1. Introduction
Hercules X-1 (Her X-1) is a well-known and studied binary system (e.g [
1,
2,
3]) composed of a neutron star Her X-1 –pulsating at 1.24 s– in a 1.7-day nearly circular orbit around its optical companion, a main sequence star HZ Her of spectral type A/F. The binary has accurately measured orbital ephemeris [
4]. The companion varies between late A type (for the back side facing away from the neutron star) and early B type (for the front X-ray illuminated side of companion). The approximate masses of neutron star and companion are ≃ 1.6 M
and ≃ 2.3 M
, respectively [
5,
6]. The main uncertainty is caused by the uncertainty in the orbital inclination, which is ∼85
o. It is located at a distance of ∼ 6.1 kpc from Earth [
5], with coordinates of RA = 16 57 49.8110126616 and dec = +35 20 32.486555472, or galactic coordinates of 58.1
o longitude and 37.5
o latitude. Her X-1 is a persistent X-ray pulsar discovered by the Uhuru satellite in 1972 along with Centaurus X-3. Since that date, both pulsars have remained among the most studied X-ray sources and continue to give new information about X-ray binary astrophysics. The system Her X-1/HZ Her is a strong emitter in X-rays, optical, and ultraviolet (e.g [
7,
8]), which enables studies of the binary in detail.
The 35-day cycle is one of the most prominent features of Her X-1 ([
9] and references therein). Its length can vary from 33 to 37 days [
10]. The cycle is produced by changes in the obscuration of the neutron star by the accretion disk [
11,
12]. The binary system is conceptually illustrated here in
Figure 1, with observer inclination at
and with a twisted and tilted accretion disk fed by an accretion stream from the Roche-lobe filling companion, HZ Her. The neutron star is directly visible in MH state, and seen partly obscured in SH.
The 35-day cycle has 8 states: Main High (MH) turn-on, MH, MH decline, Low State (LS) 1, Short High (SH) turn-on, SH, SH decline, and LS 2. The MH state (including the 3 subdivisions) lasts 10-12 days, the SH state lasts 5-7 days, and MH and SH are separated by LS lasting 8-10 days [
13]. In addition, Her X-1 has Anomalous low states (ALS) every ∼ 5 years (e.g. [
14]), where the High states fail to appear and instead exhibits extended periods of low X-ray flux. The ALS were discovered by [
15], and later shown [
9] to be indistinguishable from the regular LS based on X-ray softness ratio (SR). The ALS is likely produced by a change in the geometry of the accretion disk that prevents a direct line of sight to Her X-1 [
16].
An X-ray binary system which has a low mass (≲ 3 M
) or late-type companion star (spectral type A or later) is known as low-mass X-ray binary (LMXB). It consists of a neutron star or a black hole accreting material from its companion via Roche-lobe overflow
1, forming an accretion disk around the compact object through conservation of angular momentum. The material spirals into the deep gravitational well, with potential of order 0.1 mc
, and thus is heated to keV temperatures, causing the emission of X-rays. LMXBs are usually found in the bulge, disk and globular clusters of the Galaxy, whereas HMXBs (high-mass X-ray binaries with young massive stars as companions) are usually found close to star-forming regions in the spiral arms of the Galactic plane. LMXBs are older than HMXBs. Her X-1 has a companion which is ∼600 Myr old [
5] and is considered to be a LMXB.
The accretion stream from HZ Her enters orbit around Her X-1 and forms an accretion disk (e.g. [
17,
18]). Accretion onto Her X-1 from the inner edge of the disk proceeds through an accretion column, in which the hard X-rays (> 1 keV) are created [
19,
20], and modulated by neutron star rotation and obscuration of the accretion disk. A weaker flux of X-rays is present during low state and eclipses, which are scattered from extended matter in the system (e.g [
11,
12]). However, there are other different X-ray flux modulations that consist of sharp and non-periodic absorption events, called lightcurve dips. These numerous dips occur throughout the orbital phase and the High states of the 35-day cycle, lasting from a couple of seconds to several hours in different intensities [
21].
