Constraining the pitch angle of the galactic spiral arms in the Milky Way

Abstract

We carry out analyses of some parameters of the galactic spiral arms, in the currently available samples.

We present a catalog of the observed pitch angle for each spiral arm in the Milky Way disk. For each long spiral arm in the Milky Way, we investigate for each individual arm its pitch angle, as measured through different methods (parallaxes, twin-tangent arm, kinematical, etc), and assess their answers.

Second, we catalog recent advances in the cartography of the Galaxy (global mean arm pitch, arm number, arm shape, interarm distance at the Sun). We statistically compare the results over a long time frame, from 1980 to 2017. Histograms of about 90 individual results published in recent years (since mid-2015) are compared to 66 earlier results (from 1980 to 2005), showing the ratio of primary to secondary peaks to have increased by almost a factor of 3. Similarly, many earlier discrepancies (expressed in r.m.s.) have been reduced by almost a factor 3.

Introduction

In this contribution, we present exploratory analyses of galactic spiral arms properties, notably the pitch angle, with the aim of constraining their individual and global values, as best could be done with currently available samples.

Our knowledge of the main parameters of the spiral arms (their number, their shape, their pitch angle, and the interarm separation through the Sun between the Sagittarius and the Perseus arms) has evolved with time, but some discrepancies have lingered on.

An early picture of the location of each spiral arm is that in Courtès et al. (1969–their Fig. 6 and Table 2), with 4 arms, a pitch angle of −20°, an interarm separation of about 4 kpc, and a approximate log shape (disregarding the local Orion armlet), using 10 kpc for the distance from the Sun to the Galactic Center. A very recent model picture can be seen in Fig. 2 of Vallée (2016a), with 4 arms, a pitch angle of −13°, an interarm separation of about 3 kpc, and a logarithmic arm shape, using 8 kpc for the Sun to Galactic Center distance.

The “twin-tangent” method employs an ideal model of a spiral arm with parallel layers, each layer would contain a different tracer (dust, maser, CO in an arm). The layer closest to the direction of the Galactic Center (GC) is the hot dust tracer. A look from Earth at a tangent to an arm, looking in one layer/tracer, would give an angle from the GC (the galactic longitude of that tracer in that arm). Employing a given tracer (cold dust, say) in a long arm, on each side of the GC (in Galactic Quadrant I and IV), the two different tangent angles measured could be fitted to deduce the arm's pitch angle. Doing the same using any another tracer (CO, say), would give a similar result, hence showing very little differences (a modest spread around a mean pitch angle). The twin-tangent method uses the two tangents to the same arm, as observed on both side of the sun-galactic center line in Galactic Quadrants IV and I (Eq. (1) in Drimmel, 2000 or Eq. (10) in Vallée, 2015).

The “parallax” method looks at a slice of an arm, namely the arm's inner side closest to the GC (where all masers are located). By measuring a maser's distance from Earth, and that of neighboring masers, these masers can be plotted on the galactic plane (longitude and distance from earth). Next, a straight line can be fitted through the data (masers) representing the arm, and the line's pitch angle (arm pitch) is the angle away from a circle around the Galactic Center. Projecting an arm from a few maser locations may lead to predicting different spiral arcs, and different predicted tangents to a spiral arm. Masers are also found in short spurs or armlets, growing out of a long arm; each maser paper focuses on a specific piece of sky. Doing the same pitch angle deduction at other data located far away along the same arm (different galactic longitudes), should give a similar result, showing very little differences (a little spread around a mean pitch angle).

The “kinematic” method assumes a velocity model to obtain distances from the Sun, while the “luminosity-distance” method assumes a dust absorption model with distances. Both are employed to position the observed objects on the galactic plane, after which a pitch angle fit is extracted for the spiral arm involved.

The “positional” method extracts observational arm values (arm number, arm shape, arm pitch angle, arm separation near the Sun) from fits to different individual objects (stars, masers, HII regions, etc) positioned on the galactic plane.

In this paper, we look for signs of convergence over time (a shallower width in the distribution, a higher primary peak in the distribution).

In Sections 2 and 3, we aim to assess each spiral arm's pitch angle. Due to the inherent differences in the nature of these methods, there is a concern as to which would give the more precise determination of pitch angle. Section 4 catalogues results published since 2015, using the positional method (arm number, arm shape, arm pitch, and interarm separation near the Sun). In Section 5, the results are assessed over time, to evaluate convergences. In Section 6 we assess the results since mid-2015, comparing to those done in a 2005 study. In Section 7, we employ a proper galactic spiral arm pitch value to present a cartographic and kinematic model of the Milky Way. We conclude in Section 8.