PREFACE POLARIS REVISITED

Transcription

1 THE ASTRONOMICAL JOURNAL, 116:936È94, 1998 August ( The American Astronomical Society. All Rights Reserved. Printed in U.S.A. POLARIS REVISITED KARL W. KAMPER AND J. D. FERNIE David Dunlap Observatory, University of Toronto, Box 36, Richmond Hill, ON L4C 4Y6, Canada; fernie=astro.utoronto.ca Received 1998 February 9; revised 1998 April 13 ABSTRACT We report 212 radial velocity measures of Polaris obtained during 1994È1997 and use these to rediscuss PolarisÏs changing pulsational amplitude and rate of period change during the 2th century. In the course of this work we discovered a serious error in an earlier paper, which led to our Ðnding too steep a decline in amplitude in recent decades. We correct this error and no longer predict a cessation of pulsation in the 199s. In fact, the new, more precise radial velocities suggest that the decrease in amplitude has abruptly stopped and that the peak-to-peak amplitude is holding steady at about 1.6 km s~1, or.3 mag in V. The period, however, continues to change. Key words: binaries: spectroscopic È Cepheids È stars: individual (Polaris) PREFACE This paper was written in the concluding weeks of Karl KamperÏs life. The data presented here were all obtained and reduced by him, and 2 was written by him. I undertook the analysis and wrote the remainder of the paper, but he was able to read and approve a Ðrst draft of it.èj. D. F. 1. INTRODUCTION Polaris (a UMi, HR 424) is a Cepheid variable that has attracted particular attention since Arellano Ferro (1983) discovered that its amplitude of pulsation had been declining during the 2th century. Subsequent papers dealing with this have included Kamper, Evans, & Lyons (1984), Dinshaw et al. (1989), Fernie, Kamper, & Seager (1993, hereafter FKS), Garnavich et al. (1993), Brown & Bochonko (1994), and Kamper (1996). Data have included both photometric measures and radial velocities. However, since the full amplitude is now only about.3 mag in V, or 1.6 km s~1 in radial velocity, the best data now come from radial velocities, given that recent techniques allow these to be measured with a precision of D1 ms~1 or better, which corresponds to better than 2 mmag in V. We here present 212 radial velocities obtained between and , and in 3 and 4 we rediscuss the amplitude and period changes. 2. RADIAL VELOCITIES In 199, we began using an echelle spectrograph with CCD detector on the DDO 1.88 m reñector (earlier spectra were photographically recorded in the blue). After mastering the art of reducing such spectra, we could attain an rms error of about 2 m s~1. Early in 1994, we changed the spectral region observed to center it on the telluric O band at 629 nm. Using this band as an absorption zero-point 2 reference allowed us to reduce this error by half or more under the right circumstances. Normally, the echelle spectrograph was scheduled for Ðve to six consecutive nights to permit complete coverage of the 4 day pulsational period, with observations of Polaris being made at the beginning and again at the end of each night. For such a run, the scatter in the observations is often as low as 5 m s~1. Over longer periods, the telluric calibration is not that good. While part of this increased variation may be caused by actual changes in the behavior of 936 Polaris itself, observations of the velocity-standard star HD indicate that the largest portion is instrumental in origin. The Ðrst cause is that the wavelengths in the band depend on atmospheric conditions: temperature, pressure, and wind velocity. The temperature variation is about 14 m s~1 K~1 for the combined e ects of band wavelength changes and any thermally dependent instrumental errors, and our observations have been so corrected. Unfortunately, we did not normally monitor and record the other factors. In addition to the actual variations in the location of the band, there are the unavoidable variations in the blending with the stellar spectrum. If we had used an iodine cell, these could be modeled to some extent by making observations with and without the cell in place. No such procedure is possible for the atmospheric band. Instead we must attempt to purge the spectrum of telluric lines by the usual technique of using a scaled spectrum of a nearly lineless star as a telluric standard; then this nearly pure Polaris spectrum is removed from each nightïs observations after shifting it by an amount equal to the preliminary determination of the stellar velocity, and the Ðnal telluric correction is determined by cross-correlation of this destellared ÏÏ spectrum with the telluric standard.1 It is an ungainly process and will be replaced in any future studies here, but it is made easier by the nearly constant air mass at which Polaris is observed. Polaris being also a spectroscopic binary of 29.6 yr period, the radial velocities were corrected for orbital motion using the elements given in column (2) of Table 3 of Kamper (1996). The 212 radial velocities so obtained are, because of the cross-correlation procedure, measured relative to the Ðrst observation, and are listed in Table 1. Ninety of the frames were used in Kamper (1996), but are here completely rereduced using the same techniques as for the most recent frames. A general period search revealed no signiðcant periodicities other than that of 3.97 days, although long-term instrumental drifts might hide lowamplitude, long-period ones. ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 1 Kamper (1996) reports using the RVSAO cross-correlation routine as mated to the IRAF analysis package ÏÏ; I presume this was also used here.èj. D. F.

