Julián Jeremy J Drake
email: jeremy.1.drake@lmco.com

Alvarado Gomez

Costanza Argiroffi

Ettore Flaccomio

Cecilia Garraffo

Nicolas Grosso

Nazma Islam

Margarita Karovska

Vinay L Kashyap

Kristina Monsch

Julián Alvarado Gomez

Jan-Uwe Ness

Salvatore Sciortino

Bradford Wargelin

Breakthroughs in Cool Star Physics with the Line Emission Mapper X-ray Probe

come

The prototype for much of the physics involved in high energy processes on cool stars is of course the Sun. The solar X-ray corona comprises bright active regions characterized by plasma trapped within magnetic loops, dark coronal holes, small-scale bright points and diffuse emission components. The Sun also exhibits rapid X-ray variability and flares, resulting from the sudden release of stored magnetic energy in the form of accelerated particles, heat, and ejections of mass. Stars appear to do much of the same thing. The extent to which stellar coronae are similar to or different to the Sun has been an avenue of intense investigation since the Einstein observatory first prompted the realisation that coronae were magnetically driven (see, e.g., reviews by Refs. 38,39,19,87,23).

Although we can predict the X-ray behaviour of solar-like stars by drawing parallels with our Sun, the majority of stars differ from the Sun in mass, evolutionary phase, in rotation rate, and in metallicity-all aspects of which are expected to influence the underlying interior magnetic dynamo. Some are in close binaries that are forced to rotate at the orbital period through tidal locking. Some are involved in accretion systems, such as T Tauri stars and cataclysmic variables. In the context of the solar-stellar connection, it is these differences that enable us to use stars as a laboratory to study the general plasma physics and astrophysics of the solar corona under quite different conditions. In the astrophysical context, the solar paradigm provides a reference benchmark.

Space-based studies at X-ray wavelengths that have culminated in Chandra and XMM-Newton have provided a fairly comprehensive picture of stellar demographics. X-ray emission from stars is widespread throughout the Hertzsprung-Russell diagram, except for intermediate-mass main-sequence stars (late-B to mid-A spectral types), later-type giants, and possibly stars with spectral types later than mid-M. We now know what their X-ray spectra look like at high spectral resolution, and how their spectra change with rotation period and activity level. However, there are still fundamental problems to solve. We note just a few here that will be touched on in more detail below.

T Tauri Stars, Accretion and Feedback T Tauri stars are microcosms of high-energy astrophysics, exhibiting accretion, jets, and giant X-ray flares. However, we have only scratched the surface of how these all tie together. Key questions include how does the accretion proceed, what happens at the accretion shock on the stellar surface, how does this feed back into the corona and into jets?

Coronae on Brown Dwarfs Young brown dwarfs are readily detected in nearby star forming regions, but older and cooler objects have only been detected during flares. What their quiescent coronal properties are, how they are heated or are structured and how they build up surface magnetic stresses and flares is not known.

Magnetic Reconnection Flares Nearly all latetype stars are observed to flare, and undertanding flares is important for understanding magnetic energy cycling, space weather, and energetic particles. But there is an enormous dynamic range between solar flares and flares on the most active stars and T Tauri stars and it is not known if the same processes are at work. It is also not known if giant T Tauri flares result from star-disk magnetic fields, and chromospheric evaporation has yet to be systematically detected on stars, while large coronal loops hinted at by flare models suggest velocity signatures of plasma sloshing might also be detected.

Coronal Mass Ejections Only very scant and inconclusive evidence that CMEs occur on magnetically active stars currently exists. They are important to understand because of their potentially catastrophic impact on exoplanet atmospheres. Sensitivity to detect Doppler-shifted signals from ejected plasma have so far been out of reach of X-ray spectrometers but their signatures are in principle detectable.

Coronal Chemical Compositions The differences in chemical compositions of coronae and photospheres is now well-documented. Through the different patterns of abundances vs stellar activity level and spectral type, this chemical fractionation could provide a powerful means of investigating fundamental plasma physics at work stellar coronae. Abundances can only be reliably determined with high-resolution spectra, and a much wider sample of stars is needed to flesh out abundance patterns. Time-dependent abundance effects are also potentially powerful diagnostics that have so far only been hinted at.

Atmospheres of Transiting Gas Giants X-rays are absorbed much higher in a planetary atmosphere than optical or infrared light. In transit, X-rays can probe the scale height and bulk chemical compositions of exoplanet exospheres, probing mass loss and the influence of the ambient stellar wind on erosion and on transit signatures.

Stellar Magnetic Cycles Magnetic cycles have been detected on over 100 stars, but only a handful of cycle signatures have been seen at X-ray wavelengths. Little is known of the structuring of stellar corona other than that of the Sun, and how coronae might change through magnetic cycles in terms of plasma temperature, sizes of coronal structures, and chemical composition.

Symbiotic Stars and Cataclysmic Variables

Important for understanding binary stellar evolution and the route toward Type 1a supernovae, symbiotic stars and cataclysmic variables present laboratories for the study mass transfer, accretion, and jets. Many outstanding issues remain concerning the accretion processes, the X-ray generation mechanisms, and the interpretation of their X-ray spectra.

Novae Also a member of the cataclysmic variable family, nova explosions provide a panoply of astrophysics including mass transfer and binary star evolution, combined with explosive thermonuclear runaway. Existing observations exhibit a bewildering variety of X-ray spectra and have raised questions regarding the physics of the early explosion and interaction with the circumstellar medium, and the nature of strong variability during the onset of supersoft source phases.

IMPORTANCE OF LEM FOR COOL STAR SCIENCE

In the 1990s, the ROSAT All-sky survey and pointed observations fleshed out stellar coronal populations, while ASCA obtained many low-resolution X-ray spectra that enabled chemical compositions and coronal temperature structure to be investigated. The 2000s ushered in a sea change with Chandra and XMM-Newton and the advent of high-resolution X-ray spectroscopy capabilities sensitive enough for studying stellar coronae. This opened up spectroscopic temperature and density diagnostics, velocity resolution and the ability to see non-thermal motion, and resolved lines from different elements to measure chemical abundances. However, only relatively bright stars can be studied using these facilities. The "Line Emission Mapper" (LEM; Figure 1) is a proposed X-ray Probe mission that would launch in the mid-2030s. LEM combines two major advances into a package that achieves more than order of magnitude performance improvement over existing missions. These are its soft X-ray microcalorimeter array, which achieves a remarkable 1 eV resolution in the central array segment, and its primary mirror utilizing pairs of thin monocrystalline silicon shells (to be coated with either Ir or Pt) that affords a large effective area to mass ratio and with a 10" half power diameter. The resulting instrument achieves an impressive effective area of over 2000 cm 2 at 1 keV, with an average of 1600 cm 2 over a 0.2-2 keV bandpass. This represents a substantial increase in effective area of up to 100 times greater than the Chandra MEG, while maintaining similar spectral resolution. LEM offers two significant advantages for the study of low mass stars. First, it allows for highresolution X-ray spectra to be obtained from much fainter objects, greatly expanding the accessible volume of space and range of stars that can be studied at high resolution. Second, it provides the sensitivity needed to conduct time-dependent studies of brighter objects. One further strength of LEM for studying clusters of stars lies in its large 30'×30' field of view. Probe Class missions for the present NASA competition are mandated to allot 70% of the available observing time for General Observer access. This opens up extensive opportunities to advance our understanding of the high energy processes of cool stars and how they impact their planetary environments through dedicated pointed observations.

X-RAYS FROM T TAURI STARS

Low-mass pre-main sequence (PMS, T Tauri) stars are conspicuous X-ray emitters, displaying powerful flares, releasing ∼10 4-8 times more energy than the most X-ray energetic solar flare 33 . The analogy with solar activity has been quite successful in ascribing most of this X-ray emission to an active magnetic corona 28 . In accreting T Tauri stars, the accreted gas is channeled by the stellar magneto-sphere from the disk to the stellar surface, where an accretion shock with comparatively high plasma density compared with the ambient corona is generated, producing a plasma with a low temperature (∼4 MK) compared the coronal one (∼10 MK) in these active stars. This source of soft X-rays can be detected in addition to the harder X-rays emitted by the corona, if the emitting source-the accretion shock-is not too embedded into the stellar chromosphere or photosphere. Several accreting T Tauri stars are observed to drive strong jets, probably in the directions of their rotation axes. These stars exhibit a two-absorber X-ray spectrum revealing a strongly absorbed, hot and variable plasma component, and a less absorbed cooler plasma component. The former is associated with the active corona screened by the circumstellar disk, whereas the latter originates from shocks located above the disk midplane, near the base of the jet 31,42 .

Thanks to its high spectral-resolution an large effective area in the soft X-ray band, LEM offers breakthrough sensitivity to solve outstanding problems in our knowledge of the physics and physical conditions of accretion shocks, accretion postshocks, and shocks in jets.

