Science with eXTP

The core science case of the mission is the study of the behavior of matter under extreme conditions that cannot be attained on earth. More specifically three key objectives constitute the main eXTP science program:

• the study of matter in ultra dense condition;
• the physics and astrophysics of strong magnetic fields;
• the physics of accretion in the strong-field limit of gravity.

Dense matter with eXTP

One of the key goals of modern physics is to understand the nature of strong interactions, which determines the state of nuclear matter and sets the physics of neutron stars (NS), where gravity compresses matter to nuclear densities. Densities in NS cores can reach about 10 times the one of an atomic nucleus most likely forming “exotic” states and phases of matters, impossible to be realized in the laboratory: nuclear superfluids, strange matter such as hyperons and deconfined quarks, and the color superconductor phase. Observations of NS can allow accessing a unique regime of parameter space at high densities (e.g. high baryon chemical potential) and low temperatures, complementing therefore the research at the Large Hadron Collider and other heavy ion collision experiments, which aim to probe high temperatures and low densities. To connect strong interaction physics with observables we can use the NS equation of state (EOS) that relates pressure and density of the star. The EOS is encoded in the mass vs. radius diagram (M-R diagram) via the stellar structure equations. The knowledge of the M-R relation allows the determination of the NS EOS and enables the understanding of the microphysics at work in the extreme density regions in the interior of NS.

The research for the physics of strong interactions spans a wide parameters space, ranging from experiments at terrestrial accelerators, such as at LHC and RHIC, to observations of NS. In particular the low temperature vs. high Baryon chemical potential (e.g. extreme densities) regime can be explored by NS astrophysics. Progress in understanding NS matter will most likely reveal new matter states and phases. Figure is taken from the recent and exhaustive review by A. Watts and colleagues (2016)

Different EOS are predicted by different microphysics and convert to different M-R relations. More specifically the grey band corresponds to a range of nucleonic EOS based on chiral effective field theory. In red nucleonic EOS are shown. The black curves show the predictions of Hybrid models with strange quark core (black solid) and (black dashed) hyperon core model. Magenta: quark star model.

The key observational step is the measurement of M and R with a few % precision and for several sources. Constraints obtained so far with different techniques, such as the modeling of the spectra of thermonuclear type I bursts or radio pulsar timing (see e.g. [15, 18, 19, 20] and references therein), are weak. eXTP will mainly use two techniques to constrain M and R for several NS: pulse profile modeling and spin measurements. Hotspots developing on a low magnetized, fast spinning NS give rise to observed pulse profiles that are strongly affected by GR light-bending and relativistic Doppler boosting and aberration. These relativistic effects, which depend on (for example) NS compactness M/R, strongly affect the amplitude of the pulsation and the asymmetry and harmonic content of the emerging profiles. By fitting high quality (i.e. high statistics) profiles M and R can be recovered in spite of degeneracies due to unknown factors like e.g. the geometry of the hotspot (size and inclination) and the observer inclination.

A unique feature of eXTP arises from its polarimetry capabilities. Radiation emerging from the hotspot on the NS surface is expected to be polarized and the observed polarization degree and angle are modulated with the spin phase. From phase resolved measurements of the polarization degree and angle both the observer and the hotspot inclination angles can be constrained largely reducing degeneracies. Accretion-powered millisecond pulsars (AMPs) and burst oscillation sources are ideal eXTP targets for pulse profile observations and modeling. In general observations ranging from a few to several hundreds of ks are needed for these sources. Although relatively large, these observing times are feasible and therefore within reach of the core program.

Constraints on M and R are shown as obtained from an eXTP 100 ks observation of SAX J1808.4-3658 compared to other existing observations. The blue dashed contours show M and R constraints from pulse profile modeling based on existing RXTE observations. Similar constrains given by the eXTP LAD are shown by red solid contour and include the information obtained on the geometry with PFA observations. The nearly perpendicular dotted curves give constraints on M and R obtained by spectral evolution during photospheric radius expansion bursts as determined using the cooling tail method. The pink solid curves correspond to different equations of state of cold dense matter. The overlapping region in orange gives a robust estimate of M and R at a few % level.

Constraints on the EOS can be obtained from he fastest spin rates and in particular more rapidly spinning NS place increasingly stringent constraints on the EOS. Since eXTP would have a larger effective area than any preceding X-ray timing mission, it is well suited to discover many more NS spins, using both burst oscillations and accretion-powered pulsations. One needs the large effective area of eXTP to detect burst oscillations in individual Type I X-ray bursts to amplitudes of 0.4 % (1.3%) rms in the burst tail (rise). As an example, preliminary simulations have shown that eXTP can perform a coherent search for intermittent pulsations down to amplitudes of 0.04 % rms (bright), 0.3% rms (moderate), 1.9% rms (faint).

