Using numerical models of bow shocks to investigate the circumstellar medium of massive stars
UUsing numerical models of bow shocks to investigatethe circumstellar medium of massive stars
A.J. van Marle , L. Decin , N.L.J. Cox , Z. Meliani . Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001, Leueven, Belgium Observatoire de Paris, 5 place Jules Janssen 92195 Meudon, France APC, Universit´e Paris Diderot, 10 rue Alice Domon et L´eonie Duquet, 75205 Paris Cedex13, FranceE-mail: [email protected]
Abstract.
Many massive stars travel through the interstellar medium at supersonic speeds.As a result they form bow shocks at the interface between the stellar wind. We use numericalhydrodynamics to reproduce such bow shocks numerically, creating models that can be comparedto observations. In this paper we discuss the influence of two physical phenomena, interstellarmagnetic fields and the presence of interstellar dust grains on the observable shape of the bowshocks of massive stars.We find that the interstellar magnetic field, though too weak to restrict the general shapeof the bow shock, reduces the size of the instabilities that would otherwise be observed in thebow shock of a red supergiant. The interstellar dust grains, due to their inertia can penetratedeep into the bow shock structure of a main sequence O-supergiant, crossing over from the ISMinto the stellar wind. Therefore, the dust distribution may not always reflect the morphologyof the gas. This is an important consideration for infrared observations, which are dominatedby dust emission.Our models clearly show, that the bow shocks of massive stars are useful diagnostic toolsthat can used to investigate the properties of both the stellar wind as well as the interstellarmedium.
1. Introduction
When a star moves through the interstellar medium (ISM), its wind collides with the interstellargas. If the motion of the star is supersonic with respect to the sound speed in the ISM, thiscollision leads to the formation of a bow shock in the region ahead of the star. Because thesize and shape of a bow shock is determined by the balance between the two ram pressure (ofthe stellar wind on the inside and of the motion of the ISM relative to the star on the outside)stellar wind bow shocks are powerful diagnostic tools that can help us determine the propertiesof the ISM, and the stellar wind. In addition, the instabilities that can occur in the bow shockcan help us analyse the physical process that are taking place.
Assuming that the interaction is supersonic with respect to both the stellar wind and the ISM(which is generally the case), the bow shock structure consists of four layers: the free-streamingstellar wind, the shocked stellar wind, the shocked ISM and the unshocked ISM. The free-streaming wind is separated from the shocked wind by the wind-termination shock. Similarly, a r X i v : . [ a s t r o - ph . S R ] J u l he forward shock separates the shocked ISM from the unshocked ISM. Between the shockedwind and the shocked ISM lies a contact discontinuity.The stand-off distance ( R D ) between the star and the bow shock is determined by the rampressure of the stellar wind and the ISM. These are in balance at a distance of R D = (cid:115) ˙ M v w πρ ISM v (cid:63) , (1)with ˙ M and v w the mass loss rate and velocity of the stellar wind, ρ ISM the density of the ISMand v (cid:63) the velocity of the star with respect to the local ISM [1]. Because R D denotes the distanceat which the stellar wind and the ISM are in equilibrium with one-another it actually gives usthe location of the contact discontinuity, rather than either the wind termination shock, or theforward shock. In addition, we can use analytical approximations to determine the openingangle of the bow shock, which [1] described as R ( θ ) R D = 1sin θ (cid:115) (cid:18) − θ tan θ (cid:19) (2)with θ the angle between the direction of motion of the star and a line from the star to aparticular point along the bow shock.
2. Numerical method
Although it is possible to predict the morphology of a bow shock analytically, including thegeneral 2-D structure (E.g. [2, 3]), such analytical models are inherently limited in the amountand type of physical processes they can include as well as in their inability to quantitativelyreproduce instabilities. Therefore, it becomes necessary to use numerical simulations to modelthe stellar wind bow shocks. We use the
MPI-AMRVAC magneto-hydrodynamics code [4, 5], whichsolves the conservation equations for mass, momentum and energy on an adaptive mesh grid. Forour calculations we include radiative cooling using the method described in [6], with a coolingcurve for solar metallicity.We model each bow shock in the co-moving frame of the star. We start our simulations byfilling a 2-D cylindrical grid in the R,Z-plane with a constant density interstellar medium, whichhas a constant velocity parallel to the Z-axis and is kept constant by allowing material to flowin at the outer Z-boundary. At the lower Z-boundary, the material is allowed to flow out of thegrid. The stellar wind is introduced by filling a small half sphere, centred on the origin, withgas according to a free-streaming stellar wind profile (constant velocity and density decreaseswith the radius squared).
Table 1.
