The Astrophysical Journal, 507:L35–L38, 1998 November 1 q 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.
NUMERICAL SIMULATION OF ASYMMETRIC SPIRAL STRUCTURE IN THE LARGE MAGELLANIC CLOUD L. T. Gardiner Department of International Education, Sun Moon University, Tangjeongmyeon, Asan-kun, Chung-nam, 336-840, Republic of Korea;
[email protected]
C. Turfus Department of Mathematics, Sun Moon University, Tangjeongmyeon, Asan-kun, Chung-nam, 336-840, Republic of Korea;
[email protected]
and M. E. Putman Mount Stromlo and Siding Spring Observatories, Australian National University, Private Bag, Weston Creek Post Office, ACT 2611, Australia;
[email protected] Received 1998 June 5; accepted 1998 September 3; published 1998 September 15
ABSTRACT We have constructed a dynamical model of the Large Magellanic Cloud (LMC), based on the new propagating star formation scheme of Gardiner, Turfus, & Wang, in order to examine the effects of an off-center perturbation on the global distribution of the gas and star formation activity. The simulation generates an asymmetric spiral structure that appears to be consistent with the pattern of large-scale star formation activity and recent observations of the neutral gas distribution. We suggest that the presence of a dual asymmetry in the offset bar and spiral structure is a major factor governing the global structure, dynamics, and evolution of the LMC. Subject headings: Magellanic Clouds — methods: numerical vations depicting spiral structure, strongly suggest the importance of the “dual asymmetry” paradigm of linked bar-spiral asymmetry as a theoretical framework for the interpretation of the large-scale structure and star formation history of the LMC. In this Letter, we present a two-dimensional numerical simulation of the star formation activity and gas distribution in the LMC based on the new N-body/cellular automaton star formation code of Gardiner, Turfus, & Wang (1998, hereafter GTW98), which has been implemented following the framework of CA89’s model of galaxies with rotating off-center bars. The model scheme is summarized in the next section, and in § 3 the results are compared graphically with the observed distribution of star formation activity and recently obtained H i observations. A concluding discussion is presented in § 4.
1. INTRODUCTION
For a galaxy of late morphological type, it is now well known that the existence of an off-center bar, defined relative to various disk population centroids, can frequently give rise to another asymmetry: that found in the global spiral arm pattern. The extensive study of de Vaucouleurs & Freeman (1972, hereafter dVF72) cataloged the appearance of asymmetries in galaxies of the Magellanic irregular type, including the existence of offcenter bars and one-armed spiral structures, with particular reference to the Magellanic Clouds. More recently, Colin & Athanassoula (1989, hereafter CA89) produced numerical models demonstrating that an off-center bar potential can lead to the formation of stable one-armed spiral structures that do not owe their existence to spiral density waves. Regarding the case of the Large Magellanic Cloud (LMC), the appearance of some form of spiral structure has been a recurrent theme in observational studies, including those of young stellar indicators (see, e.g., Schmidt-Kaler 1977 and Feitzinger & Braunsfurth 1984) and emission surveys at various wavelengths (Laspias & Meaburn 1991; Klein et al. 1993; Kim et al. 1998). For the most part, researchers have tended to overlook the connection between these two characteristic asymmetries and have sought to explain the spiral pattern by alternative mechanisms, e.g., the theory of stochastic self-propagating star formation (Feitzinger et al. 1981), that rely on local processes rather than on the large-scale organization of matter by gravitational forces. Recently, however, Dottori et al. (1996, hereafter DB96), making use of the theoretical work on asymmetric barred galaxies by CA89, have suggested that the spatial distribution of young LMC star clusters could be explained in terms of spiral structures generated by an off-center bar perturbation. The situation had been complicated by the fact that observations had not generally shown clear signs of spiral structure in the underlying gas component. In contrast to previous work, recent observations of the neutral hydrogen distribution in the LMC, which are reproduced in this Letter in order to show specific detail, exhibit a more definite spiral pattern than has hitherto been revealed. The advances in the theoretical understanding of asymmetric spiral arm structures, combined with new obser-
2. NUMERICAL MODEL
