A Transition Discovered in the Subcritical Regime of 1A 0535+262

We present NICER observations of accreting X-ray pulsar 1A 0535+262 during its faint state ( ≲ 6 × 10 36 erg/s) observed in several type-I and II outbursts. We discovered a transition of temporal and spectral properties around the luminosity L t = 3 . 3 × 10 35 erg/s, below which spectra are relatively soft and the pulse profiles have only a narrow peak. The spectra are harder and a secondary hump gradually appears in pulse profiles when L ≳ L t . We discuss possible physical mechanisms for this transition, including different Comptonization seed photons, the disappearance of gas shocks on the neutron star surface, and the combination of plasma and vacuum polarization effects.

1. INTRODUCTION X-ray pulsars (XRPs) consist of a highly magnetized neutron star and an early-type (O/B) companion star, powered by the accretion process between binary systems (for a review, see Mushtukov & Tsygankov 2022).The neutron star usefully exhibits a strong magnetic field of ∼ 10 12-13 G. Therefore, around its magnetosphere the accreted material couples to magnetic field lines and is channeled onto polar caps of the neutron star, resulting in X-ray pulsations.During the last few decades, extensive theoretical studies have been done on the accreting structure in this vicinity of polar caps, and two classical accretion regimes have been proposed, depending on the accretion rate (Basko & Sunyaev 1975, 1976;Burnard et al. 1991;Postnov et al. 2015;Becker et al. 2012;Mushtukov et al. 2015;Becker & Wolff 2022).In the supercritical regime, when L ≳ 1.5 × 10 37 B are 110.3dand 0.47, respectively.In recent years, this source experienced several type-I (normal) outbursts and a type-II (giant) outburst in 2020.Type-I outbursts are normally associated with periastron passages, and have a lower peak luminosity (≤ 10 37 erg/s) compared with the giant outburst and are suitable for studies in the low accretion rate state.In this source, Tsygankov et al. (2019a) revealed the presence of two spectral components at L ∼ 7 × 10 34 erg/s, while Ballhausen et al. (2017) suggested that the spectrum can be well described as a single component continuum model at L ∼ 2 × 10 36 erg/s, and strong residuals appear around 30 keV at L ∼ 0.6 × 10 36 erg/s although they are model-dependent.This implies that a smooth evolution may occur, bridging between the two spectral shapes, and thus motivates us to perform a detailed analysis around L ∼ 10 36 erg/s.In this paper, we present the timing and spectral analysis of 1A 0535+262 during its faint state observed with NICER.This paper is structured as follows.In Section 2, we describe details of the observations and data reduction; the results are presented in Section 3; and in Section 4 we discuss the observational findings and their implications.

OBSERVATION AND DATA REDUCTION
The Neutron star Interior Composition Explorer (NICER) is a payload onboard the International Space Station, dedicated to timing and spectroscopic analysis at soft X-rays (0.2-12 keV) (Gendreau et al. 2016).Its high sensitivity makes it possible to study transient sources even in their faint states.Over the past few years, 1A 0535+262 experienced several type-I outbursts and a giant type-II outburst in 2020-2021.Since the bright state of the giant outburst has been extensively studied by different authors in different aspects (Kong et al. 2021(Kong et al. , 2022;;Wang et al. 2022;Mandal & Pal 2022;Reig et al. 2022;Hu et al. 2023;Chhotaray et al. 2023;Liu et al. 2023), it is excluded from our sample.In this paper, we focus only on 82 pointing observations from type-I outbursts and the faint state of the giant outburst, as shown in Figure 1.
The data reduction was performed by using the official software heasoft v6.31.1/nicerdas package (version 2022-12-16 V010a) and the latest calibration database (caldb, version xti20221001).We used the tool nicerl21 to screen clean events, and extracted light curves and spectra with nicerl3-lc and nicerl3-spect, respectively.We estimated the background by using the scorpeon2 model.During the timing analysis, the barycentric correction was performed by using the tool barycorr.We adopted the epoch-folding method (efsearch) to estimate the spin period of the source and folded its pulse profiles using the tool efold.The spectral analysis was performed by using the X-ray spectral fitting package (xspec) version 12.13.0c(Arnaud 1996).All uncertainties in this paper correspond to a confidence level of 68%. 3. RESULTS

