Can the 51 Peg Doppler Variations be due to Stellar Pulsations ?

G.Marcy, R.P.Butler

Dr. David Gray (Univ. Western Ontario) published a paper in Nature (1997, vol.385, p795), suggesting that some undulations or oscillations in the star, 51 Peg, are responsible for the Doppler shifts, rather than an orbiting planet. Gray states, ``Oscillatory upheavals in the star's atmosphere could reshape spectral lines through their Doppler shifts and altered radiation transfer.'' Gray's paper indicates that spectral lines vary in shape with a periodicity of 4.23 days, based on 39 spectra taken over 8 years. Dr. Gray provides a summary explaining why the planet hypothesis is no longer acceptable.

Dr. Leslie Sage (editor of Nature) concludes, ``Dr. Gray's work leaves a question-mark over the presence of other extra-solar planets.'' Sage notes that he is not criticizing the Swiss astronomers, Mayor and Queloz, who ``did the best they could with their equipment''.

In Science Magazine, Gray's collaborator, Dr. Artie Hatzes, says ``it should have been a more civilized debate.''

Sky and Telescope accurately summarizes the oscillations.

Dr. Gray is an expert in the analysis of spectra of stars and has pioneered many valuable techniques in stellar research. He is the author of several excellent textbooks on stellar spectroscopy, including the seminal ``The Observation and Analysis of Stellar Photospheres'', which has served to educate a generation of young astrophysicists.

If Gray is correct, and 51 Peg is truly pulsating non-radially (in sectors), there are many facts that severely constrain those supposed oscillations.

  1. 51 Peg has constant brightness to one part in 5000.

  2. 51 Peg exhibits only one period: P = 4.231 day. No other overtones or oscillation modes are found.

  3. Tau Boötis shows no line-profile variations. This star with a reported planet, (Period = 3.3 days, M sin i = 3.7 Jupiter masses), shows no significant variations in the shapes of its spectral lines, ruling out pulsations. The planet hypothesis is the only viable one for this case, the only one tested to date (Sept. 1997). This Tau Boötis work was done by the team of: Tim Brown, Scott Horner, Sylvain Korzennik, Ed Kennelly, R.Kotak, S. Jha, M.Krockenberger, P.Nisenson, and Robert Noyes.

  4. Among the four 51 Peg-like stars, the Doppler period does not correlate with stellar mass, density, or metallicity. Pulsation periods should be related to some stellar property, but none is seen.

  5. Extensive Helioseismology of the Sun reveals no hint of a periodicity anywhere near P = 4 days.

Detailed Discussion of Gray's Claim of Pulsations

I. Are the Spectral Lines Truly Varying?

Dr. Gray's paper claims that the asymmetry in the spectral lines of 51 Peg vary with an amplitude of 45 m/s. However his errors are probably ~20 m/s. One cannot determine these errors, as Nature publishes papers without mention of uncertainties or error bars. The supposed extent of variations in the line-profiles is only twice the errors we estimate. Thus, Gray's effect must be confirmed. Further, in the persuasive "binned" plot, Gray and Nature binned the data points together according to ``natural groupings of the points''. The data points are thus grouped together by eye, rather than in equal intervals.

Another paper accepted for publication in the Astrophysical Journal by Hatzes, Cochran, and Johns-Krull states:

``We find no evidence for variability in the velocity span of the spectral line bisectors greater than the error of the measurements (sigma = 20 m/s).''

These spectral line shapes were obtained using 50% higher spectral resolution, and they include analysis of eight spectral lines. Dr. Gray included only one line to derive the line asymmetry. However, the lines were measured slightly differently by the two research groups; perhaps Gray's measurements are intrinsically more sensitive to oscillations, though there is no evidence of this. The Hatzes paper sampled 51 Peg at only 3 different phases. Thus, Dr. Hatzes notes that he can neither confirm nor reject Dr. Gray's claim.

II. No Brightness Variations Occur in 51 Peg Stars

Photometry of the star 51 Peg shows no brightness variations, with a two-sigma limit of 0.04%. The upper limit of brightness variations is 0.0004 mag (= 0.04%) for all four 51 Peg-type stars (Greg Henry et al. 1996 , Sallie Baliunas et al. 1997). However, oscillating stars should exhibit brightness variations which are periodic with the oscillations. The Cepheid pulsating stars are the best known example.

This 0.04% observed upper limit on the brightness variations is a factor of 3 less than expected for non-radial oscillations, given the velocity amplitude of 57 m/s for 51 Peg (Hatzes et al. 1997). Therefore, 51 Peg does not show the brightness variations that should accompany the putative "oscillations" This argument is not ironclad, because Dr. Gray prefers to invoke oscillations of an unknown nature, thereby leaving us with no predictive model of the oscillations .

A stronger case applies to the star, Tau Boötis, that is a ``51 Peg-like'' star: It exhibits sine-wave Doppler variations having amplitude of 470 m/s with a 3.3-day period. These are easily interpreted as due to an orbiting planet having mass of 3.8 Jupiter masses.

