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Astronomy Reports, Vol. 48, No. 12, 2004, pp. 1019­1028. Translated from Astronomicheski Zhurnal, Vol. 81, No. 12, 2004, pp. 1119­1129. i Original Russian Text Copyright c 2004 by Cherepashchuk, Borisov, Abubekerov, Klochkov, Antokhina.

Parameters of V404 Cyg--A Black-Hole Binary
A. M. Cherepashchuk1, 2 , N. V. Borisov3, ´ M. K. Abubekerov1 , D. K. Klochkov1, and E. A. Antokhina
1 2

2

Moscow State University, Vorob'evy gory, Moscow, 119899 Russia Sternberg Astronomical Institute, Universitetski i pr. 13, Moscow, 119899 Russia 3 Special Astrophysical Observatory, Nizhni i Arkhyz, Russia
Received March 15, 2004; in final form, May 27, 2004

Abstract--We present the results of spectroscopic observations of the X-ray binary V404 Cyg obtained on the 6-m telescope of the Special Astrophysical Observatory in 2001­2002. We have used a statistical approach to interpret the radial-velocity curve of V404 Cyg. We derived the dependence of the mass of the X-ray emitting component mx on the mass of the optical component mv via an analysis of the radial° velocity curve based on profiles of the CaI 6439.075 A absorption line synthesized in a Roche model. Using the orbital inclination estimated from the ellipticity of the optical component, i = 54 -64 , and the component-mass ratio q = mx /mv = 16.7 found from the rotational broadening of the spectral lines, we obtain mx = 10.65 ± 1.95 M for the mass of the black hole. c 2004 MAIK "Nauka/Interperiodica".

1. INTRODUCTION The X-ray nova GS 2023+338 was first discovered by the Ginga space probe during an outburst on May 22, 1989 [1]. This discovery was subsequently confirmed by Sunyaev et al. [2]. During the outburst, the magnitude of GS 2023+338 changed from V 18.3m to V = 11.6m . Soon afterward, an optical counterpart to the X-ray source was identified: V404 Cyg, which had been classified as a nova after an outburst in 1938 [3, 4]. The X-ray nova V404 Cyg contains a K0IV optical subgiant that fills its Roche lobe and a black hole that accretes matter from an accretion disk. The mass function of the optical star in V404 Cyg is fv = 6.08 ± 0.06 M [5]; this is much higher than the limiting mass for neutron stars, providing evidence that the compact component in the system is a black hole. The absence of X-ray pulsations from the compact object prevents the direct determination of the mass of the optical component. Estimates of the mass of the optical star based on its spectral type vary from 0.5 M to 1.0 M [6]. Current estimates of the parameters of the X-ray source are not very accurate. Based on the I light curve, the range of possible orbital inclinations was determined to be 46 -73 and the component-mass ratio to be q = mx /mv = 8-12 [7]. The measured semi-amplitude of the radial velocity variations, Kv = 211 ± 4 km/s, yields for the mass function of the optical star fv = 6.3 ± 0.3 M . Assuming that the mass of the subgiant is close to 1.0 M , Wagner

et al. [7] concluded that the mass of the compact object is 8-12 M . A more accurate semi-amplitude for the radial velocity of the optical star was found in [5]: Kv = 208.5 ± 0.7 km/s; this corresponds to the mass function fv = 6.08 ± 0.06 M quoted above. The component-mass ratio q = 16.7 ± 1.3 was estimated from the rotational broadening of lines of metals at ° 6400­6600 A. Assuming that the highest possible orbital inclination is 80 (as follows from the absence of X-ray eclipses [8]) and that the mass of the optical star is 0.2-1.3 M , we obtain for the mass of the compact object 7-24 M . Analysis of the K light curve of V404 Cyg yields the orbital inclination i = 52 -60 [6]. Using the component-mass ratio q = 16.7 [5] and the mass of the optical component 0.5-1.0 M , we find for the mass of the compact object 10-15 M . Analysis of the H light curve of V404 Cyg yields i = 59 -73 [9]. For this range of inclinations, the mass of the black hole does not exceed 12.5 M . For the component-mass ratio q = 16.7, the mass of the black hole is close to 9.5 M . The R light curve combined with the spectroscopic component-mass ratio q = 16.7 [5] gives i = 56 ± 2 [10]; variability of the light curve on a time scale of six hours was reported in this same paper. Six-hour variability of the H profile is also observed, but the brightness and H variations of the system are not correlated [11, 12]. Hynes et al. [13] describe the growth and decline of the equivalent width and

