On the origin of cyclotron lines in the spectra of X-ray pulsars
Alexander A. Mushtukov, Juri Poutanen, Valery F. Suleimanov, Sergey S. Tsygankov, Dmitrij I. Nagirner, Victor Doroshenko, Alexander A. Lutovinov
aa r X i v : . [ a s t r o - ph . H E ] S e p The Journal’s name will be set by the publisherDOI: will be set by the publisherc (cid:13)
Owned by the authors, published by EDP Sciences, 2018
On the origin of cyclotron lines in the spectra of X-ray pulsars
A. A. Mushtukov , , , a , J. Poutanen , b , V. F. Suleimanov , , S. S. Tsygankov , , , D. I. Nagirner ,V. Doroshenko , and A. A. Lutovinov Astronomy Division, Department of Physics, POBox 3000, FI-90014 University of Oulu, Finland Sobolev Astronomical Institute, Saint Petersburg StateUniversity, Saint-Petersburg 198504, Russia Pulkovo Observatory of theRussian Academy of Sciences, Saint-Petersburg 196140, Russia InstitutfürAstronomie undAstrophysik, Kepler Center forAstroandParticlePhysics, Universität Tübingen,Sand 1, 72076 Tübingen, Germany Kazan (Volga region) Federal University, Kremlevskaja str., 18, Kazan 420008, Russia Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, FI-21500 Piikkiö,Finland SpaceResearchInstituteoftheRussianAcademyofSciences,ProfsoyuznayaStr. 84/32,Moscow117997,Russia
Abstract.
Cyclotron resonance scattering features are observed in the spectra of someX-ray pulsars and show significant changes in the line energy with the pulsar luminosity.In a case of bright sources, the line centroid energy is anti-correlated with the luminosity.Such a behaviour is often associated with the onset and growth of the accretion col-umn, which is believed to be the origin of the observed emission and the cyclotron lines.However, this scenario inevitably implies large gradient of the magnetic field strengthwithin the line-forming region, and it makes the formation of the observed line-like fea-tures problematic. Moreover, the observed variation of the cyclotron line energy is muchsmaller than could be anticipated for the corresponding luminosity changes. We arguethat a more physically realistic situation is that the cyclotron line forms when the radi-ation emitted by the accretion column is reflected from the neutron star surface. Theidea is based on the facts that a substantial part of column luminosity is intercepted bythe neutron star surface and the reflected radiation should contain absorption features.The reflection model is developed and applied to explain the observed variations of thecyclotron line energy in a bright X-ray pulsar V 0332 +
53 over a wide range of luminosi-ties.
X-ray pulsars are neutron stars in binary systems accreting matter usually from a massive companion.A strong magnetic field channels accreting gas towards magnetic poles and modifies the observedX-ray spectrum manifesting as the line-like absorption features, the so-called cyclotron lines. Suchcyclotron resonance scattering features (CRSF), sometimes also with harmonics, are observed in thespectra of several X-ray pulsars [1–3]. a e-mail: [email protected] b e-mail: juri.poutanen@oulu.fi he Journal’s name Figure 1.
Accreting X-ray pulsar geometry and the emergent spectrum. The larger is the luminosity, the higher isthe accretion column, the larger illuminated fraction of the neutron star surface, the weaker the average magneticfield, and the smaller the cyclotron line energy.
