Star-disk interactions in multi-band photometric monitoring of the classical T Tauri star GI Tau

The variability of young stellar objects is mostly driven by star-disk interactions. In long-term photometric monitoring of the accreting T Tauri star GI Tau, we detect extinction events with typical depths of $\Delta V \sim 2.5$ mag that last for days-to-months and often appear to occur stochastically. In 2014 - 2015, extinctions that repeated with a quasi-period of 21 days over several months is the first empirical evidence of slow warps predicted from MHD simulations to form at a few stellar radii away from the central star. The reddening is consistent with $R_V=3.85\pm0.5$ and, along with an absence of diffuse interstellar bands, indicates that some dust processing has occurred in the disk. The 2015 -- 2016 multi-band lightcurve includes variations in spot coverage, extinction, and accretion, each of which results in different traces in color-magnitude diagrams. This lightcurve is initially dominated by a month-long extinction event and return to the unocculted brightness. The subsequent light-curve then features spot modulation with a 7.03 day period, punctuated by brief, randomly-spaced extinction events. The accretion rate measured from $U$-band photometry ranges from $1.3\times10^{-8}$ to $1.1\times10^{-10}$ M$_\odot$ yr$^{-1}$ (excluding the highest and lowest 5% of high- and low- accretion rate outliers), with an average of $4.7 \times 10^{-9}$ M$_\odot$ yr$^{-1}$. A total of 50% of the mass is accreted during bursts of $>12.8\times10^{-9}$ M$_\odot$ yr${^{-1}}$, which indicates limitations on analyses of disk evolution using single-epoch accretion rates.


INTRODUCTION
Classical T Tauri stars (CTTSs) are low mass young stars surrounded by an accretion disk. The stellar magnetic field truncates the disk at a few stellar radii and channels gas from the disk onto the star (e.g . Camenzind 1990;Koenigl 1991;Shu et al. 1994). The measured strengths and geometries of magnetic fields and the profiles of emission and absorption lines are consistent with expectations of the magnetospheric accretion model (e.g. Johns-Krull 2007; Donati & Landstreet 2009;Hartmann et al. 2016). Magnetohydrodynamic (MHD) simulations of magnetospheric accretion suggest that the accretion flow may be stable or unstable, depending on the accretion rate, the magnetic field strength and morphology, and the inclination angle between stellar spin and magnetic dipole (e.g. Romanova et al. 2013;Blinova et al. 2016).
Photometric variability of T Tauri stars has been studied for decades (Wenzel 1969;Grinin 1988;Herbst et al. 1994;Bouvier et al. 2013;Cody et al. 2017). When star-disk interactions are steady, an accretion column and the associated inner disk warp rotates around the star, periodically occulting the central star (e.g. Bouvier et al. 2007;McGinnis et al. 2015). In non-steady accretion, these extinction events may appear more stochastically and last for days, months or even years. The obscure dust is located in a persistent puffed-up disk and inner-rim (Dullemond et al. 2003;Ke et al. 2012), a warp induced by binarity (Hamilton et al. 2001), a disk instability at larger distances (Zhang et al. 2015), or perhaps even a non-axisymmetric bridge that links an inner disk with an outer disk (Loomis et al. 2017). The changes in the height of the inner disk has also been seen in anti-correlated variability of near-and mid-IR disk emission (Espaillat et al. 2011), with a possible relationship to accretion rate (Ingleby et al. 2015). The disk interpretation is challenged in one case (J1604-2130) by the measurement of a face-on inclination of an outer disk (Ansdell et al. 2016a). In a second case (RW Aur), the occultation source is uncertain and may be a dusty wind (Petrov et al. 2015;Schneider et al. 2015b), a tidal encounter of the secondary star (Dai et al. 2015), the combination of occultation and time-variable accretion (Takami et al. 2016), or partial occultation of the inner disk (Facchini et al. 2016).
In this paper, we focus on short-and long-term extinction events detected in one CTTS, GI Tau. Stars with shortduration (1-5 d) extinction events, called dippers, are obscured by dust structures at or near the disk truncation radius (e.g. Alencar et al. 2010;Cody et al. 2014;Scaringi et al. 2016). AA Tau is the historical prototype for dippers (e.g. Bouvier et al. 1999Bouvier et al. , 2003. Periodic and quasi-periodic dippers have a periodicity distribution consistent with the dis- tributions of stellar rotations ). Long-term extinction events, called faders, occur when the star is occulted by disk components for weeks-to-years (e.g. Bouvier et al. 2013;Findeisen et al. 2013;Rodriguez et al. 2015Rodriguez et al. , 2016bLoomis et al. 2017); KH 15D is the prototype for faders (Hamilton et al. 2001). Some stars, including AA Tau, have exhibited both types of extinction events. Deep extinction events have also been called Type III variables or UXors (Herbst et al. 1994), especially when the occulted object is a Herbig AeBe star (e.g. Grinin et al. 1994a;Natta et al. 1997).
