The Rossi X-ray Timing Explorer (RXTE) collected 16 years (from its launch in December 1995 to January 2012) of data on the X-ray variations of high-energy sources (e.g., black holes, neutron stars, or pulsars, among others). The spacecraft carried the Proportional Counter Array (PCA) [42] covering the energy range 2 - 60 keV, with geometric area of 6500 cm² and time resolution of 1 microsec. It also carried the High Energy X-ray Timing Experiment (HEXTE) [43] covering an energy range of 15 - 250 keV, with geometric area of 2 × 800 cm² and the All-Sky Monitor (ASM) [44] covering and an energy range 2 - 10 keV and a sensitivity of 30 mCrab.

Here we analyze the RXTE/PCA data. The data were downloaded from the NASA’s High Energy Astrophysics Science Archive Research Center (HEASARC) web site (https://heasarc.gsfc.nasa.gov), which is a data archive for high energy astrophysics missions. The list of observations (start and end times in MJD) is given in Table 1.

The downloaded data contains 23 folders, one for each observing proposal. The standard products for bands b (2 - 4 keV), c (4 - 9 keV), and d (9 - 20 keV) were used in the current analysis. Using the standard lightcurve files, we calculate time (in Modified Julian Day), orbital phase, 35-day phase, softness ratio and its error. The time units in seconds have been converted to Modified Julian Date in Terrestrial Time using the conversion:

M J D B = T D B 24 ∗ 3600 + M J D B r e f ( T T ) (1)

where TDB is the barytime, and M J D B r e f ( T T ) is the reference time of the instrument: M J D B r e f ( T T ) = M J D B r e f , i n t + M J D B r e f , f r a c = 49353.000696574076 d.

For the calculation of the orbital ephemeris, we use:

P o r b ( t ) = P o r b ( 0 ) + ( M J D − T π / 2 ( 0 ) ) ∗ P ˙ o r b ( 0 ) (2)

where we use the constants from Table 3 of [4] : T π / 2 ( 0 ) = 46359.871940 , P o r b ( 0 ) = 1.70016759 , and P ˙ o r b ( 0 ) = − 4.85 × 10 − 11 . The average orbital period over time T π / 2 ( 0 ) to time t is:

P a v ( t ) = P o r b ( 0 ) + P o r b ( t ) 2 (3)

because the orbital period is increasing linearly with time. The time T from the reference time is T = t − T π / 2 ( 0 ) . The orbital phase, ϕ o r b , with phase reference 0 defined as mid-eclipse of the neutron star by the companion star, is given by the

fractional part of T P a v ( t ) . and the number of orbital cycles, n, is given by the integer part of T P a v ( t ) . The softness ratio, SR, here for band b over band d, is given by:

S R = b d (4)

with b and d the count rates in bands b and d, respectively.

The data were first filtered to remove the Anomalous Low States (ALS1 and ALS2, also referred to as the 2000 and 2004 ALS’s). To remove ALS1 and ALS2, we first used the intervals measured by [18] (their Table 1: MJD51256 to MJD51757 and MJD52946 to MJD53159). Ref. [45] gives similar intervals for the 2000 ALS, as MJD51224 to MJD51826, and the 2004 ALS, as MJD52945 to MJD53157. They also give an ALS from MJD57302 to MJD57372, however for that period the 35-day cycle is seen in the Swift/BAT data ( [16] ). We then we reexamined the ASM, BAT and PCA lightcurves, which led us to refine the ALS1 and ALS2 periods: from MJD 51230 (Feb. 21, 1999) to 51755 (July 30, 2000) for ALS1, and from MJD 52980 (Dec. 7, 2003) to 53100 (Apr. 5, 2004) for ALS2.

35-day phase, ϕ 35 , was calculated as:

ϕ 35 = t − t n 35 P n 35 = t − t n 35 t n + 1 35 − t n 35 (5)

where t is time of the data, t n 35 is the reference time and P n 35 is the length of 35-day cycle number n.

