The Dynamic, Chimeric Inner Disk of PDS 70

Transition disks, with inner regions depleted in dust and gas, could represent later stages of protoplanetary disk evolution when newly formed planets are emerging. The PDS 70 system has attracted particular interest because of the presence of two giant planets in orbits at tens of astronomical units within the inner disk cavity, at least one of which is itself accreting. However, the region around PDS 70 most relevant to understanding the planet populations revealed by exoplanet surveys of middle-aged stars is the inner disk, which is the dominant source of the system’s excess infrared emission but only marginally resolved by the Atacama Large Millimeter/submillimeter Array. Here we present and analyze time-series optical and infrared photometry and spectroscopy that reveal the inner disk to be dynamic on timescales of days to years, with occultation by submicron dust dimming the star at optical wavelengths, and 3–5 μm emission varying due to changes in disk structure. Remarkably, the infrared emission from the innermost region (nearly) disappears for ∼1 yr. We model the spectral energy distribution of the system and its time variation with a flattened warm (T ≲ 600 K) disk and a hotter (1200 K) dust that could represent an inner rim or wall. The high dust-to-gas ratio of the inner disk, relative to material accreting from the outer disk, means that the former could be a chimera consisting of depleted disk gas that is subsequently enriched with dust and volatiles produced by collisions and evaporation of planetesimals in the inner zone.

1. , first identified as a T Tauri star based on its infrared excess (Gregorio-Hetem et al. 1992), has emerged as a key object in studies of late-stage protoplanetary disk evolution and planet formation.The star possesses a highly structured disk with gaps in both dust and gas (Long et al. 2018;Keppler et al. 2019) within which orbit two giant planets (Keppler et al. 2018;Haffert et al. 2019), both of which exhibit signatures of circumplanetary dust and/or accretion (Haffert et al. 2019;Christiaens et al. 2019;Isella et al. 2019;Hashimoto et al. 2020;Zhou et al. 2021;Benisty et al. 2021).
PDS 70 also hosts an inner disk interior to the two planets; its ∼10 au extent is only marginally resolved by ALMA at sub-mm wavelengths (Keppler et al. 2019).Dust in this disk dominates the emission from this system in the mid-infrared (3-25m) and spectroscopy by Spizter and JWST find a dust temperature of 400-600K and strong crystalline silicate emission at 10 m (Perotti et al. 2023).The disk is gas-poor but not gas-free (Long et al. 2018;Keppler et al. 2019;Facchini et al. 2021;Skinner & Audard 2022;Portilla-Revelo et al. 2023); CO (and HCO + ) was detected at mm wavelengths (Portilla-Revelo et al. 2023) but not the 4.6-m fundamental band (Perotti et al. 2023) or its 2.3-m overtone (Long et al. 2018).H 2 O and CO 2 have been detected in emission with JWST (Perotti et al. 2023).Based on the mm-wave CO and continuum emission, Portilla-Revelo et al. (2023) estimated a gas-to-dust ratio of ∼10 , compared to the canonical ISM ratio of 100.Gas could originate in the outer disk and passing through the gap via a "bridge" suggested by ALMA imaging (Keppler et al. 2019).Micron-sized dust grains that are dynamically coupled to the gas can be carried into the inner disk, but condensation of silicates and ices at ∼30K in the outer disk and trapping of large particles in a pressure bump at its inner edge is predicted to deplete that gas.
Although Balmer H and X-ray emission from the star lie within the range of non-accreting weaklined T Tauri stars (Joyce et al. 2020) and far-UV continuum emission from accretion shocks is absent (Skinner & Audard 2022), the reversed profile of the H line and fluorescent H 2 emission point to primordial disk gas and low-level (≲ 10 −10 M ⊙ yr −1 ) accretion (Thanathibodee et al. 2020;Skinner & Audard 2022).Absorption in the 1.083 m He I triplet and emission in the forbidden [O I] 6300Å line (Campbell-White et al. 2023) reveal a wind that could drive this accretion (Thanathibodee et al. 2020).
Like many other T Tauri stars, emission from PDS 70 is variable (Batalha et al. 1998), and this variability is a probe of conditions in the inner disk.Sources of variability among T Tauri stars include; at optical wavelengths, accretion, rotation of the spotted stellar surface, and occultation by dust (Herbst et al. 1994;Cody et al. 2014); at 3-5 m, hot dusty structures near the inner disk rim; and at longer wavelengths by time-dependent selfshadowing of the disk (Muzerolle et al. 2009).In some systems, anti-correlated "see-saw" variability of infrared emission around a pivot at  ≈ 5 − 8 m is observed.The mid-infrared continuum of PDS 70 differs significantly in Spizter and JWST spectra obtained ≈15 years apart (Perotti et al. 2023).Photometry of PDS 70 by the WISE mission shows ≈0.15 mag variability in 25 m emission over two one-day intervals that is anti-correlated with that at 3.4 and 4.6 m.1 Here we present time-series photometry and spectroscopy of PDS 70 that more fully reveal its variability, and the nature of its inner disk.We propose that the variability and its time-dependence is a manifestation of the mode of accretion at the mobile inner edge of the disk, and is driven by variation in the stellar magnetic field and/or disk feedbacks on ∼1 year timescales.We also propose that the inner disk is a "chimera", consisting of depleted primordial gas mixed with the solid and gaseous products from the collisions, disintegration, and evaporation of planetesimals.

TESS photometry
The TESS mission (Ricker et al. 2014) 1).Two-minute cadence PDCSAP lightcurves from Sectors 11 and 65 processed by the TESS mission and the 10-minute cadence Science Processing Operations Center (SPOC) lightcurve from Sector 38 were retrieved from the Mikulski Archives for Space Telescopes (Fig. 1).For each lightcurve, we performed a Lomb-Scargle periodograms (Scargle 1982) and computed the asymmetry  and quasi-periodicity  parameters defined by Cody et al. (2014).
To evaluate the photometry stability of TESS photometry between sectors we identified 12 stars within 20' and 0.5 magnitudes of the Gaia -band brightness of PDS 70 that have both Sector 11 and 38 lightcurves available (Sector 65 lightcurves of these stars were not available at that time of this 1 Shadowing could also be responsible for asymmetric HCO + emission from the outer disk of PDS 70 (Long et al. 2018), but the asymmetry seems conserved between two observations separated by over a year and it is unlikely these are shadows from the inner disk.
manuscript's preparation) and compared the median PDCSAP values.The median absolute deviation is 1.2%, much smaller than the observed variation for PDS 70.

LCOGT Photometry
We analyzed photometry obtained by the 0.4-m and 1-m telescope network of the Las Cumbres Global Observatory Telescope (LCOGT) as part of the Key Project "Catch a Fading Star: Probing the Planet-Forming Zones of Circumstellar Disks with LCO" (KEY-2020-007), as well as previous observations from the public LCOGT archive.1-m and 0.4-m observations were made between 14 May and 23 June 2020 and 15 Feb and 11 May 2023, respectively (Fig. 1).Each 0.4-m telescope was equipped with an SBIG 6303 detector with 0".571 pixels and a 29'×19' field of view (FOV), while the 1-m telescopes are equipped with Sinistro 4K2 detectors with 0".389 pixels and have a 26'×26' FOV.Exposures were obtained through Sloan  ′ (4760Å) and  ′ (7720Å) filters with integration times of 10/5 sec (1-m) 280/50 sec (0.4-m).2 Pointings were designed to maximize the number of comparison stars of comparable brightness.
Images were automatically processed (bias removal, flat-fielding) using the BANZAI pipeline (McCully et al. 2018); source identification and aperture photometry was performed with SExtractor routines (Bertin & Arnouts 1996).Instrumental magnitudes were calculated from count rates in an optimal elliptical Kron aperture (Kron 1980).Lightcurves were produced using the procedures described in Gaidos et al. (2022) and summarized in Appendix A. − and −band lightcurves were combined into reddening-vs-dimming plots by pairing observations obtained within 60 minutes of each other (the typical cadence of our observations was 6 hr).We performed weighted linear regression of  −  reddening vs. -band magnitude with three-sigma outlier rejection.We also rejected points that were brighter or fainter than all other points by >0.3 mags.The former filters flares which are frequent on very young, rapidly rotating stars, the latter filters erroneous -band measurements due to confusion with unrelated fainter sources that appears as variation in -band not accompanied by any -band variation, and produce slope-one excursion in a - vs. -band diagram.Uncertainties in slope were calculated by fitting 104 Monte Carlo representations of the data constructed by bootstrap sampling with replacement.