This study represents the first application of the N-body/ cellular automaton star formation code of GTW98 to a disk galaxy. In GTW98, the scheme was applied to a “test-bed” theoretical galaxy with periodic boundaries, and a detailed description of the code is presented in that paper. We give here a short summary of its main features. The gas component of a galaxy is constituted by a number of self-gravitating particles, representing discrete gas clouds, distributed on a twodimensional surface. The gravitational forces in the current simulation are evaluated using a Fortran 90 implementation of the TREECODE algorithm of Barnes & Hut (1986). The gasdynamics is handled by the “sticky-particle” method of Roberts & Hausmann (1984). Gas cloud complexes form by gravitational instability enhanced by cloud-cloud collisions. Star formation is dealt with by a cellular automaton superposed on the particle distribution and has two basic rules: (1) spontaneous star formation occurs in a given cell if the surface number density of particles reaches a specified threshold, nsp, and (2) stimulated star formation occurs if a density threshold, nst, is equaled or exceeded, with nsp 1 nst, and, in addition, at least one neighboring cell is in an active state. The second mechanism (rule 2) above allows propagating star formation to take place, with the ratio of propagating star formation to spontaL35
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neous star formation activity typically ∼100. When star formation is deemed to occur, a star particle, representing a stellar cluster or an OB association, is formed. Each star particle deposits kinetic energy into the interstellar medium by boosting neighboring gas cloud particles for a specified period, 10 Myr (the “active” phase), after which it is deleted. We note, however, that the long-term spatiotemporal evolution of the stellar age distribution can, in principle, be studied by indefinitely retaining star particles beyond their active phase. We simulated the gas disk of the LMC with 7000 particles, representing a total gas mass of 4.2 # 10 8 M,, initially distributed uniformly on the surface of a disk of radius 3.5 kpc. In addition to experiencing their mutual gravitational forces, the particles were subjected to forces arising from external fixed potentials representing the distribution of the dynamical mass of the LMC, comprising stars and possibly dark matter. The combined external potential was given by F 5 F0 1 Fb, where F0 is the axisymmetric component and Fb represents a rotating, weak barlike distortion offset from the disk center. The center of the bar potential was displaced 0.6 kpc directly below the disk center, corresponding approximately to the observed displacement of various rotation centers and population centroids from the optical bar center (dVF72). The major axis of the bar was taken to be perpendicular to the line joining the center of the bar and the disk center. As in the formulation of CA89, the bar spins about its own axis at the same rate as it rotates around the center of the galaxy so that there exists a rotating frame where the bar is at rest.1 The potentials used are summarized below, and an isopotential plot is shown in Figure 1. The axisymmetric component is F0 (r) 5
{
A/(r 2 1 a 2 )1/2, if r ≤ Î2a; 2v2max log r 1 B, otherwise.
(1)
The bar potential is Fb (R, v) 5
cos 2v, if R ≤ b; {W(R) (C/R 1 D) cos 2v, otherwise.
(2)
The polar radial coordinate, r, is defined relative to the disk center, whereas R is relative to the bar center; v is the angular coordinate measured with respect to the orientation of the major axis of the bar. The core radius is given by a 5 1 kpc; vmax is the circular velocity at r 5 Î2a , and A and B are constant terms giving the continuity of the axisymmetric component at r 5 Î2a. The bar length parameter is given by b 5 Î2a, and C and D are constants chosen to give the continuity of the potential and its first derivative at r 5 b. The form of the bar potential was identical to that used by Schwarz (1981) and has 1 In actual fact, the line joining the bar and disk centers of the LMC makes an angle of around 307–407 with respect to the line passing through the disk center perpendicular to the bar axis (see Fig. 1 of DB96). Simulations carried out with a corresponding permanent bar orientation in the rotating frame could reproduce some aspects of the distribution of gas and star formation activity in the LMC. The additional asymmetry in the bar-disk configuration generated a spiral pattern with multiple modes and a gas concentration at one end of the bar. In all likelihood, however, the bar spins about its own center with an angular velocity differing from its rate of rotation about the disk center, with the result that the bar axis passes through all possible orientations. In this Letter, we discuss the results for the simpler configuration described in this section, leaving a detailed analysis of simulations with other bar orientations, as well as the case of the independent rotation of the bar about its own axis, to a later publication.
