# Stars/Dwarfs/Whites

A white dwarf is a small very dense star that is typically the size of a planet. A white dwarf is formed when a low-mass star has exhausted all its central nuclear fuel and lost its outer layers as a planetary nebula.

## Theoretical white dwarfs

Def. a "dying star of low or medium mass, more solid [and dense] but less bright than the sun" is called a white dwarf.
"White dwarfs are end-products of stellar evolution. The fundamental properties of the dominant group of nonmagnetic white dwarfs have been invaluable in constraining the theory of single star evolution."

## Sloan Digital Sky Survey

Of the 2551 white dwarf stars from the full spectroscopic white dwarf and hot subdwarf sample within the Sloan Digital Sky Survey (SDSS) first data release, DR1, 1888 are non-magnetic DA types and 171, non-magnetic DBs.

## Accretions

If a white dwarf has a close companion star that overflows its Roche lobe, the white dwarf will steadily accrete gas from the companion's outer atmosphere. The companion may be a main sequence star, or one that is aging and expanding into a red giant. The captured gases consist primarily of hydrogen and helium, the two principal constituents of ordinary matter in the universe. The gases are compacted on the white dwarf's surface by its intense gravity, compressed and heated to very high temperatures as additional material is drawn in. The white dwarf consists of degenerate matter, and so does not inflate at increased heat, while the accreted hydrogen is compressed upon the surface. The dependence of the hydrogen fusion rate on temperature and pressure means that it is only when it is compressed and heated at the surface of the white dwarf to a temperature of some 20 million kelvin that a nuclear fusion reaction occurs; at these temperatures, hydrogen burns via the CNO cycle.
While hydrogen fusion can occur in a stable manner on the surface of the white dwarf for a narrow range of accretion rates, for most binary system parameters the hydrogen burning is thermally unstable and rapidly converts a large amount of the hydrogen into other heavier elements in a runaway reaction, liberating an enormous amount of energy, blowing the remaining gases away from the white dwarf's surface and producing an extremely bright outburst of light. The rise to peak brightness can be very rapid or gradual which is related to the speed class of the nova; after the peak, the brightness declines steadily. The time taken for a nova to decay by 2 or 3 magnitudes from maximum optical brightness is used to classify a nova via its speed class. A fast nova will typically take less than 25 days to decay by 2 magnitudes and a slow nova will take over 80 days.
"An accreting white dwarf undergoes [near surface] nuclear burning when the accretion rate exceeds a certain limit." Due to the near surface nuclear burning, "the stellar luminosity is dominated by hydrogen burning, since the energy liberated by hydrogen burning exceeds that due to accretion on a white dwarf by an order of magnitude or more, depending on the mass of the white dwarf."
"[A]bove an accretion rate (with a hydrogen abundance of 0.7 by mass) M$_{RG}$ ≈ 8.5 10$^{-7}$ (M$_{WD}$/M$_ʘ$ -0.52)M$_ʘ$ yr$^{-1}$ (M$_{WD}$=mass of the white dwarf) the accreted matter forms a red-giant like envelope around the white dwarf, with the luminosity being generated from hydrogen shell burning."

## Dominant groups

"White dwarfs are the most readily studied of the end products of stellar evolution. Investigations of white dwarfs have generally focused on the dominant group of the nonmagnetic variety for which realistic model atmospheres can be constructed and stellar parameters deduced." "White dwarfs are intensively studied end products of stellar evolution. However, investigations of white dwarfs have generally focused on the dominant group of nonmagnetic stars for which realistic model atmospheres can be constructed and fundamental properties, such as their masses or interior chemical composition can be determined."
Notation: accretion induced collapse (AIC).
          binary millisecond pulsars (BMSPs).
          white dwarf (WD).
"If we focus on BMSPs with WD companions, which is the dominant group in the observed sample, our results indicate birth rates that are ∼ 10 times higher for BMSPs that come from the AIC route."

## X-rays

Supernova 2005ke, which was detected in 2005, is a Type Ia supernova, an important "standard candle" explosion used by astronomers to measure distances in the universe. Shown here is the explosion in optical, ultraviolet and X-ray wavelengths. This is the first X-ray image of a Type Ia, and it has provided observational evidence that Type Ia are the explosion of a white dwarf orbiting a red giant star.
An explosion called SN 2005ke is the first Type Ia supernova detected in X-ray wavelengths, and it is much brighter in the ultraviolet than expected. A Type Ia is an explosion of a white dwarf in orbit around either another white dwarf or a red giant star. The dense white dwarf can accumulate gas donated from the companion. When the dwarf reaches the critical mass of 1.4 solar masses, a thermonuclear explosion ensues.
Type Ia are called "standard candles" and are used by astronomers to measure distances in the universe, because each Type Ia shines with a known luminosity. Immler's team says it has the first observational evidence to support one theory about the origin of these supernovae.
Immler's group has found direct evidence in the X-ray and ultraviolet light of SN 2005ke that a white dwarf, now obliterated, was indeed orbiting a red giant. The scientists detected shock waves from the explosion ramming into gas from a red giant and found no evidence of a second white dwarf. This observation may help astronomers understand the birthplaces and evolution of these supernovae, so crucial to the field of cosmology and dark energy.

## Super soft X-ray sources

A super soft X-ray source (SSXS, or SSS) is an astronomical source of very low energy X-rays. Soft X-rays have energies in the 0.09 to 2.5 keV range, whereas hard X-rays are in the 1-20 keV range.
SSXSs are in most cases only detected below 0.5 keV, so that within our own galaxy they are usually hidden by interstellar absorption in the galactic disk. They are readily evident in external galaxies, with ~10 found in the Magellanic Clouds and at least 15 seen in M31.
As of early 2005, more than 100 SSSs have been reported in ~20 external galaxies, the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), and the Milky Way (MW). Those with luminosities below ~3 x 10$^{38}$ erg/s are consistent with steady nuclear burning in accreting white dwarfs (WD)s or post-novae. There are a few SSS with luminosities ≥10$^{39}$ erg/s.
Super soft X-rays are believed to be produced by steady nuclear fusion on a white dwarf's surface of material pulled from a binary companion, the so-called close-binary supersoft source (CBSS).
This requires a flow of material sufficiently high to sustain the fusion. Contrast this with the nova, where less flow causes the material to only fuse sporadically. Super soft X-ray sources can evolve into type Ia supernova, where a sudden fusion of material destroys the white dwarf, and neutron stars, through collapse.
Super soft X-ray sources were first discovered by the Einstein Observatory. Further discoveries were made by ROSAT.
Many different classes of objects emit supersoft X-radiation (emission dominantly below 0.5 keV).

### Luminous supersoft X-ray sources

Luminous super soft X-ray sources have a characteristic blackbody temperature of a few tens of eV (~20-100 eV) and a bolometric luminosity of ~10$^{38}$ erg/s (below ~ 3 x 10$^{38}$ erg/s).
Apparently, luminous SSSs can have equivalent blackbody temperatures as low as ~15 eV and luminosities ranging from 10$^{36}$ to 10$^{38}$ erg/s. The numbers of luminous SSSs in the disks of ordinary spiral galaxies such as the MW and M31 are estimated to be on the order of 10$^3$.

### Milky Way SSXSs

SSXSs have now been discovered in our galaxy and in globular cluster M3. MR Velorum (RX J0925.7-4758) is one of the rare MW super soft X-ray binaries. "The source is heavily reddened by interstellar material, making it difficult to observe in the blue and ultraviolet." The period determined for MR Velorum at ~4.03 d is considerably longer than that of other supersoft systems, which is usually less than a day.

### Close-binary supersoft sources

The close-binary supersoft source CBSS model invokes steady nuclear burning on the surface of an accreting white dwarf (WD) as the generator of the prodigious super soft X-ray flux. As of 1999, eight SSXSs have orbital periods between ~4 hr and 1.35 d: RX J0019.8+2156 (MW), RX J0439.8-6809 (LMC), RX J0513.9-6951 (LMC), RX J0527.8-6954 (LMC), RX J0537.7-7034 (LMC), CAL 83 (LMC), CAL 87 LMC), and 1E 0035.4-7230 (SMC).

### Symbiotic binaries

A symbiotic binary star is a variable binary star system in which a red giant has expanded its outer envelope and is shedding mass quickly, and another hot star (often a white dwarf) is ionizing the gas. Three symbiotic binaries as of 1999 are SSXSs: AG Dra (BB, MW), RR Tel (WD, MW), and RX J0048.4-7332 (WD, SMC).

### Noninteracting white dwarfs

The youngest, hottest WD is very close to 100,000 K, of type DO and is the first single WD recorded as an X-ray source with ROSAT.

