.Atthepresent,itisunclearwhatisthebestvalue
ionized wind coming from a solar-type star (HD 209458).
for η, but with our models we will be covering almost all
The ionizing flux was found to have a great influence
possibles values. In the literature, several authors tried to
on the neutral hydrogen escaping from the planet, produc-
constrain this factor: Tian et al. (2005) adopted a η = 0.6
ing an almost linear effect on the absorption of the wake.
forapureatomicHatmosphere,Ehrenreich&D´esert(2011)
With planetary mass loss rates within the range proposed
obtainedanη>1basedonthevaluesofmasslossratefrom
in Schneiter et al. (2007); Villarreal D’Angelo et al. (2014)
Vidal-Madjaretal.(2003)andLinskyetal.(2010)andthe
itispossibletofindEUVfluxesthatreproducetheobserved
luminosityvaluefromKashyapetal.(2008),Lammeretal.
absorption measured in Vidal-Madjar et al. (2003) down to
(2009) suggest η∼[10−25]%.
velocitieslessthan−100km s−1.Perfoming3Dsimulations
As a first aproximation, from Fig. 6, we can say that the
lowestvalueofF can’treproducetheobservedabsorption,
0
hence this models are not expected to be representative of 2 implementedasareductionofthestellargravitationalpotential
the planetary system parameters. So, the highest values of asinVidal-Madjaretal.(2003);Schneiteretal.(2007);Villarreal
η (∼[50−100]%) are not expected to define the planetary D’Angeloetal.(2014).
MNRAS000,1–9(2015)
Photo-ionization of planetary winds 9
that include the orbital motion of the planet is a natural Lecavelier des Etangs A., Vidal-Madjar A., McConnell J. C.,
wayofobtaininganon-symmetrichydrogenenvelopthatis H´ebrardG.,2004,A&A,418,L1
subject to the incoming stellar photons and wind. Linsky J. L., Yang H., France K., Froning C. S., Green J. C.,
Ourmodelsshowthatthehydrodynamicinteractionbe- StockeJ.T.,OstermanS.N.,2010,ApJ,717,1291
tweentheplanetaryandstellarwindisabletoreproducethe MatsakosT.,UribeA.,Ko¨niglA.,2015,A&A,578,A6
Murray-ClayR.A.,ChiangE.I.,MurrayN.,2009,ApJ.,693,23
asymmetric absorption towards high blue-shifted velocities,
OwenJ.E.,AdamsF.C.,2014,MNRAS,444,3761
as observed in (Vidal-Madjar et al. 2003). Such asymmet-
OwenJ.E.,JacksonA.P.,2012,MNRAS,425,2931
ric absorption has been also attributed to charge-exchange
PenzT.,etal.,2008,Planet.SpaceSci.,56,1260
between the fast stellar wind and the slow planetary wind
Sanz-ForcadaJ.,MicelaG.,RibasI.,PollockA.M.T.,EiroaC.,
(Tremblin & Chiang 2013). Velasco A., Solano E., Garc´ıa-A´lvarez D., 2011, A&A, 532,
In a subsequent paper we plan to include the effects of A6
thestellarmagneticfieldstogetherwiththecharge-exchange SchneiterE.M.,Vela´zquezP.F.,EsquivelA.,RagaA.C.,Blanco-
interaction.Thiswillallowustofurtherconstraintthepho- CanoX.,2007,ApJL,671,L57
ton flux and its influence on the acceleration of the neutral ShowmanA.P.,CooperC.S.,FortneyJ.J.,MarleyM.S.,2008,
escaping material. ApJ.,682,559
TianF.,ToonO.B.,PavlovA.A.,DeSterckH.,2005,ApJ,621,
1049
Toro E. F., 1999, Riemann Solvers and Numerical Methods for
ACKNOWLEDGEMENTS FluidDynamics.Springer
TrammellG.B.,LiZ.-Y.,ArrasP.,2014,ApJ,788,161
MS acknowledges the financial support from the PICT TremblinP.,ChiangE.,2013,MNRAS,428,2565
project 2566/OC-AR and the fellowship grant ‘BECA EX- TripathiA.,KratterK.M.,Murray-ClayR.A.,KrumholzM.R.,
TERNAAGOSTO2013’givenbyCONICET.AE,ACRand 2015,ApJ,808,173
PFVacknowledgesupportfromDGAPA-PAPIIT(UNAM) Vidal-MadjarA.,LecavelierdesEtangsA.,D´esertJ.-M.,Ballester
G. E., Ferlet R., H´ebrard G., Mayor M., 2003, Nature, 422,
grants IN109715, IG100214, and CONACYT grant 167611.
143
Authors also thank for financial support from CONACYT-
Vidal-MadjarA.,LecavelierdesEtangsA.,D´esertJ.-M.,Ballester
CONICET joint grant CAR 190489.
G.E.,FerletR.,H´ebrardG.,MayorM.,2008,ApJL,676,L57
Villarreal D’Angelo C., Schneiter M., Costa A., Vel´azquez P.,
RagaA.,EsquivelA.,2014,MNRAS,438,1654
YelleR.V.,2004,ICARUS,170,167
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