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Optical observations of close binary systems with a compact component
Augusteijn, T.
Publication date
1994
Link to publication
Citation for published version (APA):
Augusteijn, T. (1994). Optical observations of close binary systems with a compact
component.
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9 9
V4855 Centauri: a dwarf nova with a 59
m
orbital
period d
T.. Augusteijn, F. van der Hooft, J.A. de Jong, and J. van Paradijs
AstronomyAstronomy & Astrophysics accepted (1994)
Abstract t
Wee present time resolved photometry and spectroscopy of the dwarf nova V485 Cen.. The average photometric light curve at the previously detected 59 min period (Augusteijnn et al. 1993, Chapter 8) shows a single "hump*' extending over approxi-matelyy half the period. Significant radial velocity variations are detected in Ha only forr a period equal to the photometric period. The line shows two components which varyy with this period; one component dominates the line wings and has a low radial velocityy amplitude, and the second component dominates the line center and has a highh radial velocity amplitude. The phasing of the two components with respect to thee light curve is consistent with the component dominating the line center originat-ingg in the hot spot (the so-called S-wave) and the component dominating the line wingss originating from a region centered on the white dwarf, and we conclude that thee 59m is the orbital period of the system. Using various observational constraints wee derive a mass ratio of q = M W D / MS C C ~2.6 and a inclination of t ~ 20-30°.
Strongg evidence is found for a significant contribution from the secondary to the spectrumm at wavelengths longer than ~5900 A. We discuss the discovery of a 59m orbitall period in the framework of evolutionary ideas about cataclysmic variables. Thee most likely explanation is that the secondary has a low, but finite, hydrogen content. .
9.11 Introduction
Thee only physical property known accurately for a large number of cataclysmic variables (CV's) iss the orbital period (Bitter and Kolb 1994). The period distribution of CV's shows two striking features:: (i) there is a 'period gap' between ~ 2h and ~ 3h; (ii) the distribution has a cut-off at a minimumm period of ~80m. The period distribution can be understood as a result of the orbital evolutionn of CVs. The evolution from a detached binary (the pre-CV) to the semi-detached CV, andd the subsequent mass transfer and long-term evolution to shorter orbital periods is driven by thee loss of orbital angular momentum caused by gravitational radiation (e.g., Patterson 1984) andd magnetic braking (see, e.g., Verbunt and Zwaan 1981).
120 0 99 V485 Centauri: a dwarf nova with a 59"1 orbital period
Thee period gap can then be understood as the result of the termination (or substantial weakening),, at a period of ~ 3h, of the magnetic braking (Spruit and Ritter 1983, Rappaport, Verbunt,, Joss 1983): the secondary, which is out of thermal equilibrium because of the mass loss, andd therefore somewhat oversized, contracts, and as a result mass transfer ceases. The orbit continuess to shrink (but more slowly than before) due to gravitational radiation alone until the secondaryy again fills its Roche lobe at an orbital period of ~ 2h and mass transfer resumes.
Thee mass of the late-type companion in a CV decreases as it transfers mass to the white-dwarff primary. As long as the mass of the secondary star is large enough to support hydrogen burningg in its core, it is near the main-sequence mass-radius relation, and its radius decreases ass its mass decreases. However, once the late-type star has lost so much mass that it can noo longer burn hydrogen in its core, it becomes degenerate and its radius will increase as its masss decreases. As the orbital period of a CV depends to first order only on the radius of the secondaryy star, this implies that there is a minimum orbital period when the secondary star becomess degenerate. The value of this minimum orbital period depends on the total mass of the systemm and its chemical composition (Paczynski and Sienkiewicz 1981, Rappaport, Joss, and Webbinkk 1982, Sienkiewicz 1984). For a system with solar abundances this minimum period is ~ 8 0m. .
Theree is presently only one group of CV's known with orbital periods less than 80m: the AMM CVn stars. They are characterized by the total absence of hydrogen lines in their spectra, andd they show photometric and/or spectroscopic periods of 17.5-46.5m (Ritter and Kolb 1994). Thesee systems are probably CV's containing a (helium degenerate) white-dwarf secondary.
Thee variable star V485 Cen is classified in the General Catalogue of Variable Stars (Kholopov ett al. 1985) as a U Gem type dwarf nova. In an earlier article (Augusteijn et al. 1993, Chapter 8)) we reported the discovery of a 59m photometric period in this dwarf nova. We also found thatt the optical spectrum of V485 Cen shows both H and He I emission lines. In this article wee present time resolved spectroscopy and photometry of V485 Cen to investigate the nature off this period. We will show that this period represents the orbital period of this system, and discusss the implication of this period in the framework of evolutionary ideas about CV's.
9.22 Photometry
Wee observed V485 Cen in quiescence during 9 nights with a CCD attached to the 91cm Dutch telescopee at the European Southern Observatory in Chile. The source was monitored using a standardd V filter. In Table 9.1 we give a summary of our observations. In all cases the integration timee was 4 min. Differential magnitudes of the source with respect to several "comparison" stars withinn the field of view were determined using aperture photometry. The errors in the differential magnitudess taking into account only Poisson noise were typically 1-2%. The comparison stars weree checked for variability in each night separately, and over the entire data set. For stars off similar brightness to V485 Cen we find within single nights standard deviations in their brightnesss of 2-4%. For the average brightness per night of these stars taken over the entire dataa set we find standard deviations of ~ 2 % . The largest difference in the average brightness perr night for all comparison stars was ~ 6 % , practically independent of the brightness of the comparisonn stars. This latter result indicates that systematic effects dominate the calibration off the data. We believe this to be the result of using different (types of) CCDs during different observingg nights combined with the spread in colours of the comparison stars. We obtained a photometricc calibration of the differential magnitudes using the standard magnitudes of two of thee comparison stars (see Augusteijn et al. 1993, Chapter 8).
Inn the top panel of Fig. 9.1 we present the result of a Fourier spectrum analysis of all the photometricc observations in quiescence combined. The observations have been corrected for the averagee brightness in each night separately (see below). Strong peaks are found centered at a
-4; ;
d d
d d CDD O O O CL L H M 111" " " II I I I I I I I I I I I I I I I I J L * ^^ I *A A
mm mm
~ÉA ~ÉA '' ' I i I I ' I I I ' ' ' » ' ' ' ' ' ' ' I 10" " 2 x 1 0 ~44 3 x 1 0 "4 4 x 1 0 "4 5 x 1 0 "4 6 x 1 0 "4 o o 2 . 6 x 1 00 2 . 8 x 1 0 3 x 1 0 " " 5 . 2 x 1 00 ' 5 . 6 x 1 0 6 x 1 0 " "Frequencyy (Hz)
F i g u r ee 9 . 1 . Top: frequency spectrum for all the differential magnitudes in quiescence. Thee observations have been corrected for the average brightness in each night separately. Thee ordinate indicates the power, normalized on the total variance of the data, as function off frequency. Bottom left: enlargement of the region around ~ 2 . 8 x l 0 ~4 Hz. Bottom right:
enlargementt of the region around ~ 5 . 6 x l 0 ~4 Hz. Indicated are the expected positions off peaks for the fundamental and the first harmonic for a period of 0.040995 days, or 2.8233 x l O- 4 Hz (see text)
periodd of ~ lh ( ~ 2 . 8 x l 0 ~4 Hz) with t h e characteristic p a t t e r n as t h e result of t h e sampling of the observations.. T h e first h a r m o n i c of this period (at ~ 5 . 6 x l 0 ~4 Hz) is also present in the frequency
s p e c t r u m .. No other significant peaks are found at longer periods. I n t h e Fourier s p e c t r u m of the uncorrectedd d a t a m a n y peaks a p p e a r at frequency below ~ 4 . 5 x l 0 ~4 Hz ( ~ 6h; a p p r o x i m a t e l y
t h ee m a x i m u m length of any of our observing r u n s ) , a n d are t h e result of variations in t h e average brightnesss of t h e system (see Table 9.1). A l t h o u g h these variations are fairly typical of dwarf novaee in quiescence we can not exclude t h e presence of longer ( > 6h) p h o t o m e t r i c period in V485 Cen. .
