Neutron stars and black holes possess the strongest gravitational fields in the universe. They provide unique opportunities to reveal for the first time a variety of general relativistic effects and thereby investigate gravity in the strong-field regime, and to measure fundamental parameters of collapsed objects gaining important insights into the physics of matter at supranuclear densities and in supercritical magnetic fields.
LOFT is specifically designed to exploit the diagnostics of very rapid X-ray flux and spectral variability (already known to exist) that directly probe the motion of matter down to distances very close to black holes and neutron stars. Its factor of ~20 larger effective area than RXTE’s PCA (the largest area X-ray instrument ever flown) is crucial in this respect. LOFT/LAD’s much improved energy resolution, approaching that of CDD-based X-ray telescopes (better than 260 eV), will also allow the simultaneous exploitation of spectral diagnostics, in particular the relativistically broadened 6-7 keV Fe-K lines. The timescales that LOFT will investigate range from submillisecond quasi-periodic oscillations (QPOs) to years long transient outbursts, and the relevant objects include many that flare up and change state unpredictably, so relatively long observations, flexible scheduling and continuous monitoring of the X-ray sky are essential elements for success.
LOFT’s Wide Field Monitor (WFM) will discover and localise X-ray transients and impulsive events and monitor spectral state changes with unprecedented sensitivity, triggering follow-up pointed observations and constituting an important resource in its own right. A specifically dedicated on-board hardware and software (the "LOFT Burst Alert System", LBAS) will provide to the WFM the capability of identifying and broadcasting to the ground (within a delay of 30 s) the trigger time and position (~arcmin accuracy) of any bright event going off in its large field ov view.   
The observation plan of LOFT includes two major components. The core science program addresses the key science, i.e. "Dense Matter" and "Strong-field Gravity". For this science it is expected that the mission will require about 50% of its observing time (the mission lifetime has been set to 4 years to allow sufficient opportunity to observe relatively rare transient events). The remaining 50% is available for the observatory science, i.e. for observations of virtually all classes of relatively bright X-ray sources, including: X-ray bursters, High mass X-ray binaries, X-ray transients (all classes), Cataclismic Variables, Magnetars, GRBs, Nearby galaxies (SMC, LMC, M31, ...), AGNs ...
In the Sections below:
Understanding the properties of ultradense matter and determining its equation of state (EOS) is one of the most challenging problems in contemporary physics. At densities exceeding that of atomic nuclei, exotic states of matter such as Bose condensates or hyperons may appear; a phase transition to strange quark matter may take place at higher still densities. Only neutron stars probe these densities in the ‘zero’ temperature regime relevant to these transitions. Very “soft” EOSs give a maximum neutron star mass in the 1.4-1.5 solar mass (Mo) range, whereas “stiff” EOSs can reach up to 2.4-2.5 Mo before collapse to a black hole becomes unavoidable. Apart from maximum mass, the relation between the neutron star mass and radius (M-R) is a powerful probe of the EOS. With the exception of redshifts of any narrow atmospheric lines (feasible for slowly rotating stars only), all tools devised to constrain mass-radius are based primarily on accurate time-resolved and high-throughput broadband spectral measurements.  In ~25 neutron stars , spi ns are now observed in burst oscillations and/or coherent pulsations at frequencies of up to 620 Hz, proving that millisecond spins and dynamically relevant magnetic fields are common among neutron stars in low-mass X-ray binaries. LOFT will measure the masses and radii of accreting millisecond pulsars to an accuracy of 5% by modelling their pulse profiles: their fast spin and strong gravity affect the radiation from the surface hot spots producing the pulsations through relativistic beaming, time dilation, red/blue-shifts, light bending and frame dragging (hence they provide an alternative probe of strong field gravity effects as well). LOFT will be able to cross-validate these results by flux and spectral modelling at photospheric touch-down of radius-expansion thermonuclear X-ray bursts. Since the maximum rotation a neutron star can sustain depends on its mass and structure, fastest spin periods also constrain the neutron star EOS.
Given three measurements of neutron star masses and radii to 5% (shown as ellipses), we can exploit the inversion procedure outlined in Ozel & Psaltis (2009) to obtain very high precision constraints on the dense matter Equation of State, distinguishing even between models that make similar predictions for the M-R relation. The models shown here (MS, APR, ABPR, BBB, SQM) illustrate the range of theoretical possibilities for the true EoS, in terms of both composition (from pure nucleonic to EoS involving strange quark matter) and computational technique (relativistic/non-relativistic, variational methods, mean field theory calculations). All of the EoS shown are compatible with the recent discovery of a (1.97±0.04) solar mass radio pulsar by Demorest et al. (2010, Nature, 467, 1081).
Simulation of the constrains on the neutron stars M/R that can by obtained by modeling the neutron star pulsed emission (shape, energy dependence) as observed through LOFT/LAD observations (taking into account Doppler boosting, time dilation, gravitational light bending and frame dragging).
