Astronomy

Use of type-I a supernovae as standard candle

Use of type-I a supernovae as standard candle


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Why only type -Ia supernovae are used as standard candle to calculate age of universe and why not type II, type Ib, type 1c ?


A type 1a supernova forms when a white dwarf grows through accretion to a certain size, at which it becomes unstable. This means that the precursor object is always a white dwarf of mass 1.39 solar masses. As the precursor object is always of the same type and the same size, the supernova is thought to be the same brightness.

On the other hand, type II supernovae form from the collapse of giant stars. The precursor object can have a range of masses from about 10 Solar masses, to a maximum of over 100. The brightness of the supernova depends on the mass of the precursor (and other factors such as the metallicity) and so type II supernovae are not all equally bright.

The other types also have precursors which vary in size or other factors, only type 1a supernovae are thought to always have a white dwarf of mass 1.39 as a standard precursor, so only type 1a are suitable as a standard candle.


Are Type Ia Supernovae Standard Candles?

The use of standard candles for distance measurements is wide spread. Yet, we currently do not know a pure standard candle in astronomy. The concept of standard candles involves not only the secure establishment of a unique luminosity but also a clear observational distinction of the objects as a class. Even Type Ia supernovae, whose maximum luminosity shows amongst the smallest scatter known, need to be normalised to provide accurate distances. Without this normalisation the cosmological claims based on supernovae would not be possible. With a careful normalisation Type Ia supernovae are the best known distance indicators for cosmology to date. This is most easily shown by the small dispersion around the expansion line in the Hubble diagram. Problems with the empirical normalisation remain and a theoretical understanding of this normalisation is missing. This has direct ramifications on systematic uncertainties when deriving cosmological implications from Type Ia supernovae. Improving the understanding of supernova physics is now the prime task to sharpen this tool of observational cosmology. Once the explosion mechanism is revealed a serious discussion of possible evolutionary effects in Type Ia supernovae can start.

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Use of type-I a supernovae as standard candle - Astronomy

Mar 16, 2021

SN 2011fe in the galaxy M101 is a Type Ia supernova, the type used as standard candles in this study. This composite image was created from data taken by Las Cumbres Observatory and the Palomar Transient Factory. Credit: BJ Fulton / LCO / PTF.

One of the longest standing and most controversial questions in astronomy is — how fast is the universe expanding today? New work, including measurements made by Las Cumbres Observatory, has applied new techniques to the problem and found a surprising answer.

Astronomers call the local expansion rate of the universe the Hubble constant, H0, (pronounced H-naught). Measurements have gotten extremely precise in recent years — some claim to have measured it to better than a few percent. Different groups have come up with results that vary by more than 10% — far larger than the claimed uncertainty. Complicating matters, the measurements seem to cluster high or low depending on where they are made in the universe. The Hubble constant measured from nearby supernovae tends to be high, while measurements built up from the afterglow of the Big Bang — the Cosmic Microwave Background — give a low value. Some have argued that this is a crisis for the field, one requiring “new physics.” Perhaps an unknown property of Dark Energy is causing the local expansion rate of the universe to be highly sensitive to the distance at which it is measured. Others argue that there must be some kind of mistake in building the “distance ladder” — in using one set of distance indicators to calibrate another.

The new study, released March 12 in the journal Astronomy & Astrophysics, involves an international team of scientists led by Nandita Khetan, a PhD student at the Gran Sasso Science Institute in Italy, and an associate researcher at the Istituto Nazionale di Fisica Nucleare. It used the Surface Brightness Fluctuations of galaxies to calibrate the distances to nature’s best distance indicators — Type Ia supernovae. Type Ia supernovae are used as “standard candles” to map out distances in the universe. They were used to determine that the universe was accelerating in its expansion, leading to the discovery of Dark Energy that resulted in the 2011 Nobel Prize in Physics.