In Dr. Gray's hypothesis, the Doppler variations of Tau Boötis are instead due to oscillations. However, no variations in the shapes of its spectral lines are seen at all (see IV below). Furthermore, the pulsation velocity, during 1/4 period, implies that the photosphere moves by 3% of a stellar radius. These large amplitudes imply significant sloshing of fliud on the stellar surface, and the speed of the fluid would be about 1 km/s, 1/8 of sound speed. In contrast to this supposed oscillatory surface activity, the observed upper limit of brightness variations is only 0.04% for Tau Boötis. If oscillations were actually occuring, there should be brightness variations of at least 0.5%, which are clearly ruled out by the known constancy (below 0.04%) of the light from Tau Boötis. There is no plausible oscillation model whereby a star would exhibit Doppler variations of 470 m/s, thereby distorting the stellar surface by several percent of the star's radius, and yet show no brightness variation. Indeed, Gray's paper does not contain any such oscillation model or concept.

However, non-radial oscillation modes having high radial number, n, might provide such a model. If so, the star must somehow "choose" only one value of n. Calculations by Greg Ushomirsky (UC Berkeley) shows that the 115th harmonic mode would produce the observed Doppler amplitude (56 m/s) and yield the correct period (4.23 days). However the neighboring modes (112,113,114,116,117,118, etc.) should also be excited, as they differ in period by only 1% from the 4.23-day mode. Where are the other modes: they are not seen in the Doppler periodicity.?

The Chromopshere of 51 Peg also shows no periodicity at the Doppler period of 4.23 d, based on our 200 spectra of the Ca II Infrared triplet lines.

III. The Doppler Variations Exhibit Only One Period and One Amplitude.

All four 51 Peg-like stars show Doppler variations that are sine waves. For example, the Doppler variations of 51 Pegasi are indistinguishable from a sine wave.

THERE ARE NO OTHER PERIODS IN THE DOPPLER VARIATIONS.

A PERIODOGRAM (Power spectrum) of the Doppler measurements for 51 Peg shows only one peak, at the period of 4.231 days. There are no other significant peaks. All of the small peaks visible near the base of the strong peak are simply false "aliases" of the main 4.23-day periodicity, due to the actual times of observation of 51 Peg. We have synthesized this effect, reproducing both the width of the main peak and the false (aliased) small peaks.

51 Peg EXHIBITS A DELTA FUNCTION IN DOPPLER FREQUENCY.

THERE ARE NO OTHER OVERTONES OR HARMONICS.

The measured velocities scatter from a perfect sine wave by 5 m/s (RMS). The residual discrepancies between our measured velocities and the Keplerian velocity curve are simply due to our Doppler uncertainties. Indeed, the velocity "residuals" are no larger than our predicted errors based on the Number of Photons collected in the spectrum.

The additional Doppler signals due to "sloshing modes" or overtones that normally accompany oscillations are absent.

If interpreted as some exotic non-radial pulsation, the star somehow "rings" perfectly to yield a sine wave with only one exact oscillation period. Even perfectly tuned violin strings and bells exhibit multiple "modes" and harmonics as they oscillate. Our Sun shows many acoustic modes. But 51 Peg only exhibits the 4.23-day period. Nor do any of the other 51 Peg-like stars show multiple modes. Oscillations in nature (even those man-made) are never as pure as the single-period that 51 Peg exhibits in its Doppler variations. This pure periodicity in 51 Peg strongly argues against any "oscillation" explanation.

Further, the Doppler amplitude of 57 m/s remains constant over time. If interpreted as non-radial oscillations, there is no apparent ``damping'' or friction. The "oscillation" hypothesis forces us to adopt some oscillation that "selects" only one frequency and continues ringing without changing frequency or amplitude.

There is no known physics that would "pick out" only one non-radial mode, to the exclusion of all others. Indeed other non-radial pulsators (i.e., delta Scuti stars) show a large range of modes that switch from one to the other, as is physically understandable.

IV. Tau Boötis shows no oscillations.

The short-period star, Tau Boötis (Period=3.3 days, M sin i =  3.7 Jupiter masses), shows no significant variations in the shapes of the spectral lines. There are 5 Solar-type stars that exhibit Keplerian Doppler periodicities with short-periods under 40 days (Tau Boötis, 51 Peg, Ups And, 55 Rho1 Cancri, Rho Cor Bor). One of these, Tau Boo, has now been checked for variations in the spectral line shapes. Variations in the shapes of the spectral lines are absent, at a detection level 20 times below that required to explain the Doppler periodicity. Thus, the planet hypothesis is the only viable one for this case, the first tested. This Tau Boötis work was done by the team of: Tim Brown, Scott Horner, Sylvain Korzennik, Ed Kennelly, R.Kotak, S. Jha, M.Krockenberger, P.Nisenson, and Robert Noyes.

V. All 51 Peg-like Stars are Solar-Like but Exhibit Different Doppler Periodicities.

The planet hypothesis explains the diversity of observed Doppler periods naturally: Each star has a different planet with its own orbit and mass.