Spectral analysis
According to previous studies, the broadband spectrum of 1A 0535+262 can be described by phenomenological models such as a power-law component with a high energy cutoff (cutoffpl) combined with a blackbody component, and an absorption line at ∼45 keV caused by cyclotron resonance scattering features (e.g., Caballero et al. 2013;Ballhausen et al. 2017;Kong et al. 2021).However, limited by NICER's narrow band (0.5-10 keV), complex models cannot be constrained.Therefore, we fitted all the spectra with a similar but simplified model, consisting of a powerlaw and a blackbody component.In addition, a narrow Gaussian component was added to account for the Fe Kα fluorescence line.We also used the Tbabs (Wilms et al. 2000) model to described interstellar absorption, i.e., the fitting model in xspec is Tbabs*(powerlaw + bbodyrad + gauss).This model was able to fit the data well (Table A.1).We note that our aim is not to find a physical model, but to select a phenomenological model that can be used to describe the spectral shape.The evolution of spectral parameters is shown in Figure 3.In general, both blackbody and powerlaw components increase with luminosity, but the latter increases more significantly.In Figure 2 we present two representative spectral shapes for low and high luminosities.For a luminosity of ∼ 10 35 erg/s, two continuum components are comparable, while the powerlaw component is dominating for the brighter state.The luminosity was calculated as 4π C F 0.5−10 d 2 assuming an isotropic radiation, where d=2 kpc is the distance, F 0.5−10 is the flux at 0.5-10 keV obtained from spectral fits, and C = 3.073 is the bolometric correction.The equivalent hydrogen column density (N H ) and the blackbody temperature (T bb ) generally keep unchanged.On the other hand, the photon index (Γ) decreases with the increasing luminosity (L) at low luminosities, indicating a spectral hardening, while the slope seems to be lower at higher luminosities.To describe the L − Γ relation quantitatively, we fitted them with a powerlaw model and a broken powerlaw model, respectively.For the latter, the resulting transitional luminosity (L t ) is (3.3 ± 0.1) × 10 35 erg/s.We note that the scattering of Γ is dominated by systematic errors.In practice, we assumed a same systematic error (σ sys ) for all the points, and estimated its value σ sys = 0.12 by making the reduced-χ 2 =1 when fitting the points of L > 10 36 erg/s with a constant line.After considering the systematic error, the goodness-of-fits of the powerlaw model and the broken powerlaw model were χ 2 =124.42 (80 dof) and χ 2 =111.02(78 dof).We adopted the F-test for the model comparison and found a probability of chance improvement of 0.01 for the latter model.For each NICER observation we searched for its periodicity by using the epoch-folding method.Then we folded 1 sbinned background-subtracted lightcurves to extract the pulse profiles.We found that pulse profiles exhibit different patterns.To investigate the luminosity-dependent evolution, we constructed a color-coded two-dimensional matrix in Figure 4, of which each row presents a pulse profile for a given luminosity.For clarity, we aligned the pulse profiles using the cross-correlation method.Here we used data taken from all available type-I outbursts and the faint state of the giant outburst, so that the detailed evolution of pulse profiles with luminosity can be well tracked.It is clear that the pulse profile exhibits a narrow peak at low luminosities, while around 3 × 10 35 erg/s (i.e., the luminosity where the spectral shape changes), a narrow dip appears at the phase 0.5, accompanied with a secondary hump at the phase 0-0.4.The hump increases at higher luminosities and eventually has a comparable intensity to the main peak (panel c in Figure 4).For comparison, during the peak of the giant outburst, pulse profiles evolve into a double-peaked structure (panels a and b), which have been extensively studied by Wang et al. (2022); Mandal & Pal (2022).In the right panel of Figure 4, we present representative pulse profiles from low to high luminosities.In order to depict the pulse profile evolution quantitatively, we calculated the fractional root-mean-square (RMS) pulsed fraction (P F ), which is defined as where N =32 is the number of phase bins, r i is the count rate in the phase bin i and r is the phase-averaged count rate.The P F errors were estimated using Monte Carlo simulations with 10 4 samplings.The results are shown in Figure 5, where the P F − L relation shows a large scattering for L < L t , while for L > L t there is a significant negative correlation.A sudden increase of the P F may appear around L t , corresponding to the dramatic variation depicted in Figure 4. Furthermore, we studied the energy-dependent P F at different luminosities (Figure 6).The P F shows both negative and positive correlations with energy in 0.5-10 keV.The turn-over point (E p ) between negative and positive correlations (i.e., the energy having a minimum P F ) varies with luminosity.For example, the E p is around 2-3 keV for the faint state (L ∼ 10 35 erg/s), which is much lower than the results (i.e., ∼10 keV) observed with Insight-HXMT, NuSTAR and AstroSat (Wang et al. 2022;Mandal & Pal 2022;Chhotaray et al. 2023) when the source is in brighter states.