ASAS-SN photometry
ASAS-SN is a distributed ground-based transient survey (e.g., Holoien et al. 2017) with five stations of four telescopes in both hemispheres plus two more telescopes at the Cerro Tololo International Observatory (CTIO) in Chile, one at McDonald Observatory in Texas, USA, and one at the South African Astrophysical Observatory in Sutherland, South Africa.Each ASAS-SN telescope is a 14cm Nikon telephoto lenses with a back-illuminated, 2048 2 CCD camera with a 4.47×4.47-degreefield of view.A transition from Cousins -band (5420Å) to Sloan -band (4750Å) filters occurred over 2017-2018, with a one-year overlap of observations in both passbands.Currently, ASAS-SN observes the entire visible sky every clear night to a depth of  = 18.5 mag (Shappee et al. 2014;Kochanek et al. 2017;Hart et al. 2023).For a given visit ASAS-SN takes three dithered, tandem 90-sec exposures.All images are processed by a fully-automated reduction pipeline (Shappee et al. 2014).For the photometry used in this work we use the publicly accessible ASAS-SN Sky Patrol version 1 aperture photometry lightcurves3 (Kochanek et al. 2017).This tool performs forced aperture photometry at any position of the sky using a 2-pixel radius (≈16 ′′ ) aperture in the IRAF apphot package.We note 3 https://asas-sn.osu.edu/ that PDS 70 is near the optimum brightness for ASAS-SN photometric precision (see Fig. 3 in Hart et al. 2023).

ATLAS photometry
The Asteroid Terrestrial Impact Last Alert System (ATLAS; Tonry et al. 2018) utilizes four 0.5-m f/2 Wright Schmidt telescopes, two in Hawai'i on Haleakalā and Mauna Loa, one in South Africa, and one in Chile.During typical survey operations, the telescopes obtain four 30-sec exposures per field each night, allowing the survey to cover the observable sky at daily cadence for equatorial targets and a two-day cadence for polar regions.ATLAS operates with two broad filters, the "cyan" ( ≈  + ) filter (5290Å) and the "orange" ( ≈  + ) filter (6750Å, Tonry et al. 2018).We obtained ATLAS light curves of PDS 70 from the ATLAS forced point-spread function (PSF) photometry service4, and specifically from the reduced images, prior to the subtraction of a reference image.After excluding epochs with poor data quality and rejecting outliers, we combined the intra-night epochs using a weighted mean to obtain deeper limits and more robust detections.Due to the southern declination of PDS 70, the effective cadence is low prior to ATLAS's expansion to the southern hemisphere in January 2022.

WISE photometry
We obtained multi-epoch photometry produced by the WISE Cryogenic (Wright et al. 2010) mission and post-cryogenic NEOWISE (Mainzer et al. 2011) and NEOWISE Reactivation (Mainzer et al. 2014) missions from the NASA IPAC InfraRed Science Archive (IRSA).WISE cryogenic observations were made in four channels (W1-W4, centered at 3.4, 4.6, 12, and 25 m), while NEO-WISE data includes only channels W1 and W2.Magnitudes were converted to flux densities using the zero-magnitude fluxes for flat-spectrum objects published in the Explanatory Supplements to release products for the respective surveys (Cutri et al. 2013(Cutri et al. , 2015)).

LCOGT NRES spectroscopy
Optical (3800-8600Å), high-resolution (/Δ ≈ 53, 000) spectra were obtained with the Network of Robotic Echelle Spectrographs (NRES; Siverd et al. 2018) spectrograph on the 1-m node of LCOGT at CTIO between 13 May and 2 June 2023.Exposure times were 1800 sec, and the median SNR in the vicinity of the H- line was 3-9 per spectral pixel.We performed  = 11 median filtering of each spectrum and then fit a Gaussian to the smoothed version over the wavelength range 6560-6565.5Å.The equivalent width (EW) of the H- line was computed from the Gaussian fits.

HARPS spectroscopy
Twenty-two optical spectra (3780-6910Å) of PDS 70, obtained with the High Accuracy Radial velocity Planet Searcher (HARPS) spectrograph on the ESO 3.6-m telescope (Mayor et al. 2003) between 29 March 2018 and 15 March 2022, were retrieved from the ESO Archive Science Portal.The spectral resolution is 120,000 and the median SNR in the vicinity of the H line is 15-30 pix −1 , with most near 30.These spectra were processed by the HARPS pipeline5.

Variability of PDS 70 from circumstellar dust
TESS lightcurves from three 27-day sectors over 4 years (2019( -2023, Fig. 2) , Fig. 2) show photometric behavior that evolved from strongly periodic variability in Sector 11, with a 3.03 day signal previously identified as the stellar rotation period  rot (Thanathibodee et al. 2020), to stochastic, asymmetric variability with weak or no periodicity and dimming events lasting ∼1 day in Sectors 38 and 65 (insets of Fig. 2).The bottom panel of Fig. 2 shows that, after 2019, the lightcurves' quasi-periodicity parameter  (the fraction of variability not captured by the dominant periodic signal; Cody et al. 2014) increases, while their asymmetry parameter  (the skew between the 10th and 90th percentile in the brightness distribution; Cody et al. 2014) moves to positive values (more dimming than brightening) characteristic of T Tauri "dipper" stars that experience transient occultation by circumstellar dust (Cody et al. 2014;Ansdell et al. 2016).
Both the ASAS-SN and ATLAS photometry show dipper-like variability that increases in amplitude after late 2019, although some of this difference is due to the ASAS-SN change from the --band filters where scattering by dust (at shorter wavelengths) is greater (Fig. 1).The ASAS-SN data also contain a periodic signal: The upper panel of Fig. 3 shows the Lomb-Scargle wavelettransform power spectrum of the time-series photometry using using a Gabor-Morlet wavelet, with the parameter governing the trade-off between time and frequency resolution set to  = 5.Each bandpass is separately normalised to yield the same median value within the period of overlap.Spectral power at the rotational period of 3 days, and its overtones, emerges at MJD 57500, peak at around MJD 58520, and diminishes thereafter.
Time-series photometry in Sloan -and -bands obtained in 2020 with the 1-m LCOGT telescope array and nearly three years later with the 0.4-m array also contain dipping behavior (upper panels of Fig. 4).The slopes of the reddening-dimming trends constructed from these lightcurves (lower panels of Fig. 4) are consistent with occultation by dust, are much shallower than that seen among YSOs due to variable accretion or flaring (≈0.8;Gaidos et al. in prep), and have greater amplitude than the typical variability produced by rotation and spots .The best-fit slopes of the two reddeningdimming trends (black lines in in Fig. 4) differ significantly and are slightly shallower than the ISM value (blue lines).We inferred the dust size distribution by comparing these slopes to calculations of absorption and Mie scattering from a power-law particle size distribution with the complex optical constants of Budaj et al. (2015).We assumed a pure forsterite composition but the results do not change qualitatively with other silicate-dominated compositions because the extinction is primarily due to scattering.We used the template spectrum of a K7 solar-metallicity dwarf from the library of Kesseli et al. (2016) and Sloan pass-band response functions from the filter service of the Spanish Virtual Observatory.We considered two scenarios for the size distribution; one appropriate for the upper layers of a protoplanetary disk which has evolved from an ISM-like distribution where the maximum size of grains is limited by growth vs. settling; and the second appropriate for a debris disk where dust is produced by a collisional cascade and has a powerlaw distribution with index  close to 3.5 (e.g., Williams & Wetherill 1994;Tanaka et al. 1996) and a minimum size is set by Poynting-Robertson drag, radiation blow-out, or gas drag.Filled contours corresponding to the observed range of reddening-extinction slopes for PDS 70 as well as the ISM are plotted vs. maximum or minimum particle size in Fig. 5. Also plotted are contours of total opacity (scattering plus absorption) in units of 10 4 cm 2 g −1 .Either scenario requires the presence of sub-micron grains; the presence of larger grains is allowed, but only if the size distribution is steeper than canonical ( > 3.5).
Rapid (days) variability of PDS 70 is superposed on longer-term variation.Figure 1 shows there is an envelope of maximum brightness which is most obvious in the ASAS-SN lightcurves, but is also present in ATLAS and TESS data.We fit the envelope of ASAS-SN data by moving a 100-day window over the data, recording the third brightest value with the mean time, and fitting a cubic spline with a smoothing parameter  = 0.2 to those points.The number of knots in the spline was adjusted by the algorithm so that the  2 of the spline fit was < .We then fit this spline curve to the other, much sparser ATLAS photometry, allowing only the overall amplitude to vary.In the case of TESS we calculated medians of the brightest 90-99 percentile values for each sector and fit these showing the waning signal at 3.03 days taken to be the stellar rotation period (red points).In the bottom panel the asymmetry  and quasi-periodicity  parameters (Cody et al. 2014, see text) derived from the TESS lightcurves show a trend from periodic and symmetric (dashed line) behavior to more stochastic and asymmetric (more pronounced dimming) behavior.three points.The inter-sector variation of PDS 70 recorded by TESS is 6.8%, 5.5 times the standard deviation seen among nearby stars (Sec.2.1).The ASAS-SN, ATLAS, and TESS traces are plotted as the solid curves in Fig. 6a and the relative amplitudes of the curves are plotted vs. the passband wavelength in Fig. 6b.The wavelength dependence is consistent with scattering by ISM-like dust (black curve).
The cryogenic WISE and post-cryogenic NEO-WISE 3.4 m (W1) and 4.6 m (W2) lightcurves of PDS 70 also contains variation on year-long timescales, with emission appearing to increase as the star dims in the optical (Fig. 7).Most notable is the 0.7-0.9mag drop in emission for the duration  ity flag (ph_qual) is set to "A" and the contamination and confusion flags (cc_flags) are set to zero for all observations, and the ∼10% of observations where frame quality score (frame_qual) is 0 do not correspond to the epochs in question.Moreover, the lightcurves of 2MASS J14083163-4121372 and UCAC4 244-066151, the two nearest stars (= 4'.6 and 6'.8) of comparable brightness (Δ  = 1.6 and 1.2 mag) show no such dimming during this or any interval of NEOWISE observations.There is no comparable dimming in the ASAS-SN -band lightcurve at these epochs (Fig. 7), thus ruling out obscuration of the inner disk (and thus also the central star) by some external occulting object.This event is exceedingly unlikely to be two or more eclipses (e.g., by an equal-mass binary) because the dimming is consistent over ∼2 days, an eclipse longer than this would require a very wide orbit that would be statistically unlikely to be eclipsing.Also, it is unlikely that NEO-WISE would observe two successive eclipses and no others.Thus the variation must come from disk emission.Similar drops have been found in the NEOWISE lightcurves of some Herbig Ae/Be stars (Mei et al. 2023).It is remarkable that after the ).The left panel (a) is for small dust grains with a maximum size (e.g., from grain growth in a protoplanetary disk); the right panel (b) is for large grains with a minimum size cutoff (e.g. from a collisional cascade in a debris disk).The blue curve is the ISM and the black contours are of total opacity (scattering + absorption) in units of 10 4 cm 2 g −1 .drop the emission recovers to a level close to that before the event.