Physics and Astrophysics of Strong Magnetic fields

The broadband, high sensitivity, polarimetry and monitoring capability of eXTP, can provide a deep understanding of the physics in extremely strong magnetic fields. Magnetars, accreting X-ray pulsars, and rotation-powered pulsars are key targets for eXTP. The mission will also enable observational studies of QED effects. Magnetars are highly variable X-ray sources, with magnetic fields of the order of 10^14-15 G. Their flux can change by orders of magnitude. Variability occurs on different time scales, e.g. short bursts, (< 1s), intermediate flares (~1-40 seconds), giant flares (~500 s). Outbursts can last several weeks to years. Considering their variability and the WFM sky coverage, eXTP is expected to discover a new magnetar candidate every year, triggering follow up observations with the SFA and the LAD.

Simulated WFM spectrum of a 10 Crab magnetar burst (black points) lasting for 0.05 s. The assumed spectrum is a double blackbody.	Simulated LAD spectrum of the same burst, including an absorption feature at 4.5 keV. The lower panel shows the residual with respect to the best fit continuum and illustrates how the potential proton cyclotron line would be significantly observed.

Thanks to the large field of view of the WFM a large fraction of the Galactic Plane will be covered during most eXTP pointings. This allows to monitor the spin period of several magnetars, obtaining phase-connected timing solutions. Through this monitoring, eXTP can detect glitches, precession, and will accurately measure braking indices. Systematic time monitoring with eXTP will allow us to detect the amplitude of free precession down to a level of Δf~10^{-9} Hz in a magnetar like SGR 1900+14.

eXTP simulation of frequency variation due to free precession in SGR 1900+14. The input spectrum is an absorbed blackbody plus a power law. The hydrogen column density, the black body temperature and its normalization are the same as for SGR 1900+14, i.e. 1.6×1022 cm-2, 0.5 keV and 7.1 respectively. A sinusoidal modulation of the free precession is assumed. Each point has a duration of 2 ks, that for 2 weeks monitoring gives a total exposure time of 1.15×105 s.

Accreting X-ray pulsars are key targets for eXTP. Particularly relevant will be the observational studies on the polarization properties of the radiation emerging from these objects. The X-ray linear polarization depends strongly on the geometry of the emission region, and varies with energy and pulse phase, reaching very high degrees, up to 70%. We have estimated for several sources the exposure required to constrain the linear polarization fraction to better than 10% accuracy, which implies also that polarization angles will be significantly constrained too. For bright persistent sources, exposures of ~10 ks will be sufficient for phase resolved studies. For weak sources, significant polarization will be detected with exposures of ~100 ks, which still allows phase resolved studies with Ms exposures. The phase dependence of the polarization properties is closely related to the geometry of the emission region. This can be probed by eXTP through the analysis of the energy and luminosity dependence of pulse profiles and cyclotron lines. The long observations required for polarization studies will in addition yield high quality pulse profiles and will help to extend studies on the luminosity dependence of the cyclotron resonance scattering feature (CRSF) to low luminosity, probing the regime switch expected for accreting pulsars from local super-Eddington to sub-Eddington accretion.

eXTP exposure required to constrain the linear polarization degree to better than 10% accuracy. With this exposure, polarization angles will be significantly constrained as well. Three cases are shown: 1) bright source (Vela X-1, F2-10keV~1.6×10-9 erg s-1 cm-2); 2) a weak persistent source (X-Per, F2-10keV~6x10-10 erg s-1 cm-2); 3) a Be Transient in outburst (V 0332+53, F2-10keV~1.6×10-8 erg s-1 cm-2).

The variation of the CRSF energy with luminosity is shown for V0332+53. LAD observations will allow accurate measurements of the line energy even at very low luminosities, extending the study of the correlation between the line and the luminosity on a very wide luminosity range.

The eXTP mission will provide the first tests of one of first predictions of QED: vacuum polarization and the effect of strong magnetic fields on the propagation of light. Observations of NS can verify that this effect exists. For magnetars this effect is the strongest, given their fields of ~10^14-15 G. Vacuum birefringence increases the expected linear polarization of the emerging X-rays from about 5-10% to nearly 100%. It is nearly as strong for neutron stars with magnetic fields of 10¹² G.