In the midst of this extinction variability, emission is also always changing because of unstable accretion and spot rotation. Accretion variability is common on young stellar objects, as 10% of CTTSs have similar bursty lightcurves (Findeisen et al. 2013;Cody et al. 2014;Stauffer et al. 2014;Cody et al. 2017). The variable accretion process appears as changes in excess continuum and line emission above the photosphere (e.g. Alencar et al. 2012;Fang et al. 2013;Costigan et al. 2014) and the corresponding changes in photometry (Venuti et al. 2014;Sousa et al. 2016;Stauffer et al. 2016;Tofflemire et al. 2017a), driven by either unsteady star-disk connections (e.g. Romanova et al. 2013) or changes in the disk density at the inner rim (Robinson et al. 2017). Spot modulation is also commonly seen among young stars with typical variations of ∆V 0.5 mag (e.g. Herbst et al. 1994;Grankin et al. 2007), although spots in lightcurves of some CTTSs can be difficult to distinguish from extinction and accretion variations. Extinction, accretion, and spot variability each have particular patterns in high-time resolution photometry (Alencar et al. 2010;Morales-Calderón et al. 2011;Alencar et al. 2012;Cody et al. 2017), multi-band photometry (Herbst et al. 1994;Grankin et al. 2007;Venuti et al. 2015), and spectroscopic monitoring .
In this paper, we describe and analyze multi-band optical monitoring of the CTTS GI Tau obtained over two years. Our work provides a method to identify the variation mechanisms by the color information and probe the star-disk interaction at the inner edge of circumstellar disk. The paper is organized as follows. In Section 2, we describe our observation and data reduction. The photometric results and periodicity analysis are described in Section 3. In Section 4, we analyze this pho-tometric variability in terms of the warp size and changes in accretion.
2. OBSERVATIONS 2.1. Properties of GI Tau GI Tau is a Classical T Tauri star associated with the B18 cloud in Taurus star forming region (Myers 1982;Kenyon et al. 2008) and is separated by 13 arcsec from a wide companion, GK Tau (Figure 1; see, also, e.g., Kraus & Hillenbrand 2009). GI Tau has a circumstellar disk (e.g. Kenyon & Hartmann 1995;Luhman et al. 2010;Rebull et al. 2010) and ongoing accretion (e.g. Valenti et al. 1993;Gullbring et al. 1998). The average VLBI parallax distance of 140 pc to the Taurus star-forming region (Loinard et al. 2007;Torres et al. 2009Torres et al. , 2012) is adopted for the distance to GI Tau.
Companion searches with high resolution near-IR imaging (e.g. Daemgen et al. 2015) and high-resolution spectroscopy (Nguyen et al. 2012) have yielded non-detections, indicating that GI Tau is likely a single star. A ∼ 7 day period has been detected in some epochs (Vrba et al. 1986;Herbst et al. 1994) but is absent in other epochs (e.g. Grankin et al. 2007;Rodriguez et al. 2017a), perhaps because spot changes may be masked by complications in the lightcurve from extinction and accretion variability.
The estimated spectral type of GI Tau ranges from K5 -M0.5 (Rydgren et al. 1976;Herbig 1977;Cohen & Kuhi 1979;Hartigan et al. 1994;Taguchi et al. 2009;Herczeg & Hillenbrand 2014), with differences caused by methodology and a non-uniform temperature distribution on the stellar surface (see, e.g., Gully-Santiago et al. 2017). Extinction events have been previously detected from photometry (Herbst et al. 1994;Grankin et al. 2007;Rodriguez et al. 2016a). In three optical spectra, Herczeg & Hillenbrand (2014) found that fixing the spectral type to a single value required an extinction that varied from A V = 1.05 to 2.55 mag. Our analysis in §4.3 indicates a minimum A V = 0.75 − 1.0 mag, which is likely interstellar; any additional extinction is likely caused by the disk.
Adopting a spectral type of M0.4 (T eff = 3828 K) and log(L/L ) = −0.25 (Herczeg & Hillenbrand 2014; see also Grankin 2016), the mass and age are 0.53 M and 1.4 Myr as inferred from the pre-main sequence evolutionary tracks of Baraffe et al. (2015), and 0.92 M and 4 Myr from the magnetic tracks of Feiden (2016). These parameters are sensitive to the unknown spot properties of the star (Gully-Santiago et al. 2017). However, dynamical masses measured from disk rotation around stars of similar spectral types lead to masses of 0.60 -0.95 M (Simon et al. 2017).
The disk inclination has not been measured. Given a radius R = 1.7 R , rotational period P rot = 7.03 ± 0.02 d (see §3.1), and stellar rotational velocity v sin i = 12.7 ± 1.9 km s −1 (Nguyen et al. 2009), the stellar inclination is > 60 • (see also Johns-Krull & Valenti 2001). Broad redshifted absorption in He I λ10830 has a similar profile as that seen in AA Tau (Fischer et al. 2008) and supports this high inclination.

SNIFS Photometry and Spectroscopy
We obtained spectra and photometry of GI Tau with the Super-Nova Integral Field Spectrograph (SNIFS Aldering et al. 2002;Lantz et al. 2004) from 26 Nov. to 15 Dec. 2014. SNIFS is an Integral Field Spectrograph on the UH 88-inch telescope on Maunakea that produces R ∼ 1000 spectra from 3200 to 10000 Å over a 6 ×6 field-of-view (FOV). Short ac- quisition images were obtained with a 9.6 × 9.6 FOV imager with V-band filter and are used here for photometry. The full set of our SNIFS observations include spectroscopic monitoring of ∼ 30 CTTSs. GI Tau was initially selected as a target based on past identification of extinction events (see, e.g. Grankin et al. 2007;Herczeg & Hillenbrand 2014). We detected a deep extinction event at the beginning of our SNIFS campaign and decided to intensively monitor GI Tau for the remainder of our campaign. Two spectra from this spectroscopic monitoring campaign are analyzed in this paper (see §2.5).