Too look m o r e closely at t h e ~ 1 period and its first h a r m o n i c we present enlargements off t h e regions a r o u n d a frequency of 2 . 8 x l 0 ~4 Hz ( b o t t o m left in Fig. 9.1) a n d a r o u n d a frequencyy of 5 . 6 x l 0 ~4 Hz ( b o t t o m r i g h t in Fig. 9.1), respectively. T h e highest peak in t h e region
a r o u n dd ~ 2 . 8 x l 0 ~4 Hz corresponds t o a frequency of 2 . 8 2 3 2 9 x l 0 "4 Hz (P = 0 . 0 4 0 9 9 5 days), b u tt frequencies corresponding t o t h e two peaks on either side of t h e highest peak (2.82032x10""' a n dd 2 . 8 2 6 2 6 x l 0 ~4 Hz, respectively) cannot be excluded. T h e highest peak in the region of t h e firstfirst harmonic shown in t h e b o t t o m panel of Fig. 9.1 is at a frequency of 5.64660 X l O- 4 Hz, whichh is very close t o the frequency expected if the fundamental frequency is 2 . 8 2 3 2 9 x l 0 ~4 Hz.
122 2 99 V485 Centauri: a dwarf nova with a 59"" orbital period
Tablee 9.1 Arrival time of maximum light Ts t a r t(HJD) ) -2440000 0 8715.55762 2 8716.56055 5 8749.59082 2 8754.48633 3 9106.65723 3 9107.55762 2 9179.48047 7 9187.47363 3 9375.69531 1 Duration n (days) ) 0.23438 8 0.12305 5 0.14258 8 0.31543 3 0.18555 5 0.12402 2 0.09375 5 0.08105 5 0.18457 7 No.. of obs. . 67 7 37 7 42 2 58 8 53 3 37 7 26 6 20 0 46 6 Tm a x(HJD) ) -2440000 0 8715.67453(54) ) 8716.61868(57) ) 8749.6601(20) ) 8754.7007(14) ) 9106.76762(60) ) 9107.6263(13) ) 9179.5334(10) ) 9187.5285(11) ) 9375.77636(11) ) Cycle e number r 0 0 23 3 829 9 952 2 9540 0 9561 1 11315 5 11510 0 16102 2 average e VV (mag) 18.0784(80) ) 18.0608(88) ) 18.286(13) ) 18.285(20) ) 17.9859(85) ) 17.895(10) ) 18.285(12) ) 18.075(12) ) 18.2047(78) )
T h ee p e a k s corresponding t o t h e harmonics of t h e other t w o possible fundamental frequencies a r ee s u b s t a n t i a l l y smaller. W e , therefore, believe t h a t t h e peak a t a frequency of 2 . 8 2 3 2 9 x l 0 ~4 Hzz corresponds t o t h e t r u e fundamental frequency. However, m o r e closely spaced, a n d longer p h o t o m e t r i cc observations a r e needed to d e t e r m i n e t h e exact value of t h e period conclusively.
Wee performed sinusoidal fits w i t h a fixed period of 0.040995 days to t h e observations in each n i g h tt separately. T h e resulting arrival times of m a x i m u m light a n d t h e m e a n m a g n i t u d e a r e l i s t e dd in Table 9.1 t o g e t h e r w i t h t h e respective cycle n u m b e r s . T h e errors listed in this table a r ee t h e formal errors derived from the sinusoidal fit for X2ed
=
1-0- T h e errors in t h e average m a g n i t u d ee do not include t h e uncertainty in t h e absolute calibration of t h e m a g n i t u d e s which m i g h tt b e as large as 0.06 m a g (see above). From a least-squares fit t o t h e arrival times we derive t h ee following ephemeris:
TTmm„„xx(HJD)(HJD) = 244 8988.20980(27) + 0.040995001(44) x N
Cov{TCov{T00,P,P00)) = 1.7 1 0 "1 1 days2
(9.1) )
w i t hh X^ed~ l -u4 f °r 7 degrees of freedom. A 2n d-order polynomial fit to t h e arrival times does n o tt show a significant period derivative, a n d we derive a 3-0" lower limit of P / | - P | > 6 . 4 10'1 y r s . I nn F i g . 9.2 we show t h e differential m a g n i t u d e of t h e source with respect t o t h e comparison s t a r ss a s a function of phase a t a period of 0.040995 days. We show t h e error-weighted averaged
o o 1 1 o o o o 11 . . . . 1 :: ' t
-- I
1ff t
, t , , ,i
. i i ' i 'H'l l
i i
1 1
1 1
.. . i . ii i 1 iVlHll .
t ' l l
,, , i , i iIll
-i
((;
i i
, ,, i , -0.5 5 1.5 5 F i g u r ee 9.2. The differential V magnitudee of V485 Cen as a func-tionn of the 0.040995 days pe-riod.. The error-weighted average iss shown of the data in 20 phase bins.. The corresponding error in thiss average of each bin is indi-cated.. Phase zero corresponds to maximumm light. The light curve is shownn twice for clarity(usingg the errors expect from Poisson noise) of the data in 20 phase bins. Two cycles are shown forr clarity. The average light curve looks very similar to the quiescent orbital light curves of otherr dwarf novae as it shows a large "hump" which extends over approximately half the period; thiss hump is thought to be the result of the varying aspect of the hot spot. The light curve of V4855 Cen looks particularly similar to the quiescent orbital light curves of the dwarf novae Z Chaa (see, e.g, Wood et al. 1986) and OY Car (see, e.g., Schoembs and Hartmann 1983). The mainn differences are the larger amplitudes of the hump (~0.55 mag versus ~0.25 mag in V485 Cen),, and the presence of an eclipse in these objects which occurs ~0.10-0.15 in phase after the maximumm of the main hump.
9.33 Spectroscopy
9.3.11 Observations and data reduction
Too clarify the nature of the ~ lh photometric period, we obtained spectra of the source on Marchh 23r d 1993, with the 3.6m telescope at the European Southern Observatory in Chile, usingg EFOSCl and a grism (Orange 150), which covers the wavelength range 5200-6950 A. Thee detector was a TEK CCD with 5122 pixels. The pixel size of this CCD is 27/im, which
correspondss to 0V6 on the sky. The slit was orientated such that a nearby star (V=15.04(2), (B-V)=0.64(4);; Augusteijn et al. 1993, Chapter 8) located ~50" W, and ~10" S with respect too V485 Cen was observed simultaneously. The source was monitored during the night for twoo periods of ~2 and ~ 3 hours, respectively, with an interruption of ~100 min. A total of 311 spectra were obtained with an integration time of 9 min each. Helium-Argon calibration exposuress were obtained approximately every hour. A slit width of 1" was used which resulted inn a resolution of 5 A (as derived from the FWHM of the Helium-Argon calibration spectrum). Additionall spectra were obtained of both the source and the second star on the slit, and of a fluxflux standard (Kopff 27; Stone 1977), using a 10" slit. All the spectra were extracted using the optimall extraction method as described by Home (1986), and wavelength calibrated using the Helium-Argonn exposure closest in time. The wide-slit spectra were corrected for atmospheric absorptionn using the standard extinction curve for the La Silla observatory.
