Characterizing the Shape of the Large Magellanic Cloud's Bowshock

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1 Characterizing the Shape of the Large Magellanic Cloud's Bowshock Item Type text; Electronic Thesis Authors Setton, David Jonathan; Besla, Gurtina Publisher The University of Arizona. Rights Copyright is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 27/06/ :40:41 Link to Item

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3 Draft version May 3, 2017 Preprint typeset using L A TEX style emulateapj v. 01/23/15 CHARACTERIZING THE SHAPE OF THE LARGE MAGELLANIC CLOUD S BOWSHOCK David Setton Steward Observatory, University of Arizona, Tucson, AZ Gurtina Besla Steward Observatory, University of Arizona, Tucson, AZ Draft version May 3, 2017 ABSTRACT The Circumgalactic Medium (CGM) surrounding our Milky Way plays an essential role in supplying the fuel needed to drive and sustain star formation in our Galaxy. However, the CGM is extremely diffuse ( g cm 3 ), and therefore difficult to probe. Consequently, we know little about the structure, mass profile or evolution of the CGM. Using hydrodynamic simulations, we study the impact of the supersonic motions of the Large Magellanic Cloud (LMC), the largest satellite galaxy of the Milky Way, on the structure of the CGM. We conclude that the LMC must induce a large bow shock in the CGM and use simulations to characterize its size, shape, temperature, and density structure. Using these properties, we propose possible observational signatures that could be used to confirm the existence of the shock, and illustrate how the shock may provide a tool to probe the CGM. These results illustrate that the CGM is a dynamic system, affected not only by outflows from the host galaxy, but also by the motions of the satellites that orbit within it. 1. INTRODUCTION The Large Magellanic Cloud is the largest satellite galaxy of the Milky Way (MW), located roughly 50 kpc from the galactic disk in the southern sky. The LMC s orbital history has been a subject of recent theoretical and observational interest, and recent studies of proper motions of LMC stars to a high degree of accuracy have constrained the velocity of the LMC relative to the Milky Way to be 321±24 km s 1 (Kallivayalil et al., 2013). In addition, simulations of the LMC s orbit indicate that it is likely that the LMC its companion, the Small Magellanic Cloud (SMC) are recently interlopers of the local group and are on their first infall or have completed just a single orbit (Besla, 2015). The LMC is surrounded by a gaseous medium, known as the circumgalactic medium. The CGM is known to extend to at least 100 kpc based on observations of the Magellanic Stream (Fox et al. 2015, Murali+2000, Maloney and Bland-Hawthorn 1999). The CGM is a multiphase medium that spans a range of gas temperatures. There are three distinct phases that have been measured, the cool phase at 10 4 K, the warm phase at 10 5 K, and the hot phase at 10 6 K and above (Werk et al., 2014). However, the amount of gas at these temperatures is the subject of extreme uncertainty, and there are widely varying estimates for the amount of each phase present. Simulations have shown that treating the LMC s motion hydrodynamically can recreate the truncation of the LMC s disk due to the ram pressure caused by the gas s interactions with the CGM (Salem et al., 2015). As ram pressure is not significantly affected by the temperature, the gas could be assumed at a constant temperature and the simulation could be used to place constraints on the density of the CGM gas at the LMC s currently location 50 kpc from the galactic center. While the temperature of the gas does not affect ram pressure strongly, however, it does significantly impact the sound speed in the medium. For each of the phases of the CGM s gas, we can calculate a sound speed, and we find that regardless of the dominant phase of gas present in the LMC, the LMC is moving supersonically through the CGM. The supersonic motion of extended objects in gaseous mediums results in a phenomenon known as a bow shock, a detached shock front with an abrupt density jump characterized by velocity of the object relative to the medium s sound speed. Bow shocks of symmetric objects are very well studied, and their shapes and radii are well constrained to be a function of the mach number alone. However, the LMC s geometry complicates the issue of its shock, as its velocity vector is oriented 53 degrees from its disk plane, and it is not modeled in simulations as a rigid object but instead as an exponential disk profile. As such, we predict the shock surrounding the galaxy to be asymmetric. In this paper, we utilize the Salem 2015 simulation to probe the shape of the shock in the CGM conditions required to produce the ram pressure stripping that is observed in the LMC. We also explore the possible consequences of this bow shock, including its influence on mixing of gas in the CGM. We propose possible observational signatures of the shock. 2. SUPERSONIC MOTION OF THE LMC The speed of sound in a gas can be expressed as a function of the adiabatic index, the temperature, and the mean mass of gas present in the medium, as well as k, the Boltzmann constant. γkt c s = (1) m The mach number, which defines the supersonic motion of a gas through a medium, is defined as the ratio

