X-Ray Activity Variations and Coronal Abundances of the Star–Planet Interaction Candidate HD 179949

We carry out a detailed analysis of the Chandra Advanced CCD Imaging Spectrometer–Spectroscopic (ACIS-S) array spectra of HD 179949 obtained during each observation using the Sherpa fitting package (Refsdal et al. 2011) in Chandra Interactive Analysis of Observations (CIAO v4.13; Fruscione et al. 2006). We adopt a collisionally excited thermal emission model for the corona (The Astrophysical Plasma Emission Code [APEC]; Brickhouse et al. 2001; Smith et al. 2001; Foster et al. 2016), and an interstellar absorption model (Tübingen-Boulder; see Wilms et al. 2000) with the H column density fixed at N_H = 10¹⁹ cm⁻². In all cases we compute abundances relative to the solar photosphere as listed by Anders & Grevesse (1989; see Appendix A). We carry out the modeling in stages of increasing complexity, evaluating the quality of the fit at each stage and continuing with more complex models only if necessary. Our fit results are thus designed to be robust against fluctuations, and describe the most information that may be reliably gleaned from the data. The models we consider are:

• 1m. An APEC model with one temperature component, fitting normalization, temperature, and metallicity;
• 2m. An APEC model with two temperature components, fitting the normalization and temperature for each component separately and the metallicity jointly;
• 2v. As in Model 2m, but allowing the abundances to vary freely in groups based on similar first ionization potential (FIP) values, as {C,O,S}, {N,Ar}, {Ne}, {Mg,Al,Si,Ca,Fe,Ni}; and
• 2v/Z. As in Model 2v, but the abundance of a selected element Z fitted separately. For example, for model 2v/Al, the abundances are fit in groups {C,O,S}, {N,Ar}, {Ne}, {Mg,Si,Ca,Fe,Ni}, {Al}. This is designed to explore whether enhancements of specific elements are measurable.

We carry out the fits in all cases by minimizing the c-statistic (cstat; see Cash 1979) over the passband 0.4-7.0 keV. Background is negligible (<0.5%, see Table 3) in all cases and is ignored. We use the Markov Chain Monte Carlo (MCMC)-based pyBLoCXS method (van Dyk et al. 2001) as implemented in Sherpa. We compute the observed cstat _obs, and the nominal expected cstat _model , and the variance ${\sigma }_{{\mathtt{cstat}}}^{2}$ as described by Kaastra (2017), and reject the model as an adequate fit if the difference between the observed and model expected values, Δcstat = ∣cstat _obs − cstat _model∣ exceeds 2σ _cstat .

When Δcstat is deemed acceptable, we further analyze the residuals to the spectral fit, since acceptable fits may still be accompanied by structures in residuals that indicate that some aspect of the model is inadequate over small energy ranges. We evaluate the quality of the residuals by computing the cumulative sum of the residuals (CuSum) and comparing it against a null distribution generated from the fitted model. We generate fake spectra based on the best-fit parameter values, and build up a set of CuSum curves. Then we calculate measures that test both the width and strength of the residual structure by carrying out two tests:

• 1.  
  First, we compute the ±90% point-wise envelope of CuSum over the energy range 0.5–3.0 keV, and evaluate the percentage of bins, pct_CuSum, where the observed CuSum exceeds the 90% bounds. If this percentage is ≳10%, the model is considered inadequate and the next stage of complexity in the model is considered. If, on the other hand, the percentage is ≪10% this is taken as a sign of overfitting, and the less-complex model is accepted.
• 2.  
  Second, for each simulated spectrum, we calculate the total area of the CuSum curve that falls outside the 5%–95% bounds from the ensemble of the simulations and construct a null distribution of the excess area beyond the 90% bounds. We then compute the same quantity for the observed CuSum curve, and hence the corresponding p-value (p_area) with reference to the null distribution. This process is similar to the posterior predictive p-value calibration procedure described by Protassov et al. (2002). If this p_area ≪ 0.05, we consider the corresponding model an inadequate fit.

These tests are illustrated in Figure 3. The left panels in Figure 3 show two examples of pct_CuSum calculated for two successive models (2m at the top and 2v at the bottom) for the same data set (ObsID 6119). In both cases, the Δcstat is acceptable (+0.3 for model 2m and −0.86 for model 2v); using just this information, there is no reason to prefer the more complex spectral model. Considering the fraction of bins that show systematic runs shows that the structure in the residuals is reduced for model 2v, with pct_CuSum dropping from 8.6% to 4.2%. However, the magnitude of the residuals is reduced significantly for model 2v: the right panels show the computation of p_area for the same models as in the corresponding left panels, and we find p_area changes from an unacceptable 0.01 for model 2m (p_area ≪ 0.05 makes it an inadequate fit), to an acceptable 0.20 for model 2v (p_area > 0.05, and the model cannot be rejected). We thus accept model 2v as the preferred spectral model over model 2m.

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We report the results of the spectral fits for each Observation ID (ObsID) in Table 5 for the best acceptable model obtained for each case, along with the cstat, Δcstat, pct_CuSum, and p_area for the accepted model. The corresponding fits and residuals are shown in Figure 4, and the CuSum plots and distributions are shown in Figure 12 in Appendix B. We note that the data are never fit well with model 1m, and never require models more complex than model 2v. ObsID 6121 is fit adequately with model 2m; model 2v can be rejected due to an abnormally low pct_CuSum = 1.10%. In no case is model 2v/Z or other complex modifications statistically justifiable. While some exploratory fits indicated that allowing Al to be freely fit produced better fit statistics, there is no reason to choose those fits over those of model 2v. In addition to the plasma temperatures, component normalizations, abundances, and the corresponding fluxes, we also compute the FIP bias (F_bias; Wood et al. 2012; Testa et al. 2015; Wood et al. 2018). The FIP bias is a logarithmic summary of how much the abundances of high-FIP elements like C, N, O, and Ne deviate relative to a low-FIP element like Fe, in the corona relative to the photosphere,

$$\begin{eqnarray}&&{F}_{\mathrm{bias}}=\displaystyle \frac{1}{4}\displaystyle \sum _{{\rm{X}}={\rm{C}},{\rm{N}},{\rm{O}},\mathrm{Ne}}\mathrm{log}{[{\rm{X}}/\mathrm{Fe}]}_{{\mathtt{cor}}}-\mathrm{log}{[{\rm{X}}/\mathrm{Fe}]}_{{\mathtt{phot}}}.\end{eqnarray} \tag{ 1 }$$

