ABSOLUTE
WAVELENGTHS
CONVECTIVE
MOTIONS
OF FRAUNHOFER
LINES:
IN THE SOLAR PHOTOSPHERE
AND THE GRAVITATIONAL
RED SHIFT
D. L. LAMBERT* and E.A. MALLIA Dept. of Astrophysics, University Observatory, Oxford
(Received 18 September, 1967) Abstract. Absolute wavelengths for Fraunhofer lines are compared with laboratory measurements
for several atomic and molecular spectra. The wavelength differences are shown to be consistent with the proposal that the deeper layers of the photosphere are in convective motion: ve -~ 3 km/sec for log To> --1.0. Convective motions in the outer layers (logv0< --1.0) are shown to be very small. Wavelength shifts of Fraunhofer lines formed in these outer layers are in good quantitative agreement with the predictions of the General Theory of Relativity.
1. Introduction
In a recent article in this journal, DE JAGER and NEVEN (1967) presented a comprehensive discussion of line profile observations of the CI multiplet 3s3p ~ 3paD at about 10700 A. From the observed asymmetries of the profiles, the convective (or macroturbulent) velocity field was deduced. It is this result of their paper which is discussed in the present paper. The conversion of the asymmetries into a convective velocity (denoted by v~(%)) was based on the three-column Utrecht Reference Photosphere (HEINTZE et al., 1964). With the hot, average, and cold elements in the proportions 1 : 1 : 1, a simple representation of the convective velocity field was obtained: vo(%) = 0 = 2.9
for log z o ~< - 1.0 km/sec
for logz 0/> - 1.0.
In this paper, confirmatory evidence for their proposal is obtained through a comparison of absolute wavelengths in solar and laboratory spectra. The following example illustrates the arguments which led to the present study. The weak highexcitation lines of C ~, N I, and O I (W~ ~<20 mA, Z/> 8 eV) originate in those layers for which vc =2.9 km/sec. Since such lines are formed preferentially in the hot rising elements the wavelengths for the central depth suffer a blue shift of about 20 to 30 mA. The accuracy of available laboratory and solar wavelengths should suffice to enable a wavelength displacement of this magnitude to be detected. * Present Address: Mount Wilson and Palomar Observatories, Pasadena, Calif., U.S.A. Solar Physics 3 (1968) 499-504; 9 D. Reidel Publishing Company, Dordrecht-Holland
500
D . L . LAMBERT AND E.A. MALLIA
2. Method and Results A representative selection of spectra were considered. The sample included lines formed in the highest as well as the deepest layers of the photosphere. The laboratory wavelengths for standard air (2air) were taken - with the exception of the wavelengths for the M g H band - from recent laboratory measurements. References are given in the tables. The primary source of absolute solar wavelengths (2o) is the recent revision of Rowland's Preliminary Table by MooRE et al. (1966). Wavelengths for 17 strong CI lines between 9000 and 12000 A were taken from BABCOCK and MOORE (1947). For many of the weak lines in the M g H band, the solar wavelengths were remeasured on low-noise photoelectric scans with a considerable improvement in accuracy over the photographic measurements listed by MoORZ et al. (1966). The selection of lines was governed by two simple criteria: (i) A line was not considered unless both laboratory and solar wavelengths were quoted to + 1 mA. This criterion represents an attempt to ensure that the wavelengths used are accurate to + 5 m A or better. The application of this criterion was relaxed for the selection of strong CI lines in the interval 9000-12000 A. (ii) The line was rejected if Moore et al. indicate that the Fraunhofer line is a composite feature with two or more contributors. For each line, the quantity A2 = 2 o - A2rs -
•air
