X-Ray and Ultraviolet Emission of the Young Planet-hosting Star V1298 Tau from Coordinated Observations with XMM-Newton and Hubble Space Telescope

A new XMM-Newton observation of V1298 Tau was performed on 2021 August 25 (observation ID, hereafter ObsId, 0881220101, PI S. Benatti), in order to characterize the X-ray emission and variability of the host star. The exposure time was about 36 ks with EPIC as a prime instrument in the full frame window imaging mode and with the medium filter. We also acquired data from Reflection Grating Spectrometers (RGS) and Optical Monitor (OM) instruments simultaneously (Figure 1).

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The observation data files were reduced with the Science Analysis System (SAS; ver.20.0.0), following standard procedures. We obtained FITS tables of X-ray events detected by the three EPIC CCD cameras (MOS1, MOS2, and pn) and with the two high-resolution spectrographs (RGS1 and RGS2), calibrated in energy, arrival times and astrometry by means of the emchain, epchain, and rgsproc SAS tasks. An inspection of the light curve of events detected with energies >10 keV allowed us to identify and filter out several time intervals affected by high background.

V1298 Tau is sufficiently isolated to allow the extraction of the source signal from a circular region of 40'' radii for MOS and pn, and local background from an uncontaminated nearby circular region of similar size (Figure 2). With SAS we also produced the response matrices and effective area files needed for the subsequent spectral analysis. RGS source and background spectra were also extracted adopting the standard results of the SAS pipeline. Source X-ray spectra and light curves are shown in Figure 3. In the same figure, we show the OM light curve, obtained with the SAS task omfchain.

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For the measurements of X-ray line fluxes, we considered the spectrum obtained by adding the first-order RGS1 and RGS2 spectra, which cover the 5–40 Å range, with an average resolution of 0.06 Å FWHM. For improving the statistics, we also coadded the RGS spectra obtained in 2021 August with those already available from the previous XMM-Newton observation, taken in 2021 February (Maggio et al. 2022; ∼27 ks of clean exposure time), and we rebinned the resulting spectrum by a factor of 3 (Figure 4). This choice is supported by the lack of strong variability of the coronal emission (Section 4.2).

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We identified the strongest emission lines and measured their fluxes by fitting the observed spectrum in small wavelength intervals. To model the line profile, we used the RGS line spread function tabulated in the RGS response matrix file. The width of each wavelength interval was set to include the blended lines that needed simultaneous fitting. In the best-fitting function, in addition to individual line contributions, we included also a continuum component, with the temperature and normalization left free to vary. Because of the small width of the selected wavelength intervals, the continuum component, acting as an additive constant, takes into account also the integrated contribution of unresolved weak lines. Two examples of RGS line fitting are plotted in Figure 5. The measured line fluxes are listed in Table 1. The observed X-ray lines form in the temperature range ∼1–16 MK, probing the thermal structure of the stellar corona.

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Table 1. Measured X-Ray and UV Line Fluxes of V1298 Tau

