Transient classification and novae ejecta

A third parameter, in addition to luminosity and rate of brightness decline, derived from the spectra of transients is suggested as a means of more accurately classifying objects in outburst. Principal component analysis of the spectra of transients is suggested as the best way to determine the third parameter. A model is suggested for novae ejecta that is based on the ballistic ejection of an ensemble of clouds having a wide range of sizes. Short term brightness fluctuations of novae, the formation of dust, and the production of X-ray emission follow naturally from such a picture of the evolving clouds.


Introduction
Although the basics of the nova outburst have been understood for some time there is still uncertainty about some aspects of the phenomenon. Outbursts are the result of steady accretion but there may be other triggers. What causes some novae to vary 1-2 magnitudes in brightness over a few weeks time? What are the key parameters that determine how and when some novae develop copious dust? In recent years new luminous transients have been discovered that do not fit into either the normal nova or supernova paradigm, including some that are observed only in the infrared. It is important to determine what observations may be most useful in understanding the physical mechanism driving these outbursts.

Classifying Transients
The standard plot used to describe transients is one of luminosity vs. brightness decline time. The significance of this plot derives from Arp's classic study of the novae in M31 [1], which he undertook immediately after completing his doctoral thesis at Caltech with the support of W. Baade, A. Sandage, and E. Hubble shortly before the latter's death. Observing 290 clear nights on Mt. Wilson over a 1.5 yr interval in a Herculean effort Arp found that rapidly declining novae were more luminous than slow decliners. The resulting Maximum Magnitude vs. Rate of Decline (MMRD) relation, calibrated independently from the Cepheid, RR Lyrae, H II region distances for M31, was useful to Sandage as a more refined primary extragalactic distance indicator compared to the less accurate average absolute magnitude of the few novae determined by Curtis [2] in his famous debate with Shapley over the size of the Milky Way and distance to M31.
The MMRD relation has an intrinsic dispersion that has steadily increased over time with the larger sample of novae that have been observed within nearby galaxies since Arp's original survey. Until the past two decades a plot of visible luminosity vs. time of decline for transients was dominated primarily by novae and SNe that occupied a relatively small region of space in the plot. However, as seen in figure 1 whose data come primarily from the Palomar Transient Factory survey [3] [4], the MMRD relation is at best a 'tendency', with many variant outlier novae. And transients of all types occupy virtually every part of the luminosity-decay time diagram, as can be seen in figure 2.
Historically, the position of a transient on a plot of maximum magnitude vs. light decay time has been a standard way of expressing the nature or type of the transient. However, it is clear from figure 2 that there is so much overlap of different transient types in the diagram that little information on the nature of a transient results from its position in this diagram. Since many transients have a broad distribution of decay times following outburst the decline time is not much of a defining characteristic of a transient. Rather, some other parameter would be much more useful in distinguishing between different transient phenomena.  A similar situation confronted stellar population studies after studies of galaxies showed that three parameters were important for defining the stellar population of a galaxy: age, metal abundance, and star formation history. This led to the concept of the 3-dimensional population box [5]. The same situation appears to apply to transients, where the identification of a third parameter, in addition to the luminosity and decline time, would be useful in distinguishing between different classes of transients.
Spectroscopy of transients offers easily obtained information that allows kindred objects to be identified and differentiated among the different types of objects. Thus, the spectroscopic characteristics of a transient are arguably the best way to determine what the object is and how it may be similar to or different from other transients. This same problem has been addressed by the quasar community, who have applied principal component analysis (PCA) to quasar spectra [6] [7] to define those properties most useful in discriminating between different quasar properties and types.
Our understanding of transients would be greatly improved by subjecting the spectra of all such objects, i.e., novae, supernovae, stellar mergers, LBVs, [Ca II] transients, etc., to PCA. The breakdown of the main spectral features into principal components, or eigenvectors, could then be used to identify the largest PC (pc1, or eigenvector1 to use the nomenclature of the quasar community) that could be used as the third parameter to create a 3-dimensional 'transient cube', as shown in figure 3. Pc1 might or might not correspond to some clear spectroscopic property such as the continuum slope or intensity of H-alpha or strength of narrow absorption lines,  Consideration of a third parameter that characterizes the spectrum of a transient would provide important information that better allows identification of the class of the transient.

Novae Ejecta Geometry
Many novae, especially those having slower declines in brightness from maximum, show variation in visible brightness of several magnitudes over timescales of weeks. Multiple secondary maxima sometimes occur in addition to short-lived up-and-down fluctuations in brightness, i.e., jitter, that last a few days. These are no doubt due to changing conditions in the ejecta, but no systematic explanation for this behaviour has emerged.
Many novae form dust which produces an infrared continuum that is typically weaker than the optical continuum, although in the case of substantial dust formation can almost completely absorb the visible continuum, transferring most of the visible luminosity into the IR. High density regions in the ejecta that are protected to some extent from high UV radiation so that molecular species are plentiful are believed to define the locale of the dust formation.
Repeated observations of postoutburst novae by the Swift satellite have detected X-ray emission in most novae [8]. Initially, the X-rays have hard 2−10 keV energies which progressively weaken until eventually soft X-rays emerge as the expanding ejecta reveal the hot post-TNR WD surface.
All three features relating to the brightness variations, dust formation, and the evolution of the X-ray emission may be explained by constraining various ejecta parameters which do evolve over time due to their expansion. However, there has not been a coherent explanation of all of these phenomena that relates them to each other and explains how they differ so much between different novae.
We propose here that fluctuations in brightness, the formation of dust, and observed X-ray emission from novae in postoutburst decline all follow naturally from ejecta that are formed from an ensemble of dense clouds of different sizes that are ballistically ejected by the TNR. The small clouds collide with each other, emitting hard X-rays as they rapidly dissipate to form a low density ambient medium. Less common large clouds have dense cores surrounded by a photosphere that provides protection for the outer dense regions where dust can form. And when a large cloud emerges from the lower density ambient region of ejecta its radiation will produce a variation in brightness of the ensemble. The large variation in characteristics of different novae can then be understood in terms of differing size distribution of the ejected clouds from object to object. An example of the geometrical model for novae ejecta proposed here is shown in figure  4. Figure 4. An expanding large cloud emerges from the ejecta and causes a brightness variation as it dissipates. Its dense, cooler layers form dust. X-rays are produced by collisions among the numerous small clouds.