In some cases, the luminosity related changes of the line energy are observed, suggesting thatconfiguration of the line-forming region depends on the accretion rate. The line energy has beenreported to be positively-correlated with luminosity in relatively low-luminosity sources [4, 5] andnegatively-correlated in high-luminosity sources [6, 7], as well as uncorrelated with it [8].Here we will focus only on the high-luminosity case. The negative correlation of the CRSF en-ergy with luminosity is usually explained with the onset and growth of the accretion column at highluminosities [9]. In this scenario, the height of the column, and, therefore, the average displacementof the emission and the line-forming regions from the neutron star surface increase with luminosity,which to a shift of CRSF to lower energies. The problem is, however, that the predicted shift is muchlarger than the observed one. The column height depends on luminosity almost linearly [9] and themagnetic field weakens with distance as r − , and yet brightening by more than an order of magnitudeyields at most 25% decrease in the CRSF energy [7, 10]. Moreover, large gradient of the magneticfield and of the accretion velocity are expected to smear out the line-like features making it di ffi cultto explain why we observe CRSFs at all.We propose another scenario [11]. We show that a significant part of the radiation from the accre-tion column should be intercepted by the stellar surface because of the relativistic beaming (Section2.1 and [12, 13]), and the absorption features should exist in the radiation reflected from the mag-netised atmosphere (Section 2.2). Therefore, it is natural to assume that the line is formed in theatmosphere of the neutron star due to reflection of the intercepted radiation. In this case the negativecorrelation between the luminosity and the cyclotron line energy is reproduced because of the changesin the illuminated part of a stellar surface: if the B -field decreases away from the magnetic poles, therelatively high column could illuminate regions with relatively low field strength (see Fig. 1). The physical picture of the accretion on the magnetised neutron star is discussed in classical papers[9, 12]. At low accretion rate, free-falling material heat the neutron star surface near its magnetic hysics at the Magnetospheric Boundary poles, and the bright spots radiate energy in the X-ray range. At high accretion rate, the radiationpressure stops the infalling material above the neutron star surface in a radiation-dominated shock,after which the gas slowly sinks down towards the surface radiating the dissipated energy through theside walls of the accretion column. The column is expected to arise when the luminosity exceeds acritical value [9]: L ∗ ≈ × κ T κ k ! lR ! MM ⊙ ! erg s − , (1)where κ k is the electron scattering opacity along the magnetic field, κ T is the Thomson opacity, M and R are the mass and the radius of the star, l is the length of the accretion arc at the stellar surface.The column height depends on the mass accretion rate almost linearly [9, 13]: hR = ˙ m ln η + ˙ m ˙ m / ! , η = B d κ k π c √ GMR ! / = (cid:18) B × G (cid:19) / d
100 m ! / (cid:18) κ k . (cid:19) / , (2)where d is the thickness of the accretion arc, and ˙ m = L / L ∗∗ is a ratio of the X-ray pulsar luminosityto the limiting luminosity for the magnetised neutron star L ∗∗ ≈ l / d ! κ T κ k ! MM ⊙ ! erg s − . (3)Thus, the luminosity of X-ray pulsars in a bright state is in the range [ L ∗ , L ∗∗ ]. Since the radiation energy density drops o ff sharply towards the edge of the column, the height, wherematter stops, varies inside the accretion channel and depends on the distance from its edge. As a result,the height is maximal in the middle of the channel and decreases towards the borders. Therefore, theradiation from the already stopped matter should pass through a layer of the rapidly falling plasma,which is not supported by the radiation and falls down with velocity close to the free-fall velocity β = v/ c = √ r S / r (here r S = GM / c is the Schwarzschild radius). The optical thickness of theselayers is high enough to change dramatically the angular distribution of the emergent radiation, anddue to the relativistic beaming it is directed mainly towards the stellar surface. For the case of electron-scattering dominated column, the angular distribution of the column luminosity in the laboratoryframe is given by [11]: dL ( α ) d cos α = I D γ α (cid:18) + π D sin α (cid:19) , (4)where α is the angle between the photon momentum and the velocity vector, γ = / p − β is theLorentz factor, D = / [ γ (1 − β cos α )] is the Doppler factor, and I is the normalization constant.Thus, radiation from the accretion column is captured partly by the stellar surface, and its fraction L c / L could be substantial because of the beaming. The fraction obviously depends on the height ofthe column, brightness distribution over the column, radiation beam pattern and the compactness ofthe star. Fraction of the captured radiation for a case of point source above the neutron star surface asa function of the height-to-radius ratio is given in Fig. 2 and has quite high values even in a case whenthe height is comparable with the neutron star radius. he Journal’s name Radiation from the accretion column reaches the neutron star surface and is reflected. The most impor-tant process a ff ecting the spectrum of the reflected radiation is Compton scattering. The cross-sectionfor Compton scattering in a strong magnetic field is energy-dependent and has strong resonances.Photons at the resonance energies cannot penetrate deep into the atmosphere, they interact in the sur-face layers and scatter back changing the energy. This produces the lack of the photons in the linecore. In the cyclotron line wings, photons penetrate deeper into the atmosphere and scatter there alsochanging their energy. If they scatter into the resonance energy, they cannot leave the atmospherebecause of the larger optical depth there and escape instead in the line wings. Thus, the lack of