X-rays from accretion shocks at the stellar surface

3.1.1 Accretion feedback on the corona of TW Hydrae At a distance of only 60 pc, the premain sequence star TW Hydrae (TW Hya) is one of the brightest T Tauri stars in X-rays. It is accreting from its circumstellar disk, famously seen pole-on in spectacular ALMA images (Figure 2). The foreground extinction is minimal, allowing the X-ray detection of the accretion shock at the stellar surface. In this star, this shock is the main source of the observed X-ray emission and displays a lower temperature and a higher density compared to the stellar corona 54,89,9 . From the X-ray spectrum obtained with the Chandra High Energy Transmission Grating (HETG) using a 489.5 ks exposure, the He-like Ne IX line ratio diagnostics constrain the temperature to 2.50 ± 0.25 MK and the electronic density to 3.0 ± 0.2 × 10 12 cm -3 in the shock, which is consistent with magnetospheric accretion 9 . However, the He-like O VII line ratio diagnostics indicates a large post-shock coronal region where the electronic density is 5 times lower (5.7 +4.4 -1.2 ×10 11 cm -3 ) than in the accretion shock and ∼7 times lower than the model prediction 9 . By monitoring the total flux of the emission lines formed in the accretion shock (N VII, O VIII, Ne IX, Fe XVII, Mg XI), Ref. 25 identify an abrupt increase (∼26%) in this flux that lasts for 3 ks. About 2 h after this X-ray accretion event, the heated photosphere produced an increase of the optical veiling. There is a hint for a correlation between the optical veiling and the flux of the stellar corona with a delay of ∼2.5 h.

We computed LEM simulations of TW Hya assuming an emission model composed of cool (accretion shock and post-shock regions) and hot (corona) plasma components, and a single absorber (Table 6 model B parameters and turbulent velocity of 165 km s -1 from Ref. 9). For the cool component, we adopt a line of sight velocity of 38.3 km s -1 3 . In ISIS [START_REF] Houck | [END_REF] , we use the modifier of the He-like ion line emissivities [START_REF] Huenemoerder | Atomic Data Unleashed: A Compact Database of Helium Triplet X-Ray Line Emissivities 51[END_REF] to include the electronic densities obtained from the He-like triplets (Table 3 of Ref. 9). We assume signal is in a single LEM pixel of the central array with a spectral resolution of 0.9 eV, collecting 90% of the LEM point spread function. Figure 3 shows the predicted LEM spectra centered on the Ne IX and O VII lines for an exposure of Fig. 3 -Simulated He-like emission lines of the accretion shock and post-shock at the stellar surface of TW Hya, obtained with a single LEM central-array pixel and an exposure of 6 ks. Top panel: Ne IX triplet emitted by the accretion shock with cool temperature (T e = 2.5 MK) and high density (n e = 3 × 10 12 cm -3 ). Bottom panel: O VII triplet emitted by the accretion post-shock with the same temperature but lower density (n e = 5.7 × 10 11 cm -3 ). In each case, the blue solid lines are the TW Hya spectra with labels for the forbidden (f), intercombination (i), and resonance (r) lines and highly-ionized iron lines from the hot corona; the black histograms with the error bars are the simulated LEM spectra with instrumental-background subtraction for visualisation only; the red histograms are the best-fit models obtained on this energy range using modified Cash-statistics. The black histograms in each narrow bottom panel show the fit residuals. LEM will determine the plasma temperature and density of the accretion shock and post-shock from plasma diagnostics using very short exposures, opening the window to time-dependent accretion studies. 6 ks. We model simultaneously and consistently the triplet lines and their satellite lines in these small energy bands by fitting the physical parameters of a single plasma component (temperature, density, emission measure, element abundance, turbulent velocity, radial velocity). For the Ne IX complex, several iron lines emitted by the hot corona are blended with the satellite lines, therefore, additional gaussian components at fixed energy are also fitted.

From the Ne IX triplet, (1σ) uncertainties of 4% and 6% are obtained for the temperature and the density, respectively, of the accretion shock; for comparison, (1σ) uncertainties of 10% and 7% are obtained with HETG based on a 489.5 ks-exposure. From the O VII triplet, (1σ) uncertainties of 7% and 9% are obtained for the temperature and the density, respectively, of the post-shock; for comparison, (1σ) uncertainties of ∼38% and ∼50% are obtained with HETG using 489.5 ks-exposure.

Hence, using diagnostics such as the Ne IX and O VII triplets, LEM will be able to probe with for the first time on short timescales, the temperature and the density of the accretion shock, and also the hydrogen column density using, e.g., the Ne IX resonance Heα(1.022 keV)/Heβ(1.074 keV) ratio, al-lowing the monitoring of the mass-accretion rate 8 and the stability of the accretion shock 22 .

In addition, we stress that the LEM spectral resolution will allow us to measure the radial velocity of the accreting plasma component. In fact, in the TW Hya predicted spectrum, several cool lines display significant Doppler shifts in agreement with the assumed input value. As an example, in Fig. 4 we show the TW Hya expected profile of the O VIII Lyα doublet, collected in an exposure time of just 1 ks, with superimposed the best fit profile, whose redshift is 39 ± 15 km s -1 . Since the free-fall velocity of the accreting material is known, the measurement of the radial velocity component provides us with important constraints on the inclination (and hence geometry) of the accretion stream, and how it changes on short time scales.

Therefore, LEM will investigate, again for the first time on short timescales, any correlation between the physical parameters of the accretion shock and the post-shock, and the coronal variability, thereby probing for any accretion feedback on the corona.

Episodic accretion in EX Lupi

The PMS star EX Lupi is located at a distance of 155 pc and displays repetitive but irregular outbursts in the optical with decay timescales ranging from a few months to years, produced by episodic accretion [START_REF] Audard | Protostars & Planets VI[END_REF] . EX Lupi is the prototype of "EXor" eruptive variable stars identified by Herbig [START_REF] Herbig | European Southern Observatory Conference and Workshop Proceedings[END_REF] as "Stars exhibiting large-range outbursts, but having T Tauri-like spectra when bright." In 2008, it exhibited its brightest optical outburst in 50 years that lasted 8 months, peaking ∼30 times above its pre-outburst optical flux. X-ray observations with Chandra and XMM-Newton show a strong correlation between the decreasing optical and X-ray fluxes following the optical peak. The cool (∼4.7 MK) plasma component faded as EX Lupi returned to its pre-outburst optical level, which is consistent with a decrease in the overall emission measure of accretion shockgenerated plasma 91 .

We computed LEM simulations of EX Lupi using the X-ray flux that was observed a few days before the end of its 2008 outburst, when its optical flux was only 4 times above its pre-outburst level 36 , this optical flux value being typical of the peaks of more regular outbursts from EX Lupi. Fig-ure 5 shows the predicted LEM spectra centered on the Ne IX and O VII lines for an exposure of 300 ks.

From the Ne IX triplet, (1σ) uncertainties of 12% and 23% are obtained for the temperature and the density, respectively, of the accretion shock. From the O VII triplet, (1σ) uncertainties of 33% and 75% are obtained for the temperature and the density, respectively, of the accretion post-shock. This again demonstrates that LEM can probe, for the first time during an episodic accretion from He-line ions, the temperature and the density of the accretion shock, constraining the mass-accretion rate 8 , and the temperature and density of the postshock during these remarkable enhanced accretion episodes.

X-rays from a shock in the blueshifted jet of DG Tau A

DG Tau A is a T Tauri star located at a distance of 140 pc and has one of the highest mass accretion and mass outflow rates known. It drives optical jets with characteristic flow velocity of 300 km s -1 relative to the central star, with an inclination of 38 • 26,16 . DG Tau A displays a two-absorber spectrum: the hard component is associated with the active stellar corona screened by the circumstellar disk, whereas the soft component originates from shocks located above the disk midplane, near the base of the jet 31,44,42 . A prominent X-ray (blueshifted) jet and a fainter and absorbed counter X-ray jet, both coincident with the optical jet axis, are resolved with Chandra, and detected out to a distance of ∼5 from the central source 41 . The bulk of the X-ray emission of DG Tau A is from the unresolved central source.

The central soft and hard components are separated spatially by only ∼0.2 86 . The soft X-ray emission from the shock in the jet is located above the circumstellar disk midplane, and it therefore contributes to X-ray heating and ionization of the gaseous disk surface 35 . However, "the temperature [of the soft component] is only poorly constrained and plasma models with a wide range of temperatures can reproduce the observations" 45 .

We computed LEM simulations of the twoabsorber spectrum of DG Tau A 44 , applying radial velocities of +16.3 km s -1 and -235 km s -1 for the hard (embedded star) and soft (unresolved shock in the blueshifted jet) components, respectively. From the optical emission lines, the jet den-sity close to the star is ≥ 10 4 cm -3 6 , therefore, we use the smallest available value in the electron density grid (n e =10 7 cm -3 ). As this electron density is well below the critical densities of the He-like Ne IX and O VII ions, the forbidden line and intercombination line ratios will be similar for lower values still see Fig. 8 of 76 . Figure 6 shows the predicted LEM spectra centered on the Ne IX and O VII lines for an exposure of 100 ks. As a result of the low-density regime of the He-like Ne IX and O VII ions, only upper limits can be obtained for the electron density using these ions see Fig. 9 of 76 . The accretion shock and post-shock emissions are too absorbed by the circumstellar disk to be detectable, and in any case their radial velocities would be redshifted compared to the radial velocity of the star and spectrally wellresolved from the emission of the blueshifted jet.

From the Ne IX and the O VII triplets, uncertainties (1σ) of: 14% and 26%, respectively, are obtained for the temperature; and 3% and 9%, respectively, for the radial velocity. LEM will therefore determine, for the first time, the radial velocity and (unambiguously) the plasma temperature of the shock in the X-ray jet of DG Tau A that is pointing towards us. This would provide important and unique constraints for a T Tauri jet.

