# Phillips relationship

In astrophysics, the Phillips relationship is the relationship between the peak luminosity of a Type Ia supernova and the speed of luminosity evolution after maximum light. The relationship was independently discovered by the American statistician and astronomer Bert Woodard Rust and the Soviet astronomer Yury Pavlovich Pskovskii in the 1970s.[1][2][3] They found that the faster the supernova faded from maximum light, the fainter its peak magnitude was. As a main parameter characterizing the light curve shape, Pskovskii used β, the mean rate of decline in photographic brightness from maximum light to the point at which the luminosity decline rate changes. β is measured in magnitudes per 100-day intervals.[4] Selection of this parameter is justified by the fact that, at that time, the probability of discovering a supernova before the maximum light, and obtain the full light curve, was small. Moreover, the existing light curves were mostly incomplete. On the other hand, to determine the decline after the maximum light was rather simple for most observed supernovae.

In the early 1980s CCD cameras appeared, and the number of SNe discoveries increased substantially. Moreover, the probability of discovering SNe before they reached maximum light and following their brightness evolution longer also increased. The first light curves of SNe Ia obtained using CCD photometry showed that some supernovae had faster decline rates than others. Later, the low luminosity Ia SN 1991bg with a fast decline rate was discovered. All this motivated the American astronomer Mark M. Phillips to revise this relationship precisely during the course of the Calán/Tololo Supernova Survey.[5] The correlation had been difficult to prove because Pskovskii's slope (β) parameter was difficult to measure with precision in practice, a necessary condition to prove the correlation. Rather than trying to determine the slope, Phillips used a simpler and more robust procedure that consisted in "measuring the total amount in magnitudes that the light curve decays from its peak brightness during some specified period following maximum light." It was defined as the decline in the B-magnitude light curve from maximum light to the magnitude 15 days after B-maximum, a parameter he called ${\displaystyle \Delta {m}_{15}}$. The lead sentence of the final paragraph of Phillips' paper acknowledges "I am indebted to George Jacoby for suggesting the ${\displaystyle \Delta {m}_{15}}$ parameter as an alternative to Pskovskii's β." The relation states that the maximum intrinsic B-band magnitude is given by

${\displaystyle M_{\mathrm {max} }(B)=-21.726+2.698\Delta m_{15}(B).}$[6]

Phillips dedicated the journal article confirming Yuri Pskovskii's proposed correlation to Pskovskii, who died a few weeks after Phillips' evidence confirming the relationship was published.

It has been recast to include the evolution in multiple photometric bandpasses, with a significantly shallower slope[7][8] and as a stretch in the time axis relative to a standard template.[9] The relation is typically used to bring any Type Ia supernova peak magnitude to a standard candle value.

The original ${\displaystyle \Delta {m}_{15}}$ definition drawn by Phillips around 1995.

## References

1. ^ Rust, B. W. "The Use of Supernovae Light Curves for Testing the Expansion Hypothesis and Other Cosmological Relations" (PDF). [PhD thesis, University of Illinois].
2. ^ Pskovskii, Yu. P. (1977). "Light curves, color curves, and expansion velocity of type I supernovae as functions of the rate of brightness decline". Soviet Astronomy. 21: 675. Bibcode:1977SvA....21..675P.
3. ^ Pskovskii, Yu. P. (1984). "Photometric classification and basic parameters of type I supernovae". Soviet Astronomy. 28: 658–664. Bibcode:1984SvA....28..658P.
4. ^ Pskovskii, Yu. P. (1967). "The Photometric Properties of Supernovae". Soviet Astronomy. 11: 63–69. Bibcode:1967SvA....11...63P.
5. ^ Phillips, M. M. (1993). "The absolute magnitudes of Type IA supernovae". Astrophysical Journal Letters. 413 (2): L105–L108. Bibcode:1993ApJ...413L.105P. doi:10.1086/186970.
6. ^ Rosswog; Bruggen. High Energy Astrophysics.
7. ^ Hamuy, M., Phillips, M. M., Maza, J., Suntzeff, N. B., Schommer, R. A., & Aviles, R. 1995, Astronomical Journal, 109, 1
8. ^ Riess, A. G., Press, W. H., & Kirshner, R. P. 1996, AstrophysicsJournal, 473, 88
9. ^ Perlmutter, S. A., & et al. 1997, NATO ASIC Proc. 486: Thermonuclear Supernovae, 749
Calán/Tololo Survey

