Constraining the pitch angle of the galactic spiral arms in the Milky Way
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.
Section snippets
Individual arm pitch angle
Each arm can now be identified by tracers, placed in a specific order and at specific galactic longitudes. A recent study of the galactic longitude of each arm tangent (as seen from the Sun) showed longitude offsets between dust, stars and various chemical tracers such as CO (Paper VI; Vallée, 2014c). Going across galactic longitude 0°, the galactic longitudes of the tracers (CO, then dust) in Galactic Quadrant IV reversed as one went across the Galactic Meridian to Galactic Quadrant I (dust,
Histograms of the individual pitch angle, for three inner arms
The data in Table 1 can be employed to make histograms, for each arm, and for an individual method.
Positional method
In a series of papers, we have catalogued the published observational results since 1980 for the Milky Way's arms (number of arms, arm shape, pitch angle, interarm separation through the Sun's location). Results were put in blocks, each block with a minimum of 15 and a maximum of 20 results. Papers in this series were: Vallée (1995 – Paper I), Vallée (2002 – Paper II), Vallée (2005 – Paper III), Vallée (2008 – Paper IV), Vallée (2013 – Paper V), Vallée (2014a – Paper VI), Vallée (2014b – Paper
Statistical trends with time, since 1980
Here we wish to assess the evolution of our knowledge with time of some spiral arm parameters in the Milky Way disk, over the period from 1980 to 2017.
The median value of the observed pitch angle data since 2015 is near −13° with a r.m.s. near 0.5°, for the positional method (Table 2). Earlier data indicated a mean near −12° with an r.m.s. near 1° (Vallée, 2005).
The value of the observed interarm separation since 2014 is near 3.1 kpc with a r.m.s. near 0.1 kpc. Earlier data indicated a mean
Statistical convergence of recent results
Here we assess the histograms of individual spiral arm results, for the published studies since 2014 (covering Paper VIII, IX and X). We wish to assess whether we have a single peak or not, and its importance.
Fig. 4a shows a histogram from a compilation of the observed pitch angle. Each data represents one individual published study; there are 94 such data since 2014. The central peak here is about eight times higher than the adjacent secondary peak, whereas earlier it was only about three
Modeling
A review of around 50 determinations of Rsun, published between 1992 and 2011, found a weighted mean value of 8.0 ± 0.4 kpc, covering a 20-year time period (Fig. 1 in Malkin, 2013). A review of about 70 determinations of Rsun, published from 1990 up to mid-2012, was given in Gillessen et al., (2013), and their Fig. 2 showed a median near 8.1 ± 0.3 kpc. The review of Rsun by De Grijs & Bono (2016), covered 273 entries since 1918, and yielded Rsun = 8.3 ± 0.4 kpc. A review by Bland-Hawthorn &
Conclusion
By linking each arm segment in Galactic Quadrant I with its corresponding arm segment in Galactic Quadrant IV, simple trigonometry using a logarithmic shape reveals the mean pitch angle of each arm. We compared the pitch angle of individual arms (Table 1), assessing the pros and cons of the parallax method versus the twin-tangent arm method (Fig. 1, Fig. 2, Fig. 3).
We find the twin-tangent method to give a more credible ‘global arm’ pitch angle value, based on data from a larger amount of
Acknowledgements
The figure production made use of the PGPLOT software at NRC Canada in Victoria. I thank an anonymous referee for useful, careful, and historical suggestions.
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