Time domain astronomy with the THESEUS satellite

Abstract

THESEUS is a medium size space mission of the European Space Agency, currently under evaluation for a possible launch in 2032. Its main objectives are to investigate the early Universe through the observation of gamma-ray bursts and to study the gravitational waves electromagnetic counterparts and neutrino events. On the other hand, its instruments, which include a wide field of view X-ray (0.3-5 keV) telescope based on lobster-eye focussing optics and a gamma-ray spectrometer with imaging capabilities in the 2-150 keV range, are also ideal for carrying out unprecedented studies in time domain astrophysics. In addition, the presence onboard of a 70 cm near infrared telescope will allow simultaneous multiwavelegth studies. Here we present the THESEUS capabilities for studying the time variability of different classes of sources in parallel to, and without affecting, the gamma-ray bursts hunt.

Appendix

The SXI instruments is characterized by a low background rate, allowing the significant detection of faint sources providing small numbers of counts. It is therefore necessary to consider Poisson statistics to define the instrument sensitivity in these cases.

For an exposure time of duration T, we define the source detection threshold, C$_{THR}(T)$, as the number of counts that has a small probability $P_1$ of being exceeded by a statistical fluctuation of the background. If the background count rate in the detector region used to extract the source counts is $R_{BKG}$, the threshold is defined by the following equation

$$\begin{aligned} P_{POISS} (\ge C_{THR} | R_{BKG} T)= P_1 \end{aligned}$$

where $P_{POISS} (\ge N | \mu )$ is the integral Poisson probability with average $\mu$ (i.e. the probability of observing N or more counts when $\mu$ counts are expected). When searching for GRBs, the value of $P_1$ must be sufficiently small to reduce the number of false triggers to an acceptable level, also taking into account the large number of independent sky positions in the SXI field of view and of time intervals that are continuosly monitored (for example, $P_1$=10$^{-10}$ was used in simulations to estimate GRB detection rates). On the other hand, less conservative thresholds can be used for non-GRB sources.

In addition to the probability $P_1$ used to define the detection threshold, in order to derive the instrument sensitivity we need to specifiy another probability value, $P_2$. This is used to derive the source count rate $R_{SRC}$ that has a reasonable probability of exceeding the threshold:

$$\begin{aligned} P_{POISS} (\ge C_{THR} | (R_{SRC} + R_{BKG}) T)= P_2. \end{aligned}$$

The SXI sensitivity curves shown in Fig. 36 have been computed for two different pairs of $P_1$ and $P_2$. The black curve refers to $P_2$=0.95 and $P_1$=1.35$\times 10^{-3}$, i.e. it gives the source count rates yielding a 95% probability of exceeding a 3$\sigma$ threshold. A more conservative definition is represented by the red curve, computed for $P_2$=0.99 and $P_1$=3$\times 10^{-7}$ (5$\sigma$).

The count rate sensitivity curves of Fig. 36 can be converted in flux units using the conversion factors plotted in Figs. 37 and 38 for different source spectral shapes and values of absorption.

Fig. 36

SXI sensitivity as a function of exposure time. The lower curve (black) gives the count rate corresponding to a 95% probability to exceed a threshold of 3$\sigma$ ($P_1$=1.35$\times 10^{-3}$), while the upper curve (red) gives the count rate corresponding to a 99% probability to exceed a threshold of 5$\sigma$ ($P_1$=3$\times 10^{-7}$). The assumed background rate of 8.371$\times 10^{-3}$ cts s$^{-1}$ is appropriate for a source extraction region of 675 arcmin$^2$

Fig. 37

SXI counts to flux conversion rates for a power-law spectrum as a function of absorption. The lines refer to different values of the photon index. The left figure refers to absorbed fluxes and the rigth one to fluxes corrected for the absorption

Fig. 38

SXI counts to flux conversion rates for a thermal plasma spectrum (APEC in XSPEC) as a function of absorption. The lines refer to different temperatures. The left figure refers to absorbed fluxes and the rigth one to fluxes corrected for the absorption

In Fig. 39 we show the sensitivity of the XGIS instrument as a function of exposure time and for sources with power law spectra of different slopes. The plotted sensitivities are for a single XGIS unit in the fully coded field of view. Note that, by combining the two units, an equivalent sensitivity is obtained over a region of $\sim$60$\times$30 deg$^2$, similar to that of the SXI field of view.

Fig. 39

XGIS imaging sensitivity (5$\sigma$ c.l.) as a function of exposure time provided by the SDD detectors in the 2-30 keV range (top panel) and by the CsI detectors in the 30-150 keV (bottom panel). Both figures are for a single XGIS unit and are valid for sources in the fully coded field of view (the central $\sim 10\times$10 deg$^2$ of each unit’s FoV). The different lines refer to sources with a power law spectrum with the indicated photon index. By combining the two units, the sensitivity plotted here is achieved over a region of $\sim$60$\times$30 deg$^2$, similar to that of the SXI field of view