Her X-1 was observed during a long-term monitoring campaign by RXTE/ASM and Swift/BAT. The values of t n 35 and P n 35 [16] were determined by a cross-correlation analysis of the data with a 35-day template lightcurve. Tables 1 and 2 of [16] are used here because ASM and BAT values of t n 35 and P n 35 cover the same time period as the RXTE/PCA data. Unlike the RXTE/ASM and the Swift/ BAT data, the cross-correlation method does not work well for the RXTE/PCA data: the PCA data are mostly spaced irregularly with large gaps (Fig. 1 of [11] ) with poor coverage of 35-day cycles. The PCA data consists of ;1.4 × 10⁶ s integration time over a period of ;4.6 × 10⁸ s. The cross-correlation does not give clear peaks except for very few of the PCA observations which have coverage of the peak of MH state.

The tables of t n 35 and P n 35 from [16] consist of two parts: an interval of MJD 50146.553 to 53403.780 taken from the ASM table, and an interval of MJD 53437.822 to 58691.994 taken from the BAT table. The first part contains 94 cycles of ASM data and the latter contains 152 cycles of BAT data giving a total of 246 cycles². The uncertainties of 35-day phase determination from ASM and BAT are discussed in Section 4 of [16] . The mean accuracy of the cycle lengths from the ASM and BAT analysis is ±0.75 d, with a few errors exceeding 3 d (see Fig. 8 of [16] ).

The characteristic shape of the 35-day average lightcurve is well-determined from ASM, BAT and MAXI monitoring observations ( [16] for ASM and BAT, [46] for BAT and MAXI)³. The plots of RXTE/PCA count rate vs. ASM/BAT-determined 35-day phase show some incorrectly phased data, out of place compared to the characteristic shape of the 35-day lightcurve. The incorrect phasing is caused by known errors in ASM/BAT-determined 35-day phase. The errors in phase were found by examing the PCA count rates and SR vs. ASM/BAT 35-day phase. E.g. data with high count rate during LS indicated that it belonged to either MH or SH states, and a 35-day phase adjustment was needed to move it out of LS. The group of points for cycles 97 and 98 between ASM/BAT phase 0.63 ≤ ϕ 35 ≤ 0.64 with low count rate (5.88 ≤ Band b ≤ 9.15) indicating a 35-day cycle length adjustment for those cycles. We note that the phase adjustments were applied only to the 35-day cycle times, t n 35 and P n 35 , which changes only the calculated 35-day phase of the data points. All of the adjustments are listed in Table 2, ranging from 1.0 to 3.4 d. The mean adjustment of 1.7 d is consistent with the estimated ASM/BAT 35-d phase measurement errors. After these adjustments the 35-day lightcurve showed no clearly-outlying data.

The resulting 23 cycles which have RXTE/PCA observations are plotted in separate colors in Figure 2. The cycles plotted together in each panel were selected to have the least amount of overlap in 35-day phase. The longest PCA observation is that for cycle 62 (~10 d). Eight cycles have short (ˆ1 d) PCA observations: cycles 67, 75, 80, 91, 93, 100, 136 and 156.

Figure 3 (top panel) shows the resulting 35-day lightcurve including all of the PCA data, with the phase adjustments of Table 2. The lower panel shows SR vs. 35-day phase and illustrates the large number of dips (and a smaller number of eclipses) where absorption by cold matter occurs, causing SR to drop below 0.3 simultaneously with a drop in count rate4. For out-of-dip times in MH, SR ranges from 0.3 to 0.55 and in SH, SR ranges from 0.3 to 0.7.

We divide the 35-day cycle into the eight substates as listed in Table 3. Early published work on Her X-1 recognized MH, SH and LS and later work sub-divided MH into MH turn-on, MH and MH decline; SH into SH turn-on, SH and SH decline and LS into LS1 and LS2 (e.g. [14] ). We initially used the 35-day phases for the eight substates of the 35-day cycle summarized by [46] (their Table 2).

However, with the higher sensitivity of the RXTE/PCA data compared to the ASM or BAT data, we were able to better determine the 35-day phase boundaries of the states. The boundaries were determined as follows. LS1 and LS2 were defined by the periods of persistent low Band d count rate. The MH decline and SH decline were defined by the start and end of the slow declines of count rate during MH and SH, respectively. The MH turn-on and SH turn-on were defined by the beginning and end of the rapid phases of increase of count rate at the start of MH and SH. The remaining slow rise and constant count rate parts of MH and SH defined the MH and SH intervals.