Spectroscopic variability due to accretion
NRES spectra contain persistent emission in the Balmer  line of H I. The equivalent width (EW) of the line varied between 0.48 and 1.87Å, characteristic of weak-lined T Tauri stars (Barrado y Navascués & Martín 2003), with no obvious correlation with the optical variability of the star as monitored by TESS (Fig. 8).Nor does there appear to be any correlation with stellar rotational phase (adopting a period of 3.03 days) although the phase coverage is limited.This range of EW overlaps with but is shifted higher than the range found by Thanathibodee et al. (2020) from HARPS spectra obtained in 2018.
We adopted the procedure of Thanathibodee et al. (2023) to determine the magnetospheric accretion properties from the detailed profile of the H line.This procedure is appropriate for weak-lined T Tauri stars and low accretors like PDS 70 where stellar chromosphere makes a significant or dominant (and variable) contribution to the total H emission.Methods based on line luminosity alone (e.g., Alcalá et al. 2014) do not disambiguate chromospheric and accretion emission and cannot be re-liably applied PDS 70, especially since its H EW is comparable to that of non-accreting "template" stars.We fit each HARPS profile, plus the summed low-signal NRES profiles, with a grid of magnetospheric accretion flow models generated by the code of Muzerolle et al. (2001).The parameters of the model and their ranges are described in detail by Thanathibodee et al. (2020).These include accretion rate (  = 0.2 − 4.5  2023), we assumed that the cores of the lines are dominated by chromospheric emission, as expected for the low accretion rate of PDS 70, and we modeled emission with a Gaussian profile.We determined the parameters by non-linear least-squares fitting the combined Gaussian and model profile with the Python Scipy curve_fit function, which uses the Trust Region Reflective algorithm (Branch et al. 1999).
The best-fit parameters of a given observation were taken to be the mean form the 100 fits with the lowest  2 .Figure 9 shows the the H lines observed by HARPS at each epoch plus the summed NRES observations (blue lines), along with the best-fit models The inferred accretion rate and the relative rotational phases (using a 3.03-day rotation period and arbitrary zero point) are reported.The model does not reproduce some features on a few nights due to the assumed simple geometry (zero-obliquity, axisymmetric, dipolar flow), whereas real accretion flows may be much more complex, as predicted by MHD simulations and suggested by observations (e.g., Romanova et al. 2003Romanova et al. , 2021;;Zhu et al. 2024;Pouilly et al. 2021).The red-shifted absorption is particularly sensitive to the geometry, especially at low accretion rates when flows are expected to have low density and low optical depth (Thanathibodee et al. 2023).

Nature of the optical variability
Any model for the inner disk of PDS 70 should explain (1) the rapid optical variability due to submicron dust that evolves between periodic and aperiodic/stochastic behavior; (2) the long-term variability in both the baseline optical brightness and 3-5 m emission, also due to dust (although not necessarily the same dust), including the disappearance of the latter for up to one year; and (3) a persistently low but not significantly variable rate of accretion based on H line profiles.It should also explain (4) the presence of primordial H and He, as evidenced by UV H 2 line emission (Skinner & Audard 2022), a reversed H profile, and a reversed He I profile (Thanathibodee et al. 2019); and (5) a low gas-to-dust ratio based on sub-mm CO and continuum emission (Long et al. 2018), and the presence of CO 2 and H 2 O (Perotti et al. 2023).
PDS 70 is optically variable on timescale of hours to days and its variability has evolved from between purely periodic to aperiodic "dipper"-like behavior over the timescale of years (Figs. 2 and 3).While the periodic behavior during TESS Sector 11 suggests rotational variability by spots, its large and wavelength-dependent amplitude (∼0.2 mags peakto-peak in the TESS passband and larger in ASAS-SN  ′ data) and "scalloped" lightcurve morphology (Fig. 10) is similar to that seen around other young low-mass stars.This morphology been explained by scattering by sub-micron dust trapped by the stellar magnetic field at the co-rotation radius, where the orbital period equals the stellar rotation period (Stauffer et al. 2017(Stauffer et al. , 2018;;Zhan et al. 2019;Günther et al. 2022).In contrast, the later aperiodic variability of PDS 70 suggests occultation by dust located exterior to the co-rotation radius (Donati to the co-rotation radius.Our multi-band LCOGT photometry unambiguously indicates that scattering by sub-micron dust is responsible for this dimming (Fig. 4), at least during the most recent aperiodic phase.Superposed on this pattern of rapid variability is an envelope of smoother variation in brightness on the timescale of ∼1 year (Fig. 6a).
The trend of decreasing amplitude with increase wavelength (Fig. 6b) suggests that this also is due to sub-micron circumstellar dust.Such long-term variability is not highly unusual around T Tauri stars (e.g., Grankin et al. 2007;Rigon et al. 2017).deg; Keppler et al. 2019).If the inner disk is aligned with stellar rotation, then disk dust will intercept the line of sight to the star only if it is diverted well above the midplane, e.g., by the stellar magnetic field.This can occur where the disk gas is (partially) ionized, magnetic field pressure dominates over viscous stresses or ram pressure produced by accretion, and if dust is dynamically coupled to the gas.This diversion truncates the disk, and if this truncation occurs inside the co-rotation radius then disk material loses angular momentum to the star and magnetospheric accretion will occur, i.e. through "funnels" onto the star (Bouvier et al. 2007).If truncation occurs outside the co-rotation then some of the disk can be accelerated away from the star and above the mid-plane in a magnetohydrodynamic wind, with a remainder accreted onto the star in "propeller accretion".We discuss the potential mechanisms and timescale of this evolution in Secs.4.4 and 5.2.

