467
PHOTOMETRIC VARIABILITY IN THE HR-DIAGRAM
L. Eyer, M. Grenon
Geneva Observatory, CH-1290 Sauverny, Switzerland
the Atlas of Unsolved variables light curves which ABSTRACT
contains a selection of well de ned curves. Many new
variables were discovered and many others have a
The Hipparcos satellite has detected systematically
b etter de nition of their b ehaviour.
variable stars when the amplitudes exceed a mag-
nitude dep endent threshold, as small as a few mil-
Here, we attempt a more global approach, since Hip-
limag for bright stars. The published data ab out
parcos allows a general description throughout the
variable stars result from the work of two groups at
HR-diagram of stellar stability and variability. The
the Geneva Observatory and at the Royal Greenwich
HIC Hipparcos Input Catalogue, Turon et al. 1992
Observatory. It contains information ab out p erio dic
was built in order to b e a complete survey up to the
variables extrema, p erio ds and epochs and ab out
magnitude V < 7:9+ 1:1 sin b for stars earlier than
`unsolved' variables amplitudes . Here, a more gen-
G5 and V < 7:3+ 1:1 sin b for stars later than G5,
eral description of the HR-diagram is made in terms
where b is the galactic latitude. The fainter stars
of stability, microvariability,variability, and variation
in the program emerged as a selection of prop osed
time scales. A particular emphasis is put on the lim-
stars. Altogether, this gives a large sample on which
its of stability areas and their signi cation.
statistical b ehaviours can b e studied.
The choice was made to represent the HR-Diagram
in a non conventional way. That is to express it with
Key words: Variable Stars, photometry, Hipparcos.
the sp ectral classi cation. In the abscissa is displayed
the sp ectral typ e and in the ordinate the luminosity
class. The sp ectral typ es were taken from the HIP
1. INTRODUCTION
catalogue 47 p er cent of the stars have a complete in-
formation of sp ectral classi cation . This for several
reasons. First, we didn't have the parallaxes. Second,
Hipparcos furnished more than 13 million photomet-
the sp ectral classi cation o ers a natural way to bin
ric measurements for 118 204 stars, that is a mean
stars. Third, it is reddening free. Fourth, intrinsi-
of 110 Hp magnitudes per star over a time span of
cally very luminous stars with reliable parallaxes are
3.3 years. However the number of these measure-
rare.
ments may vary strongly from one star to an other
as well as the time sampling coverage over the ob-
served p erio d. The Hp passband is wide, it extends
from 320 nm up to 850 nm, with a mean wavelength
2. NON-VARIABLE STARS
of 537 nm, close to that Johnson V 556 nm .
Before Hipparcos, the systematic searches for vari-
The precision on an individual Hp magnitude de-
able stars were done photographically, with a mini-
p ends strongly on the magnitude itself, although
mum detectable amplitude of around 0.3 m .
pg
more observing time was allo cated for fainter stars.
Thus the threshold to detect stars as variable is in-
With the advance of technologies photo electric detec-
creasing with the magnitude, mainly a result of pho-
tors and CCD cameras b ecame available. The pre-
ton statistics and sky background. Constant stars
cision achieved reached few hundreds to few milli-
are then de ned as stars not detected as variable at
magnitudes. But there was no global survey of the
a certain level, magnitude dep endent.
whole sky and stars found photo electrically as vari-
able were discovered accidentally or using sp ectral
The detection threshold limit for stars with a mean
criteria. However, some general studies were done on
number of measurement N = 110 is given in Fig-
large data collections, for example with the Geneva
m
ure 1. If in the shaded area, a star must b e consid-
photometric data Grenon 1993 .
