Parenago’s Discontinuity and the Onset of Stellar Molecular Spectral Lines



     Parenago’s Discontinuity, an observational effect, confirmed in main sequence stars out to ~260 light-years, describes faster galactic revolution velocities for stars cooler than (B-V)~0.5. Previous work by this author presents speculations regarding molecular consciousness in stars. Here, it is demonstrated, using observational data published in the 1930’s for a small star sample that the onset of molecular spectral lines in stellar reversing layers occurs almost precisely at the velocity discontinuity. The shape of the previously published galactic revolution velocity vs. (B-V) color index for several thousand stars is very similar to the curve of G spectral line width vs. (B-V) for the small stellar sample considered, which suggests a connection between molecules and Parenago’s Discontinuity.


     Earlier work considered an evaluation of the scientific merit of philosopher Olaf Stapleton’s conjecture in the 1937 science-fiction novel Star Maker that a portion of stellar motion is volitional as opposed to purely gravitational [1]. It was postulated in that paper that a universal field of proto-consciousness interacts with molecular matter through the Casimir Effect. This effect describes the contribution of fluctuations in the universal vacuum in maintaining bonds between atoms in molecules.

    A search for supporting evidence revealed Parenago’s Discontinuity. Less massive, red, cooler stars tend to revolve around the galactic center a bit faster than more massive, bluer, hotter stars. A plot demonstrating this effect for several thousand main sequence stars out to ~260 light years is presented in Ref. 1 and reproduced here as Fig. 1. Data for this plot are from Allen’s Astrophysical Quantities and measurements from the ESA Hipparcos space observatory [2,3]. In this plot, stellar velocity components around the galactic center are plotted against (B-V) color indices. It was noted in Ref. 1 that Parenago’s Discontinuity occurs in the stellar temperature distribution where molecules first appear in stellar spectra.

    Other data from Hipparcos has been evaluated for the motions of giant stars out to >1,000 light years. Parenago’s Discontinuity is present in this sample as well, which may obviate many proposed local explanations [4-6]. Gaia, a successor to Hipparcos has been launched and positioned by ESA and is observing the positions and locations of ~ 1 billion stars in the Milky Way galaxy. These observations will hopefully reveal whether Parenago’s Discontinuity is a galaxy-wide phenomenon.

    The purpose of this paper is to further investigate the on-set of molecular activity in stars. Questions addressed are the spectral class at which molecules are first noted in stellar spectra, which molecules have been observed in stellar and solar spectra and the stellar layer in which stable molecules are located. Using crude observations of molecular spectral line widths from a small sample of stars vs. spectral class, a plot has been prepared for comparison with the results in Fig. 1. 

                   Molecules in Stars: What are They and Where are they Located?

     The stellar interior is a very hot place. It therefore might come as a surprise to learn that the spectral signatures of numerous molecular species have been observed in various stars. Molecules detected in the spectra of the Sun (a G2 V star with an effective photosphere temperature of 5777 K [7]) and sunspots include AlH, AlO, BH, BO, CH, CH+, CN, CO, CuH, MgF, MgH, MgO, NH, O2, OH, ScO, SiH+, SiN, SiO, SrF, TiH [8]. Simple molecules including CH and CN are seen in other G and K stars. Cooler stars have more complex molecular signatures [8].

    As discussed by Tsuji, quantitative spectral analysis of molecular spectra is much easier in the bright, nearby Sun than in more distant stars. On problem in interpreting stellar molecular spectral data is line broadening. Another is the huge number of spectral lines for some molecules, which results in an overlap of spectral bands.  Stellar layers may be less homogenous than some researchers have assumed and starspots can affect the molecular spectra in adjacent, hotter regions [9].

    Although molecular spectra can serve as a diagnostic tool in the study of stellar outer layers and circumstellar envelopes, molecular stellar spectroscopy has played a minor role in astrophysics since the 1930’s [9]. 

    Because of the Sun’s high photosphere temperature and the fact that even a cooler K2 star has a photosphere temperature of about 5000 K, it seems likely that stable molecules are likely to be found in a low-optical-thickness reversing layer above the photosphere and below the chromosphere [10]. The mass of the molecular envelope in this layer is estimated to be between one-ten-thousandth and one-millionth of the Sun’s mass in some giant stars [9]. In the Quiet Sun, the temperature minimum in this layer is about 600 km above the photosphere [11]. Blitzed has estimated the CN excitation temperature in this layer to be 4490 +/- 100 K. Other researchers cite temperatures in the range 4000-4670 K [12].

    Some researchers have used stellar molecular spectral observations to model stellar interiors. Russell investigated the role of relative element abundances. For giant K and M stars with more oxygen than carbon, CN abundance and CH abundance respectively peak at temperatures of3877 K and 4200 K. For dwarf K and M stars with more oxygen than carbon, CN peaks at 4383 K and CH peaks at 4800 K [13].