Nature of the infrared variability
To describe the infrared emission and its variability in terms of this scenario we constructed a spectral energy distribution (SED) of the inner disk from photometry cataloged by the Virtual Observatory SED Analyzer, fit a solar-metallicity BT-SETTL stellar photosphere model (Allard et al. 2012) with CFIST solar abundances (Caffau et al. 2011) at wavelengths  ≤ 1.6 m (where the disk contribution is negligible), and subtracted the best-fit model ( eff =4000K, log  = 4.5,  2 = 0.22) from the photometry at longer wavelengths (Fig. 11).We then fit a disk model consisting of a "warm", optically-thick disk with a power-law temperature distribution with semi-major axis, plus an isothermal structure representing a "hot" interior disk wall or ring.The second component is motivated in part by the shape of the SED, and by the need for occulting dust close to the star to produce the dipper-like variability; at the 3.03-day co-rotation radius the blackbody equilibrium temperature is ≈1500K.
We fixed the inner disk inclination to that of the outer disk (51.7 deg; Keppler et al. 2019), motivated by the agreement with the stellar inclination (Thanathibodee et al. 2020), leaving five free parameters: hot component area  hot and temperature  hot , outer disk edge  outer , temperature  warm at the inner disk edge, and power-law index .For this fit we omitted the NEOWISE data (see below), photometry between 7.7 and 13.1 m which is affected by silicate emission, as well as IRAS photometry at 100 m, which is dominated by emission from the outer disk that starts at ≈50 au where the blackbody temperature would be 30K (blue curve in Fig. 11).We also omitted DENIS -band photometry which is somewhat higher than 2MASS (see Sec. 5.4).We included mean values in the ranges 5-7.7m and 13.1-15.5mfrom the JWST MIRI spectrum in lieu of the actual spectrum.A satisfactory fit ( 2 = 7.5, 5 d.o.f.) was found for  hot = 1100K,  hot = 2.8 × 10 −3 au 2 ,  warm = 600K,  outer = 3.3 au, and  = 0.22, and is plotted as the black curve in Fig. 11.
Variability in the NEOWISE 3.4 and 4.6 m photometry on day-to year-timescales (Fig. 7) implies that the hot dust component must evolve.We modeled this variability by subtracting the warm disk component, assuming it is not variable or if it changes at all, does not contribute significantly at these wavelengths (Fig. 11), and that emission from the hot component can be described as a single but variable temperature.Figure 12 shows the variation in the W1 and W2 fluxes after the photosphere and small and constant warm disk contribution is removed, as well as curves of blackbody emission for a fixed temperature.The inset shows the distribution of best-fit temperatures, indicating the relatively narrow dispersion between 1000 and 1500K.The residual emission (if any) during the low emission state in 2014-2015 is consistent with emission at only ∼500K (points in lower-left of Fig. 12), and thus is likely a result of variation in or imperfect subtraction of the warm disk component.Some T Tauri stars exhibit variability at longer  > 10 m that is anti-correlated with emission at shorter wavelengths; this "see-saw" variability is thought to arise from shadowing of the disk by a dynamic inner "wall", which intercepts and reprocesses stellar radiation that is otherwise inci- In WISE photometry from the cryogenic mission, emission in the W4 (25m) channel is significantly anti-correlated with that in W1 and W2 ( = 0.001, Spearman rank test) but the variation is small and observations span just two one-day intervals.We revisited variability in emission at  ≳ 10 m with 12-and 25-m photometry from the IRAS Faint Source Catalog based on its all-sky survey (Neugebauer et al. 1984;Moshir & et al. 1990), 9-and 18-m photometry from the AKARI mission (Ishihara et al. 2010), 12-and 25-m photometry from the cryogenic WISE mission (Wright et al. 2010;Cutri et al. 2013), and synthetic photometry in the AKARI and WISE passbands using the Spizter-IRS and JWST-MIRI spectra (Fig. 13).IRAS data were obtained 23 years before the next observations, and AKARI photometry is based on 3-4 observations over the span of 477 days.Spizter and JWST spectra extend to  = 22.6m and the WISE 25-m channel is incompletely covered, so we extrapolated using a scaled version of the bestfit curve in Fig. 11.(The estimated fluxes are not sensitive to the exact form of the extrapolation.) While the flux in the 9-m AKARI passband has been stable since 2006-2007, emission at longer wavelengths show significant variation.The apparent elevated flux at 12 m observed by IRAS is likely due to a broader bandpass (dashed yellow line in lower inset of Fig. 13) that includes the 10 m silicate emission feature.The estimated 25-m flux of JWST is significantly lower than that from Spizter, echoing the results of Perotti et al. (2023), and the Spizter emission is consistent with both earlier IRAS and later WISE photometry.Moreover this decline is also manifest in estimated 18-m fluxes, probably because the ARAKI bandpass overlaps with the WISE 25-m one (bottom inset of Fig. 13).
In addition, rapid variation (∼0.15 mag over ∼1 day) is present in multi-epoch WISE W3 and W4 photometry (upper insets of Fig. 13).Emission from these wavelengths is coming from cool (≲ 300K) dust at distances where the orbital period is ∼ 1 yr and thus the variation is faster than any dynamical timescale.Shadowing by a variable inner disk wall could explain the short timescale, however, on long timescales, the overall decline at longer wavelengths is not mirrored by a contemporaneous increase in flux at 3.4 or 4.6 m (as in the case of see-saw variability).There is an overall increase in emission at these wavelengths over the duration of the NEOWISE mission but the most recent released values were obtained only 16 days before the JWST observations, and are similar to those obtained during the WISE cryogenic mission, when simultaneously measured 25-m fluxes were similar to the Spizter values.One reason for the lack of see-saw variability may be the moderate disk inclination (∼50 deg); inclinations > 70 may be required for a single fulcrum wavelength to appear in the time-dependent SED (Bryan et al. 2019).