1063-7729/04/4812-1019$26.00 c 2004 MAIK "Nauka/Interperiodica"


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Table 1. Spectroscopic observations of V404 Cyg Date July 12, 2001 July 14, 2001 July 15, 2001 July 16, 2001 June 14, 2002 July 9, 2002 July 10, 2002 July 11, 2002 July 12, 2002 UT 18:07­20:30 18:52­20:26 20:20­21:53 21:09­22:40 17:35­20:14 18:25­19:35 18:43­20:20 16:52­20:02 18:56­19:57 Exposure, s 2700 2700 2700 2700 1800 1800 1800 1800 1800 Number of spectra 3 2 2 2 5 2 3 6 2 ° Spectral interval, A 5700­8200 5700­8200 5700­8200 5700­8200 5500­6800 5500­6800 5500­6800 5500­6800 5500­6800 ° Resolution, A 5.5 5.5 5.5 5.5 3.0 3.0 3.0 3.0 3.0

variations of the H emission profile on time scales down to 1­2 h. Pavlenko et al. [10] include fluctuations of the photoionizing flux from the compact object due to local flares in the accretion disk or the disk corona among possible origins for the variation of the H emission equivalent width [13], however, the mechanism underlying the fast variations of the H equivalent width is not known with certainty. The asymmetry of the H emission wings likewise remains poorly understood (for more details see [13]). Our aim was to more accurately determine the radial-velocity curve of the X-ray nova V404 Cyg and
Table 2. Observed barycentric radial velocities of V404 Cyg (adopted zero Julian epoch is JD0 = 2448813.873 [5]) Phase 0.229 0.295 0.365 0.387 0.535 0.606 0.696 0.770 0.930 Radial velocity, km/s 187.10 195.90 161.20 139.80 -58.39 -111.09 -198.10 -212.50 -68.42

the parameters of the close binary system, as well as study the short-time-scale variability of the H emission profile. 2. OBSERVATIONAL DATA Two sets of spectroscopic observations of V404 Cyg were obtained using the 6-m telescope of the Special Astrophysical Observatory between July 12 and 16, 2001 and between June 11 and July 12, 2002. The observations were carried out at the primary focus using a UAGS high-power, long-slit spectrograph and a PM1024 CCD with 1024 â 1024 pixels and a pixel size of 24 â 24 µm. In 2001, we used a diffraction grating with a dispersion of 651 lines/mm, yielding an inverse linear dispersion ° of 3.1 A/pixel in the spectral interval studied, 5700­ ° 8200 A. The resolution of the resulting spectrograms ° was 5.5 A. In 2002, we used a R1305/17 diffraction grating with a dispersion of 1305 lines/mm, providing an in° verse linear dispersion of 1.5 A/pixel and a resolution ° ° of 3.0 A at 5500­6800 A. A log of the observations is given in Table 1. All the spectra were calibrated against a HeNe light source. The spectra were reduced using the MIDAS package, including standard flat fielding, background subtraction, bias correction, and elimination of "hot" pixels. The single white dwarf BD+284211 was used as a spectrophotometric standard for all the spectrograms. The K0IV star HR8857 [5] was used as a radial-velocity standard. The radial velocities of V404 Cyg were derived ° from the shift of blends at 6400­6520 A relative to the
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PARAMETERS OF THE X-RAY NOVA V404 Cyg

1021

Vr, km/s 240 200 160 120 80 40 0 ­40 ­80 ­ 120 ­ 160 ­ 200 ­ 240 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fig. 1. Folded observed radial-velocity curve of the optical component of V404 Cyg. The open circles show the observed radial velocities derived by Casares and Charles [5] from absorption lines of metals, while the open triangles show the radial velocities found in the present study. The solid curve is the theoretical radial velocity curve for the ° Roche model based on the synthesized CaI 6439.075 A absorption line profile assuming mx = 10.46 M , mv = 0.7 M , and i = 59 (the remaining parameters are listed in Table 3); no correction for the response function has been made. The dashed curve shows the theoretical radial-velocity curve for a point-mass model with mx = 10.46 M , mv = 0.7 M ,and i = 59 . This latter curve nearly coincides with the curve for the Roche model.

