In a high-mass X-ray binary (HMXB) a massive, early-type star transfers mass onto a compact companion, a neutron star or a black hole. The potential energy associated with the accreted matter is efficiently converted into X-rays (Davidson & Ostriker 1973). The mass transfer can take place in two different ways: (i) via the massive star's dense stellar wind which is partly intercepted by the strong gravitational field of the compact companion; or (ii) via a flow of matter towards the compact star through the inner Lagrangian point (Roche-lobe overflow). In the latter case an accretion disk is expected to be present in the system, as well as a rapidly spinning X-ray source. The massive star is either an OB supergiant with a dense radiation-driven wind or a Be-type star characterised by strong H $\alpha$ emission arising from a slowly outflowing, dense equatorial disk. For reviews on this subject we refer to Lewin et al. (1995), van Paradijs (1998) and Kaper (2001).

The accretion-induced X-ray luminosity gives a direct measure of the wind density and velocity at the orbit of the X-ray source. In this sense, the compact object acts as a probe in the stellar wind. In OB-supergiant systems, the X-ray source strongly affects the supergiant's radiation-driven wind. The X-ray source ionizes the surrounding wind regions creating an extended (Strömgren) zone of strong ionization that trails the X-ray source in its orbit. This causes the orbital modulation of ultraviolet (UV) resonance lines (Hatchett & McCray 1977; Kaper et al. 1993). Hatchett & McCray predicted this effect to be observable in UV resonance lines of the HMXB HD 153919/4U1700-37. The HM-effect has, however, not been detected in spectra obtained with the International Ultraviolet Explorer (IUE), as shown by Dupree et al. (1978). Although Hammerschlag-Hensberge et al. (1990) reported variations with orbital phase in some subordinate lines, Kaper et al. (1990) reported that these variations are caused by variable Raman-scattered emission lines and are not due to the HM-effect (see also Kaper et al. 1993).

Table 1: System parameters of the HMXBs in our sample. References are: a) Walborn (1973); b) Chevalier & Ilovaisky (1977); c) Webster et al. (1972); d) Conti (1978); e) Bregman et al. (1973); f) Osmer (1973); g) Sadakane et al. (1985); h) Heap & Corcoran (1992); i) Bolton (1975); j) Levine et al. (1991); k) Rappaport & Joss (1983); l) Nagase (1989); m) Kemp (1977); n) van Paradijs & Kuiper (1984); o) Deeter et al. (1987); p) Haberl et al. (1989); q) Bolton & Herbst (1976); r) Kaper (1998).
X-ray companion Optical primary

Name $M_{\rm X}/M$ $_\odot$ $L_{\rm X}$ (erg/s) $^{\rm r}$ Name spec. type $m_{\rm V}$ $M_{\rm\star}/M_\odot$ $R_{\rm\star}/R_\odot$ $a/R_\odot$ $P_{\rm orb}$ (d) d(kpc)

Cyg X-1 13 $^{\rm i}$ $1.3\times10^{37}$ HDE 226868 O9.7 Iab $^{\rm a}$ 8.87 $^{\rm e}$ 21 $^{\rm i}$ 18 $^{\rm i}$ 43 $^{\rm i}$ 5.60000 $^{\rm m}$ 1.8 $^{\rm d}$

LMC X-4 1.38 $^{\rm j}$ $2.2\times10^{38}$ Sk-Ph O8 V-III $^{\rm b}$ 14 $^{\rm b}$ 14.7 $^{\rm j}$ 7.6 $^{\rm j}$ 12 $^{\rm j}$ 1.40839 $^{\rm j}$ 50

SMC X-1 1.05 $^{\rm k}$ $2.6\times10^{38}$ Sk 160 B0 Ib $^{\rm c}$ 13.2 $^{\rm f}$ 17.0 $^{\rm k}$ 16.5 $^{\rm k}$ 25 $^{\rm k}$ 3.89239 $^{\rm n}$ 60