Wee used the wide-slit exposure to determine the flux calibrated spectrum of the second star onn the slit. From a comparison of this spectrum with the spectra of standard stars provided byy Suva fc Cornell (1992) and its photometric colour we derive an approximate spectral type off G2 v for this star. We then determined the ratio of the spectrum of this comparison star in eachh narrow slit exposure with the flux calibrated spectrum. Next, this "ratio" spectrum was fittedfitted as a function of wavelength using a 3th-order polynomial excluding the regions 5825-5925A 6125-63500 A, 6475-6600 A and > 6850 A, to avoid strong stellar and atmospheric features. By dividingg the spectrum of V485 Cen taken in the same narrow slit exposure by this polynomial fitfit we obtained a flux calibrated spectrum of the source. Unfortunately, the slit was not placed exactlyy over the centers of both V485 Cen and the comparison star, and the relative position off the slit with respect to the two stars was also slightly different in the two sets of exposures beforee and after the ~100 min interruption. This resulted in an off-set between the flux zero pointss in the two sets of spectra and a slight colour difference. In the second set of spectra we alsoo find a small airmass dependent change in the flux zero point and colours, which probably is thee result of the comparison star being positioned close to the edge of the slit. This particularly affectedd the last few spectra.
Inn Fig. 9.3 we present the total flux integrated over the whole wavelength range on a magnitudee scale for the individual calibrated spectra of V485 Cen as a function of Heliocentric Juliann Date; a clear variation can be seen with a period of ~ 1 hour. In the top panel of Fig. 9.4 we presentt a Fourier spectrum analysis using the Lomb-Scargle method and the CLEAN algorithm
124 4 99 V485 Centaury, a dwarf nova with a 59"1 orbital period
F i g u r ee 9.3. The total flux inte-gratedd over the wavelength range 5200-69500 A on a magnitude scale forr the individual spectra of V485 Cenn as a function of Heliocentric Juliann Date
69.66 69.7 69.8 69.9 Timee ( J Do- 2 4 4 9 0 0 0 . )
off t h e i n t e g r a t e flux. We performed sine fits to t h e two sets of spectra separately, where we e x c l u d e dd the last five s p e c t r a which are most affected by the positioning of t h e comparison star closee t o the edge of t h e slit. A s s u m i n g an integral n u m b e r of cycles between t h e average times of m a x i m u mm light in t h e two sets of spectra as determined from t h e sine fits we derive a period of 0.04060(30)) days, which is consistent with t h e period we derived from our extensive p h o t o m e t r i c d a t a - s e tt presented above. M a x i m u m light occurs a t H J D 2449069.74803(65), which corresponds t oo p h a s e 0.98(2) with respect t o the ephemeris presented in Eq. (9.1). In Fig. 9.5 we present t h ee folded light curve where we have removed the off-set between t h e two sets of spectra. Also t h ee "colour" curve, as d e t e r m i n e d by the r a t i o of the i n t e g r a t e d flux in t h e wavelength range 5200-61000 A over t h e i n t e g r a t e d flux in t h e range 6100-6950 A, shows a clear variation with this p e r i o d .. T h e folded "colour"-curve shown in Fig. 9.5 seems to be shifted slightly t o later phase, a n dd from a sine fit we derive a formal difference in phase of 0.094(27). In other dwarf novae t h a tt show a n o r b i t a l h u m p these two variations a r e generally in phase (e.g., La Dous 1993).
Inn Fig. 9.6 we present t h e average flux calibrated s p e c t r u m of V485 Cen, where we have excludedd t h e five last spectra (see above). The s p e c t r u m is very typical for a dwarf nova in quiescence,, showing double-peaked emission lines of H a , a n d He I 6678 a n d 5876 A, a n d a fairly flatflat c o n t i n u u m . A b s o r p t i o n by N a l at 5890/5896 A distorts t h e profile of the l a t t e r line. T h e b r o a dd a b s o r p t i o n feature near 6280 A is due to t h e diffuse interstellar line at 6283.9 A. T h e c o n t i n u u mm shows a change in slope around 5900 A. We carefully checked if this feature might b ee t h e result of t h e p a r t i c u l a r way in which we reduce our spectra. However, this feature can alsoo b e seen in the average of t h e raw spectra and we believe it t o be real.
9 . 3 . 22 R a d i a l - v e l o c i t y variations
T oo look for radial-velocity variations in t h e individual spectra we used the double Gaussian convolutionn technique i n t r o d u c e d by Schneider & Young (1980; see also Shafter, Szkody & T h o r s t e n s e nn 1986). In this technique two Gaussians with fixed w i d t h a n d separation are con-volvedd with an emission line. T h e position where the intensities t h r o u g h t h e two Gaussians is e q u a ll is a m e a s u r e m e n t of t h e central wavelength of t h e line. By varying t h e separation between t h ee t w o Gaussians different p a r t s of the lines can be sampled. T h e w i d t h of the Gaussians is sett e q u a l to t h e resolution. Before applying this m e t h o d we normalized t h e individual spectra byy dividing t h e m by a 6t h-order polynomial fit t o the continuum, where we exclude the
wave-l e n g t hh ranges a r o u n d t h e emission wave-lines from t h e source, and t h e a t m o s p h e r i c a n d interstewave-lwave-lar a b s o r p t i o nn features (see Fig. 9.6).
Wee looked for periodic variations in t h e radial velocity m e a s u r e m e n t s for H a a n d He I 6678 AA using a range in separations between t h e two Gaussians of 200-3000 k m / s . Significant
vari-
--11 1 , 1 I 1 I ft*ft* * ft* ftftft ftft ft* ftftft ftft.. , , , , , , ,
ft ft * ** 'ft ** * ft * ftft ft ftft ft ** * ft ft ft ft ft ft ft .. 1 . 1 , . . . 1--0) ) O O Q. .
WY^l l
3 3 O O CL L | / W V \ \ -\-\ 1 h H — H H_J\A/J
h h H — i — h hwv/V-JJ w v J v A /
00 20 40 60 F r e q u e n c yy ( c y / d a y ) 00 20 40 60 F r e q u e n c yy ( c y / d a y ) Intensity y R a d i a ll v e l o c i t y Linee c e n t e r R a d i a ll v e l o c i t y Linee w i n g sF i g u r ee 9.4. In the top two panels we show a Fourier spectrum analysis using the Lomb-Scaiglee method (on the left) and the CLEAN algorithm (on the right) of the integrated fluxflux over the wavelength range 5200-6950 A . In the middle and bottom panel we present aa Fourier spectrum analysis using the Lomb-Scargle method and the CLEAN algorithm of thee radial velocities of HQ for separations between the two Gaussians of 600 and 1800 km/s, respectively y
ationss were only found in the H a line for separations of 400-1000 k m / s a n d 1400-2600 k m / s , respectively.. In all cases t h e period was consistent with t h e period derived from the p h o t o m e t r i c brightnesss variations. In t h e middle a n d b o t t o m p a n e l of Fig. 9.4 we present a Fourier s p e c t r u m analysiss using t h e Lomb-Scargle m e t h o d a n d the C L E A N a l g o r i t h m of the radial velocities of H aa for separations between the two Gaussians of 600 a n d 1800 k m / s , respectively. It is clear fromm F i g . 9.4 t h a t t h e brightness a n d t h e r a d i a l velocities vary with t h e same period within the accuracyy of our d a t a . We do not detect any significant radial velocity variations with a period otherr t h a n the ~ lh r period.