thephotons near the resonance is not filled in and manifests itself as an absorption features in the spec-trum. The absorption features at the harmonic energies can be even stronger, because the absorbedphotons are mostly reemitted at the energy of the fundamental. The typical X-ray pulsar spectrumcuts o ff at ∼ + It is possible to estimate a line centroid energy in the context of the reflection model. Neglectingthe asymmetry in the line shape, the centroid of the CRSF in the reflected spectrum averaged over thesurface and all angles is determined by the B -field strength weighted with the distribution of flux, F ( θ ),and the line equivalent width over the neutron star surface. Assuming that the line equivalent width inthe reflected radiation is constant over the surface, the cyclotron line centroid energy is proportionalto the mean field E cycl ∝ h B i = π R B ( θ ) F ( θ ) sin θ d θ π R F ( θ ) sin θ d θ . (5)Note that the model immediately gives a limitation for changes in the cyclotron line energy. Be-cause for the dipole field, the B -field strength drops only by a factor of two from the pole to theequator, the line should lie in the energy interval [ E / E ], where E is the energy correspondingto the polar field B . A more realistic lower limit on the line energy can be obtained assuming auniformly illuminated surface, i.e. F ( θ ) = const. In that case h B i min = B π Z sin θ √ + θ d θ ≃ . B , (6)and, therefore, the model predicts the range of [0 . E ; E ] for the line centroids is in agreement withobservations [7, 10]. This prediction provides a test for the model.Thus, the problem of estimation of a line energy comes to the calculating of the flux distributionover the stellar surface. The standard deviation of the magnetic field σ B gives an estimate of the min-imum width of the line, since variations of the magnetic field over the surface lead to its smearing. Inour calculations we approximate the geometry of the accretion column by a thin stick at the magneticpole. This approximation is reasonably accurate for high B -field pulsars up to h . R . We also assumethat most of the energy is emitted in a region of characteristic scale ∆ h situated above the neutron starsurface at height h (see Fig. 1). hysics at the Magnetospheric Boundary h / R L c / L Figure 2.
Fraction of the captured radiation froma point source above the neutron star surface as afunction of the height-to-radius ratio. The dashedblue curve and the dotted red curve correspondto the isotropic source in flat space-time and inSchwarzschild metric correspondingly. The solidblack curve corresponds to the beaming patterngiven by equation (4). Here R = r S . L [10 erg s -1 ]2426283032 E c y c l [ k e V ] Figure 3.
Dependence of the cyclotron line energyon the luminosity in the X-ray pulsar V 0332 + ∆ h / h = . η = E = . L ∗∗ = × erg s − . The model was compared with the data from the X-ray pulsar V 0332 +
53 obtained with the
RXTE and
INTEGRAL observatories during outburst in 2004–2005 [7, 10]. The data set has the information aboutthe behavior of this object in a wide range of the luminosities, from ∼ up to ∼ × erg s − and shows negative correlation between the luminosity and the centroid of the CRSF.The best-fit theoretical relation of the cyclotron-line energy dependence on the luminosity forthe X-ray pulsar V 0332 +
53 [10] is shown in Fig. 3. It is clear that the data at luminosities above3 . × erg s − cannot be described by the model and we neglect them in the fits. The remainingdata are fitted with two free parameters E and L ∗∗ . We fix η =
15, because the results depend onthat parameter very weakly and vary ∆ h / h in the range between 0 and 1. The values of the limitingluminosity, L ∗∗ , obtained in the fits should be taken as the upper limits on the actual value givenby equation (3): radiation from the upper part of the column might be completely blocked by thefalling material and photons escape at a height significantly smaller than the top of the accretionshock because of their drift in the falling plasma.The fitting procedure shows that the best description of the data is achieved for a column withmost of the emission coming from its top. This does not necessarily mean that the lower part is notemitting, but rather that this emission does not hit the neutron star surface. Furthermore, our resultsare based on the assumption of the constant with latitude equivalent width of a line. Thus, our resultof the top-dominated emission from the column might be an artefact of this e ff ect. he Journal’s name A reflection model for the cyclotron line formation in the spectra of X-ray pulsars is proposed. It isbased on two facts: a large part of the column radiation is intercepted by the neutron star surface andthe absorption feature forms in the reflected radiation. Small variations of the magnetic field along thesurface imply that the line centroid energy can vary by at most 30% for a dipole field, and it makesmodel easily testable (i.e. it can be ruled out if larger variations are observed). Changes in the pulsarluminosity are expected to anti-correlate with the average magnetic field over the illuminated surfaceand, therefore, with the line centroid energy, exactly as observed during the outburst of the X-raypulsar V 0332 +
53. Our model explains well the observational data and has profound implications forthe interpretation of the data on the cyclotron lines observed in X-ray pulsars.The model implies that the cyclotron line should exhibit variations of its energy and equivalentwidth with the pulsar phase, since the observer would see di ff erent parts of the illuminated surfaceduring a pulse period. The specific model predictions are in the agreement with the pulse-resolvedobservational data obtained for the X-ray pulsar V 0332 +
53 [14].In order to predict the line parameters more accurately, a detailed model of the reflection of thecolumn radiation from the atmosphere is required. It will provide a possibility of detailed diagnosticof X-ray pulsars in a bright state.
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