### Cataclysmic variables

"Cataclysmic variables (CVs) are close binary systems consisting of a white dwarf and a red-dwarf secondary transferring matter via the Roche lobe overflow."
Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources. The accretion disk may be prone to instability leading to dwarf nova outbursts: a portion of the disk material falls onto the white dwarf, the cataclysmic outbursts occur when the density and temperature at the bottom of the accumulated hydrogen layer rise high enough to ignite nuclear fusion reactions, which rapidly burn the hydrogen layer to helium.
Apparently the only SSXS nonmagnetic cataclysmic variable is V Sge: bolometric luminosity of (1 - 10) x 10$^{37}$, a binary including a blackbody (BB) accretor at T < 80 eV, and an orbital period of 0.514195 d."
The accretion disk can become thermally stable in systems with high mass-transfer rates (Ṁ). Such systems are called nova-like (NL) stars, because they lack outbursts characteristic of dwarf novae.

### VY Scl cataclysmic variables

Among the NL stars is a small group which shows a temporary reduction or cessation of Ṁ from the secondary. These are the VY Scl-type stars or anti-dwarf novae.

### V751 Cygni

V751 Cyg (BB, MW) is a VY Scl CV, has a bolometric luminosity of 6.5 x 10$^{36}$ erg/s, and emits soft X-rays at quiescence. The discovery of a weak soft X-ray source of V751 Cyg at minimum presents a challenge as this is unusual for CVs which commonly display weak hard X-ray emission at quiescence.
The high luminosity (6.5 x 10$^{36}$ erg/s) is particularly hard to understand in the context of VY Scl stars generally, because observations suggest that the binaries become simple red dwarf + white dwarf pairs at quiescence (the disk mostly disappears). "A high luminosity in soft X-rays poses an additional problem of understanding why the spectrum is of only modest excitation." The ratio He II λ4686/Hβ did not exceed ~0.5 in any of the spectra recorded up to 2001, which is typical for accretion-powered CVs and does not approach the ratio of 2 commonly seen in supersoft binaries (CBSS).
Pushing the edge of acceptable X-ray fits toward lower luminosity suggests that the luminosity should not exceed ~2 x 10$^{33}$ ergs/s, which gives only ~4 x 10$^{31}$ ergs/s of reprocessed light in the WD about equal to the secondary's expected nuclear luminosity.

### Magnetic cataclysmic variables

X-rays from magnetic cataclysmic variables are common because accretion provides a continuous supply of coronal gas. A plot of number of systems vs. orbit period shows a statistically significant minimum for periods between 2 and 3 hr which can probably be understood in terms of the effects of magnetic braking when the companion star becomes completely convective and the usual dynamo (which operates at the base of the convective envelope) can no longer give the companion a magnetic wind to carry off angular momentum. The rotation has been blamed on asymmetric ejection of planetary nubulae and winds and the fields on in situ dynamos. Orbit and rotation periods are synchronized in strongly magnetized WDs. Those with no detectable field never are synchronized.
With temperatures in the range 11,000 to 15,000 K, all the WDs with the most extreme fields are far too cool to be detectable EUV/X-ray sources, e.g., Grw +70°8247, LB 11146, SBS 1349+5434, PG 1031+234 and GD 229.
Most highly magnetic WDs appear to be isolated objects, although G 23-46 (7.4 MG) and LB 1116 (670 MG) are in unresolved binary systems.
RE J0317-853 is the hottest magnetic WD at 49,250 K, with an exceptionally intense magnetic field of ~340 MG, and implied rotation period of 725.4 s. Between 0.1 and 0.4 keV, RE J0317-853 was detectable by ROSAT, but not in the higher energy band from 0.4 to 2.4 keV. RE J0317-853 is associated with a blue star 16 arcsec from LB 9802 (also a blue WD) but not physically associated. A centered dipole field is not able to reproduce the observations, but an off-center dipole 664 MG at the south pole and 197 MG at the north pole does.
Until recently (1995) only PG 1658+441 possessed an effective temperature > 30,000 K. Its polar field strength is only 3 MG.
The ROSAT Wide Field Camera (WFC) source RE J0616-649 has an ~20 MG field.
PG 1031+234 has a surface field that spans the range from ~200 MG to nearly 1000 MG and rotates with a period of 3$^h$24$^m$.
The magnetic fields in CVs are confined to a narrow range of strengths, with a maximum of 7080 MG for RX J1938.4-4623.
None of the single magnetic stars has been seen as of 1999 as an X-ray source, although fields are of direct relevance to the maintenance of coronae in main sequence stars.

### Novas

There are three SSXSs with bolometric luminosity of ~10$^{38}$ erg/s that are novae: GQ Mus (BB, MW), V1974 Cyg (WD, MW), and Nova LMC 1995 (WD). Apparently, as of 1999 the orbital period of Nova LMC 1995 if a binary was not known.
U Sco, a recurrent nova as of 1999 unobserved by ROSAT, is a WD (74-76 eV), L$_{bol}$ ~ (8-60) x 10$^{36}$ erg/s, with an orbital period of 1.2306 d.

### Planetary nebulas

In the SMC, 1E 0056.8-7154 is a WD with bolometric luminosity of 2 x 10$^{37}$ that has a planetary nebula associated with it.

### Super soft active galactic nuclei

Supersoft active galactic nuclei reach luminosities up to 10$^{45}$ erg/s.

### Large amplitude outbursts

Large amplitude outbursts of super soft X-ray emission have been interpreted as tidal disruption events.

## Ultrasoft X-rays

"[T]he ultrasoft X-ray emission (peak energy 30-50 eV) observed in the three strong (≥ 4 10$^{37}$-10$^{38}$ erg s$^{-1}$) LMC X-ray sources CAL83, CAL87 and RXJ0527.8-6954 can be explained by steady nuclear burning of hydrogen accreted onto white dwarfs with masses in the range of 0.7 to 1.2 M$_ʘ$."