Variability in accretion
The accretion rate inferred from model-fitting of the Balmer H line was consistently below a few times 10 −10 M ⊙ yr −1 over a baseline of nearly three years (Fig. 14), at the lower end of the observed distribution among T Tauri stars (Hartmann et al. 1998;Manara et al. 2022).However, due to the large uncertainties in the values, we are unable to detect significant variation ( 2 = 6.1 for  = 22).The large uncertainties are due to the degeneracy with the gas temperature, which is unconstrained and subject to vary with changes in the magnetospheric accretion radius (see Sec.We describe the dynamic behavior of PDS 70 in terms of the relative location of four locations in the disk: (1) the co-rotation radius   inside or outside of which disk loses or gains angular momentum through magnetic coupling to the star; (2) the truncation radius   where the disk is vertically diverted by the large-scale stellar magnetic field; (3) the disk ionization radius   interior to which the disk is affected by the magnetic field; and (4) the dust sublimation radius   .Figure 15 illustrates this behavior (described in more detail below).Liffman et al. (2020) proposed an analogous scenario to explain the variable infrared emission of the pre-transition disk LRLL 31, i.e., from a dust "fan" ejected from the inner disk by a jet/wind.In their model, variation in accretion rate drives variation of the disk truncation radius and the speed of the wind, which in turn controls the height of the dust fan and thus the level of infrared emission.
If the truncation radius is exterior to the dust sublimation radius, dust that is dynamically bound to the diverted gas could produce both the optical and infrared variability, by scattering along the line of sight, and emission, respectively.Whether the flow is magnetically "funneled" onto the star (Fig. 15a) or diverted into a "propeller" outflow and wind (Fig. 15b) then depends on the whether the truncation ra-dius is interior or exterior to the co-rotation radius given by: where  * and  * are the the stellar radius and mass in solar units (Ustyugova et al. 2006;Bessolaz et al. 2008).Takasao et al. (2022) carried out three-dimensional magnetohydrodynamic (MHD) simulations of this phenomenon and found that the magnetic truncation radius   closely followed the scaling relationship proposed by Ghosh & Lamb (1979): where  * is the large scale dipole field evaluated at the stellar surface (in kG), and the accretion rate  −10 is in units of 10 −10  ⊙ yr −1 .We adopted a value of 0.44 kG for the largescale dipole field evaluated at the stellar surface of 22% of the total field strength as found by Lavail et al. (2019) to be typical (see discussion in Gehrig et al. 2022).The total field strength was in turn based on a relation with the Rossby number , the period rotation (3.03 d, Thanathibodee et al. 2020) normalized by the convective turnover time  rot /  , i.e. "slow" rotator relation in Table 2 of Reiners et al. (2022).The convective turnover time   was estimated as 21.7 d by scaling the solar value with luminosity  −1/2 * (Jeffries et al. 2011), yielding  = 0.16.For accretion rate we adopted the range of 0.6-2.2×10 −10  ⊙ yr −1 found by Thanathibodee et al. (2020).
A third boundary is the radius at which mid-plane temperatures reach ≈1000K and alkali metals become partially ionized.This could also be a transition from region of low turbulent (eddy) viscosity ("dead zone") to a high diffusion region where the magnetorotational instability (MRI) drives turbulence (Desch & Turner 2015).At this point, disk models predict a pressure maximum, and the potential for trapping of solids with sizes such that the Stokes number (ratio of stopping time to orbital time) St will be O (0.1) (Dzyurkevich et al. 2010).Depending on grain growth and collisional fragmentation, this could lead to a concentration of dust at the pressure bump and depletion elsewhere in the disk.The maximum Stokes number (collisional case) is: where   and  are the internal density and size of the dust, and Σ  is the mass surface density of gas.Using the relationship for the mass accretion rate in an "alpha turbulent disk"  = 2  Σ  , where  is the turbulent viscosity parameter,   the sound speed, and  the vertical scale height of the gas, and the relationship between , temperature , and Keplerian orbital period   , Eqn. 3 can be re-expressed as: Taking the mid-plane temperature to be 1000K, this results in the scaling: where  is in m and  is in au.For  ∼ 10 −2 and  ∼ 0.1, only cm-sized particles will achieve St ∼ 0.1 and be trapped.Thus the dust responsible for the variability and infrared excess is not itself trapped at any dead zone boundary, but it could be produced by fragmentation of trapped particles.Ueda et al. (2019) explored the conditions for dust trapping, finding a limiting turbulent parameter  in the dead zone that is a function of the dust fragmentation velocity.
We calculated the semi-major axis of dust in radiative equilibrium with the star with temperatures that are below the dust condensation temperature but above 1000K.The lower limit is the minimum temperature consistent with the observations (see Fig. 13) and is also the temperature at which disk gas starts to ionize (i.e., constituent potassium and sodium) and becomes influenced by the stellar magnetic field.Condensation temperature varies with disk gas pressure and composition, which also changes depending on what has already condensed out is possibly removed from equilibrium with the gas by gravitational settling, and growth into planetesimals; we adopt values of 1290-1500K depending on the mineral (Lodders 2003;Wood et al. 2021).
Equilibrium temperatures depend on grain size and composition through the absorption (= emission) cross-sections integrated over the stellar SED and 1200K infrared emission (Eqn.6) using the wavelength-dependent optical coefficients of Budaj et al. (2015).From radiative equilibrium, the dust sublimation radius is where  * is the stellar effective temperature, and  abs * is the absorption cross-section averaged over the entire stellar spectrum.We considered Fe-free forsterite (MgSiO 2 ) and enstatite (MgSiO 3 ) as well as olivine and pyroxenes, magnesium silicates with Fe substituting for 20-50% of Mg.The optical absorption cross-sections of the latter are significantly higher due to the presence of Fe (Budaj et al. 2015) and their equilibrium temperatures will be higher at the same stellar distance.
If the accretion rate is low or the magnetic field is strong, then magnetic pressure overcomes disk ram pressure, the truncation radius moves outward to the distance where the disk temperature is 1000K, since below this temperature the disk ceases to be ionized and respond to the stellar magnetic field.The truncation radius remains at approximately this distance and the flow and resulting IR emission should be relatively stable.If accretion rates are sufficiently high or the magnetic field is weak, then the magnetic truncation radius can migrate inside the condensation temperature of the dust, and gas diverted above the mid-plane in magnetospheric flow would be dust free (Fig. 15c).If magneticallydiverted, dusty accretion flows are responsible for the dipper-like variability of PDS 70, then, during this latter, dipping should cease.Based on the ASAS-SN data (Figs. 1 and 3) the interval at MJD ∼ 57000 would appear to be more quiescent, but the lack of data at earlier times makes this conclusion tentative.
The likelihood that dust will occult the star and the emitting area of its infrared emission, will depend on the vertical distance   which dust reaches above the mid-plane.This is set by the balance of gas drag (i.e., Epstein drag, Li et al. 2022) and vertical stellar gravity: where   is the local gas density and  is the wind half-opening angle (up to 30 deg for a magnetized wind, Blandford & Payne 1982).Assuming axisymmetric flow  away from the disk plane from the truncation radius and at the sound speed in a layer that is one gas scale height thick; which leads to the relation for the geometric area subtended by the dusty flow: where   is in g cm −3 .The optical depth of the flow will be where  is the dust-to-gas ratio by mass and  is the optical constant averaged over the emission spectrum (e.g. a blackbody at 1200K).This leads to where μ is the mean atomic weight of the gas (1.85 for a solar composition).We calculated the effective emitting area as (1 −  − ).
Figure 16 shows regions of semi-major axis  vs. grain size  where the temperature is between 1000-1400K and the effective emitting area is in the range inferred from black-body fitting to the WISE 3.4-and 4.6-m photometry (1 − 4 × 10 −3 au 2 ; Fig. 7); each region is specific to an assumed dust composition (color-coded).The positions of the co-rotation radius and the disk truncation radius for two values of the large-scale dipole magnetic field evaluated at the surface are indicated as vertical lines.The total optical depth due to scattering and absorption in the Sloan  band-pass from the same dust structure (integrating over the stellar SED and response function) is shown as the black contours in Fig. 16.Finally, we assumed that the inner disk is co-planar with the outer disk (51.9 ± 0.1 deg; Keppler et al. 2019) and with the star's rotation axis ( = 50 ± 8 deg; Thanathibodee et al. 2020) so that occultation along our line of sight does not occur unless the dust reaches a height  =  cot  (red line in Fig. 16).
Large (>1 m) dust with olivine and pyroxene compositions will have temperatures in the necessary temperature range at the predicted magnetic truncation radius, whereas small grains will remain too cool or will vaporize (Fig. 16).Forsterite and enstatite of any size will be too cool at the relevant distances (Fig. 16).More exotic compositions such as graphite and metallic iron (not shown) can also satisfy the temperature/flux constraints, but these are expected to readily condense only in a strongly reducing, H-rich disk.The presence of H 2 O and CO 2 and absence of detectable organic molecules (Perotti et al. 2023) indicates oxidizing (low C/O ratio) conditions in the inner disk, more favorable to the condensation of Fe-rich magnesium silicates.) In scenario (a) an elevated disk accretion rate or weak magnetic field means that   lies at or interior to   and non-axisymmetric magnetospheric accretion occurs via onto the star via streams or "funnels".Hot dust in the raised inner edge of the disk is responsible for excess emission at 3.4 and 4.6 m but the star is only occulted periodically by accretion streams.In scenario (b) a low accretion rate or stronger magnetic field moves   beyond   but inside   , and the disk is diverted into a magnetized dusty wind which produces a large 3.4/4.6m excess, partially shadows the outer part of the inner disk, and continuously occults the star.In scenario (c) an interval of magnetic reversal with a very weak dipole component moves   inside   so that magnetospheric accretion is dust-free and there is little disk emission at 3.4 and 4.6 m.Optical and infrared spectra of PDS 70 contain evidence for a disk wind, i.e. emission in the forbidden line of O I at 6300Å (Campbell-White et al. 2023) and an inverse P Cygni-like profile with blueshifted absorption in the metastable triplet of He I at 1.083 m (Thanathibodee et al. 2019).The former is exceptionally high compared to stars with disks with similar accretion luminosity, is highly broadened (FWHM ≈90 km s −1 ) relative to nearly all disks, and slightly blue-shifted (8 km s −1 ).This suggests emission from a wind arising 0.1-0.2au from the star (Campbell-White et al. 2023), a distance that overlaps with our predictions for the disk truncation and dust emission radii (Fig. 16).

A Disk Wind
While red-shifted absorption in either H or triplet He I would correspond to gas inside the co-rotation radius accreting onto the star, the combination of emission and blue-shifted absorption and emission in the He I triplet line is typically produced by a stellar wind (Edwards et al. 2006).Variable, blue-shifted (-35 to -110 km s −1 ) and redshifted (∼140 km sec −1 ) absorption components are seen in He I spectra of PDS 70 obtained at three epochs prior to MJD=58900 (Thanathibodee et al. 2020(Thanathibodee et al. , 2022)), indicative of magnetospheric accretion.After MJD=58900, when the photometric behavior has transitioned from a periodic to aperiodic dipper-like behavior, He I spectra at two separate epochs at the end of 2020/early 2021 lack any red-shifted absorption and instead have red-shifted emission and strong blue-shifted absorption, suggestive of a disk wind (Campbell-White et al. 2023).This is also coincident with a decrease in the baseline stellar brightness and rise in infrared emission (Fig. 6).A spectrum obtained with the iSHELL infrared spectrograph on IRTF in mid-May 2023 (R. Lee, pers. comm.)shows the return of magnetospheric accretion signatures, contemporaneous with the re-emergence of a weak periodic signal (Figs. 1 and 3), increase in the baseline optical brightness, and decline in infrared emission (Fig. 6).This is consistent with a dusty wind as the source of both the variable emission and optical emission, although not necessarily the same dust at the same distance along the wind.We caution that the available spectroscopy has limited rotational phase coverage and non-axisymmetric flow could be also be responsible for the observed changes.
We propose that the fluorescent UV H 2 emission detected by Skinner & Audard (2022) also emerges from this wind.For one thing, a wind would screen the disk itself from the Lyman- photons that pump such emission, precluding it from being the source.Such emission is common among classical T Tauri stars, generally arises from the inner (≲1 au) disk region (Arulanantham et al. 2021;France et al. 2023), and a correlation with the narrow-line component of forbidden atomic emission, i.e. [O I] (Gangi et al. 2023) suggests a connection with winds.Fluorescent H 2 emission is rare among weak-lined and low-accreting T Tauri stars; another notable exception is EP Cha (RECX-11, France et al. 2012), which is also a "dipper" star.
In addition to the [O I] 6300Å line, emission in mid-IR forbidden lines of Ne II (12.81 m) and Ne III (12.55 m), whose high ionization potentials mean they can only arise from very hot, escaping gas, are excellent tracers of photoevaporative winds from the disks of T Tauri stars.Pascucci et al. (2020) has proposed that anemic Ne emission relative to O emission can be explained in terms of an inner MHD wind shielding the disk further out from the hard stellar X-rays that heat the gas (the O I primarily arising from the MHD wind).Variability in Ne emission from SZ Cha has been interpreted in the context of a screening wind (Espaillat et al. 2023).Both Ne lines are detected in MIRI spectrum of PDS 70, but are weak, and the Ne III line is blended with H 2 O lines.The flux in the Ne II line (3.5 × 10 −16 erg s −1 cm −2 , and the red point in Fig. 17) is well below that expected for its [O I] emission based on models of photoevaporative winds (dashed lines in Fig. 17; Ercolano & Owen 2010), presumably due to the presence of the wind at the time of the JWST observation6