The "oscillation" hypothesis cannot explain why nearly identical Solar-like stars would "ring" with totally different pure-tone periods and amplitudes. Indeed, the Sun shows no such oscillation at all.

Properties of the 51 Peg-Like Stars

Star Name sp Prot (d) Velocity Period (d) Vel. Amplitude (m/s)
51 Peg G2.5V 37 4.23 57
Tau Boötis F7V 4 3.3 469
Rho1 55 Cancri G8V 44 14.65 77.1
Upsilon And F8V 12 4.61 74.1
Data From: Baliunas et al. 1997, Astrophysical Journal Letters, vol.474


The four 51 Peg-like stars are very similar. All are Sun-like, within 10%. They all have masses between 0.9 and 1.1 of the Sun's mass.

However, the periods of the Doppler variations and the amplitudes are quite different (by a factor of 10 in amplitude and a factor of 4 in period). A hypothesis that these similar stars are "oscillating" fails to explain the great differences in the periods and amplitudes. Objects in nature ring or oscillate with frequencies that depend only on their size and construction (such as the period of a pendulum or the pitch of a violin string.) These similar stars, if oscillating, disobey that critical rule, since they are similar in structure, yet so different in observed resonance properties.

Further, the Doppler characteristics are uncorrelated with spectral type, or any other stellar parameter. There is no physics of oscillations that can explain the large differences in Doppler peridicities, for such similar Sun-like stars.

VI. Non-Radial Pulsation (NRP) Plausibility

  1. What plausibly excites these different oscillation modes in each star?

  2. What maintains the amplitude for hundreds of cycles, with no decay?

  3. If oscillations are correct, why do only a few F and G stars show the 51 Peg phenomenon?

    The 51 Peg phenomenon is absent in the Sun and dozens of other G dwarfs in our sample. But the 51 Peg phenomenon is not confined to evolved Solar-type stars. The other three members aren't old.

    The rarity of the 51 Peg phenomenon is explained naturally within the planet interpretation as due to the diversity of protoplanetary disks, seen clearly in the Hubble Space telescope images of young stars in Orion. Therefore, some stars are endowed with disks that yield planets. The "oscillation" hypothesis offers no such explanation for the existence of oscillations for a few stars, but not the rest.

  4. How can oscillations be excited with VERY DIFFERENT dominant mode frequencies and different amplitudes, both being independent of stellar properties. That is, 55 Rho1 Cnc has a 14.7-day period, while Tau Boo has a 3.3-day period. Different planetary orbits explains this easily, while no oscillation explanation exists.

VII. A Planet Explanation Naturally Explains All Data:

VIII. Possible Reconciliation: The Planet Exerts Gravitational Forces on Star

A planet provides a natural gravitational DRIVER for non-radial oscillations. The planet certainly raises tides on the star, though they would occur TWICE per 4.2-day orbital period, which is not seen in Gray's data.

Nonetheless, it is conceivable that the gravitational forces exerted by the planet on the turbulent, convective photospere of the star could alter the basic gas flows. In this model, the planet alters the flows, which have intrinsic velocities of about 1000 m/s, by a small fraction. This could yield changes in the line shapes by some tens of m/s.

Alternatively, the gravity of the planet could serve as the driver of resonances in the star, such as buoyant modes, or "gravity-modes".

This gravitational explanation would yield constant amplitude, phase and period in a star. The travelling bulge on the star could explain the spectral line variations that Dave Gray suggests. The orbiting planet could excite one (and only one) particular natural mode or oscillation period within the star. Thus, the spectroscopic observations by Gray could represent a remarkable confirmation of the close planet. However, the above reconciliations represent completely ad hoc efforts to include Gray's observed line-prorile variations, which remain in need of confirmation. Models to explain them seem implausible.

SUMMARY

There are several possible interpretations of the present data for 51 Pegasi:
  1. There is no planet, but instead there is an intrinsic, single-frequency pulsation, of single mode, having unknown excitation mechanism and an unknown nature. It is present in 51 Peg and in some rare solar type stars, but is somehow not present in the Sun.

  2. There is a low frequency pulsation that is excited by the gravity of the planet. This possibility at least would have the advantage of explaining the stable, single period observed.

  3. The asymmetrical shape of the absorption lines of any solar-type star is caused by radiative transfer of light in the atmosphere just above the convective zone. The gravitational perturbation of the outer atmosphere by the planet will affect the velocities of the convective cells and the shape of the lines. This case probably will not affect the global luminosity too much.

  4. The outer atmosphere of the planet eclipses the star. This was first suggested in a paper entitled, `The cometary-like tail of giant extrasolar planets in close orbit', (1997, J. Schneider, H. Rauer, Lasota J.-P., Bonazzola S. and Chassefière E.), submitted to the Proceedings of the `Workshop on Brown Dwarfs and Extrasolar Planets' held in Tenerife in March 1997.

  5. The data from Dr. Gray may be incorrect. The quoted change in the velocity span of 45 m/s is only somewhat larger than the errors of 20 m/s. The "oscillation" conclusion by Dr. Gray is not empirically strong, is not confirmed, and is difficult to understand in terms of oscillation physics.

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