The standard candle method relies on measuring the apparent brightness of a distant known light, say a 100W light bulb, and using the difference between the apparent and intrinsic brightness to work out how far away the light is. This requires knowing the intrinsic power output —the wattage — of the “standard candle,” something that is unknown for Type Ia supernovae. Astronomers have to calibrate their brightness using a handful of nearby supernovae in galaxies with distances determined by other means. Traditionally this has been done with galaxies whose distances are known from observations of Cepheid variable stars. The new paper research swaps out the Cepheids for a different fundamental calibrator, Surface Brightness Fluctuations. This measures the resolution of individual stars in different galaxies, since stars tend to blur together the farther away a galaxy is. It is similar to how a street will appear rough when photographed up close, but smooth when seen from farther away.

The new study found an answer that is in between the two discordant values of the expansion rate of the universe. This argues that perhaps new physics isn’t needed after all. It may be that previous researchers overestimated the precision of their studies.

Andy Howell, a staff scientist at Las Cumbres Observatory, and adjunct faculty at the University of California Santa Barbara, is the Principal Investigator of the Global Supernova Project, a worldwide collaboration that provided some of the observations of supernovae used in the study. He explains, “At a recent conference about this Hubble Constant crisis, after each speaker walked through their methodology, I couldn’t find any problems with what they were doing. I started to question whether we do need new physics to explain the different Hubble constants. But now we, like several studies before ours, found an answer in the middle. Maybe there’s some weirdness to some of the other measurements that we don’t fully understand. That’s more comforting, because you don’t want to upend our understanding of physics unless you have to.”

The new work does not undermine the discovery or characterization of Dark Energy, since that relies on only relative, not absolute, measurements of supernovae and has been verified by other means.

The new supernova observations were obtained with Las Cumbres Observatory’s worldwide network of robotic telescopes, specifically designed to study time-variable phenomena like supernovae. Howell adds, “Supernovae are hard to observe, because you need just a little bit of telescope time per night, over months. But a robotic telescope network is perfect for this — nobody has to travel — the telescopes can make the observations wherever and whenever they are needed. This is what we built Las Cumbres Observatory for and I’m delighted to see it being used to refine our understanding of the universe.”

The study “A new measurement of the Hubble constant using Type Ia supernovae calibrated with surface brightness fluctuations” involves an international team of scientists with expertise in supernova observations, Surface Brightness Fluctuations, and theory working, at the Gran Sasso Science Institute, INAF, INFN, DARK-Niels Bohr Institute, University of Copenhagen, Centre for Astrophysics and Supercomputing, Swinburne University, Las Cumbres Observatory, UC Santa Barbara, and UC Davis.


Faint Supernovae Remain Unexplained

By: Camille M. Carlisle July 10, 2008 4

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The joy — and the frustration — of astronomy is that so much remains that we don’t know. Supernovae, for example, are phenomena that astronomers like to think they understand. But Mansi Kasliwal (Caltech) and her colleagues have observed something strange: a supernova called SN2007ax, which they claim is the faintest and reddest Type Ia supernova yet observed. Using optical, ultraviolet, and near-infrared observations, they conclude that supernovae like SN2007ax prove that we still do not fully grasp the scope of physical processes involved in exploding stars.

SN1604, or Kepler's Supernova remnant, has long sparked debate amongst astronomers as to whether it actually was a Type Ia supernova. This image combines data from three space-based telescopes: the Chandra X-ray Observatory, the Spitzer Space Telescope and the Hubble Space Telescope.

In this NASA illustration, a close pair of orbiting white dwarf stars throw off spiral waves of gravitational radiation.

results will appear in the Astrophysical Journal Letters.


Standard candles


To measure the expansion of the Universe, cosmologists utilize standardized references. One such standard reference is standard candles. These are objects where the intrinsic luminosity of the object is known – that is, how much light/radiation is emitted by the object at source. By comparing this amount with how much light from the objects reaches us, the apparent luminosity, we get a measure of how far away the object is from us. Combined with an estimate of the relative size of the Universe at the time the object emitted the light, we can then map the expansion history of the Universe.

Two key aspects of establishing a standard candle is the class definition (how to define and select the objects) and calibration (how to bring the objects to a common reference point). The class definition must be restricted enough to provide something standardizable, and calibration must be accurate enough to provide good distance measurements.