The Orion Nebula Cluster

The Chandra Orion Ultradeep Project (COUP) 34,29 , an 850 ksec long continuous observation of the Orion Nebula Cluster (ONC), was arguably one of the most successful Chandra observations of star forming regions and young stars. More than 1600 sources were detected in the Chandra ACIS FoV. Although many sources are concentrated around the center of the ONC and will not be accessible at the spatial resolution of LEM due to confusion, the outer regions are much less dense and individual stars will be resolved. Thanks to the larger field FoV of LEM with respect to Chandra ACIS, a much larger region will be observable in a single exposure, including more sparse regions outside of the cluster center. For studies such as that of bright flares, discussed below, source confusion will not be an issue since these events are typically two dex higher in count rate than the quiescent level. Hence they will be easily recognized above the "background" level due to the unresolved emission from the weak and spatially unresolved sources. ). The color coding is the same as in Fig. 3. Using He-like ions, LEM will be able to probe the physics of an episodic accretion burst of EX Lupi, including the temperature and the density of the accretion shock and post-shock. The color coding is the same as in Fig. 3. In the top panels, the solid lines in blue are the theoretical spectra for a radial velocity of -235 km s -1 between the X-ray emitting shock and the more embedded star; for comparison purposes, the dashed lines in blue indicate the positions of the He-like emission lines for the radial velocity of the star. LEM will determine the plasma temperature of the X-ray emitting shock from plasma diagnostics, and for the first time its radial velocity.

We have performed a simulation of a 1 Ms LEM observation of the ONC-comparable to the COUP Chandra exposure-in order to estimate the number of PMS stars that will be observable (i.e. not confused) and the signal-to-noise ratio expected for the resulting X-ray spectra. Figure 7 shows a false color image of the central part of the LEM field as obtained with the SOXS simulator. Source position and spectral models (for 1-or 2-T absorbed thermal plasma) for the central part of the field, observed by the COUP project, were taken from Ref. 34. Outside of this area we adopted a list of candidate cluster members from Refs. 79,47 . For these we adopted an average spectrum and estimated the flux from the mean J magnitude vs. L X relation.

The simulated dataset also included a crude 34 . Outer sources are simulated from a list of candidate members 79,47 using the average spectrum of ONC members and a flux determined from the mean J magnitude vs. L X relation. Two diffuse emission regions, detected in XMM-Newton data (Ref. 41; see their Fig. S1), are also simulated with the intensity and spectral shape reported in that work. Their spatial extent is schematically represented by the two reddish areas in the bottom-right part of the image. Three X-ray spectral bands, 200-900 eV, 900-1500 eV, and 1500-3000 eV are used for the red, green, and blue components of the false color image, respectively. Red circles, with source IDs above them, indicate the positions of a sample of sources studied by 27 , which experienced strong flares during the COUP observation. The circles are also used as photon extraction regions for the spectra shown below. The two green circle in the northern diffuse emission regions was also used to extract events for spectral analysis.

representation of the extended emission detected by XMM-Newton 41 . The two reddish areas in the bottom-right of the image in Figure 7 represent these two soft emission regions (one of which extends beyond the FoV), each simulated with its published spectrum, and with an approximate (boxy) geometrical shape.

A sample of 32 stars in which bright X-ray flares occurred 27 during the COUP observation is marked with red circles, with the respective COUP source numbers plotted above them. The circles also correspond to the areas from which photons were extracted for spectral analysis. The larger green circle in the northern diffuse emission region was also used for spectral extraction.

A significant fraction of the stars studied by Ref. 27, which we take as a representative sample of "interesting" sources, is isolated enough to allow the analysis of their spectra without contamination from any surrounding sources. Two such spectra, simulated with the models derived from COUP data 34 , are shown in Fig. 8 to illustrate the foreseen range of quality of spectra. Approximately 100 COUP sources have more photon events than COUP 43, the faintest of the two.

In addition, LEM will be able to diagnose the densities of accretion shocks in these Orion stars, building up a large sample of objects to allow systematic study of accretion properties and how they correlate with disk and stellar properties. An example is shown in Figure 9 illustrating the Ne IX Helike complex in COUP 1150 in which a cool plasma component likely associated with accretion was detected.

Figure 10 shows spectra extracted from the two green circles in Figure 7 background-subtracted using a nearby region of similar area (not shown). The input spectrum was based on the XMM-Newton detection 41 . The X-ray emitting plasma fills a stellarwind bubble, nicknamed the Veil bubble, which has a 2.7 pc radius, centered at a projected distance 1.5 pc South-West from the Trapezium cluster 72,73 . The adiabatic expansion of this ionized bubble inside the surrounding neutral gas produces a symmetrical shell, expanding at a bulk velocity of 13 km s -1 (see Fig. 3

of Ref. 74).

Note the high signal-to-noise ratio of the simulated spectra in Figure 10 and the wealth of detail. The low energy sensitivity of LEM will enable a detailed spatial analysis of the soft diffuse emission. The best fit to the simulated LEM spectrum in Fig. 10 indicates that the uncertainty on the radial velocity, left as a free parameter along with temperature and abundances, is of the order of 1 km s -1 , which is easily sufficient for investigating the plasma dynamics. LEM will obtain the plasma temperature of the collisional plasma inside the Veil bubble from two complementary methods: the fit of the full spectrum and the He-like line ratio, G = ( f + i)/r. Inconsistent results between the former and the latter will point to the contribution of charge exchange 97 .

In a collision-dominated plasma, the bright-est line of the He-like triplet is the resonance line, whereas charge exchange produces no continuum emission and a He-like triplet where the brightest line is the forbidden line (see Fig. 6 of Ref. 76). Therefore, the G ratio is sensitive to any contribution of charge exchange, since here photoionization that could otherwise skew the line ratios can be excluded. Indeed, a contribution of charge exchange to the X-ray diffuse emission that is observed in massive star-forming regions has been proposed 93,61 .

Based on the strong O VII triplet of the ONC diffuse X-ray emission (top panel of Fig. 10), LEM will diagnose any contribution of non-thermal X-ray emission that could be produced by charge exchange between the recombining O VIII ions and neutral elements.

X-RAYS FROM YOUNG BROWN DWARFS

In contrast to young stars, which are massive enough to trigger at their center the fusion of hydrogen as they evolve towards the main sequence, brown dwarfs are of lower mass than the H-burning minimum mass of 0.075 M /78.5 M Jup 11 . Since they cannot burn hydrogen, they slowly cool down as they evolve. Not surprisingly, field brown-dwarfs were first identified in the near-infrared 66,82 . But a few young brown dwarfs were also detected in Xrays by ROSAT in star-forming regions 69,60 .

With XMM-Newton and Chandra, the detected number of young brown dwarfs in clusters in X-rays exceeds now the one of field brown dwarfs, which are older and hence cooler, and, therefore, mainly detected during X-ray flares 84,[START_REF] Stelzer | [END_REF] . In the Orion nebula cluster, only 9 of the 34 young brown dwarfs observed by Chandra were detected, those mainly being the ones having an extinction lower than 5 mag 78 . In the Taurus molecular cloud (TMC), half of the sample (9 out of 17 brown dwarfs) was detected by XMM-Newton (7 of these brown dwarfs were detected for the first time in X-rays), including an X-ray flare 37 . The atmospheres of the young brown dwarfs are likely warm enough to be mildly ionized and, therefore, to sustain coronal activity.

We focus here on the young brown dwarfs of the TMC, which are closer (located at 140 pc) and less extinguished than the young brown dwarfs of the Orion nebula cluster, and use for our LEM simulations the best-fit X-ray parameters 37 . We select For each source we show, from top to bottom: the full spectrum simulated with the 2 Å-resolution response matrix appropriate for the outer part of the microcalorimeter array, in the 5-50Å wavelength range; the same spectrum in the 10-22 Å range; the spectrum simulated with the 0.9 Å-resolution response matrix corresponding to the central 7 arcmin region of the array, in the same 10-22 Å range. In all cases, the simulated spectrum is plotted in green and the best-fit model in red. In the bottom panels some prominent lines are marked with the ion that produces them. two representative young brown dwarfs of this TMC sample: MHO 4 (M7 spectral type, corresponding to T eff ∼2850 K), which is the brightest in X-rays, and 2MASS J0422, which has the later spectral-type (M8 spectral-type, corresponding to T eff ∼2700 K) of the X-ray detected, young brown dwarfs of this sample (Fig. 11).

The comparison between the LEM simulated normalized spectra (left panels of Figure 11 and the previously obtained XMM-Newton EPIC spectra (Fig. 4, top rows of Ref. 37) shows the giant leap in spectral resolution that will be achieved with LEM in 100 ks and 500 ks, respectively, for MHO 4 and 2MASS J0422, which will allow, for the first time, the detailed study of young brown dwarf coronae.

The Ne IX triplet emission will be obtained with an exposure of only 100 ks for MHO 4; a 10 times deeper exposure will be need for the fainter 2MASS J0422. LEM will probe from the Ne IX triplet, for the first time in young brown dwarfs, the temperature and the density of the cool plasmacomponent, providing insights into its nature and structuring.

Fig. 9 -Simulated LEM spectrum of COUP 1150 at 0.9 eV resolution, focusing on the Ne IX triplet. The color coding is the same as in Fig. 3. A cool plasma component was detected from CCD spectroscopy with Chandra in this isolated (closest neighbor at ∼15.1 ) accreting young star. LEM will be able to diagnose the density of the accretion shock.

