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THE UNIVERSITY OF ALABAMA' University Libraries The Nonradial Mode Identification of 53 Persei during Late 1977 and 1978 R. Buta – University of Texas at Austin M. Smith – University of Texas at Austin Deposited 08/01/2019 Citation of published version: Buta, R., Smith, M. (1979): The Nonradial Mode Identification of 53 Persei during Late 1977 and 1978. The Astrophysical Journal, 232(L193-L197). DOI: https://doi.org/10.1086/183063 © 1979. The American Astronomical Society. All rights reserved. ,-..:i N C') N Tm: ASTl!OPHYSICAL JOURNAL, 232 :L193-L197, 1979 September 15 © 1979. The American Astronomical Society. All rights reserved. Printed in U.S.A. THE NONRADIAL MODE IDENTIFICATION OF 53 PERSEI DURING LATE 1977 AND 1978 MYRON A. SMITH AND RONALD J. BUTA Department of Astronomy and McDonald Observatory, University of Texas, Austin Received 1979 April 30; accepted 1979 June 15 ABSTRACT . Vario1;1s th~oretical constr:iin~s are imposed on simultaneous light, color, and line profile observa­ t10ns to 1~ent1ty the surface md1ces of two nonradial modes present in the line profile variable B star 53 Perse1 durmg late 1977 and 1978. Excellent quantitative agreement between linear nonradial theory and the observations is reached for the modes l = 3, m = - 2 and -3 but for no other modes. This unambiguous mode identification is made possible because of the 1fortunate circum­ stance that the light variations in this long-period pulsator are evidently due to geometric and not temperature effects. Subject headings: stars: pulsation - stars: variables I. INTRODUCTION both authors on the 30 inch (76 cm) or 36 inch (91 cm) In this Letter we intend to show that light and color telescopes of McDonald Observatory (see BS for ob­ curves, when combined with high-resolution spectros­ serving_ and reduction de!ails). The 3.0 A mm-1 spec­ copy, can lead to the identification of the l, m surface troscopic plates were obtained at the coude focus of the indices of the nonradially pulsating star 53 Persei. To Struve 82 inch (2.1 m) reflector. do this it is first necessary to summarize portions of Spectroscopic line profiles of the Si II XM128-4130 recent work by Buta and Smith (1979, hereafter BS) region are presented in Figure 1 along with a traveling concerning the peculiar spectroscopic and photometric wave fit. This fit was achieved by using a velocity field behavior of this sharp-lined, middle B-type star. due to an l = 3, m = -3 mode viewed at an inclina­ Periodic line profile variations in this star have been tion of i = 60°. These parameters follow from the attributed to traveling wave nonradial oscillations solution derived later. Additional parameters required (Smith and McCall 1978). Stromgren v filter observa­ to achieve profile fits were standard values of the rota­ tions of 53 Per during 13 nights in 1977 November tional velocity (V sin i = 17 km s-1) and radial-tan­ through 1978 January, suggested the presence of beat­ gential macroturbulence (M = 10 km s-1) (Smith and ing due to a pair of nearly equal-amplitude modes McCall 1978). The required pulsational velocity ampli­ 12 1, closely spaced in frequency (Pi = 1. 74 days, and P 2 = tude, km s- to make the fit is typical for this star. 2.04 days). Their mean period, 1.88 days, agreed with The period following from these seven profiles, 1. 7 days the period obtained from line profile variations in is sufficiently close to both 1.74 and 1.88 days that on~ November. The phasing between the spectroscopic and cannot be sure whether one or two modes are active photometric results is consistent with the light varia­ during this time. tions being caused by geometric distortions of the star Figure 2 shows the photometry for November 17, from its spherical shape. From an analysis of the photo­ the night immediately preceding the spectroscopic run. metric data, BS concluded that the two inferred modes The rms errors between the two standards, HR 1261 are rotationally split m-modes satisfying the condition and H~ 1482 (both near AO), during this particularly t::..m = 1. All constraints at that time led to the desig­ good mght were 0.0017 mag. The zero point in the light nation l = 2 or 3, m = -l, -l + 1, for the two modes. curve (upper panel) is that adopted by BS. No period In this Letter these constraints are refined on the basis can be estimated from this night alone, though it is of new 1978 data. The analysis to follow will apply only consistent with a 1. 7 or 1.88 day period. If one adopts to the modes associated with the ,_,1.9 day period, and P = 1. 