    For giant stars richer in carbon than oxygen, such abundance peaks with temperature are not as distinct. In dwarf stars richer in richer in carbon than oxygen, CN abundance peaks near 3252 K and CH abundance peaks near 3150 K. For giants with equal amounts of carbon and oxygen, the temperatures for peak abundances of CH and CN are respectively 3877 K and 3055 K [13].

    Russell’s model also predicts that molecules are rare or non-existent in giants earlier than F4 and in dwarfs earlier than F7. In dwarfs, CH and CN maximum abundance occurs respectively in spectral classes K2 and K4. In giants, CH and CN maximum abundance occurs respectively in spectral classes G7 and K1. For temperatures greater than 4500 K, the predicted CN abundance is slightly less in giants than in dwarfs [13].


      Observations of Molecular Line Width vs. (B-V) Color Index for a Small Stellar Sample

     In 1937, Rense and Hynek published a study of the G Band in the spectra of 25 stars [14]. The G band extends 4203-4317 Angstroms, in the extreme blue region of the visible spectrum. This band can be used as an approximate measure of CH abundance sine some CH spectral absorption lines are within this band. They reported that the G band is somewhat more pronounced in giants than in dwarfs. Partial pressure is about 80X greater in F8 dwarfs than in G0 giants and association of atoms into molecules is 4.5X greater in f8 dwarf stars than in G0 giants. For dwarf stars hotter than F5 in their observational sample, all G band spectral lines are atomic [14]. In Ref. 14, CN spectral lines used were 4192.57 and 4197.10 Angstroms. CH spectral line used were 4293.12 and 4303.94 Angstroms.

    Table 1 is a partial representation ofthe Rense/Hynek results. Only single stars are included in Table 1, with the exception of η Cor., which is a binary consisting of two nearly identical G dwarf stars. Variable stars are also omitted. The BS# designations are from Hoffleit’s 1964 catalogue [15]. Spectral and luminosity classes and the (B-V) color indices are from Johnson et al’s 1966 photometric observations of many bright stars [16], except where otherwise noted. The (B-V) of the Sun is from Croft et al [17].

    A subset of the data presented in Table 1 was used to prepare the graphical representation of G line width vs. (B-V) color index for giant/bright giant stars (luminosity classesIII and II) and dwarf/sub-giants (luminosity classes V and IV) presented in Fig. 2.  Supergiants were not included because contemporary studies of Parenago’s Discontinuity in this stellar luminosity class have not been located by this author.

    At least one other team obtained similar but less quantitative observational results [18]. Investigating spectra of 28 stars for CH and 9 stars for CN., Swings and Struve found the hot-star limit for CH and CN is F8 stars, with photosphere temperatures of ~6500 K. In only one of eight F5 stars was a faint indication found for CN. CN becomes progressively stronger in stars cooler than the Sun [18].


      Based upon the small stellar sample used to prepare Fig. 2, it is evident that Parenago’s Discontinuity occurs almost exactly at the point in the stellar photosphere temperature distribution where the spectra of simple molecules appears in stellar spectra. It is also interesting to note that the increase in stellar galactic revolution velocities for (B-V) less than about 0.4 is very similar in shape to an increase in G line width at about the same value of (B-V) color index.

    The similarity of the two curves is certainly suggestive and supports the hypothesis discussed in Refs. 1, 5 and 6 that a portion of stellar motion is volitional and, to a certain extent, self-organization occurs at the stellar level. However, it must be remembered that the stellar spectra sample used to prepare Fig. 2 is very small and it is not yet known whether Parenago’s Discontinuity is a galactic phenomenon.



  1. G. L. Matloff, “Invited Commentary—Olaf Stapledon and Conscious Stars: Philosophy or Science”, JBIS, 65, 5-6 (2012).
  2. G. F. Gilmore and M. Zelik, “Star Populations and the Stellar Neighborhood”, in Allen’s Astrophysical Quantities, 4th ed, A. N. Cox, Ed., Springer-Verlag, NY (2000), Chap. 19.
  3. J. J. Binney, W. Dehnen, N. Houk, C. A. Murray, and M. J. Preston, “Kinematics of MainSequence Stars from Hipparcos Data”, in Proc. ESA Symposium Hipparcos-Venice ’97, ESA-SP402, Venice, Italy, 13-16 May 1997, pp 473-477 (July, 1997).
  4. R. L. Branham Jr., The Kinematics and Velocity Ellipsoid of G III Stars”, Revisita Mexicana de Astronomia y Astrofisca, 47, 197-209 (2011).
  5. G. L. Matloff, “On the Nonlocality of Parenago’s Discontinuity and Universal Self-Organization”, Axiom, 1, No. 2, 14-19 (Dec., 2015). Also presented at 9th IAA Symposium on the Future of Space Exploration, Turin, Italy, 7-9 July 2015.
  6. G. L. Matloff, Starlight, Starbright—Are Stars Conscious?, Curtis, Norwich, UK (2015).
  7. W. C. Livingston, “The Sun”, in Allen’s Astrophysical Quantities, 4th ed, A. N. Cox, Ed., Springer-Verlag, NY (2000), Chap. 14.
  8. R. W. Nicholls, “Transition Probability Data for Molecules of Astrophysical Interest”, Annual Review of Astronomy and Astrophysics, 15, 197-234 (1977).
  9. T. Tsuji, “Molecules in Stars”, Annual Review of Astronomy and Astrophysics, 24, 197-234 (1986).
  10. E. Novotny, Introduction to Stellar Atmospheres and Interiors, Oxford U. P. Press, NY (1973), pp. 192-193.
  11. E. H. Avrett, “The Solar Temperature Minimum and Chromosphere,” Current Theoretical Models and High Resolution Solar Observations, ASP Conference Series, Vol. 286, ed. A. A. Pevtsov and H. Uitenbroek, pp. 419-429.