λ1	Ion 2	$\mathrm{log}{T}_{\max }$ 3	Fobs 4		EMD1 5	((Fobs − Fpred)/σ) 6	EMD2 5	((Fobs − Fpred)/σ) null
6.18	Si xiv Si xiv	7.20	610	250			*	1.43
8.42	Mg xii Mg xii	7.00	56	49	*	−0.39	*	−0.56
9.17	Mg xi	6.80	64	41	*	0.41	*	0.30
10.24	Ne x Ne x	6.80	117	32	*	1.59	*	2.59
10.98	Fe xxiii Ne ix Fe xxiii Na x Fe xvii	7.20	102	42	*	1.1	*	1.67
12.13	Ne x Ne x Fe xvii Fe xxiii	6.75	254	55	*	−3.20	*	−0.23
12.28	Fe xxi Fe xvii	7.05	97	40	*	1.06	*	0.28
13.45	Ne ix Fe xix Fe xix	6.60	71	40	*	−2.07	*	−0.98
13.52	Ne ix Fe xix Fe xix Fe xxi	7.00	91	37	*	0.12	*	0.08
13.70	Ne ix	6.55	161	40	*	1.83
14.20	Fe xviii Fe xviii	6.90	93	26	*	−0.48	*	0.11
15.01	Fe xvii	6.75	188	30	*	0.97	*	0.98
15.08	Fe xix	6.95	64	25	*	2.01	*	2.06
15.21	Fe xix O viii O viii	6.95	63	32	*	1.11	*	1.61
15.26	Fe xvii	6.75	31	27	*	−0.60	*	−0.50
16.00	Fe xviii O viii O viii	6.90	103	24	*	1.25	*	2.97
16.07	Fe xviii Fe xix	6.90	58	22	*	0.65	*	0.24
16.78	Fe xvii	6.75	82	24	*	−0.41	*	−0.17
17.05	Fe xvii Fe xvii	6.75	204	33	*	−0.54	*	0.23
18.63	O vii	6.35	8	12	*	−0.35	*	0.59
18.97	O viii O viii	6.50	373	34	*	3.65	*	9.77
21.60	O vii	6.30	37	32	*	−1.04	*	0.92
21.81	O vii	6.30	77	35	*	1.97
22.10	O vii	6.30	61	27	*	0.60
33.73	C vi C vi	6.15	38	27	*	0.03	*	0.22
1174.93	C iii	4.95	9.6	0.8			*	0.48
1175.26	C iii	4.95	10.2	1.1			*	3.23
1175.71	C iii C iii C iii	4.95	39.1	1.1	*	−1.55	*	−1.51
1176.37	C iii	4.95	11.6	0.8			*	4.00
1206.50	Si iii	4.80	67.3	1.1
1218.35	O v	5.35	6.9	1.1	*	−3.12	*	−0.50
1238.82	N v	5.30	21.5	1.1	*	0.09	*	−0.13
1242.81	N v	5.30	11.8	0.9	*	1.16	*	1.26
1253.81	S ii	4.50	0.9	0.3	*	−0.02	*	−0.40
1264.74	Si ii Si ii	4.45	4.2	0.3	*	2.44
1266.11	⋯	0.00	1.1	0.2
1294.55	Si iii	4.80	1.1	0.3	*	2.68
1298.95	Si iii Si iii	4.80	3.0	0.6	*	3.71
1309.28	Si ii	4.45	1.6	0.3	*	−2.31
1323.95	C ii C ii C ii	4.75	0.8	0.3	*	−0.57	*	0.71
1334.53	C ii	4.60	32.7	0.9	*	−27.91	*	−1.84
1335.71	C ii C ii	4.60	69.5	1.2	*	27.99	*	1.41
1351.44	⋯	0.00	3.3	0.6
1354.07	Fe xxi	7.05	5.5	0.5	*	0.88	*	−0.67
1364.22	⋯	0.00	−0.4	0.3
1371.30	O v	5.35	1.9	0.4	*	−1.56	*	4.55
1393.76	Si iv	4.90	41.6	2.6	*	−2.54	*	−1.42
1401.16	O iv	5.15	3.4	0.5	*	−23.68	*	−0.99
1402.77	Si iv	4.90	23.6	0.9	*	−0.59	*	1.65
1407.38	O iv	5.15	0.6	0.3			*	−0.47
1548.19	C iv	5.05	83.0	2.4	*	0.87	*	−0.73
1550.78	C iv	5.05	44.8	2.0	*	0.91	*	1.57

Notes.

¹Wavelengths (Å). ²Multiple identifications indicate unresolved lines in the CHIANTI database, which contribute to the measured flux. ³Temperature (kelvins) of maximum emissivity. ⁴Measured fluxes (10⁻¹⁶ erg s⁻¹ cm⁻²) with uncertainties at the 68% confidence level. ⁵Asterisks indicate lines selected for the EMD reconstruction with each method. ⁶Comparison between observed and predicted line fluxes (method (1)). ⁷Comparison between observed and predicted line fluxes (method (2)).

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V1298 Tau was observed with HST during three consecutive orbits to acquire spectra in FUV with the COS spectrograph. The central wavelength was 1291 Å covering about the 1150–1450 Å wavelength range. About 55 minutes were available during each orbit for science and acquisition exposures of V1298 Tau. The actual exposure times were 2249.2, 2634.1, and 2634.2 s, respectively, during the three orbits totalling about 7517.5 s. The orbits were simultaneous with the second half of the XMM-Newton observation during which the star appears quiescent in X-rays. The standard calibration operated with CalCOS (v. 3.3.10) at STScI was deemed sufficient, and thus, the reduced spectra were downloaded from the HST archive and ready for the subsequent analysis. The archive provides the spectra accumulated during each orbit and their average spectrum. We checked that the ion lines have similar intensities during each orbit. Because the star was quiescent in X-rays, we determined to analyze the average spectrum (Figure 6) so to maximize the count statistics.

