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  • 1. Kajava, J. J. E.
    et al.
    Koljonen, K. I. I.
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Suleimanov, V.
    Poutanen, J.
    Variable spreading layer in 4U 1608-52 during thermonuclear X-ray bursts in the soft state2017In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 472, no 1, p. 78-89Article in journal (Refereed)
    Abstract [en]

    Thermonuclear (type-I) X-ray bursts, observed from neutron star (NS) low-massX-ray binaries (LMXB), provide constraints on NS masses and radii and consequently the equation of state of NS cores. In such analyses, various assumptions are made without knowing if they are justified. We have analysed X-ray burst spectra from the LMXB 4U 1608-52, with the aim of studying how the different persistent emission components react to the bursts. During some bursts in the soft spectral state we find that there are two variable components: one corresponding to the burst blackbody component and another optically thick Comptonized component. We interpret the latter as the spreading layer between the NS surface and the accretion disc, which is not present during the hard-state bursts. We propose that the spectral changes during the soft-state bursts are driven by the spreading layer that could cover almost the entire NS in the brightest phases due to the enhanced radiation pressure support provided by the burst, and that the layer subsequently returns to its original state during the burst decay. When deriving the NS mass and radius using the soft-state bursts two assumptions are therefore not met: the NS is not entirely visible and the burst emission is reprocessed in the spreading layer, causing distortions of the emitted spectrum. For these reasons, the NS mass and radius constraints using the soft-state bursts are different compared to the ones derived using the hard-state bursts.

  • 2. Kajava, J. J. E.
    et al.
    Nättilä, Joonas N.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Poutanen, Juri
    Cumming, A.
    Suleimanov, V.
    Kuulkers, E.
    Detection of burning ashes from thermonuclear X-ray bursts2017In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 464, no 1, p. L6-L10Article in journal (Refereed)
    Abstract [en]

    When neutron stars (NS) accrete gas from low-mass binary companions, explosive nuclear burning reactions in the NS envelope fuse hydrogen and helium into heavier elements. The resulting thermonuclear (type-I) X-ray bursts produce energy spectra that are fit well with black bodies, but a significant number of burst observations show deviations from Planck spectra. Here we present our analysis of RXTE/ PCA observations of X-ray bursts from the NS low-mass X-ray binary HETE J1900.1-2455. We have discovered that the non-Planckian spectra are caused by photoionization edges. The anticorrelation between the strength of the edges and the colour temperature suggests that the edges are produced by the nuclear burning ashes that have been transported upwards by convection and become exposed at the photosphere. The atmosphere model fits show that occasionally the photosphere can consist entirely of metals, and that the peculiar changes in blackbody temperature and radius can be attributed to the emergence and disappearance of metals in the photosphere. As the metals are detected already in the Eddington-limited phase, it is possible that a radiatively driven wind ejects some of the burning ashes into the interstellar space.

  • 3. Kuuttila, J.
    et al.
    Kajava, J. J. E.
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Motta, S. E.
    Sanchez-Fernandez, C.
    Kuulkers, E.
    Cumming, A.
    Poutanen, J.
    Flux decay during thermonuclear X-ray bursts analysed with the dynamic power-law index method2017In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 604, article id A77Article in journal (Refereed)
    Abstract [en]

    The cooling of type-I X-ray bursts can be used to probe the nuclear burning conditions in neutron star envelopes. The flux decay of the bursts has been traditionally modelled with an exponential, even if theoretical considerations predict power-law-like decays. We have analysed a total of 540 type-I X-ray bursts from five low-mass X-ray binaries observed with the Rossi X-ray Timing Explorer. We grouped the bursts according to the source spectral state during which they were observed (hard or soft), flagging those bursts that showed signs of photospheric radius expansion (PRE). The decay phase of all the bursts were then fitted with a dynamic power-law index method. This method provides a new way of probing the chemical composition of the accreted material. Our results show that in the hydrogen-rich sources the power-law decay index is variable during the burst tails and that simple cooling models qualitatively describe the cooling of presumably helium-rich sources 4U 1728-34 and 3A 1820-303. The cooling in the hydrogen-rich sources 4U 1608-52, 4U 1636-536, and GS 1826-24, instead, is clearly different and depends on the spectral states and whether PRE occurred or not. Especially the hard state bursts behave differently than the models predict, exhibiting a peculiar rise in the cooling index at low burst fluxes, which suggests that the cooling in the tail is much faster than expected. Our results indicate that the drivers of the bursting behaviour are not only the accretion rate and chemical composition of the accreted material, but also the cooling that is somehow linked to the spectral states. The latter suggests that the properties of the burning layers deep in the neutron star envelope might be impacted differently depending on the spectral state.