­ ­ ­ ­

Vr, km/s 240 200 160 120 80 40 0 ­40 ­80 120 160 200 240 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fig. 2. Radial velocities averaged over phase intervals (filled circles). For comparison, theoretical radial-velocity curves for the Roche model (solid) and point-mass model (dashed) for the case mx = 10.46 M , mv = 0.7 M , and i = 59 are shown.

blends in the same wavelength interval of the radialvelocity standard HR 8857. Table 2 gives the observed radial velocities of the optical component of V404 Cyg corrected for the Earth's motion and the systemic velocity. We constructed the folded radial-velocity curve using our spectroscopic data along with the radial velocities from [5], which were derived from the shift for ° the wavelength interval 6212­6605 A relative to this same interval in the spectrum of the radial-velocity standard, HR 8857. The folded curve enabled us to determine the orbital period of the V404 Cyg binary more precisely. We adopted JD0 = 2448813.873 for the zero Julian epoch [5]. The new orbital period, . Porb = 6d4715 ± 0.0001, agrees with the old value, d4714 ± 0.0001 [5], within the errors. Porb = 6 . The folded observed radial-velocity curve based on our spectroscopic data and the data of [5] is shown in Fig. 1. The radial velocities were averaged over phase intervals to reduce the influence of random errors (Fig. 2). Since the observed radial velocities are not distributed in phase very uniformly, the rms deviation of the mean radial velocity at phase 0.508
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is 37.80 km/s (or 18.1% of the radial-velocity semiamplitude). This large rms deviation is due to the large gradient of the regular radial-velocity variations near phase 0.5. Since the rms deviation of the observed radial velocity Vr at phase 0.508 is much larger than in other phase intervals (where it is 2­ 3% of the radial-velocity semiamplitude; Fig. 2), and thus gives rise to an appreciable "perturbation" of the residuals [see (1) below], we excluded the mean observed radial velocity at phase 0.508 when fitting the mean radial-velocity curve. 3. FITTING OF THE MEAN RADIAL-VELOCITY CURVE The optical component of V404 Cyg fills its inner Roche lobe. The tidal action of the relativistic companion makes the shape of the optical star nonspherical. The side of the optical component facing the relativistic object is heated by the incident X-ray emission. Therefore, we fit the mean radial velocities using a Roche model that is able to take into account this interaction between the components to some extent. The parameters of the Roche model for the X-ray binary V404 Cyg are given in Table 3. The presence of observable X-ray emission from theV404 Cyg binaryprovidesevidencethatthe K0IV optical star fills its Roche lobe. Since this star fills its Roche lobe over a time determined by its nuclear evolution time scale, which is 1010 yr, the orbit of the close binary has enough time to circularize, and the rotation of the optical component becomes


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Table 3. Numerical input parameters for the synthesis of the radial-velocity curves of the optical component of V404 Cyg in the Roche model P ,day e i,deg µ f Teff ,K kx A u 6.4715 0.0 Period Eccentricity

54, 59, 64 Orbital inclination 1.0 1.0 5500 0.08 0.03 1.0 0.5 Roche lobe filling factor for optical component Ratio of the rotational velocity of the optical star to the synchronous rotational velocity Effective temperature of the optical component Gravitational darkening coefficient Ratio of the X-ray luminosity of the relativistic component and bolometric luminosity of the optical component, Lx /Lv Coefficient of reprocessing of incident X-ray radiation Limb-darkening coefficient