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We identified and measured the strongest UV emission lines in this averaged spectrum. The line fluxes were obtained by fitting the observed spectrum in small wavelength intervals, assuming for the line profile a beta model (also known as Moffat line profile):

$$\begin{eqnarray}&&f\left(\lambda \right)={f}_{\max }{\left[1+{\left(\displaystyle \frac{\lambda -{\lambda }_{{\rm{c}}}}{{\rm{\Delta }}\lambda }\right)}^{2}\right]}^{-\beta };\end{eqnarray} \tag{ 1 }$$

with Δλ = 0.03 Å, and β = 1.6 kept as fixed parameters. We adopted these line shape and parameters after having checked that this function reproduces well the observed line profile of strong and isolated lines. The width of the selected wavelength intervals was set to eventually include blended lines, for which simultaneous fitting is needed. We also included a constant function in addition to the line contributions in each interval, to fit also the continuum level. Two examples of COS line fitting are shown in Figure 7, and the case of a few lines possibly altered by opacity effects is described in Appendix A.

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Besides our 2021 August HST/COS G130M observation, we have also considered a previous observation of V1298 Tau taken with the G160M grating on 2020 October 17 (ObsId lebw02koq, PI P.W. Cauley), and available in the MAST archive. The aim was to measure the flux of the C iv doublet at ∼1550 Å, which is important to better constrain the thermal structure of the stellar chromosphere (Section 4.3). Since this observation was acquired in a different epoch, we checked again for the presence of variability by comparing the fluxes of the Si iv doublet at ∼1400 Å, which is present in both the 2021 and 2020 spectra. As a result, we corrected this effect by dividing the C iv flux by a factor of 2.7.

All the measured line fluxes are listed in Table 1. This list comprises UV lines that form in the temperature range ∼30,000–200,000 K, thus probing the thermal structure of the high chromosphere and the transition region of the star. In the same list, we reported also the fluxes of a couple of lines with no clear identification. We instead did not include some O i emission lines, usually present in COS spectra, because of their geocoronal contamination.

We observed V1298 Tau within a dedicated Director Discretionary Time (DDT) program (ID: A42DDT5, PI: A. Maggio) at the Telescopio Nazionale Galileo (TNG, La Palma, Canary Islands) by using the HARPS-N high-resolution spectrograph (Cosentino et al. 2014) in the visible band (383–690 nm). We obtained six spectra of the target between 2021 February 23rd and February 26th, in order to perform a follow-up of the first XMM-Newton observation through the monitoring of the chromospheric emission in the Ca ii H&K lines. Three additional spectra of V1298 Tau were collected between Aug 23rd and Aug 26th to support the coordinated XMM-Newton-HST observation within the Global Architecture of Planetary Systems (GAPS) project. Moreover, a large amount of data (almost 190 spectra between 2019 March and 2022 March) has been collected with the aim to measure the masses of the four planets of the system, because V1298 Tau is also in the young objects subsample of the GAPS observing program (Carleo et al. 2020). For all data sets, we calculated the values of the $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ activity index by using the procedure described in Lovis et al. (2011, and references therein) available on the YABI workflow interface, implemented at the INAF Trieste Observatory. ¹¹

The use of the GAPS data allows us to perform a comparison of the values of $\mathrm{log}R{{\prime} }_{\mathrm{HK}}$ obtained during the XMM-Newton-HST observations with its typical behavior over 4 yr. Figure 8 shows the time series of this chromospheric activity index obtained as part of the GAPS program (black dots), and the values taken during the DDT program in 2021 February (red dots) and the additional observations in 2021 August (orange dots). No significant difference is visible between our first set of DDT data and the GAPS ones, because the chromospheric indexes appear well within the mean distribution. Instead, we observe an excess in the value of $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ (> −4.15) for one spectrum of the second set of DDT data (on 2021 August 26 at 05:16 UT) and for two GAPS spectra (on 2021 September 4 at 04:51 UT, and on 2022 Jan 08 at 01:03 UT, respectively). We note that the mean value of the $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ appears slightly larger in the last season than in the previous ones, as indicated by the median values drawn in Figure 8 as horizontal lines, suggesting an enhancement of the stellar activity, in full agreement with what we found in X-rays. We hypothesize that the spectra showing the highest values of $\mathrm{log}{R}_{\mathrm{HK}}^{{\prime} }$ could have caught the star during large stellar flares. For a double check, we extracted the Hα index from those spectra by using the ACTIN code (Gomes da Silva et al. 2018). Actually, we observed a higher value also for this chromospheric proxy, which corroborates the flare hypothesis (see, e.g., Di Maio et al. 2020), although the optical spectra show no significant emission in the Hα line core.