  • 4. Li, Zhaosheng
    et al.
    Suleimanov, Valery F.
    Poutanen, Juri
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Space Research Institute of the Russian Academy of Sciences, Russia; University of Turku, Finland.
    Salmi, Tuomo
    Falanga, Maurizio
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Xu, Renxin
    Evidence for the Photoionization Absorption Edge in a Photospheric Radius Expansion X-Ray Burst from GRS 1747-312 in Terzan 62018In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 866, no 1, article id 53Article in journal (Refereed)
    Abstract [en]

    Thermonuclear X-ray bursts on the surface of neutron stars (NSs) can enrich the photosphere with metals, which may imprint photoionization edges on the burst spectra. We report here the discovery of absorption edges in the spectra of the type I X-ray burst from the NS low-mass X-ray binary GRS 1747-312 in Terzan 6 during observations by the Rossi X-ray Timing Explorer. We find that the edge energy evolves from 9.45 +/- 0.51 to similar to 6 keV and then back to 9.44 +/- 0.40 keV during the photospheric radius expansion phase and remains at 8.06 +/- 0.66 keV in the cooling tail. The photoionization absorption edges of hydrogen-like Ni, Fe, or an Fe/Ni mixture and the bound-bound transitions of metals may be responsible for the observed spectral features. The ratio of the measured absorption edge energy in the cooling tail to the laboratory value of the hydrogen-like Ni(Fe) edge energy allows us to estimate the gravitational redshift factor 1 + z = 1.34 +/- 0.11(1 + z = 1.15 +/- 0.09). The evolution of the spectral parameters during the cooling tail are well described by metal-rich atmosphere models. The combined constraints on the NS mass and radius from the direct cooling method and the tidal deformability strongly suggest very high atmospheric abundance of the iron group elements and limit the distance to the source to 11 +/- 1 kpc.

  • 5. Nauman, Farrukh
    et al.
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Exploring helical dynamos with machine learning: Regularized linear regression outperforms ensemble methods2019In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 629, article id A89Article in journal (Refereed)
    Abstract [en]

    We use ensemble machine learning algorithms to study the evolution of magnetic fields in magnetohydrodynamic (MHD) turbulence that is helically forced. We perform direct numerical simulations of helically forced turbulence using mean field formalism, with electromotive force (EMF) modeled both as a linear and non-linear function of the mean magnetic field and current density. The form of the EMF is determined using regularized linear regression and random forests. We also compare various analytical models to the data using Bayesian inference with Markov chain Monte Carlo (MCMC) sampling. Our results demonstrate that linear regression is largely successful at predicting the EMF and the use of more sophisticated algorithms (random forests, MCMC) do not lead to significant improvement in the fits. We conclude that the data we are looking at is effectively low dimensional and essentially linear. Finally, to encourage further exploration by the community, we provide all of our simulation data and analysis scripts as open source IPYTHON notebooks.