Physical parameters of the wind of α -Orionis and the local ISM, used as input for oursimulations. Mass loss rate ˙ M = 3 . × − M (cid:12) yr − Wind velocity v ∞ = 15.0 km s − Velocity w.r.t. ISM v (cid:63) = 28.3 km s − ISM density ρ ISM = 10 − . g cm − ISM temperature T ISM = 10 KISM magnetic field B = 3.0 μ G . The influence of interstellar magnetic fields on the bow shock of α -Orionis Recent
Herschel observations [7] show us that the bow shock of α -Orionis, a red supergiant (RSG)type evolved star is smooth, without large instabilities. However, both analytical predictions [2]and numerical models [8–10] indicate that a bow shock of this kind, where the stellar velocitythrough the ISM is larger than the wind velocity, should show large scale instabilities. Severalexplanations for this discrepancy have been offered, such as the possibility that the bow shockis too young [11, 12], or that the presence of ionizing photons reduces the instability [13]. Analternative explanation, as shown in [14], is that the interstellar magnetic field inhibits thegrowth of instabilities. The ISM in the galaxy contains magnetic fields than can stretch out over large distances( (cid:39)
100 pc) [15–18]. Estimates for the magnetic field in the Orion arm of the Galaxy at adistance of 8 000 kpc from the Galactic centre (corresponding to the approximate location of α -Orionis) range from 1 . ± . μ G [19] through 2-3 μ G in the region near our solar system [20] to3.7-5.5 μ G as obtained from
Voyager measurements [21]. These values coincide with the valuesfor the interstellar field in the galaxy at large obtained from
WMAP data [22, 23].
We use the basic numerical set-up described in Section 2, but include a magnetic field parallel tothe Z-axis (and therefore parallel to the direction of motion of the star). This direction is chosento preserve the 2-D symmetry of the problem and avoid the necessity to run the simulation in3-D. For our computational grid we choose an initial size of of 160 ×
160 grid cells, covering aphysical domain of 2 × MPI-AMRVAC , we allow the codeto refine this grid up to four times, depending on variations in the local gas velocity, which givesus 2 560 × The result of our simulations, shown in Figs. 1 and 2, clearly demonstrate the influence of themagnetic field. Figure 1 shows the model without a magnetic field after 100 000 years physicaltime. The bow shock is clearly unstable at the contact discontinuity with both Kelvin-Helmholtzand Rayleigh-Taylor instabilities. These instabilities, which start out small in the region directlyahead of the star increase in size when they move down stream until they grow so large thatthey distort the general shape of the bow shock. For the model that includes an interstellarmagnetic field (Fig. 2, the result is completely different. Instabilities do form initially at thefront of the bow shock. However, rather than growing in size, they remain small as they movedownstream. Also, the small scale structures that are clearly visible in the non-magnetic modelare completely absent and the instabilities are limited to a single wavelength. This behaviourcorresponds to the predictions of, for example, [25, 26], which show that a magnetic field inhibitsthe growth of instabilities with short wavelengths, with the critical wavelength determined bythe magnetic field strength, the density contrast across the discontinuity and the angle betweenthe wave-vector and the magnetic field. This was further demonstrated by [14], which showedmodels for a range of magnetic field strengths.
It is clear from our models that the presence of an interstellar magnetic field can suppress thegrowth of instabilities in the bow shock of a RSG type star. Of course, this model is limitedy the fact that we have to align the magnetic field with the direction of motion of the star.Further study (in 3D) will be necessary to quantify this effect for magnetic fields at other angles.
Figure 1.
Density in g cm − for the non-magnetic model of the bow shock of α -Orionis. Note that the 2-D model has beenreflected in the Z-axis to show a completebow shock. The interface between theshocked wind and shocked ISM is clearlyunstable. Figure 2.
Similar to Fig. 1, but with aninterstellar magnetic field of 3 μ m. Thefield lines of the magnetic field are shown inthe right side of the panel. The instabilitiesare much smaller than for the non-magneticmodel. Table 2.