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Finally, we used a subset of these HARPS-N data to obtain a coadded spectrum aiming to perform a comparison between the photospheric abundances with those in the outer stellar atmosphere probed by the XUV lines. To derive an estimate of the metallicity, we performed the comparison with synthetic spectra (calculated using MOOG and a grid of Kurucz model atmospheres), which include Fe i lines. We obtained T_eff = 4980 K, $\mathrm{log}g=3.95\pm 0.15$ dex, V_microt = 0.85 km s⁻¹, and the resulting [Fe/H] is 0.00 ± 0.15 dex (with $\mathrm{log}\epsilon {({Fe})}_{\odot }=7.50)$, in agreement with the solar abundance reported by Suárez Mascareño et al. (2022). The combination of relatively high rotational velocity and low effective temperature prevents us from deriving accurate abundances of other elements, because of possible unknown line blending and NLTE effects for carbon, silicon, and magnesium (see also Suárez Mascareño et al. 2022).

The EPIC X-ray light curves of V1298 Tau (Figure 3) show low-level but significant time variability in the first 15 ks of the 2021 August XMM-Newton observation, with a peak count rate ∼60% higher with respect to the average quiescent level observed in the next 21 ks time segment. This behavior is more clear in the MOS light curves, less affected by high background contamination than pn. The simultaneous near-UV light curve obtained with the OM shows just some flickering at the level of ∼30% with respect to the average count rate.

Although no large flare is evident, we analyzed separately the EPIC spectra accumulated in the two time segments, which we dubbed quiescent and high-state, in order to check for possible variations of the characteristics of the coronal plasma. A further assessment of the long-term variability of V1298 Tau is postponed to the end of Section 4.2.

For the spectral analysis, performed with xspec V12.12.0, we proceeded as in Maggio et al. (2022). Initially we applied a best-fitting procedure only to the EPIC (MOS1, MOS2, and pn) X-ray spectra. We adopted an optically thin coronal emission model (AtomDB v3.0.9, Foster et al. 2012) composed of three isothermal components (3T, vapec), with the abundances of all elements linked to the iron abundance. Next, we added also the combined RGS1 and RGS2 high-resolution spectra, and allowed up to nine elements as free parameters: C, N, O, Ne, Mg, Si, S, Ar, and Fe. A global interstellar absorption was also included in the model with a multiplicative component (phabs).

Eventually, we reduced the number of free parameters by fixing the interstellar hydrogen column density, N_H, and the abundances of C, N, and Ar, because these parameters were poorly constrained. In fact, the best-fit value of N_H was consistent with the value derived from the known B-V color excess, E(B − V) = 0.024 ± 0.015 (David et al. 2019), which implies an extinction A_V = 0.074 ± 0.05, and N_H = 1.6 ± 1.1 × 10²⁰ cm⁻²; hence, we fixed this parameter to the nominal value. Similarly, the best-fitting procedure yields just uninformative upper limits for both the C and N abundances, and we decided to fix both of them to the oxygen abundance, guided by the similarity of the first ionization potentials (FIPs) of these elements (see Section 4.4). The line complex of Ar xvii and Ar xviii at 3.14 and 3.32 keV, respectively, is quite evident in the combined spectrum (Figure 3), and the best-fit abundance is near the solar value, but we fixed it to the abundance of neon due to the large uncertainties.

Table 2 reports the parameters from the best-fit models to EPIC and RGS spectra of the quiescent and high-state time segments. We also show the results of the fitting of the 2021 February spectra and of the combined spectra obtained by adding the 2021 February and 2021 August data, performed with the same procedure. During the 2021 August observation, the coronal plasma of V1298 Tau was characterized by a cold temperature component (T1) at 4–5 MK, and a second component (T2) at 10 MK. The volume emission measures (EMs) of these components did not change appreciably from the quiescent to the high-state phase, and they appear similar also to those probed by the 2021 February observation. Moreover, there is evidence in all cases of very hot plasma, at 15–25 MK (T3), which is responsible for most of the observed variability: this component has a very low EM during the quiescent phase in 2021 August, while it becomes the dominant one during the high-state phase. A comprehensive view of the results of these multicomponent isothermal fittings of the XMM spectra is displayed in Figure 9. This is typical behavior for the variability of the coronal plasma in young active stars.