The most important standard candles today are Type Ia supernovae, whose pioneering use led to the discovery of dark energy, based on the Phillips relationship discovered by Mark M. Phillips in 1993. The first discovered standard candles are cepheid variables, stars whose period of variation in luminosity can be translated into a distance. These were first identified by Henrietta Swan Leavitt in 1908, and more conclusively established in 1912. Thanks to the cepheid standard candles, Edwin Hubble could later measure the distance to nebulae and show that they were located outside the Milky Way. Thereby, “the Great Debate” on whether the Milky Way constitutes all of the Universe or whether there are other distant galaxies was settled.


Supernovae as near-infrared Standard Candles: Measuring H0

The field of precision cosmology is at a fascinating juncture, as elaborated in Astrobites’ reporting of the subject in the last few months. Various measurements of H0 – the expansion rate of the universe – are at disagreements with each other. In the tale of performing H0 measurements with a variety of probes, today’s bite touches upon the local and ‘direct’ measurements of H0 from supernovae i.e. exploding stars!

Fig 1. SN 1994D (lower left), a Type Ia supernova in all its glory, accompanying its host galaxy NGC 4526 (Photo Credit: NASA/ESA – HST)

Supernovae and the distance ladder

Supernovae are a crucial component of the cosmic distance ladder. Astrophysicists use direct measurements of nearby objects (e.g. stars) to quantify distances of intermediate objects, to quantify distances of intermediate objects (e.g. variable stars like RR Lyrae and Cepheid variables), to quantify distances to far-away objects, and so on. One of the highest rungs in this ladder are Type Ia supernovae (SNe). These supernovae (SNe) form from a fixed known mechanism (a binary white dwarf star accreting matter from a companion star and exploding at a fixed mass and ‘brightness’), which makes them reliable distance indicators. We know what brightness to expect from these SNe if they exploded next door, and their actual observed brightness shall tell us exactly how far they are! This is called being a standard candle. Type Ia SNe are standard candles. Well, sort of.

Fig 2. Supernovae light curves – magnitude vs time. B band light curves have a single peak magnitude, while J band light curves have two. (Credit: Swinburne Astronomy/COSMOS)

Photometrically, most work done in the field of supernova cosmology revolves around taking images of SNe in ‘optical’ wavelength bands (e.g. B, V filters) over time. Plotting absolute magnitudes (or luminosity/ intrinsic brightness) of an observed Type Ia supernova vs time in different wavelength ranges looks something like Fig 2 (Going redder as we go up in the light curve plot). It can be seen that observing Type Ia SNe in bluer bands like B (

4500 Angstroms) generally shows one luminosity peak, while looking in redder bands like J (

12000 Angstroms), we see two peaks.

Keeping this in mind, it is important to discuss the various caveats that go into performing distance measurements via SNe:

  1. It is generally observed that B band peak luminosities vary much more from supernova to supernova than J band peak luminosities. This ‘scatter’ subsequently propagates as systematic uncertainty that directly affects cosmology measurements i.e. our constraints on H0.
  2. Also, B band peak luminosities suffer from more reddeningthan J band peak luminosities i.e. more of their blue light gets scattered. This is another systematic! – the relationship between the peak luminosity and the width of the peak in Type Ia SNe – is a bigger source of uncertainty in B band peak luminosities than J band peak luminosities.

This is where today’s paper comes into the picture.

This work : Supernovae as near-infrared standard candles

Dhawan et al. suggest using J band peak magnitudes (or magnitudes from other near-infrared wavelength bands) to quantify distances to these SNe (see a treatment of luminosity distances and H0 in the links at the beginning). Due to lower intrinsic systematics in J band peak magnitudes, a supernova in near-infrared (J, H) could potentially act as more standard of a candle than in the optical (B, V). This implies that near-infrared light curves could complement or even improve the H0 measurements, using Type Ia SNe as near-infrared standard candles.

Fig 3. Two Type Ia Supernovae light curves in J-band – magnitudes vs time – used in this work. The plots below reflect the uncertainties. 27 SNe and their fitted light curves were used to calculate J-band peak magnitudes. (Figure A2 of Dhawan et al.)