The average value F_bias,ObsID and the propagated error bars σ_bias,ObsID are shown in Table 6 for each ObsID, and these individual measurements are combined to form a weighted estimate

$$\begin{eqnarray*}&&\langle {F}_{\mathrm{bias}}\rangle =\displaystyle \frac{{\sum }_{\mathrm{ObsID}}{F}_{\mathrm{bias},\mathrm{ObsID}}\cdot {w}_{\mathrm{ObsID}}}{{\sum }_{\mathrm{ObsID}}{w}_{\mathrm{ObsID}}},\end{eqnarray*}$$

with the weights ${w}_{\mathrm{ObsID}}=\tfrac{1}{{\sigma }_{\mathrm{bias},\mathrm{ObsID}}^{2}}$ . The weighted variance

$$\begin{eqnarray*}&&\mathrm{wtVar}=\displaystyle \sum _{\mathrm{ObsID}}\displaystyle \frac{{\left({F}_{\mathrm{bias},\mathrm{ObsID}}-\langle {F}_{\mathrm{bias}}\rangle \right)}^{2}\cdot {w}_{\mathrm{ObsID}}^{2}}{{\left({\sum }_{\mathrm{ObsID}}{w}_{\mathrm{ObsID}}\right)}^{2}},\end{eqnarray*}$$

represents the scatter in the individual estimates (Särndal et al. 2003). The average of the individual variances,

$$\begin{eqnarray*}&&\mathrm{avVar}=\displaystyle \frac{1}{5}\displaystyle \sum _{\mathrm{ObsID}}{\sigma }_{\mathrm{bias},\mathrm{ObsID}}^{2}\end{eqnarray*}$$

represents an average measurement error. We find

$$\begin{eqnarray}&&\langle {F}_{\mathrm{bias}}\rangle \pm \sqrt{\mathrm{wtVar}}\pm \sqrt{\mathrm{avVar}}=-0.33\pm 0.03\pm 0.32.\end{eqnarray} \tag{ 2 }$$

on using photospheric abundances of C,O and Fe from Luck (2018), and N form Ecuvillon et al. (2004), and

$$\begin{eqnarray}&&\langle {F}_{\mathrm{bias}}\rangle \pm \sqrt{\mathrm{wtVar}}\pm \sqrt{\mathrm{avVar}}=-0.09\pm 0.02\pm 0.29,\end{eqnarray} \tag{ 3 }$$

using photospheric abundances of C, N, O and Fe from Brewer et al. (2016; see Appendix A for values scaled to Anders & Grevesse 1989). Note that in both cases, we adopt [Ne/O] _phot∣angr = + 0.48 from Drake & Testa (2005). In both cases, we find the estimated F_bias to be high compared to the value expected for late-F stars (Wood et al. 2012, 2018; Testa et al. 2015). However, these values are consistent with those measured for other hot Jupiter hosting stars with suspected SPI like HD 189733 and τ Boo (see discussion in Section 4).

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Table 5. Parameters of Fitted Spectral Models

Parameters a	Observation IDs (ObsIDs)
	5427	6119	6120	6121 a	6122
TLow [MK]	${2.00}_{-2.00}^{+3.73}$	${2.09}_{-0.75}^{+0.75}$	${4.87}_{-0.67}^{+0.67}$	${2.55}_{-1.94}^{+1.94}$	${5.10}_{-1.67}^{+1.67}$
	7.02[1.86 − 9.86]	2.06[1.64 − 3.24]	5.11[4.64 − 5.80]	2.60[1.28 − 6.73]	5.80[4.99 − 6.73]
THigh [MK]	${6.61}_{-0.31}^{+0.31}$	${6.62}_{-0.32}^{+0.32}$	${11.02}_{-1.64}^{+1.64}$	${6.73}_{-0.86}^{+0.86}$	${10.79}_{-3.40}^{+3.40}$
	6.63[5.10 − 7.54]	6.73[6.26 − 7.31]	11.71[5.34 − 19.49]	6.61[5.22 − 7.54]	10.97[9.05 − 17.86]
N c	${1.25}_{-1.25}^{+1.31}$	${2.10}_{-2.10}^{+2.73}$	${0.69}_{-0.69}^{+0.94}$	0.21	${0.00}_{-0.00}^{+0.60}$
	1.79[1.03 − 4.24]	1.48[1.62 − 4.49]	0.76[0.10 − 2.22]	0.18	0.10[0.00 − 0.71]
O c	${0.12}_{-0.12}^{+0.16}$	${0.39}_{-0.39}^{+0.38}$	${0.06}_{-0.06}^{+0.08}$	0.21	${0.17}_{-0.23}^{+0.23}$
	0.13[0.05 − 0.36]	0.50[0.12 − 0.57]	0.09[0.01 − 0.19]	0.18	0.27[0.11 − 0.40]
Ne c	${0.00}_{-0.00}^{+0.09}$	${0.00}_{-0.00}^{+0.21}$	${0.00}_{-0.00}^{+0.09}$	0.21	${0.00}_{-0.00}^{+0.08}$
	0.02[0.00 − 0.13]	0.03[0.00 − 0.16]	0.04[0.00 − 0.14]	0.18	0.01[0.00 − 0.10]
Fe c	${0.20}_{-0.05}^{+0.05}$	${0.45}_{-0.23}^{+0.23}$	${0.20}_{-0.08}^{+0.08}$	${0.21}_{-0.10}^{+0.10}$	${0.21}_{-0.09}^{+0.09}$
	0.27[0.18 − 0.32]	0.48[0.31 − 0.73]	0.21[0.13 − 0.30]	0.18[0.14 − 0.24]	0.23[0.16 − 0.29]
EMLow d	${0.26}_{-0.26}^{+0.57}$	${0.38}_{-0.38}^{+0.53}$	${2.67}_{-1.00}^{+1.02}$	${0.52}_{-0.27}^{+0.63}$	${2.34}_{-0.71}^{+0.35}$
	0.32[0.07 − 1.04]	0.16[0.03 − 0.69]	2.04[1.57 − 2.90]	0.62[0.18 − 1.41]	2.22[1.54 − 2.81]
EMHigh d	${2.40}_{-0.59}^{+0.55}$	${0.95}_{-0.43}^{+0.43}$	${0.33}_{-0.22}^{+0.21}$	${2.02}_{-0.62}^{+1.43}$	${0.75}_{-0.72}^{+0.53}$
	1.66[0.49 − 2.36]	0.78[0.51 − 1.09]	0.05[0.00 − 0.30]	1.85[1.22 − 2.84]	0.33[0.11 − 0.68]
Flux (0.15–4 keV)	${2.48}_{-0.02}^{+0.09}$	${2.06}_{-0.07}^{+0.08}$	${2.33}_{-0.07}^{+0.07}$	${2.44}_{-0.07}^{+0.06}$	${2.59}_{-0.05}^{+0.06}$
[10−13 erg s−1 cm−2]
Fit Characteristics
model	2v	2v	2v	2m a	2v
cstat/dof	164.444/445	140.063/445	184.616/445	201.862/448	218.968/445
$\tfrac{{\rm{\Delta }}{\mathtt{cstat}}}{{\sigma }_{{\mathtt{cstat}}}}$	−0.30	−0.86	+0.91	+1.82	+1.30
pctCuSum [%]	11.26	4.19	5.74	4.86	12.58
parea	0.09	0.20	0.10	0.23	0.07