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Table 2. Best-fit Parameters from Modeling of the EPIC and RGS Spectra of V1298 Tau

Observation Id	T1	EM1	T2	EM2	T3	EM3	χ2	d.o.f.	fX	LX		Abundances and 90% Confidence Ranges (Solar Units; Anders & Grevesse 1989)
	106 K	1052 cm−3	106 K	1052 cm−3	106 K	1052 cm−3			10−12 erg s−1 cm−2	1030 erg s−1		Mg	Fe	Si	S	C	O	N	Ca	Ne
											FIP (eV)	7.65	7.90	8.15	10.36	11.26	13.62	14.53	15.76	21.56
2021 Feb	${2.9}_{-0.3}^{+0.6}$	${2.7}_{-0.7}^{+0.7}$	${8.0}_{-0.5}^{+0.3}$	${6.7}_{-1.5}^{+1.9}$	${16.5}_{-1.9}^{+2.7}$	${3.9}_{-1.0}^{+0.9}$	532.8	431	${1.24}_{-0.02}^{+0.01}$	${1.74}_{-0.03}^{+0.01}$	2021 Feb	0.33	0.17	0.25	=O	=O	0.29	=O	=Ne	0.95
												[0.20, 0.50]	[0.13, 0.22]	[0.15, 0.38]			[0.23, 0.37]			[0.95, 1.63]
Quiescent	${4.9}_{-0.6}^{+0.8}$	${5.8}_{-1.6}^{+1.5}$	${10.8}_{-0.7}^{+0.6}$	${13.1}_{-3.0}^{+1.1}$	${43.5}_{-23.4}^{\mathrm{unbound}}$	${1.3}_{-0.8}^{+2.2}$	605.0	510	${1.52}_{-0.08}^{+0.01}$	${2.13}_{-0.11}^{+0.02}$	Quiescent	0.19	0.10	0.10	=O	=O	0.22	=O	=Ne	0.47
												[0.09, 0.28]	[0.08, 0.12]	[0.03, 0.17]			[0.16, 0.29]			[0.37, 0.70]
High-state	${4.3}_{-0.7}^{+0.8}$	${4.7}_{-1.3}^{+1.4}$	${10.7}_{-0.7}^{+0.7}$	${8.7}_{-2.5}^{+3.6}$	${24.3}_{-3.1}^{+6.5}$	${8.8}_{-2.5}^{+1.7}$	474.8	422	${2.04}_{-0.05}^{+0.01}$	${2.85}_{-0.07}^{+0.02}$	High-state	0.25	0.19	0.08	=O	=O	0.38	=O	=Ne	0.65
												[0.07, 0.47]	[0.14, 0.26]	≤0.23			[0.28, 0.51]			[0.39, 0.97]
Combined	${4.8}_{-0.5}^{+0.5}$	${5.3}_{-0.8}^{+0.8}$	${10.3}_{-0.5}^{+0.5}$	${9.0}_{-1.5}^{+1.8}$	${24.3}_{-4.1}^{+13.9}$	${3.4}_{-1.4}^{+1.2}$	1645.6	1315	${1.46}_{-0.02}^{+0.01}$	${2.05}_{-0.03}^{+0.01}$	Combined	0.21	0.13	0.15	0.26	=O	0.28	=O	=Ne	0.61
												[0.14, 0.29]	[0.11, 0.15]	[0.10, 0.21]	[0.13, 0.40]		[0.24, 0.33]			[0.50, 0.73]
											EMD method 1	0.32	0.13	0.81	0.23	0.18	0.20	0.41		0.91
												[0.09, 1.20]	[0.09, 0.19]	[0.51, 1.29]	[0.12, 0.45]	[0.13, 0.26]	[0.12, 0.35]	[0.35, 0.48]		[0.47, 1.78]
											EMD method 2	0.41	0.15	1.49	0.35	0.25	0.03	0.23		0.59
												[0.10, 0.55]	[0.14, 0.16]	[1.45, 1.50]	[0.24, 0.41]	[0.24, 0.26]	[0.02, 0.04]	[0.20, 0.28]		[0.46, 1.68]

Note. Unabsorbed X-ray flux and luminosity in the 0.1–10 keV band. Errors are quoted at the 90% confidence level.

