Exploring helical dynamos with machine learning

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.Comment: accepted by A&A, 11 pages, 6 figures, 3 tables, data + IPython notebooks: https://github.com/fnauman/ML_alpha

X-ray bursts as a tool to constrain the equation of state of the ultra-dense matter inside neutron stars

Neutron stars are one of the most dense objects in the Universe. However, the exact description of the equation of state (EoS) of the cold ultra-dense matter inside them is still a mystery. In this thesis, we measure the size of some neutron stars using astrophysical observations of X-ray bursts that are produced by thermonuclear runaways in the uppermost layers of the star. By measuring the size, we can then set constraints on the nuclear physics of the interiors and ultimately on the EoS of the cold dense matter. The size measurements are done by comparing the cooling of the neutron star surfaces after the bursts to theoretical atmosphere model calculations. Hence, accurate modeling of the emergent radiation from the atmospheres is needed. In the first part of this thesis, I have studied how the emergent spectra differ if the atmosphere is enriched with nuclear burning ashes from the bursts. This gives us new tools to understand and interpret the X-ray burst observations. In addition, I have shown how the emerging radiation is modified when it originates from rapidly rotating oblate neutron stars. Furthermore, we must also be careful in selecting only those bursts that are not influenced by the infalling material. In the second part of the thesis, I have focused on studying the astrophysical environments of the X-ray bursts in order to quantify the effect of accretion on the mass and radius measurements. Importantly, it is shown that only the bursts that occur during the low-accretion-rate (hard) state can be used for the size determination because otherwise the accretion flow might influence the cooling of the stellar surface. After taking these steps into account, it is possible to set constraints on the mass, radius, distance, and atmosphere composition of neutron stars exhibiting X-ray bursts. In the third part of the thesis, I have used the aforementioned models and methods to constrain the mass and radius of neutron stars using the hard state X-ray bursts. The method has been applied to three neutrons stars in low-mass X-ray binary systems 4U 1702-429, 4U 1724-307, and SAX J1810.8-260 for which the radius is measured to be between 10.9 - 12.4 km (68% credibility). The newly computed atmosphere models have also been used to detect a presence of burning ashes in the atmosphere of the neutron star in HETE J1900.1-2455. Later on, an improved Bayesian method of fitting the atmosphere models directly to the observed spectra has also improved the radius constraints of 4U 1702-429 to R = 12.4 +- 0.4 km (68% credibility). These results are in a good agreement with the current nuclear physical predictions and demonstrate how astrophysical measurements can be used to gauge the unknown nuclear physics of neutron stars.Neutronitähdet ovat universumimme tiheimpiä tähtiä. Niiden sisältämän erittäin tiheän kylmän aineen tilanyhtälö ja tarkka käyttäytyminen ovat kuitenkin vielä tuntemattomia. Tässä väitöskirjassa näytän kuinka kaukaisenkin neutronitähden koko voidaan mitata hyödyntäen niin kutsuttujen röntgenpurkausten lähettämää säteilyä. Röntenpurkaukset saavat alkunsa termisestä fuusioreaktiosta joka tuottaa valtaisan räjähdyksen tähden pintakerroksissa. Mittaamalla ja mallintamalla näistä purkauksista syntyvää säteilyä, saamme tietoa neutronitähtien sisältämän aineen käyttäytymisestä ja siten myös kylmän tiheän aineen tilanyhtälöstä. Mittaukset tehdään vertaamalla neutronitähtien pinnalta alkunsa saavaa säteilyä teoreettisiin ilmakehämalleihin jotka ennustavat kuinka pinnan tulisi jäähtyä purkausten jälkeen. Tämän takia tarvitsemme tarkkoja malleja säteilyn kulusta ilmakehässä. Ensimmäisessä osassa väitöskirjaani olen tutkinut kuinka ilmakehässä olevat raskaat fuusioreaktioissa syntyneet alkuaineet vaikuttavat tämän säteilyn etenemiseen ilmakehän plasmassa. Tämä auttaa meitä ymmärtämään ja tulkitsemaan myös röntgenpurkauksista tehtyjä havaintoja. Lisäksi olen näyttänyt kuinka havaittu säteily muuttuu, kun se saa alkunsa erittäin nopeasti pyörivästä ja navoiltaan litistyneestä neutronitähdestä. Tarkkojen ilmakehämallien lisäksi meidän täytyy myös ymmärtää mitä neutronitähden ympärillä tapahtuu. Väitöskirjani toisessa osassa tutkin kuinka ympäristö voi vaikuttaa herkkiin tähden säteen mittauksiin, koska joskus neutronitähden pinnalle putoava materia voi häiritä mittauksia. Tärkein löydöksemme on, että säteen luotettavaan mittaamiseen voidaan käyttää vain sellaisia purkauksia, jotka tapahtuvat kun putoavaa materiaa on erittäin vähän. Kun edellä mainitut seikat huomioidaan on mahdollista mitata neutronitähden koko, etäisyys, ja ilmakehän koostumus vertaamalla oikeiden, havaittujen röntgenpurkausten jäähtymistä mallien ennusteisiin. Viimeisessä osassa väitöskirjaani olen tutkinut kolmen eri neutronitähden röntgenpurkausten säteilyä. Kyseiset neutronitähdet sijaitsevat kaksoistähtijärjestelmissä 4U 1702-429, 4U 1724-307, ja SAX J1810.8-260. Kyseisten neutronitähtien säde on mittauksieni mukaan 10.9 ja 12.4 km välillä (68% luottamustaso). Uusien ilmakehämallien avulla olemme myös todistaneet, että kaksoistähtijärjestelmässä HETE J1900.1-2455 sijaitsevan neutronitähden pintakerrokset sisältävät fuusioreaktion aikana syntyneitä raskaita alkuaineita. Kehitin myös uudenlaisen Bayesilaisen metodin, jossa ilmakehämalleja voidaan sovittaa suoraan röntgenpurkauksista tehtyihin havaintoihin. Tätä metodia käyttäen mittasin 4U 1724-429:ssä sijaitsevan neutronitähden säteeksi R=12.4 +- 0.4 km (68% luottamustaso). Nämä uudet tulokset ovat sopusoinnussa uusien ydinfysikaalisten ennusteiden kanssa. Lisäksi ne näyttävät kuinka astrofysikaalisia mittauksia voidaan käyttää apuna ydinfysiikan tutkimuksessa