Timescales and drivers of accretion variability
If the primary source of optical dimming and 3-5 m emission is dust that is kinematically coupled to magnetized gas in an accretion flow and/or wind from the inner disk, then while variation (i.e., dimming) on the timescale of days can be explained by orbital motion, variation on time scales of months to years, i.e., much longer than the orbital time at the inner disk edge, must be caused by changes in either the geometry of that flow or dust loading of the gas.In principle, variation in accretion could drive these changes (Eqn.2).We are unable to detect significant variability in accretion rate based on modeling of the H profile (Fig. 14), but any (detected) variation could also simply reflect changes in the relative amounts of flow through a wind vs. accretion onto the star, rather than the rate through the disk.
At least three timescales are relevant to variable accretion of disk gas (Fischer et al. 2022): the dy-namical time scale, which can be as short as ∼1 day at the inner disk edge (too short to be relevant), the viscous diffusion time, which is at least 10 4 times the orbital time (too long), and the thermal time, which is ∼ 10 2 times longer and thus months to years near the inner disk edge (perhaps just right).In addition, there is a magnetic (Ohmic) diffusion time scale   ∼ ℎ 2 / =  0 ℎ 2 (e.g., Liffman et al. 2020) where  0 is the permittivity of free space,  the electrical conductivity, and ℎ the relevant scale length, e.g.disk scale height.
In a low-accretion, passively heated disk, disk ionization will depend on irradiation by the star (optical and X-rays) (Jankovic et al. 2021).The viscous time scale   =  2 / for a turbulent (e.g., MRI-driven) -disk disk hotter than 1000K is at least a century: This might create a positive, destabilizing feedback: disk shadowing could lead to suppression of the MRI close to the star, a lower accretion rate, expanded truncation radius, elevated disk rim, and more disk shadowing.However, again, this cannot explain the year-long variability seen in the optical and infrared.7 Variation in the strength of the large-scale dipole field (i.e., stellar magnetic cycle) could also move the disk truncation radius with respect to the corotation radius.Armitage (1995) showed that magnetic cycles could produce variability in accretion and emission among T Tauri stars, especially in the ultraviolet, and could even be responsible for accretion-driven outbursts (Armitage 2016).Magnetic cycles are widespread among solar-type stars; little is known about the magnetic behavior of cooler, fully-convective pre-main sequence objects, but Finociety et al. (2023) report variation of a factor of three in the dipole strength of the T Tauri star V1298 Tau over three years.Full 3-d simulations of fully-convective main sequence M dwarfs (as analogs) suggest that the overall behavior is similar to that of partially-convective stars (e.g., Käpylä 2021;Bice & Toomre 2023a).Ortiz-Rodríguez et al. (2022) found that cycles appear in fully-convective M dwarfs if the magnetic Prandtl number  (ratio of turbulent to magnetic diffusivities   /) is < 2. The timescale for the reversal is related to that of large-scale diffusion of magnetic fields through the dynamo (convective) region (e.g., Augustson et al. 2015), and will be of order years, consistent with the few available cases where cycling has been observed for fully convective stars (e.g., Ibañez Bustos et al. 2019Bustos et al. , 2020;;Klein et al. 2021).Generally, more rapidly rotating stars have shorter magnetic cycles (Saar & Brandenburg 1999;Suárez Mascareño et al. 2016).Bice & Toomre (2023b) found that magnetic cycle time  cycle normalized by  in cool dwarf models spanning a large range of parameters scaled as Pm 0.35 Re 0.93 Ro −1.78 , and is predicted to be O (300) (days) for Ro ≈0.16 (see also Strugarek et al. 2018).Moreover, Lin et al. (2023) find variation in the photometric behavior among 16 T Tauri stars on a timescale of 1.5-4 years.Thus, cycle times of ∼3 yr are plausible, and would be consistent with the time-scale of long-term variation in optical and infrared brightness seen in PDS 70 (Fig. 6).However, if the time-scale for removal of angular momentum from the local disk is much longer than the magnetic cycling time the disk will only respond to the long-term average dipole field strength.
The disappearance of emission from the disk at 3.4 and 4.6 m for up to one year at the end of 2014 (around MJD=57000, Fig. 6) requires a temporary halt in accretion towards the inner disk edge, a dramatic drop in dust load (e.g., by trapping further out), or a very different geometry of inner disk dust, i.e. one that intercepts much less stellar irradiation close to the star.The viscous time scale of ≳ 10 2 yr, even at the inner edge, rules out the first scenario.The second is probably precluded by the very small Stokes number of dust and tight coupling of dust to gas in the inner disk (Eqn.5).If the disk was truncated (by a stronger magnetic field) at a distance where the temperatures were significantly cooler than the 1000K this would null the 3.4/4.6mexcess, but this would require a significant source of ionizing radiation (Desch & Turner 2015).
Alternatively, dramatic weakening of the dipole field during a particularly prolonged polarity reversal (DeRosa et al. 2012) would allow the disk inner edge to migrate interior to the dust sublimation radius.For example, reduction of the dipole strength by a factor of three (and magnetic energy by a factor of ∼10) as seen in the Sun (DeRosa et al. 2012), moves the truncation radius well inside the sublimation radius of Fe-bearing dust and the co-rotation radius of PDS 70 (Fig. 16).Magnetospheric accretion could still occur, but the gas would be dust free and will have low continuum emission.8The relatively "flat" disk geometry exterior to the sublimation radius would intercept and reprocess much less stellar radiation.It is possible that shorter episodes occur but have been missed due to the 6-month cadence of NEOWISE monitoring .

Composition of the inner disk
As opposed to the outer disk, the inner disk cannot be "primordial": combining an inner disk gas mass of 7.6 × 10 −4 M JUP (Portilla-Revelo et al. 2023) with an accretion rate of 0.6−2.2×10−7 M JUP yr −1 (Thanathibodee et al. 2019) returns a residence time of 3-12 kyr, far shorter than the star's estimated age of 5 ± 1 Myr (Keppler et al. 2018) 9.This would be the case even if the gas mass is underestimated due to depletion of CO (which is used to estimate total gas mass) by freeze-out in the outer disk.
The inner disk must be resupplied across the gap from the outer disk, and/or regeneration of gas/dust from collisions, disruption, or evaporation of planetesimals.Detection of H (red-shifted H absorption and H 2 emission) and He (reversed triplet He I line) unambiguously indicate the presence of primordial gas (from the outer disk), possibly via a "bridge" structure in the gap identified in ALMA imaging of both gas and dust (Keppler et al. 2019).Partial trapping of condensible solids (including, possibly, CO ice) is expected in the pressure bump at the inner edge of the outer disk (Pinilla & Youdin 2017), and can explain the observed concentration of dust there (Portilla-Revelo et al. 2023).Thus disk material passing within the gap should be dust-poor, as is observed (dust:gas ratio of ≈630, Portilla-Revelo et al. 2023).
The inner disk itself, however, appears to be gaspoor or dust-rich.Portilla-Revelo et al. ( 2023) derived an inner disk gas-to-dust ratio of ∼10 (dustrich relative to ISM) based on relative line ( 12 CO) vs. continuum emission at mm wavelengths.The gas-to-dust ratio along the line of sight to the star (i.e., in the wind) can also be estimated by comparing absorption of X-rays (Wilms et al. 2000) where   is the hydrogen column density inferred from X-ray absorption (assuming a solarmetallicity gas10),   is the proton mass,   is the specific mean opacity of the dust in a optical passband, and Δ is the corresponding dimming in that passband.Joyce et al. (2023) obtained 0.2-12 keV X-ray spectra of PSD 70 with the XMM-Newton telescope at 6 epochs spaced a day apart.They derived a mean   of 2.2 ± 0.2 × 10 20 cm −2 but there is evidence for variability ( 2 = 28.7 for 5 degrees of freedom).We set Δ = 0.25 mags based on ASAS-SN photometry during the XMM-Newton observations, and  = 2×10 4 cm 2 g −1 based on Fig. 5, and derive a gas-to-dust ratio of ≈60.This value applies only along the line of sight to the star and should be considered an upper bound to the disk value because, if the inclination of the inner disk is ≈50 deg (Thanathibodee et al. 2020), the line of sight will probe far above the disk mid-plane where depletion of dust due to gravitational settling will be significant.
Freeze-out and trapping of CO by the predicted bump at the inner edge of the outer disk would deplete CO gas sourced to the inner disk, and thus lead to an erroneously low CO-based estimate of gas mass based on a canonical abundance.However, condensible solids (i.e., dust-forming elements in the inner disk) should be depleted by at least as much, and thus the gas-to-dust ratio should only increase.Moreover, we would expect the growth of planetesimals and planets in the inner disk to sequester solids, increasing the gas-to-dust ratio.As suggested by Benisty et al. (2021), evidence for a dust-rich disk thus suggests internal production of dust analogous to that in a debris disk, i.e. by planetesimal collisions, disruption, or evaporation.
Emission from PDS 70 in infrared H 2 O lines falls along an inverse trend with the slope of the continuum emission in the 13-30 m range from T Tauri stars, explainable by the formation of a gap or central cavity (Perotti et al. 2023).This emission is dominated by a compact (∼ 7 × 10 −3 au 2 ) source at ∼600K (Perotti et al. 2023).The absence of H 2 O emission at a temperature corresponding to the ∼1200K dust component suggests that H 2 O is efficiently sequestered somewhere in the inner disk and does not reach the point where the MHD wind is launched.The cooler H 2 O emission could be explained by a wind that shields the disk from the stellar XUV radiation that normally heats the disk atmosphere lying above the mid-IR continuum  = 1 level (Woitke et al. 2018).11There is also CO 2 emission is from cool gas.Photometry by ASAS-SN during JWST-MIRI observations indicates the system was in the "dipper" mode (Figs. 1 and 3) with relatively low emission at 25m (Fig. 13) suggestive of shadowing, which could partially explain the cool emission temperature of CO 2 .Importantly, any variability at ≥ 25 m (Fig. 13) could affect the continuum slope and  13−31 .
Although the term "hybrid disk" seems appropriate for the inner disk of PDS 70, this term has already been adopted for disks that are depleted in dust relative to the T Tauri phase for a given mass of gas (Péricaud et al. 2017;Miley et al. 2018).Thus we call a dust-rich disk that is comprised of primordial gas that is depleted of dust but enriched by secondary debris and gas from planetesimals a "chimera disk".