The adjusted 35-day phase boundaries of the substates are shown as vertical lines in Figure 3 (top panel). The 35-day lightcurve for the PCA data show a fast turn-on and a slow decline for MH and for SH states. All eight substates are better defined by the PCA 35-day lightcurve here compared to the BAT or ASM 35-day lightcurves [16] because of the higher sensitivity of the PCA data, the updated 35-day cycle timing here, and the ability to separate dip data from non-dip data.

A binned 35-day lightcurve (data averaged into 100 equally spaced phase bins) is shown in Figure 4. To create this we removed eclipse data (including ingress and egress) between orbital phases 0.00 - 0.09 and 0.91 - 1.00, which removed ;7400 times from the original ;97,500. Then we removed dip data so that we do not average dip and non-dip data by removing data with SR < 0.3, which removed another ;29,700 data points. This removed most of the dips but not the lowest count rate part of the dips where the SR increases again (see Figure 9 below). To remove these dip points we removed data points with Band d count rate < 12 c/s for all states except LS1 and LS2. LS1 and LS2 had 964 and 1028 data points, respectively. The remaining data are plotted against the 35-day phase in Figure 4 (blue points). The red curve is the result of averaging the data into 100 phase bins. The variability of the lightcurves for the 16 different MH states observed by RXTE/PCA has been shown in Figures 2 and 3 of [47] . Comparison of the PCA data plotted against MJD shows that the binned lightcurve is significantly distorted by combining data from different 35-day cycles of different peak brightness and by the uneven sampling.

Orbital lightcurves generated for Band d and SR (Band b/Band d) are shown in Figure 5, for MH and MH turn-on (left panel) and for MH decline (right panel). Band d and SR lightcurves are shown in Figure 6 for SH, SH decline and SH turn-on (left panel), and for LS1 and LS2 (right panel).

The decline of MH and of SH is not clearly shown by panel (c) in Figure 5 and panel (c) in Figure 6. This is because the declines for MH and SH each last several orbits, and because there are different 35-day cycles with different strengths

(maximum Band d count rate) plotted together. To show the decline, the 20 orbits that make up the SH decline are plotted separately in Figure 7. The decline can now been seen in the successive orbits for the different 35-day cycles (noted in the Figure caption). This also shows the variability between of SH decline between different 35-day cycles. Similar properties (the variability and the decline within a given 35-day cycle) apply to MH decline, however the number of orbits observed for MH decline is significantly larger (~50) making it more difficult to identify trends.

Eclipses during MH are well defined and occur over orbital phases 0 to 0.07 for egress and 0.93 to 1.0 for ingress (e.g. Fig. 1 of [5] ). To clearly see the eclipse lightcurves, some data on either side of eclipse is included here, i.e. the orbital phases plotted are extended to 0 to 0.1 and 0.9 to 1.0. 1 has been added to the 0.0 to 0.1 orbital phase data to make the phase continuous across the eclipse (0.9 to 1.1). Due to the large dynamic range of count rates, the resulting lightcurves are plotted on logarithmic scale. Figure 8 shows the eclipse lightcurves in Band d for MH, MH decline and MH turn-on (top left); for SH, SH decline and SH turn-on (top right) and for LS1 and LS2 (lower panel). The scatter of the points is explained by countrate errors. For the weak count rates the relative errors are the largest, e.g. 0.5 c/s has a typical error of ;0.35 - 0.45 c/s.

The unbinned 35-day lightcurves are shown in the upper panel of Figure 3. The lower panel shows the SR, which indicates absorption by a value ˆ 0.3 and no absorption by a value ‰ 0.3. The relation between SR and absorption by dips was demonstrated by [34] [35] and absorption by companion eclipses by [48] . The time resolution of the ASM and BAT lightcurves [16] was low enough that most dips are not resolved so that dip and non-dip data are mixed. However, the 16 s time resolution of the PCA standard products is sufficient to resolve and separate dip data from non-dip data [35] .

The PCA 35-day lightcurve shows numerous dips, consistent with the finding by [11] that for a significant fraction of the time Her X-1 shows absorption. After removing the absorbed data with SR < 0.3, the 35-day lightcurve retains a factor ~2 variation at any given 35-day phase. This was previously known from the long record of 35-day cycle strengths from ASM and BAT (e.g. Fig.1 of [18] for ASM or Fig.2 of [16] for BAT). The PCA 35-day lightcurve presented here will be a valuable input for models of the 35-day cycle which are used to constrain the shape of the accretion disk, similar to the work of [8] [15] .