Notes.

^a The upper row represents the best-fit value and the 95% equal-tail bounds on the parameter, while the lower row represents the mode and the 90% highest-posterior density intervals obtained using MCMC sampling with pyBLoCXS. ^b The best-fit model for ObsID 6121 is model 2m, with all abundances tied together. ^c Fractional number abundances $\tfrac{A(X)/A(H)}{{\left(A(X)/A(H)\right)}_{{\mathtt{angr}}}}$ relative to solar photospheric (Anders & Grevesse 1989). ^d Emission Measure at the source, EM = normalization × 4 π × distance², in units of [10⁵¹ cm⁻³].

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3.2.1. Light Curves

In order to explore the temporal variability in HD 179949, we construct light curves of counts in all the passbands of interest (see Table 4). We employ the Bayesian Blocks algorithm (Scargle et al. 2013) to build adaptively binned count rates, using the implementation by Astropy Collaboration et al. (2022).

We modify the process by which the blocks are constructed in two ways: first, we discard any change points that occur <10τ after another as unlikely to be physically meaningful (τ = 3.24104 s is the CCD readout time in all of the ObsIDs); second, we recalibrate the parameter p₀ that controls the false alarm probability (FAP) to both account for the 10τ filter as well as to calibrate the steepness of the prior distribution. We accomplish this via simulations involving the same number of photons as in the observed data, 9963, spaced uniformly over a normalized time duration equal to the full observation duration, 152,295/τ. That is, each simulation represents events that would be obtained from a flat light curve that has zero true change points. Change points for several values of p₀ were computed for the same set of event times. We discard all change points that follow another by <10, and record the number of change points ${n}_{\mathrm{sim}}^{\mathrm{cp}}({p}_{0})$. Because the simulated events have zero true change points, every change point found, at any given p₀, represents false positives. The fraction

$$\begin{eqnarray*}&&{p}_{\mathrm{true}}^{\mathrm{sim}}({p}_{0})={n}_{\mathrm{sim}}^{\mathrm{cp}}({p}_{0})/{N}_{\mathrm{sim}}\end{eqnarray*}$$

thus represents the actual false alarm probability parameterized by p₀ for data sets of the size we are dealing with. We repeat the simulations 50 times, and estimate p_true(p₀) as the average over the simulations at each given p₀. The result of these computations is shown in Figure 5. The range of p₀ ∈ (10, 55)% is approximately linear, and we fit a quartic polynomial to this range and extrapolate it to smaller values of p_true. We find that a value of p_true = 0.01, corresponding to a 1% false alarm probability, is obtained for p₀ ≈ 0.06, and hence adopt p₀ = 6% for all the change point calculations carried out below.

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We show the Bayesian Blocks count rate light curves for the broad band in Figure 6 for all five data sets (the light curves for the remaining passbands are available via Zenodo). ⁷ We compute several measures of variability:

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Average Block size: 〈Δt_bin〉 is the average of the block sizes Δt_bin found with Bayesian Blocks, and represents the timescale over which the algorithm requires changes in its piece-wise constant light-curve model.

Number of blocks: The number of blocks, N_blocks = n^cp − 1, defined by n^cp change points found by Bayesian Blocks. This number complements 〈Δt_bin〉 to show the range and ubiquity of variability.

Chi-square: A reduced χ², defined as

$$\begin{eqnarray}&&{\chi }_{\mathrm{red}}^{2}=\displaystyle \frac{1}{({N}_{{blocks}}-1)}\displaystyle \sum _{B}\displaystyle \frac{{\left({\mathrm{rate}}_{B}-{\mathrm{rate}}_{\mathrm{ObsID}}\right)}^{2}}{{\sigma }_{B}^{2}},\end{eqnarray} \tag{ 4 }$$

where ${\mathrm{rate}}_{B}=\tfrac{{\mathrm{counts}}_{B}}{{\rm{\Delta }}{t}_{B}}$ is the observed rate in block B when counts_B counts are observed over a duration Δt_B , rate_ObsID is the count rate for the full data set (the orange horizontal line in Figure 6), and ${\sigma }_{B}=\tfrac{\sqrt{{\mathrm{counts}}_{B}}}{{\rm{\Delta }}{t}_{B}}$ is the uncertainty on the rate. This represents the quality with which a model with unvarying intensity can be fit to the adaptively binned light curves.

These quantities are reported in Table 7 for all the passbands and for all ObsIDs, and show that there is clear evidence for variability in the light curves over a broad range of timescales from ≈100 s to ≈5 ks. We confirm that invariably ${\chi }_{\mathrm{red}}^{2}\gg$ 1, and thus variability in HD 179949 is ubiquitous across passbands and data sets.