2.3. Subsequent photometric campaigns (2014 -2016) Following our SNIFS photometry, we monitored GI Tau from 2014 -2016 with eleven other telescopes. The details of the telescopes, instruments, and observations are described in Table 1. The complete set of photometry is listed in an online Table. From 16 Dec. 2014 (MJD 57007) until 25 Mar. 2015 (MJD 57108), photometry was obtained in the V-band filter with a cadence of 1 -2 visits per night. From Oct. 2015 -Feb. 2016, multi-band photometry was obtained in B, V, R, and I bands, and U when available. Different observational strategies were set based on the time allowance of each telescope. SLT, 1 m Thailand Southern Telescope, and 1.3 m JCBT observed the selected field 1 to 3 times on each clear night. The 0.5 m at TNO and 2 m HCT also contributed weeks-long observations. The NOWT (Liu et al. 2014) and NBT monitored GI Tau for 4-6 hrs for 7 and 3 consecutive nights, respectively, to measure variations on short timescales.

Data Reduction of Photometry
The data were reduced with custom-written routines in IDL. The images were corrected for detector bias, flat-field, and cosmic rays. The stellar brightness of GI Tau, GK Tau, and many field stars in the frame are measured with aperture photometry. For field stars, the sky background is measured in an annulus with 8 arcsec inner radius and 10 arcsec outer radius around the star. Since the distance between GI Tau and GK Tau is only 13.2 arcsec, the background levels are adopted directly from the sky background of the nearby reference star. The counts for each star are then extracted using a radius equal to two times the seeing (in FWHM), with an upper limit on radius of 6. 5 arcsec. Photometry with fixed apertures of 1, 3, and 6 and PSF-fitting yield results that are generally consistent with our approach, but with larger standard deviations in the photometry.
Four bright stars are identified as non-variables ( Figure 2) and are selected as reference stars to calibrate the BVRI photometry of GI Tau. The measured standard deviations of all reference stars are 0.017 mag in I, 0.028 mag in V and 0.042 mag in B-band, after excluding the images obtained during the full moon. The measurements are less reliable (∆I > 0.05 mag) in observations with seeing larger than 4 . The number of reference stars used for each telescope depends on the FOV and is listed in Table 1.
In U-band observations, only one field star, with m U =13.50 mag 13 , that is located within the 10 × 10 FOV is bright enough to be used as a calibrator. Unsaturated images in B,V and I-band indicate that this calibrator is not variable. The accuracy of our U-band observations is typically limited to ∼ 0.05 mag by the S/N of GI Tau. The differential effects of telluric absorption versus airmass are not corrected.
A reflection nebulosity around GI Tau and GK Tau (Arce & Sargent 2006) is detected in stacked images, with a surface brightness of I = 22.8 mag/arcsec 2 and B = 25.5 mag/arcsec 2 . The flux contribution from the nebulosity within a 6. 5 radius aperture is 17.5 mag in the I-band and 20.2 mag in B-band, or ∼ 4 mag fainter than the faintest measurements of GI Tau. Compared with the photometric accuracy and variability of GI Tau, the differential flux contribution from the nebulosity introduced by the use of different aperture sizes is negligible.
For absolute photometric calibration, we observed the GI Tau field and the region PG 02331 from Landolt (1992) at a range of airmasses with the 2 m Himalayan Chandra Telescope on 1 Dec. 2015. The atmospheric extinction and instrument coefficients are measured from PG 02331 and applied to bright stars in the GI Tau field. The standard magnitudes of these reference stars are then used to apply the zero-point shifts to each observation obtained by all other telescopes in this study.
The absolute photometric calibration accuracy should be ∼ 0.02 mag in V and I bands and 0.05 mag in B band, following the uncertainties in the Landolt star calibrations. However, an absolute offset of 0.09 mag in V-band calibration is identified when comparing our photometry to the historical photometry of Grankin et al. (2007) (see Figure 5) and to the synthetic photometry obtained from our flux-calibrated SNIFS spectra. The source of this problem could not be identified. Our relative photometric calibration should be unaffected. The synthetic ∆V between our SNIFS spectra is within 0.01 mag of the directly-measured ∆V obtained in our acquisition images.

Data Reduction of Spectroscopy
The SNIFS spectra of GI Tau and the spectrophotometric standard G191B2B (Oke 1990) were reduced with customwritten routines in IDL. The emission is split at ∼ 5200 Å by a dichroic into separate red and blue channels. The raw images consist of 225 separate spectra, each from a given spaxel in the 15 × 15 integral field unit. The counts in each spectrum are extracted by fitting a cross-spectrum profile, measured from flats, to each wavelength pixel. The spectra in each spaxel was then wavelength-calibrated to ∼ 10 km s −1 using  arc lamps, flat-corrected in each spaxel, and then re-gridded onto the same wavelength scale.
The final spectra are extracted from the data cube by fitting a 2D profile and sky background at each wavelength bin. The spectra of GI Tau were then flux-calibrated using G191B2B spectra obtained within 1 hr of GI Tau. The average airmass correction was calculated using spectra of G191B2B over the 20-night run and was then applied to each epoch. Two spectra were selected for use in this paper because they were obtained in photometric conditions, near in time to the photometric calibrators, and at the local minimum and maximum of the lightcurve.

RESULTS AND ANALYSIS
In the 2014 -2015 light curve of GI Tau, the most prominent features are several extinction events with depths of ∆m V > 2.5 mag and durations of 3 -5 days (see Figure 3). The 2015 -2016 light curve of GI Tau began with a dim epoch that lasted ∼ 50 days, followed by a period with smaller periodic brightness variations ( Figure 4).