was calculated. Here A2rs is the gravitational red shift predicted on the basis of the General Theory of Relativity. Results for A2 for several spectra are presented in Tables I - I I I . Several interesting results are apparent from an inspection of these tables. Considerable blue shifts (A2 negative) are found for those lines which are formed in the deepest layers: i.e. the N I lines in Table I and the weak C~ lines in Table II. T h e values of A2 for lines formed in the upper layers of the photosphere are equal to zero i.e. for the NaI, KI, C 2 and M g H lines in Table I, the strong CI and Sir lines in Table II and III respectively. For CI and SiI it can be seen that the 2 shifts diminish with increasing line intensity. Furthermore, the shifts are apparently independent of wavelength. 3. The Convective Velocity Field Since the presence of a marked blue shift for weak high-excitation lines and the absence of a shift for metallic and molecular lines appeared to be consistent with the convective velocity field proposed by DE JAGLI~ and NEVZN (1967), a quantitative comparison between the present results and the predicted displacements for a simple model was made. The three-column U R P model was adopted. It is known that the temperature distribution in this model has a number of shortcomings but these should have little relevance to the present problem. For log Zo ~< - 1 . 1 5 the model has a single column
ABSOLUTE WAVELENGTHS OF FRAUNHOFER LINES
501
and the convective velocity was assumed to be zero in these layers. For log r o/> - 1 . 1 5 the convective velocities given with the original model (HEINTZE et al., 1964) were discarded and replaced by a uniform convective velocity o f 3 km/sec. It was further assumed that the hot, average, and cold elements were present in equal proportions. It should be noted that this composite model is very similar to that which was shown by De Jager and Neven to be consistent with the Cl 10700 A line profiles. The predicted displacement of the line centre for a typical line of each species is given in Tables I - I I I . These predictions are in g o o d agreement with observed shifts. The approximate insensitivity o f the 2 shifts to wav61ength over the interval 4000-8000 A is reproduced by the prediction. This result is attributable to the increase in the continuous absorption at the longer wavelength and the outward decrease in the temperature differences between the columns. These differences are principally responsible for the observed shifts. A detailed comparison of the present results with predictions for various models of the convective velocity field was not attempted. However, it is instructive to indicate certain evidence which supports the proposal by De Jager and Neven for the onset o f convection at log To -~ - 1.0. TABLE I Wavelength Displacements A2 Spectrum NI OI NaI All KI CaiI C2 MgH
Wavelength Interval (~) 8200 8800 7775 4400-6200 5500-7900 4000-7000 5000-8300 5050-5200 5050-5200
Average Exc. pot. (eV) 10.3 9.1 2.1 3.5 0.8 7.0 0.0 0.0
(Wz) (m~,)
No. of Lines
10 50-80 45 15 65 20 25 15 0
3 3 9 7 5 6 26 24
A2 (m~) Observed Predicted --45 4- 10 --7 • 3 0• 3 --12• • 1 • 10 --7 • 6 0• 2 -I 2 • 4
--40 --4 • 2 4 0 --3 0 0
Notes: The Laboratory wavelengths were taken from the following sources: NI: ERIKSSON(1958) OI: ERIKSSONand ISBERG(1963b) MgH: WATSONand RUDNICK(1927) Ah: ERIKSSONand ISBERG(1963a) NaI: RISB~RG(1956) Can: EDLENand RISBERG(1956) KI: RISB~RG(1956) C2: PHILLIPS(1967)
It is possible to trace in Table I a correlation between the displacement A2 and the depth o f formation of the line. F o r the molecular lines M g H and C 2 and the strong CI and SiI lines which are formed at log To ~< - 1 . 2 the displacements are equal to zero to within the r.m.s, errors. A second group of lines (the OI 7774 • triplet, A h and Call lines) with depths of formation at log To-~ - 0 . 9 show a small negative displacement. This suggests that the onset of convection occurs at about log To-~ - 1 . 0 . Line-profile studies can provide more detailed information on the depth dependence
502
D . L . LAMBERT A N D E . A . MALLIA
TABLE II The Wavelength Displacements for CI lines Wavelength Interval (A) 7000-8000 5000-7000 4000-5000 9000-12000