Table 7. Summarizing the Variability in Light Curves

	ObsID
Passband	Parameters	5427	6119	6120	6121	6122
Oxy	〈Δtbin〉	257τ	193τ	226τ	309τ	237τ
	Nblocks	36	48	41	30	42
	${\chi }_{\mathrm{red}}^{2}$	15.3	7.7	14.0	5.1	9.4
Fe	〈Δtbin〉	264τ	206τ	238τ	221τ	331τ
	Nblocks	35	45	39	42	32
	${\chi }_{\mathrm{red}}^{2}$	8.1	11.1	7.9	7.9	8.4
Ne	〈Δtbin〉	250τ	215τ	215τ	309τ	255τ
	Nblocks	37	43	43	30	39
	${\chi }_{\mathrm{red}}^{2}$	16.1	13.7	16.3	6.7	6.2
Mg	〈Δtbin〉	257τ	201τ	281τ	238τ	267τ
	Nblocks	36	46	33	39	37
	${\chi }_{\mathrm{red}}^{2}$	12.5	11.4	9.3	15.9	8.1
u	〈Δtbin〉	237τ	265τ	290τ	226τ	231τ
	Nblocks	39	35	32	41	43
	${\chi }_{\mathrm{red}}^{2}$	7.6	9.3	7.9	14.8	8.8
s	〈Δtbin〉	201τ	226τ	265τ	244τ	343τ
	Nblocks	46	41	35	38	29
	${\chi }_{\mathrm{red}}^{2}$	6.9	9.4	10.0	8.7	11.7
m + h	〈Δtbin〉	257τ	201τ	273τ	238τ	255τ
	Nblocks	36	46	34	39	39
	${\chi }_{\mathrm{red}}^{2}$	12.3	11.7	9.6	15.9	8.7
broad	〈Δtbin〉	250τ	211τ	299τ	265τ	293τ
	Nblocks	37	44	31	35	34
	${\chi }_{\mathrm{red}}^{2}$	6.9	10.8	8.9	5.9	7.7

Note. Note that the high values of ${\chi }_{\mathrm{red}}^{2}$ indicates significant variability. Further, the 〈Δt_bin〉 values indicate a range of 27–48 blocks, consistent with the N_blocks values for the typical observation durations of ≈30 ks.

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Table 8. Colors for Different Passband Combinations for All ObsIDs

	ObsID
Color a	5427	6119	6120	6121	6122
C[u/s]	$-{0.52}_{-0.01}^{+0.03}$	$-{0.48}_{-0.02}^{+0.03}$	$-{0.48}_{-0.02}^{+0.03}$	$-{0.52}_{-0.02}^{+0.03}$	$-{0.59}_{-0.01}^{+0.03}$
C[u/m + h]	$+{0.40}_{-0.04}^{+0.03}$	$+{0.53}_{-0.04}^{+0.06}$	$+{0.46}_{-0.04}^{+0.04}$	$+{0.43}_{-0.04}^{+0.03}$	$+{0.30}_{-0.04}^{+0.03}$
C[s/m + h]	$+{0.90}_{-0.03}^{+0.04}$	$+{1.02}_{-0.05}^{+0.03}$	$+{0.94}_{-0.05}^{+0.03}$	$+{0.94}_{-0.04}^{+0.03}$	$+{0.87}_{-0.04}^{+0.02}$
C[Oxy/Fe]	$-{0.40}_{-0.03}^{+0.03}$	$-{0.37}_{-0.03}^{+0.03}$	$-{0.36}_{-0.03}^{+0.03}$	$-{0.38}_{-0.03}^{+0.03}$	$-{0.39}_{-0.02}^{+0.04}$
C[Oxy/Ne]	$-{0.03}_{-0.03}^{+0.04}$	$+{0.11}_{-0.04}^{+0.04}$	$+{0.04}_{-0.04}^{+0.03}$	$+{0.04}_{-0.04}^{+0.03}$	$-{0.06}_{-0.03}^{+0.03}$
C[Oxy/Mg]	$+{0.25}_{-0.04}^{+0.04}$	$+{0.39}_{-0.05}^{+0.05}$	$+{0.31}_{-0.05}^{+0.04}$	$+{0.29}_{-0.04}^{+0.04}$	$+{0.21}_{-0.03}^{+0.04}$
C[Fe/Ne]	$+{0.37}_{-0.02}^{+0.03}$	$+{0.47}_{-0.03}^{+0.04}$	$+{0.39}_{-0.02}^{+0.03}$	$+{0.34}_{-0.02}^{+0.03}$	$+{0.32}_{-0.02}^{+0.03}$
C[Fe/Mg]	$+{0.65}_{-0.04}^{+0.03}$	$+{0.75}_{-0.04}^{+0.05}$	$+{0.67}_{-0.04}^{+0.03}$	$+{0.67}_{-0.04}^{+0.03}$	$+{0.59}_{-0.03}^{+0.04}$
C[Ne/Mg]	$+{0.27}_{-0.04}^{+0.04}$	$+{0.30}_{-0.06}^{+0.04}$	$+{0.28}_{-0.05}^{+0.03}$	$+{0.33}_{-0.05}^{+0.03}$	$+{0.26}_{-0.03}^{+0.04}$

Note.

^a Showing the mode and the 68% highest-posterior density intervals for the overall color for different passbands given by Equation (5).

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3.2.2. Hardness Ratios

There are insufficient counts in the blocks found for the counts of light curves (Section 3.2.1) to allow time-resolved spectroscopy. Instead, we calculate the evolution of hardness ratios over time and evaluate the strength of the evidence for spectral variability (for analyses that highlight how hardness ratios can be useful, see, e.g., Noel et al. 2022; Di Stefano et al. 2021). Specifically, we compute the color

$$\begin{eqnarray}&&C[{\rm{A}}/{\rm{B}}]={\mathrm{log}}_{10}\displaystyle \frac{\mathrm{counts}\,\mathrm{in}\,\mathrm{band}\,{\rm{A}}}{\mathrm{counts}\,\mathrm{in}\,\mathrm{band}\,{\rm{B}}},\end{eqnarray} \tag{ 5 }$$

for various combinations of pairs of passbands in Table 4. We consider different combinations of the Chandra Source Catalog (CSC) bands and the line-dominated bands. Variations in plasma temperatures would be reflected in changes in the CSC colors, while abundance variations could become discernible in the line-dominated band ratios. We use BEHR (Bayesian Estimation of Hardness Ratios; Park et al. 2006) to account for background and estimate the most probable values (modes) and uncertainties (68% highest-posterior density [HPD] intervals) of the color in each time interval considered.

In order to define appropriate time intervals, we use the change points found in the light curves by Bayesian Blocks (Section 3.2.1) analysis of the corresponding passbands. These change points are then combined and pruned to form time bins, and the color is computed independently for counts collected in each bin. The process is described in detail below.