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Fig. 1.—Isopotential contour plot for the displaced bar model. The bar used in the simulations is indicated with a line of length 2b (≈2.8 kpc), where b is the bar length parameter (see § 2). Length units are in tens of kiloparsecs.
a bar length parameter equal to the turnover radius of the axisymmetric rotation curve. The axisymmetric component of the potential gives a rotation curve that is broadly consistent with the observed rotation curves of Luks & Rohlfs (1992) and Meatheringham et al. (1988). The model rotation curve rises to a maximum value of around 70 km s21 at about 1.4 kpc and then stays constant beyond the turnover radius. The maximum perturbation due to the bar is 3% for the potential and 15% for the force. After some experimentation, a bar pattern speed was chosen such that the ends of the bar roughly corotate with the turnover points of the (axisymmetric) rotation curve, giving a bar pattern speed of Qb 5 50 km s21 kpc21. This pattern speed implies that there is no inner Lindblad resonance and places the corotation resonance and outer (m 5 1) Lindblad resonance within the gas disk. For comparison, a corotation radius of 1.7 kpc was deduced by DB96, which implies a bar pattern speed of ∼40 km s21 kpc21 from their Figure 6.2 The particles were initially given a circular velocity to balance the forces implied by the axisymmetric potential in equation (1) combined with the effective contribution from the uniform self-gravitating gas particle disk. Identical to GTW98, the time step was equivalent to 0.5 Myr, and a second-order Runge-Kutta scheme was used for the integration of the equations of motion. 3. SIMULATION RESULTS AND OBSERVATIONS
We adjusted various simulation parameters, including the elasticity of cloud-cloud collisions, star formation thresholds, the kinetic boost parameter, as well as the strength of the bar 2 On the other hand, a value of ∼14 km s21 kpc21 was derived by DB96 from star cluster group ages for the angular velocity of the perturbation associated with the bar related to the propagation of star formation in the disk. Such a low pattern speed would not permit the generation of spiral features (Sanders 1977) since the corotation and outer Lindblad resonances would lie near or beyond the edges of the gas disk (refer to Fig. 6 of DB96).
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Fig. 2.—Simulation results and observations. Top left: H i peak intensity distribution in the LMC. Some filtering of low-level emission was performed in order to highlight the spiral structure. Bottom left: vacuum UV observations of the LMC reproduced from SCH87 showing the bar (dashed contour), supergiant shells (dotted contours), and Shapley constellations (Roman numerals). Top right: gas particle distribution generated by the model at approximately 400 Myr after the start of the simulation. The model disk has been projected on the sky plane using an inclination of 307 and a position angle of the line of nodes of 1707 (Luks & Rohlfs 1992). The simulated bar is represented by the solid line. The rotation of the LMC disk is clockwise. Length units are in tens of kiloparsecs, with 1 kpc equivalent to 17. 15 for an LMC distance of 50 kpc. The equivalent angular scale is approximately the same as for the H i distribution map, whereas the relative magnification of the vacuum UV plot is 1.5. Bottom right: star particle (age less than 12 Myr) distribution generated by the model.
potential, in order to achieve simulations capable of reproducing the observed distribution of star formation activity in the LMC. In practice, an activity level of approximately 5% of the galactic surface produced simulations that sufficiently delineated the major spiral arm features without producing too much scattered star formation activity. Employing the same nomenclature as in GTW98, a suitable parameter set was found to be fcol 5 0.6, nsp 5 6, nst 5 3, and v bst 5 6 km s21. Spiral features were found to develop fully by T 5 150 Myr in the simulation. The simulations did not reach stationarity because of the continuous evolution of the radial angular momentum distribution that resulted in matter becoming concentrated toward the central regions. Moreover, the total angular momentum of the system was not constrained to be fixed because the interaction between the bar and the gas component was not treated self-consistently. Nevertheless, a relatively stable spiral structure could be observed over a period representing at least 1 Gyr. A snapshot of the gas and star particle distribution at around 400 Myr following the start of the simulation is presented in Figure 2, along with plots depicting the distribution of neutral hydrogen and that of recent star formation activity in the LMC. The pattern of recent star formation in the LMC is indicated by the vacuum UV observations of Smith, Cornett, & Hill
(1987, hereafter SCH87), while the gas distribution is indicated by a reproduction of the H i peak intensity map of Putman et al. (1998) in the region of the LMC. This map was created with data from the H i Parkes All Sky Survey (Staveley-Smith 1997). It is therefore sensitive to much larger spatial scales than the interferometer map of Kim et al. (1998) (which is insensitive to structures larger than 07. 6) and has a brightness temperature sensitivity 3 times that of previously obtained single-dish maps (see, e.g., Luks & Rohlfs 1992). The most notable feature of the gas particle distribution is the trailing outer spiral arm that extends from the southeast end of the bar in a long arc up toward the northwest of the galaxy. The gas particle distribution between the southern part of this spiral feature and the bar is strongly depleted. The asymmetric spiral structure of the LMC is evident in the H i distribution map, which shows two distinct outer spiral features near the edge of the gas distribution, one south of the bar, extending from east to west, and one extending from south to north along the western edge. The area between the southern H i spiral feature and the bar region (the bar itself is not well delineated in either the H i map or the gas particle distribution) is a region where the gas is depleted, in agreement with the simulation. The outer spiral arm defined above appears in both the simulated and observed star formation activity plots, being