Vela X-1 1.77 $^{\rm l}$ $4.6\times10^{36}$ HD 77581 B0.5 Iab $^{\rm d}$ 6.88 $^{\rm g}$ 23.0 $^{\rm l}$ 34.0 $^{\rm l}$ 52.9 $^{\rm l}$ 8.964416 $^{\rm o}$ 1.9 $^{\rm g}$

4U1700-37 1.8 $^{\rm h}$ $9.8\times10^{35}$ HD 153919 O6.5 Iaf $^{+{\rm a}}$ 6.51 $^{\rm h}$ 52 $^{\rm h}$ 18 $^{\rm h}$ 36 $^{\rm h}$ 3.411652 $^{\rm p}$ 1.7 $^{\rm q}$

**Table 1:** System parameters of the HMXBs in our sample. References are: a) Walborn (1973); b) Chevalier & Ilovaisky (1977); c) Webster et al. (1972); d) Conti (1978); e) Bregman et al. (1973); f) Osmer (1973); g) Sadakane et al. (1985); h) Heap & Corcoran (1992); i) Bolton (1975); j) Levine et al. (1991); k) Rappaport & Joss (1983); l) Nagase (1989); m) Kemp (1977); n) van Paradijs & Kuiper (1984); o) Deeter et al. (1987); p) Haberl et al. (1989); q) Bolton & Herbst (1976); r) Kaper (1998).
X-ray companion	Optical primary
Name	$M_{\rm X}/M$ $_\odot$	$L_{\rm X}$ (erg/s) $^{\rm r}$	Name	spec. type	$m_{\rm V}$	$M_{\rm\star}/M_\odot$	$R_{\rm\star}/R_\odot$	$a/R_\odot$	$P_{\rm orb}$ (d)	d(kpc)

Cyg X-1	13 $^{\rm i}$	$1.3\times10^{37}$	HDE 226868	O9.7 Iab $^{\rm a}$	8.87 $^{\rm e}$	21 $^{\rm i}$	18 $^{\rm i}$	43 $^{\rm i}$	5.60000 $^{\rm m}$	1.8 $^{\rm d}$
LMC X-4	1.38 $^{\rm j}$	$2.2\times10^{38}$	Sk-Ph	O8 V-III $^{\rm b}$	14 $^{\rm b}$	14.7 $^{\rm j}$	7.6 $^{\rm j}$	12 $^{\rm j}$	1.40839 $^{\rm j}$	50
SMC X-1	1.05 $^{\rm k}$	$2.6\times10^{38}$	Sk 160	B0 Ib $^{\rm c}$	13.2 $^{\rm f}$	17.0 $^{\rm k}$	16.5 $^{\rm k}$	25 $^{\rm k}$	3.89239 $^{\rm n}$	60
Vela X-1	1.77 $^{\rm l}$	$4.6\times10^{36}$	HD 77581	B0.5 Iab $^{\rm d}$	6.88 $^{\rm g}$	23.0 $^{\rm l}$	34.0 $^{\rm l}$	52.9 $^{\rm l}$	8.964416 $^{\rm o}$	1.9 $^{\rm g}$
4U1700-37	1.8 $^{\rm h}$	$9.8\times10^{35}$	HD 153919	O6.5 Iaf $^{+{\rm a}}$	6.51 $^{\rm h}$	52 $^{\rm h}$	18 $^{\rm h}$	36 $^{\rm h}$	3.411652 $^{\rm p}$	1.7 $^{\rm q}$

Table 2: SWP number, Reduced Julian Day (RJD) = JD-2440000 and mid-exposure orbital phase $\phi$ of the IUE spectra. Spectra used to construct $\phi \sim 0$ and $\phi \sim 0.5$ averages are indicated by a suffix $\circ$ and +, respectively. Orbital parameters:
HDE 226868/Cyg X-1 $\phi _0 \equiv$ RJD 2804.245 P= $5{\hbox{$.\!\!^{\rm d}$ }}60000(24)$ (Kemp 1977)

Sk 160/SMC X-1 $\phi _0 \equiv$ RJD 3000.1626(8) P= $3{\hbox{$.\!\!^{\rm d}$ }}89239(2)$ (van Paradijs & Kuiper 1984)

Sk-Ph/LMC X-4 $\phi _0 \equiv$ RJD 7742.4904(2) P= $1{\hbox{$.\!\!^{\rm d}$ }}40839(1)$ (Levine et al. 1991)

HD 77581/Vela X-1 $\phi _0 \equiv$ RJD 4279.0466(37) P= $8{\hbox{$.\!\!^{\rm d}$ }}964416(49)$ (Deeter et al. 1987)

HD 153919/4U1700-37 $\phi _0 \equiv$ RJD 6161.3400(30) P= $3{\hbox{$.\!\!^{\rm d}$ }}411652(26)$ (Haberl et al. 1989).