## Blues

"Novae possess a number of attributes that make them potentially valuable standard candles. They are luminous (approaching M$_V$ = -10) and easy to recognize. Because they belong to an old stellar population, they are found predominantly in ellipticals and the bulges of spirals [...]; such environments are relatively dust-free and photometrically smooth, so that observations of novae beyond the Local Group are simpler and easier to interpret than observations of Cepheids. The available evidence suggests that observations of novae are not strongly affected by metallicity effects [...]. Finally, the calibration of novae as standard candles possesses relatively low intrinsic scatter [...], and is well understood theoretically [...]."
"All [or nearly all early] observations of extragalactic novae were made in continuum blue light."
"The relationship between the maximum luminosity (magnitude) of a nova and its rate of decline (MMRD) is the usual starting point for deriving extragalactic distances. [L]uminous novae decay more rapidly than intrinsically faint novae [...]. The MMRD correlation for Galactic novae [has been confirmed. In addition there are] expansion parallaxes for a number of (previously undetected) spatially resolved shells around old Galactic novae. The physical basis for the MMRD relation [is that] more massive white dwarfs require less accreted matter to produce a thermonuclear runaway, and these lower mass envelopes can be ejected more rapidly; thus the most luminous novae are also the fastest."
"To measure the distance to an external galaxy using the MMRD relation, it is necessary to determine the apparent magnitudes of novae at maximum light, and a mean rate of decline over two magnitudes. At present the calibration of the MMRD relation is in the B or m$_{pg}$ bands [...], so that observations through these bandpasses are preferred. It is essential that the observations sample the light curves of novae frequently enough near maximum light that m$^{max}$ can be estimated for the fastest (i.e., brightest) novae. The signal to noise ratio of the photometry should be high enough that novae discovered near maximum light can be followed at least 2 magnitudes below this level."
"The calibration can be effected in two ways: (1) using Galactic novae (in which case the use of the MMRD relation is a primary distance indicator, calibrated using geometrical techniques); or (2) using novae in M31 (in which case the distance scale is tied to the distance of M31)."
At right is a graph of the maximum "magnitude-rate of decline relation for Galactic novae [...]. Closed symbols represent the novae designated high quality [...]; the solid line [from the equation below] is a least-squares fit to the high-quality data."
An "MMRD relation for Galactic novae is given by:"
    $M_{V}^{max}=-9.96-2.31\times log{\dot {m}},$
"where ${\dot {m}}$ is the mean rate of decline (in mag d$^{-1}$) over the first 2 magnitudes. The mean scatter around this relation is ± 0.52 mag (1 ) for the high quality subset [data]. The data and fit are shown in [the graph at the right]. A slightly different result is obtained if the Galactic data are corrected for the constancy of M$_B$ 15 days after maximum light [...]. In principle such a correction removes systematic errors in the absolute magnitudes, and results in a tighter MMRD correlation (σ ≃ 0.47 mag for all objects)."
"An alternate calibration of the MMRD relation is obtained by studying novae in the nearby spiral galaxy M31. [...] Only about 1/3 of the known novae in M31 have sufficient information in their light curves to be useful in determining the MMRD relation, and only about 1/4 of these possess good quality light curves with a well-observed maximum and rate of decay. [...] The 1 σ scatter around the mean relation depends on the subset of data chosen, and is in the range 0.20 - 0.28 mag [...]."
"To compare the M31 MMRD data with the mean Galactic MMRD, we assume (m - M)$_B$ ≃ 24.6 for M31 [...], (B - V)$^{max}$ ≃ 0.23 [...], and (m$_{pg}$ - B) ≃ -0.17 [...]. With these assumptions, [...] the agreement between the Galactic and M31 MMRD relations is not good: the flattening observed in the M31 MMRD relation for bright and faint novae is not seen for Galactic novae. In addition, there appears to be a systematic offset of about 0.3 mag between the two MMRD relations, in the sense that Galactic novae are fainter than M31 novae. (This offset would increase to ~ 0.5 mag if the mean internal absorption for M31 novae were 0.2 mag [...]. However, we note that [there may not be] any systematic difference in the MMRD relation for novae close to and far from obvious dust patches in the bulge of M31.)"
"The flattening at faint magnitudes in the M31 MMRD relation may be due to Malmquist bias: in the presence of a magnitude limit, only the brightest novae will be detected. Whether or not this flattening is real has little effect on distance determinations outside the Local Group, because it is predominantly the most luminous novae that are detected at large distances. The flattening of the M31 MMRD relation for luminous novae is a more difficult problem. If one aligns the MMRD relations for Galactic and M31 novae in the linear (-1.3 ≲ log mdot ≲ -0.7) regime, then the luminous (log mdot ≲ -0.6) Galactic novae lie an average of ~ 0.8 mag above the M31 MMRD relation. One possible explanation for this is that maximum light for M31 novae is not as well sampled as it is for Galactic novae; this is particularly apparent in the light curves of Arp 1 and Arp 2 [...]."
"The shift of the Galactic and M31 MMRD relations relative to each other seems to imply that the true distance modulus of M31 is 0.3 mag less than the value obtained with quality distance indicators (e.g., RR Lyrae stars, IR observations of Cepheids). However, [...] this discrepancy vanishes if a different sample of objects is chosen to define the Galactic MMRD, and if uncorrected M$_V$$^{max}$ values are used for the Galactic nova sample (instead of M$_V$ values corrected for the Buscombe - de Vaucouleurs effect). It is also worth noting that the theoretical MMRD [...] possesses a flatter slope than that observed for [...] data on Galactic novae, and hence provides a better overall fit to the S-shaped MMRD relation observed for M31 novae."
It "should be noted that the Galactic MMRD relation is defined with far fewer objects than is the case for M31; furthermore, the overall quality of the Galactic data (as demonstrated by the scatter in the MMRD relation) is considerably lower than for M31, probably due to such effects as uncertain Galactic absorption, and due to the assumption of spherical symmetry that is inherent in Cohen's application of the expansion parallax technique [...]. In fact, the offset between the Galactic and M31 MMRD relations is almost exactly what would be expected if the prolate geometry of nova shells is not taken into account when applying the expansion parallax technique [...]."
"In view of all of the above, it seems somewhat safer to employ the M31 MMRD relation as the calibrator for the extragalactic distance scale. This makes the distance scale dependent on an assumed distance to M31. However, [...] there is concordance in most distance estimates for M31 (except those derived using novae!); using the M31 calibration is therefore a more prudent approach at the present time."
"Several other methods for using novae as distance indicators have been proposed in the literature. Here we give a brief discussion of some of these methods, and their limitations."
"<M$_{15}$>: [The] mean magnitude of an ensemble of novae 15 days after maximum light was a constant; from the most recent data on Galactic novae, [...] <M$_1$5> ≃ -5.60 ± 0.14, where the quoted error is the 1 σ error in the mean. The rough constancy of <M$_{15}$> is a consequence of the MMRD relation [...]. For Virgo cluster novae, <B$_{15}$> ≃ +26 if (m - M) = 31.5; hence the <M$_{15}$> distance indicator will be strongly affected by Malmquist bias at the distance of the Virgo cluster unless the observational completeness limit goes somewhat fainter than B > 26. Note that there are exceptional objects (e.g., M31 novae Arp 1, 2, and 3) that suggest this method be used with caution."
"Luminosity Function of Novae: The luminosity function of novae at maximum light is approximately Gaussian [with] the mean magnitude of this Gaussian to determine the distance to M31. [...] The most recent compilation of M31 nova data [...] appears to show a double-peaked luminosity function; [using] the magnitude of the minimum between the two peaks as a distance indicator. Yet another method is to use the integral luminosity function of novae at maximum light; this function is linear over a wide range of magnitude, and possesses a well-defined intercept [...]."
"The use of the luminosity function of novae at maximum light as a distance indicator demands large samples of novae that are essentially complete at the faintest magnitudes; it is therefore unlikely that this method will be useful for any but the nearest luminous galaxies (i.e., those with high nova rates). [Using] the dip between two peaks in the luminosity function is not completely reliable, because, [...] different samples of M31 novae have luminosity functions with very different structure. (The very existence of this dip is in some question [...]"
The "luminosity function of all M31 nova observations (i.e., random phases) possesses no useful information that can be used in determining extragalactic distances [...]."
"Period of Visibility: [There] exists a strong correlation between the mean period of visibility of novae (down to some limiting magnitude m$_{lim}$, and the absolute magnitude that this m$_{lim}$ corresponds to. Application of this correlation (calibrated using M31 data) to the Virgo elliptical observations [...] yields a distance modulus that is similar to that obtained using the MMRD relation. This method needs complete samples of novae down to some chosen m$_{lim}$, but the samples do not have to be large. (With a large sample of novae, it would in principle be possible to apply this technique at several different m$_{lim}$ values.)"

## Reds

"Supernovae [especially Type Ia (SNe Ia)], as extremely luminous (M$_B$ ~ -19.5) point sources, offer an attractive route to extragalactic distances. [...] Type II supernovae have a wide range in peak absolute magnitude and can not be treated as standard candles. Distances to individual SNe II can be estimated by means of the expanding photosphere (Baade-Wesselink) and the expanding radiosphere methods, but only elementary applications based on simplifying assumptions have been made to SNe II beyond the Local Group [...]. [Applications] of the method to SN 1987A in the Large Magellanic Cloud [have been] based on detailed calculations [...]. Supernovae of Type Ib, Type Ic, or Type II-L may turn out to be good standard candles but the present samples are small and all three subtypes have the disadvantage of being less luminous than Type Ia."
"Supernovae of Type Ia lack hydrogen lines and helium lines in their optical spectra; during the first month after maximum light they do have a strong absorption feature produced by the red doublet (λ6347, λ6371 Å) of singly ionized silicon. [... One model is that] Type Ia supernovae are the result of the nuclear detonation of a white dwarf which is at or near the Chandrasekhar mass limit [...]. Since such stars are present in the old stellar populations of all galaxies (but see Foss et al. 1991), there is good reason to believe that Type Ia supernovae behave as standard candles."
"Numerous analyses of unrestricted samples of SNe Ia, involving various assumptions about relative distances and interstellar extinction, have produced values of the dispersion in peak M$_{pg}$ or M$_B$ that are generally consistent with [early results having a] determined σ = 0.6 mag. Smaller dispersions of 0.3-0.5 mag have been obtained by restricting the SN Ia samples to those beyond the Local Supercluster [...], in elliptical galaxies [...], in the Virgo cluster [...], and in the Coma cluster [...]. The restriction to remote samples lowers the dispersion by a combination of two effects: (1) the avoidance of the problem of uncertain relative distances for the nearby galaxies, and (2) the tendency to select against SNe Ia that are observationally subluminous (whether they are intrinsically subluminous or are highly extinguished)."
A "small intrinsic dispersion for ordinary SNe Ia that may be ≲ 0.3 mag. Most SNe Ia that are observationally subluminous tend to be red and in inclined disk galaxies, and probably just suffer high interstellar extinction. The peculiar, intrinsically subluminous SN 1991bg also was red. If observationally faint events enter into samples of remote SNe Ia, in spite of the selection against them, they can be recognized by their colors, and, in the case of those that are intrinsically abnormal, by their spectra. There is not yet any solid evidence for anomalously bright SNe Ia."
"From the Hubble diagram for [a] sample of 35 SNe Ia"
    $M_{B}=-18.13+5logh,$
with an error on the first constant of ± 0.08, "where h is the Hubble constant in units of 100 km s$^{-1}$ Mpc$^{-1}$."
"From a sample of 40 SNe"
    $M_{B}=-18.36+5logh,$
with an error on the first constant of ± 0.04.
"The difference is primarily due to the fact that [for the first equation no] corrections for parent-galaxy extinction, while [for the second] an inclination-dependent correction to those SNe Ia in spirals that appear to be subluminous [has been applied]. Perhaps the most accurate available estimate for the intrinsic absolute magnitude is [for] for nine SNe Ia in ellipticals:"
    $M_{B}=-18.33+5logh,$
with an error on the first constant of ± 0.11.
"The standard model for a Type Ia supernova is the thermonuclear disruption of a carbon-oxygen white dwarf that has accreted enough mass from a companion star to approach the Chandrasekhar mass [...]. The nuclear energy released in the explosion unbinds the white dwarf and provides the kinetic energy of the ejected matter, but adiabatic expansion quickly degrades the initial internal energy and the observable light curve is powered by delayed energy input from the radioactive decay of $^{56}$Ni and $^{56}$Co. This model brings with it a self-calibration of the peak luminosity. Arnett (1982a) predicted on the basis of an analytical model that the SN Ia peak luminosity would be equal to the instantaneous decay luminosity of the nickel and cobalt, in which case the peak luminosity follows directly from the ejected nickel mass and the rise time to maximum light. The rise time can be inferred from observation but owing to uncertainties in the physics of the nuclear burning front [...] the amount of synthesized and ejected $^{56}$Ni cannot yet be accurately predicted by theory. [The] nickel mass can be estimated indirectly from spectra and light curves. The more nuclear burning, the more $^{56}$Ni and kinetic energy, and the greater the blueshifts in the spectrum and the faster the decay of the light curve. [From] the blueshifts in the spectra [...] the nickel mass must be in the range 0.4 to 1.4 M$_⊙$ [with] a value of 0.6 M$_⊙$ (as in the particular carbon deflagration model W7 [...]). Adopting a rise time to maximum of 17 ± 3 days and distributing the luminosity according to the observed ultraviolet-deficient flux distribution of SNe Ia, [provides an] estimated M$_B$ = -19.5$^{+0.4}$$_{-0.9}$) at bolometric maximum, which corresponds to M$_B$ = -19.6 with limits of -19.2 and -20.5 at the time of maximum blue light a few days earlier."