STELLAR FLARE PHYSICS

Flares in Stellar Clusters

The large LEM fov and angular resolution will allow, for the first time, to obtain with a single pointing 2eV (or better) resolution spectra of several tens or even hundreds members of young clusters (e.g., the Pleiades) and star forming regions (e.g., Cha-II, Orion, ρ Oph) allowing to systematically investigate possible relations between the stellar and/or the circumstellar disk parameters and/or the evolutionary stage of the systems and spectroscopically-revealed features in X-ray spectra: coronal chemical composition, density of emitting plasma and its possible variation during a flare, bulk velocity of emitting plasma etc.

Available observations (e.g. the COUP or DROXO) that a fraction of 1-3 Myr old YSOs show evidence of intense long-decay flares that require the existence of confined structures (loop-like) 10 times or more longer than the one associated with "normal" solar and stellar flares. It is still matter of debate 33,81 if such structure footpoints are both anchored on the stellar surface, like solar coronal loops, or if one is on the star and other on the circumstellar disk near the corotation radius 27,81 , or even both on the disk 32 . Fig. 10 -Simulated LEM spectra of the diffuse emission, as extracted from the two green circles in Fig. 7. For a description of the panels and color coding see Figure 8. Note that the flux scale in the two bottom panels is logarithmic. Left panels show the normalized X-ray spectrum of the absorbed, two-component plasma 37 . Right panels illustrate the Ne IX triplet emission of the cool plasma (T e = 4.6 MK) assuming a (putative) high-density (n e = 3 × 10 12 cm -3 ) to mimic an accretion shock. The color coding is the same as in Fig. 3.

The Chandra ONC Ultradeep Project (nicknamed COUP) has allowed to detect about 30 such intense flares during the 850 ksec long continuous observation. The flare peak X-ray luminosities in the 0.5-8.0 keV bandpass are in the range L X ∼ 10 31 -810 32 erg/sec, f X ∼ 4 10 -13 -3 10 -11 erg/sec/cm 2 27 , the emitting plasma has a rather high temperature in the 50-100 MK range. The predicted LEM count rate should be sufficient to perform spectroscopy of flare emission with a time resolution of about 1 ksec. Considering big flare frequency (30 out of 1600 sources during 850 ksec of Chandra observation), the predicted LEM rates and the extents of the ACIS and LEM fov, one can predict than in a 300 ksec long LEM observation at least 10 big flares will occur and at least 3-4 of them with LEM rates adequate for a detailed investigation. This number rises to more than 10 events in a 1 Ms legacy observation, analogous to COUP. Time-resolved spectroscopy of one of such large flare with a time resolution of about 1ks should be sufficiently sensitive to detect the sloshing ("up and down") velocities at flare onset (cf. Fig. 3 of Ref. 4 and constrain the nature of the structure where the flare occurs.

While COUP has shown the existence of more than 1600 sources in the Chandra FoV (mostly concentrated around the center of the Orion Nebula Cluster), for investigating the nature of large intense flares source confusion will not be a problem since such flare emission is typically two dex higher that the quiescent level, and hence it easily recognized above the pedestal "background" level due to the unresolved emission from the weak, and possibly spatially unresolved, sources.

Flares on Active Field Stars

AB Dor (K0V+M8) is a well known young stellar system in the constellation Dorado. The primary is a flare star that shows periodic increases in activity. AB Dor has been extensively studied with the XMM-Newton EPIC/PN and RGS and detailed best fit to its coronal emission have been published 43 both for the quiescent and flare emission. Adopting AB Dor as a prototype of a possible source for a LEM study one can start from those published results.

By assuming that during a flare rising phase (with a typical duration of ∼ 1 ksec) some bulk motion of the emitting plasma is thought to occur as a result of chromosheric evaporation of plasma into the flaring loop. One can simulate the predicted source emission and investigate the capability of LEM to recover a Doppler shift velocity (more precisely its projection along the line of sight) of 100 km/s, with an integration time of 1 ksec. Such a value is consistent with several solar studies as well as with a few stellar studies 4 . Since the plasma bulk motion should be mainly concentrated during the flare onset, the strategy of improving the line signalto-noise ratio by increasing the integration time can hardly work since it will imply a smearing of observable velocity shift.

For all simulated spectra it has been assumed that the flare occurs "on top" of the quiescent emission (that is modelled according to published best fits) and that the X-ray flux, f X , during flare (indeed during the fraction of flare light-curve considered) is 2× the quiescent f X . The simulations have been performed assuming f X equal, 10 and 100 times weaker than the AB Dor case observed (heretofore the nominal) one. The quiescent AB Dor f X is 4 10 -11 erg/sec/cm 2 in the 0.3-10 keV band pass. The quiescent emission is modeled as a 3 Temperature Vapec and the (additional) flare as an absorbed Doppler-shifted 4 Temperature Vapec. The LEM predicted quiescent and flare nominal f X in the 0.2-2.0 keV bandpass are ∼ 3.8 10 -11 and ∼ 7.2 10 -11 erg/sec/cm 2 , respectively, corresponding to count rates of ∼ 5.8 10 1 and 1.1 10 2 count/sec.

The simulated spectra allow us to investigate for the 3 f X values: a) the capability to recover the input Doppler shift velocity by studying a single isolated rather strong emission line; b) the capability to recover various input parameters (Doppler shift ve-locity, abundances, kTs, normalizations) by fitting the model to the entire spectrum, i.e. to all spectral lines (a procedure usually adopted for optical spectra). In the simulated spectra all the strong lines are in the 10-20 Ang range (Figure . 12), which is exactly the "sweet spot" of the LEM bandpass. The Fe XVII line at 15.014 Å (E= 825.763 eV), is the second strongest line and is almost isolated (according to the adopted APEC model). Energy resolution at the FeXVII rest energy is ∼ 25% better than for the strongest line, OVIII 18.967 Å.

The capability to recover the Doppler shift velocity by analyzing a single line of a source with f X ∼ 5-8 10 -11 erg/sec/cm 2 in the 0.2-2.0 keV bandpass is shown in Figure 13. The best fit Doppler velocity is 101.8± 2.5 km/sec, to be compared with the input value of 100 km/sec. Note the characteristic features that appear in the residual plots (center and right panels) when the model Doppler velocity if far off the best-fit value.

The recovery capability is reduced for a 10 times lower source f X ; in this case the best fit Doppler velocity is 96.3 ± 8.1 km/sec. In this or even 10 times lower flux (i.e. down to ∼ 7 10 -13 erg/s/cm 2 ) regime one can resort to a global fit that accounts for the contributions of all emission lines. With such an approach the Doppler velocity can be recovered within a factor 2 even if some other fitted parameters are much less well constrained. An analysis of the best fit parameters obtained with a global fit shows that for the nominal flux most of them can be recovered within a factor 2 with the exception of some element abundances that are poorly constrained for the lack of strong emission lines of those elements in the LEM bandpass.

Based on hardness ratio variations, it has been suggested 1 that abundance upwellings have been observed to occur in the corona of HD 179949 during the course of a Chandra CCD observation. LEM, with its higher effective area and higher resolution, will be able to detect such changes directly by monitoring the emission in individual lines, even during quiescence.

CORONAL MASS EJECTIONS

Coronal mass ejections (CMEs) are among the most powerful magnetic phenomena occurring in the atmospheres of late type stars. In late type stars CMEs are expected to produce substantial effects on both stellar evolution and exoplanetary systems e.g. 21,71 . Nonetheless, because of current instrumental limitations, observations of stellar CMEs are very few and uncertain e.g. 62 . The LEM combination of large effective area and high spectral resolution in the soft X-ray band will boost our current capabilities to detect and identify stellar CMEs.

Solar observations show that CMEs usually occur simultaneously with flares. Each flare-CME pair is thought to originate from the same magnetic energy release. The mean CME mass (M CME ) and kinetic energy (K CME ) scale with the energy radiated by the flare in the X-ray band (E X ). Solar flares emit at most E X of ∼ 10 31 erg. The few observations of candidate stellar CMEs are indeed associated with much more energetic flares, with E X ranging from 10 31 to 10 38 erg. The properties of these candidate stellar CMEs suggest that the extrapolation of the solar relation between M CME and E X approximately holds up to the highest energy regimes. Conversely, for very high flare energy, the kinetic energy K CME of the associated stellar CMEs appears to be lower by two orders of magnitude the extrapolation of the solar case, being approximately of the same order of E X .

Since both the CME and the flare emit in X-rays and involve substantial plasma motions, we simultaneously synthesized the X-ray emission of both these components. We took as a reference the X-ray flare observed in detail on Prox Cen [START_REF] Güdel | [END_REF] . This flare represents a well suited case because: its moderate E X (i.e. ∼ 1.5 × 10 32 erg) makes plausible the assumption that the solar flare-CMEs relations hold; the detailed HD model developed for this flare 80 Fig. 13 -AB Dor simulated spectra of the isolated FeXVII line at 15.014 Ang (points with error bars) for an assumed Doppler shift velocity of 100 km/s compared with model predictions (solid histogram) for the resulting best fit (left panels), no Doppler shift (centre panels) and Doppler shift of 300 km/s, respectively.