Kilohertz quasi-periodic oscillations from neutron star spreading layers

When the accretion disc around a weakly magnetised neutron star (NS) meets the stellar surface, it should brake down to match the rotation of the NS, forming a boundary layer. As the mechanisms potentially responsible for this braking are apparently inefficient, it is reasonable to consider this layer as a spreading layer (SL) with negligible radial extent and structure. We perform hydrodynamical 2D spectral simulations of an SL, considering the disc as a source of matter and angular momentum. Interaction of new, rapidly rotating matter with the pre-existing, relatively slow material co-rotating with the star leads to instabilities capable of transferring angular momentum and creating variability on dynamical timescales. For small accretion rates, we find that the SL is unstable for heating instability that disrupts the initial latitudinal symmetry and produces large deviations between the two hemispheres. This instability also results in breaking of the axial symmetry as coherent flow structures are formed and escape from the SL intermittently. At enhanced accretion rates, the SL is prone to shearing instability and acts as a source of oblique waves that propagate towards the poles, leading to patterns that again break the axial symmetry. We compute artificial light curves of an SL viewed at different inclination angles. Most of the simulated light curves show oscillations at frequencies close to 1kHz. We interpret these oscillations as inertial modes excited by shear instabilities near the boundary of the SL. Their frequencies, dependence on flux, and amplitude variations can explain the high-frequency pair quasi-periodic oscillations observed in many low-mass X-ray binaries.Comment: accepted to A&A; 22 pages, 21 figur

Models of neutron star atmospheres enriched with nuclear burning ashes

Low-mass X-ray binaries hosting neutron stars (NS) exhibit thermonuclear (type-I) X-ray bursts, which are powered by unstable nuclear burning of helium and/or hydrogen into heavier elements deep in the NS "ocean". In some cases the burning ashes may rise from the burning depths up to the NS photosphere by convection, leading to the appearance of the metal absorption edges in the spectra, which then force the emergent X-ray burst spectra to shift toward lower energies. These effects may have a substantial impact on the color correction factor $f_c$ and the dilution factor $w$, the parameters of the diluted blackbody model $F_E \approx w B_E(f_c T_{eff})$ that is commonly used to describe the emergent spectra from NSs. The aim of this paper is to quantify how much the metal enrichment can change these factors. We have developed a new NS atmosphere modeling code, which has a few important improvements compared to our previous code required by inclusion of the metals. The opacities and the internal partition functions (used in the ionization fraction calculations) are now taken into account for all atomic species. In addition, the code is now parallelized to counter the increased computational load. We compute a detailed grid of atmosphere models with different exotic chemical compositions that mimic the presence of the burning ashes. From the emerging model spectra we compute the color correction factors $f_c$ and the dilution factors $w$ that can then be compared to the observations. We find that the metals may change $f_c$ by up to about 40%, which is enough to explain the scatter seen in the blackbody radius measurements. The presented models open up the possibility for determining NS mass and radii more accurately, and may also act as a tool to probe the nuclear burning mechanisms of X-ray bursts.Comment: 14 pages, 7 figures, to be published in A&

Relativistic Collisionless Shocks in Inhomogeneous Magnetized Plasmas

Relativistic collisionless shocks are associated with efficient particle acceleration when propagating into weakly magnetized homogeneous media; as the magnetization increases, particle acceleration becomes suppressed. We demonstrate that this changes when the upstream carries kinetic-scale inhomogeneities, as is often the case in astrophysical environments. We use fully-kinetic simulations to study relativistic perpendicular shocks in magnetized pair plasmas interacting with upstream density perturbations. The upstream fluctuations are found to corrugate the shock front and generate large-scale turbulent shear motions in the downstream, which in turn are capable of accelerating particles. This can revive relativistic magnetized shocks as viable energization sites in astrophysical systems, such as jets and accretion disks. The generation of large-scale magnetic structures also has important implications for polarization signals from blazars.Comment: 8 pages, 5 figure