The Calán/Tololo Supernova Survey was a supernova survey that ran from 1989-1995 at the University of Chile and the Cerro Tololo Inter-American Observatory to measure a Hubble diagram out to redshifts of 0.1. It was founded by Mario Hamuy, Jose Maza, Mark M. Phillips, and Nicholas B. Suntzeff in 1989 out of discussions at the UC Santa Cruz meeting on supernovae on how to improve the Hubble diagram using Type Ia supernovae. It was also motivated by the suggestion of Allan Sandage to restart a supernova survey after the Sandage and Tammann survey failed due to poor quality photographic plates in 1986. The Survey built on the original supernova survey of Maza done at the f/3 Maksutov Camera at the Cerro Roble Observatory of the University of Chile between 1979 and 1984. The Survey used the CTIO Curtis Schmidt telescope with IIa-O photographic plates, each plate covering a field of 25 sq-deg on the sky. The plates were developed and sent to Santiago Chile the next morning, and searched for supernovae at the Department of Astronomy at the University of Chile. Any supernova candidates were then observed the next night using the 0.9m telescope at CTIO with a CCD camera. This was one of the first studies done in astronomy where the telescope time was scheduled to observe objects not yet discovered.

The survey discovered 50 supernovae between 1990 and 1993, of which 32 were Type Ia supernovae. The survey provided a uniform photometric and spectroscopic dataset of all classes of supernovae, which led to the discovery of a method of using Type Ia supernovae as standard candles, the Phillips relationship, as well as providing data for a Hubble diagram of Type II supernovae using the Expanding Photosphere method.The calibration of Type Ia supernovae as standard candles led to the precise measurements of the Hubble Constant H0 and the deceleration parameter q0, the latter indicating the presence of a dark energy or cosmological constant dominating the mass/energy of the Universe.

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Mark M. Phillips

Mark M. Phillips (born March 31, 1951) is an American astronomer who works on the observational studies of all classes of supernovae. He has worked on SN 1986G, SN 1987A, the Calán/Tololo Supernova Survey, the High-Z Supernova Search Team, and the Phillips relationship. This relationship has allowed the use of Type Ia supernovae as standard candles, leading to the precise measurements of the Hubble constant H0 and the deceleration parameter q0, the latter implying the existence of dark energy or a cosmological constant in the Universe.

He is the past director of Cerro Tololo Inter-American Observatory of the National Optical Astronomy Observatory and is the Associate Director and Carnegie Staff Member at Las Campanas Observatory in Chile, part of the Observatories of the Carnegie Institution for Science.

He received his undergraduate degree in Astronomy from San Diego State University in 1973, and his Ph.D., also in Astronomy & Astrophysics in 1977, from the University of California, Santa Cruz and Lick Observatory where he was a student of Professor Donald Osterbrock. After graduate school, he was a postdoc at CTIO, then at Anglo-Australian Observatory, moving back to Chile in 1982 to become a staff astronomer at CTIO.

In addition to his work on supernovae, he has also worked extensively on the spectroscopic studies of Active Galactic Nuclei.

Stagflation

In economics, stagflation, or recession-inflation, is a situation in which the inflation rate is high, the economic growth rate slows, and unemployment remains steadily high. It presents a dilemma for economic policy, since actions intended to lower inflation may exacerbate unemployment, and vice versa.

The term, a portmanteau of stagnation and inflation, is generally attributed to Iain Macleod, a British Conservative Party politician who became Chancellor of the Exchequer in 1970. Macleod used the word in a 1965 speech to Parliament during a period of simultaneously high inflation and unemployment in the United Kingdom.

Warning the House of Commons of the gravity of the situation, he said: "We now have the worst of both worlds—not just inflation on the one side or stagnation on the other, but both of them together. We have a sort of "stagflation" situation. And history, in modern terms, is indeed being made."Macleod used the term again on 7 July 1970, and the media began also to use it, for example in The Economist on 15 August 1970, and Newsweek on 19 March 1973.