2 POLARIS REVISITED 937 TABLE 1 RADIAL VELOCITIES OF POLARIS, CORRECTED FOR THERMAL EFFECTS AND ORBITAL MOTION, RELATIVE TO THE FIRST OBSERVATION Relative Radial Relative Radial Relative Radial Relative Radial Velocity Velocity Velocity Velocity HJD (km s~1) HJD (km s~1) HJD (km s~1) HJD (km s~1) 2,449, ^.4 2,449, ^.8 2,449, ^.8 2,45, ^.2 2,449, ^.4 2,449, ^.8 2,449, ^.1 2,45, ^.3 2,449, [.34 ^.4 2,449, ^.8 2,449, ^.9 2,45, ^.3 2,449, [.192 ^.5 2,449, ^.8 2,449, ^.9 2,45, ^.3 2,449, [.18 ^.5 2,449, ^.8 2,449, [.179 ^.6 2,45, ^.3 2,449, [.313 ^.7 2,449, ^.8 2,449, [.189 ^.7 2,45, ^.3 2,449, [.237 ^.5 2,449, ^.1 2,449, [.27 ^.7 2,45, [.37 ^.3 2,449, [.239 ^.5 2,449, ^.11 2,45, ^.5 2,45, [.35 ^.2 2,449, [.258 ^.5 2,449, ^.1 2,45, ^.7 2,45, ^.3 2,449, ^.5 2,449, ^.13 2,45, ^.7 2,45, [.285 ^.3 2,449, ^.5 2,449, ^.11 2,45, ^.6 2,45, [.279 ^.3 2,449, ^.6 2,449, ^.1 2,45, ^.5 2,45, [.292 ^.2 2,449, ^.6 2,449, ^.1 2,45, ^.5 2,45, [.97 ^.1 2,449, ^.14 2,449, ^.1 2,45, ^.5 2,45, [.117 ^.9 2,449, ^.4 2,449, ^.11 2,45, ^.6 2,45, [.74 ^.9 2,449, ^.4 2,449, [.127 ^.1 2,45, ^.6 2,45, ^.7 2,449, ^.4 2,449, [.196 ^.1 2,45, ^.6 2,45, ^.7 2,449, ^.4 2,449, [.215 ^.1 2,45, ^.6 2,45, ^.8 2,449, ^.4 2,449, ^.5 2,45, ^.6 2,45, ^.3 2,449, ^.6 2,449, ^.5 2,45, ^.5 2,45, ^.3 2,449, [.55 ^.5 2,449, ^.5 2,45, ^.6 2,45, ^.2 2,449, [.58 ^.5 2,449, [.284 ^.5 2,45, ^.5 2,45, ^.6 2,449, ^.3 2,449, [.245 ^.5 2,45, ^.5 2,45, ^.6 2,449, ^.3 2,449, [.267 ^.5 2,45, [.26 ^.5 2,45, ^.5 2,449, ^.3 2,449, ^.4 2,45, [.457 ^.5 2,45, ^.2 2,449, ^.7 2,449, ^.4 2,45, [.48 ^.4 2,45, ^.3 2,449, [.37 ^.6 2,449, ^.4 2,45, [.51 ^.5 2,45, ^.2 2,449, ^.5 2,449, ^.5 2,45, [.472 ^.5 2,45, ^.1 2,449, ^.5 2,449, ^.5 2,45, [.447 ^.4 2,45, ^.11 2,449, ^.5 2,449, ^.4 2,45, [.423 ^.4 2,45, ^.1 2,449, ^.1 2,449, [.262 ^.5 2,45, [.454 ^.4 2,45, [.66 ^.9 2,449, ^.1 2,449, [.268 ^.4 2,45, ^.3 2,45, [.27 ^.7 2,449, ^.1 2,449, [.218 ^.4 2,45, ^.4 2,45, [.35 ^.8 2,449, ^.1 2,449, ^.7 2,45, ^.4 2,45, [.42 ^.7 2,449, ^.1 2,449, ^.6 2,45, ^.9 2,45, [.41 ^.7 2,449, ^.1 2,449, ^.7 2,45, ^.8 2,45, [.417 ^.7 2,449, ^.1 2,449, ^.4 2,45, ^.2 2,45, ^.9 2,449, ^.1 2,449, ^.5 2,45, ^.3 2,45, ^.8 2,449, ^.1 2,449, ^.5 2,45, ^.2 2,45, ^.8 2,449, ^.1 2,449, ^.5 2,45, ^.1 2,45, ^.9 2,449, ^.1 2,449, ^.5 2,45, ^.1 2,45, ^.8 2,449, ^.1 2,449, ^.5 2,45, ^.3 2,45, ^.4 2,449, ^.9 2,449, ^.6 2,45, ^.2 2,45, ^.4 2,449, ^.9 2,449, ^.6 2,45, ^.2 2,45, ^.4 2,449, ^.9 2,449, ^.6 2,45, ^.3 2,45, ^.4 2,449, ^.8 2,449, ^.5 2,45, ^.3 2,45, ^.5 2,449, ^.8 2,449, ^.5 2,45, ^.3 2,45, ^.4 2,449, ^.8 2,449, ^.5 2,45, ^.3 2,45, [.295 ^.5 2,449, [.236 ^.8 2,449, ^.9 2,45, [.327 ^.2 2,45, [.287 ^.5 2,449, [.267 ^.8 2,449, ^.9 2,45, [.287 ^.3 2,45, [.287 ^.5 2,449, [.245 ^.8 2,449, ^.1 2,45, [.332 ^.3 2,45, ^.7 2,449, ^.8 2,449, ^.8 2,45, ^.2 2,45, ^.6 2,449, ^.8 2,449, ^.8 2,45, ^.2 2,45, ^.6 NOTE.