These photometric variations are summarized by the colorcolor and color-magnitude diagrams in Figure 5. The V-band brightness varied by 2 mag, the V − I color by 0.8 mag, and the B − V color by 0.5 mag. The locus of points on the colormagnitude diagram is similar to that seen in long-term monitoring of GI Tau by Grankin et al. (2007), except for the offset in V-band discussed in §2.4.
In faint epochs, a 'blue turnaround' is seen, in which the color variation is achromatic with further dimming of V. This blue turnaround, also seen in AA Tau (Bouvier et al. 1999) and other CTTSs (Grankin et al. 2007), is likely caused by an increased importance in scattered light, since stars with edge-on disks typically appear blue at optical wavelengths (e.g. Padgett et al. 1999;Herczeg & Hillenbrand 2014). These epochs are ignored when calculating accretion rates. However, if the bluer colors are caused by higher accretion rates during these faint epochs, then this choice would bias our results.
In this section, we describe how the light curves are combined with the color-color and color-magnitude diagrams are used to identify variability caused by stellar spots, circumstellar extinction events, and accretion bursts.

Spot modulation in 2015 -2016
Periodicity in the 2015 -2016 lightcurve is most prominent in the I-band. The Generalized Lomb-Scargle (GLS) periodogram (Zechmeister & Kürster 2009) of the I-band lightcurve yields a best-fit period of 7.03 ± 0.02 d, with the error bar adopted from the FWHM of the periodogram profile ( Figure 6). Prior to the fit, the long-term trends were approximated as a third-order polynomial and were removed from the data (Zajtseva 2010). Fitting parameters to B, V, and I-band lightcurves are shown in Table 2.
The sinusoidal morphology of the phase-folded light curves indicates the presence of a single large spot, similar to some other young stars with similar spectral types (e.g. Alencar et al. 2010;Rebull et al. 2016;Gully-Santiago et al. 2017). The standard deviation of the residual of 0.11 mag is likely caused by extinction and accretion events (discussed in §3.2 -3.4). The power of the periodogram, ζ = p max /σ p , is highest in the I-band, since the other bands are more sensitive to accretion and extinction variations. The variations in the colors are synchronous (Figure 7).
False-alarm probabilities 14 for the period are computed using a Fisher randomization test with input periods between 2 -100 days (e.g. Linnell Nemec & Nemec 1985). The 7.03 day period exceeds the 99% confidence level. This period is consistent with past measurements of the photometric period (Table 6). In other epochs, including our monitoring in 2014 -2015 and the 2008 -2014 light curves described by Rodriguez et al. (2017b), any modulation from spots is masked by much stronger variability caused by extinction.

Extinction events in 2014 -2015
Several photometric dips are shown in the V-band light curve of 2014 -2015 campaign, with depths of 1.5 -3.1 mag relative to the out-of-extinction brightness of ∼ 12.5 mag and durations of 3 -5 days (see list of extinction dips in Table 3).
The lightcurve of GI Tau reveals a wide range of durations and frequencies of extinction events. Our initial SNIFS monitoring included a double-dip extinction event, during which the V-band emission from the star faded, brightened, and then quickly faded again. The separation of the two minima is 5 days, and the total combined duration of 11 days, longer than one stellar rotation period. The R V measurement based on spectra will be discussed in §4.2.
Subsequent follow-up photometry over the next months led to the detection of four dips with A V > 1.5 mag (see Table  3). These dips have a centroid time that repeats with a ∼ 21 day period. However, the preceding double-dip is inconsistent 14 False-alarm probabilities are the fraction of permutations (ie. shuffled time-series) that include a peak higher than that of the periodogram of the unrandomized dataset at any frequency. This therefore represents the probability that, given the frequency search parameters, no periodic component is present in the data with this period. To ensure reliable significance values, the number of permutations was set to 1000. If the false alarm probabilities lie between 0.00 and 0.01, then the quoted period is a correct one with 95% confidence. The periodogram is computed at 5000 frequencies between 0 and 0.5 d −1 .   with this quasi period. The extinctions that occur in the following year, described below, are also inconsistent with any periodicity.

Extinction events in 2015 -2016
The lightcurve during our 2015 -2016 campaign is initially dominated by a gradual fade that reaches ∆V = 1.5 mag and then returns to the bright state, in total covering a period of ∼ 80 days (Figure 4). In addition to this months-long fading event, several small and large photometric dips are detected with durations of 3 -8 days, after correcting for spot-induced periodicity (see Figures 4 and 8 and Table 3). Figure 4 shows a brief (∼ 3 day) dip in the spot-corrected lightcurve at Day 397, with a depth of ∆I = 0.39 mag, ∆V = 0.45 mag, and ∆B=0.56 mag. A deeper and longer dip occurred around day 440, lasting for ∼ 8 days (Figure 8). Gaussian fits to the dips, as measured after accounting for spot rotation, yield A I = 0.60 mag, A V = 1.22 mag and A B = 1.56 mag and FWHM of 3.73, 3.52 and 3.76 days, respectively. In those fits, the depths are measured relative to the post-dip lightcurve, which is well fit by a sine curve. There is no obvious periodicity of this extinction event.
3.4. Short timescale bursts Photometry in the U-and B-bands is more sensitive to accretion than photometry with longer-wavelength filters. At short wavelengths, the photospheric emission of GI Tau is faint relative to the continuum emission produced by the accretion shock (see review by Hartmann et al. 2016). In our monitoring, the U-and B-bands exhibit stronger variations than the V and I-bands.