## Materials

"Type Ia supernovae result from the explosions of white dwarf stars. These supernovae vary widely in peak brightness, how long they stay bright, and how they fade away, as the lower graph shows. Theoretical models (dashed black lines) seek to account for the differences, for example why faint supernovae fade quickly and bright supernovae fade slowly. A new analysis by the Nearby Supernova Factory indicates that when peak brightnesses are accounted for, as shown in the upper graph, the late-time behaviors of faint and bright supernovae provide solid evidence that the white dwarfs that caused the explosions had different masses, even though the resulting blasts are all “standard candles.”"
"Sixteen years ago two teams of supernova hunters, one led by Saul Perlmutter of the U.S. Department of Energy’s Lawrence Berkeley National Laboratory (Berkeley Lab), the other by Brian Schmidt of the Australian National University, declared that the expansion of the universe is accelerating – a Nobel Prize-winning discovery tantamount to the discovery of dark energy. Both teams measured how fast the universe was expanding at different times in its history by comparing the brightnesses and redshifts of Type Ia supernovae, the best cosmological “standard candles.”"
"These dazzling supernovae are remarkably similar in brightness, given that they are the massive thermonuclear explosions of white dwarf stars, which pack roughly the mass of our sun into a ball the size of Earth. Based on their colors and how fast they brighten and fade away, the brightnesses of different Type Ia supernovae can be standardized to within about 10 percent, yielding accurate gauges for measuring cosmic distances."
"Until recently, scientists thought they knew why Type Ia supernovae are all so much alike. But their favorite scenario was wrong."
"The assumption was that carbon-oxygen white dwarf stars, the progenitors of the supernovae, capture additional mass by stripping it from a companion star or by merging with another white dwarf; when they approach the Chandrasekhar limit (40 percent more massive than our sun) they experience thermonuclear runaway. Type Ia brightnesses were so similar, scientists thought, because the amounts of fuel and the explosion mechanisms were always the same."
“The Chandrasekhar mass limit has long been put forward by cosmologists as the most likely reason why Type Ia supernovae brightnesses are so uniform, and more importantly, why they are not expected to change systematically at higher redshifts.”
“The Chandrasekhar limit is set by quantum mechanics and must apply equally, even for the most distant supernovae.”
"But a new analysis of normal Type Ia supernovae, led by SNfactory member Richard Scalzo of the Australian National University, a former Berkeley Lab postdoc, shows that in fact they have a range of masses. Most are near or slightly below the Chandrasekhar mass, and about one percent somehow manage to exceed it."
"While white dwarf stars are common, it’s hard to get a Chandrasekhar mass of material together in a natural way.”
"A Type Ia starts in a two-star (or perhaps a three-star) system, because there has to be something from which the white dwarf accumulates enough mass to explode."
"Some models picture a single white dwarf borrowing mass from a giant companion."
“The most massive newly formed carbon-oxygen white dwarfs are expected to be around 1.2 solar masses, and to approach the Chandrasekhar limit a lot of factors would have to line up just right even for these to accrete the remaining 0.2 solar masses.”
"If two white dwarfs are orbiting each other they somehow have to get close enough to either collide or gently merge, what Scalzo calls “a tortuously slow process.” Because achieving a Chandrasekhar mass seems so unlikely, and because sub-Chandrasekhar white dwarfs are so much more numerous, many recent models have explored how a Type Ia explosion could result from a sub-Chandrasekhar mass – so many, in fact, that Scalzo was motivated to find a simple way to eliminate models that couldn’t work."
"He and his SNfactory colleagues determined the total energy of the spectra of 19 normal supernovae, 13 discovered by the SNfactory and six discovered by others. All were observed by the SNfactory’s unique SNIFS spectrograph (SuperNova Integral Field Spectrograph) on the University of Hawaii’s 2.2-meter telescope on Mauna Kea, corrected for ultraviolet and infrared light not observed by SNIFS."
"A supernova eruption thoroughly trashes its white dwarf progenitor, so the most practical way to tell how much stuff was in the progenitor is by spectrographically “weighing” the leftover debris, the ejected mass. To do this Scalzo took advantage of a supernova’s layered composition."
"A Type Ia’s visible light is powered by radioactivity from nickel-56, made by burning carbon near the white dwarf’s center. Just after the explosion this radiation, in the form of gamma rays, is absorbed by the outer layers – including iron and lighter elements like silicon and sulfur, which consequently heat up and glow in visible wavelengths."
"But a month or two later, as the outer layers expand and dissipate, the gamma rays can leak out. The supernova’s maximum brightness compared to its brightness at late times depends on how much gamma radiation is absorbed and converted to visible light – which is determined both by the mass of nickel-56 and the mass of the other material piled on top of it."
"The SNfactory team compared masses and other factors with light curves: the shape of the graph, whether narrow or wide, that maps how swiftly a supernova achieves its brightest point, how bright it is, and how hastily or languorously it fades away. The typical method of “standardizing” Type Ia supernovae is to compare their light curves and spectra."
“The conventional wisdom holds that the light curve width is determined primarily or exclusively by the nickel-56 mass, whereas our results show that there must also be a deep connection with the ejected mass, or between the ejected mass and the amount of nickel-56 created in a particular supernova.”
“The white dwarfs exploding as Type Ia supernovae have a range of masses, and the resulting light-curve width is directly proportional to the total mass involved in the explosion.”
"For a supernova whose light falls off quickly, the progenitor is a lot less massive than the Chandrasekhar mass – yet it’s still a normal Type Ia, whose luminosity can be confidently standardized to match other normal Type Ia supernovae."
"The same is true for a Type Ia that starts from a “classic” progenitor with Chandrasekhar mass, or even more. For the heavyweights, however, the pathway to supernova detonation must be significantly different than for lighter progenitors. These considerations alone were enough to eliminate a number of theoretical models for Type Ia explosions."
"Carbon-oxygen white dwarfs are still key. They can’t explode on their own, so another star must provide the trigger. For super-Chandrasekhar masses, two C-O white dwarfs could collide violently, or one could accrete mass from a companion star in a way that causes it to spin so fast that angular momentum supports it beyond the Chandrasekhar limit."
"More relevant for cosmolology, because more numerous, are models for sub-Chandrasekhar mass. From a companion star, a C-O white dwarf could accumulate helium, which detonates more readily than carbon – the result is a double detonation. Or two white dwarfs could merge. There are other surviving models, but the psychological “safety net” that the Chandrasekhar limit once provided cosmologists has been lost. Still, says Scalzo, the new analysis narrows the possibilities enough for theorists to match their models to observations."
“This is a significant advance in furthering Type Ia supernovae as cosmological probes for the study of dark energy, likely to lead to further improvements in measuring distances. For instance, light-curve widths provide a measure of the range of the star masses that are producing Type Ia supernovae at each slice in time, well back into the history of the universe."