Physical parameters of the wind of an O-supergiant and the local ISM, used as inputfor our simulations.Mass loss rate ˙ M = 1 . × − M (cid:12) yr − Wind velocity v ∞ = 2300 km s − Velocity w.r.t. ISM v (cid:63) = 77 km s − ISM density ρ ISM = 10 − . g cm − ISM temperature T ISM = 10 000 Kdust grain sizes a , a , a = 0.071 μ m, 0.19 μ m, 0.37 μ m
4. Dust and gas in circumstellar bow shocks
The introduction of satellites like
Spitzer and
Herschel , has allowed us to resolve circumstellarstructures,such as bow shocks, in the infrared. However, rather than observing the morphologyof the gas directly, these infared observations actually show us the distribution of dust grains,which are the primary source of infrared radiation. Therefore, it is absolutely necessary toinvestigate whether such dust grains, typically more than 0.5% of the total circumstellar mass,are representative for the gas. This was done for a red supergiant type star by [10] where thestar itself was assumed to be the primary source of dust. These simulations showed that largerdust grains ( > . μ m) tend to decouple from the gas, once the gas is decelerated by the bowshock.e now investigate the behaviour of dust grains in the bow shock of a hot star, where thesituation is reversed. The wind of a hot massive star does not contain dust, therefore the mainsource for dust is the interstellar medium. We use the basic numerical set-up described in Section 2 and include the presence of theinterstellar dust grain by filling the interstellar medium with dust grains of three different radii(radii of 0.071 μ m, 0.19 μ m, and 0.37 μ mrespectively), each representing a ’bin’ of grain sizes.These dust grains are treated as pressure-less gasses according to the same method describedin [10], with the interaction between dust and gas included in the form of a drag force [27]. Weassume that the total dust mass equals 0.5% of the ISM gas mass. The number densities of thethree dust types are scaled in such a way that al three ’bins’ contain an equal amount of massand that the dust follows the size distribution of n ( a ) ∝ a − . with n the particle density and a the grain radius described by [28]. The stellar wind and ISM parameters for our simulationare given in Table 2, based on the O4 supergiant BD+43 3654 [29], with stellar wind propertiesfor such a star estimated according to [30]. We assume a warm ISM (10 000 K) because thestellar radiation can be expected to ionize the surrounding hydrogen, creating an HII regionthat extends well beyond the bow shock [31].For this simulation we use a basic grid of 160 ×
160 cells covering a physical domain of 10 × × The result of our simulation is shown in Figs. 3 and4. The gas (left side of Fig. 3) shows that theforward shock is highly radiative, causing the shocked ISM to be compressed into a thin shell.The smallest dust grains (right side of Fig. 3) show much less compression. These grains, whichoriginate in the ISM, penetrate the shocked ISM shell and enter the shocked wind region behindit. They only come to a stop at the wind termination shock due to the increases drag forcegenerated by the unshocked wind moving in the opposite direction. the intermediate and largedust grains (left and right side of Fig. 4) show that these grains, which have a larger momentumcompared to their surface area are able to penetrate into the unshocked wind.
Our simulations show that under the circumstances of our particular model, the dust distributioncan deviate considerably from the gas morphology. This can have serious consequences forobservations of such bow shocks. In this particular case, observations at visual wavelengths,dominated by gas emission would show a thin, highly compressed bow shock (the high densityshell of shocked ISM), whereas infrared observations, dominated by the dust, would show a thickshell.
5. Conclusions
We have shown that numerical models can be used to reproduce the bow shocks of massivestars. These models can also be used to investigate the effect of physical phenomena, suchas magnetic fields and the presence of dust grains, which can influence the structure of thebow shock and/or the manner in which it will appear in observations. In the future we hopeto continue our research in this field by including additional physical effects, such as thermalconduction and the interaction between dust grains and the magnetic field. We also intend toextend our models to 3-D in order to investigate what occurs/ when the 2-D symmetry is broken.E.g. when magnetic field and direction of motion are not aligned. igure 3.
Gas density in g cm − of thegas (left) and number density for smalldust grains (right) for the bow shockof a massive O4 supergiant. The gasshows a thin, unstable shell of shockedISM, whereas the dust grains are spreadout over the entire shocked gas regionwith the highest concentration at the windtermination shock. Figure 4.
Similar to Fig. 3, but for thenumber density of intermediate (left) andlarge (right) dust grains. Owing to theirlarger inertia, these grains cross both theshocked ISM and the shocked wind andenter the free-streaming wind region beforethe drag-force stops them, with the largestgrains showing the deepest penetration.
Acknowledgments
A.J.v.M. acknowledges support from FWO, grant G.0277.08, K.U.Leuven GOA/2008/04 andGOA/2009/09.
References [1] Wilkin F P 1996
ApJL
L31[2] Dgani R, van Buren D and Noriega-Crespo A 1996
ApJ
A&A
A13[4] van der Holst B, Keppens R and Meliani Z 2008
CoPhC
JCoPh
C&F A&A
A113[8] Brighenti F and D’Ercole A 1995
MNRAS
A&A
ApJL
L26[11] Mohamed S, Mackey J and Langer N 2012
A&A
A1[12] Mackey J, Mohamed S, Neilson H R, Langer N and Meyer D M A 2012
ApJL
L10[13] Meyer D M A, Gvaramadze V V, Langer N, Mackey J, Boumis P and Mohamed S 2014
MNRAS
L41[14] van Marle A J, Decin L and Meliani Z 2014
A&A
A152[15] Rand R J and Kulkarni S R 1989
ApJ
MNRAS
ASTRA MNRAS
MNRAS
ApJ
Natur
ApJ
ApJL
L11[24] Ueta T, Izumiura H, Yamamura I, Nakada Y, Matsuura M, Ita Y, Tanab´e T, Fukushi H, Matsunaga N andMito H 2008
PASJ ApJ
A&A
ApJ
ApJ
A&A
L23[30] Muijres L E, Vink J S, de Koter A, M¨uller P E and Langer N 2012
A&A
A37[31] McKee C F, van Buren D and Lazareff B 1984
ApJL278