  • 6.
    Nättilä, Jonas
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Miller, M. C.
    Steiner, A. W.
    Kajava, J. J. E.
    Suleimanov, V. F.
    Poutanen, J.
    Neutron star mass and radius measurements from atmospheric model fits to X-ray burst cooling tail spectra2017In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 608, article id A31Article in journal (Refereed)
    Abstract [en]

    Observations of thermonuclear X-ray bursts from accreting neutron stars (NSs) in low-mass X-ray binary systems can be used to constrain NS masses and radii. Most previous work of this type has set these constraints using Planck function fits as a proxy: the models and the data are both fit with diluted blackbody functions to yield normalizations and temperatures that are then compared with each other. For the first time, we here fit atmosphere models of X-ray bursting NSs directly to the observed spectra. We present a hierarchical Bayesian fitting framework that uses current X-ray bursting NS atmosphere models with realistic opacities and relativistic exact Compton scattering kernels as a model for the surface emission. We test our approach against synthetic data and find that for data that are well described by our model, we can obtain robust radius, mass, distance, and composition measurements. We then apply our technique to Rossi X-ray Timing Explorer observations of five hard-state X-ray bursts from 4U 1702-429. Our joint fit to all five bursts shows that the theoretical atmosphere models describe the data well, but there are still some unmodeled features in the spectrum corresponding to a relative error of 1-5% of the energy flux. After marginalizing over this intrinsic scatter, we find that at 68% credibility, the circumferential radius of the NS in 4U 1702-429 is R = 12.4 +/- 0.4 km, the gravitational mass is M = 1.9 +/- 0.3 M-circle dot, the distance is 5.1 < D/kpc < 6.2, and the hydrogen mass fraction is X < 0.09.

  • 7.
    Nättilä, Joonas
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Pihajoki, P.
    Radiation from rapidly rotating oblate neutron stars2018In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 615, article id A50Article in journal (Refereed)
    Abstract [en]

    A theoretical framework for emission originating from rapidly rotating oblate compact objects is described in detail. Using a Hamilton-Jacobi formalism, we show that special relativistic rotational effects such as aberration of angles, Doppler boosting, and time dilatation naturally emerge from the general relativistic treatment of rotating compact objects. We use the Butterworth-Ipser metric expanded up to the second order in rotation and hence include effects of light bending, frame-dragging, and quadrupole deviations on our geodesic calculations. We also give detailed descriptions of the numerical algorithms used and provide an open-source implementation of the numerical framework called BENDER. As an application, we study spectral line profiles (i.e., smearing kernels) from rapidly rotating oblate neutron stars. We find that in this metric description, the second-order quadrupole effects are not strong enough to produce narrow observable features in the spectral energy distribution for almost any physically realistic parameter combination, and hence, actually detecting them is unlikely. The full width at tenth-maximum and full width at half-maximum of the rotation smearing kernels are also reported for all viewing angles. These can then be used to quantitatively estimate the effects of rotational smearing on the observed spectra. We also calculate accurate pulse profiles and observer skymaps of emission from hot spots on rapidly rotating accreting millisecond pulsars. These allow us to quantify the strength of the pulse fractions one expects to observe from typical fast-spinning millisecond pulsars.

  • 8. Pihajoki, Pauli
    et al.
    Mannerkoski, Matias
    Nattila, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Johansson, Peter H.
    General Purpose Ray Tracing and Polarized Radiative Transfer in General Relativity2018In: Astrophysical Journal, ISSN 0004-637X, E-ISSN 1538-4357, Vol. 863, no 1, article id 8Article in journal (Refereed)
    Abstract [en]

    Ray tracing is a central tool for constructing mock observations of compact object emission and for comparing physical emission models with observations. We present ARCMANCER, a publicly available general ray-tracing and tensor algebra library, written in C++ and providing a Python interface. ARCMANCER supports Riemannian and semi-Riemannian spaces of any dimension and metric, and has novel features such as support for multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. The ARCMANCER interface is extensively documented and user friendly. While these capabilities make the library well suited for a large variety of problems in numerical geometry, the main focus of this paper is in general relativistic polarized radiative transfer. The accuracy of the code is demonstrated in several code tests and in a comparison with GRTRANS, an existing ray-tracing code. We then use the library in several scenarios as a way to showcase the wide applicability of the code. We study a thin variable-geometry accretion disk model and find that polarization carries information of the inner disk opening angle. Next, we study rotating neutron stars and determine that to obtain polarized light curves at better than a similar to 1% level of accuracy, the rotation needs to be taken into account both in the spacetime metric and in the shape of the star. Finally, we investigate the observational signatures of an accreting black hole lensed by an orbiting black hole. We find that these systems exhibit a characteristic asymmetric twin-peak profile both in flux and polarization properties.