SWP RJD $\phi$ 1968 3699 0.775 21569 5656 0.728 22324 5752 0.407 4753 3958 0.2124

Cyg X-1 2020 $^\circ$ 3705 0.221 21607 5660 0.888 32961⁺ 7214 0.432 5180 4003 0.3758

1273 $^\circ$ 3599 0.929 2044 $^\circ$ 3708 0.906 21608 $^\circ$ 5660 0.019 32967⁺ 7215 0.543 25586 6160 0.7770

1445 3629 0.317 6203 $^\circ$ 4102 0.185 21609 $^\circ$ 5660 0.066 33085⁺ 7233 0.550 25587 6160 0.7884

1451⁺ 3629 0.441 6207⁺ 4103 0.406 21611 5661 0.166 46144 8933 0.165 25588 6160 0.8020

1478 $^\circ$ 3632 0.971 6219⁺ 4104 0.705 21612 5661 0.217 46151 8934 0.278 25589 6160 0.8169

1500⁺ 3636 0.540 6224 $^\circ$ 4105 0.949 21613 5661 0.267 46167 8935 0.406 25590 6160 0.8299

1515 $^\circ$ 3638 0.047 7092 4182 0.826 21614 5661 0.315 4U1700-37 25591 6160 0.8423

1979 3701 0.270 7094 4182 0.878 21615 5661 0.360 1476 3632 0.7960 25592 6160 0.8545

2049⁺ 3708 0.538 8662 $^\circ$ 4334 0.850 21616 5661 0.408 1714 $^\circ$ 3664 0.0093 25596 $^\circ$ 6161 0.0976

3012 3799 0.714 8673 4335 0.130 21617 5661 0.454 1960 3700 0.6277 25597 6161 0.1074

3079 3802 0.257 8687 4336 0.396 21618⁺ 5661 0.494 1961 3700 0.6393 25598 6161 0.1228

3107 3804 0.640 8701 4337 0.617 21619⁺ 5661 0.534 1969 3701 0.8508 25599 6161 0.1371

3518 $^\circ$ 3845 0.024 LMC X-4 21625 $^\circ$ 5662 0.003 1970 3701 0.8669 25600 6161 0.1462

3535 3848 0.388 1477 $^\circ$ 3632 0.950 Vela X-1 1972 3701 0.9098 25607 6162 0.3640

3940 3892 0.281 2045 3708 0.587 1442⁺ 3628 0.453 1973 $^\circ$ 3701 0.9241 25608 6162 0.3746

3965 3894 0.732 6202 4102 0.368 1488 $^\circ$ 3634 0.057 1975 $^\circ$ 3701 0.9619 25609 6162 0.3844

3966 3894 0.744 6204⁺ 4102 0.505 2087 3712 0.856 1986 3702 0.2536 25610 6162 0.3954

5178 $^\circ$ 4002 0.049 6208 4103 0.115 3510 3845 0.604 1987 3702 0.2740 25611 6162 0.4068

5181 4003 0.084 6220 $^\circ$ 4104 0.945 3519 3846 0.714 1991 3703 0.4572 25612 6162 0.4174

5183 4003 0.110 6223⁺ 4105 0.482 3550 3850 0.140 1992⁺ 3703 0.4716 25613 6162 0.4279

5475 4035 0.780 6225 4105 0.609 3649⁺ 3862 0.537 1994⁺ 3703 0.5038 25614 6162 0.4377

7784 4265 0.953 6226 4105 0.660 4718 3954 0.770 1995 3703 0.5186 25615 6162 0.4550

