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Mira Variables, Common Envelope Binaries?

(Original Title: Those Outrageous Miras)

Mira Ceti
Mira Ceti - HST

Installed 14 May 2000. - Most recent update 30 Jul 2017.
New material or changes are printed in bold.

Copyright © 2000-2017 - Robert S. Fritzius
A Shade Tree Physics On Line Publication
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Key Words
Mira Variables, Long Period Variables, Non-pulsating variables


Besides having generally longer periods, Miras differ in very significant and seemingly inexplicable manners from other periodic variables. The following paragraphs touch on a few of these differences. A number of comments from Paul W. Merrill 1940 (1) are included which offer pointers toward a new hypothesis as to what may be going on with Miras. A specially prepared light curve along with radial velocity line profile data, based on Alfred H. Joy's 1954(2) article on Mira Ceti, is also included.

Special Note

In the author's current opinion Miras are not pulsating variables, but contrary to his earlier opinion, they are not Ritzian systems (i.e., c+v arrival-time modulators) either. (See A Ritzian Interpretation of Variable Stars.) The periodic magnitude and spectral variations of Miras may be considered as intrinsic, as compared to to the hypothetical extrinsic nature of the variableness of Ritzian systems, Cepheids for example. He also feels that it will soon become apparent that many astronomers have long been refusing to believe their eyes about Miras' buried treasures! [This note was modified on 17 August 2003, primarily to replace the author's final phrase "but there's a special whammy" with something slightly more erudite, and more importantly, to announce that evidence of the buried treasures may be beginning to surface. See: Mira Variables explained by a planetary companion interaction: A means to drop the pulsation paradigm?

* * *

The radial-velocity [atomic absorption] curves for long-period variables (LPVs or Miras) are nearly "inverted" or "flip-flopped" compared to the radial-velocity curves for Cepheids. For Cepheids the peak approaching radial-velocity approximately coincides with the brightness peak of the light-curve but for Miras the peak receding velocity is what coincides with the light-curve maximum.

"The radial-velocity curve of o Ceti, the LPV most extensively observed, resembles the light-curve in shape and phase." (Merrill, p. 94)

(Mira emission line profiles are a different story.)

The range of Mira apparent magnitude variations are much greater than for Cepheids (sometimes on the order of up to ten magnitudes). This suggests that a radically different process is at work.

Even though Miras are relatively cool stars, they produce strong sharp emission lines (Hydrogen Balmer series and some metals). These emission lines are normally associated with a cool gaseous medium that is being illuminated by a hot body (rich in UV) from behind, or below.

"Strange as it may seem to place the origin of the bright lines below, or partially below, the reversing layer, this seems at present to be our best working hypothesis." (Merrill, p. 71)

". . . in long-period variables we must look to changes in surface brightness rather than in size for the explanation of essentially all the light range."(Merrill, p. 94)

Following up on Merril's line of thought, I suggest that Miras are, in fact, close binaries (really close!) where the primary body is typically a red giant which has a hot main-sequence star orbiting inside/below its reversing layer. (They could be called Common Envelope Binaries.) This model may well satisfy the majority of the theoretical difficulties encountered in trying to interpret the remarkably rich observational information we have on Miras.

The following figure shows a hot-star orbiting beneath the reversing layer of a red giant. In this case the orbital plane of the hot-star is such that for a portion of its orbit it is completely out of sight of the observer. During this time of eclipse the Mira system will display a type M spectrum only. (Nebular emission lines in the vicinity of the red giant may sometimes provide evidence of the hot star's presence even when it is out-of-sight to the observer.) Merrill summarizes this nebular material issue with regard to C.O. Lampland's photographs of R Aquarii taken in 1921. (Merrill, p. 87ff.)

Figure 1. Light and Radial-Velocity Curves for a Typical Mira Variable
(Spectral lines shown are based on data from Alfred H. Joy 1954)

Zero radial velocity (with respect to the binary center-of-mass) corresponds to approximately 58 Km/Sec Heliocentric in Joy's data.

The solid black line on the light-curve section corresponds to the composite visible magnitude for both stars. Yellow represents the hot-star and red represents the red giant's energy in the visible spectrum. (Up to 90 percent or more of the red giant's energy is in the infra-red and is not represented in this figure.) The orange at the bottom represents the superposition of the red and yellow.

It has long been surmised that long period variables show evidence of an outward directed mass flow shortly after maximum light. The Hydrogen and metallic emission lines provide invaluable information to allow hydrodynamicists to model this flow. The hot star (hot spot) presumably heats the overlying layers of the common atmosphere to induce the outward flow. This flow may create a rooster tail effect whose observables would be expected to lag behind maximum brightness.

According to the sub-surface orbiting hot star hypothesis the maximum light of the binary should occur when the hot sub-surface star is closest to the observer, i.e., between the observer and the red giant's center of mass.

In cases where a hot-star goes into total eclipse, the spectrum of the red-giant should step-wise brighten during the eclipse. (This is not stated quite right.) The brightening would probably be more noticeable in infra-red and at longer wavelengths than in visible light or UV.

At the American Astronomical Society 198th Meeting in June 2001, R.R. Thompson and M.J. Creech-Eakman presented a paper titled Departures from spherical symmetry in Mira Variables at PTI. Eight of ten Miras studied show evidence of a departure from spherical symmetry. Candidate causes named were: star spots, limb-darkening, binarity and non-radial pulsation induced outflows.

A Space Telescope Science Institute (STScI) press release titled Hubble Telescope Measures Diameters of Pulsating Stars reported that Mira variables aren't round but are egg-shaped. [STSci-1996-26]

If we consider the red-giant part of the hypothetical binary to be egg shaped (the hot interior star being the cause of the distortion), then we should expect to see a quadrapole brightness curve for that component. It's cross-sectional area, as presented to the observer, will max out twice during each orbit of the hot star. That is, each time the hot star is at one of the limbs of the red giant the latter will present increased cross sectional area to the observer. (Since the red-giant is the darker of the two in the visible spectrum, these variations may be a challenge to measure.) The diagram above has been modified to show this predicted quadrapole effect. (Apologies all the way around if an infra-red brightness curve quadrapole effect is already documented.)

On page 47 of ref (1), Merrill said, "The most striking result concerning long-period variables is that during the light-cycle the variation in total energy is less than one-fiftieth of the variation in visual intensity." This leads me to think that the red giant part of LPVs emit as much as 50 X 50 (2500) times more total energy than the visible energy that reaches the red giant's surface (in our direction) from hypothetical run-around sun-like sub-surface bodies. [Added 29 Jul 2017.]

In his article on Star Luminosity, Frazier Cain says, "A red giant may be releasing 1,000-10,000 times the luminosity of the Sun." [Added 30 Jul 2017.]

If the preceding scenario (two or more stars vice one) comes to be accepted then a lot of UBV photometry may need to be re-evaluated. (An underlying assumption in UBV work is that you are working with single stars.) Where two or more stars with differing spectral profiles co-inhabit a given volume of space, single star vitals will be of questionable value.)

For a Hubble Space Telescope photograph of the variable Mira which shows potential evidence of a hot star orbiting inside a red giant, see the Astronomy Picture of the Day (APOD) for October 11, 1998.


(1) Merrill, Paul .W., (1940), Spectra of Long-Period Variable Stars, University of Chicago Press.

(2) Joy, Alfred H., (1954) Ap. J. Supp. 1, 39. NADS

Other Links and Recommended Reading

Alfred H. Joy Bibliography [Added 10 Dec 2005.]

Contact Robert Fritzius at