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The unabsorbed flux and the luminosity of V1298 Tau in the quiescent phase are ${f}_{{\rm{x}},{\rm{q}}}={1.4}_{-0.2}^{+0.1}\times {10}^{-12}$ erg s⁻¹ cm⁻², and ${L}_{{\rm{x}},{\rm{q}}}={2.0}_{-0.3}^{+0.2}\times {10}^{30}$ erg s⁻¹, respectively in the band 0.1–2.4 keV. These values are about 20% higher than those observed in 2021 February. A further increase of ≳30% occurred during the variable phase in 2021 August, characterized by an average flux and luminosity of ${f}_{{\rm{x}},{\rm{v}}}={1.82}_{-0.08}^{+0.03}\times {10}^{-12}$ erg s⁻¹ cm⁻², and ${L}_{{\rm{x}},{\rm{v}}}={2.56}_{-0.11}^{+0.04}\times {10}^{30}$ erg s⁻¹. A slightly larger variability can be derived in the broader X-ray band 0.1–10 keV (Table 2). Considering also previous ROSAT and Chandra observations (Poppenhaeger et al. 2021), the X-ray emission of V1298 Tau shows a long-term variability within a factor ∼2.

Finally, we evaluated that the X-ray to bolometric luminosity ratio, $\mathrm{log}{L}_{{\rm{x}}}/{L}_{\mathrm{bol}}$, ranged from −3.35 to −3.15 in the time span between 2021 February and 2021 August, and the flux at the stellar surface, F_x, was between 1.7 × 10⁷ and 2.6 × 10⁷ erg s⁻¹ cm⁻². These surface fluxes are 10–100 times higher than in the case of the Sun at the maximum and minimum of its magnetic activity cycle (Chadney et al. 2015).

The significant but low-amplitude variability of V1298 Tau is also confirmed by considering the 3 yr time series of the chromospheric Ca ii H&K emission lines (Figure 8), where the $\mathrm{log}R{{\prime} }_{\mathrm{HK}}$ index shows a full range of variation ≲0.2 dex. These measurements can be converted into the pure activity-related ${R}_{\mathrm{HK}}^{+}$ index by Mittag et al. (2013), and we have employed the latter to predict the X-ray to bolometric luminosity ratios by means of the chromospheric to coronal flux–flux relationship derived by Fuhrmeister et al. (2022) for active G-type stars. We found a full range of $\mathrm{log}{L}_{{\rm{x}}}/{L}_{\mathrm{bol}}$ between −3.7 and −3.2, i.e., a possible variability of about a factor 3.

The full set of UV and X-ray line fluxes probes emission from material with temperatures ranging from 3 × 10⁴ to 2 × 10⁷ K. This line set allows us to derive the emission measure distribution (EMD) versus temperature of the entire stellar atmosphere, from the chromosphere to the corona. To this aim, we assume that the emission is due to a collisionally excited optically thin plasma. We have checked that deviations from this hypothesis affect only marginally some strong lines, which form at chromospheric temperatures (see Appendix A).

The lack of significant variability of the chromospheric ${R}_{\mathrm{HK}}^{{\prime} }$ index and of the coronal emission between 2021 February and 2021 August observations (Section 4.1), except for the thermal components hotter than ∼10 MK, supports our assumption that the same occurred for the strength of the EUV emission lines.

The interstellar absorption, assuming N_H = 1.6 × 10²⁰ cm⁻², was properly taken into account for computing unabsorbed X-ray line fluxes, while we have employed the Fitzpatrick (1999) extinction law for the UV lines.

We employed two different and independent methodologies for the reconstruction of the EMD versus temperature. We have first derived the EMD following Sanz-Forcada et al. (2003b; method (1)). An initial EMD with 0.1 dex resolution in temperature, based on global fitting results, is used to calculate the expected line fluxes for the source. These calculations include contributions from all lines in identified blends, according to the AtomDB (v3.0.9) database. The ratio between observed and predicted line fluxes is used to modify the EMD and the abundances of the elements in an iterative process, thus obtaining the best result to minimize these line ratios. The EMD is computed initially using abundances relative to iron. At the end of the process, the whole EMD is shifted by +0.89 dex, to correct for the [Fe/H] = − 0.89 value determined with the global fitting of the combined spectrum (Section 4.2). The method provides also uncertainties on both EMD and abundances with a Monte Carlo method, which takes into account the uncertainties on the measured line fluxes, but keeping fixed the iron abundance.