ÈQuoted uncertainties are standard errors. 3. AMPLITUDE VARIATION The radial velocities were next assembled into convenient groups according to proximity in date and phased on a period of days (based on previous work); a Ðrstorder Fourier Ðt made to them, and the amplitude and HJD of maximum radial velocity determined. The results for each group are listed in Table 2. For purposes of discussion, it was necessary to Ðnd the relation between times of maximum radial velocity and maximum V light. This was determined from data presented by Arellano Ferro (1983), who made overlapping obser- vations of both V magnitude and radial velocity. By making Fourier Ðts to his data we found that HJD(V max ) \ HJD(RV max ) ] 1.652, and this has been used to produce the second column of Table 2. While assembling Table 2, we discovered that in an earlier paper (FKS) we had made a major error. That paper had been prepared and written by J. D. F., but all the results from our DDO radial velocities had been arrived at by K. W. K. It was assumed by J. D. F. that the amplitudes

3 938 KAMPER & FERNIE Vol. 116 TABLE 2 O[C VALUES AND PEAK-TO-PEAK AMPLITUDES BASED ON DDO RADIAL VELOCITIES O[C Amplitude Year E (days) (km s~1) N ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^.8 24 FIG. 1.ÈRelationship between light amplitude and radial velocity amplitude for lower amplitude Cepheids. Circles are fundamental pulsators, triangles are overtone pulsators. supplied by K. W. K. from these data were full, peak-topeak ones, when in fact they were semi-amplitudes. The latter is the number that emerges naturally from a Fourier analysis. We were both potentially aware that such an error could arise, but most unfortunately, we failed to check with each other about it. As a result, of course, our diagram of amplitude versus year in FKS underplotted these amplitudes by a factor of 2. This was exacerbated by the fact that our one photometric amplitude reported in FKS was unusually low and fell among the erroneous spectroscopic points, thus not only arousing no suspicion of their error, but seeming to conðrm them. The photometric V amplitude in FKS was given as.1 ^.2 mag. Brown & Bochonko (1994) suggested that perhaps we had oversmoothed our data, thus obtaining too low an amplitude. Their analysis of our published observations yielded.18 ^.6 mag, although a new analysis of those