Using LabVIEW for Simulation and Theoretical Studies in Astrophysics

Author(s):
Andrei Pavlov - Kepler Simulation Lab

Industry:
Imaging Equipment

Products:
LabVIEW

The Challenge:
Creating a new application of LabVIEW for scientific simulation and theoretical studies in astrophysics to simulate gravitational contraction of complex N-body systems.

The Solution:
Developing an original algorithm and simulation program using NI LabVIEW to simulate formation of spiral galaxies and calculate dynamics of the gravitational system, its thermodynamics and mechanical properties.

Scientific Simulations in Astrophysics
We demonstrate a new application of LabVIEW as a tool for scientific simulation of very complex systems and processes. The graphical development environment language of LabVIEW has many great advantages. Not only is it a revolutionary tool for engineering applications, but also for academic scientific research. We use LabVIEW for scientific simulations in astrophysics.

The purpose of this study is to determine the basic conditions of formation of spiral galaxies and the creation of a new algorithm for modelling the galaxy evolution as a self-gravitating system. Only gravitational forces are present in the galaxy. We base the algorithm on calculations of the gravitational acceleration and displacement of each particle of the galaxy by using the gravitational law in its original differential form instead of the calculation of the gravitational potential. The Newtonian law is indifferent to mass of the particle and here it works well because of large distances between the particles. The rotational velocities wi are calculated by applying the Kepler’s second law for small angles given by. During gravitational attraction, the velocities of the stars increase toward the center of mass. The total velocity of a particle is a vectorial sum of the radial and tangential velocities. An increase of the radial velocity results in an increase of the rotational velocity calculated from Kepler’s formula. As a result, the remote particles rotate more slowly than those situated closer to the centre. Because of nonspherical geometry of the cluster, the spiral develops. In addition, rotational movement of the galaxy leads to its shrinking along the z-axis and a flattening of the galaxy. The number of arms of the spiral is determined by the initial shape of the galaxy given by a shape function F(r,,). It equals the number of extremum minima, dF/dr = 0, of the shape function of the galaxy on equatorial plane at =/2. For a spherical galaxy F(r,,) = R at any angle, the spiral can only be S0-type. For an ellipsoid, the number of extremum minima is two and, therefore, the spiral will have two arms. The rarely encountered triangle-shaped galaxy will have three arms, and so on. An irregular galaxy will produce a nonsymmetrical spiral.

A Special Program for Simulation of Galaxy Evolution
We designed a special computer program using LabVIEW for the simulation of the galaxy evolution. The elliptical E-type shape of the galaxy is obtained by proportional shrinking the spheroid along y- and z-axes by 0.8, the most frequently observed apparent axis ratio. Initially, the particles are randomly distributed within this volume. The initial radial velocities of all particles are zero. The galaxy has slow rotation on z-axis. The number of the particles in the galaxy N = 2,000. In addition, 300 particles are created outside the body of the galaxy to study the dynamics of the process in more detail. The galaxy has the total mass of 1x1043 kg, a typical galaxy’s mass. The particles have equal masses m=5x1039 kg. The starting angular velocity was of the order of 1x10-15 rad/s and the corresponding initial period of rotation T = 2/w was about two hundred million years.

The initial radius along x-axis is 750 kpc. The galaxy rotates anticlockwise in xy-plane. The time of formation of the spiral is about 4x1015 seconds, which is a little smaller than the initial period of rotation. The formation of the spiral can be divided in three stages. The first stage lasts from the beginning of the contraction until the formation of two different geometrical shapes, the central part and two regions apart of it, after 3.35x1015 s. The central part of the galaxy becomes more spherical, and this is the future core of the spiral. The particles outside this region become more flattened and concentrated inside two symmetrical regions opposite to each other. These form the two arms of the spiral. The second stage is further development of the core structure and the two arms. It lasts between 3.35x1015 and 3.90x1015s. At the end of this stage, the spiral forms. During the last stage, the further evolution of the galaxy can be considered as the contraction of two different systems, the core and the two arms. The core of the galaxy rotates and contracts much faster than the arms. During this stage, most dynamics occur in the core, and the arms of the spiral receive only minor changes.

The angular velocity wi depends on the distance from the centre of the galaxy at different times. The particles situated nearby the center rotate much faster than the remote ones when the spiral is formed. Their maximum angular velocity is increased more than 100 times. The particles situated farther than one-half of the galaxy’s size have almost equal rotational velocities. The core of the galaxy rotates and contracts much faster than the arms in the spiral and breaks away from the arms at about 4.10x1015/s.

The comparison of the photo images of these type spiral galaxies, such as NGC1566, NGC 300 and others, reveals an excellent similarity of the shape of the arms and the core. We can conclude that almost any shape of a galaxy transforms into spheroid and surrounding it spiral arms and disks are a reminder of this transformation.

The time evolution of the E-type elliptical galaxy and its transformation to Seyfert Sc-type spiral is demonstrated in the image above. The galaxy rotates counter clockwise. After 3.7x1015 seconds of the gravitational contraction, the core of the galaxy rotates more than 10 times faster than the arms.

The dependence of the angular velocity wi on the distance from the center of the galaxy at different times. The initial angular velocity of all particles is 1.0x10-15 rad/s. The corresponding times are 1.5x1015/s (curve 1), 2.6x1015/s (curve 2), 3.35x1015/s (curve 3), 3.90x1015/s (curve 4), and 4.225x1015/s (curve 5).

Different spiral galaxies obtained by gravitational contraction of the same initial elliptical galaxy having different initial rotational velocities (Figure 4a-4c). Some galaxies have equal total masses of M=1x1043 kg, and different initial rotational velocities, w0 = 5x10-16 rad/s (Figure 1a), w0=1x10-15 rad/s (Figure 1b), w0=2x10-15 rad/s (Figure 1c). The contraction time of these galaxies is 4.2x1015 s, or 130 Myr. One galaxy has the total mass of 5x1042 kg, and w0=1x10-15 rad/s. The formation of this galaxy takes longer time, 6x1015 seconds or 190 Myr.

For more information, contact:
Kepler Simulation Lab
11 Sturton Street
Cambridge, CB1 2SN, UK

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