In this process, special attention was made to the consistency of spectral line fluxes of similar ions or temperature of formation, excluding some of them (e.g., Si iii 1206.50 Å). A special treatment was also applied to the C iii multiplet at ∼1176 Å, having inaccurate atomic data in AtomDB v3.0.9. In this case, we adopted the Raymond (1988) atomic data to evaluate the flux of the whole multiplet.

Then, we derived an alternative solution for the plasma EMD and abundances by employing the Markov Chain Monte Carlo (MCMC) approach implemented in the PINTofALE software suite (v2.954; Kashyap & Drake 1998). In applying this procedure (method (2)), we adopted the CHIANTI (v7.13) atomic database, since it appears more reliable than APEC in reproducing some strong lines in the UV range. We considered a subset of measured line fluxes, as reported in Table 1. In particular, we did not consider density-sensitive lines, lines with uncertain identification, and lines whose fluxes appear incompatible among themselves in the hypothesis of collisionally excited plasma. ¹² To obtain absolute abundances and to better constrain the hottest components of the EMD, we complemented these selected line fluxes with the measurements of the total flux (lines + continuum) in five wavelength intervals, including also intervals at short wavelengths where the emission is dominated by the hot plasma (Pillitteri et al. 2022). To this aim, we selected the intervals reported in Table 3. The observed fluxes in these intervals were obtained from the EPIC data with XSPEC. We computed the total emissivities associated to these measurements including, in addition to the continuum contribution, the contribution of all the emission lines contained in the considered wavelength interval. We run the MCMC procedure several times, adjusting at each step this emissivity on the basis of the inferred abundances.

Table 3. Measured X-Ray Fluxes in Selected Wavelength Bands of V1298 Tau

λa	Eb	$\mathrm{log}{T}_{\max }$ c	Fd	$\tfrac{({F}_{\mathrm{obs}}-{F}_{\mathrm{pred}})}{\sigma }$ e
2.48–4.13	3.00–5.00	8.00	46.8 ± 2.9	−0.76
4.13–5.17	2.40–3.00	8.00	39.2 ± 1.9	−2.79
8.49–8.92	1.41–1.46	7.80	14.9 ± 0.3	−0.49
27.55–30.24	0.41–0.45	6.55	28.6 ± 0.5	0.47
5.17–123.99	0.10–2.40	6.15	1040.0 ± 10	−7.34

Notes.

^a Wavelength range (Å). ^b Energy range (keV). ^c Temperature (kelvins) of maximum emissivity. ^d Observed fluxes (10⁻¹⁵ erg s⁻¹ cm⁻²). ^e Comparison between observed and predicted line fluxes.

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Considering the temperature ranges covered by the emissivities of the selected lines, we derived the EMDs over a temperature grid ranging from $\mathrm{log}T=4.0$ to $\mathrm{log}T=7.5$, with ${\rm{\Delta }}\mathrm{log}T=0.1$. The results are shown in Figure 10, together with plots of the residuals between observed and predicted line fluxes with the two methods (Table 1).

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The EMD obtained with method (1) appears smoother than the other, but the two solutions turned out to be consistent within 1σ uncertainties, except for a few bins, in spite of a slightly different set of emission lines and methodologies of EMD reconstruction. Note that method (1) joins the estimated EM values between $\mathrm{log}T=5.5$ and 6.1 K with a few bins without formal errors, because this is the temperature range less constrained by the available UV and X-ray emission lines. The same occurs for the EMD at $\mathrm{log}T\geqslant 7.3$ K. Method (2) extends the reconstructed EMD up to $\mathrm{log}T=7.5$ K thanks to the inclusion of the narrowband X-ray fluxes, which inform on the continuum emission level. Moreover, the 0.1–2.4 keV broadband flux and the Li-like lines of C and N have emissivity functions with significant contributions also from plasma in the $\mathrm{log}T$ range 5.5–5.9 K. It is because of these emissivities that the EMD can be constrained with method (2) also in this temperature range, although with large error bars.

In Appendix B, we show a comparison of the EMD of V1298 Tau with those of other G–K stars having different activity levels.