A recent study of orbital X-ray lightcurves of Her X-1 was done by [1] using RXTE/ASM, MAXI and Swift/BAT data. That considered the six 35-day substates of MH turn-on, MH, MH decline, LS 1, SH combined (SH turn-on, SH and SH decline) and LS 2, then subdivided MH into four pieces (MH-a, MH-b, MH-c and MH-d) for study of the main dip progression with 35-day phase. With the low sensitivity of ASM, MAXI and BAT data and the long-term observations, the orbital lightcurves were created using binned data. The PCA data analysed here has much higher sensitivity (smaller errors by a factor of ~10). This allows creation of PCA lightcurves for the eight 35-day substates using unbinned data, which reveals the dips and the variability of Her X-1 at each orbital phase.

The MAXI, BAT and ASM lightcurves from [1] (their Fig.1 and Fig. A1) show significant differences between the different 35-day substates, which can be compared to what is seen in the PCA lightcurves (Figure 5 and Figure 6). In particular, for MH the lightcurve is nearly flat-topped except near eclipse egress and for dips after orbital phase ~0.75. The better time resolution and sensitivity of the PCA data show that MH has a rapid rise at eclipse egress not seen in the MAXI, BAT and ASM lightcurves. The bump at orbital phase 0.9 in the MAXI/ BAT/ASM lightcurves is seen by the PCA data to be caused by a mixture of unabsorbed data with absorbed data, which are not time-resolved in the MAXI/ BAT/ASM data. For MH turn-on, the BAT/MAXI/ASM lightcurves show two maxima at orbital phases 0.3 and 0.8; however, the PCA data shows only a single maximum at orbital phase 0.8. This is probably due to the incomplete coverage of different 35-day cycles by the PCA, so it missed catching MH turn-ons near orbital phase 0.3. The MH decline for the BAT/MAXI/ASM lightcurves has a dip at orbital phase 0.4 which is seen in the PCA MH decline lightcurve (Figure 5).

For SH, the PCA lightcurve has a smooth maximum near orbital phase 0.4 similar to that seen in the BAT/MAXI/ASM lightcurves. For the BAT/MAXI/ASM SH lightcurves, late orbital phases (‰0.5) are quite weak. The PCA SH lightcurves show that this is caused by the much higher incidence of dips after orbital phase 0.5 ((c) of Figure 6). The LS 1 and 2 lightcurves show clear modulation in the PCA data not seen in the BAT/MAXI/ASM SH data, because of the lower sensitivity and larger background uncertainties for the latter.

A new result here is that eclipse lightcurves (Figure 8) have now been produced for states other than MH, including MH decline, SH, SH decline and the Low States 1 and 2. The evidence for a bowl-shaped eclipse, previously known for MH only, is now demonstrated for these other states. The evidence is clear for the six MH and SH substates. Because of the large number of data points during eclipse, the statistical evidence for the bowl-shaped emission during eclipse is very strong (e.g. for MH see [41] ). The evidence is less secure for the Low States, because of the incomplete observations. Future observations of eclipses with other instruments with better time coverage of LS, such as those on the AstroSat satellite, could confirm the bowl-shaped eclipses for the LS.

Ref. [41] analyzed binned data for MH eclipses using a corona model. The bowl-shaped eclipse is evidence for an extended electron scattering corona in the binary system: it has to be larger than the companion star HZ Her, in order to yield residual X-ray flux at mid-eclipse. The unbinned eclipse data presented here in Fig. 7 shows that the lower pre-ingress flux than post-egress flux for MH is caused by more numerous dips in the pre-ingress period than in the post-egress period, rather than a different flux emitted by the neutron star.

The corona model from [41] was fitted to the new eclipse lightcurves here for substates with enough data: MH, MH decline, SH, SH decline, and the combined data from Low States 1 and 2. The phase interval from post-stellar ingress (0.932) to pre-stellar-egress (1.068) was fit using χ² minimization with normalization C as the single fit parameter. The corona model lightcurves (without companion ingress and egress models) are shown in Figure 8. Table 4 shows the results of the fits, with C, χ² and χ²/dof values, where dof means degrees of freedom.