• 1.  
  We begin by constructing the union of the set of change points from both passbands to form a single set of change points in temporally sorted order.
• 2.  
  All pairs of change points which are separated by <10τ ≈ 32 s are then grouped together and replaced by their average, for consistency with how the change points are initially determined. This grouping and averaging is carried out iteratively until no such pairs are found. We call these merged change points close mergers.
• 3.  
  We repeat the above pair-wise merging process for all remaining points which are separated by <30τ ≈ 100 s. While this removes any sensitivity in our process to spectral changes at timescales shorter than 100 s, the likelihood of such quick changes being visible in low-density hot coronal plasma dominated by radiative cooling processes is low. We name such merged points loose mergers.

The time points left in the set at the end of the above merging procedure are used as the bin boundaries for events collected in both passbands. We show an example of variations in the color ratio of the Oxy and Fe passbands in Figure 7. The figure shows the mode of C[Oxy/Fe] (blue stepped curve) and associated 68% HPD uncertainty (blue vertical bars), along with the close mergers (red vertical lines) and loose mergers (gray vertical lines). The color estimate obtained for the full data set is also shown (orange horizontal line, values listed in Table 8), illustrating the scope of departure from constancy. As with the count rate light curves, we again compute a reduced χ² as a measure of variability,

$$\begin{eqnarray}&&{\chi }_{\mathrm{red}}^{2}=\displaystyle \frac{1}{{N}_{\mathrm{bins}}-1}\displaystyle \sum _{k}\displaystyle \frac{{\left(\langle C{[{\rm{A}}/{\rm{B}}]}_{k}\rangle -\langle C{[{\rm{A}}/{\rm{B}}]}_{\mathrm{ObsID}}\rangle \right)}^{2}}{\mathrm{Var}{[C[{\rm{A}}/{\rm{B}}]}_{k}]},\end{eqnarray} \tag{ 6 }$$

where N_bins are the number of bins in the light curve of C[A/B] after the merging process, 〈C[A/B]_k 〉 is the mean color estimated from BEHR draws in each bin k, Var[C[A/B]_k ] is the corresponding variance, and 〈C[A/B]_ObsID〉 is the mean color estimated for the full ObsID. These ${\chi }_{\mathrm{red}}^{2}$ values are reported in Table 9, with values of ${\chi }_{\mathrm{red}}^{2}\gt 1+\sqrt{\tfrac{2}{{N}_{\mathrm{bins}}-1}}$ marked in italic, and ${\chi }_{\mathrm{red}}^{2}\gt 1+3\sqrt{\tfrac{2}{{N}_{\mathrm{bins}}-1}}$ marked in bold. It is apparent that the magnitude of the spectral variations is significantly smaller than the intensity variations. This suggests that count rates in the different bands tend to rise and fall in tandem, with most of the variations attributable to emission measure changes. Nevertheless, spectral variations over timescales of the observation duration is definitely present and are indeed detectable, as seen in several cases where significant deviations in ${\chi }_{\mathrm{red}}^{2}$ is seen. Furthermore, detailed examination of the color light curves can yield information on smaller timescale variations, as, e.g., the large rise in C[Oxy/Fe] seen in ObsID 5427 between times 11–15 ks after the start of the observation (top panel of Figure 7). A similar, but smaller variation is also seen in C[Oxy/Ne] over the same period, but no variability is present in either the CSC band colors C[s/m + h] or in C[Fe/Ne] (see Figure 8). This is a strong indication of a temporary surge in the abundance of oxygen, reminiscent of variations seen in streamers and plumes around active regions on the Sun (see, e.g., Raymond et al. 1998; Raymond 1999; Guennou et al. 2015). All of the color C[A/B] spectral variability plots are available via Zenodo (see footnote 7).

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Table 9. Summary of Spectral Variability ^a

	ObsID
ColorObsID	5427	6119	6120	6121	6122
C[u/s]	1.4 (59)	1.6 (56)	1.2 (48)	1.9 (55)	1.8 (53)
C[u/m + h]	0.9 (44)	0.8 (39)	1.2 (38)	1.1 (43)	1.1 (48)
C[s/m + h]	1.6 (49)	0.9 (41)	1.3 (46)	1.3 (45)	0.8 (41)
C[Oxy/Fe]	1.1 (38)	1.6 (52)	1.1 (47)	1.0 (50)	1.7 (45)
C[Oxy/Ne]	1.3 (39)	1.3 (57)	1.2 (46)	1.1 (38)	1.5 (51)
C[Oxy/Mg]	1.2 (35)	0.6 (34)	1.0 (40)	0.9 (33)	0.8 (44)
C[Fe/Ne]	1.0 (46)	1.1 (56)	1.5 (51)	1.0 (51)	1.4 (51)
C[Fe/Mg]	1.4 (43)	1.1 (41)	1.2 (46)	1.2 (45)	0.8 (40)
C[Ne/Mg]	1.0 (41)	0.9 (35)	1.2 (42)	1.3 (38)	0.9 (49)

Note.

^a The values of ${\chi }_{\mathrm{red}}^{2}$ (Equation (6)) are shown, along with the number of bins N_bins in parentheses. Values with deviations >1σ are marked in italic and deviations >3σ are marked in bold.

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3.2.3. Periodicity Analysis

After fitting the spectral models for the five data sets, we calculate the resultant fluxes in the 0.15–4.0 keV energy range. The results are shown in Table 5 and in Figure 2 along with flux data from XMM-Newton (Scandariato et al. 2013) and Swift (D'Elia et al. 2013). We choose to compare against Swift fluxes obtained assuming a plasma with temperature ≈5 MK as that is comparable to the plasma temperatures we find (Table 5. We remove three flaring events (with flux ≫7 × 10⁻¹³ erg s cm⁻²) from the Swift data set to focus only on periodic variability of the quiescent flux. In addition, we normalize the XMM-Newton and Swift flux values to the average Chandra flux to remove systematics like calibration uncertainties and long-term activity variations. The resultant fluxes are shown in the bottom plot of Figure 2.