  • 9. Salmi, T.
    et al.
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Poutanen, Juri
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland; Institute of the Russian Academy of Sciences, Russia.
    Bayesian parameter constraints for neutron star masses and radii using X-ray timing observations of accretion-powered millisecond pulsars2018In: Astronomy and Astrophysics, ISSN 0004-6361, E-ISSN 1432-0746, Vol. 618, article id A161Article in journal (Refereed)
    Abstract [en]

    We present a Bayesian method to constrain the masses and radii of neutron stars (NSs) using the information encoded in the X-ray pulse profiles of accreting millisecond pulsars. We model the shape of the pulses using oblate Schwarzschild approximation, which takes into account the deformed shape of the star together with the special and general relativistic corrections to the photon trajectories and angles. The spectrum of the radiation is obtained from an empirical model of Comptonization in a hot slab in which a fraction of seed black-body photons is scattered into a power-law component. By using an affine-invariant Markov chain Monte Carlo ensemble sampling method, we obtain posterior probability distributions for the different model parameters, especially for the mass and the radius. To test the robustness of our method, we first analysed self-generated synthetic data with known model parameters Similar analysis was then applied for the observations of SAX J1808.4-3658 by the Rossi X-ray Timing Explorer (RXTE). The results show that our method can reproduce the model parameters of the synthetic data, and that accurate constraints for the radius can be obtained using the RXTE pulse profile observations if the mass is a priori known. For a mass in the range 1.5-1.8 M-circle dot, the radius of the NS in SAX J1808.4-3658 is constrained between 9 and 13 km. If the mass is accurately known, the radius can be determined with an accuracy of 5% (68% credibility). For example, for the mass of 1.7 M-circle dot the equatorial radius is R-eq = 11.9(-0.4)(+0.5) km. Finally, we show that further improvements can be obtained when the X-ray polarization data from the Imaging X-ray Polarimeter Explorer will become available.

  • 10. Suleimanov, Valery F.
    et al.
    Kajava, Jari J. E.
    Molkov, Sergey V.
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Lutovinov, Alexander A.
    Werner, Klaus
    Poutanen, Juri
    Basic parameters of the helium-accreting X-ray bursting neutron star in 4U 1820-302017In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 472, no 4, p. 3905-3913Article in journal (Refereed)
    Abstract [en]

    The ultracompact low-mass X-ray binary 4U 1820-30 situated in the globular cluster NGC 6624 has an orbital period of only approximate to 11.4 min, which likely implies a white dwarf companion. The observed X-ray bursts demonstrate a photospheric radius expansion phase and therefore are believed to reach the Eddington luminosity, allowing us to estimate the mass and the radius of the neutron star (NS) in this binary. Here, we re-analyse all Rossi X-ray Timing Explorer observations of the system and confirm that almost all the bursts took place during the hard persistent state of the system. This allows us to use the recently developed direct cooling tail method to estimate the NS mass and radius. However, because of the very short, about a second, duration of the cooling tail phases that can be described by the theoretical atmosphere models, the obtained constraints on the NS radius are not very strict. Assuming a pure helium NS atmosphere, we found that the NS radius is in the range 10-12 km, if the NS mass is below 1.7 M-circle dot, and in a wider range of 8-12 km for a higher 1.7-2.0 M-circle dot NS mass. The method also constrains the distance to the system to be 6.5 +/- 0.5 kpc, which is consistent with the distance to the cluster. For the solar composition atmosphere, the NS parameters are in strong contradiction with the generally accepted range of possible NS masses and radii.