Dips were studied by [
22], where their spectra exhibited X-ray absorption by cool material and Thompson scattering by ionized gas. According to [
23,
24] dips can also be caused by partially ionized matter or cool bobs of material immersed in hot ionized gas. [
13] analyzed the pre-eclipse dips using RXTE/ASM data, confirming the marching phenomenon where dips progress to earlier orbital phase as 35-day phase increases. [
17] modeled the stream-accretion disk impact and concluded that the dips properties can be explained by this model when the impact site of the accretion stream on the accretion disk obscures the X-ray source. Dips and orbital phase lightcurves were studied by [
1] using RXTE/ASM, Swift Burst Alert Telescope (BAT) [
25] and Monitor of All-sky X-ray Image (MAXI) [
26] data. The absorption dips exhibit a drop in the SR simultaneous with a drop in the count rate. [
27] reported a new phenomenon for dips during MH state using LAXPC instrument on board of the AstroSat Observatory [
28]: several dips showed constant SR as count rate decreased instead of the usual behaviour for absorption dips. These dips could be caused by highly ionized matter blocking the X-rays (and so the spectrum doesn’t change as count rate decreases), or by partial coverage of very dense matter.
Ionized gas in Her X-1 was demonstrated by [
2]. [
29] presented a model for the large-scale electron scattering corona by analysis of RXTE/PCA eclipse lightcurves in MH state. The corona was approximated by a spherically symmetric electron density distribution, since a more detailed corona would not be justified due to the large errors in mid-eclipse lightcurve. Their model allows for three possible scenarios: the expected temperature from heating by Compton scattering is similar to that required to keep the corona in hydrostatic equilibrium; the entire corona is a fast outflow; or the corona could be hybrid, with an inner hydrostatic region and an outer-low region with low outflow velocity. Moreover, they detected a bump in the eclipse lightcurve at orbital phase 0.945 (eclipse ingress) that may be caused by the impact of the accretion stream with the disk [
29].
In this work we analyse the entire RXTE/PCA database of observations of Her X-1 to obtain high sensitivity 35-day and orbital lightcurves.
Section 2 describes the data and analysis; and section 3 presents the lightcurves. In section 4 we discuss the new results and conclude in section 5.
5. Conclusions
We report an analysis of the entire archive of Standard 2 data on Her X-1 collected by the RXTE/PCA instrument to generate lightcurves for 35-day phase, orbital phase and eclipses. The start times and lengths of the 35-day cycles observed by PCA were updated from initial values derived from RXTE/ASM and Swift/BAT observations [
10] to be consistent with the PCA data. Using the higher sensitivity 35-day lightcurve from PCA, the boundaries of the eight states of the 35-day cycle (i.e. MH turn-on, MH, MH decline, LS 1, SH turn-on, SH, SH decline and LS 2) were refined, and the boundaries of the ALS were adjusted to be more accurate. For MH a rapid turn-on is seen followed by a slower rise to peak and an even slower decline. SH follows the same pattern but with a peak at
% of the MH peak. Absorption dips are present throughout the MH and SH states, and more prevalent during SH. The orbital lightcurves for the different 35-day states show a progression of changes with 35-day phase similar to those demonstrated in ASM and BAT data [
1,
13], but with clear indentification of the importance of dips on the lightcurves, using SR. The data coverage of the LS states is incomplete and will require observations with newer X-ray instruments.
Eclipse lightcurves of Her X-1 were generated for the different 35-day states, and show that the bowl-shape during eclipse is present for all states. The PCA data show that the extended scattering corona, found during MH [
29], is present for the entire 35-day cycle. The scattered intensity from the corona changes only moderately (∼30%,
Table 3) with 35-day phase, which is consistent with a corona larger than the accretion disk, which is partially blocked by the disk as the disk rotates with 35-day phase.
A search for dips using the 2-5, 5-9 and 9-20 keV PCA data (bands b, c and d) was carried out. The standard absorption dips were found. However we did not find any no-absorption dips similar to those reported by [
27] in any of the MH or SH states in the entire PCA archive of Her X-1 data. Because the sensitivity of RXTE/PCA is similar to that of AstroSat/LAXPC, any no-absorption dips observed should have been detected. In future work the LAXPC data can be reanalysed with the updated LAXPC analysis software and updated background model. If the no-absorption dips are verified in LAXPC data, then these must be a rare phenomenon not detected by the PCA instrument.