Our campaign included five nights with constant monitoring of GI Tau on NOWT, during which several short bursts occurred (Figure 9). The largest burst in B, detected during the first night, reached a peak ∆B ∼ 0.3 mag and lasted ∼ 3.5 hr. Four other shorter, smaller bursts are detected in the last two days. The average duration of these five bursts detected by NOWT is ∼ 1.7 hr, and the maximum amplitude in B-band is 0.31 mag. The change in brightness caused by these accretion bursts are an order of magnitude smaller than those caused by the deep extinctions. The corresponding increases of accretion rate during these bursts are calculated in §4.3. In one case, the B-band brightness is consistent with a non-detection, so the minimum and maximum accretion rates before and dur-ing the burst are not reported. These short bursts are attributed here to accretion but could alternately be attributed to stellar flares (e.g. Kowalski et al. 2016;Tofflemire et al. 2017a,b).

Color Analysis
Variable extinction, accretion, and spot coverage are all identified from the optical lightcurve of GI Tau. The traces of different phenomena in the color-magnitude diagrams can be used to distinguish the variation mechanisms. In this section, we describe the different signatures that changes in each of these properties imprints in color-color and color-magnitude diagrams ( Figure 10).
The short extinctions dips in the 2015 -2016 campaign exhibit similar changes in the color-magnitude diagram with ∆V = 2.10 ± 0.08 ∆(V − I) and ∆I = 0.7 ± 0.1 ∆(B − I). The long-term variation seen in the first half of the 2015 -2016 campaign appears similar to the dips and is also attributed to extinction. These empirical relationships are consistent with expectations for dust reddening. The accretion bursts appear as horizontal changes in B − I versus I, indicating that the accretion only has a minor effect on the I-band brightness and that the B − I color is a good tracer of accretion. In this case, accretion is much flatter than extinction in the I versus B − I diagram ( Figure 10 and Table 5). Venuti et al. (2015) obtained similar results in two weeks of monitoring young stars in NGC 2264 with CFHT in u and r bands.
As the spot rotates, the V − I colors change by 0.06 mag while the B − V colors change by 0.08 mag. These small color changes during spot modulation are consistent with those of the weak-line T Tauri star LkCa 4 during three decades of photometry (Grankin et al. 2008;Gully-Santiago et al. 2017). The locus that spot modulation traces on the color-magnitude diagrams has a slope between those of accretion and extinction. However, since the spot modulation has a unique periodicity, the spot information is readily extracted from a frequency analysis.
Pre-main-sequence stellar evolution tracks from Baraffe et al. (2015) are also presented in the color magnitude diagrams, with colors adopted from Allard (2014). In distant clusters, properties of low mass stars are often inferred from photometry (e.g. Reggiani et al. 2011;Jose et al. 2016;Beccari et al. 2017). Extinction events, accretion bursts, and spots each influence the inferred mass and age of member stars. Extinction curves are parallel to the color isochrone of cool stars in V − I versus V diagram, which indicates that the age determination from V and I-band photometry is robust to extinction changes (see also discussion in Sicilia-Aguilar et al. 2005). The age of GI Tau inferred from the Baraffe et al. (2015) models is consistently between 1-2 Myr (see also the age estimation in §2.1). However, the V − I color range introduces uncertainty in mass or T eff estimates when analysis is restricted to photometry, with larger uncertainties when using non-simultaneous photometry.

DISCUSSION
Photometric dips, accretion bursts, and a 7.03 d periodicity all shape the light curve of GI Tau during our monitoring over two years. The properties of the inner edge of circumstellar disk and the star-disk interactions can be determined from the morphology and color changes during the variation events. The existence of quasi-periodic extinctions in the first year and the non-detection during our second campaign, and the change in morphology and frequency of events within   Figure 9. * * : The mass accretion rates are in unit of 1 × 10 −9 M yr −1 . a : The B-band photometry is below the detection limit set in §5.3 each campaign, indicate an evolution of the inner disk structure over at most a few orbital timescales. In this section, we discuss the 2014 -2015 quasi-periodicity in terms of a warp model, the extinction curve, and the distribution of accretion rates.
4.1. The slow warp model for the quasi-periodic dips of 2014 -2015 Emission from young stars is periodically occulted by the inner edge of the circumstellar disk, when the disk is viewed close to edge-on. The presence of asymmetric disk warps or puffed-up inner rims will extinct the stellar brightness (see e.g., the radiative transfer simulations of Kesseli et al. 2016). Figure 11 presents the periods and amplitudes of extinction events seen on young stars. For most dippers, these occultations are thought to occur once per stellar period, last ∼ 1 day, and are caused by inner disk warps related to accretion funnel flows (e.g. Bouvier et al. 2007;Romanova et al. 2013). For faders, the occultations are prolonged and may last months or In 2014 -2015 monitoring, the (quasi)-periodic dips of 1.5 − 2.5 mag in V occurred every ∼ 21 days. In contrast, all previous periodic dippers have periodicity on much shorter timescales that are consistent with the stellar rotation period (Grankin et al. 2007;Bouvier et al. 2007;Alencar et al. 2010;McGinnis et al. 2015) and have depths of A V = 0.1 − 1 mag. The deep obscuration depth of GI Tau in this campaign is comparable to UXors, which are usually early type PMSs undergoing variable extinctions with depths A V > 1 mag (Grinin et al. 1991(Grinin et al. , 1994bHerbst et al. 1994;Natta et al. 1997;Dullemond et al. 2003). However, no clear periodicity has been reported on UXors.
