Galactic coordinate system

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Short description: Celestial coordinate system in spherical coordinates, with the Sun as its center
Artist's depiction of the Milky Way Galaxy, showing the galactic longitude. A vector matching the plane of the galaxy, at 0° longitude, notably has the Galactic Center and intersects arms directly beyond. Far less of the galaxy lies at all points with opposing 180° longitude

The galactic coordinate system is a celestial coordinate system in spherical coordinates, with the Sun as its center, the primary direction aligned with the approximate center of the Milky Way Galaxy, and the fundamental plane parallel to an approximation of the galactic plane but offset to its north. It uses the right-handed convention, meaning that coordinates are positive toward the north and toward the east in the fundamental plane.[1]

Spherical coordinates

Galactic longitude

The galactic coordinates use the Sun as the origin. Galactic longitude (l) is measured with primary direction from the Sun to the center of the galaxy in the galactic plane, while the galactic latitude (b) measures the angle of the object above the galactic plane.

Longitude (symbol l) measures the angular distance of an object eastward along the galactic equator from the Galactic Center. Analogous to terrestrial longitude, galactic longitude is usually measured in degrees (°).

Galactic latitude

Latitude (symbol b) measures the angle of an object northward of the galactic equator (or midplane) as viewed from Earth. Analogous to terrestrial latitude, galactic latitude is usually measured in degrees (°).

Definition

The first galactic coordinate system was used by William Herschel in 1785. A number of different coordinate systems, each differing by a few degrees, were used until 1932, when Lund Observatory assembled a set of conversion tables that defined a standard galactic coordinate system based on a galactic north pole at RA 12h 40m, dec +28° (in the B1900.0 epoch convention) and a 0° longitude at the point where the galactic plane and equatorial plane intersected.[1]

In 1958, the International Astronomical Union (IAU) defined the galactic coordinate system in reference to radio observations of galactic neutral hydrogen through the hydrogen line, changing the definition of the Galactic longitude by 32° and the latitude by 1.5°.[1] In the equatorial coordinate system, for equinox and equator of 1950.0, the north galactic pole is defined at right ascension 12h 49m, declination +27.4°, in the constellation Coma Berenices, with a probable error of ±0.1°.[2] Longitude 0° is the great semicircle that originates from this point along the line in position angle 123° with respect to the equatorial pole. The galactic longitude increases in the same direction as right ascension. Galactic latitude is positive towards the north galactic pole, with a plane passing through the Sun and parallel to the galactic equator being 0°, whilst the poles are ±90°.[3] Based on this definition, the galactic poles and equator can be found from spherical trigonometry and can be precessed to other epochs; see the table.

J2000.0 equatorial coordinates approximating the galactic reference points[1]
  Right ascension Declination Constellation
North Pole
+90° latitude 		12h 51.4m +27.13° Coma Berenices
(near 31 Com)
South Pole
−90° latitude 		0h 51.4m −27.13° Sculptor
(near NGC 288)
Center
0° longitude 		17h 45.6m −28.94° Sagittarius
(in Sagittarius A)
Anticenter
180° longitude 		5h 45.6m +28.94° Auriga
(near HIP 27180)
Galactic north pole.png
Galactic north 		Galactic south pole.png
Galactic south 		Galactic zero longitude.png
Galactic center

The IAU recommended that during the transition period from the old, pre-1958 system to the new, the old longitude and latitude should be designated lI and bI while the new should be designated lII and bII.[3] This convention is occasionally seen.[4]

Radio source Sagittarius A*, which is the best physical marker of the true Galactic Center, is located at 17h 45m 40.0409s, −29° 00′ 28.118″ (J2000).[2] Rounded to the same number of digits as the table, 17h 45.7m, −29.01° (J2000), there is an offset of about 0.07° from the defined coordinate center, well within the 1958 error estimate of ±0.1°. Due to the Sun's position, which currently lies 56.75±6.20 ly north of the midplane, and the heliocentric definition adopted by the IAU, the galactic coordinates of Sgr A* are latitude +0° 07′ 12″ south, longitude 0° 04′ 06″. Since as defined the galactic coordinate system does not rotate with time, Sgr A* is actually decreasing in longitude at the rate of galactic rotation at the sun, Ω, approximately 5.7 milliarcseconds per year (see Oort constants).