4 2 Setton of the velocity of an object to the speed of sound in the medium in which the object is travelling. A mach number greater than 1 indicates supersonic motion, which we would expect to result in a bow shock. m M = v (2) γkt The Salem 2015 simulation assumes a gas composed of hydrogen with mean molecular weight, µ = 0.6, an adiabatic index γ = 5/3, and temperature in the hot phase at 10 6 K. Using these parameters, as well as the LMC velocity, we find that the LMC is moving with a mach number of around 2, indicating supersonic motion. If the CGM were dominated instead by cooler varieties of gas at 10 4 or 10 5 K, we calculate that the mach number would be on the order of 6.7 and 21.2 respectively. As such, we can confidently state that regardless of the medium that the LMC is passing through at a given time, its velocity should be supersonic and a bow shock should result. From these temperature jump conditions, we observe that regardless of what the dominant phase of gas present in the CGM, the jumps should require that the gas within the shocked region should be in the hot phase, indicating that its observational signatures will not differ much based on the temperature of the ambient CGM. 3. ANALYTIC DESCRIPTION OF BOW SHOCKS 3.1. Shock Conditions Due to the complicated nature of hydrodynamic equations, complicated bow shock behavior such as that of the LMC cannot be modeled analytically. However, the front region of a shock can be approximated as a onedimensional shock, and therefore can be analyzed to first order using fluid equations. We can obtain an estimate for the physical size of the shock by comparing it to the mean free path in the medium (Shu, 2009). x = l = 1 ση = m σρ (3) Assuming the gas is composed of atomic hydrogen at a density on the order of g cm 3, we find that the size of the shock front should be on the order of 30 parsecs. The Rankine-Huginoit jump conditions, which characterize the strength of the jump in terms of temperature and density ratios based on the mach number and the ratio of the specific heats (Shu, 2009). T 2 = [(γ + 1) + 2γ(M 1 2 1)][(γ + 1) + (γ 1)(M1 2 1)] T 1 (γ + 1) 2 M1 2 (4) ρ 2 (γ + 1)M1 2 = ρ 1 (γ + 1) + (γ 1)(M1 2 1) (5) Utilizing γ=5/3 and M 1 =2.07, the values from the simulation, we predict a temperature jump T2 T 1 = 2.17 and a density jump ρ2 ρ 1 = The magnitude of the temperature jumps increases immensely if we assume a cooler gas. The 10 5 K gas with M 6.7 would experience jumps on the order of T2 T 1 = and ρ2 ρ 1 = In the case where the gas is all in the cold phase, we predict jumps of T2 T 1 = and ρ2 ρ 1 = We note that the temperature jump is much mores sensitive to changes in the mach number than the density jump is, and can span as much as two order of magnitude depending on the temperature that we assume for the CGM Bow Shock Shape Shocks surrounding blunt objects which are symmetric about the velocity of the wind have been shown to have shocks whose properties depend only on the radius of the shock-producing object, the mach number and γ (Farris and Russell, 1994). The stand off radius is defined as the distance from the center of the object to the tip of the shock directly along the velocity vector. This can be calculated either analytically or empirically, as demonstrated in Farris and Russell, 1994, and Thun et al., The analytical result for the stand off distance is given by the following relation. R so = R( (γ 1)M (γ + 1)(M1 2 (6) 1)) R so is the stand off radius, and R is the radius of the blunt object that is producing the shock. The empirical result for a bow shock s stand off radius, that has been shown to agree well with both simulations and actual wind tunnel data, can be written as follows (Billig 1967, Thun et al. 2016). R so = R( e 3.24 M ) (7) Thun et al also gives an empirical form for the shape of the shock that we compare to the shape found in the simulation. y = 3R so 1 x (8) R so These equations apply only in the situation of symmetric objects, and as such we do not anticipate that they will provide a perfect fit for the LMC, which will have an asymmetric shock, but we can use them along with our simulated stand off radius to gain insight into what geometric properties of the LMC may factor into a first order approximation of the shock it produces. In addition, while these equations may not be absolutely applicable in the study of the bow shocks of disk systems like the LMC, they have found applications in works such as Su et al in the study of spherically symmetric galaxies such as NGC THE LMC BOW SHOCK 4.1. Simulation Due to the complicated geometry of the LMC s bow shock, in our study we repurpose the simulation of the LMC s infall from Salem et al. 2015, which treats the LMC hydrodynamically using the AMR code ENZO. The original simulation was run in a (60 kpc) 2 box, placing the LMC at the center of an ambient gas and applying a velocity to the gas which mimics the galaxy s orbit. The simulation uses values of the temperature and the density of the gas to accurately reproduce the observed ram pressure stripping and disk truncation of the LMC,