## Radiative zones

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority (approximately 80%) of all observed white dwarfs..
DA spectral type, having only hydrogen absorption lines in its spectrum, white dwarf material is initially plasma—a fluid composed of nuclei and electrons. "Helium is unquestionably absent from the atmospheres of ... DA stars, and [there is a] low metal abundance".
"In a DA star the "radiative layer ... lies above the convective zone."
Only a small number of white dwarfs have been examined for fields, and it has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).

## Single white dwarfs

The youngest, hottest WD is very close to 100,000 K, of type DO and is the first single WD recorded as an X-ray source with ROSAT.

## Pulsating white dwarfs

Period: hundreds to thousands of seconds.
Pulsating white dwarf (or pre-white dwarf) are non-radially pulsating stars with short periods of hundreds to thousands of seconds and tiny fluctuations of 0.001 to 0.2 magnitudes including the DAV, or ZZ Ceti, stars, with hydrogen-dominated atmospheres and the spectral type DA; DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB; and GW Vir stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars may be subdivided into DOV and PNNV stars.

## Nova-like stars

"There exist two sub-classes of nova-like stars, the DQ Herculis stars and the AM Herculis stars, whose white dwarfs possess magnetic fields of appreciable strength which dominate the accretion disk and basically all phenomena related to it."

## DQ Herculis stars

The "DQ Herculis stars [are] cataclysmic variables containing an accreting, magnetic, rapidly rotating white dwarf. These stars are characterized by strong X-ray emission, high-excitation spectra, and very stable optical and X-ray pulsations in their light curves."
"The white dwarfs' magnetic moments are in the range 10$^{32}$-10$^{34}$ G cm$^3$, slightly weaker than in AM Her stars but with some probable overlap."
"DQ Hers have broken synchronism [which] is probably [due to] their greater accretion rate and orbital separation."
"X-ray emission from short-period systems appears to be weaker and softer."
Studying "the light curve of the remnant of Nova Herculis 1934 (=DQ Herculis), Merle Walker found strictly periodic variations with the amazingly short period of 71 s (Walker 1954, 1956)."
X-ray source: 2RXP J180730.0+455136
SIMBAD Query : otype='DQ*' lists 49 *s.

## GK Persei

X-ray source: 1A 0327+43, 3A 0327+438, 2E 785, 2E 0327.7+4344, PBC J0331.1+4353, 1RXS J033111.9+435427, SWIFT J0331.1+4355, SWIFT J0331.2+4354.
"Using NASA’s Chandra X-ray Observatory, astronomers [...] pointed the telescope at GK Persei, an object that became a sensation in the astronomical world in 1901 when it suddenly appeared as one of the brightest stars in the sky for a few days, before gradually fading away in brightness."
"GK Persei [is] an example of a “classical nova,” an outburst produced by a thermonuclear explosion on the surface of a white dwarf star, the dense remnant of a Sun-like star."
"Chandra first observed GK Persei in February 2000 and then again in November 2013. This 13-year baseline provides astronomers with enough time to notice important differences in the X-ray emission and its properties."
"This new image [on the right] of GK Persei contains X-rays from Chandra (blue), optical data from NASA’s Hubble Space Telescope (yellow), and radio data from the National Science Foundation’s Very Large Array (pink). The X-ray data show hot gas and the radio data show emission from electrons that have been accelerated to high energies by the nova shock wave. The optical data reveal clumps of material that were ejected in the explosion. The nature of the point-like source on the lower left is unknown."
"The X-ray luminosity of the GK Persei remnant decreased by about 40% over the 13 years between the Chandra observations, whereas the temperature of the gas in the remnant has essentially remained constant, at about one million degrees Celsius. As the shock wave expanded and heated an increasing amount of matter, the temperature behind the wave of energy should have decreased. The observed fading and constant temperature suggests that the wave of energy has swept up a negligible amount of gas in the environment around the star over the past 13 years. This suggests that the wave must currently be expanding into a region of much lower density than before, giving clues to stellar neighborhood in which GK Persei resides."

## AM Herculis stars

In "the AM Herculis stars, the magnetic field of the white dwarf prevents the formation of an accretion disk.
The "AM Herculis stars [are] additionally characterized by spin-orbit synchronism and the presence of strong circular polarization."

## Dwarf novas

In "dwarf novae and nova-like stars the binary system itself is visible, [with] processes which can be traced back directly to the presence of an accretion disk in these systems."
The "primary component of which is a white dwarf."
"The secondary components of cataclysmic variables are cool main sequence stars of spectral type approximately solar of later. Such stars are known to possess fairly active surfaces having large star spots associated with appreciable magnetic activity. Even in single stars the physical structure of such an atmosphere is not well understood, and a consistent theory is still to be developed."
"The first known detection of a dwarf nova [U Geminorum] was recorded by Hind (1856), who describes how on 1855 December 15 he discovered a ninth-magnitude star in a field which he knew well and which he had been monitoring for 5 (!) years."
"Another dwarf nova (we now call it SS Cygni) was detected in 1886; by 1918 the number had increased to eight (Müller and Hartwig, 1918)".
"Currently we know of some 200 dwarf novae and of several hundred nova-like stars and novae."
"Joy pointed out (Joy 1954b) that the spectra of the dwarf novae SS Cyg and RU Peg were rather similar to those of AE Agr and that a physical relationship seemed possible. [In] intervals of about one year AE Aqr underwent outburst-like brightness increases, by one to two magnitudes (Zinner, 1938), that resemble dwarf nova outbursts [...] the explosive U Geminorum requires [...] two stars in a short-period orbit as a necessary, though not sufficient, condition."
EY Cyg is a dwarf nova.
"The most spectacular events in the lives of dwarf novae are the outbursts."
"Instabilities on the surface of the white dwarf lead to nova eruptions."
Dwarf novae are distinct from classical novae in other ways; their luminosity is lower, and they are typically recurrent on a scale from days to decades.
The luminosity of the outburst increases with the recurrence interval as well as the orbital period.

## Recurrent novas

A recurrent nova is produced by a white dwarf star and a red giant circling about each other in a close orbit. About every 20 years, enough material from the red giant builds up on the surface of the white dwarf to produce a thermonuclear explosion. The white dwarf orbits close to the red giant, with an accretion disc concentrating the overflowing atmosphere of the red giant onto the white dwarf. If the white dwarf accretes enough mass to reach the Chandrasekhar limit, about 1.4 solar mass, it may explode as a Type Ia supernova.
V1017 Sgr is a recurrent nova.

## Symbiotic novas

Symbiotic novae are slow irregular eruptive variable stars with very slow nova-like outbursts with an amplitude of between 9 and 11 magnitudes. The symbiotic nova remains at maximum for one or a few decades, and then declines towards its original luminosity. Variables of this type are double star systems with one red giant, which probably is a mira variable, and one white dwarf, with markedly contrasting spectra and whose proximity and mass characteristics indicate it as a symbiotic star. The red giant fills its Roche lobe so that matter is transferred to the white dwarf and accumulates until a nova-like outburst occurs, caused by ignition of thermonuclear fusion. The temperature at maximum is estimated to rise up to 200,000 K, similar to the energy source of novae, but dissimilar to the dwarf novae. The slow luminosity increase would then be simply due to time needed for growth of the ionization front in the outburst.
It is believed that the white dwarf component of a symbiotic nova remains below the Chandrasekhar limit, so that it remains a white dwarf after its outburst.
One example of a symbiotic nova is V1016 Cygni, whose outburst in 1971–2007 clearly indicated a thermonuclear explosion. Other examples are HM Sagittae and RR Telescopii.
"Though typical symbiotic systems consist of a M giant and a white dwarf companion, systems containing a G or K giant ("yellow symbiotic") are known as well."

## Supernovas

"A supernova [in the movie at right] is one way that a star can end its life, exploding in a display of grandiose fireworks. One family of supernovae, called Type Ia supernovae, are of particular interest in cosmology as they can be used as standard candles to measure distances in the Universe and so can be used to calibrate the accelerating expansion that is driven by dark energy. One defining characteristic of Type Ia supernovae is the lack of hydrogen in their spectrum. Yet hydrogen is the most common chemical element in the Universe. Such supernovae most likely arise in systems composed of two stars, one of them being the end product of the life of sun-like stars, or white dwarfs. When such white dwarfs, acting as stellar vampires that suck matter from their companion, become heavier than a given limit, they become unstable and explode."