Ref. [41] (their Figure 4) shows an excess at orbital phase 0.94 above the coronal model best fit for MH eclipse. We verify the excess here for MH: the fit of the coronal model to data not including the excess region (orbital phase 0.935 to 0.96) is a significant improvement over the fit to data including the excess region (see comparison of “MH” and “MH no excess” fits in Table 4, decrease in χ² of 940 for a decrease of 531 in dof). For the other states, the data are too sparse to determine whether there is an excess at similar or different orbital phases during the eclipse. The proposed explanation of the excess is scattered X-rays from the accretion stream. The changing geometry of the accretion stream and its impact site on the accretion disk surface, described by the model of [24] , implies that the excess should change its orbital phase with 35-day cycle phase. More complete observation of eclipses for different 35-day phases are needed in order to test this.

Table 4 shows that the normalization of the corona, C, is similar for MH (no excess) and MH decline (by <3σ) but significantly lower for SH and SH decline (SH lower than MH decline by ~4σ and SH decline lower than MH decline by ~10σ). The normalizations for SH, SH decline and LS differ by <3σ. Some change in the normalization of intensity from the corona is expected because the changing orientation of the accretion disk implies changing visibility of the inner regions of the corona. More complete observations of the eclipses would allow

(a): MH turn-on and SH turn-on did not have enough data to fit; LS 1 and LS 2 data were combined into LS1 + 2; the orbital phases of eclipse that were fit are 0.0935 to 1.065. (b): 1σ errors are given in brackets. (c): for this fit the region with the excess between phases 0.935 and 0.960 was omitted.

testing the shape of the corona by applying a model for the partial eclipse of the corona by the rotating accretion disk shape (Figure 1).

As noted above, absorption dips are identified by a decrease in SR that coincides with a decrease in count rate, whereas no-absorption dips show no change in SR as the count rate decreases. To identify both types of dips, SR vs. count rate was examined for each state. Eclipses (orbital phases 0.0 to 0.07 and 0.93 to 1.0) were filtered out of the data prior to the search.

Figure 9 (left panel) shows the resulting SR vs. band d count rate for the MH turn-on, MH and MH decline (with the MH on points superimposed on the MH decline points to better see the three sets; the MH decline points cover the entire region below the MH points) Absorption dips can be seen by the sharp decrease in SR for the points below the main cluster of unabsorbed data which lies between SR of 0.4 and 0.5. Although there are small decreases in count rate without decreases in SR (without absorption) within the main cluster of points, there are no deep drops in count rate without a drop in SR. I.e., we don’t find any no-absorption dips in the MH states.

The right panel of Figure 9 shows SR vs. band d count rate for the LS (combined), SH turn-on, SH decline and SH (with the LS points plotted on top, then SH turn-on, then SH decline, and SH below). Absorption dips in the three SH states are identified by the drop in SR below 0.3 associated with a decrease in band d count rate. For the SH states the fraction of data showing absorption is ~70%, in contrast to the MH states with a proportion of data with absorption of ~30%., consistent with [11] . The errors in SR for LS points (and all other points with count rate ˆ 6) are large enough that absorption (or its absence) cannot be detected.

The previous report of no-absorption dips by [39] used 5 - 9 and 9 - 20 keV bands from Large Area X-ray Proportional Counter (LAXPC) on Astrosat. For a closer comparison to this analysis we analysed SR vs count rate with SR given by PCA Bands c (4 - 9 keV) and d (9 - 20 keV). Using SR = Band c/Band d results in absorption dips following a nearly linear decrease of SR with count rate, in agreement with [39] (their Fig.7) instead of the curved trajectory of points for SR = band B/Band d as seen in Figure 9 here. However, we found no no-absorption dips in the PCA data.

In summary, we did not find any no-absorption dips in our thorough search. We checked two different definitions of SR, and searched all three MH states and all three SH states in the entire RXTE/PCA archive of observations of Her X-1. The AstroSat collaboration has updated the LAXPC data processing software including a new background model (see http://astrosat-ssc.iucaa.in/laxpcData). Thus it is possible that the detection of no-absorption dips by [39] was caused by errors in background subtraction using the older data analysis package.