Future directions
Obviously, additional JWST observations of PDS 70 or more advanced analysis of existing observations (Perotti et al. 2023) could play an important role in understanding the inner disk of PDS 70.JWST NIRSpec observations of PDS 70 at 0.6-5 m have already been performed and would provide additional insight into its composition.
Particularly important in more fully describing the behavior of the inner disk of PDS 70 and testing the scenarios presented here would be longterm, parallel monitoring of indicators of the wind and accretion ([O I],triplet He I), dust occultation (optical photometry), and emission in the infrared.For the latter, while NEOWISE monitoring at 3.4 and 4.6m is sensitive to changes in the inner disk, its cadence is limited to a day-long visit every six months.The AKARI mission observed the sky at multiple epochs (Tachibana et al. 2023) but these data are not yet publicly available.
On the other hand, excess emission from the inner disk is readily detected in the 2.2 m -band (Fig. 11) from the ground.Fig. 18 plots the distribution of -bands magnitudes predicted from the black-body fits performed on the NEOWISE photometry and compares these to 2MASS, two epochs of DENIS photometry, and a lower limit on the value from the resolved component from VLTI-GRAVITY (Wang et al. 2021).The discrepancy between the 2MASS and DENIS photometry is not due to a difference in the response function since these are very similar.We propose that the offset of the distribution from the photosphere value inferred from stellar model fitting (vertical dashed line in Fig. 18) is the minor contribution of the disk beyond its inner edge to the -band flux, i.e. a hot dusty upper atmosphere.The distribution shows that time-series monitoring of PDS 70 at 2.2 m with 2MASS-like precision could successfully track inner disk emission.
The large uncertainty in the accretion rate of PDS 70 inferred from model fits to the H line profile is due to the degeneracy with gas temperature (Muzerolle et al. 2001).The accretion rate of PDS 70 can be better constrained by modeling the profiles of multiple H I lines (rather than only the Balmer  line) that form at different temperatures/regions in the accretion flows.The unknown, variable chromospheric emission in H lines also contributes to the uncertainty at the low accretion rates of PDS 70.High-resolution, simultaneous spectroscopy of the Balmer and Paschen lines are required to better distinguish the chromospheric contribution of each line and break the accretion rate-gas temperature degeneracy.
High-resolution interferometry in the infrared could resolve the actual inner disk structure of PDS 70 and determine if the emission at shorter wavelengths is coming from a wind or fan.Wang & Chen (2019) resolved half of the photometricallyestimated excess emission from the disk in -band at 0.2-0.5 au scales with the GRAVITY beam combiner on the Very Large Telescope Interferometer (VLTI).While they attributed the difference to unresolved emission at ≪0.2 au, another explanation is variability.On brighter stars, GRAVITY interferometry can reconstruct simple parameterized images of inner disks, as was done for the case of DoAr 44, which is about one mag brighter than PDS 70 (Bouvier et al. 2020).GRAVITY+, which will be an upgrade with laser guide-star adaptive optics, could perform similar observations of PDS 70 (Gravity+ Collaboration et al. 2022).Future interferometry in -band (3.5 m, e.g., Laugier et al. 2023) would exploit the higher disk emission at that wavelength.
Measurement of the magnetic field of PDS 70, especially its large-scale dipole component, would allow more robust comparison of disk truncation measurements to theory (Eqn.2, Gregory et al. 2016).While measurement of Zeeman broadening in unpolarized light provide information on total field intensity, spectroscopic monitoring of Stokes  (circular) polarization over a full rotation cycle (Zeeman Doppler Imaging or ZDI) can be used to infer the large-scale topology of the field, direct measurement of the large-scale dipole requires measurements of all four Stokes parameters (Gehrig et al. 2022).Such studies require high signal-to-noise, are preferably performed in the near-infrared where the Zeeman effect is stronger, and are observationally expensive.Line broadening by rapid rotation and line veiling also make these observations challenging.Recent detailed studies, e.g., of V410 Tau (Carroll et al. 2012;Yu et al. 2019;Finociety et al. 2021) and V1298 Tau (Finociety et al. 2023), demonstrate the potential of the suite of high-resolution infrared spectrographs which, when deployed on 8-m or larger telescopes, could perform similar observations of PDS 70.
Alternatively, conditions for trapping of occulting dust near the co-rotation radius, if confirmed, could constrain the strength of the magnetic dipole field, provided the dust particle size and gas density are  7), binned in 0.02 mag intervals (the approximate limiting precision of ground-based infrared photometry).Also shown is the 2MASS measurement in 1999 and observations at two epochs from the DENIS survey (3rd release) separated by 100 days in 1998.The limit from the 2018 VLTI-GRAVITY observations (Wang et al. 2021) is the 6% of the total flux (which must equal or exceed that of the photosphere) that was resolved (>0.2 au).The photosphere value, based on the best-fit of stellar models to data at shorter wavelengths is indicated as the dashed line, and the corresponding bin contains 38 epochs.
known (Zhan et al. 2019, see also Sanderson et al. 2023).Dust size can be determined by reddeningextinction trends, e.g., Fig. 5 and gas density can be estimated by X-ray observations (e.g., Joyce et al. 2023) or inferred from the accretion rate.
6. SUMMARY Time-series photometry and spectroscopy reveal the dynamic nature of the inner disk of PDS 70, and multi-wavelength observations point to a chimeric composition brought about by the segregation of the inner and outer disk by the system's two giant planets.We draw the following conclusions or inferences based on these data: • PDS 70 is optically variable on the timescale of day or days due to intervening sub-micron dust located near the inner edge of this disk.
• The optical lightcurve of PDS 70 evolves between a periodic and approximately symmetric behavior, and stochastic, asymmetric and "dipper"-like behavior.This could be due to the changing position of the inner edge of the magnetically truncated relative with respect to the co-rotation radius which alternatively drives magnetospheric accretion vs. "propellor"-like accretion with a magnetized wind.
• The infrared SED of the inner disk of PDS 70 can be modeled as a warm ( ≲ 600K), radially extended disk and a quasi-isothermal component at 1000-1500K, with the latter entirely responsible for emission at 3.4 and 4.6 m.The temperature range of the hot dust spans the ionization temperature of disk gas and typical dust sublimation temperatures.
• Variability of PDS 70 at 3.4 and 4.6 m is produced by changes in the magnetic truncation radius of the disk relative to the corotation radius and the location at which disk material is diverted vertically by the field and the extent which it intercepts and reprocesses stellar irradiation.This variability is pronounced in the case of PDS 70 due to the low disk accretion rate and the proximity of the disk truncation, co-rotation, and dust sublimation radii.
• At high field strength disk gas is diverted outside the co-rotation radius into a magnetized, non-axisymmetric wind which elevates dust into a "fan" that partially occults the star along our line of sight and produces episodic dimming as well as excess emission at 3.4 and 4.6 m.
• At lower field strength, disk gas is diverted closer to the star, and at/within the corotation radius; the occultation ceases and infrared emission is diminished; gas reaching the co-rotation radius is accreted onto the star through funnels that periodically occult the line of sight producing a strongly periodic signal and weaker infrared emission.
• During magnetic reversals, the weak or absent dipole field means that the disk accretes almost directly onto the star, dust is sublimated before that point, there is little or no occultation or excess emission at 3.4 and 4.6 m.
• Variability in disk accretion may be selfexciting as the disk wall shadows the disk further out, cooling it below 1000K and the minimum temperature for ionization and MRI instability.Accretion could also be governed by dust loading and dynamical interaction with protoplanets in the disk • The residence time of primordial, H/Hedominated gas in the disk is < 10 5 yr, much shorter than the age of PDS 70, and thus ongoing accretion in the inner disk is sustained by gas from the outer disk crossing the gap occupied by the two giant planets.
• Gas crossing the gap from the outer disk is observed to be depleted in solids, including ices, perhaps due to a pressure bump where temperatures are ≲30K, however we find the inner disk to be enhanced in dust, consistent with sub-mm observations.
• Gas sourced from the outer disk could be recharged with dust and volatile heavy elements (in the form of H 2 O and CO 2 ) from a population of planetesimals that are now evaporating, disintegrating, and/or colliding.
Future time-series observations, especially infrared photometry and spectroscopy, promise to more fully elucidate the dynamic behavior of the the quality of the solution.As more of the most discrepant stars were removed in each iteration, the median error decreased, but as sample size decreased error eventually increased again; we adopted the solution at the minimum median error for calculating light curves for each star.To achieve successful convergence it was necessary to restrict reference stars to those with similar Gaia -magnitude and   −   colors.