Pulse profile, and phase dependent degree and angle of polarization expected in 1Ms observation of AXP 1RXSJ170849.0-400910 assuming the twisted magnetosphere model. The points have been simulated taking into account QED effects (blue line). The red curve (no QED effects) is not consistent with the observed data.

Accretion in strong field gravity

One of the major challenges of modern astrophysics is the study of matter close to the event horizon of black holes, where gravity is in the strong-field regime. The motion of matter near super-massive black holes (in AGN) and stellar-mass black holes (in X-ray binaries), dominated by gravity, provides a powerful diagnostic to study the deep potential well generated by the central object, infer its mass and spin, and verify some of the crucial predictions of General Relativity (GR) in the strong-field regime. The two most important direct diagnostics of matter behavior in the strong-field regime are relativistically broadened Fe lines and relativistic time-scale variability, in particular quasi-periodic oscillations (QPOs). eXTP combines the spectral resolution required for resolving relativistic lines with the large photon throughput required to study their variability on time scales down to well below the dynamical time scale of the strong-field region. In addition, polarization information will allow us, for the first time, to investigate the accretion/ejection flows around black hole using different techniques that will complement each other.

In the simulation illustrated in the figures below, we show on the left panels the spectrum of a 0.5 Crab BH with maximal spin (e.g. GRO J1655-40). An eXTP observation can provide a measurement the inner radius of the disc and the radial emissivity with 1-2% accuracy in only 100s. Such unprecedentedly short timescale enables for the first time the study of the variability of the innermost region on a time-scale comparable to variations of outflow components such as winds and jets. This will open a new observational window on how the ejection properties are linked to the inner accretion flow. In the right panels of the same figure, we show the eXTP spectrum obtained by a 100 ks integration of a 2 mCrab AGN, with spin parameter a=0.5. Our simulations show that in AGN the energy resolution of eXTP together with the large effective area and broadband energy coverage provided by the SFA and LAD combination, allow us to disentangle the spectral complexities in the Fe K region and measure the reflection continuum shape, to successfully extract the relativistic reflection parameters and recover the black hole spin to 10% accuracy.

Upper left panel: eXTP broadband (SFA+LDA) spectrum for an exposure of 0.1 ks of a 0.5 Crab, maximally rotating XRB BH such as GRO J1655-40. Upper right panel: eXTP spectrum obtained with a 100 ks integration of a 2 mCrab, spin a= 0.5 AGN. Lower panels, confidence levels for the disc emission vs. inner radius for XRB (left ) and inclination vs. black hole spin for AGN (right ) (1, 2, and 3 sigma solid, dotted, and dashed lines respectively).

The broad band pass from 0.5 to 30 keV of eXTP, the good energy resolution, and its large photon throughput, enables the reverberation lags of the disk blackbody, Fe K lines and Compton reflection humps to be measured simultaneously, so that each provides a separate measure of the disk inner radius. This allows an accurate and independent determination of the BH spin, if the disk extends to the ISCO. Another technique to measure the radius (at ISCO) of the of the accretion disk in XRBs and hence the spin of the BH is given by the continuum-fitting method. A wide range of spins has been measured with this technique, but in many case errors are large and systematic errors cannot be excluded. By combining its powerful spectral-timing approach eXTP will allow a big step in the accuracy of the use of disk thermal emission fitting to map the innermost regions and measure BH spins.

As a second enlightening example, we show in the other figure below the sensitivity (in fractional rms) of the eXTP instruments (LAD, SFA and the combination of the two) for the detection of a QPO with a FWHM of 10 Hz. The left panel shows the case if we fix the exposure time to 10 ks and for a flux variable between 0.001 to 1 Crab (the flux range of most XRBs). The right panel shows the case for a source at 1 Crab flux, and for a variable exposure time between 100 s and 10 ks. eXTP will bring an improvement of at least one order of magnitude in sensitivity compared to RXTE/PCA, still the best instrument allowing high time resolution studies so far. eXTP’s large effective area will allow us to measure the QPO waveforms either directly, for QPOs that will for the first time be detected coherently, or by Fourier reconstruction. Coherent detection requires the collection of a sufficient number of photons for detection within the signal’s coherence time, and hence can be confidently predicted for signals that are only incoherently detected in current data. So far, coherent detection has been limited to a few, high coherence low frequency QPOs and even in those cases S/N, spectral resolution, or both were insufficient to study the phase dependence of the spectral shape. With eXTP, coherent detection will be common for low-frequency QPOs. Most neutron star kHz QPOs, well detected in previous missions, will be detected for the first time coherently with eXTP. In addition, the LAD will enable phase-resolved spectroscopy of QPOs. With a 50 ks eXTP observation of GRS 1915+105, phase-resolved spectra in 20 QPO phases can be significantly constrained. This implies that the change in shape of the iron line as a function of QPO phase resulting from Lense-Thirring precession of the inner flow can be clearly detected.

