Symbiotic stars are binaries consisting of a cool evolved G-M/S/C I-III star accreting onto a smaller companion---but the accretion disk itself is rarely detected. Accretion signatures like hard X-rays and optical/ultraviolet flickering are usually suppressed or outshone by shell burning on the accreting white dwarf, the luminous giant, and the giant's wind nebula. In Chapters 2 and 3, we present a new way to find symbiotics that is less biased against accreting-only, non-burning symbiotics with directly detectable accretion disks. Our search methodology is based on finding outliers in SkyMapper Southern Sky Survey broad-band and intermediate-band photometry, using a parameter space built from reconstructed u-g u-v snapshot colors and rapid variability between the three exposures of a 20-minute SkyMapper Main Survey filter sequence, from a sample of luminous red objects selected with 2MASS and Gaia. In a pilot survey employing this new search design, we discovered 12 new symbiotics, including four symbiotics with optical accretion disk flickering and at least two with boundary-layer hard X-rays, as well as 10 new symbiotic candidates. We also discovered optical flickering in the known symbiotic V1044 Cen (CD-36 8436). We conclude that at least 20% of the true population of symbiotics exhibits detectable optical flickering from the inner accretion disk, a substantial fraction of which would not meet the usual H-alpha equivalent width detection thresholds typically used to find symbiotics with traditional narrow-band emission line photometry surveys. There is a significant population of optically-flickering symbiotics hidden both within and beyond the known catalogs of symbiotic stars---however, the question of whether the true population of accreting-only symbiotics is larger than the population of burning symbiotics remains unanswered. We also find that our methods probe a completely different region of parameter space than recent work by the Munari et al. (2021) search for accreting-only symbiotics, while being surprisingly in harmony with the Akras et al. (2019) infrared selection criteria. As an intermediate step in our pilot survey, we explored several outlying regions in our SkyMapper parameter space with optical spectroscopy of 234 luminous red objects, which we present in a 248-page spectral atlas. Our results identify a zone of the u-g u-v snapshot color-color diagram in which virtually all objects are symbiotics. When all-sky uvg colors become available through future DRs of SkyMapper and MEPHISTO, between about 51 and 117 symbiotics missed by previous surveys (of which 11 to 17 have been reported in this work) will be discoverable using only this mostly-symbiotic zone of the color-color diagram, with a near-zero contamination rate. Main Survey filter-sequence variability is also a powerful tool for finding hidden, flickering symbiotics both inside and outside of the mostly-symbiotic color-color zone, but variability must still be used in conjunction with color; there must be enough of an accretion disk contribution to the u-band for it to exhibit detectable variability. We show that yellow post-AGB stars with strong Balmer jump absorption (along with the symbiotic Southern Crab) are outliers with large positive u-v, while some S and carbon stars are outliers with large negative u-v. We also show that it is important to correct the results of SkyMapper's catalog pipeline for variability when dealing with samples containing large-amplitude pulsating stars. In Chapters 4 and 5, we present an in-depth study of one of the few optically-flickering symbiotic stars previously known, MWC 560 (V694 Mon). The persistent outflow from MWC 560 is known to manifest as broad absorption lines (BALs), most prominently at the Balmer transitions. In Chapter 4, we report the detection of high-ionization BALs from C IV, Si IV, N V, and He II in International Ultraviolet Explorer spectra obtained on 1990 April 29-30, when an optical outburst temporarily erased the obscuring "iron curtain" of absorption troughs from Fe II and similar ions. The C IV and Si IV BALs reached maximum radial velocities at least 1000 km/s higher than contemporaneous Mg II and He II BALs; the same behaviors occur in the winds of quasars and cataclysmic variables. An iron curtain lifts to unveil high-ionization BALs during the P Cygni phase observed in some novae, suggesting by analogy a temporary switch in MWC 560 from persistent outflow to discrete mass ejection. At least three more symbiotic stars exhibit broad absorption with blue edges faster than 1500 km/s; high-ionization BALs have been reported in AS 304 (V4018 Sgr), while transient Balmer BALs have been reported in Z And and CH Cyg. These BAL-producing fast outflows can have wider