The deep events of GI Tau recur near every ∼ 3 stellar rotation periods and may be evidence of the slow warp in the MHD simulations of magnetospheric accretion by Romanova et al. (2013). In these simulations, two warps form in the circumstellar disk: a thin warp located at the co-rotation radius (R cor ) and a thick warp outside of the co-rotation radius. Material can be trapped by the thick warp because of coupling between the stellar rotation and global oscillations in the disk. The thick warp is expected to rotate several times more slowly than the star, since it is located at a larger radii in the disk, and also cause dips that are more optically-thick than thin warps at the inner disk edge. The thick warp has a high scale height, so that it periodically intercepts our line-of-sight and causes extinction. Although this slow warp was quasi-periodic over ∼60 days, the feature was short-lived: it formed soon after our initial 20-night monitoring and had evolved or dissipated by the next year.
The ∼80 day-long fade and return at the end of 2015 is much shorter than equivalent events on other stars, such as the years-long fading on AA Tau and V409 Tau (Bouvier et al. 2013;Rodriguez et al. 2015). The obscuration source may be an azimuthally symmetric warp located close to the inner edge of the disk (e.g. Dullemond et al. 2003), distant disk structures (e.g. Zhang et al. 2015) or a bridge between an outer and inner  Ansdell et al. (2016b) are shown as circles and cluster at periods consistent with stellar rotation and extinctions of 0.1-1 mag. Periodic variation of AA Tau is marked by green. Long-term extinction events of the faders KH 15D, RW Aur, V 409 Tau, and DM Ori from (Kearns & Herbst 1998;Rodriguez et al. 2015Rodriguez et al. , 2016b are triangles and plotted with "timescale" indicating the duration of the event. These extinction events are usually deeper, though this may be an observational bias. disk (Loomis et al. 2017).
As the obscuration source of the extinction dips is located not far from the inner edge of circumstellar disk or co-rotation and truncation radius, we calculate the co-rotation radius of GI Tau based on the stellar parameters, and spin period obtained from this work.
The morphology of the dips is related to the disk inclination, orientation of magnetic field dipole, and warp opacity. The short-durations of the dips detected on GI Tau indicates a moderate inclination viewing angle (Bodman et al. 2017).
The shape of the dips depends on the ingress timescale, i.e., the timescale for the structure to move in front of the star. The orbital velocity is calculated by the duration of the ingress time following the equation: where the definition of L is half of the angular size of the warp (Bouvier et al. 1999), and the t ingress should around half of the total obscuration time. As shown in Figure 8, the typical t ingress is 4 days while the occultation last for 8 days. A disk warp located at ∼ 1.5 R cor has a local disk rotation velocity v rot = 43.5 km/s. A Gaussian shape warp modeled by Romanova et al. (2013) with v warp = 0.25 v rot should have a width L = 6.9 R * in horizontal size for an 8-day duration.
The maximum observed duration of the dips in 2014 -2015 campaign is 5 days, or 25% of the occultation period (P ∼ 20 days). If we assume the warp system is located at 1.2 to 1.5 co-rotation radius, as indicated by the Romanova et al. (2013) simulations, the angular width of the warp L is as large as 2.35 R cor or ∼18.6 R * . A hydrogen gas column density is derived by Bohlin et al. (1978): N H /E(B− V)=5.8 × 10 21 cm −2 mag −1 , assuming a R V = 3.85 extinction (See §4.2). We also assume an ISM gas-to-dust ratio as 100 : 1, although this may not be valid for inner disks. The gas mass within the warp is then roughly estimated by: where m H is the atomic mass of hydrogen and S warp represents the cross-section area of warp. We infer from the lightcurve that the warps have a Gaussian shape with a central height H = 2 R * . The estimated gas mass is 1.6 × 10 20 g for warps with an average extinction of A V = 1 mag. The short-duration extinction events in 2015 -2016 are less deep and would therefore either have less mass or a lower scale height.
4.2. The Extinction Curve of the Dips of GI Tau Extinction events in single-band photometry have degenerate explanations: the star may be entirely occulted by dust described by some column density and extinction law, or a fraction of the star may be entirely occulted by a large column of dust (see discussion in, e.g. Bodman et al. 2017). If the star is entirely occulted by dust, then the wavelength dependence of the extinction will lead to an estimate of grain growth, as long as reflected light is not significant. If only a fraction of the star is covered by opaque dust, then the star will get fainter but the color will not change. Figure 12 shows flux-calibrated spectra of GI Tau obtained at minimum brightness during an extinction event and maximum brightness obtained at the end of that event. The ratio of the two spectra demonstrate that GI Tau is much redder during occultation than out of occultation. The TiO band ratios and Balmer Jumps are similar, indicating that the changes are caused by extinction rather than any change in spot coverage or accretion. The redder spectrum in this epoch is consistent with our other spectra obtained during the same run, the few spectra analyzed by Herczeg & Hillenbrand (2014), and our photometric results.
The flux ratio between 4000-8500 Å is fit with an extinction curve from (Cardelli et al. 1989), with free parameters A V and a total-to-selective extinction R V between 2.1 -5.8. The best-fit R V = 3.85 ± 0.5 indicates possible grain growth relative to the ISM. This fit is constrained primarily by flux at < 5000 Å. The flux ratio 16 of the spectrum deviates from the fit above 8000 Å for all R V . This analysis ignores any contribution from dust scattering, which is likely important at bluer wavelengths (see, e.g., analysis of AA Tau by Schneider et al. 2015a). The V-band magnitude of the fainter spectrum is in the range where the "blue turnaround" makes the spectrum appear bluer than one would expect from extinction alone. If considered, scattering would lead to a lower R V and may also explain the deviation at red wavelengths. If some fraction of the star is covered by a much higher dust extinction, then R V would need to be much lower for the visible fraction of the star.