12. L. Blitzer, “The Excitation Temperature of the Solar Reversing Layer from CN (λ 3883)”

      Astrophysical Journal, 91, 421- 427(1940).

13. Henry Norris Russell, “Molecules in the Sun and Stars”, Astrophysical Journal,  Vol. 79

      317- 342 (1934).

14. W. A. Rense and J. A. Hynek, “Photometry of the G Band in Representative Stellar Spectra”, 

      Astrophysical Journal86, 460-469(1937).

15. D. Hoffleit, Catalogue of Bright Stars, 3rd Revised Ed., Yale Univ. Observatory, New Haven,

      CT (1964).

16. H. L. Johnson, R. I. Mitchell, B. Iriate, and W. Z. Wisniewski, “UBVRIJKL Photometry of the

      Bright Stars”, Communications of the Lunar and Planetary Laboratory, Communication No.

      63, Vol. 4, Part 3, University of Arizona Press, Tucson AZ (1966). 

17. S. K. Croft, D. H. McNamara, K. A. Feltz Jr., “The (B-V) and (U-B) Color Indices of the

        Sun”,  Pub. Astro. Soc. Pacific, 84, 515-518 (1972).

18. P. Swings and O. Struve, “The Bands of CH and CN in Stellar Spectra”, Physical Review,

        39, pp. 142-150 (1932).




































Fig. 1. Star Motion in Direction of Galactic Rotation (V) vs. (B-V) Color Index. Blue

                   Diamonds are from Gilmore and Zelik [2]. Red Squares are from Binney et al.












                             Fig. 2. G Line Width vs. (B-V) Color Index for Rense/Hynek Stars.

                    Green Points: giants & bright giants. Blue points: dwarfs & sub-giants



















TABLE 1. CN Molecular and G Equivalent Absorption Observational Estimates from Rense and Hynek (1937). G Line Absorption is a Measure of CH Abundance. Unless Noted, Spectral/Luminosity Class and B-V are from Johnson et al, 1966, Unless Otherwise Noted.


Star Name     BS#     Spectral/Luminosity Class  (B-V)   G Line Width   CN Relative Absorption


  η  Lep.          2085            F0 V                           0.33          4.5              0

20 Can. Ven.  5017            F0 II-III                       0.30             4.9              0

81 Leo.           4408            F2 V+                         0.37+            3.6            >0  

53 Vir.             4981            F5 III-IV++                  0.47++          4.5                >0 

  τ Boo.           5185            F2 V                        0.48             4.6               >0

  α Per.           1017               F5 I                           0.48             6.0               >0

  η Cas.            219               G0 V                         0.58           10.9                 0

     Sun+++                              G0 V                         0.63             9.4                 1

  η Cor.          5727/5728  G2V (G1V + G3V)       0.58             7.5                 2

  β Lep.           1829               G5 III                      0.82           11.5                 2

 σ 2 Eri.           1325               K1 V                         0.82             9.6                 1

  ε Gem.          2473            G8 I                        1.40           13.2                 3

  ε Eri.               984               K2 V                         0.88           12.3               >1  

  τ Ceti            509               G8 V                         0.72           12.8                 1

  α Boo.           5340               K2 III                      1.23          14.5              3

   ι  Aur.           1577              K3 II                      1.53          14.0               >2

   α Ori.            2061               M1/2 I                    1.84          10.7              3


BS# are Bright Star Numbers from: D. Hoffleit, Catalogue of Bright Stars, 3rd Revised Ed., 

      Yale Univ. Observatory, New Haven, CT (1964).

Variable and multiple stars from Rense/Hynek list are omitted except forη Cor., which is a

      double with nearly identical members.  

  + : Also in Wikipedia.

++ : Also in Wikipedia.

+++ :  Ref. 17