synchronous with the orbital motion. Therefore, our calculations assume that the orbit of V404 Cyg is circular and the ratio of the spin and orbital rotational velocities is f = 1.0. We consider the masses of both components and the orbital inclination of V404 Cyg to be unknown parameters. We found the solution via a step-by-step search through the parameter values considered. We obtained a set of masses for the compact object mx for masses of the optical component mv of 0.5 M , 0.7 M , and 0.9 M and orbital inclinations i of 54 , 59 , and 64 . This yields the dependence of the mass of the compact object on the mass of the optical component and orbital inclination. The orbital inclinations were selected based on earlier fitting of the R, K , and H light curves of the close binary, which gave the estimates 56 ± 2 [10], 56 ± 4 [6], and 59 - 73 [9], respectively. The statistical adequacy of the model was tested at the = 5% significant level. Since the radial velocity of the optical component was determined from absorption lines of metals at ° 6200­6500 A both in the present study and in [5], our theoretical radial velocities are based on syn° thesized profiles of the CaI 6439.075 A absorption line. Since absorption lines of metals in the spectrum of the optical component of V404 Cyg have small ° widths (1 A), the theoretical radial-velocity curves ° were computed from the CaI 6439.075 Aprofile convolved with a Gaussian instrumental profile with a ° full width at the half maximum of FWHM = 0.5 A. This FWHM was adopted because most of the radial velocities included in the folded curve (Fig. 2) were

derived from spectra obtained with an instrumental ° FWHM = 0.5 A [5]. For comparison purposes, we also fit the observed mean radial-velocity curve of ° V404 Cyg using synthesized CaI 6439.075 Aprofiles without convolving with a response function. Figure 3 ° shows the synthesized CaI 6439.075 A absorption profiles at orbital phases of 0.00 and 0.25 for both cases. The residual differences between the mean observed and theoretical radial-velocity curves were computed as
M

(nj - 1) M

M

nj (Vj
j =1 M j =1

teor

¯ - Vj

obs 2 )

(mx ) =

j =1

, (1) nj (nj - 1)
2 j

¯ is the observed radial velocity averaged where Vj ¯ over a phase interval centered at j , Vj teor is the theoretical radial velocity at the same phase, j is ¯ obs from the observed radial the rms deviation of Vj ¯ velocity in the phase interval with its center at j , M is the number of phase intervals, and nj is the number of individual averaged observations in phase interval j . The value of (mx ) is distributed according to a Fisher law FM, M (nj -1), [14]. We can find the set
j =1

obs

of acceptable values for mx for a given significance level and a specified value of mv . This set contains
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PARAMETERS OF THE X-RAY NOVA V404 Cyg

1023

I 1.01

()

I 1.01

(b)

0.99

0.99

0.97

0.97

0.95

0.95

0.93

0.93

0.91

0.91

0.89 0.87 6437

0.89 0.87 6437

6438

6439

6440

6441 ° , A

6438

6439

6440

6441 ° , A

° Fig. 3. (a) Synthetic profiles of the CaI 6439.075 A absorption line calculated in the Roche model for mx = 10.46 M , mv = 0.7 M , and i = 59 (for the remaining parameters see Table 3) at orbital phases 0.00 (solid) and 0.25 (dashed). ° (b) The same profiles convolved with a Gaussian response function with FWHM = 0.5 A. The profiles at orbital phase 0.25 are corrected for the Doppler shift.

values of mx obeying the condition (mx ) F
M j =1

M,

(nj -1),

.

The algorithm used to compute the theoretical absorption-line profiles and theoretical radial-velocity curves is described in [15, 16], and we do not present it here. Note, however, that computing the local shape ° of the CaI 6439.075 A absorption profile using this algorithm requires the solution of the radiative-transfer equation for each area element. This differs from the algorithm for synthesizing radial-velocity curves from the H absorption profile applied in [17], which included computation of the local shape of the profile from an area element via the interpolation of tabulated values of this profile given by Kurucz [18]. The residuals found by fitting the mean observed radial-velocity curve are shown in Fig. 4; this figure shows that it is important to take into account the instrumental profile. The theoretical radial-velocity curves computed without including the effect of the ° response function on the synthesized CaI 6439.075 A
ASTRONOMY REPORTS Vol. 48 No. 12 2004