T h ee observations are spaced in t i m e in such a way t h a t t h e spectra are grouped together in phasee as a function of t h e ~ 1 period. They fall into six phase intervals containing between 4 a n dd 6 spectra. In these groups the spread in phase of the different spectra is in one case 0.09 in p h a s e ,, a n d in the other five cases 0.03 in phase. We, therefore, decided t o average t h e spectra inn these six phase bins, thereby increasing t h e signal-to-noise r a t i o in t h e resulting spectra. We t h e nn determined radial velocities for these average spectra using the double Gaussian technique. Too investigate t h e radial-velocity variations in m o r e detail we fitted t h e derived velocities withh a non-linear least-squares fit of t h e form
126 6 99 V485 Centauri: a dwarf nova with a 59"" orbital period CD D en en CXI I
d d
m m 11 1 1 1 1 , 1 -- A* *
* *
* * * *
A A 11 | 1 1 1 1 | ;; i, *-- #
I* *
* *
.. 1** *
** *
** i
*
** *
* *
* *
** * *
11 . . . . 1 . . 11 ' 1 ' ** * ~** *
-* -*
* *
11 1 1 l" 11 1 1 1**
-ii i 1 i 0.55 1 1.5 Phase e o o o o • * * o o c c CD D CDD o c c >> o o o o o in n to o enn m EE ^ £ £ CD D in n I I ii | i i i i | i i i i | i i i i | i i i i | i 0.55 1 1.5 Phase eF i g u r ee 9 . 5 . In the top left panel we show the total flux integrated over the wavelength rangee 5200-6950 A folded on the 0.04060 days period. The data from the two sets of spectraa have been normalized to their respective average. In the bottom left panel we show thee folded "colour" curve as defined by the ratio of the integrated flux in the wavelength regionss 5200-6100 A and 6100-6950 A. In the top right panel we show the radial-velocity variationn of the component that dominate the line center, and in the bottom right panel thee radial-velocity variation of the component that dominate the line wings as a function off the 0.04060 days period. For the former component we show the radial velocities as derivedd by eye from the average spectra in the 6 orbital phase bins (see text), for the laterr as derived from the double-Gaussian method for a separation of 2400 km/s (see text). Alsoo shown are the sine fits representing the radial velocity variations corresponding to the orbitall elements presented in Table 9.2. Phase zero correspond to photometric maximum. Thee data are shown twice for clarity
w h e r ee (p is t h e average p h a s e in each phase bin which was calculated using the period derived fromm t h e brightness variations in t h e integrated flux of the calibrated s p e c t r a (see above), and c o n s t r u c t e dd a socalled " d i a g n o s t i c d i a g r a m " (Shafter 1983) where we show the system p a r a m -eterss as a function of t h e s e p a r a t i o n (a) of the two Gaussians.
Inn Fig. 9.7 we show t h e "diagnostic d i a g r a m " for H a in which we plot K, its associated error <TX/'K,, 7 , a n d t h e p h a s e as a function of a. Here, phase corresponds to t h e time of superior conjunction,, where p h a s e zero corresponds t o p h o t o m e t r i c m a x i m u m . This figure shows t h a t t h e r ee a r e two c o m p o n e n t s present in the line which vary w i t h t h e 0.04060 days period. One c o m p o n e n tt d o m i n a t e s in t h e line center a n d has a high velocity a m p l i t u d e , a n d t h e second c o m p o n e n tt d o m i n a t e s in t h e line wings a n d has a low velocity a m p l i t u d e . T h e component w h i c hh d o m i n a t e s t h e line center trail the line wings by ~ 0 . 4 in phase. T h e large value of o-^/K
ll 1 1 1 1 1 1 1 1 1 1 1 1 r
/ : :
— i — i — i — ii i i i i i i i i i i i
55000 6000 6500
Wavelengthh (A)
F i g u r ee 9.6. The average flux calibrated spectrum of V485 Cen. The last five spectra were excludedd from this average (see text)
a n dd t h e lack of significant radial velocity variation a t a separation of 1200 k m / s (see Fig. 9.7) cann be u n d e r s t o o d as t h e result of t h e two components being comparable in s t r e n g t h at this separationn between t h e two Gaussians, a n d practically half a cycle out of phase.
Forr separations of t h e two Gaussian smaller t h a n t h e separation between t h e two peaks in the emissionn line profile, t h e double Gaussian m e t h o d is not very well suited t o determine velocities. Inn some cases it finds velocities which correspond t o one of the two peaks instead of t h e peak whichh corresponds t o t h e emission component which dominates t h e variations in t h e line center. We,, therefore, determined the velocity of this component in the six average phase binned spectra byy eye. T h e resulting orbital elements are listed in Table 9.2. These results are within t h e errors equall t o those d e t e r m i n e d with t h e double Gaussian m e t h o d for a separation of a = 800 k m / s , wheree OKJK reaches a local m i n i m u m .
Too derive t h e orbital elements of t h e line wings we took t h e values t h a t correspond t o the largestt separation j u s t before <r/<- / K shows a sharp increase, i.e. for a = 2400 k m / s . T h e resulting orbitall elements are listed in Table 9.2. T h e reason for choosing this p a r t i c u l a r separation is t h a t
Tablee 9.2 Orbital elements
77 (km/s) KK (km/s) Phase e linee center 199 (28) 3899 (38) 0.551(16) ) linee wings 12(7) ) 79(10) ) 0.138(20) )
m m
CN N O Od d
d d
128 8 99 V485 Centauri: a dwarf nova with a 59™ orbital period
b b
E E
o o
F i g u r ee 9.7. The "diagnostic dia-gram"" for Ha. We show K, its as-sociatedd error <TK/K, J, and the phasee as a function of a. Here, phasee corresponds to the time of superiorr conjunction, where phase zeroo corresponds to photometric maximum m
10000 2000
Gaussiann separation ( k m / s )
a n yy d i s t o r t i o n due t o variations a t low (Keplerian) velocities (e.g., from a hot spot) is expect t o bee m i n i m a l in t h e line wings, whilst at very large separations the velocity m e a s u r e m e n t s become lesss reliable because t h e two Gaussians a r e sampling an increasingly smaller p a r t of t h e line wings.. Fig. 9.7 seems t o i n d i c a t e t h a t any distortion due t o the component at low velocities in t h ee disk is confined t o low velocities and well separated from the line wings at a > 1600 k m / s . However,, b o t h K a n d 7 show a t r e n d towards smaller K a n d m o r e positive 7 going from a = 18000 t o 2400 k m / s , whilst O~K /K reaches a local m a x i m u m at a = 2000 k m / s . This might reflect aa d i s t o r t i o n of t h e line a t relative high velocities which diminishes as one moves out to higher velocities,, a n d one m u s t consider t h e possibility t h a t high-velocity non-Keplerian m o t i o n in t h e diskk might still distort t h e line wings. We also performed single-Gaussian fits t o t h e H a line profilee excluding p a r t of t h e line centered a r o u n d t h e rest wavelength. For excluded wavelength intervalss larger t h a n 40 A t h e fits t o the derived velocities were very poor. However, for widths b e t w e e nn 20 a n d 40 A t h e resulting orbital elements r e m a i n practically constant. T h e best fit wass o b t a i n e d excluding t h e central 30 A of the line with resulting values of: 7 = - 2 2 ( 8 ) k m / s ,
KK = 89(10) k m / s , a n d phase = 0.135(57). These values compare well t o t h e orbital elements
listedd in Table 9.2, a n d give us some confidence t h a t t h e orbital elements derived for t h e line wingss a r e not strongly d i s t o r t e d a n d describe the o r b i t a l m o t i o n of t h e white dwarf.
I nn t h e lower panels of F i g . 9.5 we show the radial-velocity variation of t h e components t h a t d o m i n a t ee t h e line center a n d t h e line wing as a function of the 0.04060 days period. For t h e formerr component we show t h e radial velocities as derived by eye from t h e average spectra d i v i d e dd in 6 o r b i t a l phase bins (see above). P h a s e zero correspond t o p h o t o m e t r i c m a x i m u m . Alsoo shown in F i g . 9.5 a r e t h e sine fits representing t h e radial-velocity variations corresponding t oo t h e orbital elements presented in Table 9.2.