John Maynard Keynes did not use the term, but some of his work refers to the conditions that most would recognise as stagflation. In the version of Keynesian macroeconomic theory that was dominant between the end of World War II and the late 1970s, inflation and recession were regarded as mutually exclusive, the relationship between the two being described by the Phillips curve. Stagflation is very costly and difficult to eradicate once it starts, both in social terms and in budget deficits.

Supernova

A supernova ( plural: supernovae or supernovas, abbreviations: SN and SNe) is a transient astronomical event that occurs during the last stages of the life of a massive star or white dwarf, whose destruction is marked by a titanic explosion. This causes the sudden appearance of a "new" star, which then fades over several weeks or months or years.

Supernovae are more energetic than novae. In Latin, nova means "new", referring astronomically to what appears to be a temporary new bright star. Adding the prefix "super-" distinguishes supernovae from ordinary novae, which are far less luminous. The word supernova was coined by Walter Baade and Fritz Zwicky in 1931.

Only three Milky Way, naked-eye supernova events have been observed during the last thousand years, though many have been observed in other galaxies. The most recent directly observed supernova in the Milky Way was Kepler's Supernova in 1604, but the remnants of recent supernovae have also been found. Observations of supernovae in other galaxies suggest they occur in the Milky Way on average about three times every century. These supernovae would almost certainly be observable with modern astronomical telescopes.

Theoretical studies indicate that most supernovae are triggered by one of two basic mechanisms: the sudden re-ignition of nuclear fusion in a degenerate star or the sudden gravitational collapse of a massive star's core. In the first instance, a degenerate white dwarf may accumulate sufficient material from a binary companion, either through accretion or via a merger, to raise its core temperature enough to trigger runaway nuclear fusion, completely disrupting the star. In the second case, the core of a massive star may undergo sudden gravitational collapse, releasing gravitational potential energy as a supernova. While some observed supernovae are more complex than these two simplified theories, the astrophysical mechanics have been established and accepted by most astronomers for some time.

Supernovae can expel several solar masses of material at speeds up to several percent of the speed of light. This drives an expanding and fast-moving shock wave into the surrounding interstellar medium, sweeping up an expanding shell of gas and dust observed as a supernova remnant. Supernovae are a major source of elements in the interstellar medium from oxygen through to rubidium. The expanding shock waves of supernova can trigger the formation of new stars. Supernova remnants might be a major source of cosmic rays. Supernovae might produce strong gravitational waves, though, thus far, the gravitational waves detected have been from the merger of black holes and neutron stars.

The Flame Within (film)

The Flame Within is a 1935 American drama film written and directed by Edmund Goulding. The film stars Ann Harding, Herbert Marshall, Maureen O'Sullivan, Louis Hayward, Henry Stephenson and Margaret Seddon. The film was released on May 17, 1935, by Metro-Goldwyn-Mayer.

Type Ia supernova

A type Ia supernova (read "type one-a") is a type of supernova that occurs in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white dwarf.Physically, carbon–oxygen white dwarfs with a low rate of rotation are limited to below 1.44 solar masses (M☉). Beyond this, they reignite and in some cases trigger a supernova explosion. Somewhat confusingly, this limit is often referred to as the Chandrasekhar mass, despite being marginally different from the absolute Chandrasekhar limit where electron degeneracy pressure is unable to prevent catastrophic collapse. If a white dwarf gradually accretes mass from a binary companion, the general hypothesis is that its core will reach the ignition temperature for carbon fusion as it approaches the limit.

However, if the white dwarf merges with another white dwarf (a very rare event), it will momentarily exceed the limit and begin to collapse, again raising its temperature past the nuclear fusion ignition point. Within a few seconds of initiation of nuclear fusion, a substantial fraction of the matter in the white dwarf undergoes a runaway reaction, releasing enough energy (1–2×1044 J) to unbind the star in a supernova explosion.This type Ia category of supernovae produces consistent peak luminosity because of the uniform mass of white dwarfs that explode via the accretion mechanism. The stability of this value allows these explosions to be used as standard candles to measure the distance to their host galaxies because the visual magnitude of the supernovae depends primarily on the distance.

In May 2015, NASA reported that the Kepler space observatory observed KSN 2011b, a type Ia supernova in the process of exploding. Details of the pre-nova moments may help scientists better judge the quality of Type Ia supernovae as standard candles, which is an important link in the argument for dark energy.

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