unsmoothed data by ourselves gives only.12 ^.4. In any case, our photometry of Polaris with a.6 m telescope necessitated switching a neutral density Ðlter in and out between Polaris and its comparison star, and it is now clear that this introduced noise and possibly systematic e ects into our data, so while we have retained this result in our present analysis, we do not give it high weight. A remaining matter in compiling the amplitude-year diagram afresh is the ratio of radial velocity amplitude in km s~1 to V amplitude. We previously adopted a value of 5 for this ratio, but as Brown & Bochonko point out, other values exist in the literature. Moreover, we now know that Polaris is an overtone pulsator (Feast & Catchpole 1997), so the question whether overtone pulsators obey the same relation as other Cepheids becomes germane. We have investigated this by using an electronic database of Cepheid properties (Fernie et al. 1995), which lists radial velocity and V amplitudes where available. The high-amplitude stars introduce a good deal of scatter into a plot of radial velocity amplitude versus light amplitude, so we arbitrarily restricted our investigation to Cepheids with RV \ 26 km s~1. This provided 23 stars with the necesssary amp data, of which 11 were overtone pulsators. As Figure 1 shows, there is no evidence that the latter obey any di erent a relation than the fundamental pulsators; if anything, the overtone cases show less scatter in the V versus RV diagram. amp amp Using all 23 stars, we Ðnd RV /V \ 5.8 ^ 1.6 km s~1 mag~1. amp amp For consistency with previous work, however, we shall continue to use a value of 5. Figure 2 illustrates the changing amplitude of Polaris compiled from Table 4 of FKS and Table 2 of this paper. The curve drawn through the points is a regression of V \ A M1 [ exp [b(y [ Y )]N, amp where Y signiðes year, A \.137 ^.17, b \.18 ^.5, and Y \ 26.9 ^ 2.8. Compared with the corre- sponding Figure 2 in FKS, the slope of the curve near the end of the century is much shallower, and Y (the year when zero amplitude would be predicted) is now 27, compared with 1994 in FKS. However, the bunching of points in the lower right of Figure 2 hides an important change. Figure 3 is an enlargement of this part of Figure 2, and it shows that the radial velocity data of the past few years indicate a constant FIG. 2.ÈAmplitude of PolarisÏs light curve during the 2th century. Filled circles represent photometric determinations, open circles those derived from radial velocity determinations. The curve is a regression line representing the equation given in the text.