Too d e m o n s t r a t e t h e presence of t h e two components m o r e clearly we show in Fig. 9.8 a grey-scalee plot of t h e H a emission line as a function of phase at the p h o t o m e t r i c period. In this figure t h ee d a t a have b e e n s m o o t h e d in t h e phase direction for representation purposes only. Looking
2 2
1.5 5
CD D CO O55
1
Q_ _0.5 5
0 0
F i g u r ee 9.8. Grey-scale plot of the Haa emission line as a function off phase at the 0.04060 days pe-riod.. In this figure the data have beenn smooth in the phase direction forr representation purposes only. Phasee zero corresponds to photo-metricc maximum. Two periods are shownn for clarity
65500 6 5 7 5
Wavelengthh (A)
a tt this figure t h e i n t e r p r e t a t i o n of t h e two components is straightforward. T h e component which d o m i n a t e ss in t h e line center is t h e so-called "S-wave", which results from emission from t h e h o t spott at t h e outer edge of t h e disk a n d reflects its radial-velocity variation. T h e component which dominatess in t h e line wings is p r e d o m i n a n t l y formed in t h e inner disk a n d is thought t o reflect t h ee radial-velocity variations of t h e white dwarf.
If,, like in o t h e r dwarf novae, m a x i m u m light corresponds t o viewing the hot spot face-on (see Sect.. 9.2.1) superior conjunction of t h e white dwarf is expected to occur ~ 0 . 1 0 - 0 . 1 5 in phase afterr m a x i m u m light, whilst for the S-wave superior conjunction should occur a r o u n d phase 0.5. T h ee phasing of t h e radial velocity variations from t h e line wings and from t h e line center listed inn Table 9.3 are consistent with this i n t e r p r e t a t i o n . We, therefore, concluded t h a t t h e 0.041 day periodd is the orbital period. T h e orbital p h o t o m e t r i c a n d spectroscopic variations of V485 Cen a r ee very similar t o those of other ( " n o r m a l " ) dwarf novae.
Inn Fig. 9.9 t h e average profiles of H a a n d t h e He I lines are presented on a velocity scale, wheree t h e individual spectra first have been corrected t o the rest frame of the hot spot a n d of t h ee white dwarf, respectively, using t h e elements listed in Table 9.2. T h e profiles corrected t o t h ee rest frame of t h e white dwarf are practically t h e same as the average uncorrected profiles. T h ee intensity of t h e different lines have been scaled arbitrarily. T h e average line profile of H Q correctedd for t h e S-wave shows a clear emission component in the line center. A similar feature
130 0 99 V485 Centauri: a dwarf nova with a 59"" oibital period a a o o Vi Vi u u <a a u u +-> > - ] — I — I — I — | — I — I — i — | — r r ii I i i _ll I I I L
-2000.000 0.00 2000.00
VV ( k m / s e c )
o o u u u u -t-> -t->< <
- 2 0 0 0 . 0 00 0.00 2000.00
VV ( k m / s e c )
F i g u r ee 9.9. The average profiles of Ha and the He I lines are presented on a velocity scale weree the individual spectra first have been corrected to the rest frame of the hot spot (left) andd the white dwarf (right), respectively, using the elements listed in Table 9.2
m a yy b e present in He I 5876 A, b u t this line is heavily affected by the N a i absorption lines. T h e H ee I 6678 A line does not show a clear emission c o m p o n e n t . T h e line profiles in the rest frame of t h ee w h i t e dwarf are t h e typical double peaked emission lines one would expect from an accretion diskk centered a r o u n d t h e white dwarf. T h e separation between t h e two peaks is significantly widerr for t h e He I lines (2000 100 k m / s ) c o m p a r e d t o H a (1150 50 k m / s ) . A simple e x p l a n a t i o nn for this m i g h t be t h a t t h e outer disk is too cool t o excite helium sufficiently, which r e s u l tt in an effectively smaller disk from which t h e line emission originates. If t h e separation off t h e two p e a k s reflect t h e Keplerian velocity of t h e outer edge of t h e respective (disk shaped) emissionn regions this would imply a radial extent of t h e H a e m i t t i n g region which is ~ 3 times largerr t h a n t h e He I e m i t t i n g region. The line wings in t h e average line profiles corrected for the m o t i o nn of the white dwarf are quite similar, a l t h o u g h the line wings of H a can be traced further o u t w a r dd as this line is relatively stronger. For H a we derive a H W Z I of 2250 k m / s . T h e central depressionn seen in t h e line profile of He I 5876 A is m u c h deeper t h a n those of H a and the H e i 66788 A line.
9 . 3 . 33 T h e s p e c t r a l d i s t r i b u t i o n
Ass our s p e c t r a are flux calibrated we looked at t h e intrinsic variation in the shape of t h e s p e c t r u mm as a function of o r b i t a l phase. To avoid any colour effects as a result of the comparison s t a rr moving out of t h e slit we excluded the last few spectra (see above). For those observations t h a tt were included t h e "colour" (see Sect. 9.3.1) of t h e atmospheric extinction corrected spectra off t h e comparison star were within 2% equal t o t h e "colour" of t h e flux calibrated s p e c t r u m of t h ee s t a r derived from t h e s p e c t r u m obtained with t h e 10" slit. Average flux calibrated spectra weree d e t e r m i n e d in t h e six phase intervals as defined above. T h e spectra averaged in each phase b i nn were chosen such t h a t in each bin 2 s p e c t r a from the first, a n d 2 spectra from t h e second sett of exposures were included. This was done t o reduce t h e effect of t h e offset in brightness
ÖÖ [
££ d
LO Oo o
\
^
^
^ ^
5500 0
6 0 0 00 6 5 0 0
Wavelengthh (A)
F i g u r ee 9.10. The average flux calibrated spectrum of V485 Cen at photometric maximum (upperr curve) and at photometric minimum (middle curve). The lower curve is the difference betweenn the upper two curves, and represent the spectrum of the varying component (see text).. This later curve has been shifted upward by 0.1 mJy
betweenn t h e two sets of s p e c t r a (see Fig. 9.3).
Inn Fig. 9.10 we show t h e average flux calibrated s p e c t r u m of V485 Cen near p h o t o m e t r i c m a x i m u mm (top curve; average phase 0.99) a n d near p h o t o m e t r i c m i n i m u m (middle curve; av-eragee phase 0.48). It is clear from this figure t h a t t h e change in slope near ~ 5 9 0 0 A is m o r e pronouncedd in t h e s p e c t r u m near p h o t o m e t r i c m i n i m u m . If we now s u b t r a c t e d the s p e c t r u m nearr p h o t o m e t r i c m i n i m u m from the s p e c t r u m near p h o t o m e t r i c m a x i m u m we o b t a i n t h e spec-t r a ll shape of spec-t h e varying componenspec-t. This "difference" s p e c spec-t r u m is shown in Fig. 9.10 as spec-the lowerr curve. It can be seen t h a t t h e varying component has a smooth flat s p e c t r u m with a slope differentt from t h a t of t h e average s p e c t r u m . T h e fact t h a t the there is no change in slope near ~ 5 9 0 00 A in the s p e c t r u m of t h e varying component indicates t h a t this is a persistent feature in t h ee spectrum.