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We search for periodicity in the combined flux data f using the Lomb–Scargle (L-S) periodogram ${ \mathcal L }{ \mathcal S }(f)$ (Lomb 1976; Scargle 1982), as implemented by VanderPlas (2018; see left panel of Figure 9). In order to obtain better resolution in phase, we split the Chandra data further into segments of ≳5 ks in each ObsID, converting the net counts to fluxes using a counts-to-energy conversion factor computed separately for each ObsID as the ratio of the flux measured (Table 5) to the net count rate (Table 3) for that ObsID.

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We account for the effects of statistical fluctuations and the windowing function via bootstrapping. We first scramble the fluxes f using a random permutation operator Scr( · ) to obtain a new set of fluxes g_k = Scr_k (f), where k = 1,...,5000. We compute ${ \mathcal L }{ \mathcal S }({g}_{k})$ for each of these permutations. When averaged, $\langle { \mathcal L }{ \mathcal S }(g)\rangle$ represents a periodogram that is devoid (due to the scrambling) of an intrinsic periodic signal, but includes effects due to spacing and data level. The scatter in the bootstrapped periodograms, $\mathrm{stddev}[{ \mathcal L }{ \mathcal S }(g)]$ provides a measure of the statistical and data spacing noise. The difference ${ \mathcal L }{ \mathcal S }(f)-\langle { \mathcal L }{ \mathcal S }(g)\rangle$ represents the residual signal that can be attributed to intrinsic periodicity.

We then compute the window function by constructing the L-S periodograms of a unit flux data set sampled at the same times as f. In order to ameliorate numerical instabilities, we allow for a jitter in the unit flux, obtaining values in each case drawn from a Gaussian with mean 1 and width equal to the fractional error on each flux value. We calculate the window function 5000 times and average the resulting periodograms to obtain $\langle { \mathcal L }{ \mathcal S }(W)\rangle$ (see right panel of Figure 9).

We then extract the de-aliased, window-scaled, signal of intrinsic periodicity

$$\begin{eqnarray}&&{ \mathcal P }(f)=\displaystyle \frac{{ \mathcal L }{ \mathcal S }(f)-\langle { \mathcal L }{ \mathcal S }(g)\rangle }{\langle { \mathcal L }{ \mathcal S }(W)\rangle }.\end{eqnarray} \tag{ 7 }$$

This scaled periodogram is shown in Figure 10 as the magenta curve, with select periods marked with vertical bars. We also show the expected 2σ uncertainty, constructed as $2\cdot \tfrac{\mathrm{stddev}[{ \mathcal L }{ \mathcal S }(g)]}{\langle { \mathcal L }{ \mathcal S }(W)\rangle }$, and shown as the gray-shaded region (for visibility, the 2σ curve is placed above ${ \mathcal P }(f)$, covering it where it crosses). It is clear that several peaks are present in ${ \mathcal P }(f)$ at or close to periods of relevance to the HD 179949 system: we detect periodicities at the stellar polar rotational period (≈10 days), the planetary orbital period (≈3 days), and the beat period of the stellar polar and planetary orbital periods (≈4.5 days, consistent with some Ca ii H&K modulations found by Fares et al. 2012) at significances >95%. While each of these is not definitively above the usually adopted "3σ" threshold, the confluence of all three inter-related signals suggests that these periodicities do exist in the HD 179949 system.

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We further explore the properties of HD 179949 in the context of similar stars (see Table 10), by comparing the relative X-ray luminosity $\tfrac{{L}_{{\rm{X}}}}{{L}_{\mathrm{bol}}}$, effective temperature, rotation period and metallicity. In Figure 11, we show the variation in $\tfrac{{L}_{{\rm{X}}}}{{L}_{\mathrm{bol}}}$ with the Rossby number R₀ (the ratio of the equatorial rotational period P_Rot and the convective turnover timescale τ_C ), where HD 179949 is represented with a red block whose height represents the variation in measured L_X, and for R₀ calculated using τ_C from Gunn et al. (1998). HD 179949 is unremarkable in this space, with a slightly lower activity than expected by the trend line, but consistent with other F dwarfs of similar milieus. Other physical parameters like effective temperature are also consistent with other F7V-F9V stars.

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Table 10. Sample of Nearby F7V-F9V Stars

Name	Spectral type	B − V	Teff (K)	(Fe/H) phot	log(LX/LBol)	${R}_{0}^{-1}$	Reference
β Vir	F8IV-F8V	0.550	6071	+0.03A09	−5.65	0.628	(1,2,3,4,11)
θ Per	F7V	0.514	6196	−0.16G07	−5.81	0.621	(1,2,3,4,11)
ζ dor	F7V-F8V	0.526	6153	−0.40A09	−4.60	2.913	(1,2,3,4,11)
36 UMa	F8V	0.515	6172	−0.25A09	−5.43	0.724	(1,2,3,4,11)
υ And a	F8V	0.540	6106	−0.07A09	−5.85	0.621	(1,2,4,5,11)
ι Psc	F7V	0.500	6241	−0.24A09	−5.92	0.628	(1,2,3,4,11)
99 Her	F7V	0.520	5947	−0.73A09	−5.83	0.637	(2,3,4,6)
HD 10647 a	F8V-F9V	0.551	6151	−0.18A09	−5.47	0.956	(2,3,4,7)
o Aql	F8V	0.560	6120	−0.05A09	−5.84	0.850	(2,4,8,9,11)
HD 154417	F8.5V	0.580	6042	−0.14A09	−4.85	1.224	(2,4,9,10,11)
HD 16673	F6V-F8V	0.524	6301	−0.12A09	−5.22	0.941	(2,8,4,9,11)
HR 4767	F8V-G0V	0.557	6038	−0.23A09	−5.50	0.647	(2,3,4,7,11)
ψ1 Dra B	F8V-G0V	0.510*	6223	−0.15G07	−5.16	0.649	(2,3,4,7,12)
HR 5581	F7V-F8V	0.530	6156	−0.06G07	−5.38	0.577	(2,3,4,7,11)
HR 7793	F7V	0.510**	6261	−0.26S15	−5.44	0.826	(2,4,8,9)
HD 33632	F8V	0.542	6074	−0.36A09	−5.19	0.687	(2,3,4,7,11)

Note.

^a Star with a confirmed close-in giant planet (Stassun et al. 2019a).