4 No. 2, 1998 POLARIS REVISITED 939 FIG. 3.ÈEnlargement of the lower right portion of Fig. 1. The curve is the same one as shown in Fig. 1. Note the abrupt leveling o of the most recent points, suggesting the historical decline in amplitude may have stopped. amplitude of about.32 mag. (Note also the much improved precision of these recent data.) It would seem that the decline has stopped abruptly. We can o er no explanation for this, but continued monitoring of the amplitude clearly will be important. 4. PERIOD CHANGE Figure 4 shows the O[C diagram for Polaris. The new data of this paper (triangles) continue the general trend found in previous publications. Figure 5 shows the same data with second- and seventh-order polynomials Ðtted to them. The quadratic Ðt is the canonical curve used to describe a constant rate of period change, and it can be seen that in broad, rough terms, this is true of Polaris. There are, however, signiðcant departures from the quadratic, and the seventh-order curve is the lowest order polynomial that describes the full set of data accurately. It has been argued elsewhere (Fernie 199) that terms higher than order 2 by no means vitiate the interpretation of the O[C curve in terms of stellar evolution, and we still consider this to be the most likely explanation of the changing period. FIG. 5.ÈO[C diagram showing regression Ðts of second- and seventhorder polynomials. The quadratic Ðt produces a rate of period change of ]3.4syr~1, but we caution that in the higher order Ðt this number shows considerable Ñuctuation. Figure 6 shows the rate of period change as predicted by second-, Ðfth-, and seventh-order polynomials. (The Ðfth-order case Ðts the O[C data very nearly as well as the seventh-order one, and would be virtually indistinguishable on the scale of the diagram shown here.) Although there are obvious edge ÏÏ e ects near E \[6 and ]5, where the data string begins and ends, it is clear that during the intervals when there was a departure from the quadratic, the rate of period change could vary signiðcantly and even change sign. In short, the overall rate of change derived from the quadratic is only a rough guide at best, at least in the case of Polaris. 5. POLARIS AND THE INSTABILITY STRIP In response to a suggestion made by Dinshaw et al. (1989), FKS commented that Polaris is not situated near the red edge of the Cepheid instability strip, and its decline in amplitude is therefore not due to its evolving out of the strip. In particular, Polaris was compared to RT Aur, a close match in observed period and color and, therefore, it was assumed, in position in the strip. Yet RT Aur has an FIG. 4.ÈO[C diagram for Polaris. Solid circles represent photometric determinations, open circles those from radial velocity data, and triangles those reported in this paper (all from radial velocities). FIG. 6.ÈRate of period change, as predicted by second- (solid line), Ðfth- (dashed line), and seventh-order (dotted line) polynomial Ðts to the O[C diagram points.

5 94 KAMPER & FERNIE amplitude of.8 mag in V, compared with PolarisÏs.3 mag. This comparison was rendered invalid by the discovery that Polaris is an overtone pulsator (Feast & Catchpole 1997), while RT Aur is not. (We assume that overtone pulsators are s-cepheids; RT Aur, from its Fourier coefficient ratios, is not an s-cepheid.) However, Polaris, being higher in the strip than previously thought, may in fact be close to the red edge of the Ðrst-overtone Cepheids and evolving into the domain of fundamental pulsators, i.e., its amplitude may eventually increase again, but with the fundamentalmode period of D5.6 days. (This suggestion, we believe, was Ðrst made by Siobahn Morgan [1995, private communication].) On the other hand, the amplitude seems to have been holding steady for some years now, and there is no sign of a change in period behavior, but of course any putative switch might take a much longer time. We thank the various operators of our 1.9 m telescope for their assistance in obtaining data over the years. REFERENCES Arellano Ferro, A. 1983, ApJ, 274, 755 Fernie, J. D., Kamper, K. W., & Seager, S. 1993, ApJ, 416, 82 (FKS) Brown, C. F., & Bochonko, D. R. 1994, PASP, 16, 964 Garnavich, P., Yang, S., Matthews, J. M., Walker, G. A. H., & Dinshaw, N. Dinshaw, N., Matthews, J. M., Walker, G. A. H., & Hill, G. M. 1989, AJ, 1993, JRASC, 87, , 2249 Kamper, K. W. 1996, JRASC, 9, 14 Feast, M. W., & Catchpole, R. M. 1997, MNRAS, 286, L1 Kamper, K. W., Evans, N. R., & Lyons, R. W. 1984, JRASC, 78, 173 Fernie, J. D. 199, PASP, 12, 95 Fernie, J. D., Beattie, B., Evans, N. R., & Seager, S. 1995, Inf. Bull. Variable Stars, No. 4148