Figure 1 .
Figure 1.Optical lightcurves of PDS 70 by ASAS-SN and ATLAS, plus symbols marking the epochs of other groundand space-based observations used in our analysis.

Figure 2 .
Figure 2. Photometry from TESS highlights the evolution of the photometric behavior of PDS 70 over four years.The top row of sub-panels shows lightcurves in units of relative magnitudes from TESS (black lines) during Sectors 11, 38, and 65 as well as ASAS-SN (green points).The middle row of sub-panels contains Lomb-Scargle periodograms of the TESS lightcurves showing the waning signal at 3.03 days taken to be the stellar rotation period (red points).In the bottom panel the asymmetry  and quasi-periodicity  parameters (Cody et al. 2014, see text) derived from the TESS lightcurves show a trend from periodic and symmetric (dashed line) behavior to more stochastic and asymmetric (more pronounced dimming) behavior.
Figure3.Top: Wavelet-transform power spectrum of ASAS-SN data, shown using a colormap indicating higher power in darker regions.White areas indicate gaps in the ASAS-SN time series.Spectral power at the rotational period of 3 days and its overtones can be seen to emerge starting at MJD 57500, peak at around MJD 58520; and diminish thereafter.Intervals contemporaneous with observations by TESS (Sec.2.1) and the NRES and HARPS spectrographs (Secs.2.1 and 2.7) are marked by vertical dotted lines.Bottom: Periodograms constructed from integrating the wavelet power spectrum within the intervals indicated in the top panel, and separately normalised to yield unit integral to permit comparison between temporal baselines of different length.

Figure 5 .
Figure5.Combinations of dust size distribution power-law index (vertical axis) and size cutoff (horizontal axis) for single Mie scattering models that reproduce the Δ( − ) vs. Δ reddening-extinction slopes obtained from 1-m (red regions) and 0.4-m data (indigo regions) of PDS 70 (bottom panels of Fig.4).The left panel (a) is for small dust grains with a maximum size (e.g., from grain growth in a protoplanetary disk); the right panel (b) is for large grains with a minimum size cutoff (e.g. from a collisional cascade in a debris disk).The blue curve is the ISM and the black contours are of total opacity (scattering + absorption) in units of 10 4 cm 2 g −1 .

Figure 6 .
Figure 6.Left (a): From bottom to top: photometry of PDS 70 in ASAS-SN -band (green), ATLAS -band (cyan), ATLAS -band (orange), and TESS -band (red).Solid curves represent a spline curve constructed using the upper boundary of ASAS-SN photometry, and then refit to the other data sets, allowing the amplitude to vary.Right (b):relative variability in the different passbands vs. wavelength.The abscissa is the mean wavelength of the passband transmission function, and the error bars span the effective width.The grey line is the expected trend for ISM-like dust using the extinction coefficients ofYuan et al. (2013).

Figure 7 .
Figure 7. WISE 3.4 (W1, orange) and 4.6 m (W2, red) relative lightcurves of PDS 70 compared to the ASAS-SN -band (blue) and -band (green) lightcurves.The solid red and yellow lines connect the median values in each biannual visit during the post-cryogenic NEOWISE mission while the earliest, unconnected data are from the Cryogenic mission.The solid green/blue curve is a spline curve fit to the upper envelope of ASAS-SN photometry.The correspondingly-colored dotted lines indicated the expected disk-less photosphere emission based on the 2MASS   (2.2m) brightness of the star.

Figure 8 .
Figure 8. Left (a): Time-series spectra of the Balmer H line of PDS 70 obtained with the LCOGT NRES spectrograph, with each spectrum placed in observation time relative to the first (obtained on MJD=60077.28).In addition to the individual data points, an 11-point running median (colored curve) and a best-fit Gaussian (black curve) is plotted.Points in the grey regions were excluded from the fit.Right (b): TESS Sector 65 lightcurve (solid line) and H equivalent width from best-fit Gaussians (points and dashed lines).

Figure 9 .
Figure9.Magnetospheric accretion model fit to H profiles of PDS 70 obtained with HARPS and NRES.The photosphere-subtracted spectra are plotted in blue.The grey lines are the 100 best fits for a given observation, with the red lines as their averages.The orange lines are the average Gaussian modeling the chromospheric emission, and the black dot-dashed lines are the combined magnetospheric+chromospheric profiles.The observation epochs, rotation phases, and mass accretion rates in M ⊙ yr −1 are reported in each panel.et al. 2019).The periodic signal (and its upper harmonic) was already present in ASASA-SN data by May 2014, peaked in intensity for about two years beginning mid-2018, then decreased in intensity and disappearing by March 2021, suggesting changes in the innermost location of dust relative to the co-rotation radius.Our multi-band LCOGT photometry unambiguously indicates that scattering by sub-micron dust is responsible for this dimming (Fig.4), at least during the most recent aperiodic phase.Superposed on this pattern of rapid variability is an envelope of smoother variation in

Figure 10 .
Figure 10.TESS Sector 11 lightcurve (black lines) and concurrent ASAS-SN Sloan  ′ photometry (green points) of PDS 70 phased to the 3.03-day rotation period showing the "scalloped" morphology and the larger amplitude variation in the shorter-wavelength ASAS-SN photometry.

Figure 11 .
Figure11.Photosphere-subtracted infrared photometry and spectroscopy of PDS 70 compared to a best-fit SED model (black curve) consisting of an inner disk rim (red curve), and a power-law disk (magenta curve).Black points are those used in the fit.The blue curve is the expected emission from the outer disk starting at ≈50 au.This is the dominant contribution to the 100 m point, which is excluded from the fitting.The grey points at 3.4 and 4.6 m are the (excluded) NEOWISE photometry.

Figure 13 .
Figure 13.Mid-infrared photometry or synthetic photometry (from Spizter IRS and JWST MIRI spectra) of PDS 70 vs time.IRAS observations occurred in 1983 (MJD=45374-45659, off-scale to the left).The AKARI observations occurred during a 477-day all-sky survey represented by the horizontal error bars.The top and middle insets show details of multi-epoch W3-and W4band photometry obtained over two ∼one-day intervals during the WISE cryogenic mission.The JWST spectrum is plotted as the black-line in the bottom inset, with the grey dashed line an extrapolation using the best-fit model in Fig. 11.Colors correspond to passbands, not necessarily the telescope, and the response profiles are plotted in the lower inset.The dashed yellow and brown lines are the IRAS 12-and 25-m profiles.

Figure 14 .
Figure 14.Accretion rate inferred from fitting an magnetospheric accretion model to the H emission line profile obtained by the HARPS and NRES spectrographs.

Figure 15 .
Figure15.Schematic illustrating how variation in the inner disk truncation radius   , relative to the corotation radius   , dust sublimation radius   , and gas ionization radius   could produce the observed pattern of optical and infrared variability of PDS 70.(The viewing geometry is 51 deg inclination and nothing is to scale.)In scenario (a) an elevated disk accretion rate or weak magnetic field means that   lies at or interior to   and non-axisymmetric magnetospheric accretion occurs via onto the star via streams or "funnels".Hot dust in the raised inner edge of the disk is responsible for excess emission at 3.4 and 4.6 m but the star is only occulted periodically by accretion streams.In scenario (b) a low accretion rate or stronger magnetic field moves   beyond   but inside   , and the disk is diverted into a magnetized dusty wind which produces a large 3.4/4.6m excess, partially shadows the outer part of the inner disk, and continuously occults the star.In scenario (c) an interval of magnetic reversal with a very weak dipole component moves   inside   so that magnetospheric accretion is dust-free and there is little disk emission at 3.4 and 4.6 m.

Figure 16 .
Figure16.Ranges of dust grain size and semimajor axis that realize equilibrium temperatures between 1000K (the minimum consistent with the observations and the ionization temperature of disk gas) and the ∼1300K condensation temperature of the particular mineral.In the smaller, more heavily shaded regions, dust lofted in magnetically diverted disk gas has an emitting area consistent with values inferred from 3.4 and 4.6 m photometry (1-4 ×10 −3 au 2 ).Black contours are lines of constant optical depth of the stellar radiation in the Sloan -band due to absorption plus scattering.The red line is maximum dust size that can reach a height that it occults our line of sight, assuming an inner disk inclination of 52 deg.The co-rotation radius and magnetic truncation radius of the disk (the latter based on a mean accretion rate of 0.67 × 10 −10 M ⊙ yr −1 and either a 0.44 kG or 0.15 kG large-scale dipole field) are marked by vertical dashed and dotted lines, respectively.

Figure 18 .
photosphere and the inclination of the magnetic axis  (30 − 75 • ).The last is nominally the same as the known stellar in- clination (≈50 deg) at each epoch, but was allowed to vary in case the stellar rotation and magnetic axes are not aligned.The model line profiles were convolved by the instrumental resolutions before fitting.As inThanathibodee et al. (