3 V337 Aql

V337 Aql (HD 177284) has been known as an eclipsing variable for a long time. A photoelectric light curve at an effective wavelength of $\lambda = 5150$ Å was obtained by Catalano et al. (1971). Later, Alduseva (1977) presented UBV light curves, which, however, suffer from a rather poor phase coverage. The period of the binary was studied, among others, by Mayer et al. (1998). The period is not constant, and reasons for its variability so far remain unclear. One conceivable explanation is the suggested light-time effect due to a third body. For the phasing of our radial velocities the following linear ephemeris was used:

$${\rm Prim.~min.} = {\rm HJD}~~2448779.5175 + 2\fd7338794 \cdot E .$$

Radial velocities were already measured by Neubauer (1943) and Feast & Thackeray (1963). However, in the first paper only the mean of 6 measurements was given, and no variability of the radial velocity was recognized. Feast & Thackeray first classified the spectra as being of SB2 type and measured radial velocities on plates from 4 nights (but the lines appeared resolved into two components on one plate only).

Figure 1: Spectrum of V337 Aql at phase 0.766.

An example of a spectrum is given in Fig. 1. Only H$\beta$ and He  I (4922 and 5015) lines are present. When measuring radial velocities, we noticed that the H$\beta$ line profile strongly deviated from a simple Gaussian, while an approximation of the observed profile by two Gaussians of different widths and depths gave a reasonably good representation of the line features. Velocities of the primary component of the H$\beta$ line are systematically more negative by about 16 km s^-1 compared to the same component of the He  I 4922 line. Most probably, this effect is due to the contribution of the Pickering He  II 4859.32 Å  line. The secondary component is not well separated, and hence its velocities less certain. The same behaviour was observed by us in the case of the O 8-type binary AB Cru (Lorenz et al. 1994), where this systematic deviation reached 27.7 km s^-1. Unfortunately, we do not know the strength of other He  II lines to study the effect of blending of hydrogen Balmer lines with He  II components on the radial velocities more quantitatively.

 

 

Table 1: Journal of new spectra and measured radial velocities.

JD (mid-exp.)	exp. time	phasea	spectral
-2 400 000	(min)		region
V337 Aql:				Prim.: 4922	Sec.: 4922	Prim: H$\beta$	Sec.: H$\beta$
49909.374	90	0.2816	4826-5035	-79.6	342.6	-96.0	325.3
49909.439	90	0.3054	4826-5035	-75.3	328.3	-97.4	325.7
49909.500	60	0.3277	4826-5035	-72.2	304.5	-88.3	305.8
49913.366	90	0.7418	4826-5035	161.9	-282.6	158.1	-277.1
49913.431	90	0.7656	4826-5035	170.0	-273.8	154.3	-263.4
49913.490	60	0.7871	4826-5035	159.1	-266.2	156.0	-276.9
49914.491	60	0.1533	4826-5035	-59.4	276.4	-77.4	285.2
49914.524	30	0.1654	4826-5035	-63.5	291.5	-94.4	303.4
V649 Cas:				Prim.: 4922	Sec.: 4922
49907.434	30	0.3078	6510-6720	-117.1	244.2
49907.559	20	0.3601	4668-4880	-110.1
49907.633	30	0.4036	4826-5035	-77.9	159.7
49908.397	20	0.7105	4826-5035	103.7	-285.0
49908.424	40	0.7218	4826-5035	104.9	-287.9
49908.451	30	0.7331	4826-5035	106.2	-287.9
49908.481	40	0.7456	4826-5035	104.9	-284.9
49908.560	40	0.7787	4826-5035	108.0	-291.0
49908.590	40	0.7912	4826-5035	104.9	-285.0
49909.631	15	0.2266	4826-5035	-125.4	263.2
49909.642	15	0.2312	4826-5035	-126.6	260.2
49914.435	30	0.2355	4826-5035	-126.2	257.5
49914.456	25	0.2443	4826-5035	-126.2	251.4
49915.675	20	0.7541	4826-5035	109.3	-290.9
V382 Cyg:				Prim.: 4542	Sec: 4542	Prim.: 4686	Sec.: 4686	Prim.: H$\beta$	Sec.: H$\beta$
49526.378	60	0.7020	4524-4736	257.4	-349.7	277.0	-362.6
49526.433	60	0.7312	4524-4736	271.1	-339.6	275.6	-362.0
49526.475	60	0.7535	4524-4736	268.1	-344.5	283.0	-356.6
49526.525	60	0.7800	4524-4736	273.0	-338.0	277.1	-336.9
49526.643	60	0.8426	4666-4879			233.5	-282.9	203.3	-296.6
49527.365	60	0.2255	4524-4736	-241.6	374.7	-257.2	370.6
49527.412	60	0.2504	4524-4736	-241.7	383.2	-259.1	376.3
49527.458	60	0.2748	4524-4736	-231.5	378.0	-260.1	383.3
49527.496	45	0.2950	4524-4736	-221.3	373.9	-247.1	376.5
49528.363	60	0.7548	4674-4888			261.0	-349.5	233.8	-362.6
49528.409	60	0.7792	4674-4888			254.1	-333.6	223.8	-358.7
49529.362b	60	0.2846	6515-6725					-254.0	308.8
49530.644	30	0.9645	6515-6725
49908.365	60	0.2907	4826-5035					-263.4	316.3
49915.644	60	0.1512	4826-5035					-241.1	270.9
V431 Pup:				Prim.: 4713	Prim.: 4922	Sec.: 4922	Prim.: H$\beta$	Prim.: H$\alpha$
48674.696	65	0.7436	4590-4905	-73.7
48678.613	65	0.1618	4590-4905	140.6
48679.615	65	0.2688	4590-4905	127.6
49024.538	60	0.0969	4628-4953	138.2	149.9	-206
49026.595	50	0.3165	4628-4953	87.4	96.3
49029.610	60	0.6385	4628-4953	-49.5	-52.1	199
49146.470	60:	0.1154	4826-5143		153.0	-162	140.0
49148.494	60:	0.3315	4826-5143				69.3
49151.461	60:	0.6483	4826-5143		-70.8		-77.8
49449.534	30	0.4746	4903-4942		21.9
49450.565	30	0.5846	4903-4942		-32.5
49451.518	30	0.6863	4903-4942		-68.9	144
49452.559	45	0.7974	6534-6592					-67.3