Ass t h e slope of the s p e c t r u m of the varying component is different from t h e slope of t h e aver-agee s p e c t r u m on either side of ^-5900 A there seem t o be at least three components contributing t oo t h e overall s p e c t r u m . As t h e h u m p in t h e orbital light curve is t h e result of t h e varying aspect off t h e hot spot the "difference" s p e c t r u m should represent the s p e c t r u m of t h e hot spot. T h e r e iss a second component which d o m i n a t e s t h e blue p a r t of t h e s p e c t r u m and which has a different slopee t h a n the s p e c t r u m of t h e hot spot, and which most likely can be identified with emission fromm t h e disk. T h e third component becomes visible in the red p a r t of t h e s p e c t r u m a n d might bee identified with a contribution from t h e secondary (see also Sect. 9.5).
132 2 99 V485 Centauri: a dwarf nova with a 59™ orbital period
F i g u r ee 9 . 1 1 . The drawn curve showss the relation between the masss of the white dwarf and the orbitall inclination using the ob-servedd radial velocity amplitude of thee white dwarf (see Table 9.2) and aa mass ratio of q = 2.6 (see text). Wee also show this relation if we as-sumee values of q corresponding to a 2<77 variation in the ratio K/V^\s^. Thee dashed line corresponds to q == 1.8, the dotted-dashed line cor-respondss to q = 4.0. The dotted linee represents the lower limit to the masss of the white dwarf as a func-tionn of the inclination derived from thee HWZI of the Ha line. The ver-ticall line on the right gives the up-perr limit to the inclination (for q = 2.6)) implied by the lack of a pho-tometricc eclipse. All lines extend upwardd to a value of MWD— 1.44 M0 0
9.44 System p a r a m e t e r s
F r o mm t h e results we derived in t h e previous section we can limit t h e system p a r a m e t e r s of V485 C e n .. Warner (1976) derived a relation between t h e r a t i o of the radial velocity a m p l i t u d e (K) a n dd t h e projected velocity of t h e outer disk rim (Vdisk), and t h e mass r a t i o . Vdisk can be derived
fromm t h e half s e p a r a t i o n of t h e double peaked emission lines (see H o m e and Marsh 1986). As m e n t i o n e dd above t h e separation of t h e double peaked emission line is different for the He I lines a n dd H a . As t h e t e m p e r a t u r e in t h e outer disk in CV's is expected to be sufficiently high t o p r o d u c ee H a emission (see, e.g., La Dous 1993) t h e half separation of the double peaked H a line s h o u l dd reflect t h e velocity at t h e disk r i m , and we adopt a value of Vjisk= 575(25) k m / s (see a b o v e ) .. Using this value a n d t h e relation presented by Warner (1976) we derive a m a s s r a t i o q
== MYVD/MSCC ~ 2 . 6 ; if the velocity at the disk r i m is lower t h a n derived from H a , i.e. the H a
linee e m i t t i n g region does not extend to t h e disk r i m , t h e derived m a s s r a t i o is an upper limit. Usingg the observed radial-velocity amplitude of the white dwarf (see Table 9.2) and the above e s t i m a t ee of t h e mass r a t i o we derive a relation between the mass of t h e white dwarf and t h e i n c l i n a t i o nn ( t h e drawn line in Fig. 9.11). We also derived t h e same relation taking values for the m a s ss r a t i o corresponding t o a 2-CT variation in t h e ratio K/Vdisk t o reflect possible systematic e r r o r ss in the relation between this ratio a n d q. In Fig. 9.11 the lower dashed line corresponds t oo q = 1.8, t h e u p p e r dashed line corresponds t o q = 4.0.
AA lower limit to t h e m a s s of t h e white dwarf can be derived from the HWZI of the H a e m i s s i o nn line: if t h e line wings reflect the Keplerian m o t i o n in the disk then the velocity of t h e e x t r e m ee line wings does not exceed the Keplerian velocity at the surface of the white dwarf. By u s i n gg a mass-radius relation for white dwarfs ( H a m a d a and Salpeter 1961) we obtain from the H W Z II a lower limit t o the m a s s of the white dwarf as a function of the inclination (see, e.g., E q .. (7.8); Augusteijn 1994, C h a p t e r 7). For V485 Cen we derive M W D > 0.40 M0/ s i n i . This
lowerr limit is shown in Fig. 9.11 as the d o t t e d line. T h e vertical line on the right in Fig. 9.11 3 00 60 90
showss the upper limit to the inclination (for q = 2.6) derived from the lack of eclipses in the photometricc light curve. The precise value of this inclination depends only weakly on q. All the liness in Fig. 9.11 extend upward to M \ V D = 1-44 M0.
Takingg the different constraints shown in Fig. 9.11 we find that the system has a fairly low inclinationn of i ~20-30° and a white dwarf with a fairly high mass M\VD~0.7 M0, i.e. it is
mostt likely a CO white dwarf. Taking the relation between the mass of the white dwarf and the inclinationn for a value of q = 4.0 (i.e., the upper dashed curve in Fig. 9.11) as an upper limit too the allowed system parameter we derive an upper limit to the inclination of i <46°, and a lowerr limit to the mass of the secondary of Ms e c= 0.14 M@.
Thee inclination is not easy to constrain in an independent way. We compared the line profile off Ha to the theoretical profiles calculated by Home and Marsh (1986) for optically thick lines, andd we find that the relative depth of the central part of the line best agrees with that of the theoreticall profile for an inclination of i = 30°. We also compared the amplitude of the orbital humpp (see Sect. 9.2.1) to that of some other dwarf novae in quiescence which have orbital periodss below the period gap. Unfortunately, only very few dwarf novae show a well developed stablee orbital hump in quiescence. We find that the amplitude of the orbital hump in V485 Cen iss similar to that of SW UMa (Robinson et al. 1987), and slightly smaller than that of VW Hyi (see,, e.g., Van Amerongen et al. 1987). The former system has an inclination of 8 degrees, andd the latter 0 degrees (Ritter and Kolb 1994). The corresponding crude estimate oft for V4855 Cen are in reasonable agreement with the constraints shown in Fig. 9.11.
9.55 Discussion
0.5.11 Evolutionary considerations
Itt is generally accepted that (pre-) CVs are produced through a common-envelope phase in which aa low-mass star spirals into the envelope of a giant star. During this spiral in phase the envelope off the giant is expelled, and a large amount of orbital angular momentum lost; what remains is a compactt detached binary consisting of the low-mass star and a white dwarf (the core of the red giantt that lost its envelope). The evolution of the AM CVn type CVs is very different since its intermediatee predecessor is thought to have been a pair of detached white dwarfs in close orbit aroundd each other. This pair of white dwarfs is presumably formed through a second common-envelopee phase in which the white dwarf spirals into the envelope of the secondary which has evolvedd into a giant. What remains is the degenerate core of the giant in close orbit around the originall white dwarf (see, e.g., Iben and Tutukov 1984a). If the secondary in V485 Cen would bee a degenerate dwarf the lower limit to its mass derived in the previous section gives an upper limitt to its size which is an order of magnitude smaller than its Roche-lobe. This, together with thee fact that hydrogen lines are observed in the optical spectrum of V485 Cen, shows that this systemm is different from AM CVn type CVs; its mass donor is not fully degenerate.
Inn principle the secondary in a CV with an orbital period of 1 hr might be a normal main-sequencee like star, but this is only possible if such a system becomes semi-detached (i.e., it startss transferring mass and becomes observable as a CV) practically at this period, and the secondaryy is not far out of thermal equilibrium as a result of the continuous mass transfer duringg its evolution towards a shorter period. However, observing a system in this particular stagee seems very unlikely. The mass of the secondary in such a system is expected to be ~0.1 M©© (see, e.g., King 1988), which is somewhat below the lower limit we derived in the previous section. .