Conversion between equatorial and galactic coordinates

An object's location expressed in the equatorial coordinate system can be transformed into the galactic coordinate system. In these equations, α is right ascension, δ is declination. NGP refers to the coordinate values of the north galactic pole and NCP to those of the north celestial pole.[5]

[math]\displaystyle{ \begin{align} \sin(b) &= \sin(\delta_\text{NGP})\sin(\delta)+\cos(\delta_\text{NGP})\cos(\delta)\cos(\alpha-\alpha_\text{NGP}) \\ \cos(b) \sin(l_\text{NCP}-l) &= \cos(\delta)\sin(\alpha-\alpha_\text{NGP}) \\ \cos(b) \cos(l_\text{NCP}-l) &= \cos(\delta_\text{NGP}) \sin(\delta) - \sin(\delta_\text{NGP}) \cos(\delta) \cos(\alpha - \alpha_\text{NGP}) \end{align} }[/math]

The reverse (galactic to equatorial) can also be accomplished with the following conversion formulas.

[math]\displaystyle{ \begin{align} \sin (\delta) &= \sin (\delta_\text{NGP}) \sin(b) + \cos (\delta_\text{NGP}) \cos(b) \cos(l_\text{NCP} - l) \\ \cos (\delta) \sin(\alpha - \alpha_\text{NGP}) &= \cos(b) \sin(l_\text{NCP} - l) \\ \cos (\delta) \cos(\alpha - \alpha_\text{NGP}) &= \cos (\delta_\text{NGP}) \sin(b) - \sin(\delta_\text{NGP}) \cos(b) \cos(l_\text{NCP} - l) \end{align} }[/math]

Where:

[math]\displaystyle{ \alpha_\text{NGP}=12^h 51.4^m \qquad \delta_\text{NGP}=27.13^{\circ} \qquad l_\text{NCP}=122.93314^{\circ} }[/math]

Rectangular coordinates

In some applications use is made of rectangular coordinates based on galactic longitude and latitude and distance. In some work regarding the distant past or future the galactic coordinate system is taken as rotating so that the x-axis always goes to the centre of the galaxy.[6]

There are two major rectangular variations of galactic coordinates, commonly used for computing space velocities of galactic objects. In these systems the xyz-axes are designated UVW, but the definitions vary by author. In one system, the U axis is directed toward the Galactic Center (l = 0°), and it is a right-handed system (positive towards the east and towards the north galactic pole); in the other, the U axis is directed toward the galactic anticenter (l = 180°), and it is a left-handed system (positive towards the east and towards the north galactic pole).[7]

The anisotropy of the star density in the night sky makes the galactic coordinate system very useful for coordinating surveys, both those that require high densities of stars at low galactic latitudes, and those that require a low density of stars at high galactic latitudes. For this image the Mollweide projection has been applied, typical in maps using galactic coordinates.

In the constellations

The galactic equator runs through the following constellations:[8]


See also

References

  1. ↑ 1.0 1.1 1.2 1.3 Blaauw, A.; Gum, C.S.; Pawsey, J.L.; Westerhout, G. (1960). "The new IAU system of galactic coordinates (1958 revision)". Monthly Notices of the Royal Astronomical Society 121 (2): 123. doi:10.1093/mnras/121.2.123. Bibcode: 1960MNRAS.121..123B. 
  2. ↑ 2.0 2.1 Reid, M.J.; Brunthaler, A. (2004). "The Proper Motion of Sagittarius A*". The Astrophysical Journal 616 (2): 874, 883. doi:10.1086/424960. Bibcode: 2004ApJ...616..872R. 
  3. ↑ 3.0 3.1 James Binney, Michael Merrifield (1998). Galactic Astronomy. Princeton University Press. pp. 30–31. ISBN 0-691-02565-7. https://books.google.com/books?id=arYYRoYjKacC&q=rotation+%22proper+motion%22+galaxy+OR+galactic&pg=PA675. 
  4. ↑ For example in Kogut, A. (1993). "Dipole Anisotropy in the COBE Differential Microwave Radiometers First-Year Sky Maps". Astrophysical Journal 419: 1. doi:10.1086/173453. Bibcode: 1993ApJ...419....1K. 
  5. ↑ Carroll, Bradley; Ostlie, Dale (2007). An Introduction to Modern Astrophysics (2nd ed.). Pearson Addison-Wesley. p. 900-901. ISBN 978-0805304022. 
  6. ↑ For example Bobylev, Vadim V. (March 2010). "Searching for Stars Closely Encountering with the Solar System". Astronomy Letters 36 (3): 220–226. doi:10.1134/S1063773710030060. Bibcode: 2010AstL...36..220B. 
  7. ↑ Johnson, Dean R.H.; Soderblom, David R. (1987). "Calculating galactic space velocities and their uncertainties, with an application to the Ursa Major group". Astronomical Journal 93: 864. doi:10.1086/114370. Bibcode: 1987AJ.....93..864J. 
  8. ↑ "SEDS Milky Way Constellations". http://messier.seds.org/more/mw_con.html. 

External links



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