5 Characterizing the LMC Bow Shock 3 Figure 1. A plot of density versus radius along a ray extending from the center of the LMC along the velocity vector. The plot can ve divided into three distinct regions: the LMC disk, the shocked region, and the unshocked ambient CGM. The sharp discontinuity between rho 2 and rho 1 is determined by taking a numerical derivative of this curve and finding the minimum value in the region of interest. resulting in values of T = 1.18x10 6 K and ρ = 1.12x10 28 g cm 3 at the location of the LMC. These values are fairly constant in the simulation box of the present day LMC snapshot. The LMC disk is modeled as an exponential profile composed entirely of gas, with the values for characteristic scale heights being a gas = 1.7kpc and b gas =.34kpc. However, due to the truncation effect of ram pressure, the gas disk s radius is about 6 kpc in the snapshot of the LMC at present. The total gas mass is assumed to be M gas = 5x10 8 M (Tonneson and Bryan, 2009). The paper also assumes an exponential stellar disk and a static dark matter profile. The stellar disk is not affected by the hydrodynamic interactions being modeled, and therefore does not suffer from truncation. ρ gas (R, z) = 0.52 M gas 2πa 2 gasb gas sech( R a gas )sech( z b gas ) (9) The one factor that we do change from the original simulation is the box size; to avoid boundary conditions of the shock touching the edge of the box from affecting the shock shape, we adapt a (100 kpc) 2 box. This has the effect of increasing the size of the grid cells of the simulation. However, in section 2.1, we show that the size of the shock is about 30 parsecs. In either case, the grid sizes at the position of the shock for the simulation are larger than that value by about an order of magnitude, indicating that we are not fully resolving the shock anyways, so we do not believe that this change makes any difference in the simulation s accuracy Studying the Shock In order to study the shape and properties of the shock, we utilize the yt package, a set of python libraries built to visualize and analyze data from hydrodynamic simulations. Our method of determining the position of the shock is to draw a ray out at some arbitrary angle from the center of the LMC. We then take the derivative of this density Figure 2. Functional forms for the stand off radius as a function of mach number for both the theoretical and empirical relations given in equations 6 and 7. Despite both cases using different values for R eff, the curves they produce are very similar, although they vary by about 1 kpc in the value that they approach at high mach number. numerically and select the position in the shocked region, which generally consists of 3-5 points in our grid, which has a minimum in dρ dr to be the location of the shock along this sight line. In Figure 1, we show the density profile in the line of sight directly along the velocity vector of the shock. We see clear evidence of the shock. In the first region of density, we see the profile of the LMC itself along this vector. We then move out of that region to the shocked region, rho 2, and then we abruptly enter the unshocked region, rho 1. We characterize the radius along this vector as R so = 6.69 kpc. In order to further probe the shock, we create a basis of orthogonal vectors, with the velocity vector serving as our first vector. Using that vector, as well as two arbitrary perpendicular ones, we draw rays out in a multitude of directions to obtain a 3-dimensional set of points which characterizes the shock Effective Radius As previously stated, the LMC s complicated geometry makes it difficult to do analytic calculations for the stand off radius of the bow shock. However, we can work around this complicated geometry by using the value of R so from our simulation and defining an effective radius that can then be used to recover R so if we vary the mach number. Using our value of R so =6.69 kpc with the theoretical equation 6, we find R eff =4.49 kpc. Integrating over the density profile of the LMC disk using this radius and a large value for z, we find that about 71% of the LMC s mass is contained within this radius, and that at this radius the surface density has fallen off to about 14% of its original value. When we use the empirical result in equation 7, we find R eff =3.97 kpc. Calculating the same quantities at this radius, the mass contained is about 64% and the surface density has fallen to about 19% its original value. Both these fits appear to be fairly similar in shape, although there is some disagreement in the values they approach at large mach number. If the CGM were composed largely in the cold phase at about 10 4 with corresponding mach number of 20, the theoretical result for the stand off radius is roughly 5.4 kpc, whereas the empirical one is about 4.6 kpc. In either case, the stand off radius is not a particularly strong function of the mach number for the range of temperatures that the CGM gas could have, indicating that the LMC s bow shock should have a similar structure to the one in the simulation. Works on spherical galaxies have used R as the total radius of the galaxy to theoretically arrive at an accurate