In the upper plots the source X-ray flux in the LEM 0.2-2.0 keV bandpass is fx ∼ 7 10 -11 erg/sec/cm 2 , in the bottom plots fx is 10 times lower. For all simulated spectra the integration time is 1 ksec; in all plots the lower sub-panel shows the data residuals with respect to the model. spheric evaporation. Starting from the observed flare E X , we inferred the mass of the associated CME (3 × 10 17 g) from the solar case relation. Since solar CMEs are usually composed of plasma at different temperatures (from 10 4 to a few 10 6 K), we assumed that only 10% of the CME mass is hot enough to contribute to the CME X-ray emission. To be conservative, we set the CME terminal kinetic energy assuming it is 10 times higher than E X (i.e. 1.5 × 10 33 erg, i.e. more than one order of magnitude lower than that corresponding to the solar case extrapolation (i.e. 4 × 10 34 erg). To synthesize the X-ray emission of the CME we made assumptions on how it moves, expands, and cools down. In particular, using as a reference the evolution of the solar CME studied by Ref. 83, we assumed that: the temperature evolution with respect to the stellar radius is exactly the same; the CME velocity evolution with respect to the stellar radius is equivalent with only a higher terminal value (i.e. v ≈ 10 3 km s -1 , in agreement with CME mass and terminal kinetic energy); the CME expansion rate with respect to the stellar radius is equivalent with only a different initial value (i.e. at r = 1.5 R we assumed that CME volume is 10 times the volume of the flaring loop).

We synthesized the predicted X-ray emission of the CME, including also the contribution of the flaring loop (assumed to have half-torus shape) and quiescent corona. Assuming we are observing the flaring loop from above and that the CME is ejected in that direction, the predicted X-ray spectrum. As an example we report the profile of the O VIII lyman alpha line, integrated over an exposure time of 500 s (corresponding to the initial phases of the CME motion, i.e. from 2 to 6 R ) in fig. 14, assuming the Prox Cen distance and the 0.9 eV spectral resolution. We find that: the blue-shifted CME contribution is clearly detectable in addition to the flaring and quiescent emission; the velocity difference of the CME and flaring plasma at a few MK allows us to resolve the two contributions even assuming CME lower radial velocities; several X-ray lines, produced by plasma a few MK, display profiles similar to that shown in fig. 14, indicating that multiline analysis would allow us to detect the CMEassociated blue-shifted emission also in sources at larger distances.

CHEMICAL ABUNDANCES AS PROBES OF CORONAL PLASMA PHYSICS

Observations of the solar corona at EUV and X-ray wavelengths beginning in the 1960s found evidence that the chemical composition of coronal plasma is significantly different to that of the solar photosphere (see, e.g., the review by Ref. 56). The abundance differences are strongly correlated with the element first ionization potential (FIP) and the abundance anomaly is now commonly referred to as the "FIP Effect". Elements with low FIP (FIP≤ 10 eV, e.g., Si, Mg, Fe) are enhanced on average in the solar corona by factors of 2-4 relative to elements with high first ionization potentials (FIP≥ 10 eV, e.g., N, Ne, Ar). However, different regions of the solar corona are now known to exhibit different magnitudes of FIP effect, with quiet Sun and coronal holes showing very little, if any, FIP-based abundance bias, and active regions generally showing the largest effect 56 .

In the 1990's, the ASCA and EUVE satellites found that stellar coronal abundances also differed from photospheric values [START_REF] Drake | Cool Stars, Stellar Systems[END_REF][START_REF] Drake | Cosmic Abundances[END_REF][START_REF] White | Cool Stars, Stellar Systems, and the Sun[END_REF]18 . Chandra and XMM-Newton confirmed the results in much greater detail with high-resolution X-ray grating spectroscopy. Stars of "low" magnetic activitylike the Sun-showed similar abundance anomalies to the solar FIP Effect. However, magnetically active stars tended to show the opposite: an "inverse FIP" (iFIP) effect where low-FIP abundances are depleted relative to high-FIP elements 10,20 .

As more stars were observed, an additional dependence of the FIP and iFIP effects on stellar spectral type emerged 96 . The "FIP bias"-an average of high FIP element abundances relative to the low FIP element Fe compared with a solar photospheric mixture-based on an analysis of a sample Chandra/LETG+HRC-S spectra 96 is illustrated in Figure 15. The FIP bias is negative for the solar FIP effect in which low FIP elements are relatively enhanced, and positive for the inverse FIP effect. The data show a trend of increasing FIP bias with later spectral type, together with an increase in FIP bias with increasing activity level reminiscent of the early stellar results.

The FIP boundary that differentiates low and high FIP behaviour is approximately 10 eV, corresponding to a temperature of (∼ 10, 000 K) and pointing to the chromosphere as the fractionation site. Mechanisms that might explain the fractionation remained elusive until it was realised that the ponderomotive force exerted by Alfvén waves ex- cited by convection and turbulence and propagating into the chromosphere could provide the selective acceleration of ions, enhancing their abundances 56 . The variation in FIP effect with spectral type indicates that the Alfvén wave intensity and spectrum probably change. This is not surprising since the depth and characteristics of the convection zone change with effective temperature (T eff ). Alfvén waves are thought to be important as sources of coronal heating and for driving the winds of solarlike stars. Coronal abundances then offer the tantalizing possibility of providing unique diagnostics of Alfvén waves in stellar coronae.

The mechanism that drives the FIP effect is still unresolved. Monitoring of the high-cadence variations in individual spectral lines during the onset of a flare and searching for time lags will constrain these mechanisms. LEM will directly observe whether FIP or inverse-FIP effects are preceded by flare-induced chromospheric evaporation effects by detecting time lags in flare onset in lines arising from different species.

There is evidence that given the uncertainties in abundance measurements, the FIP bias is consistent with 0, or is at least increased from negative values, for hot Jupiter hosting stars 1 . The high spectral resolution and effective area of LEM will definitively answer this question when coronal and photospheric abundances of planet-bearing stars are compared.

Alfvén waves are also likely to be initiated from above in the corona through perturbations driven by magnetic reconnection, especially in more active stars.

Differences in chemical composition of the corona will also impact the radiative loss function and thus the cooling rates and energy balance of coronal plasma. A metal-poor corona would naively be expected to be hotter because of the absence of metal lines that dominate the radiative loss at temperatures T 10 7 K. This is indeed what was found for the Pop II interacting close binary HD89499, whose coronal temperature based on ASCA spectra was 2.5 × 10 7 K 30 , or approximately 10 7 K hotter than typical for the Pop I interacting binaries 14 .

EXOPLANET SCIENCE

The high effective area of LEM will make it possible for the exospheres of several transiting systems to be detectable, as was found for HD 189733 with Chandra observations 75 .A new method to model transit light curves 46 using a realistic model of the absorption of coronal X-rays by the intervening planetary exosphere holds promise that LEM data can be analyzed to obtain the size and composition of the atmospheres of transiting exoplanets. The model parameterizes the exosphere by the base density, scale height, and composition of the exosphere, and computes the absorption numerically at different orbital phases. Realistic coronal spectra are used to determine the absorption effects in different passbands and even in individual lines. Systematic effects such as varying numbers of spots and active regions on the stellar surface are included by considering variations modeled on observed solar active regions see 57 .

As a practical strategy to minimize the effects of active region inhomogeneities, LEM will adopt a strategy of observing a transit several times so that the effects of variations during any single pass are averaged out over multiple passes, bringing out the signature of the transit clearly. We demonstrate this with simulations (see Figure 16). In particular, the high spectral resolution of LEM will allow us to measure the depth of the absorption edges with high precision, yielding accurate and direct mea- 16 -Demonstration of the suitability of LEM to estimate abundances in exospheres. The plot shows the depth of the O edge for three separate scenarios: one where the planet has had its atmosphere entirely ablated (brown curve), one with a relatively oxygen-poor atmosphere (solar composition; orange curve), and one with planetary atmospheric abundance enhanced 10× relative to solar (blue curve with synthetic data points overplotted). The three scenarios are sketched for illustration in the upper part. surements of the C, N, and O abundances in the exosphere.

Soft X-rays also play an important role in the heating and thus dispersal of planet-forming disks and consequently can have strong impact on giant planet migration and where these planets ultimately end up within a planetary system. Knowing the Xray emission of planet-hosting stars can therefore be important in understanding the observed demographics of exoplanetary systems.

Soft X-rays also heat exoplanetary atmospheres of sub-Neptunes and are an important ingredient in the model for the "photoevaporation valley" that is observed for super Earths/sub-Neptunes.

Superflares can be extraordinary events with measurable effects on the ablation of exospheres. While an observational program that waits for su-perflares to occur is not practical, in synergy with synoptic surveys like Rubin LSST, it is possible for LEM to follow up rapidly if a superflare were to occur on a planet hosting star. If the planet happens to have been in the path of the blast, LEM can target the transits that occur immediately after. If exosphere gets ablated, it will leave a comet-like tail that will alter the transit profile.