^a Heliocentric correction applied.
^b Instead of H$\beta$, radial velocities measured for H$\alpha$ are given.

The He  I line components are well separated, and for the 4922 line easily measurable. The mean difference of both methods mentioned above (SPEFO versus GAUSS) is +0.9 km s^-1  for the primary and +1.7 km s^-1  for the secondary. Averages from both methods are given in Table 1. However, the primary component in the 5015 line always exhibits some asymmetry.

 

 

Table 2: Parameters of V337 Aql, V649 Cas and V382 Cyg.

Parameter	unit	V337 Aql		V649 Cas		V382 Cyg
		individual $V\gamma$	common $V\gamma$	individual $V\gamma$	common $V\gamma$	individual $V\gamma$	common $V\gamma$
K1	km s-1	123.4	122.8	116.8	117.4	267	268
K2	km s-1	309.8	308.9	275.8	276.5	367	367
$V_1\gamma$	km s-1	+40.2	37.5	-9.0	-11.7	+7.8	+9.9
$V_2\gamma$	km s-1	+32.2	37.5	-15.8	-11.7	+14.3	+9.9
$a\sin i$	$R_{\odot}$		23.4		18.6		23.6
$m_1\sin^3 i$	$M_{\odot}$		16.52		10.6		29.0
$m_2\sin^3 i$	$M_{\odot}$		6.58		4.5		21.0

Figure 2: Radial velocity curve for V337 Aql; filled circles - He  I; crosses - H$\beta$.

Figure 3: Light curve of V337 Aql obtained by Catalano et al. (1971) at an effective wavelength of 5150 Å  (open circles: normal points) together with the best fit MORO solution (solid line).

Due to these reasons, we consider only the velocities measured for the 4922 line as reliable. The corresponding radial velocity curve is shown in Fig. 2 and the resulting parameters of the orbit are given in Table 2. The value of inclination $i=86\degr$ found by Catalano et al. (1971) appeared us rather uncertain, so we solved the light curve published by Catalano et al. again using the MORO code (Drechsel et al. 1995). The results are given in Table 3. The normal points as given by Catalano et al. at an effective wavelength of 5150 Å  together with the best fit solution (solid line) are shown in Fig. 3. The corresponding system configuration in terms of a meridional intersection of Roche equipotentials is displayed in Fig. 4. The system is semi-detached, with the secondary filling its critical Roche volume.

 

 

Table 3: Light curve solution of V337 Aql.

Fixed parameters:
q (= M2/M1)	0.398
$T_{\rm eff}(1)$	28 000 K
$A_1\ ^{a}$	1.0
$A_2\ ^{a}$	1.0
$g_1\ ^{b}$	1.0
$g_2\ ^{b}$	1.0
$x_1(\lambda 5150)\ ^{c}$	0.26
$x_2(\lambda 5150)\ ^{c}$	0.29
Adjusted parameters:
i	$80\fdg7 \pm 0\fdg5$
$T_{\rm eff}(2)$	$23~900~{\rm K} \pm 700$ K
$\Omega_1$	$2.939 \pm 0.057$
$\Omega_2$	$2.624 \pm 0.024$
$L_1(\lambda 5150)\ ^{d}$	$0.696 \pm 0.013$
$l_3(\lambda 5150)\ ^{e}$	0.000
$\delta_1\ ^{f}$	$0.023 \pm 0.013$
$\delta_2\ ^{f}$	$0.013 \pm 0.005$
Roche radii: g
$r_1({\rm pole})$	$0.381 \pm 0.008$
$r_1({\rm point})$	$0.425 \pm 0.014$
$r_1({\rm side})$	$0.397 \pm 0.023$
$r_1({\rm back})$	$0.411 \pm 0.011$
$r_2({\rm pole})$	$0.288 \pm 0.005$
$r_2({\rm point})$	$0.391 \pm 0.005$
$r_2({\rm side})$	$0.302 \pm 0.006$
$r_2({\rm back})$	$0.394 \pm 0.009$

^a

Bolometric albedo.

^b

Gravitational darkening exponent.

^c

Linear limb darkening coefficient; theoretical value taken from Wade & Rucinski (1985).

^d

Relative luminosity L₁/(L₁ + L₂).

^e

Fraction of third light at maximum.

^f

Radiation pressure parameter, see Drechsel et al. (1995).

^g

Fractional Roche radius (relative to separation of mass centers).

Figure 4: Semi-detached system configuration of V337 Aql corresponding to the light curve solution shown in Fig. 3; solution parameters are given in Table 3.