9340 4412 0.169 7066 4179 0.508 18823⁺ 5323 0.457 2002 3703 0.6092 25616 6162 0.4658

9364 4416 0.834 7091 4182 0.454 18958⁺ 5341 0.529 2003 3703 0.6357 25617⁺ 6162 0.4778

9394 4419 0.395 8663 4334 0.396 18970 5343 0.743 2004 3703 0.6540 25618⁺ 6163 0.4880

9397 4419 0.491 8664⁺ 4334 0.446 18983 $^\circ$ 5345 0.976 2006 3704 0.7411 25619⁺ 6163 0.4996

9413 4422 0.940 8674 4335 0.175 19012 5351 0.609 2008 3704 0.7672 25620⁺ 6163 0.5295

9421 4423 0.117 8675 4335 0.221 19061 5357 0.282 2009 3704 0.7818 25621⁺ 6163 0.5413

9439 4425 0.474 8686 4336 0.802 22278 5746 0.733 2106 $^\circ$ 3715 0.0384 28730 6632 0.1508

9459 4426 0.767 8688 4336 0.896 22287 5747 0.845 2153 3720 0.4570 28731 6632 0.1638

SMC X-1 8689 4336 0.937 22297 $^\circ$ 5748 0.975 4742 $^\circ$ 3957 0.9378 28732 6632 0.1775