Wavelength Displacement A2(mA) Wz ~< 40 mA Wz ~> 90 mA Observed
Predicted
27 ~=6 (3) 20 • 4 (5) 26 • 6 (6)
- 18
Observed
Predicted
- 20 2•
(17)
0
Notes:
The Laboratory wavelengths were taken from JOHANSSONand LITZ~N (1965) and JOHA~SSON (1966). The excitation potentials range from 7.5 to 8.9 eV. The number of lines in each category is given in parentheses following the r.m.s, error for A2. TABLE III The Wavelength Displacements for Sii lines Wavelength Interval (A) 8000-9000 7000-9000 6000-7000 5000-6000 4000-5000 4000-8000 Predicted Displacements
Wz ~< 25 mA - 26 ~- 10 (6) - 16 (1) - - 6 - - 4 (4) --2 • (10) - 2 0 = : 4 (4) - 12 4- 3 (25) - 7
Wavelength Displacement A2 (mA) 25 < Wz 60 mA W~ > 60 mA -- 17 • 3 (8) - 8 4-6 (3) -7-t=7 (12) - 4 • (10) - 18 (2) - 9 i 3 (2) -- 6
-- 8 ==3 (9) -0• (8) - 5 (2) - 6 • (3) --7 (1) --4 • 2 (23) -- 0
Notes:
The laboratory wavelengths were taken from RADZIEMSKIand ANDREW(1965). The lower excitation potentials for these lines range from 5.0 to 6.3 eV. The number of lines in each category is given in parentheses following the r.m.s, error for A2. of the convective velocities. Indeed, the dependence derived by De Jager a n d N e v e n is directly related to their o b s e r v a t i o n that the cores of the CI lines are symmetrical with a rather sudden appearance of asymmetry in the wings. It is of interest to note that for the OI 7774 A triplet a m e a s u r a b l e asymmetry can be traced to very near the line centre (OLSON, 1962). This indicates that the cores of this triplet are formed in regions subjected to convective motions. The a p p a r e n t absence of convective m o t i o n s in the outer layers of the photosphere is of interest since studies of the centre-limb variation of the M g H a n d C2 lines (Wn-HBROW, 1967) indicate that the temperature inhomogeneities extend further o u t w a r d t h a n was supposed in the U R P model. The M g H molecule, because of its low dissociation energy a n d the low i o n i s a t i o n potential of n e u t r a l m a g n e s i u m is formed p r e d o m i n a n t l y i n the cooler elements. This bias is m u c h less p r o n o u n c e d for C2 because of its high dissociation energy a n d the reduction at lower temperatures of the partial pressure of c a r b o n owing to the e n h a n c e d f o r m a t i o n of c a r b o n monoxide. The cores of the strong infrared CI lines are formed p r e d o m i n a n t l y in the hotter elements.
ABSOLUTE WAVELENGTHS OF FRAUNHOFER LINES
503
The observational result that the wavelength displacements A2 for MgH, C 2 and the strong CI lines are identical and equal to zero to within the observational errors indicates that, although temperature inhomogeneities may persist in the outer layers, the convective motions must be small, that is vc(zo)~<0.1 km/sec for log z o ~<- 1.2. 4. The Gravitational Red Shift
The evidence suggesting an absence of convective motions in the outer layers of the photosphere is especially relevant to a discussion of the gravitational red shift. The most direct interpretation of the present result that A2 = zero for all Fraunhofer lines formed in these outer layers is that their wavelengths are displaced to the red by the amount predicted by Einstein from the General Theory of Relativity. Several earlier investigations (see, e.g., ADAM, 1959) indicated that the gravitational red shift at the centre of the solar disk was substantially less than the predicted amount. The probable explanation for this apparent disagreement is that, at the centre of the disk, the wavelengths of the lines (primarily medium-strong FeI lines) used in the earlier investigations are displaced to the blue by the convective motions. This conclusion is supported by the work of SCHROTER (1956). He proposed a two-stream model (rather similar to the one under discussion) in which the temperature differences were negligible for logz 0 < - 1 . 