absorption profile are not in agreement with the observed data: the close-binary models are rejected at the = 5% significance level (Fig. 4b). Table 4 presents the relation between the component masses for various orbital inclinations derived in the Roche model based on the synthesized ° CaI 6439.075 A profiles convolved with the response function. The same relation without this convolution is presented in Table 5. The results are shown in graphical form in Fig. 5. Since the residual differences between the theoretical and observed radial-velocity curves are unacceptably large at the = 5% significance level when the response function is not taken into account, the confidence intervals for the mass of the compact object are omitted in Table 5 and Fig. 5b. 4. DEPENDENCE OF THE SHAPE OF THE RADIAL-VELOCITY CURVE OF V404 Cyg ON ORBITAL INCLINATION We carried out special calculations of the theoretical radial-velocity curves in the Roche model to study the dependence of the shape of the radial-velocity curve on the orbital inclination of V404 Cyg. The


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CHEREPASHCHUK et al.

2.1 () 59° 54°

2.1 (b) 64° 59°

54°

2.0

64°

2.0

1.9

1.9

1.8

8

9

10

11

12

13 mx

1.8

8

9

10

11

12

13 mx

Fig. 4. (a) Residuals for the fitting of the radial-velocity curve derived in the Roche model for mv = 0.7 M and orbital inclinations i = 54 , 59 , and 64 (for the remaining parameters see Table 3). The curve is based on the synthesized ° ° CaI 6439.075 A profile and includes the effect of a response function with FWHM = 0.5 A. (b) Same as (a) but without the effect of the response function.

mass of the optical star was taken to be mv = 0.7 M , and the mass of the black hole to be mx = 10 M . Calculations were carried out for inclinations i = 40 , 54 , 64 , and 80 , with the remaining parameters of the Roche model unchanged (see Table 3). Since the radial-velocity semiamplitude Kv increases with the orbital inclination, the computed theoretical radial velocity curves were normalized to the maximum radial velocity in the phase interval 0.0­0.5. The difference in the shapes of the radial-velocity curves is maximum at phase = 0.36. The difference of the radialvelocity curves for i = 40 and i = 80 was 0.3% of the semiamplitude Kv when the response function was taken into account when computing the synthe° sized CaI 6439.075 A profiles and 0.5% when the response function was not taken into account. For comparison, the difference in the shape of the radialvelocity curves for close binaries with parameters similar to that of Cyg X-1 (q = mx /mv 0.5) was 3% of Kv when the orbital inclination was varied from i = 40 to i = 80 [19]. In the case of the X-ray nova V404 Cyg, increasing the orbital inclination from i = 54 to i = 64 resulted in variations of the shape of the radialvelocity curve of the semiamplitude Kv by 0.10% or

° 0.13% when the CaI 6439.075 Aprofile was or was not convolved with the response function. Because the shape of the radial-velocity curve varies little with such variations of the orbital inclination, the residual minima for the different inclinations do not differ as much as in the case of Cyg X-1 [19, Fig. 5] (Fig. 4). The rms error Vr of the observed mean radialvelocity curve of V404 Cyg is (2­3)% of its semiamplitude Kv , preventing estimation of the orbital inclination as was done for Cyg X-1 [19]. However, the Roche model can be used to estimate the orbital inclination from the radial-velocity curve, since the minimum residuals are different for different inclinations (Fig. 4). This is especially clearly visible in Fig. 4b. For successful estimation of the orbital inclination of V404 Cyg from the radial-velocity curve, Vr must be 0.10% of Kv or, in absolute units, 0.2 km/s. Therefore, further high-quality spectroscopic observations of V404 Cyg are promising for this purpose. 5. COMPONENT MASSES IN V404 Cyg The component-mass ratio q = mx /mv from the rotational broadening of metal lines spectrum of the optical component of V404 16.7 [5]. By drawing the corresponding line
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found in the Cyg is in the

2004


PARAMETERS OF THE X-RAY NOVA V404 Cyg Table 4. Dependence of the mx on mv in the Roche model. The effect of the response function on the synthesized CaI ° 6439.075 Aprofile is taken into account mx , M i = 54 0.5 0.7 0.9 11.87 12.22 12.56


