M40 - Double Star or Binary Star ?

RA =  12h 22m 12sec,  DEC = +58° 4' 59"

Distance = ?   Binary Star system ?

M40, also known as WNC 4 (Winnecke 4, WDS 12222 +5805, SAO 28353 and 28355, TYC 3840:1031 and 3840:0564), is a faint double star originally found by Charles Messier in 1764.  He catalogued it in his famous list  in 1764. Since no known nebula exists at this location, historians have suggested that Messier made a mistake in this entry. The galaxy, NGC 4290, m = 12.7 is 9 arc minutes west of M40, but was probably too faint to be seen by Messier in his 3½ inch telescope.  WNC 4 consists of two stars with visual magnitudes 9.7 and 10.1. Only a few measurements of position angle and separation of the pair appear in the literature and in NASA’s Astronomical Data Center’s database, with the most recent one from the Hipparcos/Tycho astrometry mission. An investigation was made by this author combining data from the Tycho-2 Catalog and other scarce sources to determine if WNC 4 is a real binary system that is physically connected or a chance optical alignment of two stars. 

Winnecke (1869) published the position angle and separation of the pair as 88.0° and 49.2" for the epoch 1863. In 1991, Tycho positions from the Hipparcos/Tycho astrometry mission showed only a small change in position angle and separation to 77.0° and 52.8". Only a few other measurements of the pair exist from the archives of the Washington Double Star Catalog (Worley & Douglass 1996).

                       Figure 1. M40 are the 2 bright stars are below center, NGC 4290 is the galaxy on the right.

 No trigonometric parallax data were available for the pair prior to the Hipparcos/Tycho astrometry mission. The Hipparcos-Tycho Catalog gives a parallax p = 6.4 ± 17.9 mas for the primary and a negative parallax for the secondary. With this information the distance to the primary (brighter) component is computed as 150 pc, but with the error nearly 300% larger than the parallax, this distance is meaningless.  However, this parallax and error give an estimate for the minimum distance to the primary. Based upon the spectral types of the primary and secondary, K0III and G0V from Skiff (2001), the absolute visual magnitudes are  M_v  = +0.88 and +4.0, and masses are 1.1M_¤ and 1.2M_¤  respectively (Lang 1992).  

Using the method of spectroscopic parallaxes, distances of  590 ± 230 pc and 170 ± 70 pc are computed for the primary and secondary.  Obviously with estimated distances being over 300 pc, there is probably no way that these two stars are physically connected in the binary star sense. If we assume the distance to WNC 4 is at least 100 pc, the observed separation of 50" yields a physical separation of at least 5,000 AU.  Since the 50" measurement  is a projected separation, the 5,000 AU distance represents a minimum distance between the primary and secondary components. There are no known binaries with this large physical separation in the literature.  Assuming  Keplerian orbits, the period  P (in years) is related to the separation of the pair a, (in units of AU) from Kepler's well known 3rd law::

                                                                P² = [4p² / G(M₁ + M₂)] a³                                            

 Using 5,000 AU for a (seperation), M₁ + M₂ = 4.6 x 10³³ gm, G the gravitational constant, the period comes to 232,000 years. (At 150 pc distance, a = 7,500 AU, P = 427,000 yrs).  This result alone, independent of observed orbital motion, clearly shows the implausibility of the pair being a real  binary star system.

 Additional evidence to discount the physical association of the pair comes from the change in position angle. The observed change in position angle is only 11° in 128 years. While this position angle change is not uncommon in close  (< 2") binary pairs, it is unheard of with large separations in the 50" range. If we again  assume circular Keplerian orbits, independent of any projection effects, and extrapolate this motion to 360° (a complete orbit) this corresponds to a period of  some 4,400 years, a very high value. Even with this period, the physical separation computes to over 355 AU. While this separation is not unrealistic for a binary, the distance to the system with a 50" observed separation would be 7.1 pc.  If the apparent orbit were projected in such a way so that the actual separation were 500 AU, the distance to the system would be 10 pc.  Obviously, these distances are gravely inconsistent from the observed Tycho  mission parallaxes.

 The Tycho-2 proper motion data are graphically shown as Figure 2 below. For a true binary system, the motion of the pair’s barycenter should remain constant across the sky.  The proper motions of WNC 4 show the two stars moving in discordant directions 55° from one another. Earlier proper motion data from the SAO (SAO staff, 1966) and the PPM  (Roeser & Bastian 1988) catalogs also show different motions for the components of WNC 4. The Tycho-2 proper motions support these earlier results. 

       Figure 2.  "S" is the secondary star, "P" is the Primary Star of the system M40. The arrows indicate each star's proper motion (apparent motion across the sky, not to scale). For a true binary star system, the proper motion vectors should be pointing in the same direction.   

For a true visual binary star system, parallax, proper motion and observed orbital data should be in agreement within the observational errors.  For WNC 4, the new Tycho and Tycho-2 data do not add any support for any real physical association of the pair. The highly accurate Hipparcos/Tycho parallaxes have given astronomers some surprises, but such is not the case for WNC 4. The apparent orbital motion of the pair can be explained by the proper motion of two optically aligned stars, indicating no physical connection. Tycho and spectroscopic parallax data verify the distance to the fainter star is at least 150 pc and to the brighter star 570 pc.  At 150 pc distance, the calculated physical separation is 7,500 AU which is unrealistic for a binary. 

The addition of radial velocity data for the WNC 4 stars will not likely change the case presented here for the non physical association of the pair.  No such radial velocity data exists currently, thus future work in this area can add to our knowledge of WNC 4.  

 It is concluded that WNC 4, more commonly known as M40, is thus a optically aligned pair of stars, and not physically connected.

                                                  REFERENCES

Lang, K., 1992, Astrophysical Data: Stars and Planets, Springer-Verlag, New York..

Mallas, J., Kreimer, E., 1978, The Messier Album, Sky Publishing Corporation, p. 93.

Nugent, R.L., 1998, New Measurements of the Expansion of the Crab Nebula, Publications of the Astronomical Society of the Pacific,  110, 831

Nugent, R.L., 2002, The Nature of the Double Star M40, Journal of the Royal Astronomical Society of Canada, 96, p 63-65.

Roeser S., Bastian U., 1988, Catalogue of Positions and Proper Motions, A&AS, 74, 449

SAO Staff 1966, Smithsonian Astrophysical Observatory Star Catalog, Smithsonian Institution of  Washington,  Publication Number 4562.

Schlegal, D.J., Finbeiner, D.P., Davis, M., 1998, ApJ, 500, 525

Skiff, B., 2001, private communication

Winnecke 1869, Astron Nach, 73, No. 1738, p.145-160.

Worley, C.E. and Douglass, G.G., 1996, Washington Double Star Catalog, Astronomical Data Center Catalogue #1237.