DISCUSSION
Using NICER observations, we studied the temporal and spectral properties of accreting X-ray pulsar 1A 0535+262 during its faint state with a luminosity range of (0.8 − 56) × 10 35 erg/s in 0.1-100 keV.The critical luminosity, corresponding to the onset of the accretion column, has been reported to be ∼ 6 × 10 37 erg/s based on the variations of cyclotron line energies (Kong et al. 2021).Therefore, the results presented in this paper are concluded under the sub-critical accretion regime.We found that the 0.5-10 keV spectra can be well described as a simple model, i.e., the combination of a blackbody component and a powerlaw component.The spectral parameters are luminosity-dependent and a transitional luminosity L t = 3.3 × 10 35 erg/s is clearly discovered (Figure 3), which corresponds to an accretion rate of Ṁ = 2×10 15 g/s assuming the neutron star of a 1.4M ⊙ mass and a 10 6 cm radius.For L ≲ L t , the Γ−L relation is steeper and the relative contribution from the blackbody component is more significant, suggesting that the spectra are softer at low luminosities and are consistent with previous reports in GX 304-1, GRO J1008-57 and 1A 0535+262 (Tsygankov et al. 2019b;Lutovinov et al. 2021;Tsygankov et al. 2019a).The pulse profiles also show a transitional evolution around L t , from a narrow peak at low luminosities to a borad peak at high luminosities.This difference can be demonstrated in the pulsed fraction (P F ) (Figure 5), where the P F is relatively lower at low luminosities and the negative P F − L is only shown at high luminosities.Theoretical models of the accretion structure have been made by many authors assuming different considerations (Langer & Rappaport 1982;Becker et al. 2012;Mushtukov et al. 2021;Sokolova-Lapa et al. 2021;Becker & Wolff 2022).Generally, it is believed that the spectrum originates from Comptonization processes with seed photons from blackbody, bremsstrahlung and cyclotron emissions.In soft X-rays, the blackbody is expected to be the dominant component of seed photons when the accretion rate is low, while the bremsstrahlung is the primary source at high accretion rates (see Figure 7 and 9 in Becker & Wolff 2022).Thus, the variable combination of seed photons can naturally interpret the spectral evolution we observed.And in this case changes of pulse profiles can also be explained since the beam patterns of different Comptonization processes are different.However, current models do not quantitatively predict at what luminosity the contributions of the two seed photons are comparable.To verify this picture, detailed theoretical calculations around the luminosity L t are required to compare with broadband spectral observations.The observed phenomenon may be caused by other possibilities.For example, as suggested by Langer & Rappaport (1982), the final deceleration of the matter will occur via a gas-mediated collisionless shock near the surface of the neutron star, which may lead to changes of timing and spectral properties.This scenario was proposed to interpret the luminosity-dependent cyclotron line energy in Cepheus X-4 (Vybornov et al. 2017).But we note that in 1A 0535+262 the cyclotron line energy keeps constant at low accretion rates (Tsygankov et al. 2019b), which makes the existence of the collisionless shock unclear.In any case, if it is real, the transition from the Coulomb stopping (at higher luminosities) to the collisionless shock will happen around L coul ≈ 1.17 × 10 37 B −1/3 12 erg/s (see Figure 1 in Becker et al. 2012).This is inconsistent with the L t we observed.On the other hand, the gas shock is expected to disappear at a very low accretion rate L ≪ L coul , which might lead to a transition as well.However, since it is still unknown about the physics in the shock, there are no theoretical calculations available to compare with observations.While X-rays propagate in the highly magnetized plasma, both plasma and vacuum polarization effects are important for the cross section and therefore the radiation transfer in the neutron star atmosphere (for a review, see Harding & Lai 2006).Wang et al. (1988) suggested that the relative importance of plasma and vacuum effects can be characterised by the ratio ω δV = 45π α ωpe ω , where ω pe = 4πn e e 2 /m e is the plasma frequency, m e is the election mass, ω is the frequency of the photons propagating in the medium, α is the fine structure constant, and E cyc is the cyclotron line energy.If ω δV ≪ 1, the X-ray propagation is mainly affected by the vacuum polarization, while the plasma effect dominates when ω δV ≫ 1.Both effects need to be taken into account for ω δV ≈ 1.For the transitional luminosity L t , the number density of electrons n e can be estimated as Ṁ Svmp , where m p is the proton mass and S = 5.2 × 10 8 cm 2 is the area of spots at the neutron star surface calculated by using Equation 1 in Mushtukov et al. (2021).v should be approximately the free-fall velocity v ≈ v ff = ( 2GM R ) 1/2 , or v ≈ v ff /4 if a gas shock appears (Bykov & Krasil'Shchikov 2004).For 1 keV X-rays, ω δV equals 2 and 0.5 in the cases with and without the gas shock, not significantly larger or smaller than unity.This means that the transition around L t might be related to the combination of plasma and vacuum effects, i.e., the former and the latter dominate the luminosity range L ≳ L t and L ≲ L t , respectively.This possibility can be verified via polarization observations in the further, because the polarization angle is expected to be different between high and low states (Lai & Ho 2002).
Another scenario for the transition might be related to interactions between the magnetosphere and outside accretion flows.For example, it is known that when the accretion rate is very low, the system will evolve into the "propeller regime" (i.e., the accreting matter is stopped by the centrifugal barrier by the dipole magnetic field), associated with significant temporal and spectral variations (Campana et al. 2002;Tsygankov et al. 2016).However, the slow rotation of 1A 0535+262 makes the propeller effect only work when L < L prop ≈ 4 × 10 37 k 7/2 B 2 12 P −7/3 erg s −1 ≈ 2 × 10 33 erg s −1 , where k is assumed to be ∼ 0.5 for a disk geometry (Ghosh & Lamb 1978), which is inconsistent with the transitional luminosity we detected.
The data are obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center.This work is supported by the National Natural Science Foundation of China under grants No. 12173103.1.17 +0.13 −0.03 2.17 +0.28 −0.35 6.31 +0.17