Diffuse interstellar bands (see review by Herbig 1995) are not detected in any spectrum, but would be expected to be strong if the dust composition were similar to the ISM (Friedman et al. 2011). These bands are strong in lines-of-sight through molecular clouds (e.g. Vos et al. 2011), and when seen in the spectra of some young stars (e.g. Oudmaijer et al. 1997;Rodgers et al. 2002) are likely caused by the interstellar medium rather than the disk. Dust heating and processing within the disk of GI Tau must have destroyed the complex molecules that cause these bands. This difference could provide a method to distinguish disk extinction from interstellar extinction.
The flux in the [O I] 6300 Å emission does not change between epochs, despite the change in extinction. Highresolution spectra of GI Tau includes broad and narrow components (e.g. Simon et al. 2016). The bulk of this emission must originate above the star, where the outflow would not be occulted by a inner disk warp.
The wavelength-dependent ratio of the two spectra is consistent with the other spectra obtained during the rise from day 52 -54. The Balmer jump and therefore the accretion changes between days 54 -56, so the later spectra are not immediately useful for R V calculations. On the other hand, when calculated from our photometry of extinction events (see Table 5), we obtained R V = A V /(A B − A V ) ∼ 5 for the long-term extinction (fader), and the dip on Day 440 (dipper) yields R V = 3.6. The fits to the long-term fade may be less reliable because they include different points for each band and cover accretion bursts and spot rotation.
The R V measurement indicates a low opacity of the obscuration source, in contrast to previous interpretations that the periodic dips of AA Tau are optically-thick (Bouvier et al. 2003). Any optically-thin dust in the accretion flow or at the inner disk edge should be quickly destroyed by strong stellar irradiation. In MHD simulations, the accretion stream drags dust grains from the optically-thick disk (Romanova et al. 2003), which may replenish the dust in our line-of-sight. However, the occultation timescales of the dips (e.g. 5 days) are relatively long compared with the crossing-timescale of an inner disk warp at the co-rotation radius. Alternative explanations that the dust is located in disk winds at larger radii , rather than the disk itself, could explain the long survival time of the dust (Bans & Königl 2012;Petrov et al. 2015.

Accretion on different timescales
Mass accretion rates (Ṁ acc ) are measured here by calculating the excess continuum and line emission produced by the accretion flow. Our B-band and limited U-band monitoring of 2015 -2016 are shown in Figure 4, with variations caused by changes in accretion, extinction, and spot coverage. Because scattered light during deep extinction events strongly affects the colors (the 'blue turnaround'), accretion rates are calculated only for epochs when V < 14.0 mag.
To measure the excess U-band luminosity, we first remove the spot modulation effects by a 7.03-day sinusoidal lightcurve. We then extract the extinction-corrected photospheric emission from the flux-calibrated optical spectra of Herczeg & Hillenbrand (2014). The combined fit of a photospheric template and accretion continuum to the spectrum yields photospheric luminosities of U photosphere = 14.54 ± 0.1 mag, B photosphere = 13.44 ± 0.05 mag, and I photosphere = 10.43 ± 0.05 mag, when corrected to A V = 0 mag. Any extinction-corrected U-band emission above this brightness is attributed to accretion. The color of accretion is calculated as U − I ∼ 0.15 mag, using assumptions for the accretion continuum from Herczeg & Hillenbrand (2014), as estimated from veiling measurements of Fischer et al. (2011). The color variations are then calculated for a variable extinction, following the R V = 3.85 curve from Cardelli et al. (1989) with A U = 1.47 A V , A B = 1.25 A V , and A I = 0.56 A V . Figure 13 shows how extinction and accretion affect the U − B-and Iband magnitude of GI Tau.
The optical spectral energy distributions of spot and extinction removed examples are presented in Figure 14. The accretion excess usually contributes ∼ 60% of the emission in the U-band filter but only ∼ 15% of the emission in the Bband filter on median mass accretion rateṀ acc = 1 ∼ 4 × 10 −9 M yr −1 , consistent with expectations from accretion models (e.g. . A similar relationship is seen by comparing the left and right panels of Figure 13 where the data points are more scattered in U. Following the empirical relationship from Gullbring et al. (1998), log(L acc /L ) = 1.09 +0.04 −0.18 log(L ex U /L ) + 0.98 +0.02 −0.07 , the accretion luminosity of GI Tau is calculated by the U-band accretion luminosity, L acc by L acc U = 4πd 2 F zeropoint × (10 −0.4U unred − 10 −0.4U photosphere ), (4) where F zeropoint is the zero point of generic U-band, distance d = 140 pc, and U unred is spot modulation and extinction reddening removed U magnitude. The accretion luminosity ranges from ∼ 0 to 41 × 10 −2 L . The accretion rateṀ acc is then derived from the accretion luminosity, where R * and M * are radius and mass of GI Tau. The calculated mass accretion rate of GI Tau ranges from ∼ 0−52×10 −9 M yr −1 , for stellar parameters R * = 1.7 R and M * = 0.53 M .
We also develop a method to estimate accretion rate from B-band photometry, because our time coverage in B is more extensive than in U. After removing the sinusoidal spot modulation, the extinction and accretion for each B and I data point is estimated from the grid shown in Figure 13. The excess B-band emission produced by accretion is calculated by where B unred is the de-reddened magnitude in B-band using extinction curve of R V = 3.85. Figure 15 shows a linear relationship between nearly-simultaneous U ex and B ex , with a best-fit U ex = 0.93B ex + 0.52.