Oblate Schwarzschild approximation for polarized radiation from rapidly rotating neutron stars

We have developed a complete theory for the calculation of the observed Stokes parameters for radiation emitted from the surface of a rapidly rotating neutron star (NS) using the oblate Schwarzschild approximation. We accounted for the rotation of the polarization plane due to relativistic effects along the path from the stellar surface to the observer. The results were shown to agree with those obtained by performing full numerical general relativistic ray-tracing with the \textsc{arcmancer} code. We showed that the obtained polarization angle (PA) profiles may differ substantially from those derived for a spherical star. We demonstrated that assuming incorrect shape for the star can lead to biased constraints for NS parameters when fitting the polarization data. Using a simplified model, we also made a rough estimate of how accurately the geometrical parameters of an accreting NS can be determined using the X-ray polarization measurements of upcoming polarimeters like the Imaging X-ray Polarimeter Explorer (IXPE) or the enhanced X-ray Timing and Polarimetry (eXTP) mission.Comment: 11 pages, 10 figures, accepted in A&

Magnetospheric return-current-heated atmospheres of rotation-powered millisecond pulsars

We computed accurate atmosphere models of rotation-powered millisecond pulsars in which the polar caps of a neutron star (NS) are externally heated by magnetospheric return currents. The external ram pressure, energy losses, and stopping depth of the penetrating charged particles were computed self-consistently with the atmosphere model, instead of assuming a simplified deep-heated atmosphere in radiative equilibrium. We used exact Compton scattering formalism to model the properties of the emergent X-ray radiation. The deep-heating approximation was found to be valid only if most of the heat originates from ultra-relativistic bombarding particles with Lorentz factors of $\gamma \gtrsim 100$. In the opposite regime, the atmosphere attains a distinct two-layer structure with an overheated optically thin skin on top of an optically thick cool plasma. The overheated skin strongly modifies the emergent radiation: it produces a Compton-upscattered high-energy tail in the spectrum and alters the radiation beaming pattern from limb darkening to limb brightening for emitted hard X-rays. This kind of drastic change in the emission properties can have a significant impact on the inferred NS pulse profile parameters as performed, for example, by Neutron star Interior Composition ExploreR. Finally, the connection between the energy distribution of the return current particles and the atmosphere emission properties offers a new tool to probe the exact physics of pulsar magnetospheres.Comment: 13 pages, 10 figures, published in A&

Kilohertz quasi-periodic oscillations from neutron star spreading layers

When the accretion disc around a weakly magnetised neutron star (NS) meets the stellar surface, it should brake down to match the rotation of the NS, forming a boundary layer. As the mechanisms potentially responsible for this braking are apparently inefficient, it is reasonable to consider this layer as a spreading layer (SL) with negligible radial extent and structure. We perform hydrodynamical 2D spectral simulations of an SL, considering the disc as a source of matter and angular momentum. Interaction of new, rapidly rotating matter with the pre-existing, relatively slow material co-rotating with the star leads to instabilities capable of transferring angular momentum and creating variability on dynamical timescales. For small accretion rates, we find that the SL is unstable for heating instability that disrupts the initial latitudinal symmetry and produces large deviations between the two hemispheres. This instability also results in breaking of the axial symmetry as coherent flow structures are formed and escape from the SL intermittently. At enhanced accretion rates, the SL is prone to shearing instability and acts as a source of oblique waves that propagate towards the poles, leading to patterns that again break the axial symmetry. We compute artificial light curves of an SL viewed at different inclination angles. Most of the simulated light curves show oscillations at frequencies close to 1 kHz. We interpret these oscillations as inertial modes excited by shear instabilities near the boundary of the SL. Their frequencies, dependence on flux, and amplitude variations can explain the high-frequency pair quasi-periodic oscillations observed in many low-mass X-ray binaries

Evidence for quark-matter cores in massive neutron stars

The theory governing the strong nuclear force—quantum chromodynamics—predicts that at sufficiently high energy densities, hadronic nuclear matter undergoes a deconfinement transition to a new phase of quarks and gluons1. Although this has been observed in ultrarelativistic heavy-ion collisions2,3, it is currently an open question whether quark matter exists inside neutron stars4. By combining astrophysical observations and theoretical ab initio calculations in a model-independent way, we find that the inferred properties of matter in the cores of neutron stars with mass corresponding to 1.4 solar masses (M⊙) are compatible with nuclear model calculations. However, the matter in the interior of maximally massive stable neutron stars exhibits characteristics of the deconfined phase, which we interpret as evidence for the presence of quark-matter cores. For the heaviest reliably observed neutron stars5,6 with mass M ≈ 2M⊙, the presence of quark matter is found to be linked to the behaviour of the speed of sound cs in strongly interacting matter. If the conformal bound c2s≤1/3 (ref. 7) is not strongly violated, massive neutron stars are predicted to have sizable quark-matter cores. This finding has important implications for the phenomenology of neutron stars and affects the dynamics of neutron star mergers with at least one sufficiently massive participant.publishedVersio