6 4 Setton Figure 3. A sample slice plot through a velocity vector that demonstrates the asymmetry of the shock. The shock protrudes significantly farther at the bottom of the plot where there is more disk material present. radius for the shock that matches with observations (Su et al., 2016). This indicates that the geometric factor of the LMC disk s orientation relative to its velocity vector likely plays a much larger role in the determination of the stand off radius than the mass profile does. It is outside the scope of this paper, but future simulations of galaxies at different orientations or wind tunnel studies of disks at different orientations could help to obtain empirical descriptions that could be applied to arbitrary galaxies at given radii, mach numbers, and γ. Using these values, one could make predictions without running a complicated simulation for the shape of a shock and match it to observations. This would allow for the shocks of disk galaxies to be treated more carefully than by assuming an effective radius Jump Conditions Using our line of sight directly along the velocity vector of the LMC, find the temperature of the CGM gas jumps from 2.81x10 6 K to the ambient 1.18x10 6 K, with ratio T2 T 1 = We find that the density jumps from 3.07x10 28 g cm 3 to the ambient 1.12x10 28 g cm 3, with ratio ρ2 ρ 1 = These do not match one-to-one with the theoretical conditions derived in section 2.1, with predicted temperature and density ratios of 2.17 and 2.35 respectively, but they are fairly close. This indicates that we can trust our theoretical predictions for the jump conditions of the shock in different temperature regimes, and our predictions for the temperature and density jumps in the cool and warm phases of the CGM should hold. 5. DISCUSSION 5.1. Shock Shape The 3D shape of the LMC s shock is, as we suspected, highly asymmetric. The asymmetry appears to be directly related to the orientation of the disk of the galaxy. As a baseline for comparison, we use the empirical shock shape in equation 6 at R so =6.69 kpc. This curve appears to represent somewhat of a minimum for the shock Figure 4. A plot of the same slice shown in the previous figure. The points obtained from our probing of the shock are plotted in blue, while the empirical fit from equation 8 for R so=6.69 kpc is overplotted in green. This curve fits the points very well along the side of the curve where the LMC is oriented away from the shock, but does a poor job in the region where the LMC disk is oriented towards the shock. shape. Looking at multiple slice plots, the shock is often larger than the empirical curve, but in the region where the shock is on the side where the LMC is sloping away from the shock, the shock fits very well to the empirical fit. These variations from the empirical fit are substantial enough that we would miss out on a large amount of shocked gas by assuming the empirical fit rotated around the LMC represents the shape of the shock properly. The inflated shock distances relative to the empirical fit on the one side indicates that even though the disk s density drops as the radius increases, that effect is overcome by the tendency of the disk being much closer to the location of the empirical shock. Figures 3 and 4 demonstrate the asymmetry of the shock visually, showing for a given slice through the LMC how the presence of disk material near to the shock pushes the shock from the empirical fit. Figure 5 demonstrates the 3D structure of the shock from our viewing perspective, to be compared to Figure 6, the yt generated plot of projected density in our viewing frame. Our analysis focuses on the area immediately surrounding the LMC, where the density jump is strongest, but the shock s shape does extend out to substantially larger distances than we studied Observability of the Shock Concrete calculations of the observability of the shock is a subject of future work, but in this section we discuss the different avenues that we intend to explore. The most obvious observational signature of the shock would be an observation of a difference in the emission between the shocked and the unshocked regions. If the temperatures are on the order of 10 6 K, we would expect emission to occur in the x-ray, but lower values of gas would radiate at different characteristic spectral lines. If we assume a metallicity for the CGM, we can utilize the Trident synthetic spectral generation tool to use our simulation of the CGM and predict what lines will be present at given intensities, both inside and outside the

