Spiral Arms in the Milky Way Galaxy
Joachim Köppen Kiel Nov 2024

This is a simple modeling of the spiral arms of the Milky Way galaxy. Given a prescription for the galactic rotation curve, and their parameters (density, pitch angle [kpc/turn], initial radial offset, and arm width) two spiral arms are shown in a view onto the Galactic Plane (left map). Parts that are visible from the Sun (specified by minimum and maximum distances and a range of galactic longitude) are rendered white. Note that from central Europe and North America the Galactic Plane is visible only between longitudes 355..240°. HI clouds in the plane of the Milky Way galaxy are assumed to move on circular orbits around the Galactic Centre. If we look from the Sun (small yellow/red circle) into the direction of galactic longitude long a parcel of gas on this line of sight but at radius r from the centre (small white circle) and thus with circular velocity V_rot(r) appears to have a radial velocity with respect to our Sun's motion:

The background image of the map indicates whether a position in the Galactic Plane appears as a red- or blue-shifted object. The Mouse position gives the relevant data values.

The right hand map displays how these visible parts of the arms appear in the galactic longitude vs. radial velocity map. The yellow curves give the limiting values for the radial velocity (maximum in the first quadrant (0 < long < 90°) and minimum in the fourth quadrant). The brightness is coded with the rainbow colours between a minimum (dark violet) and a maximum value (red). Please note that the brightness does not take into account the distance to the HI clouds or that the density in the disc usually decreases with increasing distance from the Galactc Centre.

For the shape of the arms, the user may choose between:

• one and two circular rings. The radii are given by the radial offset with respect to the solar orbit. Thus, 0 kpc corresponds to the circle of the solar orbit, 3 kpc to an outer circle with radius r_SUN+ 3 kpc.
• one or two spiral arms, with radial offsets from the solar position. Thus, an arm with 0 kpc offset passes through the sun. The pitch of the arms are specified in kpc per turn around the Galactic Centre. The arms may be chosen to run clock-wise or counter clock-wise around the centre.