References. For spectral types and L_X/L_Bol: [1] Schmitt & Liefke (2004), [6] Suchkov et al. (2003), [7] Hinkel et al. (2017), and [9] Freund et al. (2022); for T_eff and [Fe/H] _phot : [2] Stassun et al. (2019a, 2019b); for B − V: [11] Boro Saikia et al. (2018), **[8] Baliunas et al. (1996), *[12] Fabricius et al. (2002); P_Rot is estimated from B-V and S_HK relation from [3] (Noyes et al. 1984), or directly obtained from [5] Shkolnik et al. (2008), [8] Baliunas et al. (1996), or [10] Donahue et al. (1996); τ_C values from [4] Gunn et al. (1998) calculated using B − V values are used with P_Rot to obtain the Rossby number R₀; [Fe/H]_ph measurements converted to Anders & Grevesse (1989) from [A09] Asplund et al. (2009), [G07] Grevesse et al. (2007), and [S15] Scott et al. (2015).

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In contrast, we find that the photospheric abundances are higher than similar stars. Typically, [Fe/H] _phot ≲ − 0.1 for dF stars of similar activity and distance, but is ≳0 for HD 179949Gonzalez & Laws (2007; corrected to Anders & Grevesse 1989). Note however that this appears to be a characteristic of the presence of close-in giant planets (Fischer & Valenti 2005; Wang & Fischer 2015); indeed, for the stars listed in Table 10, we find that for those without confirmed exoplanets (14 stars), 〈[Fe/H] _phot 〉 = −0.22 ± 0.18 while for stars with confirmed exoplanets (3, including HD 179949), 〈[Fe/H] _phot 〉 = −0.06 ± 0.10.

As we show in Section 3.2, considerable variability is present in both intensity and color over a range of timescales. We first note that the existence of close and loose mergers of change points from several bands point to there being substantial energy release incidents that reinforce the presence of ubiquitous variability in the corona of HD 179949. Several passband color combinations show the presence of variability over the durations of the observations (see Table 9, and small timescale changes (see Figures 7, 8).

While the source is not bright enough to allow us to carry out time-resolved spectroscopy, we can infer the presence of spectral variability through hardness ratio light curves. We find that pervasive variability at timescales ∼ksec is present throughout the Chandra observations (see Section 3.2.2). Table 9 lists the estimated goodness of a constant hardness ratio model for all passband combination for all passband combinations and observations; we find that ${\chi }_{\mathrm{red}}^{2}\gtrsim 3$ for all cases. This variability suggests that the corona of HD 179949 is dynamic, with intermittent impulsive energy releases occurring continuously.

This small timescale variability also translates to the corona in its gross characteristics over the ≳8 hr observation durations. Variations of factors of 2× is present in all fitted parameters (Table 5). Nevertheless, it is notable that large flares are not present. We speculate that this is due to the inhibition of large stresses from being built up in the magnetic loops in the corona because periodic interference of the planetary magnetic field which would act to dissipate the stresses continuously. The estimated abundances show that Fe is depleted in HD 179949 (see Section 4.4). Further, due to the underabundance of Neon, following from Laming (2015), we conclude that the star is not active. A comparison of $\tfrac{{L}_{{\rm{X}}}}{{L}_{\mathrm{bol}}}$ which is found to be [−5.6, −5.5] for HD 179949 with other F-type stars like HD 17156 with $\tfrac{{L}_{{\rm{X}}}}{{L}_{\mathrm{bol}}}$ = [−5.8, −6.0] further supports the state of quiescence (Maggio et al. 2015).

From the Lomb–Scargle periodogram analysis (Section 3.2.3, Figure 10), we note a definitive correlation with stellar polar rotation, in agreement with Scandariato et al. (2013). Apart from this, the periodogram also suggests likely variability with the planetary orbital period, thus confirming past results of chromospheric observations (Shkolnik et al. 2003, 2005, 2008). Lastly, it is also likely that there is variability tied to the beat frequency between the stellar polar rotation and the planetary orbital period, which was suggested by Fares et al. (2012). These results can further be improved with more observations to improve phase coverage.

Note that Shkolnik et al. (2008) suggested an on/off nature of star–planet interactions, and during two out of six observation epochs, they found a periodicity of ≈7 days. We have not detected this period in our results, but the nondetection of SPI in some observations is understandable, as the field stretching effect discussed earlier should occasionally cease. This could be due to the decay of the active polar region on the star, or because the connection to the star is broken by excessive "field wrapping" due to the differing P_orb and P_polar. In either case, some time would be needed to reestablish a sturdy star–planet connection. In Scandariato et al. (2013), their X-ray light curves also suggest variability tied to a period of ≈4 days, apart from variability with the stellar polar rotation. Due to limitations of the data used, and due to nondetection of variability tied to the planetary orbital period, they did not conclude the presence of SPI. However, we believe our result of possible variability tied to the beat period of the stellar polar rotation and the planetary orbital period agrees with their measured period of ≈4 days, and could be indicative of the presence of SPI. Alternatively, the 4 day signal could be due to two active longitudes on the star at a latitude a bit removed from the equator.

We find consistent coronal abundance measurements for A(O)/A(Fe) and A(Ne)/A(Fe) across all data sets, with A(O)/A(Fe) ∼ 0.7 and A(Ne)/A(Fe) ≪ 0.1. In contrast, A(N)/A(Fe) is found to be ≫1.0 for some data sets (ObsIDs 5427, 6119, and 6120). Further, the average Z_Fe ∼ 0.2 for all data sets except 6119, where it rises to ≈0.45. Note that for ObsID 6119 (phase ϕ ≈ 0.1 occurring just after planetary conjunction), the abundances of other metals are boosted as well, though within the uncertainty bounds from other ObsIDs. Overall, we conclude that the corona of HD 179949 is significantly deficient in Fe relative to the Sun. We also find indications of abundance variations at small timescales in the color light curves. For instance, we find an extended duration (≳3 ks) where C[Oxy/Fe] and C[Oxy/Ne] increase (see Section 3.2.2) without an accompanying change in the temperature sensitive C[s/m + h] or in C[Fe/Ne], suggesting a short duration surge in O abundance. However, detailed spectral analyses, exploring whether the abundances in specific elements can be estimated, are statistically unsupportable. None of the models 2v/Z were found to be required to explain the spectra, though some instances of models of 2v/Al suggest that Al/Fe > solar.