5 and the convective velocities increased from zero at this depth to reach about 3 km/sec at log zo ~-0. This model predicted displacements in good quantitative agreement with the wavelength observations at the centre of the disk and their centre-limb variation. It should be noted that the present conclusions are derived from weak lines or very strong lines with symmetrical cores. The model-atmosphere predictions suggest that weak lines should be highly symmetrical. The Oxford photoelectric spectrometer (BLAcKWELLet aL, 1967) was used to obtain low-noise scans of the number of regions containing MgH and C 2 lines. The C2 lines show no measurable and systematic asymmetry. A small asymmetry in MgH lines is attributed to the isotopic lines (Mm;LIA, 1967) but this asymmetry is too small to affect measurements of the wavelengths of the line centre, which are obtained by either visual measurement of photographic plates or from photoelectric tracings. Indeed the wavelengths derived from the low-noise scans do not differ systematically from those given by MooRE et al. (1966). In conclusion, it is asserted that the present comparison of solar and laboratory wavelengths has demonstrated that the Fraunhofer lines are displaced to the red in good quantitative agreement with the prediction based on the General Theory of Relativity. 5. Conclusions and Discussion
The two principal conclusions of this paper will be briefly restated. Firstly, supporting evidence has been adduced for the model of the convective motions in the photosphere which was proposed by D~ JAGER and NEVEN (1967). Secondly, the wavelengths of
504
D . L . LAMBERT AND E.A. MALLIA
all Fraunhofer lines are displaced to the red according to the prediction f r o m the General Theory of Relativity but for lines formed in the regions below log Zo = - 1.0, an additional shift (generally to the blue) resulting f r o m convective m o t i o n is superimposed on the gravitational red shift. There is considerable scope for future observations. It is urged that future line profile observations be combined with measurements of the absolute wavelengths. A n extension of accurate wavelength determinations to the interval 15000-17000/k, in which the continuous absorption coefficient attains a m i n i m u m value would be o f the greatest interest in determining the convective velocity field in the deepest layers o f the photosphere. Observations with the highest possible spatial resolution are to be encouraged. I n this context it should be noted that an investigation of the spectrum of granules (or 'wiggles') provides additional evidence for the presence o f the convective velocity field in the deeper layers but which is absent in the upper layers o f the photosphere (EDMONDS et al., 1965).
References
ADAM,M.G.: 1959, Monthly Notices Roy. Astron. Soc. 119, 460. BABCOCK,H.D. and MOORE,C.E:: 1947, The Solar Spectrum 26600 to 213495. Carnegie Inst., Washington. BLACKWELL,D.E., PETFORD,A.D., and MALLIA,E.A.: 1967. Monthly Notices Roy. Astron. Soc. 136, 365. DE JAGER,C. and NEVEN,L~: 1967, Solar Phys. 1, 27. EDLEN,B. and RtSBERG,P.: 1956, Arkiv Fysik 10, 553. EDMONDS,F.N., MICHARD,R., and SERVAJEAN,R.:1965, Ann. Astrophys. 28, 534. ERIKSSON,K. B. S. : 1958, Arkiv Fysik 13, 429. ERIKSSON,K.B.S. and ISBERG,H. B. : 1963a, Arkiv Fysik 23, 527. ERIKSSON,K.B.S. and ISBERG,H.B. : 1963b, Arkiv Fysik 24, 549. HEINTZE,J. R.W., HUBENET,H., and DE JAGER,C. : 1964, Bull. Astron. Inst. Neth. 17, 442. JOHANSSON,L. : 1966, Arkiv Fysik 31, 201. JOHANSSON,L. and LrrZEN, U. : 1965, Arkiv Fysik 29, 175. MALLIA,E.A. : 1967, Thesis, University of Oxford. MOORE,C.E., MINNAERT,M., and HOUTGAST,J. : 1966, Second Revision of Rowland's Preliminary Table of Solar Spectrum Wavelength. N. B. S. Monograph, 61. OLSON,E.C.: 1962, Astrophys. J. 136, 946. PHILLIPS,J. G. : 1967, Private communication. RADZIEMSKI,L.J. and ANDREW,K.L.: 1965, J. Opt. Soc. Am. 55, 474. RISBERG,P.: 1956, Arkiv Fysik 10, 583. SCHR6TER,E.H.: 1956, Z. Astrophys. 41, 141. WATSON,W.W. and RtrDNICK,P. : 1927, Phys. Rev. 29, 413. WITHBROE,G.L. : 1967, Solar Phys. 3, 146.