## Binary stars

A nova-like star is a close binary system with a white dwarf as a primary and a "late-type main-sequence secondary" star filling its Roche lobe. "The secondary loses mass through the inner Lagrangian point and in order to conserve angular momentum the transferred material usually forms an accretion disk around the white dwarf component. A hot spot originates at the place where the mass-transfer stream impacts the disk." In these star systems the degree of magnetic fields ranges from non-magnetic to highly magnetic. "For systems in which the primaries have strong magnetic fields, the process of forming the accretion disk is disturbed. The transferred material is forced to follow the field lines and creates accretion columns near one or both of the white dwarfs magnetic poles."
"The shortest orbital periods imply typical dimensions for the systems to be of the order of a solar diameter."

## PG 1159 stars

PG 1159 stars are a group of very hot, often pulsating WDs for which the prototype is PG 1159 dominated by carbon and oxygen in their atmospheres.
PG 1159 stars reach luminosities of ~10$^{38}$ erg/s but form a rather distinct class. RX J0122.9-7521 has been identified as a galactic PG 1159 star.

## Blue subdwarfs

"The dominant population" in the Palomar-Green Catalog of Ultraviolet Excess Stellar Objects "is that of the hot, hydrogen atmosphere subdwarfs, the sdB stars, which comprise nearly 40 percent of the sample." "The helium-rich sdO stars account for 13% of the total. The hot white dwarfs of spectral types DA, DB, and DO account for 21%, 2.8%, and 1.0% of the sample; cooler DC or DZ white dwarfs add another 1.2%"

## Yellow degenerates

EG 5 is a yellow degenerate. EG 5 is another designation for Van Maanen's star.
Van Maanen's star (van Maanen 2) is a white dwarf that is the third closest to the Sun, after Sirius B and Procyon B, in that order, and the closest known solitary white dwarf.
The optical negative at right was taken earlier than the current coordinates for Van Maanen's star, which are at the center of the negative.
Van Maanen's star has a radius of 9,000 ± 1,400 km. It's effective surface temperature is 6,220 ± 240 K.
Degenerate stars are white dwarfs of spectral luminosity class VII.
Some yellow degenerate stars are of white dwarf spectral type DC (which show no detectable lines) mostly below T$_{eff}$ < 10,000 K.
At left is an Hertzsprung-Russell diagram which shows that luminosity class VII has color class G stars within.
At lower right is a close to true color visual image of GJ 3223, a yellow degenerate white dwarf. It is similar to other luminosity class VII yellow degenerates LHS 3369 and LHS 3399. Each is color class G, often written "g" when referring to white dwarfs.

## Barium stars

Barium stars are spectral class G to K giants, whose spectra indicate an overabundance of s-process elements by the presence of singly ionized barium, Ba II, at λ 455.4 nm. Barium stars also show enhanced spectral features of carbon, the bands of the molecules CH, CN and C$_2$.
Observational studies of their radial velocity suggested that all barium stars are binary stars Observations in the ultraviolet using [the] International Ultraviolet Explorer detected white dwarfs in some barium star systems.
Barium stars are believed to be the result of mass transfer in a binary star system. The mass transfer occurred when the presently-observed giant star was on the main sequence. Its companion, the donor star, was a carbon star on the asymptotic giant branch (AGB), and had produced carbon and s-process elements in its interior. These nuclear fusion products were mixed by convection to its surface. Some of that matter "polluted" the surface layers of the main sequence star as the donor star lost mass at the end of its AGB evolution, and it subsequently evolved to become a white dwarf. We are observing these systems an indeterminate amount of time after the mass transfer event, when the donor star has long been a white dwarf, and the "polluted" recipient star has evolved to become a red giant.
Barium stars exhibit carbon and s-process elements at their surfaces suggesting surface fusion possible during mass transfer or without it.
The mass transfer hypothesis predicts that there should be main sequence stars with barium star spectral peculiarities. At least one such star, HR 107, is known.
Prototypical barium stars include zeta Capricorni, HR 774, and HR 4474.

## CH stars

CH stars are particular type of carbon stars which are characterized by the presence of exceedingly strong CH absorption bands in their spectra. They belong to the star population II, meaning they're metal poor and generally pretty middle-aged stars, and are underluminous compared to the classical C–N carbon stars. Many CH stars are known to be binaries, and it's reasonable to believe this is the case for all CH stars. Like Barium stars, they are probably the result of a mass transfer from a former classical carbon star, now a white dwarf, to the current CH-classed star.
The mass transfer hypothesis may be needed to explain elemental occurrences on their surfaces such as carbon and s-process elements otherwise due to surface fusion.

## AG Draconis

According to SIMBAD, AG Draconis is spectral type K3IIIep, and an X-ray source as detected by the Einstein X-ray Observatory and ROSAT.
"An abundance analysis of the yellow symbiotic system AG Draconis reveals it to be a metal-poor K-giant ([Fe/H] = -1.3) which is enriched in the heavy s-process elements."
"A comparison of the heavy-element abundance distribution in [AG Draconis] with theoretical nucleosynthesis calculations shows that the s-process is defined by a relatively large neutron exposure (τ=1.3 mb$^{-1}$), while an analysis of the rubidium abundance suggests that the s-process occurred at a neutron density of about 2 [x] 10$^8$ cm$^{-3}$."
The "K giant in AG Dra [has a] T$_{eff}$ ~ 4100 - 4400 K. ... [With a best fit to spectroscopic data of T$_{eff}$ = 4300 K.]"
Observed heavy-element abundances may be used "to probe two aspects of the s-process:
* ... determine the neutron exposure τ characterizing the s-process efficiency, and
* using the abundance of Rb, whose s-process abundance is sensitive to neutron density [to] obtain constraints on the s-process neutron density N$_n$."
For any ongoing surface fusion on AG Dra the observed s-process heavy-element abundances probably need no correction. However, without acknowledgment of likely surface fusion, the presence of the s-process elements must be accounted for by some processes associated with inner-core fusion to move s-process elements to the surface, or surface fusion on or above a compact companion.
"The composite nature of the spectrum exhibited by symbiotic stars, consisting of a nebular continuum superimposed on hot and cool stellar continua, is best explained by a binary model ... In such a model [K giants may have larger mass-loss rates], either through a wind or through Roche lobe overflow, [that] falls onto a compact companion (generally a white dwarf), possibly via an accretion disk. The energy released by such an accretion process heats the matter, thereby producing the hot photons [X-rays] observed in symbiotic stars."
"The operation of the s-process is commonly associated with He-burning thermal pulses occurring on the asymptotic giant branch (AGB). As a result of the so-called 'third dredge-up' on the AGB, s-process enriched material is brought to the star's surface ... Barium stars [and] CH stars ... are too hot and of too low a luminosity to have undergone third dredge-up on the AGB. [Because both types] are all single-lined spectroscopic binaries, where the unseen component is almost certainly a white dwarf (WD) ... their chemical peculiarities [are] attributed to mass transfer across the binary system. When the current WD companion of the barium star was a thermally-pulsing AGB star, it transferred s-process- and C-rich material onto its companion, which is now viewed as a barium or CH star."
With a binary model in which the two components have changed roles perhaps more than once, "the observed s-process abundances [must be corrected] for the initial heavy-element distribution [ε$_i$] in AG Dra's unprocessed material. ... plus an s-process enrichment component ε$_s$
    $\epsilon _{obs}=f\epsilon _{s}+(1-f)\epsilon _{i},$
where f is the fraction of the current envelope mass consisting of processed material accreted from the TP-AGB star."
The "initial heavy-element distribution [ε$_i$] in AG Dra's unprocessed material" requires an assumption. Rather than using a solitary KIII of comparable metallicity, "ε$_i$ [is assumed] to be identical to the solar-system heavy-element abundances ... scaled down to AG Dra's metallicity assuming [s/Fe] ≈ 0.0."
Comparisons are made to abundance tables for s-process nucleosynthesis using a 'goodness of fit' criterion. A "single neutron exposure [provides] a better fit ... [yielding] τ = 1.3 mb$^{-1}$".

## SN 2005ke

A Type Ia supernova is an explosion of a white dwarf in orbit around either another white dwarf or a red giant star. The dense white dwarf can accumulate gas donated from the companion. When the dwarf reaches the critical mass of 1.4 M$_⊙$, a thermonuclear explosion ensues. As each Type Ia shines with a known luminosity, Type Ia are called "standard candles" and are used by astronomers to measure distances in the universe.
SN 2005ke is the first Type Ia supernova detected in X-ray wavelengths, and it is much brighter in the ultraviolet than expected.