We further estimate the abundances of high-FIP elements like C, N, O, and Ne relative to Fe in the corona in order to evaluate the FIP bias in HD 179949. We find that typically the ranges in [C,O/Fe] _cor∣angr ≈ −0.37 to + 0.04 and [Ne/Fe] _cor∣angr ≈ −0.87 to −0.56 are subsolar, and the range in [N/Fe] _cor∣angr ≈0 to + 1 is supersolar (Table 6). We compute the FIP bias by comparing our measurements with those compiled in the literature. In particular, we use the measurements of Ecuvillon et al. (2004); Brewer et al. (2016); Luck (2018) together with an assumed photospheric correction for [Ne/O] _{DT 05∣angr} = +0.48 (see Appendix A) to compute F_bias (see Equation (1)). F_bias < 0 indicates that stars have a solar-like FIP effect, and F_bias > 0 incidates an inverse-FIP effect. For stars of type late-F and relatively low activity like HD 179949 (L_X/L_Bol ≈ 3 × 10⁻⁶, ${R}_{0}^{-1}\approx 1;$ see Figure 11), F_bias ≲ −0.5 are expected (Wood et al. 2012; Testa et al. 2015; Wood et al. 2018). Here, we find estimates (see Table 6) based on Brewer et al. (2016) to be F_bias∣ _B+16 = −0.09 ± 0.02 scatter ± 0.29 statistical and based on Ecuvillon et al. (2004) and Luck (2018) to be F_bias∣ _{E+04,Lu 18} = −0.33 ± 0.03 scatter ± 0.32 statistical. These two estimates differ from each other, though the statistical uncertainties are large enough that they are not statistically inconsistent. Both estimates are however larger than the nominal expected value.

However, Wood et al. (2018) suggest that F_bias is larger than the nominal trend for stars with close-in Jupiter-mass planets: τ Boo A has an observed F_bias = −0.21 ± 0.9 when the expected value is ≈ −0.50, and HD 189733 is observed to be at 0.24 ± 0.22 instead of the expected ≈ −0.2. In both these cases, as well as for HD 179949, the observed F_bias is less solar-like than expected and consistent with a reduced magnitude of the FIP effect. We speculate that this is due to the FIP effect being diluted due to mechanical mixing (see Section 4.5).

The star's large-scale magnetic geometry which has been mapped using ZDI (Zeeman-Doppler Imaging; Semel 1989; Donati & Brown 1997) and near contemporaneously with Chandra observations during 2007 and 2009 (Fares et al. 2012). The well-observed 2009 data yield a strongly dipolar configuration, but with the magnetic pole inclined 70° to the rotational axis. Our detection of periodicity corresponding to the polar rotational period thus implies magnetic activity around the magnetic equator but confined to the rotational pole. The emission measures we estimate from the spectral analysis (see Table 5) suggest that the active area ranges from 1-20% of the surface area depending on the assumed coronal plasma density, ⁸ and is thus consistent with this scenario.

Cauley et al. (2019) study SPI in the context of several models of potential interactions, specifically testing which models can generate sufficient power to generate the observed enhancement in Ca ii H&K emission of several systems, including HD 179949. They found reconnection (flaring) between the star and planet was insufficient to heat H&K in many cases; instead, a model where heating is derived from field line stretching was found more adequate to the task. Here we employ the same models to test whether the (weaker) coronal enhancement might be reconnection heated. The two main models are heating by reconnection (Lanza 2009, 2012), and heating by field line stretching (Lanza 2013). In the reconnection case (i.e., essentially flaring between star and planet as proposed by Cuntz et al. 2000), the expected power due to reconnection,

$$\begin{eqnarray*}&&{P}_{r}=\gamma (\pi /\mu ){R}_{p}^{2}{B}_{p}^{2/3}{B}_{* }{\left({a}_{p}\right)}^{4/3}{v}_{\mathrm{rel}},\end{eqnarray*}$$

where 0 ≤ γ ≤ 1 is a constant related to the relative magnetic geometry between star and planet, μ is the magnetic permeability of the vacuum, R_p and B_p are the planetary radius and dipolar magnetic field strength, respectively, B_*(a_p ) is the stellar field strength at the location of the planet, and v_rel is the relative velocity between the orbiting planet and the rotating magnetic footpoint on the star. We assume that the stellar dipole field strength scales as the cube of the distance, i.e., ${B}_{* }({a}_{p})={B}_{* }({R}_{* })\cdot {\left({a}_{p}/{R}_{* }\right)}^{-3}\approx 0.005$ G. For γ ≈ μ ≈ 1 and v_rel = 150 km s⁻¹ the Keplerian velocity of the planet in its orbit, we find (see Table 1) P_r ≈ 6 × 10²⁵ erg s⁻¹, consistent with the estimate by Lanza (2012).

In the field stretching case, the stellar field power available due to field stretching,

$$\begin{eqnarray*}&&{P}_{s}=\displaystyle \frac{2\pi }{\mu }{f}_{{B}_{p}}{R}_{p}^{2}{B}_{p}^{2}{v}_{\mathrm{rel}}.\end{eqnarray*}$$

where ${f}_{{B}_{p}}$ is the fractional area of the planet covered by the magnetic footprint. Using the values from Table 1, we find ${P}_{s}\approx 5\times {10}^{30}\tfrac{{f}_{{B}_{p}}}{0.1}$ erg s⁻¹. Note that the average X-ray luminosity of HD 179949 is L_X ≈ 2 × 10²⁸ erg s⁻¹, with variations ΔL_X ≳ 10²⁷ erg s⁻¹ between observations. Thus, P_s ≫ L_X > ΔL_X ≫ P_r , and we conclude that only the field stretch model of Lanza (2013) is capable of producing the required power for HD 179949. Thus, while the SPI appears magnetic in origin (viz. Saar et al. 2004), the power requirements point to a nonflare-like origin.

Additional justification for this picture comes from the estimate of the FIP bias, which measures the relative abundances of high-FIP and low-FIP elements between the corona and the photosphere. The estimated value of the FIP bias, F_bias = ( −0.33–0.09) for HD 179949 (see Section 4.4), suggests that FIP mechanisms operating in solar-like situations, such as ponderomotive forces (Laming 2015) or proton drag in the chromosphere (Wang 1996), could be diluted. We speculate that the driver for this dilution is the direct mechanical mixing of the metals in the corona leading to the homogenization of abundances between the photosphere and corona. That is, the stretching and kneading of flux tubes due to magnetic SPI could set up flows that move metals from the photosphere up to the corona, leading to a FIP bias closer to zero.