The elemental abundances in the corona of V1298 Tau, derived from the global analysis of the combined XMM-Newton spectra (Section 4.2), are shown in Figure 11 as a function of FIP. Similar values were obtained also for the single observations in 2021 February and 2021 August, as well as for the quiescent and high-state segments (Table 2). Elements with low FIP (Fe, Mg, and Si) are systematically underabundant with respect to elements with FIP ≳ 12 eV, such as O, N, or Ne. This trend, dubbed inverse FIP effect, is typical of young active stars (Maggio et al. 2007; Scelsi et al. 2007).

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In the same figure are shown the values derived together with the EMDs, which resulted in fair agreement with the values from the global fitting of X-ray spectra, except for the case of silicon. In this case, we are assuming that the abundances of elements such as O and Si remain constant in the full range of temperatures explored, but we recognize that the abundances could change somewhere between the chromosphere and the corona. Moreover, some differences may be due to the two different atomic databases employed for the analysis of the emission lines.

We recall also that the abundances of V1298 Tau in the chromosphere and corona are scaled with respect to the solar photospheric abundances (Anders & Grevesse 1989). Stellar abundances for each element should be employed for a proper assessment of any trend with the FIP (Sanz-Forcada et al. 2004), but unfortunately, accurate photospheric abundances cannot be determined for V1298 Tau (Section 3.3), except for the iron. In this latter case, the difference between the photosphere and the corona is clearly established.

We have employed the EMDs presented above to compute the X-ray luminosity in the 5–100 Å band, and the EUV luminosity in the 100–920 Å band. We have obtained L_X = 2.26 × 10³⁰ erg s⁻¹, and ${L}_{\mathrm{EUV}}={1.60}_{-0.60}^{+0.95}\times {10}^{30}$ erg s⁻¹ with method (1), and L_X = (2.02 ± 0.05) × 10³⁰ erg s⁻¹, and L_EUV = (0.95 ± 0.30) × 10³⁰ erg s⁻¹ with method (2). The 1σ uncertainties on luminosities from method (2) were evaluated from the luminosity distributions obtained from the Monte Carlo sampling of the EMD(T) and abundances parameter space. In the case of method (1), we assume an uncertainty on L_X equal to the range measured between the 2021 February observation and the high-state at the 2021 August epoch, which is 1.6–2.4 × 10³⁰ erg s⁻¹ in the 5–100 Å band, while the uncertainty on the EUV luminosity was computed by generating the spectra relative to the upper and lower boundaries of the EMD range.

In Figure 12, we plotted the values derived with the two methods, and a few other benchmark stars employed in the past to calibrate the old scaling laws proposed by Sanz-Forcada et al. (2011; hereafter SF11), Chadney et al. (2015; hereafter C15), and King et al. (2018; hereafter K18), and the new scaling laws by Johnstone et al. (2021; hereafter J21), Sanz-Forcada et al. (2022; hereafter SF22). In Figure 12, we do not show the C15 scaling law, because it was computed in a different EUV band (80–350 Å).

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In the cases C15, K18, and J21, the original scaling laws employed X-ray and EUV fluxes at the stellar surface; hence, we computed scaling laws in luminosity assuming two different stellar radii, 0.7 R_⊙ and 1.3 R_⊙, representative of stars ranging from an early M-type dwarf such as AU Mic to a pre-main-sequence solar-mass star such as V1298 Tau. In the case SF22, in Figure 12, we show the confidence region at the 95% level of the least squares linear regression, in the range of validity of this scaling law, and its extrapolation to the position of V1298 Tau.

Among the benchmark stars, selected to cover a wide range of activity levels, we included our Sun, with flux ranges derived from Johnstone et al. (2021) and based on observations with the Sollar EUV Experiment on the NASA TIMED mission. As intermediate-activity stars, we show the cases of HD 189733 (SF11; and Bourrier et al. 2020) and Eri (SF11; C15; and K18). For the latter, we adopted the X-ray luminosity range derived by Coffaro et al. (2020), because the EUV measurement is not simultaneous. Finally, as a prototype of a young high-activity red dwarf, we selected AU Mic (K18; and C15), with X-ray and EUV luminosity ranges taking into account source variability and/or measurement uncertainties. We stress that the most recent scaling laws (J21; and SF22) are based on a few tens of stars observed in X-rays and UV or EUV wavelengths at different epochs.