7 Characterizing the LMC Bow Shock 5 Figure 5. The 3D structure of the LMC bow shock presented in the viewing perspective from the Milky Way. The blue points plotted are the locations of the shock determined by our shock finding methods. The red point represents the center of the LMC. shock. The problem with this method that we are sure to encounter is that regardless of how strong the temperature jump between the regions may be, the density jump is small regardless of what temperature the gas. The jump in the intensity of radiation between the shocked and unshocked region may not be above the signal-noise cut of any reasonable observational facilities that can be accessed. However, if the gas is primarily in the very low temperature regime, the many orders of magnitude may result in a very different set of ionized species, allowing this method to be used. A common method of probing CGM gas is the use of background quasars in the COS Halos Survey (Werk et al., 2014). This method probes absorption features in the high energy radiation emitted by these background objects and uses it to constrain properties of the gasses, but we could potentially use sight lines inside and outside the shocked and unshocked regions and demonstrate that there is an increased column density in the shocked region. The projected size of the front of the shock in our viewing frame is on the order of 3 kpc at a distance of roughly 50 kpc, so the angular size of the shocked region is large, so it is very possible that the sight line quasars that we need exist. However, this method of observation has some of the same difficulties as detecting emission due to the extremely rarefied nature of CGM gas. The likely pitfall is that the difference in absorption through the shocked and unshocked regions would not be significant enough to be detected. The other elephant in the room with regards to the observability is that in our simulation, we assume the CGM to be a homogeneous medium at a single temperature and density. However, studies have shown that is not the case, and there are definite heterogeneities present in the CGM (Werk et al., 2014). Those heterogeneities could complicate any observations of the CGM by introducing emission and absorption features that we are not accounting for. The presence of these heterogeneities, however, is exactly why a detection of the LMC s bow shock would Figure 6. A plot of the projected density in the simulation in the line of sight towards the Milky Way. The shape of the projected shock in this plot appears to agree well with the shape of the shock generated from our shock finding methods. be so exciting, because the possibility exists that the LMC and its shock s motion could induce mixing in the CGM, wiping out heterogeneities and producing regions that truly are homogeneous in the areas surrounding the galaxy. Furthermore, a detection of a shock shape and stand off radius could provide another observational tool to constraining CGM temperatures similarly to the way that ram pressure stripping can in simulations. The detection of the shock could also place further constraints on the LMC s velocity. The wide range of applicability of measurements of the shock make them worth pursuing, even if they are time intensive due to the low density of the gas Future Plans In the future, we intend to attempt to quantify the observability of the shock more rigorously by looking into the amount of shocked gas that we expect. We also plan to look into the locations of other Milky Way satellites relative to the LMC, as we expect that many of them should reside within the shocked region. The higher temperature and density of the gas in the shocked region could result in differing properties for the satellite galaxies present, and it may be possible that a significant number of galaxies are located outside of the shock, indicating that the interaction has in some way affected the orbits of the satellites. 6. ACKNOWLEDGEMENTS We would like to acknowledge the contributions from Cameron Hummels, who was instrumental in getting yt up and running and helping us to generate plots of the LMC. We would also like to thank the University of Arizona for the use of the El Gato HPC for computations and plotting. Finally, we would like to thank the Honors College for their aid in funding my trip to AAS, where I gained insight on this project. REFERENCES Besla, G arxiv: Billig, F. S. 1967, J. Spacecraft Rockets, 4, 822

8 6 Setton Farris, M. H.; Russell, C. T Journal of Geophysical Research 99 Kallivayalil, Nitya; van der Marel, Roeland P.; Besla, Gurtina; Anderson, Jay; Alcock, Charles 2013 ApJ, 764, 161 Munier, S.; Besla, G.; Bryan, G.; Putman, M.; Van Der Marel, R. P.; Tonnesen, S. 1978, ApJ, 815, 77 Shore, S. N Astrophysical Hydrodynamics. WILEY-VCH Verlag GmbH & Co. KGaA Shu, Frank H The Physics of Astrophysics Volume II: Gas Dynamics Su, Y.; Kraft, R. P.; Nulsen, P. E. G.; 2016 arxiv: Thun, D.; Kuiper, R.; Schmidt, F.; Kley, W; 2016 Astronomy and Astrophysics 589, A10 Tonneson, S.; Bryan, G, 2009 arxiv: Werk, J.; Prochaska, J.; Tumlinson, J.; Peeples, M.; Tripp, T ApJ, 792, 8