Right Panel: simulated eXTP sensitivity in fractional rms% for QPO with FWHM=10 Hz as a function of exposure for a source with flux equal to 1 Crab. Right Panel: simulated eXTP sensitivity in fractional rms% for QPO with FWHM=10 Hz as a function of flux for 10ks exposure. In both panels each stripe marks the 3 sigma and 5 sigma significance levels (lower and upper boundary, respectively). Different colors correspond to different instrument: RXTE, 5 PCUs (magenta); SFA (erroneously labeled as LFA in the figure), 11 telescopes (red); LAD, 40 elements (blue), sum of SFA (0.5-10 keV) and LAD (2-30 keV) (white).

A unique capability of eXTP will be the combination of X-ray polarimetric and timing information. This is enabled by the PFA and the LAD combination, which allows the photon polarization signal obtained by the PFA to be cross- correlated with the very high S/N light curves obtained by the LAD, to allow the time-dependent polarization signal to be extracted using similar approaches to spectral-timing measurements such as reverberation and QPO phase resolved studies. Although the details of the technique are out of the scope of this paper, we wish to show in the figure below (black points) the resulting phase-folded polarization degree (left) and angle (right) plotted as a function of QPO phase for a GRS 1915+105-like source. The points are clearly not consistent with constant polarization properties. The red line on each plot shows the input modulation. The technique provides again a powerful independent diagnostics of the accretion flow geometry, and constraints on key parameters like the BH spin. As discussed above, information on the accretion flow and measurements of the BH spin can be independently obtained by iron lines studies, including reverberation mapping and QPO phase resolved spectroscopy, continuum-fitting method and QPO phase resolved polarization studies. In addition, a fourth probe can be used: the energy dependence of the polarization angle and degree of the accretion disk emission, which significantly changes with the BH spin. Such an impressive combination of independent methods makes eXTP unique for strong-field accretion studies.

Measured (black points) and input (red lines) polarization degree (left) and angle (right) as a function of QPO phase from our simulation of a 1 Hz QPO. We see that the modulations in polarization properties are recovered well by eXTP . A 1 kHz QPO was simulated for a GRS 1915+105-like source in its intermediate state

eXTP as an observatory

With a uniquely high throughput, good spectral resolution, wide sky coverage, and polarimetry capability, eXTP is a powerful observatory very well suited for a variety of studies complementing the core science objectives. The SFA will provide high sensitivity in a soft but wide bandpass of 0.5 to 10 keV, the PFA will provide X-ray polarimetry capability, the LAD will provide the best timing and spectroscopic studies ever for a wide range of high energy sources brighter than 1 mCrab in the 2 to 30 keV band, and the WFM, with its unprecedented combination of field of view and imaging down to 2 keV, makes eXTP a discovery machine of the variable and X-ray transient sky. The WFM will reveal many new sources for follow-up with the SFA, PFA, LAD and other facilities. The WFM will also be monitoring daily hundreds of sources, to catch unexpected events and provide long-term records of their variability and spectroscopic evolution. We observe that no other All Sky Monitor is currently planned for the 2020s. eXTP will be a unique, powerful X-ray partner for other new large-scale facilities across the spectrum likely available in the 2020s, such as gravitational waves and neutrino experiments, SKA and pathfinders in the radio, LSST and E-ELT in the optical, and CTA at TeV energies. In particular eXTP will be a powerful complement for the exploration of the gravitational waves sky, since it will reveal the electromagnetic signals and hence the counterparts associated to many of the still to be discovered sources of gravitational waves. In addition the eXTP’s core program will synergically explore key physics issues at the core of gravitational wave astronomy. A number of key targets for the observatory science program (e.g., low-mass X-ray binaries or LMXBs) coincide with those that will be observed as part of the eXTP’s core program. Some observatory science goals will thus be pursued from the same observations and do not require additional exposure time. Other targets of the observatory science program (e.g., accreting white dwarfs, blazars, high mass X-ray binaries), can in turn provide useful comparative insights for the core science objectives.

Multi-messenger facilities relevant to eXTP. Colors indicate similar wavebands from the radio (brown) via IR (red) and optical (green) to X-rays (blue) and gamma rays (purple). Grey bands: gravitational wave and neutrino detectors. Dark colors: current end of funding, light colors: expected lifetime, where known, independent of funding decisions. The thin line separates space-based (top) from ground-based (bottom) facilities.