ered as of unknown status, constantorvariable with
a p eak-to-p eak amplitude lim zone b etween the solid and dotted lines, it is de ned alogues and three atlases were pro duced: the Cat- as a susp ected variable and as a con rmed variable if alogues of Perio dic stars and of Unsolved stars, the ab ove the dotted line with 0:1 p er cent probability Atlas of Perio dic stars folded curves , the Atlas of to b e constant. Light Curves of stars in common with AAVSO, and 468 Six di erent tests were used to detect variables, with The applied pro cedure provides the main mo de, in di erent sensitivities to light-curve features. The case of pulsation, whereas many stars as Scuti mathematical expression for the limiting amplitude or SPB Slowly Pulsating B stars show a complex is given in Section 4. power sp ectrum of oscillation. The p eculiar time sampling by Hipparcos pro duces For constant stars, i.e. with A < 0:02 mag or so, quite easily spurious short p erio ds. In case of doubt, the standard error on the median magnitude may the p erio d was tested for its robustness. All solutions be extremely small less than 1 mmag . The set of pro duced by b oth teams were carefully compared. constant stars provides a high accuracy photometric reference system. Nevertheless the very high precision on Hp is de- med 3.1. Perio d Distribution in the HR Diagram graded when Hp magnitudes are transformed into Johnson V or Str mgren y magnitude b ecause of In order to investigate the intrinsic prop erties of sin- residuals on transformation equations, function of the gle stars, the con rmed or susp ected eclipsing bina- star temp erature, gravity, reddening or even metal- ries were removed from the sample. Sp ectroscopic licity. binaries may still contaminate the sample, namely in the area of G0-G5 I I I-IV stars. For all sp ectral typ es a broad p erio d luminosity re- lation exists see Figure 2 , the high luminosity stars having the longest p erio ds. Outside the main stability areas, we observe three main instability zones. That of early typ e stars, shows the shortest p erio ds for Cepheids stars in the luminosity range class II-III to IV. Late B and early A main sequence stars show p erio ds around 1 day SPB, Bp . Around the classical instability strip, the dichotomy known for RR Lyrae stars, i.e. RRc and RRab is also found for p opulation I stars. Ftyp e subgiants < F1 showP<0.2 day and of ab out 1 day if near the red edge of the instability strip. Both G and early K dwarfs show p erio ds within 2 to 10 days, when the variability is rotationally induced. The p erio d increase with luminosity and with de- creasing temp erature is very conspicuous for late K and M giants and sup ergiants. Because of abundance e ect b oth on the luminosity Figure 1. Limits between constant, suspected variable, class and on the sp ectral typ e, p opulation I I stars as and variable stars for stars with a mean number of obser- RR Lyrae and RVTau are not considered. vations. Short p erio ds 2{5 days are present for hot sup er- The con rmation of the variability character from giants, these mo des are p ossibly sup erimp osed on Hipparcos time series requires careful examination. longer p erio d variations. Atypical case is HIP 67261 Outliers due to light contamination, image over- with an oscillation p erio ds of around 4 days. lapping, misp ointing may mimic ares or eclipses. Trends due to incorrect colour used in the reduction mimic secular changes as observed for some Be stars. 4. AMPLITUDE VARIABILITY LEVEL As a result of the data analysis, most spurious events are agged in the ep o ch photometry. When the metho ds fail to detect any p erio dic signal, the star is put in the Catalogue of Unsolved variables. 3. PERIODIC VARIABLES This do es not necessarily mean that the star is not p erio dic. We mighthave missed the p erio d e.g. HIP 29055 or some minima for eclipsing binaries due to When the ratio of the exp ected amplitude over the the p eculiar sampling, or the p erio dic b ehaviour is noise was ab ove a threshold tuned to leave less than to o complex to be describ ed with the present data 5 p er cent of spurious detections as variable Eyer et set e.g. multip erio dic variables . In most cases, the al. 1994 , a search for p erio dicitywas done. Several variations are indeed ap erio dic as it can b e seen in the metho ds were used dep ending on the variabilitytyp e Atlas of light curves of Unsolved variables Grenon van Leeuwen 1997 . Once the p erio d was found a et al. 1997 . curve tting pro cess was applied to pro duce quanti- ties as Hp , Hp , the amplitude, the ep o chs and In order to characterize quantitatively the unsolved min max the errors on these parameters. variables, in addition to their light curves, we de ned 469 STELLAR VARIABILITY STELLAR VARIABILITY in the HR-Diagram in the HR-Diagram Luminosity class Luminosity class Ia Ia Ib Ib II II II-III II-III III III III-IV III-IV IV IV IV-V IV-V V V 0 0 F0 B0 A0 K0 F0 G0 B0 A0 K0 M0 G0 M0 Period in days : < 0.2 Spectral type Percentage of Amp > 0.05 : <2 Spectral type 0.2 - 0.5 2 - 4 0.5 - 2.0 4 - 6 2.0 - 5.0 6 - 8 5.0 - 10.0 8 - 15 10.0 - 20.0 15 - 20 20.0 - 50.0 20 - 40 50.0 - 100.0 40 - 80 > 100.0 >80 Figure4. HR-diagram labeledinfraction of variables. Figure2. HR-diagram labeledinperiods. STELLAR VARIABILITY in the HR-Diagram Luminosity class Ia Ib II II-III III III-IV IV IV-V V 0 F0 B0 A0 K0 G0 M0 Variability level in mmag: <2 Spectral type 2 - 4 e5. The Mv= V I diagram for variable stars in 4 - 6 Figur 6 - 8 ap. Symbol colours: black dots: A < 8 - 15 the south galactic c 15 - 20 blue: A = 0.02{0.05; green: A = 0.05{0.10; 20 - 40 0.02 mag; 40 - 80 A = 0.10{0.25; red: A > 0.25. >80 yel low: Figure3. HR-diagram labeledinmean intrinsic scatter. 