The bolometric correction of B-band excess is then combined with Equation 7 and the empirical relationship given by Gullbring et al. (1998), as log(L acc /L ) = 1.22 +0.05 −0.19 log(L ex B /L ) + 1.46 +0.06 −0.10 . (8) Based on the accuracy of our photometry and the correction for spots, estimated as ∼ 0.1 mag in both B and Uband, our detection limits of accretion rate measurement are set as log(M acc /M yr −1 ) > −9.0 for B-band and > −10.0 for U-band. The correlation between near-simultaneous Bband and U-band accretion rates is tight at rates higher than log(M acc /M yr −1 ) > −8.2 but unreliable at lower accretion rates.
The mass accretion rates of GI Tau calculated from U and B-band excesses are summarized in Figure 16. As measured from the U-band excess, the 5th to 95th percentile range of log(M acc /M yr −1 ) is −7.89 to −9.77, with a center of −8.70 and sigma as 0.53 dex in the Gaussian fit. These results are consistent with results from the more-extensive B-band photometry, which yielded an average log M acc /M yr −1 = −8.55 with 0.6 dex scatter. These estimates are obtained by creating mock sets of accretion rates over a range of values for the average and standard deviation and assuming  Table 2. The horizontal lines indicate accretion rates for the same extinction, while the diagonal lines indicate the extinction for the same accretion rate. This grid is calculated based on two assumptions: a) I = U − 0.15 as the accretion and b) extinction amplitudes in each band follow the R V = 3.85 curve from Cardelli et al. (1989). The estimated extinction ranges from A V = 0.5 to 2.5 mag assuming out of extinction brightness I = 10.43 mag (Herczeg & Hillenbrand 2014). Figure 14. The optical spectral energy distributions of GI Tau obtained at five different accretion rates, alongside a photospheric template (red). The photometry has been corrected for extinction. The photospheric template is U photosphere = 14.54 mag, B photosphere = 13.59 mag, V photosphere = 12.29 mag and I photosphere = 10.43 mag.
a Gaussian distribution and upper limits. The adopted values are then obtained from maximizing the probability from a Kolmogorov-Smirnov test between the observed distribution and each mock data set. The distribution of B-band accretion rates includes the NOWT data sampled at a time-resolution of one hour. The best-fit B-band data over predicts the number of data points at high accretion rates, as seen in Figure 16. Differences in results between B-band and U-band accretion rates are likely attributed to the large scatter in B-band at average and weaker accretion rates.
This distribution of accretion rates is consistent with the distribution of accretion rates measured for stars of similar mass (e.g. Fang et al. 2013;Venuti et al. 2014;Manara et al. 2017). However, the distribution demonstrates the importance of accretion bursts in models of disk evolution. The average Figure 15. The correlation of U-and B-band excess of GI Tau, both generated by accretion. The photometry has been corrected for spots, de-reddened, with an excess then measured against an estimated photospheric magnitude of U photosphere = 14.54 mag; B photosphere = 13.44 mag. The best linear fitting result is: U ex = 0.93B ex + 0.52. mass accretion rate of GI Tau is 4.7 × 10 −9 M yr −1 , two times faster than the average inferred from the log(M acc /M yr −1 ). Moreover, a total of 50% of the mass is accreted when the accretion rate is higher than 12.8 × 10 −9 M yr −1 , during accretion bursts (Figure 17). Such bursts are seen in our highcadence NOWT monitoring, where for example the accretion rate increased from ∼ 2.3 × 10 −9 M yr −1 to 7.3 × 10 −9 M yr −1 in several hours on Day 458.
The periods of high accretion deplete most of the disk; the periods of low accretion are irrelevant. However, models of disk evolution (e.g. Rosotti et al. 2016;Rafikov 2017;Mulders et al. 2017;Lodato et al. 2017) assume that the accretion rates are static. Although these distributions cannot be fully explained by variability (Costigan et al. 2014;Venuti et al. 2015), and surely include some stars that are strong accretors Figure 16. Histograms of accretion rates calculated by U (left) and B-band (right) excess through the entire 2015 -2016 campaign. The data points taken within 2 hours are binned as one. The mass accretion rate higher and lower than the detection limit are shown by pink and grey, respectively. Gaussian fits of the histograms are shown by thick lines. Figure 17. The distribution of mass accretion rate measured by U (black) and B (blue) band photometry. Vertical dash/dot lines from left to right indicate the accretion rate above which half the mass is accreted, the average accretion rate, and the average mass accretion rate in log space. and others that are weak, bursts should be expected to play a significant role in the mass accretion. The distribution of high accretion rates could also be in excess over a Gaussian distribution. Future analyses should incorporate time-averaged accretion rates (e.g. Venuti et al. 2015) over many epochs and perhaps even many years.

CONCLUSIONS
Our two-year multi-band photometric monitoring of the classical T Tauri star GI Tau revealed variability caused by extinction, accretion, and spots, each with unique signatures in color-magnitude diagrams. The deep extinction events of ∆V = 2 − 3 mag were seemingly stochastic in their timing and duration, with some occultations lasting 3-5 days and one 80 day long dimming. During 3 months in 2014 -2015, the short dips recurred with a quasi-period of ∼ 21 days, as might be expected from the sub-Keplerian slow warp seen in the simulations of Romanova et al. (2013). The stellar rotation period of 7.03 ± 0.02 days is recovered from the second half of the 2015 -2016 lightcurve but is not apparent in our earlier lightcurve, consistent with previous period estimates from some epochs Table 6 Photometric period of GI Tau