1520⁺ 3639 0.361 9366 4416 0.372 22301 $^\circ$ 5749 0.068 4751 3958 0.1839

1533 $^\circ$ 3642 0.930 21472 5646 0.585 22309 5751 0.290 4752 3958 0.1978

**Table 2:** SWP number, Reduced Julian Day (RJD) = JD-2440000 and mid-exposure orbital phase $\phi$ of the IUE spectra. Spectra used to construct $\phi \sim 0$ and $\phi \sim 0.5$ averages are indicated by a suffix $\circ$ and +, respectively. Orbital parameters:
HDE 226868/Cyg X-1	$\phi _0 \equiv$ RJD 2804.245	P= $5{\hbox{$.\!\!^{\rm d}$ }}60000(24)$	(Kemp 1977)
Sk 160/SMC X-1	$\phi _0 \equiv$ RJD 3000.1626(8)	P= $3{\hbox{$.\!\!^{\rm d}$ }}89239(2)$	(van Paradijs & Kuiper 1984)
Sk-Ph/LMC X-4	$\phi _0 \equiv$ RJD 7742.4904(2)	P= $1{\hbox{$.\!\!^{\rm d}$ }}40839(1)$	(Levine et al. 1991)
HD 77581/Vela X-1	$\phi _0 \equiv$ RJD 4279.0466(37)	P= $8{\hbox{$.\!\!^{\rm d}$ }}964416(49)$	(Deeter et al. 1987)
HD 153919/4U1700-37	$\phi _0 \equiv$ RJD 6161.3400(30)	P= $3{\hbox{$.\!\!^{\rm d}$ }}411652(26)$	(Haberl et al. 1989).
SWP	RJD	$\phi$	1968	3699	0.775	21569	5656	0.728	22324	5752	0.407	4753	3958	0.2124
Cyg X-1	2020 $^\circ$	3705	0.221	21607	5660	0.888	32961⁺	7214	0.432	5180	4003	0.3758
1273 $^\circ$	3599	0.929	2044 $^\circ$	3708	0.906	21608 $^\circ$	5660	0.019	32967⁺	7215	0.543	25586	6160	0.7770
1445	3629	0.317	6203 $^\circ$	4102	0.185	21609 $^\circ$	5660	0.066	33085⁺	7233	0.550	25587	6160	0.7884
1451⁺	3629	0.441	6207⁺	4103	0.406	21611	5661	0.166	46144	8933	0.165	25588	6160	0.8020
1478 $^\circ$	3632	0.971	6219⁺	4104	0.705	21612	5661	0.217	46151	8934	0.278	25589	6160	0.8169
1500⁺	3636	0.540	6224 $^\circ$	4105	0.949	21613	5661	0.267	46167	8935	0.406	25590	6160	0.8299
1515 $^\circ$	3638	0.047	7092	4182	0.826	21614	5661	0.315	4U1700-37	25591	6160	0.8423
1979	3701	0.270	7094	4182	0.878	21615	5661	0.360	1476	3632	0.7960	25592	6160	0.8545
2049⁺	3708	0.538	8662 $^\circ$	4334	0.850	21616	5661	0.408	1714 $^\circ$	3664	0.0093	25596 $^\circ$	6161	0.0976
3012	3799	0.714	8673	4335	0.130	21617	5661	0.454	1960	3700	0.6277	25597	6161	0.1074
3079	3802	0.257	8687	4336	0.396	21618⁺	5661	0.494	1961	3700	0.6393	25598	6161	0.1228
3107	3804	0.640	8701	4337	0.617	21619⁺	5661	0.534	1969	3701	0.8508	25599	6161	0.1371
3518 $^\circ$	3845	0.024	LMC X-4	21625 $^\circ$	5662	0.003	1970	3701	0.8669	25600	6161	0.1462
3535	3848	0.388	1477 $^\circ$	3632	0.950	Vela X-1	1972	3701	0.9098	25607	6162	0.3640
3940	3892	0.281	2045	3708	0.587	1442⁺	3628	0.453	1973 $^\circ$	3701	0.9241	25608	6162	0.3746
3965	3894	0.732	6202	4102	0.368	1488 $^\circ$	3634	0.057	1975 $^\circ$	3701	0.9619	25609	6162	0.3844
3966	3894	0.744	6204⁺	4102	0.505	2087	3712	0.856	1986	3702	0.2536	25610	6162	0.3954
5178 $^\circ$	4002	0.049	6208	4103	0.115	3510	3845	0.604	1987	3702	0.2740	25611	6162	0.4068
5181	4003	0.084	6220 $^\circ$	4104	0.945	3519	3846	0.714	1991	3703	0.4572	25612	6162	0.4174
5183	4003	0.110	6223⁺	4105	0.482	3550	3850	0.140	1992⁺	3703	0.4716	25613	6162	0.4279
5475	4035	0.780	6225	4105	0.609	3649⁺	3862	0.537	1994⁺	3703	0.5038	25614	6162	0.4377
7784	4265	0.953	6226	4105	0.660	4718	3954	0.770	1995	3703	0.5186	25615	6162	0.4550
9340	4412	0.169	7066	4179	0.508	18823⁺	5323	0.457	2002	3703	0.6092	25616	6162	0.4658
9364	4416	0.834	7091	4182	0.454	18958⁺	5341	0.529	2003	3703	0.6357	25617⁺	6162	0.4778
9394	4419	0.395	8663	4334	0.396	18970	5343	0.743	2004	3703	0.6540	25618⁺	6163	0.4880
9397	4419	0.491	8664⁺	4334	0.446	18983 $^\circ$	5345	0.976	2006	3704	0.7411	25619⁺	6163	0.4996
9413	4422	0.940	8674	4335	0.175	19012	5351	0.609	2008	3704	0.7672	25620⁺	6163	0.5295
9421	4423	0.117	8675	4335	0.221	19061	5357	0.282	2009	3704	0.7818	25621⁺	6163	0.5413
9439	4425	0.474	8686	4336	0.802	22278	5746	0.733	2106 $^\circ$	3715	0.0384	28730	6632	0.1508
9459	4426	0.767	8688	4336	0.896	22287	5747	0.845	2153	3720	0.4570	28731	6632	0.1638
SMC X-1	8689	4336	0.937	22297 $^\circ$	5748	0.975	4742 $^\circ$	3957	0.9378	28732	6632	0.1775
1520⁺	3639	0.361	9366	4416	0.372	22301 $^\circ$	5749	0.068	4751	3958	0.1839
1533 $^\circ$	3642	0.930	21472	5646	0.585	22309	5751	0.290	4752	3958	0.1978

Dupree et al. (1980) did detect the HM-effect in IUE spectra of HD 77581/Vela X-1. The B-supergiant's wind profiles are less saturated while the Strömgren zone is expected to be larger than in the case of HD 153919/4U1700-37. A detailed study of the orbital modulation of the UV resonance lines of HD 77581/Vela X-1 indicated that the velocity and density structure of the stellar wind cannot be a monotonically rising function with distance from the star (Kaper et al. 1993), a conclusion that has been derived from observations of single early-type stars as well (Lucy 1982). Additional absorption (e.g. due to material trailing the X-ray source in its orbit) appears in the line profiles at late orbital phases (Sadakane et al. 1985; Kaper et al. 1994).