LOFT will search for periodic signals with unprecedented sensitivity. Models indicate that the pulsation amplitude in fast spinning neutron stars in X-ray binaries should be as low as 0.1%, so the effective area of LOFT/LAD is needed to detect these pulsations in a typical 104 s observation of a 100 mCrab source. The recent discoveries of a few intermittent X-ray pulsars, with small pulse amplitudes over short periods of time, indicate that it should be possible to build up a much better spin period distribution for accreting neutron stars than has been possible with RXTE. These intermittent pulsations were also very hard, underscoring the need for a timing mission with a good hard X-ray response. LAD can search for them with an unprecedented sensitivity of 0.5-0.8% amplitude in 100 s (for 100-300 mCrab sources).  A different approach has recently emerged from the discovery of global seismic oscillations (GSOs) in the tens of Hz to kHz range from magnetars during the rare and extremely luminous giant flares emitted by these sources. The lower frequency GSOs likely arise from torsional shear oscillations of the crust and their frequency, in combination with the magnetic field inferred from the magnetar spin-down, tightly constrains the EOS. The identification of an n = 1 radial overtone allows to estimate crust thickness. LOFT will detect and study GSOs for the first time in ‘intermediate’ flares, which are tens of times more frequent than giant ones, down to amplitudes of 0.7%, an order of magnitude lower than seen up to now. This will open a new window in the study of neutron star structure through asteroseismology.
About 40 compact objects accreting matter in binaries are now known to display variability arising in, and occurring at the (millisecond) dynamical timescale of their inner accretion flows: black holes and neutron stars, respectively, show QPOs of up to 450 and 1250 Hz. These QPOs require an explanation that involves the fundamental frequencies of the motion of matter in the inner, strong-field gravity-dominated disk regions.
In the absence of sufficient guidance from observations, modelling has so far been to a large extent phenomenological, and different interpretations are still viable. For example, competing models variously identify observed QPOs with therelativistic radial and vertical epicyclic frequencies or relativistic nodal and periastron precession.
LOFT will be able to follow the evolution in time of the QPOs, removing the observational constraints of the previous generation instruments on-board, e.g.,  RXTE/PCA (represented with a blue obscuring rectangular in the upper panel).
LOFT simulations for black hole high-frequency QPOs. Left panel: prediction of the evolution within the epicyclic resonance model. Right panel: corresponding evolution for the relativistic precession model. The curves correspond to: 1 Crab, fractional rms 2.8% and 6.2% (blue), 400 mCrab, fractional rms 1.4% and 3.1% (green), 300 mCrab, fractional rms 0.7% and 1.5%. The exposure is 16 ks in all cases.
Very high-signal-to-noise LOFT/LAD measurements of the QPOs will unambiguously discriminate between such interpretations and in the process tease out yet untested general relativistic effects such as frame dragging, strong-field periastron precession, and the presence of an innermost stable orbit. Crucially, LOFT will provide access for the first time to types of information in these signals that are qualitatively new due to the capability to measure dynamical timescale phenomena within their coherence time, where so far only statistical averages of signals were accessible. This will allow studies that directly witness QPO formation and propagation and tie in with what state-of-the-art numerical work is just beginning to address.
An example of the improvement of the LOFT/LAD timing capabilities due to its huge increase in effective area for the source XTEJ1550-564 (1 ks). As comparison an effective 55 ks observation of RossiXTE data is shown in the inset.
Simulated color-coded power spectra versus time of the fast variability of an accreting stellar mass black hole. QPOs show at broad stripes in this representation (black corresponds to the highest power). The figure illustrated the improved capabilities of LOFT/LAD (top) versus RXTE/PCA (bottom) based on the predictions of frequencies by the relativistic resonance model (left, Abramowicz and Kluzniak 2001) and the relativistic precession model (right, Stella, Vietri, Morsink 1999).
Not only LOFT will determine frequencies with better accuracy, but it will also detect more frequencies and enable their time variations to be measured. The frequencies are computed assuming a 6 solar mass black hole. The amplitudes of the QPOs are consistent with previous measurements or upper limits. The black hole spin is 0.8 for the RRM and 0.35 for the RPM. Those two spins are such that the mean value of the relativistic periastron precession frequency in the RPM is equal to the radial epicyclic frequency of the RRM. In the RRM, the frequencies and amplitudes of the QPOs are assumed to be constant throughout the observations (last over 4000 seconds). So far only the frequencies in a 3:2 ratio have been observed, and LOFT will have the capability to detect any additional frequencies with different ratios (1:2 and 3:5 in this case). On the other hand, the RPM predicts variable frequencies. Illustrating the idea that we may have seen only the tip of the iceberg with the PCA, we have further assumed that the amplitude of the four RPM QPOs decreased on both side of their mean frequency on the timescale of the simulated data set. As can be seen, despite the decrease of their amplitude, the frequency of the four QPOs can still be easily tracked in the LOFT data.