STELLAR CYCLES

Of order 100 nearby stars are known to have stellar cycles, but fewer than ten have had regular X-ray monitoring. Of those, X-ray intensities over a cycle typically vary by factors of a few, as opposed to roughly 10-20% in CaII HK or a few percent in optical photometry. Although the current sample is very small, X-ray cycles also often appear to be more regular than in other bands, for example in ι Hor 85 and Eri 13 , perhaps because of X-rays' greater emission volume and correspondingly less sensitivity to viewing geometry effects. With LEM's large collecting area, spectral analysis of emission from cycle maxima and minima 70 would not only determine the temperatures and surface coverage fractions of quiet emission, active regions, and AR cores, but also easily compare coronal abundances over a cycle. Cycles have recently been reported in F stars 59 , which have very thin convective zones, and, very surprisingly, in fully convective M stars 90 , both subjects of great relevance to the study of magnetic field generation and stellar evolution. Currently, however, only one fully convective star, Proxima Cen, has a stellar cycle amenable to detailed study in any band because of the faintness of such small stars.

Observations of the Pleiades cluster (136 pc, age 100 Myr) would provide an efficient means to monitor cycles in many young stars at once over a wide range of spectral type. To date, the youngest star with X-ray monitoring is ι Hor (F8, age ∼600 Myr). Young, i.e. active, stars have cycle periods approximately proportional to their convective turnover time scales 51 ; for F,G, and K stars in the Pleiades, P cycle is generally under 5 years, and two or three observations of 20 ks per year would allow accurate measurements of cycle amplitudes. Symbiotic stars, which are interacting binaries where an accreting compact object (e.g., White Dwarf) closely orbits a red giant, are crucial for the understanding of the origin of asymmetric Planetary Nebulae and some SN Type Ia. Understanding how mass builds up in the compact object is a key to determining the potential of symbiotics as progenitors of a fraction of Type Ia supernovae -key cosmological distance indicators. Several symbiotics see e.g., 58 have been identified and observed with existing observatories. LEM, with its significantly higher effective area, will expand the reach to increase the symbiotics' sample size by a factor of at least an order of magnitude.

The morphology and X-ray spectra of some Symbiotic Systems (e.g., CH Cyg, R Aqr, RT Cru) show great similarity with the morphology and spectral distribution of AGN (e.g., Seyferts), and are therefore sometimes called nano-quasars 94,92 . LEM spectroscopy will provide information needed for understanding the underlying accretion and jet powering mechanisms of these systems and their large "cousins", which otherwise differ by orders of magnitude in spatial, velocity, and mass scales.

A major limitation of current studies of symbiotics is to understand the origin of the emission components. It is unclear where precisely the observed soft emission arises, whether it is detected due to patchy absorption in and around the accretion disk, or occurs due to periodic outbursts of jet-like emission, or both. The observed spectrum is typically a combination of emission from the central source, an accretion disk, and a jet. Hence, component separation must be carried out spectroscopically. We expect that emission from the accretion disk will be Doppler broadened by >500 km s -1 , while jets should exhibit Doppler shifts >500 km s -1 . A simple measurement of Doppler shifts in lines or line broadening attributable to rotational smearing can pin down the source of the emission, and LEM is capable of distinguishing these scenarios. We show in Figure 17, simulations made for two representative lines (with fluxes based on a 35 ks XMM/RGS observation of CH Cyg 92 ). Even measurements based on individual lines (Fe XVII 17.05 Å and O VIII 18.96 Å are shown) are capable of detecting Doppler shifts of as small as V orb ≈200-300 km s -1 and line broadening V rot >300 km s -1 in observations with durations as small as 5 ks. When data from several lines from similar species are modeled together, the uncertainties can be reduced further.

In addition, the spectra of symbiotics is likely to also include reflection/photoionization components which have been hard to pin down because of large background and low effective areas in current highresolution instruments 98 . With its high effective area and high spectral resolution, detailed sifting of the emission components becomes feasible in LEM spectra.

CATACLYSMIC VARIABLES

Cataclysmic variables (CVs) are interacting binaries, which consists of a white dwarf (WD) and a Roche lobe filling low mass companion star (usually late type main sequence star). Depending on the strength of the magnetic fields of the WD, they are classified into non-magnetic CVs where the accretion disk extends up to the primary WD, and magnetic CVs where the magnetic fields are strong enough to prevent the formation of an accretion disk, at least close to the WD. An intermediary subclass of magnetic CVs are Intermediate Polars (IPs) where a partial accretion disk exists and accretion onto the white dwarf is magnetically funneled onto its poles from the inner edge of the truncated accretion disk.

While the general broad brush picture of CV behaviour resulting from Roche lobe overflow and accretion has been accepted for a number of years, as is often the case the details of this picture come into question and still remain to be fleshed out.

In IPs, the X-ray emission originates from the accreted matter shock heated up to high temperatures (kT∼10-50 keV), which must cool before settling onto the surface of the WD. Therefore the X-ray spectrum is expected to be the resultant emission from a multi-temperature plasma, which has a continuous temperature distribution from the shock temperature (of kT∼10-50 keV) to the WD photospheric temperature (kT∼0.02 keV). The post-shock plasma in many IPs can be well represented by a cooling flow model, which contains a bremsstrahlung continuum and collisionallyexcited emission lines from a range of temperatures 15,64 . The emergent X-ray emission from this shock-heated, multi-temperature plasma is modified by the presence of a complex distribution of absorbers in the pre-shock region. Given the X-ray fluxes from the post-shock plasma region, we expect these complex absorbers to be ionized, which is observationally motivated by the presence of photoionized emission lines and warm absorber features in the soft X-ray spectra of IPs 52 .

In Ref. 52, an ionized absorber model zxipab was used to model the Chandra/HETG spectrum of two IPs: NY Lup and V1223 Sgr. The ionized absorber model along with a cooling flow model describes well many of the H-and He-like emission lines from medium-Z elements, which arise from a collisionally-excited plasma. However the model fails to account for some of the He-like triplets from the medium Z elements. Using a combination of collisionally ionized plasma with a cooling flow model and photoionized models, 12 suggested a hybrid origin of O VII, O VIII, Ne IX, Ne X, and Mg XI lines in the Chandra/HETG spectrum. These issues indicate that we are still some way from understanding the accretion scenario in IPs and the factors that go into shaping the emerging spectra.

Other aspects of the behaviour of IPs that remain to be understood are orbital and spindependent variationsin X-ray emission. For a magnetic pole closely aligned with the WD rotation axis, spin modulation is expected to be small. However, variations in the height of the accretion shock are thought to be likely candidates explaining spin modulation. 65 Spectroscopic diagnostics of the emitting regions could help with this, although existing instrumentation is insufficiently sensitive and requires of the order of 100 ks exposure times for a single spectrum of the brighter sources 63 . Moreover, Helike diagnostics of plasma density are prone to contamination by FUV radiative excitation effects-an aspect that has been put to good use in the study of X-rays from the winds of massive stars. 53 Other diagnostics immune to such effects are available, in the "L shell" lines of Fe for example, but these are too faint to be of practical use with current generation spectrometers.

There are at least two breakthroughs that LEM will make in the study of CVs. In the example above, the high sensitivity of LEM would be crucial in understanding the origin of He-like emission lines in IPs, and get an accurate picture of the accretion, reflection and absorption components, and being able to utilise density diagnostics of weaker lines. The second is pushing studies toward timedependent spectroscopic probes of the accretion physics, in which LEM spectra can provide significant signal-to-noise ratio in short exposures, or enable phase-folding into sufficiently finely resolve bins to unveil the underlying behaviour.

NOVAE

Nova explosions arise from the interaction between a white dwarf and a close companion star from which hydrogen-rich matter is accreted onto the white dwarf surface that is genuinely hydrogenpoor. When the accreted gas density and temperature exceeds a critical threshold, runaway nuclear fusion occurs in the form of CNO burning (fusing hydrogen to helium). The resulting explosion expels the outer layers into space, emitting intense radiation across all wavelengths, depending on the opacity of the ejecta. Directly after the initial detonation, a nova is brightest in the optical/UV because the high-energy radiation produced via nuclear burning on the white dwarf surface undergoes complex radiation transport processes through the large optically thick ejecta. Nuclear burning continues for several weeks to months powering continuous expansion via radiation pressure, and the ejecta become gradually optically thinner. Radiation transport through an atmosphere with a smaller radius allows the radiation to escape after fewer interactions with dense matter, and what escapes from the photosphere will thus be of successively higher energy. The gradual shift of the peak of the Spectral Energy Distribution (SED) from low to higher energies has been observed to stop in the soft X-ray regime peaking at 0.5-1 keV, observable as a Super-Soft-Source (SSS) spectrum. The brightness and effective temperature of these spectral yield radii consistent with typical white dwarf radii, and this emission can thus be considered the closest we can get to observe nuclear burning in vivo. Typical SSS spectra fit perfectly into the sensitive energy range of LEM.

Until the dynamic hot photosphere from steady-state surface nuclear burning emits an SSS spectrum, the white dwarf itself is X-ray dark. However, there are multiple other X-ray emission processes from novae including accretion onto the white dwarf, shock heating of the ejected material and circumbinary medium, the interaction between the expelled gas and intense magnetic fields. Observations of this X-ray emission provide crucial insights into the dynamics of the explosion, as well as the properties of the accretion disk and circumstellar material. Consequently, nova explosions are recognized as key events for our understanding of binary stellar evolution and the behavior of matter and radiation in extreme environments, including high-energy astrophysics of non-equilibrium nuclear fusion, shock waves, particle acceleration and radiatively-driven outflows.

Similarly to the advances LEM can bring to other areas of stellar physics, advances in our understanding of novae will come from both the ability to obtain high-resolution spectra for sources up to two orders of magnitude fainter than existing instrumentation, and the opening up of the time domain to high-resolution study.