HD 153919 and HD 77581 are the only OB-supergiants in HMXBs bright enough in the UV to have been observed with sufficient signal-to-noise in the high-resolution mode of IUE. Kallman et al. (1987) and Payne & Coe (1987) studied the HD 77581/Vela X-1 system in low-resolution mode and trailing mode, respectively, to search for the signature of rapid modulation of the Strömgren zone as a reaction to the periodically varying X-ray emission from the pulsar. Although these early experiments with IUE were unsuccessful, the periodic modulation was recently detected using the Faint Object Spectrograph onboard the Hubble Space Telescope (HST) by Boroson et al. (1996). Treves et al. (1980) detected the orbital modulation of UV resonance lines in low-resolution IUE spectra of HD 226868/Cyg X-1. This source is too faint to obtain useful high-resolution IUE spectra (Davis & Hartmann 1983). Bonnet-Bidaud et al. (1981) and van der Klis et al. (1982) discussed the appearance of the HM-effect in low-resolution IUE spectra of Sk 160/SMC X-1 and Sk-Ph/LMC X-4. Two high-resolution UV spectra of Sk 160/SMC X-1 confirmed the orbital modulation of the Si IV resonance doublet (Hammerschlag-Hensberge et al. 1984). Vrtilek et al. (1997) and Boroson et al. (1999) discussed observations of LMC X-4, including high-resolution HST/GHRS spectra, in terms of a shadow wind. In this system the X-ray flux is so strong that only in the X-ray shadow behind the supergiant companion a normal stellar wind can develop (Blondin 1994). This represents the most extreme case of the HM effect; in practice, only Roche-lobe overflow systems will include a shadow wind. Recent HST/STIS observations by Kaper et al. (in preparation) confirm the presence of a shadow wind in LMC X-4, as well as a photo-ionization wake at the (leading) interface between the shadow wind and the X-ray ionization zone. We have not included the peculiar O7 III/black-hole candidate system #32/LMC X-1 (Hutchings et al. 1983, 1987; Cowley et al. 1995) because the system is embedded in a nebula with strong (UV) emission lines.

Although detailed observational studies of the HM effect in individual systems exist, a quantitative analysis based on state-of-the-art stellar-wind models is lacking. In the past two decades significant improvement has been made in modelling the stellar-wind profiles of (single) OB-type stars (Groenewegen et al. 1989; Groenewegen & Lamers 1989, 1991; Haser et al. 1998). We present a quantitative analysis of the UV spectral variability in the five HMXBs with OB-supergiant companion observed with IUE, comparing the complete set of IUE spectra. The model spectra are obtained using a modified version of the Sobolev Exact Integration (SEI) method introduced by Lamers et al. (1987). Our new method allows to take into account the non-monotonic wind structure observed in many (single) OB-type stars by adding "turbulence'', as well as an extended Strömgren zone around the X-ray source. With this analysis, fundamental parameters of the system are derived.

An overview of the data and spectral line variability is given in Sect. 2. X-ray eclipse spectra, UV continuum lightcurves and additional photometry are described in Appendices A-C, and the applied variability and error analysis method is described in Appendix D. Section 3 introduces the radiation transfer code "SEI'' (Lamers et al. 1987) and the modifications that we implemented to be able to compute line profiles for HMXBs. Section 4 describes our attempts to model the UV line variability observed in HD 77581/Vela X-1 and HD 153919/4U1700-37. The derived terminal velocities, ionization fractions and sizes of the ionization zones are discussed in Sect. 5.

1 Introduction