7 days one finds a phase cp = 0.02 at the time not to periods dominant before (Smith and McCall of the zero-crossing in the light curve of Figure 2. This 1978) or since (Smith, Buta, and Africano, in prepara­ corresponds to </> = 0. 77 (i.e., broad-lined phase, cp "" tion) the interval between 1977 November and 1979 0. 75) at maximum light, or the same spectroscopic­ early January. photometric relationship found by BS from the 1977 data. This confirmation fixes rather firmly the phasing II. 1978 DATA AND THEIR IMPLICATIONS correspondence. The 1978 data consist of four nights of photometry The lower panel of Figure 2 illustrates the (v - y) during 1977 November to 1978-1979 January in both color behavior of 53 Per. The low ratio in the color-to­ the Stromgren v and y filters as well as three nights of light amplitude, t::..(v - y) / t::..v = 0.10 ± 0.02, will place photographic spectroscopy following a photometric important constraints on the modal interpretation. night in November. The photometry was obtained by Therefore in an attempt to confirm this ratio we ob- L193 © American Astronomical Society • Provided by the NASA Astrophysics Data System ,-'I N M "' L194 SMITH AND BUTA Vol. 232 53 PER NOV 18 - 20, 1978 NT I </i3' 0 .50 ,oo[ NT 2 6:08 U.T. "'3 '1.20 80 4'3'0.54 ! P, 1~70 ! NT 3 A3, 12 i , 60° </i 3' 1.63 "'3' 0.62 [ ! .,,3' 1.70 NT 2 <Ii , 1.07 3 [ ! oAt. U4128-30 FIG. !.-Spectroscopic line profiles obtained for 53 Per on 1978 November 18-20. Solid line, traveling wave fits to the data, assuming -m = l = 3 and i = 60°. tained additional photometry on three nights in De­ cember and January. The results are shown in Figures ... .. 3 through 5. Inclement weather prevented us from ..... 53 PER acquiring data during intervening nights. Nevertheless, - .895 -.04 ... a few statements can be made from these observations: w 0 (1) only incomplete portions of a cycle are represented :::) f­ ... on any of these nights; (2) the slopes are rather shallow . z ... ~ ... These remarks point to a period which is much longer ::;; - .875 -.0 2 than 6 hours. It is probably 1.88 or 1. 74 days, as it was .. in late 1977. Continuing: (3) the mean amplitude is ... small compared with that in Figure 2, suggesting that .. .. two modes are beating together, again as in 1977; and - .855 0 .... (4) the color variation is imperceptible on any given night. In fact, if one combines the extreme light levels JD 2443829.6 J O 2443830.0, of December 23 and January 1, one can compute a I ratio A(v - y)/ Av = 0.09 ± 0.025. This is in excellent - 0 .03 agreement with the value 0.10 ± 0.02 obtained from Figure 2. It also agrees with the lack of color variations >, inferred from Percy's (private communication) nega­ ~ -0.02 -·-- . -------•- ·-~----.::..!..=· -•- -••••----- ·-•---!.._---•- - tive results in 1978 October, namely, <0.12. The mean -0.01 of these three attempts, +o.10 ± 0.02, fully confirms the BS value. 4 6 10 UT 16 / 17 NOV , 1978 III. CONSTRAINTS ON MODAL IDENTIFICATION FIG. 2.-Stromgren light and color curves of 53 Per for the a) Line Profile Variations: m = -l, l ~ 4 night of 1978 November 17. Magnitudes are relative to the standards (outer ordinate scale) or relative to the zero point taken The star 53 Per exhibits profile variations character­ from BS (inner ordinate scale) . istic of its variable class. Its profiles vary in shape but © American Astronomical Society • Provided by the NASA Astrophysics Data System ,-..:i N C') N No. 3, 1979 53 PERSEI Ll95 T 53 PER -0.89 ~ 53 PER w -0.87 0 w -a.ff! ~ 0 .____!__!_. -~-~.--•• -•--- ~•-.-· E :::, • • • z ~-0.85 ~ - - - - - - - - - - - - ::, -0.85 ......... -•• ~ _.. > -0.83 -0.83 -0.01 -0.01 >, I - Q.Q2 •••• ~-0.02 -•----.----.-·······-·-··•-.- . - - .-•-·-~ > -003 -003 2 3 4 5 6 7 8 7 8 9 10 II UT JAN 5 , 1979 UT DEC 23. 1978 FIG. 5.-Light ana color curves for 1979 January 5 FIG. 3.-Light and color curves for 1978 December 23 red asymmetry-narrow-line-blue asymmetry-broad­ line phases. This behavior is an unmistakable signature of a direct traveling wave, m < 0. The above conditions impose the constraints on -0.91 53 PER modes observed at all times so far in 53 Per: w 0 f= -0.89 m::::: -l , l = 1, 2, 3, or 4. (1) z ~ ._._e.....!-•~·• ::; -0.87 b) m-mode Splitting: fl.m = 1 > -·_!....•·-•-·- ·----·-•-- The double-mode solution BS found for their 1977 photometric data gives a frequency splitting, fl.u = -0.85 '----'----'---'----'----'----'----'--.J 0.54 ± 0.04 (est. error) radians per day. Applying this value to the standard rotational m-mode splitting -0.01 equation (Ledoux 1951), and inserting Vrot sin i = ;'°' -0.02 - -~-~--•-•__,,.c____,._.
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