## Sakurai’s Object

"The object [in the image on the right] is actually a small white dwarf star undergoing a helium flash — one of only a handful of examples of such an event ever witnessed by astronomers."
"Normally, the white dwarf stage is the last in the life cycle of a low-mass star. In some cases, however, the star reignites in a helium flash and expands to return to a red giant state, ejecting huge amounts of gas and dust in the process, before once again shrinking to become a white dwarf."
"It is a dramatic and short-lived series of events, and Sakurai’s Object has allowed astronomers a very rare opportunity to study the events in real time. The white dwarf emits sufficient ultraviolet radiation to illuminate the gas it has expelled, which can just be seen in this image as the ring of red material."

## Mira B

At left is a radiated object, the binary star Mira, and its associated phenomena.
"Ultra-violet studies of Mira by NASA's Galaxy Evolution Explorer (Galex) space telescope have revealed that it sheds a trail of material from the outer envelope, leaving a tail 13 light-years in length, formed over tens of thousands of years. It is thought that a hot bow-wave of compressed plasma/gas is the cause of the tail; the bow-wave is a result of the interaction of the stellar wind from Mira A with gas in interstellar space, through which Mira is moving at an extremely high speed of 130 kilometres/second (291,000 miles per hour). The tail consists of material stripped from the head of the bow-wave, which is also visible in ultra-violet observations. Mira's bow-shock will eventually evolve into a planetary nebula, the form of which will be considerably affected by the motion through the interstellar medium (ISM).
At second right is the only available X-ray image, by the Chandra X-ray Observatory, of Mira A on the right and Mira B (left). "Mira A is losing gas rapidly from its upper atmosphere [apparently] via a stellar wind. [Mira B is asserted to be a white dwarf. In theory] Mira B exerts a gravitational tug that creates a gaseous bridge between the two stars. Gas from the wind and bridge accumulates in an accretion disk around Mira B and collisions between rapidly moving particles in the disk produce X-rays."
Mira A, spectral type M7 IIIe, has an effective surface temperature of 2918–3192. Mira A is not a known X-ray source according to SIMBAD, but here is shown to be one.

## Planetary nebulae

The white dwarf is surrounded by an expanding shell of gas in an object known as a planetary nebula. Planetary nebulae seem to mark the transition of a medium mass star from red giant to white dwarf. X-ray images reveal clouds of multimillion degree gas that have been compressed and heated by the fast stellar wind.

## Trigonometric parallax

"The most reliable independent observational constraint for DA white dwarfs comes from trigonometric parallax measurements. [...] there exists a very good correlation between spectroscopically based photometric distance estimates and those derived from trigonometric parallaxes. Here we compare absolute visual magnitudes instead of distances. We first combine trigonometric parallax measurements with V magnitudes to derive M$_V$ (π) values. We then use the calibration of Holberg & Bergeron (2006) to obtain M$_V$ (spec) from spectroscopic measurements of T$_{eff}$ and log g. [...] the bright white dwarf 40 Eri B for which a very precise trigonometric parallax and visual magnitude have been measured by Hipparcos. These measurements yield M$_V$ = 11.01 ± 0.01, [...] atmospheric parameters determined from the spectroscopic technique remain in excellent agreement with the constraints imposed by trigonometric parallax measurements."
"From the accurate trigonometric parallax [...], the effective temperature (T$_{eff}$ = 10, 900 K) and the stellar radius (R = 0.00368 R$_⊙$) are directly determined from the broad-band spectral energy distribution — the parallax method. The effective temperature and surface gravity are also estimated independently from the simultaneous fitting of the observed Balmer line profiles with those predicted from pure-hydrogen model atmospheres— the spectroscopic method (T$_{eff}$ = 10, 760 K, log g = 9.46). The mass of LHS 4033 is then inferred from theoretical mass-radius relations appropriate for white dwarfs. The parallax method yields a mass estimate of 1.310–1.330M$_⊙$, for interior compositions ranging from pure magnesium to pure carbon, respectively, while the spectroscopic method yields an estimate of 1.318–1.335 M$_⊙$ for the same core compositions. This star is the most massive white dwarf for which a robust comparison of the two techniques has been made."
"LHS 4033 (WD 2349−031) is a white dwarf [that] has also been part of the Luyten Half Second (LHS) survey μ ≥ 0.6′′ yr$^{−1}$ white dwarf sample [...] virtually all of which have been targeted for accurate trigonometric parallaxes at the U.S. Naval Observatory, for purposes of estimating the luminosity function of cool white dwarfs."
Here are the "optical and infrared photometry for LHS 4033":
* V = 16.98 ± 0.02
* B–V = +0.19 ± 0.03
* V – I = +0.07 ± 0.03
* J = 16.97 ± 0.05
* J–H = +0.05 ± 0.07
* H–K = −0.10 ± 0.07
* π$_{abs}$ (mas) = 33.9 ± 0.6
* μ$_{rel}$ (mas yr$^{−1}$) = 701.4 ± 0.2
PA (deg) = 66.3 ± 0.1 Distance (pc) = 29.5 ± 0.5 M$_V$ = 14.63 ± 0.04
"Since the spectral type of LHS 4033 is DA and non-magnetic, the mass may be estimated by fits to the Balmer lines (see, e.g., Bergeron et al. 1992) in a much more rigorous fashion. The surface gravity used with suitable evolutionary models yields independent determinations of the mass and radius. The effective temperature may also be estimated from broad-band photometry once the dominant atmospheric constituent is known. This, along with an accurate trigonometric parallax, permits a different estimate of the luminosity, radius, and mass (Bergeron et al. 2001). While it has been possible to compare the parameter determinations of these methods for limited samples of white dwarfs, it is particularly interesting to do so for a massive star."
"Trigonometric parallax observations were carried out over a 6.05 year interval (1997.76 – 2003.81) using the USNO 1.55 m Strand Astrometric Reflector equipped with a Tek2K CCD camera (Dahn 1997). The absolute trigonometric parallax and the relative proper motion and position angle derived from the 150 acceptable frames [...]. The parallax and apparent V magnitude then yield an absolute magnitude [...]."
Optical "spectroscopy was secured on 2003 October 1 using the Steward Observatory 2.3-m reflector telescope equipped with the Boller & Chivens spectrograph and a UV-flooded Texas Instrument CCD detector. The 4.5 arcsec slit together with the 600 lines mm$^{−1}$ grating blazed at 3568 Å in first order provided a spectral coverage of 3120–5330 Å at an intermediate resolution of ~ 6 Å FWHM. The 3000 s integration yielded a signal-to-noise ratio around 55 in the continuum."
"We first assume log g = 8.0 and determine the effective temperature and the solid angle, which, combined with the distance D obtained from the trigonometric parallax measurement, yields directly the radius of the star R. The latter is then converted into mass using an appropriate mass-radius relation for white dwarf stars. Here we first make use of the mass-radius relation of Hamada & Salpeter (1961) for carbon-core configurations. This relation is preferred to the evolutionary models of Wood (1995) or those of Fontaine et al. (2001), which extend only up to 1.2 and 1.3M$_⊙$, respectively. [...] In general, the value of log g obtained from the inferred mass and radius (g = GM/R$^2$) will be different from our initial assumption of log g = 8.0, and the fitting procedure is thus repeated until an internal consistency in log g is achieved. The parameter uncertainties are obtained by propagating the error of the photometric and trigonometric parallax measurements into the fitting procedure."
Our "spectroscopic solution T$_{eff}$ = 10, 760 ± 150 K and log g = 9.46 ± 0.04, which translates into M = 1.335± 0.011 and R = 0.00358± 0.00019 R$_⊙$ using the Hamada-Salpeter mass-radius relation for carbon-core configurations, is in excellent agreement with the solution obtained with the photometry and trigonometric parallax method. This is arguably the most massive white dwarf subjected to a rigorous mass determination [...]. Note that despite the extreme surface gravity of LHS 4033, the Hummer-Mihalas formalism used in the line profile calculations remains perfectly valid, since the density at the photosphere remains low (ρ ~ 10$^{−5}$ g cm$^{−3}$) as a result of the high opacity of hydrogen at these temperatures."
The "parallax method with the Mg configurations yields a mass of 1.310 M$_⊙$ (instead of 1.330 when C configurations are used), while the spectroscopic method yields a mass of 1.318 M$_⊙$ (instead of 1.335 M$_⊙$)."
"Observations of [SSSPM J2231-7514 and SSSPM J2231-7515 imaged at right in the violet band] were carried out using the Danish Faint Object Spectrograph (DFOSC) on the Danish 1.54m Telescope in La Silla. Data were taken during the nights starting June 19-20, 2001 (local time) in relatively good almost photometric conditions."
For the blue (B) band, "[A grism was] used, number-7 (3800-6800°A, 5250°A blaze, 1.65°A/pixel resolution – a 1800s and a 1300s spectroscopic observation). Two spectrophotometric standards were taken using [the] grism, LTT 7379 and LTT 9239 [...], as well as a large number of zero, flat (both for imaging and spectroscopy for all grisms used) and arc-lamp (for both grisms) calibration frames. For broad-band photometric calibrations, Landolt standard fields (Landolt 1992) were observed repeatedly [...] a spectrum of one of the objects, SSSPM J2231-7515, which was discovered independently, had already been observed half a year earlier. The spectrum of this star was observed with the EFOSC spectrograph on the ESO 3.6m telescope during the night of 2 December 2000. A slit width of 1.5 arcsec was used with grism number 1 (3185-10940°A, 4500°A blaze, 6.30°A/pixel resolution) for three exposures of 300s each."
A "wide pair (93 arcsec angular separation) of extremely cool (T$_{eff}$ < 4000 K) white dwarfs [have] a very large common proper motion (~1.9 arcsec/yr). The objects were discovered in a high proper motion survey in the poorly investigated southern sky region with δ < −60° using SuperCOSMOS Sky Survey (SSS) data. Both objects, SSSPM J2231-7514 and SSSPM J2231-7515, show featureless optical spectra. Fits of black-body models to the spectra yield effective temperatures of 3810 K and 3600 K, respectively for the bright (V = 16.60) and faint (V = 16.87) component. Both degenerates are much brighter than other recent discoveries of cool white dwarfs with comparable effective temperatures and/or [blue] B$_J$ − R colours."
"After measuring photometric zeropoints in 6 standard fields (Landolt 1992), we adopted a zeropoint of 24.66 (for 1s exposure time and airmass of 1.45 – the airmass of our acquisition frames) in the Bessel V-band. Examination of the measured zeropoints shows that conditions were very close to photometric (with a hint of very weak cirrus in some cases). Using this zeropoint, we measured the (Vega) magnitudes of the two objects to be 16.60 and 16.87 in V (Bessel). We also measured the magnitude of the extra object, accidentally landing on our 2 arcsec wide slit [...] to be 16.86 [...]. Instrumental magnitude errors are small (1-2%), the main source of error is the determination of the zeropoint. We therefore estimate the overall accuracy of these magnitudes to be better than 5%."
"Spectroscopic frames (science and standard fields and calibration frames) were also bias and zero subtracted, trimmed and flatfielded (using different flat-field frames for the two grisms). The only complication was the removal of focal plane geometric distortions to improve the sky subtraction. This was done by tracing lines in the wavelength calibration frames. A smooth distortion map was fitted to the results and was applied to all frames."
"All objects on the slit were traced along the dispersion axis. Sky subtraction was done through fitting in a 35 arcsec wide band, centered on the object, excluding the central 16 arcsec region. A relatively wide aperture was defined for all objects, which includes all the flux (but degrades the S/N slightly). Object spectra were ‘optimally’ extracted within this aperture, with both cosmic-ray removal (based on photon statistics) and a weighted sum based on estimated signal-to-noise ratio."
"Wavelength calibration was done using He-Ne arc exposures. For the number-7 grism (bluer, higher resolution) the procedure worked quite well (0.06Å RMS, 0.15Å maximum deviation) in the wavelength range 3889-6717Å."
"A detailed photometric and spectroscopic analysis of all known cool white dwarfs (4000 K< T$_{eff}$ < 12000 K) with trigonometric parallax measurements [exists]. [One] cool white [dwarf] with [an] effective [temperature] below 4000 K [...], WD 0346+246, has a trigonometric parallax measurement"
"With the [...] temperatures [...] of 3810 K and 3600 K (3100 K to 3800 K), the newly discovered objects are comparable to the coolest known white dwarf WD0346+246 with 3750 K [...] for which a trigonometric parallax of 36±5 mas (28±4 pc) has been measured".
"If we assume our objects to have the same physical properties (temperature, mass, chemical composition) as WD0346+246, we can estimate their distance from a comparison of their apparent V magnitudes. With V = 19.06 [...], WD0346+246 is more than two magnitudes fainter than our objects (16.60 and 16.87), and consequently we get distance estimates of 9 pc and 10.2 pc. These distance estimates have the same relative uncertainty as for the comparison object, i.e. ±1.3 pc and ±1.5 pc, respectively, and rely on the assumption of identical physical properties, which is unlikely to be the case."
As of 2002, "there are only 11 cool white dwarfs with T$_{eff}$ < 5000 K and trigonometric parallaxes of less than 25 pc [...]. All presently known or suspected degenerates with T$_{eff}$ < 4000 K are at trigonometric or photometric distances of more than 25 pc".