AA much more likely possibility is that the secondary is not fully degenerate, and has a low, but finite,finite, hydrogen content. Theoretical calculations have been made to determine the minimum periodd as a function of hydrogen content of the secondary (see, e.g., Sienkiewicz 1984, Nelson,
134 4 99 V485 Centauri: a dwarf nova with a 59"1 orbital period
R a p p a p o r tt a n d Joss 1986), which show a s m o o t h decrease in t h e m i n i m u m period as a function off t h e h y d r o g e n content. For a 1 hour period this gives an u p p e r limit of 30%. However, these calculationss a s s u m e a homogeneous distribution of t h e hydrogen in the secondary, a n d do not t a k ee t h e previous evolution of t h e system into account. In this case the previous evolution of V 4 8 55 Cen m u s t have b e e n different from t h a t of t h e " n o r m a l " CVs. A possible evolutionary s c e n a r i oo for s y s t e m s like V485 Cen has b e e n discussed by Iben & Tutukov (1984b), Tutukov ett a l . (1985), a n d P y l y s e r a n d Savonije (1989). A system like V485 Cen might be produced iff t h e low-mass s t a r h a s a m a s s of ~ 1 . 5 M0, a n d s t a r t s transferring m a s s ( u p o n first contact
w i t hh i t s Roche lobe) n e a r t h e end of its main-sequence life t i m e . Since t h e donor is t h e n m o r e m a s s i v ee t h a n t h e w h i t e dwarf, t h e initial p h a s e of m a s s transfer will be u n s t a b l e a n d proceed on aa s h o r t time-scale (M ~ 1O~7M0 y r- 1) , a p p r o x i m a t e l y t h e t h e r m a l time-scale of the secondary,
u n t i ll t h e m a s s of t h e secondary h a s decreased t o less t h a n ~ 7 0 % of t h a t of the white dwarf. D u r i n gg this p h a s e t h e source m i g h t resemble t h e ultra-soft X-ray sources as proposed by Van d e nn Heuvel et al. (1992). After this phase of r a p i d m a s s transfer the secondary has a high h e l i u mm content, which will r e m a i n high because of the transfer of t h e (relatively) hydrogen rich envelopee m a t e r i a l . According t o the evolutionary calculations such a system can sustain a m a s s t r a n s f e rr r a t e of M ~ 1 - 5 X 10~wMo/yr at periods below t h e 80 m i n u t e period cut-off of
h y d r o g e nn rich s y s t e m s .
P r e l i m i n a r yy results of recent detailed m o d e l calculation have been published by Singer et al. (1993)) and Ratter (1994). These authors calculated the evolution of a CV using a full stellar codee a n d including c o m p u t a t i o n of the m a s s transfer. Models were calculated s t a r t i n g with sec-o n d a r i e ss with t h e central hydrsec-ogen burnt u p tsec-o a varying fractisec-on. These calculatisec-ons shsec-ow t h a t t h ee m i n i m u m p e r i o d of CVs as function of t h e central hydrogen a b u n d a n c e (Xc) slowly decreases a n dd only sharply drops for very low values of Xc (U. Kolb 1994, private c o m m u n i c a t i o n ) .
I nn all these different models t h e authors find t h a t the m i n i m u m period can get ~ 2 0 m i n lowerr t h a n t h e m i n i m u m p e r i o d for a ZAMS secondary, b u t only for very low values of Xc (i.e.,
XXcc ~ 0 . 0 ) . T h i s would indicate t h a t the secondary in V485 Cen has a low value of Xc and is closee t o its m i n i m u m period. However, there is still considerable u n c e r t a i n t y in determining the m i n i m u mm p e r i o d , largely as a result of the poorly known opacities at low t e m p e r a t u r e s . We are s o m e w h a tt concerned t h a t in all these models at t h e m i n i m u m period t h e mass of the secondary iss 0.05-0.10 M Q , which does not agree with t h e constraints we derived in Sect. 9.4.
Wee have also considered t h e possibility t h a t V485 Cen is a P o p u l a t i o n II object. P o p u l a t i o n III s t a r s are smaller (R jR ~ 0 . 8 - 0 . 9 ) in comparison to P o p u l a t i o n I stars resulting in a smaller valuee of the m i n i m u m period for a CV. However, recent m o d e l calculations (Stehle 1993) show t h a tt t h e m i n i m u m p e r i o d of population II CVs with respect to P o p u l a t i o n I CVs is reduced by ~ 1 11 m i n , which is n o t enough t o explain t h e observed p e r i o d of V485 Cen.
9 . 5 . 22 T h e m a s s t r a n s f e r r a t e
Forr " n o r m a l " C V s P a t t e r s o n (1984) found a close inverse relation between the equivalent w i d t h ( E W )) of H/3 a n d t h e m a s s accretion rate, i n which t h e E W of H/3 increases with decreasing m a s s a c c r e t i o nn r a t e . Using this r e l a t i o n a n d the E W of H/3 for V485 Cen (see Augusteijn et al. 1993, C h a p t e rr 8) would imply a m a s s accretion r a t e M ~ 1 X l O- 9M0/ y r . However, as t h e accreted
m a t e r i a ll is h y d r o g e n p o o r , H/3 will b e relatively weak compared to " n o r m a l " CVs with t h e same a c c r e t i o nn r a t e , a n d P a t t e r s o n ' s relation does not apply to V485 Cen; it is expected t h a t t h e a c c r e t i o nn r a t e is lower t h a n t h e value derived above from t h e E W of H/3.
A n o t h e rr way t o d e t e r m i n e t h e accretion r a t e of a dwarf nova is by using t h e absolute magni-t u d ee d u r i n g magni-t h e peak of magni-t h e o u magni-t b u r s magni-t s , which is fairly well esmagni-tablished amagni-t M y ~ 4 . 7 (Vogmagni-t 1981, W a r n e rr 1987). T h e o r e t i c a l calculations (see, e.g., P o j m a n s k i 1986) indicate t h a t with decreasing h y d r o g e nn a b u n d a n c e s for a given accretion r a t e the disk will be brighter. O n t h e other h a n d
Warnerr (1987) has shown that the absolute magnitude of a dwarf nova in outburst is a function off orbital period, with decreasing brightness for shorter orbital periods. As, furthermore, the inclinationn of V485 Cen derived in the previous section is not extremely high or low we will adoptt a value of My—4.7 for the absolute magnitude of V485 Cen in outburst.
Thee hump seen in the light curve during quiescence is the result of the varying aspect of the hott spot. This hump has an amplitude of ~0.25 mag in the V band light curve (see Fig. 9.2). Followingg Paczynski and Schwarzenberg-Czerny (1980) we consider the hot spot as a fiat disk perpendicularr to the orbital plane which radiates only outward, and assume a limb-darkening coefficientt of u = 0.6. For an inclination angle of i ~30° (see Sect. 9.4), the absolute magnitude inn outburst, and the observed outburst amplitude (AV ~4 mag; Ritter & Kolb 1994) we derive forr the visual brightness of the hot spot averaged over the orbital period My, HS= H-2 mag.
Too derive the bolometric luminosity we need to apply the bolometric correction. The spectral distributionn of the radiation from the hot spot is shown in Fig. 9.10 (lower curve). If we assume Black-bodyy radiation, we find that a reasonable fit to the slope of this spectrum can only be obtainedd for temperatures >20000 K. Taking a B.C.~ -1.5 (T = 20000 K) we derive MBot, Hs=
9.77 mag, or LBOI,HS~ 0.01 LQ. If we now assume that all the kinetic energy of the infalling matterr onto the hot spot is converted in radiation we can derive the mass accretion rate from thee secondary from the equation
GMWDM GMWDM
LHSLHS = — ^ •
it-disk it-disk
Forr a mass of the white dwarf of 1.0 M&, a mass ratio of q = 2.6 (see Sect. 9.4) and a disk which
hass a radius of 0.8 of the Roche-lobe radius we derive a mass accretion rate of ~ 1 X 10~loMo/yr.