Early Onset X-rays and Blast Waves

As CNO burning produces intense high-energy radiation, it is expected that the initial blast should be observable in the X-ray regime for a short time until the outer layers start to lift off the surface via radiation pressure. Observations of the early blast wave are only possible in serendipitous observations as this phase is too short to point an X-ray telescope via a ToO observation. Such a serendipitous observation was achieved with eROSITA during one of the systematic scans of the sky, and 55 described a SSS spectrum similar to the SSS spectra observed later during the outburst.

Probing early shock emission

Before the bright SSS emission dominates X-ray observations, X-ray observers are entertained with faint emission originating from shock emission. Such emission consists of bremsstrahlung continuum and emission lines, and there are several ways of producing such emission. Shocks can occur between the ejecta and pre-existing circumstellar material, e.g. a stellar wind of the companion star, ejecta from a previous outburst, or even material of a planetary nebula. There can also be shocks between shock fronts moving at different velocities. This emission is faint and requires deep X-ray observations.

Probing the Supersoft Source evolution

Models of the opacity evolution of the ejecta assume a homogeneous evolution, however, observations reveal extreme variability by more than an order of magnitude on short time scales of <hours. Further, quasi-periodic transient modulations of <100 seconds have been detected in some novae which might be related to nuclear-burning instabilities. Highspectral resolution timing studies would constitute an important contribution to understanding the origin of these periods.

Understanding the origin of these short-term variations requires not only high spectral resolution. High-resolution timing requires high sensitivity allowing the observations to be spliced into short time segments while still yielding well-exposed highresolution spectra. The shorter the sub-time intervals, the lower the number of counts in each spectrum, and even for these very bright sources, the time resolution with which spectral variations can be studied require the high sensitivity of LEM.

The diagnostic power of high time and spectral resolution is demonstrated with Figures 18 and19 for the example of the recurrent nova RS Oph. An XMM-Newton observation taken on Mach 11, 2006 (26.1 days after the 2006 outburst) contains simultaneous high-resolution spectra from the RGS and high-sensitivity data from the EPIC. The X-ray light curve contained an increase in count rate by a factor ∼ 3 starting ∼ 1.2 hours after the start of the observation, and the origin of this brightness increase is of interest for understanding the opacity evolution of the nova ejecta. Figure 18 demonstrates that the brightness increase resolves into the appearance of a number of soft emission lines between 26 and 30 Å 68,67 . They lived for only half an hour, after which the N VII line at 24.8 Å became stronger, thus the overall flux hardly changed while important changes took place. The simultaneous EPIC spectra yield perfect blackbody spectra, and without high spectral resolution, these important spectral changes completely escape our attention.

In Figure 19, it can seen that during the rise to-wards the higher count rate level, a 35-second period appeared for a short time. Such a transient period was seen at much higher significance during later X-ray observations and is thus considered real. This short appearance of the 35s-periodic signal can only be seen in the EPIC light curve. The RGS data are too noisy to resolve it at such high time resolution, let alone allowing extraction of high-resolution spectra that could probe the spectral changes with the 35s-period.

We have thus demonstrated that slicing high spectral-resolution observations into very short time slices yields important new physical insights, and the high sensitivity of LEM is can thus making transformative progress in this field by increasing the time resolution in which we can investigate brighter sources, and in pushing the high-resolution observational capability to much fainter novae.

SERENDIPITOUS SCIENCE

It is worth noting that studies of stellar coronal transients like the flares and the CMEs will likely be possible also with the analysis of interesting events that serendipitously will occur on late type stars falling in the LEM fov when observing a variety of non-stellar targets. The archive of LEM observations will be a valuable resource of interesting events. An estimate of the number of "serendipitous coronal sources" on which interesting events could occurs can be computed from the RASS source list derived on a band-pass that is quite similar to the LEM one. The latest RASS2 catalogue contains about 135000 distinct X-ray sources and about 39700 of them have as a counterpart a normal star 7 .

The RASS limiting flux is about 2 10 -13 erg/sec/cm 2 (cf. Fig. 20); one can, probably conservatively, assume that the (stellar) sources for which it will be valuable to perform time resolved high resolution spectroscopy should have an X-ray flux higher than about 10 -12 erg/sec/cm 2 . The number of RASS2 sources above this flux limit is about 5270 and 430 of them have a normal star as counterpart.

We show in Fig. 21 the accessible distance (assuming negligible absorption) as a function of the logarithm of stellar X-ray luminosity. Log (L X ) ranges between about 26.5 and 29. Fig. 21 -The curves show the predicted maximum accessible distance for a (stellar) source as a function of its X-ray luminosity for the RASS typical limiting flux (black. f X = 2 10 -13 erg/sec/cm 2 ) and for f X = 10 -12 erg/sec/cm2 (red), respectively. The vertical dashed line are the typical scale height values for the young (green) and old (orange) stellar populations.

lar population (eg. 77 ), with median values of about 27.2 and 30.0, respectively. Given the size of the LEM fov and the planned duration of its operative life one can estimates that LEM will cover about 10% of the entire sky with the vast majority of observations performed at high galactic latitude. It is worth to note that at the flux f X = 1e -12 erg/sec/cm 2 the spatial distribution of old population stars can be considered as almost uniform, since the accessible distance is smaller than the scale height of 300 pc of this population, the situation is different for the young stellar population whose scale height is about 100 pc, much smaller than the predicted accessible distance. and whose spatial distribution, as GAIA has clearly shown, can hardly be considered as uniform (e.g. 79 ). As a consequence one can predict that the LEM archive could sample transient phenomena in "old" stars, while a proper coverage of "young" stars will require properly selected observations. In conclusion we expect about 40-50 serendipitous stellar sources in the LEM archive for which time-resolved high resolution spectroscopy can reliably be performed, assuming 20-30% of them will host transient phenomena the number of expected interesting events will likely range between 8 and 15.

The LEM archive will also be very valuable for all the high resolution studies based on stellar Xray spectra serendipitously collected during the program of GO observations. For all the stellar sources that have been detected with the RASS good quality spectra could be collected if the source serendipitously fall in a LEM fov. Overall several thousands of stellar spectra will be available as can easily be extimatedd with a simple extrapolation based on the RASS2 source list. Moreover in the case of deeper GO observations one can expect to collect high quality spectra for numerous stellar sources fainter that those detected with the RASS.

Stacking Analyses

While the effective area of LEM is unprecedented for a high-resolution X-ray spectrometer, there are still key parts of high energy stellar physics that will remain out of its reach within reasonable pointed observation exposure times. In some of these cases, stacking analysis based on the known positions of stars from deep surveys such as Gaia can provide key insights into the X-ray characteristics of groups of similar types of stars, such as plasma temperature distributions, densities, and chemical compositions. We cite three examples here, each of which are relevant for exoplanet science as well as intrinsic astrophysical interest.

High-mass stars with masses M > 6M and spectral types O to early B generate copious Xrays through instabilities and resulting shocks in their radiatively-driven winds. Low-mass stars with masses M < 1.5M generate X-rays through convection and rotation-driven magnetic activity. The intermediate mass later B-and A-type stars are Xray dark. Little is known about the transitions between these regimes. Stacking analysis of intermediate mass stars will probe the physics and plasma conditions of these boundaries.

Little is known about magnetic activity at the end of the main-sequence. The very cool, neutral photospheres of late M dwarfs and brown dwarfs should be largely incapable of sustaining magnetic stresses, yet flaring on these objects is frequent. Generally too X-ray faint for detailed study, these objects are sufficiently numerous in the solar vicinity that stacking of LEM spectra can be key for revealing the details of their plasma physics.

Radiative losses from stellar coronae are dominated by metal lines. One outstanding problem in coronal physics is whether metal-poor stars sustain X-ray emitting coronae, and if so what is the effect of metal paucity on the coronal energy balance. Population II stars are metal-poor, but they are also old and expected to be of low magnetic activity and faint in X-rays. Stacked LEM spectra of Population II stars will provide a window into this astrophysical regime that will be generally inaccessible through pointed observations.

CONCLUDING REMARKS

We have outlined some of the major aspects of the scientific case for next generation soft X-ray spectroscopy of cool stars. The great strength of LEM in the realm of cool star physics is its substantial effective area, coupled with the inherent energy resolution of its microcalorimeter, which easily achieves resolving powers of 1000. The resulting high sensitivity enables the observation of much fainter and more distant stars, greatly broadening the range and number of potential targets for high-resolution study.

For brighter sources, this next generation sensitivity level facilitates time-domain studies, where enough signal can be collected in short exposures to enable the study of source variability on short timescales.

Finally, the large 30'×30' field of view of LEM will produce a spectacular and rich array of spectra of stars in star forming regions and in open clusters that will be invaluable for probing stellar physics and its evolution in time.

Fig. 1 -

 1 Fig.1-Schematic illustration of the Line Emission Mapper X-ray Probe showing the key aspects that make it a powerful tool for cool star research: a microcalorimeter array schiving a resolving power of 1 eV in the field center, fed by large area soft Xray mirror with a field of view of 30'×30' and 10" spatial resolution.

Fig. 2 -

 2 Fig. 2 -ALMA 870 µm continuum image from Ref. 2 of the protoplanetary disk around the nearest T Tauri star, TW Hydrae. The inset corresponds to a region 0.2" square and shows the gap near 1 AU from the star that could be due to interactions of the disk with newly-formed planets 2 .