  • 11. Suleimanov, Valery F.
    et al.
    Poutanen, Juri
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Kajava, Jari J. E.
    Revnivtsev, Mikhail G.
    Werner, Klaus
    The direct cooling tail method for X-ray burst analysis to constrain neutron star masses and radii2017In: Monthly notices of the Royal Astronomical Society, ISSN 0035-8711, E-ISSN 1365-2966, Vol. 466, no 1, p. 906-913Article in journal (Refereed)
    Abstract [en]

    Determining neutron star (NS) radii and masses can help to understand the properties of matter at supra-nuclear densities. Thermal emission during thermonuclear X-ray bursts from NSs in low-mass X-ray binaries provides a unique opportunity to study NS parameters, because of the high fluxes, large luminosity variations and the related changes in the spectral properties. The standard cooling tail method uses hot NS atmosphere models to convert the observed spectral evolution during cooling stages of X-ray bursts to the Eddington flux F-Edd and the stellar angular size Omega. These are then translated to the constraints on the NS massMand radius R. Here we present the improved, direct cooling tail method that generalizes the standard approach. First, we adjust the cooling tail method to account for the bolometric correction to the flux. Then, we fit the observed dependence of the blackbody normalization on flux with a theoretical model directly on theM-R plane by interpolating theoretical dependences to a given gravity, hence ensuring only weakly informative priors for M and R instead of FEdd and Omega. The direct cooling method is demonstrated using a photospheric radius expansion burst from SAX J1810.8-2609, which has happened when the system was in the hard state. Comparing to the standard cooling tail method, the confidence regions are shifted by 1 sigma towards larger radii, giving R = 11.5-13.0 km at M = 1.3-1.8M(circle dot) for this NS.

  • 12. Watts, Anna L.
    et al.
    Yu, WenFei
    Poutanen, Juri
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, .
    Zhang, Shu
    Bhattacharyya, Sudip
    Bogdanov, Slavko
    Ji, Long
    Patruno, Alessandro
    Riley, Thomas E.
    Bakala, Pavel
    Baykal, Altan
    Bernardini, Federico
    Bombaci, Ignazio
    Brown, Edward
    Cavecchi, Yuri
    Chakrabarty, Deepto
    Chenevez, Jerome
    Degenaar, Nathalie
    Del Santo, Melania
    Di Salvo, Tiziana
    Doroshenko, Victor
    Falanga, Maurizio
    Ferdman, Robert D.
    Feroci, Marco
    Gambino, Angelo F.
    Ge, MingYu
    Greif, Svenja K.
    Guillot, Sebastien
    Gungor, Can
    Hartmann, Dieter H.
    Hebeler, Kai
    Heger, Alexander
    Homan, Jeroen
    Iaria, Rosario
    in 't Zand, Jean
    Kargaltsev, Oleg
    Kurkela, Aleksi
    Lai, XiaoYu
    Li, Ang
    Li, XiangDong
    Li, ZhaoSheng
    Linares, Manuel
    Lu, FangJun
    Mahmoodifar, Simin
    Mendez, Mariano
    Miller, M. Coleman
    Morsink, Sharon
    Nättilä, Joonas
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). University of Turku, Finland.
    Possenti, Andrea
    Prescod-Weinstein, Chanda
    Qu, JinLu
    Riggio, Alessandro
    Salmi, Tuomo
    Sanna, Andrea
    Santangelo, Andrea
    Schatz, Hendrik
    Schwenk, Achim
    Song, LiMing
    Sramkova, Eva
    Stappers, Benjamin
    Stiele, Holger
    Strohmayer, Tod
    Tews, Ingo
    Tolos, Laura
    Torok, Gabriel
    Tsang, David
    Urbanec, Martin
    Vacchi, Andrea
    Xu, RenXin
    Xu, YuPeng
    Zane, Silvia
    Zhang, GuoBao
    Zhang, ShuangNan
    Zhang, WenDa
    Zheng, ShiJie
    Zhou, Xia
    Dense matter with eXTP2019In: Science China Physics, Mechanics & Astronomy, ISSN 1674-7348, Vol. 62, no 2, article id 029503Article, review/survey (Refereed)
    Abstract [en]

    In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is expected to be launched in the mid 2020s.

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