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associated with the spiral arm B of SCH87, linking complexes B3–B29–B2–B1. The outer spiral arm and southern void are stable features of the simulation. In contrast, a shorter inner spiral feature emerging from the opposite end of the bar tends to be more ill-defined and transitory in nature. The inner spiral feature appears to be associated with the spiral arm A of SCH87, linking features A2–A1–supergiant shell 1. The spiral arm A includes the bar itself, with ongoing but patchy star formation evident in the bar in both observation and simulation plots. The two spiral arms together trace out a characteristic “banana”-shaped envelope delineating star formation activity in the LMC. The mechanism of propagating star formation in our simulation code leads to the generation of expanding shells of gaseous material as star formation propagates outward from activity centers situated in gas cloud complexes (see GTW98 for a detailed description of the evolution of such features). Such structures may be associated with the supergiant shells and Shapley constellations indicated in the vacuum UV plot in Figure 2. In our simulation, a single isolated condensation that forms a gas cloud complex typically develops to a linear size of around 500 pc, and star formation activity lasts for about 25 Myr. However, pairs or small groups of condensations, such as the one located at around (0.3, 0.3), are also frequently formed. In these structures, propagating star formation plays a subtle role, sometimes igniting star formation in neighboring condensations, which results in significantly larger complexes. These structures reach sizes of around 1 kpc, and star formation may carry on for 30–50 Myr. For comparison, Grebel & Brandner (1998), using Cepheid and supergiant stars as age tracers, find that supergiant shells contain stars that are up to 25 Myr old, and that typical timescales for continuing star formation on length scales of 0.5–1 kpc range from 15 to 30 Myr. 4. DISCUSSION
The theory of stochastic self-propagating star formation (SSPSF), applied to the LMC by Feitzinger et al. (1981), has often been cited to account for the morphology of spiral arm features. Since our star formation code incorporates a mechanism for propagating star formation, we initially set up a simulation without a bar perturbation to see if spiral features could be produced in a similar way to the SSPSF mechanism. Transient spiral features occasionally form as a result of the differential rotation of the disk acting to stretch out loose con-
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centrations of gaseous material, but the shear due to differential rotation also eventually results in the destruction of such features on timescales of less than 40 Myr. Such transient structures seem to be unable to give rise to the large-scale spiral features observed in the LMC. In both our model and the models of CA89, the off-center bar asymmetry leads to the production of a dominant trailing one-armed spiral feature. DB96 also found significant m 5 1 spiral components by spatial Fourier analysis of the distribution of LMC star clusters up to 70 Myr old. However, in some cases, the components were found to correspond to leading spiral arms. The above authors point out that this may be the result of the subsequent dynamical evolution of the stellar clusters within the disk after having originated in trailing arms. The age distribution pattern derived from simulations in which the evolution of star particles has been followed for up to 100 Myr, i.e., beyond their active phase, supports this particular interpretation. The origin of the displacement of the bar of the LMC remains unclear. Kunkel et al. (1997) briefly report that off-center bars were produced in their numerical simulations of the LMC in which this galaxy experiences a tidal impulse due to an encounter with the SMC. We remark, however, that the existence of such displacements is a phenomenon frequently associated with SBm galaxies and is seen in systems that are not obviously and closely interacting (see dVF72). Recent theoretical work on the production of m 5 1 asymmetries in nonbarred spiral galaxies (see Junqueira & Combes 1996 and references therein) has suggested that certain types of gravitational instabilities can lead to the displacement of the gaseous and stellar components from the center of mass of the system, thereby exciting an m 5 1 spiral mode. In conclusion, we have shown that a weak rotating off-center bar potential can produce an asymmetric spiral pattern that exhibits several similarities to the overall distribution of gas and star formation activity in the LMC. A more extensive discussion of various aspects of the model in relation to detailed observational results, including the velocity structure and star formation history of the LMC, will be presented elsewhere. The authors are grateful to K. Freeman for his helpful comments on the manuscript. L. T. G. and C. T. acknowledge the financial support of the Sun Moon University Research Center. M. E. P. acknowledges the support of an Australian DEETYA Overseas Postgraduate Research Scholarship.
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