Fig. 4 -

 4 Fig. 4 -Simulated O VIII Lyα doublet profile of TW Hya, collected in a simulated exposure of just 1 ks. The black solid histogram represents the expected TW Hya spectrum. Gray dashed lines indicate the rest wavelengths of the two contributions to the O VIII doublet. Red solid line marks the best-fit profile, corresponding to the superposition of two Gaussian functions (red dotted lines) that mimic the two doublet contributions. The best-fit redshift, 39 ± 15 km s -1 , is consistent with the assumed input value.

Fig. 5 -

 5 Fig.5 -Simulated He-like emission lines of accretion shock and post-shock at the stellar surface of EX Lupi, obtained with a single LEM central-array pixel and an exposure of 300 ks. Left panel: Ne IX triplet emitted by the accretion shock with cool temperature (T e = 4.7 MK) and high density (n e = 3 × 10 12 cm -3 was assumed). Right panel: O VII triplet emitted by the accretion post-shock with same temperature but lower density (n e = 5.7 × 10 11 cm -3 ). The color coding is the same as in Fig.3. Using He-like ions, LEM will be able to probe the physics of an episodic accretion burst of EX Lupi, including the temperature and the density of the accretion shock and post-shock.

Fig. 6 -

 6 Fig.6 -Simulated He-like emission lines of a shock in the blueshifted jet of DG Tau A, obtained with a single LEM central-array pixel and an exposure of 100 ks. Left panel: Ne IX triplet. Right panel: O VII triplet. The color coding is the same as in Fig.3. In the top panels, the solid lines in blue are the theoretical spectra for a radial velocity of -235 km s -1 between the X-ray emitting shock and the more embedded star; for comparison purposes, the dashed lines in blue indicate the positions of the He-like emission lines for the radial velocity of the star. LEM will determine the plasma temperature of the X-ray emitting shock from plasma diagnostics, and for the first time its radial velocity.

Fig. 7 -

 7 Fig.7 -Simulated LEM observation of the Orion Nebula Cluster. Point sources in the central parts of the field are simulated with the same Chandra-determined position, spectrum and flux of those detected in the COUP observation34 . Outer sources are simulated from a list of candidate members79,47 using the average spectrum of ONC members and a flux determined from the mean J magnitude vs. L X relation. Two diffuse emission regions, detected in XMM-Newton data (Ref. 41; see their Fig.S1), are also simulated with the intensity and spectral shape reported in that work. Their spatial extent is schematically represented by the two reddish areas in the bottom-right part of the image. Three X-ray spectral bands, 200-900 eV, 900-1500 eV, and 1500-3000 eV are used for the red, green, and blue components of the false color image, respectively. Red circles, with source IDs above them, indicate the positions of a sample of sources studied by27 , which experienced strong flares during the COUP observation. The circles are also used as photon extraction regions for the spectra shown below. The two green circle in the northern diffuse emission regions was also used to extract events for spectral analysis.

Fig. 8 -

 8 Fig.8 -Simulated LEM spectra for two COUP sources, COUP 43 on the left (7021 Chandra counts 42000 simulated LEM counts) and COUP 1568 on the right (89400 Chandra/730000 LEM). Both sources are isolated and uncontaminated by neighbouring sources, with the closest neighbor at ∼24 and ∼20 , respectively. For each source we show, from top to bottom: the full spectrum simulated with the 2 Å-resolution response matrix appropriate for the outer part of the microcalorimeter array, in the 5-50Å wavelength range; the same spectrum in the 10-22 Å range; the spectrum simulated with the 0.9 Å-resolution response matrix corresponding to the central 7 arcmin region of the array, in the same 10-22 Å range. In all cases, the simulated spectrum is plotted in green and the best-fit model in red. In the bottom panels some prominent lines are marked with the ion that produces them.

Fig. 11 -

 11 Fig.11 -Simulated spectra of the young brown dwarfs MHO 4 (top row) and 2MASS J0422 (bottom row) in the Taurus molecular cloud, obtained with a single LEM central-array pixel and an exposure of 100 ks. Left panels show the normalized X-ray spectrum of the absorbed, two-component plasma37 . Right panels illustrate the Ne IX triplet emission of the cool plasma (T e = 4.6 MK) assuming a (putative) high-density (n e = 3 × 10 12 cm -3 ) to mimic an accretion shock. The color coding is the same as in Fig.3.

Fig. 12 -

 12 Fig.12 -The simulated spectrum of AB Dor in the 10-20 Å range obtained with a 1 ksec LEM observation with a resolution of 0.9eV. The model spectrum includes the quiescent and the flare emission components. All emission lines are thermally-broadened and the flare component is Doppler-shifted with a velocity of 100 km/sec. The two most prominent emission lines are the OVIII and FeXVII with rest wavelengths of 18.967 Ang and 15.014 Ang, respectively.

Fig. 14 -

 14 Fig. 14 -Simulated profile of the O VIII line at 18.97 Å of a flare-CME event from Prox Cen, assuming that the CME ejection occurs along the line of sight. The dotted line marks the position of the strongest contribution of the doublet, used as a reference for the velocity axis.

Fig. 15 -

 15 Fig. 15 -The "FIP bias" as a function of spectral type from Ref. 96. Active stars are shown as red points. The FIP bias is the average ratio of high FIP element abundances to that of Fe relative to the solar mixture. The results indicate both a spectral type and activity dependence of the FIP effect.

  Fig.16 -Demonstration of the suitability of LEM to estimate abundances in exospheres. The plot shows the depth of the O edge for three separate scenarios: one where the planet has had its atmosphere entirely ablated (brown curve), one with a relatively oxygen-poor atmosphere (solar composition; orange curve), and one with planetary atmospheric abundance enhanced 10× relative to solar (blue curve with synthetic data points overplotted). The three scenarios are sketched for illustration in the upper part.

Fig. 17 -

 17 Fig. 17 -Demonstrating LEM's ability to detect Doppler shifts (top) and Doppler broadening (bottom) in symbiotic spectral lines Fe XVII at 17.05 Å (left) and O VIII at 18.96 Å (right). Line fluxes are as in CH Cyg 92 . The bands are uncertainty ranges based on 200 simulations, with the different colors representing different exposure times as listed in the legend.

Fig. 18 -

 18 Fig. 18 -The spectral time-map of the XMM-Newton observation of the recurrent nova RS Oph on day 26.1 after its 2006 outburst. Top left: spectra extracted over selected time intervals showing line identifications and also noting the wavelengths of unidentified features. The color coding of the different spectra corresponds to the intervals indicated in the lower right panel. Top right: a color bar assigning a color to each intensity. Bottom right: EPIC/pn and MOS2 light curves showing the brightness evolution in count rate with time running downward, and intervals of spectrum extraction noted that correspond to the spectra in the upper left panel. Bottom left (main panel): the time evolution of the spectrum using the colors defined in the top right. Taken from Ref. 68.

Fig. 19 -

 19 Fig. 19 -Similar to Figure 18, showing the data on the recurrent nova RS Oph observed with XMM-Newton on day 26.1 after its 2006 outburst. This figure concentrates on the periodogram and its variations. Top left: periodogram extracted over selected time intervals indicated in the lower right panel. Color coding of the periodograms corresonds to the extraction interval illustrations. In addition to the two power spectra from the colored partial light-curve intervals, the power spectrum from the full light-curve is also shown in black, containing no significant signal. Top right: a color bar assigning a color to each Fourier power. Bottom right: modulation amplitude of the signal with time running downwards. Bottom left (main panel): the time evolution of the periodogram computed from 24 overlapping 1000s time segments from the pn light curve. The colors indicate the power (corresponding to detection likelihood, see scale in the top right): blue colors mark periods with >90% confidence, red marks 30-80%, and yellow/light green reflect noise. Taken from Ref. 68

Fig. 20 -

 20 Fig.20-The yellow histogram shows the flux distribution of the RASS2 sources derived assuming a conversion factor from rate to flux of 6 10 -12 cnt/erg/cm 2 , while the red histogram shows the same flux distribution for the sources having as a counterpart a normal star as listed in available catalogues.

  allows an accurate synthesis of the flaring loop X-ray emission, including Doppler shifts due to chromo-

							3×105
		2×106										2×106
	counts keV-1	106 1.5×106				counts keV-1	2×105				counts keV-1	106 1.5×106
							105
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		0 5×104					0 5×104					0 5×105
	counts s-1 keV-1	-5×104 0				counts s-1 keV-1	-5×104 0				counts s-1 keV-1	0
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		0.82	0.822	0.824	0.826	0.828	0.82	0.822	0.824	0.826	0.828	0.82	0.822	0.824	0.826	0.828
				Energy (keV)					Energy (keV)					Energy (keV)
		3×105					3×105					3×105
	counts keV-1	2×105				counts keV-1	2×105				counts keV-1	2×105
		105					105					105
		0 5×104					0 5×104					0 105
	counts s-1 keV-1	0				counts s-1 keV-1	-5×104 0				counts s-1 keV-1	0 5×104
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		0.82	0.822	0.824	0.826	0.828	0.82	0.822	0.824	0.826	0.828	0.82	0.822	0.824	0.826	0.828
				Energy (keV)					Energy (keV)					Energy (keV)