Wee believe that this, admittingly very rough estimate, reflects the right order of magnitude and wee note that it is in consistent with the theoretical models mentioned above.
0 . 5 . 33 T h e s e c o n d a r y
Ass we mentioned in Sect. 9.3.3 there is a strong indication that the secondary contributes significantlyy to the flux distribution at wavelengths longer than ~5900 A. The main problem in quantifyingg this contribution is the lack of knowledge of the spectral type of the secondary, the limitedd spectral range of our data, and the strongly varying depth of the molecular absorption bandss as a function of spectral type in late type stars.
Lookingg at Fig. 9.5 one might argue that the secondary does not contribute to the spectrum att wavelengths shorter than ~5900 A, and that this part of the spectrum reflects only contribu-tionss from the disk and the hot spot. By drawing a line through the continuum of the spectrum att wavelengths shorter than ~5900 A and extrapolating it to longer wavelength we estimate the contributionn of the secondary to the continuum at Ha to be ~10%.
Inn the article by Ritter (1994) on model calculations of CV evolution the author presents thee mean density versus effective temperature of the secondary for different values of Xc. From
thee value of the orbital period of V485 Cen we can directly derive the mean density of the secondaryy (e.g., Warner 1976), and we find pmean= 114 g c m- 3. From Ritter (1994; his Fig. 2)
wee then derive an upper limit to the effective temperature of the secondary of ~3500 K, which correspondss to a spectral type of M l - 2 v (Johnson 1966). For such a spectral type one expects aa fairly strong (with a depth of ~30%) absorption band of TiO at ~6800 A. In the spectrum coveringg the range 5700-10000 A we presented in Augusteijn et al. (1993, Chapter 8; their Fig.. 4) there is indeed some indication for this absorption band with a depth of at most 5%, whichh would indicate a contribution of the secondary at this wavelength of less than 15%.
Iff we assume that the V485 Cen has My=4.7 in outburst, i.e. in quiescence My= 8.7 (see above),, we can derive an upper limit to the contribution from the secondary using the upper
136 6 References s
limitt to the effective temperature given above. Given the orbital period, a mass of the white dwarff of 1.0 M©, and a mass ratio of 2.6 (see Sect. 9.4) we can derive the size of the secondary. Forr an effective temperature of 3500 K we then derive for the secondary My—12.2, i.e. the secondaryy contributes at most ~ 4 % to the total brightness in V. For the brightness in the R bandd (i.e., in the region of Ha) we find MR— 10.7. Using the observed spectral distribution, and assumingg no interstellar redenning, we derive for the total system M R = 8.2, i.e. the secondary contributess at most ~10% of the light in R. Considering the uncertainties involved the different estimatess are fairly consistent, but more detailed observations, especially in the infrared, will be neededd to constrain the parameters of the secondary sufficiently.
Acknowledgements Acknowledgements
Wee are grateful to Hugo Schwarz for obtaining the spectroscopic observations at ESO. We thank V.S.. Dhillon for supplying the 'PERIOD' analysis package, which we used for part of our data analysis.. TA acknowledges support by the Netherlands Foundation for Research in Astronomy (NFRA)) with financial aid from the Netherlands Organisation for Scientific Research (NWO) underr contract number 782-371-038.
References s
Augusteijn,, T., van Kerkwijk, M.H., van Paradijs, J. 1993, A&A, 267, L55 Augusteijn,, T. 1994, A&A, in press
Hamada,, T., Salpeter, E.E. 1961, ApJ, 134, 683 Home,, K. 1986, PASP, 98, 609
Home,, K., Marsh, T.R. 1986, MNRAS, 218, 761 Iben,, I, Tutukov, A.V. 1984a, ApJ Suppl., 54, 335 Iben,, I, Tutukov, A.V. 1984b, ApJ, 284, 719 Johnson,, H.L. 1966, ARA&A, 4, 193
Kholopov,, P.N., Samus, N.N., Frolov, M.S., et al. 1985, General Catalogue of Variable Stars, Thirdd Edition (Nauka, Moscow)
King,, A. 1988, Qua. Journ. Royal Astron. Soc, 29, 1
Laa Dous, C. 1993, in "Dwarf Novae and Nova-Like Variables", Cataclysmic Variables, NASA/CNRSS Monograph Series on Non-Thermal Phenomena in Stellar Atmospheres, Eds. M.. Hack and C. La Dous
Nelson,, L.A., Rappaport, S., Joss, P.C. 1986, ApJ, 304, 240 O'Donoghue,, D., Kilkenny, D. 1989, MNRAS, 236, 319
Paczynski,, B., Schwarzenberg-Czerny, A. 1980, Acta Astron., 30, 127 Paczynski,, B., Sienkiewicz, R. 1981, ApJ, 248, L27
Patterson,, J. 1984, ApJ Suppl., 54, 443 Press,, W.H., Rybicki, G.B. 1989, ApJ, 338, 277 Pojmariski,, G. 1986, Acta Astron., 36, 69 Pylyser,, E., Savonije, G.J. 1988, A&A, 191, 57 Pylyser,, E., Savonije, G.J. 1989, AfcA, 208, 52
Rappaport,, S.A., Joss, P . C , Webbink, R.F. 1982, ApJ, 254, 616 Rappaport,, S.A., Verbunt, F., Joss, P.C. 1983, ApJ, 275, 713
Ritter,, H. 1994, in Evolutionary links in the zoo of interacting binaries, Ed. F. D'Antona, Mem-oriee della Societa Astronomica Italiana, in press
Ritter,, H., Kolb, U. 1994, in X-ray Binaries, Eds. W.H.G.Lewin, J. van Paradijs and E.P.J, van denn Heuvel (Cambridge Univ. Press), in press
Schneider,, D.P., Young, P.J. 1980, ApJ, 238, 946 Schoembs,, R., Hartmann, K. 1983, A&A, 128, 37 Shafter,, A.W. 1983, ApJ, 256, 222
Shatter,, A.W., Szkody, P., Thorstensen, J.R. 1986, ApJ, 308, 765 Sienkiewicz,, R. 1984, Acta Aston., 34, 325
Silva,, D.R., Cornell, M.E. 1992, ApJ Suppl., 81, 865
Singer,, R., Kolb, U., Ritter, H. 1993, Astron. Ges. Abstract Ser., 9, 39 Spruit,, H.C., Ritter, H. 1983, A&A, 124, 156
Stehle,, R.H. 1993, Habilitation Thesis, Universitat München Stone,, R.P.S. 1977, ApJ, 218, 767
Szkody,, P., Mateo, M. 1984, ApJ, 280, 729
Tutukov,, A.V., Fëdorova, A.V., Ergma, E.V., Yungel'son, L.R. 1985, Pis'ma Astron. Zh., 11, 123 3
Vann Amerongen, S., Damen, E., Groot, M., Kraakman, H., Van Paradijs, J. 1987, MNRAS, 225, 93 3
Vann den Heuvel, E.P.J., Bhattacharya, D., Nomoto, K., Rappaport, S.A. 1992, A&A, 262, 97 Verbunt,, F., Zwaan, C. 1981, A&A, 100, L7
Vogt,, N. 1981, Mitt. Astron. Gesell., 57, 79
Warner,, B. 1976, IAU Symposium 73: Structure and Evolution of Close Binary Systems, Eds. P.. Eggleton, S. Mitton and J. Whelan (Reidel),85
Warner,, B. 1987, MNRAS, 227, 23