470 their intrinsic amplitudes, i.e. their p eak-to-p eak am- 4.1. Mean Intrinsic Scatter plitudes corrected for photon and reduction noises. The mean intrinsic scatter < > computed from all int The estimated scatter due to photon and reduction stars, constant, microvariable and variable is indica- noises, is subtracted quadratically from the ob- int tive of the variability level across the HR-diagram. A 2 served scatter . If the variations were sine data robust estimator of < > is given in Figure 3 for p int curves, the amplitude A would b e equal to 2 2 , bin of sp ectral subtyp e and luminosity class. int the intrinsic scatter. A correction, function of the asymmetry s , allows to estimate correctly the ampli- Highly stable areas exist on b oth sides of the classi- 3 tude even in case of very asymmetric light curves as cal instability strip extending from F0V to F8I I and for EB typ e variables. The co ecients in the formula ab ove. The blue domain is narrowing towards high given b elowwere tuned, using s and the amplitude luminosity. B8-A3 IV and V stars app ear to b e the 3 obtained from p erio dic variables with well de ned most stable whereas early B typ e stars are nearly all curves tting. The comparison between the ampli- variable. We notice the shift towards lower T of e tude estimator A and the true p eak-to-p eak ampli- unstable B subgiants with resp ect to dwarfs. tude Hp Hp is given in Figure 6. It should min max The stable domain at the right of the instability strip b e noticed that for small amplitudes the two ampli- is contaminated by stars showing probably comp osite tude estimators converge, with the di erences that A sp ectra as the G0-G2 I I I, G2-G5 I I I-IV for which the may represent the combination of several mo des in variability is non intrinsic. G8I I to G8V stars are case of multip erio dicity, whereas Hp Hp is min max photometrically the most stable. the amplitude of the main mo de. With the development of activity and star sp ots the The formulae used in the de nition of amplitudes are: variability increases from G8 to M2 dwarfs. Main sequence stars in the instability strip are mostly 2 2 2 = int data int microvariable with < > up to 6{8 mmag. int p 1 The amplitude-luminosity relation is conspicuous for 2 2:56 A =2 int 2 late K and M giants and sup ergiants as well as the 0:64s 3 amplitude-temp erature relation for M giants, the lat- est showing the largest intrinsic scatter. p 0:18 A =2 2 +0:43 lim int 2 0:003 N +0:5 m 4.2. Amplitudes ab ove 0.05 mag where N is the numb er of measurements used. m An other waytocharacterize the distribution of the variability is through the p ercentage of variables with amplitudes exceeding a given threshold. The statis- tics has to b e p erformed with stars having A less or lim equal to the selected threshold. Avery clear delimi- tation of variability area is found when the threshold is set to 0.05 mag, see Figure 4. Nearly 50 p er cent of B1-2 V stars, 15{20 p er cent of B3-B4 I I I have A > 0.05 mag; they de ne precisely the instability strip for B stars. The general structure of this diagram is similar to that of Figure 3 with the di erence that in some area almost all stars are stable at the 0.05 mag level whereas in other they are nearly all variable, namely the M giants and the Ia sup ergiants. 4.3. The Distribution of Amplitudes The mean amplitude or the fraction of stars ab ove a threshold are crude estimators of the amplitude distribution, and they may be misleading if several mo des or variabilitytyp es are present in a given area of the HR-diagram. In well p opulated areas the distribution of amplitudes Figure6. Comparison between the estimated amplitudes may b e describ ed. It is the case for most of the main and the amplitudes from the catalogue of periodic vari- sequence, the blue giants and the red giants domains. ables. As an example we give see Figure 7 the case of the class I I I M giants, of typ e M0, M3 and M4 with 2 Due to statistical uncertainties, may b e negative. corresp onding temp erature from 3800 to 3300 K. int This quantitymay nevertheless b e used with its sign where mean levels of variability are considered in bin The distributions of red giants amplitudes are uni- of sp ectral typ e and luminosity class. mo dal with their mo des as well as their spread getting 471 larger when the temp erature gets lower. Furthermore ACKNOWLEDGMENTS there is a minimum amplitude which is increasing with decreasing temp erature. At M4 the minimum Wewould like to thank warmly Luc Web er for his ef- amplitude is around 0.04 mag. cient help for the pro duction of the colour diagrams. REFERENCES Eyer, L., Grenon, M., Falin, J.-L., Fro eschle, M., Mignard, F., 1994, Solar Physics 152, 91-96 Grenon, M., 1993, Astron. So c. Paci c. Conf. Series 40, 693 Grenon, M., et al. 1997, ESA SP{1200, Volume 12 Turon, C., et al. 1992, ESA SP{1136, Volume 1{7 van Leeuwen, F., 1997, ESA SP{402, this volume Figure7. Distribution of amplitudes of M giants. 4.4. Variability in the Mv= V I Plane For intermediate to low luminosity stars, parallaxes may be used to build the HR-diagram in terms of absolute magnitude Mv and V I , see Fig- ure 5. Among 21 657 stars at South Galactic Cap b < 40 4824 stars have < 0:2 and among Mv them 627 show signi cant amplitudes. Microvariables, A < 0:02, are found mainly in the upp er main-sequence, V I < 0:0, in the clump of red giants in core He-burning phase and in the adjacent giant branch. Red subgiants show larger amplitudes. The zone around V I =0:0 in the main sequence is nearly depleted from variables. The highest densityofvariables with A =0:05 0:10 is found for subgiants and dwarfs in the V I range 0.30-0.45. Larger amplitude variables are asso ciated to the clas- sical instability strip. They are concentrated at b oth edges of the Bhm-Vitense gap at V I =0:50.