1025

Table 5. Dependence of mx on mv in the Roche model. The effect of the response function on the synthesized CaI ° 6439.075 Aprofile has not been included mx , M i = 54 0.5 0.7 0.9


mv , M
+0.24 -0.22 +0.30 -0.27 +0.28 -0.27

mv , M


i = 59 10.13 10.46 10.78

i = 64 8.87 9.21 9.53



i = 59



i = 64 8.86 9.18 9.48



+0.21 -0.23 +0.25 -0.23 +0.26 -0.25

+0.22 -0.19 +0.21 -0.18 +0.20 -0.19

11.83 12.20 12.54

10.10 10.42 10.77

plot showing the relation between the component masses (Fig. 5), we find that, for i = 54 -64 , the masses of the black hole and optical star are mx = 8.7-12.6 M and mv = 0.52-0.76 M .Thus, the mean mass of the black hole in V404 Cyg is 10.65 ± 1.95 M . 6. VARIABILITY OF THE H EMISSION PROFILE Casares et al. [11] were the first to point out the S-wave variability of the H emission profile; they estimated the period of this variability to be 5.7 h. Later, the more accurate period of 5.656 h was found from a larger number of spectrophotometric observations obtained in 1990­1991 [12]. The most detailed study of the short-time optical variability and behavior of the H line in V404 Cyg was carried out by Hynes et al. [13], who found a qualitative correlation between the behavior of the continuum and the H equivalent width. An increase of the continuum is observed with increase in the H equivalent width. Both the continuum from the accretion disk and the H flux vary by more than a factor of two over one to two hours. During the nights of June 14 and July 11, 2002, ° we obtained five and six spectra at 5500­6800 A (Table 1), enabling us to study the behavior of the H line on time scales 30 min. The H emission profiles are shown in Fig. 6, and the profiles averaged over a night are shown in Fig. 7. We determined the mean profile by taking the arithmetic mean of all H profiles obtained during a night. Figures 6 and 7 show that the emission profile not only experiences significant variations during the course of a night, but also varies strongly from night to night. We investigated the short-term variability of the H emission profile. We estimated the deviation of a given H profile from the profile averaged over the night using the Fisher statistical criterion, averaging the relative intensities of the H emission lines over
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° wavelength intervals of 5 A. The residuals were computed as
M

(nj - 1) M (2) (t))2 ,

(I
M

obs

(t)) =

j =1

nj (Ij â
j =1 M j =1

mean

¯ - Ij

obs

nj (nj - 1)

2 j

¯ obs where Ij is the observed mean relative intensity of ¯ the H line in the wavelength interval centered at j mean at time t, Ij is the mean relative intensity of the averaged H line profile in the wavelength interval ¯ centered at j at time t, j is the rms deviation of obs ¯ ¯ Ij (t) in a given wavelength interval centered at j , M is the average number of wavelength intervals, and nj the number of averaged relative intensities in the wavelength interval j . We found the times t when the H profile deviated significantly from the nightly averaged profile for a specified significance level . The deviation of a profile from the mean profile was considered to be significant if (I
obs

(t)) F

M j =1

M,

(nj -1),

.

We considered the = 5% significance level for our analysis. The results are presented in Fig. 8, which shows that significant deviations from the mean level occurred on a time scale of about two hours on the night of June 14, 2002, and on a time scale of 0.5­1 h on the night of July 11, 2002. The behavior of the line is striking. A phase of intense growth of the emission line component can suddenly change into a decrease, and vice versa. The change of phases may occur in 0.5 h (Figs. 6b and 8b).


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mx 13 (a) 12

q = 16.7 i = 54°

mx 13 (b) 12
i = 54°

11

i = 59°

11
i = 59°

10
i = 64°

10
i = 64°

9

9

8 0.4 0.5 0.6 0.7 0.8 0.9 1.0 m

8 0.4 0.5 0.6 0.7 0.8 0.9 1.0 m

Fig. 5. (a) Relation between the masses of the compact object and optical star in V404 Cyg derived via analysis of the mean ° radial-velocity curve in the Roche model based on the CaI 6439.075 Aprofile and convolved with a Gaussian response function ° The straight line corresponds to the component-mass ratio q = mx /mv = 16.7 [5]. (b) Same as (a) with FWHM = 0.5 A. without including the effect of the response function.