opening angles than has been previously supposed. BAL symbiotics are short-timescale laboratories for their giga-scale analogs, broad absorption line quasars (BALQSOs), which display a similarly wide range of ionization states in their winds. In Chapter 5, we investigate how the accretion disc of MWC 560 is affected by its outflow. We performed optical, radio, X-ray, and ultraviolet observations of MWC 560 during its 2016 optical high state. We tracked multi-wavelength changes that signalled an abrupt increase in outflow power at the initiation of a months-long outflow fast state, just as the optical flux peaked: (1) an abrupt doubling of Balmer absorption velocities; (2) the onset of a 20 𝜇Jy/month increase in radio flux; and (3) an order-of-magnitude increase in soft X-ray flux. Juxtaposing to prior X-ray observations and their coeval optical spectra, we infer that both high-velocity and low-velocity optical outflow components must be simultaneously present to yield a large soft X-ray flux, which may originate in shocks where these fast and slow absorbers collide. Our optical and ultraviolet spectra indicate that the broad absorption-line gas was fast, stable, and dense (⪞10⁶.⁵ cm⁻³) throughout the 2016 outflow fast state, steadily feeding a lower-density (⪝10⁵.⁵ cm⁻³) region of radio-emitting gas. Persistent optical and ultraviolet flickering indicate that the accretion disc remained intact. The stability of these properties in 2016 contrasts to their instability during MWC 560's 1990 outburst, even though the disc reached a similar accretion rate. We propose that the self-regulatory effect of a steady fast outflow from the disc in 2016 prevented a catastrophic ejection of the inner disc. This behaviour in a symbiotic binary resembles disc/outflow relationships governing accretion state changes in X-ray binaries.

I develop the first magnetospheric accretion model to take account of the observed complexity of T Tauri magnetic fields, and the influence of stellar coronae. It is now accepted that accretion onto classical T Tauri stars is controlled by the stellar magnetosphere, yet to date the majority of accretion models have assumed that the stellar magnetic field is dipolar. By considering a simple steady state accretion model with both dipolar and complex magnetic fields I find a correlation between mass accretion rate and stellar mass of the form M[dot above] proportional to M[asterisk subscript, alpha superscript], with my results consistent within observed scatter. For any particular stellar mass there can be several orders of magnitude difference in the mass accretion rate, with accretion filling factors of a few percent. I demonstrate that the field geometry has a significant effect in controlling the location and distribution of hot spots, formed on the stellar surface from the high velocity impact of accreting material. I find that hot spots are often at mid to low latitudes, in contrast to what is expected for accretion to dipolar fields, and that particularly for higher mass stars, accreting material is predominantly carried by open field lines. Material accreting onto stars with fields that have a realistic degree of complexity does so with a distribution of in-fall speeds. I have also modelled the rotational modulation of X-ray emission from T Tauri stars assuming that they have isothermal, magnetically confined coronae. By extrapolating from surface magnetograms I find that T Tauri coronae are compact and clumpy, such that rotational modulation arises from X-ray emitting regions being eclipsed as the star rotates. Emitting regions are close to the stellar surface and inhomogeneously distributed about the star. However some regions of the stellar surface, which contain wind bearing open field lines, are dark in X-rays. From simulated X-ray light curves, obtained using stellar parameters from the Chandra Orion Ultradeep Project, I calculate X-ray periods and make comparisons with optically determined rotation periods. I find that X-ray periods are typically equal to, or are half of, the optical periods. Further, I find that X-ray periods are dependent upon the stellar inclination, but that the ratio of X-ray to optical period is independent of stellar mass and radius. I also present some results that show that the largest flares detected on T Tauri stars may occur inside extended magnetic structures arising from the reconnection of open field lines within the disc. I am currently working to establish whether such large field line loops can remain closed for a long enough time to fill with plasma before being torn open by the differential rotation between the star and the disc. Finally I discuss the current limitations of the model and suggest future developments and new avenues of research.