LOFT will allow direct measurements of the black hole mass and spin through timing measurements, to compare with other estimates such as mass from optical studies or spin from the thermal X-ray continuum or the Fe K-line profile. The spectral capabilities of LOFT will allow use of the energy dependence of amplitudes and phase delays in the QPOs together with the Fe-K line profiles to measure the compact object’s mass and spin, the disk inclination and to study massive black holes in the brightest active galactic nuclei (AGNs) by measuring with unprecedented accuracy the profiles and variability of their Fe K-lines. Additionally, LOFT's good response to higher-energy X-rays is crucial for most of this work; the discoveries of the highest-frequency quasi-periodic oscillations from black holes – the ones which can be used to probe the mass and spins of the black holes were made only above 13 keV, despite the much higher count rates at lower energies. Similarly, reliable measurements of Fe lines can only be made when both the Fe spectral edges around 8-9 keV and thecontinuum at energies significantly higher than these edge energies can be well measured.
Simulation of phase resolved spectroscopy of the Fe-K line from a hot spot orbiting on the accretion disk at 4 Rg (gravitational radii), along the innermost stable circular orbit of a 2x107 Mo black hole with spin a = 0.5 in a 2.5 mCrab AGN (such as MGC 6-30, see left panel).
The hot spot lasts for 4 orbits (total integration time 24 ks). Line variations (between 4-7 keV) due to the orbiting spot (shown here as residuals after subtraction of the integrated spectrum) over 6 different phase intervals are clearly distinguishable (only the 3 brightest intervals are shown for clarity). The insert shows the integrated broad Fe-line profile as measured by the XMM-Newton/EPIC-pn (red) and the LOFT/LAD (black). The total exposure time in this case is 200 ks for both instruments.
The simulated (150 ks exposure) broadband LOFT/LAD spectrum of a ~2 mCrab (4.5e-11 cgs in 2-10 keV) AGN are compared with a simple power law fitted  ignoring the Fe K and Compton hump energy bands (4-7.5 keV and 10-30 keV). The ratio plot shows the main spectral components which are: (1) the power law continuum, (2) ionized absorption features in the Fe K region due to warm gas, (3) a strong smeared ionized reflection component comprising the relativistic (a=0.9)  broad Fe line, a Compton hump and the excess below 3 keV, (4) cold reflection components (both narrow Fe K line and Compton hump) produced far away the central supermassive black hole. The LAD is able to resolve all these features with a very high S/N.
In this example, the precessing inner torus model for black hole low-frequency QPOs (Ingram et al. 2012, MNRAS, 427, 934) is tested by exploiting the combination of the LOFT/LAD timing measurements. The precessing inner torus model predicts both how the torus relativistic nodal precession frequency relates to fundamental GR frequencies and how varying irradiation of the thin thermal disk by the precessing thick inner hot torus produces Fe line profile variations taking place periodically on the QPO frequency.
Right: Five phases of the relativistic nodal precession cycle of the inner disk (tilt angle of 15°) as viewed by an observer at an inclination angle of 60°. The irradiation from the flow incident on the disk is colour-coded, with the brightest and dimmest regions shown in orange and black. The precession generates a low frequency QPO signal in the X-ray flux and modulates the Fe-line profile. Because the material in the disk is orbiting in the same direction as precession, the approaching region is preferentially illuminated as the observed flux rises to its peak and the receding region is illuminated when the observed flux is falling to its trough.
Left: A simulated LOFT observation of the resulting spectra selected from the rising (blue), maximum (black), falling (red) and minimum (green) phases of the precession 0.145 Hz QPO cycle (plotted as a ratio to a power law with photon index 1.6), assuming a 5 ks exposure of a 0.66 mCrab 10M BH, with spin parameter 0.5. Because the approaching and receding sides of the disc are illuminated during the QPO rise and fall respectively, the iron line shifts from blue to red shifted across the QPO cycle. Such an observation would provide incontrovertible evidence for a relativistic precession origin of the low frequency QPOs (Ingram & Done 2012).
In the tables below we report a very preliminary master observig plan for LOFT. It has been designed to ensure the achievement of all core science goals.
(1) Average time per pointing is total time/total pointings. If the total number of pointings is a concern, pointings of less than 10 ks can be added up to make pointings of at least 10 ksec in length.
(2) For some ~10 of AGN2 sources additional offset background fields are needed (~700ks total). There should be several “standard” background fields that must be quasi-periodically revisted to monitor the evolution of background. This should be ~3% of net observing time.
LOFT will additionally be a powerful tool for studying the X-ray variability and spectra of a wide range of objects, from accreting pulsars and bursters, to magnetar candidates (Anomalous X-ray Pulsars and Soft Gamma Repeaters), cataclysmic variables, bright AGNs, X-ray transients and the early afterglows of Gamma Ray Bursts.
Through these studies it will be possible to address a variety of problems in the physics of these objects. A summary is provided in the table below.