I 3.5

June 14, 2002

()

I 3.5

July 11, 2002

(b)

2.5
19h 42m

2.5

19h 31m

18h 59m

19h 12m

18h 28m

1.5
18h 39m

1.5
17h 57m

18h 07m

17h 25m

0.5
17h 35m

0.5
16h 52m

­ 0.5 ­ 0.5 6530 6540 6550 6560 6570 6580 6590 6600 6530 6540 6550 6560 6570 6580 6590 6600 ° ° , A , A
Fig. 6. H emission profiles obtained on (a) June 14, 2002 at orbital phase = 0.365 and (b) July 11, 2002 at orbital phase = 0.535. For ease of viewing, the profiles have been shifted vertically relative to one another.

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PARAMETERS OF THE X-RAY NOVA V404 Cyg
I 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 6530 6540 6550 6560 6570 6580 6590 ° , A

1027

3.0 2.6 2.2 1.8 1.4 1.0 0.6 17.0 12 8 4 0 16.5

June 14, 2002

(a)

17.5

18.0

18.5

19.0

19.5

20.0 UT (b)

July 11, 2002

Fig. 7. Mean H emission profiles obtained during the nights of June 14, 2002 at orbital phase = 0.365 (solid) and July 11, 2002 at orbital phase = 0.535 (dashed).

17.0

17.5 18.0 18.5

19.0

19.5

20.0 UT

The origin of the H variability has not been established. Proposed sources of the S-wave variability include the motion of a hot spot in the accretion disk [12], chromospheric activity of the optical component, and reconnection of magnetic field lines in the accretion disk [13]. No unique mechanism for the S-wave short-time-scale variability of the H emission in V404 Cyg is known. Correct interpretation of the data requires a long series of observations with high time resolution, and studies in this direction should be continued. 7. CONCLUSION The main result of our study is our derivation of the relation between the masses of the two components in the X-ray nova V404 Cyg in a Roche model for orbital inclinations i = 54 -64 . Combined with the spectroscopically determined component-mass ratio q = 16.7 [5], these dependences yield mx = 10.65 ± 1.95 M for the mass of the black hole and mv = 0.64 ± 0.12 M for the mass of the optical star. It is not currently possible to constrain the orbital inclination of V404 Cyg using the observed mean radial-velocity curve. The accuracy required for this is 0.10% of the radial-velocity semiamplitude Kv , while the accuracy of the observed mean radialvelocity curve is (2-3)% of Kv . Thus, the averaged effects of the orbital variability of the absorption-line profiles contributing to the radial-velocity curves of low-mass X-ray binary systems (q 1) influence the shape of the line relatively weakly. Therefore, the orbital inclinations of low-mass X-ray binary systems must be determined directly from the orbital variability of absorption-line profiles [20, 21]. This requires
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Fig. 8. Deviations of the H emission profile from the nightly averaged profile on (a) June 14, 2002 at orbital phase = 0.365 and (b) July 11, 2002 at orbital phase = 0.535. The straight lines show critical levels of the residuals for the Fisher criterion for the = 5% significance level.

high-quality spectra of V404 Cyg with resolution R 50 000 on the largest 8­10 m new-generation telescopes. We also determined the typical time scales for variability of the H emission profile. Significant variations of the profile shape and equivalent width occur on time scales of 0.5-2 h. The origin of variability of the photoionizing flux has not been established [13], and studies of this problem require further spectroscopic observations of V404 Cyg. ACKNOWLEDGMENTS This work was supported by Russian Foundation for Basic Research (project no. 02-02-17524) and a grant from the program "Leading Scientific Schools of Russia" (NSh 388.2003.2). REFERENCES
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Translated by L. Yungel'son

ASTRONOMY REPORTS

Vol. 48 No. 12

2004