Figure 1 .
Figure 1.Long-term lightcurve of 1A 0535+262 observed with Swift/BAT in the energy range of 15-50 keV.This source experienced several type-I outbursts and a giant outburst around MJD 59180.NICER observations used in this paper are marked with green arrows.

Figure 3 .
Figure 3.The evolution of spectral parameters in the faint states of 1A 0535+262 using the model of Tbabs*(powerlaw + bbodyrad + gauss).The green line shows the evolution of the photon index modelled with a broken powerlaw function.The black dashed lines represent the transitional luminosity Lt at ∼ 3.3 × 10 35 erg/s.

Figure 4 .
Figure 4. Left: the evolution of pulse profiles with luminosity.For clarity, we normalized the pulse profiles by their peak values.Right: representative pulse profiles at luminosities of 4.4 × 10 36 erg/s (panel c), 3.3 × 10 35 erg/s (panel d) and 1.2 × 10 35 erg/s (panel e), which are marked in the left panel with dashed lines.For the sake of comparison, we also present two pulse profiles (panels a and b) observed in the brighter states with luminosities of 8.0 × 10 37 erg/s and 4.3 × 10 37 erg/s, respectively.

Figure 5 .Figure 6 .
Figure 5. Evolutions of pulsed fraction (P F ) with luminosity for different NICER observations.The black dashed line indicates the transitional luminosity obtained from the spectral analysis.

Table A .
1. Best-fitting spectral parameters of NICER observations.

Table A .
1 continued on next page Table A.1 (continued)

Table A .
1 continued on next page