## Gaia

"All-sky view [page top] showing the position and brightness of some 230 000 white dwarfs discovered with ESA's Gaia satellite. White dwarfs are the remnants left behind when medium-sized stars like our Sun reach the end of their lives."
"Prior to the second Gaia data release, made public in 2018, only about 30 000 white dwarfs had been discovered. Using date from Gaia, 486 641 white dwarf candidates have been detected, with 260 000 of these being high-confidence candidates, as reported in a catalogue compiled by Nicola Pietro Gentile Fusillo and collaborators. Discovering more of these mysterious objects enables us to gain better knowledge of their properties, improving our understanding of how they fit into the overall picture of stellar evolution."
"Thanks to Gaia's incredible ability to pinpoint the 3D position of huge numbers of stars, not only are we finding many more white dwarfs than we previously knew to exist, but our knowledge of their distances is hugely improving. This allows us to decipher other properties of these stars better than we ever could in the past."
"The huge number of newly-discovered white dwarfs also means that many new classes and configurations have been revealed that didn't appear in the original 30 000. These include the first triple white dwarf system described [...]: the triplet features three white dwarfs of the same age, which is strange if we consider that these objects are the relics of dead stars and therefore should all have formed at different times."
"The Gaia catalogue includes lots of particularly cool white dwarfs, usually difficult to spot because they are so dim [...]."
"One of the most interesting discoveries to come out of this data release [...] was the revelation that the cores of white dwarfs turn solid as they cool down, effectively forming extremely giant cosmic diamonds that are a million times denser than the Earth-based diamonds we are used to. This phenomenon was predicted 50 years ago by Hugh van Horn but little was understood about the process until Gaia data indicated white dwarfs release latent heat as they transform into crystals, slowing down the cooling process temporarily. The results suggest that after the Sun becomes a white dwarf in five billion years, it will take another five billion years for its core to turn solid."
"The majority of white dwarfs are made up of mostly one element – typically hydrogen or helium, and in rare cases, carbon. But some have thick atmospheres, which can be polluted with heavier elements such as calcium, magnesium and iron. The new data contains information on previously-unknown polluted white dwarfs [...]; these objects are interesting because the polluting elements are thought to come from surrounding dusty disks or even unseen exoplanets or asteroids that have merged with the white dwarfs' outer layers."
"Many new extremely low-mass white dwarfs have also been discovered in the new catalogue [...]. The origin of these low-mass white dwarfs remains a mystery, and they don't fit with current models of stellar evolution. Finding more of them could help us better understand stars overall."
"Gaia is enabling astronomers to study pulsating white dwarfs in greater detail. This special variety of white dwarf allows astronomers to carry out 'asteroseismology' research and study their interiors, just like seismology on Earth is used to understand the interior of our planet. [Others] used data from Gaia's second release to investigate the interaction between a pulsating white dwarf and its red-dwarf companion. Another [...] looked for pulsations in white dwarf companions to millisecond pulsars, which are rapidly rotating, highly magnetised neutron stars – the endpoint of massive stars – and found pulsating emission from one such pair."
"This diagram, known as Hertzsprung-Russell diagram (after the astronomers who devised it in the early 20th century to study stellar evolution) combines information about the brightness, colour and distance of more than 15 000 white dwarfs within 300 light years of Earth. The data, shown as black dots, are from the second release of ESA's Gaia satellite."
"In the diagram, blue lines show the cooling sequence of white dwarfs with different masses – 0.6, 0.9, and 1.1 times the mass of the Sun, respectively – as predicted from theoretical models."
"Analysing the Gaia data, scientists found a pile-up of white dwarfs of certain colours and luminosities (highlighted with orange lines) that were otherwise not linked together in terms of their evolution. They realised that this pile-up was not a distinct population of white dwarfs, but the effect of the cooling and crystallisation of the originally hot matter inside the star's core."
"This is the first evidence of crystallisation inside white dwarfs, a process that has been predicted in 1968."