This paper employs 9 Type Ia SNe as calibrators (their luminosity distances are already well known), and uses their near-infrared light curves to estimate luminosity distances to 27 other SNe. This work, as mentioned above, assumes the SNe are standard candles in their J-band peak magnitudes. These peaks are calculated using a technique called Gaussian process interpolation fit (see Fig 3). The simplicity of this paper’s approach lies in the fact that this work does not make any standard corrections to these peak magnitudes. What’s special about that, you ask? The beauty here is that unlike the analysis involving optical (B-band) peak magnitudes, this analysis does not correct for light-curve shape (Phillips’ relation!) or reddening (scattering!). Then, the peak magnitudes are directly used to calculate the distances to these SNe (via fitting a Bayesian model to the total data set and performing an MCMC sampling of the posterior distribution). You must wonder – with these assumptions, how good would the luminosity distance (and H0) calculations be?

This work finds that the median H0 = 72.78 +1.6 -1.57 km s -1 Mpc -1 (Fig 4). This implies a 2.2% uncertainty that is in good agreement with median values and uncertainties from SNe analyses involving optical peak magnitudes! Moreover, it is also seen that tweaking the SNe sample – using only the farthest SNe, or only using SNe from a specific survey which would have their own systematics – changes the H0 value by 1-2% at most. These, and several other `extensive cross-checks’ in this work establish that J-band peak magnitudes can be used as robust estimators of H0, and are valuable rungs on the cosmic distance ladder. Moreover, the consistency between H0 values from near-infrared and optical peak magnitudes in SNe (and a slight difference from the CMB value of H0) demonstrates that ‘wavelength-dependent systematic uncertainties’ – reddening and light-curve shape – may not be majorly responsible for the tension between SNe and CMB measurements of H0.

Fig 4. The Hubble Diagram (top), containing the 27 Type IA SNe used in this work. This gives a median H0 value consistent with other SNe estimates, as well as an H0 uncertainty comparable to other work (bottom). (Figure 3 of Dhawan et al.)

What next for Supernova Cosmology?

Dhawan et al. have hinted at the efficacy of using SNe as near-infrared standard candles over SNe as optical standard candles with systematic corrections, and have obtained comparable values of H0. Expanding this sample to a higher number of SNe, as well as using H-band light curves to further constrain luminosity distances will certainly improve this analysis in time to come. As the Astrobites linked above have repeatedly mentioned, the field of making precise measurements of the expansion rate of the universe is just getting into its groove, with new surveys, new probes and new methodologies, just like today’s paper. Watching this space might just be worth your time!


Contents

At the base of the ladder are fundamental distance measurements, in which distances are determined directly, with no physical assumptions about the nature of the object in question. The precise measurement of stellar positions is part of the discipline of astrometry.

Astronomical unit Edit

Direct distance measurements are based upon the astronomical unit (AU), which is defined as the mean distance between the Earth and the Sun. Kepler's laws provide precise ratios of the sizes of the orbits of objects orbiting the Sun, but provides no measurement of the overall scale of the orbit system. Radar is used to measure the distance between the orbits of the Earth and of a second body. From that measurement and the ratio of the two orbit sizes, the size of Earth's orbit is calculated. The Earth's orbit is known with an absolute precision of a few meters and a relative precision of a few parts in 100 billion ( 1 × 10 −11 ).

Historically, observations of transits of Venus were crucial in determining the AU in the first half of the 20th century, observations of asteroids were also important. Presently the orbit of Earth is determined with high precision using radar measurements of distances to Venus and other nearby planets and asteroids, [2] and by tracking interplanetary spacecraft in their orbits around the Sun through the Solar System.

Parallax Edit

The most important fundamental distance measurements come from trigonometric parallax. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in an isosceles triangle, with 2 AU (the distance between the extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal length legs. The amount of shift is quite small, measuring 1 arcsecond for an object at 1 parsec's distance (3.26 light-years) of the nearest stars, and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of parsecs (parallax arcseconds) light-years are used in popular media.

Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars which are near enough to have a parallax larger than a few times the precision of the measurement. In the 1990s, for example, the Hipparcos mission obtained parallaxes for over a hundred thousand stars with a precision of about a milliarcsecond, [3] providing useful distances for stars out to a few hundred parsecs. The Hubble telescope WFC3 now has the potential to provide a precision of 20 to 40 microarcseconds, enabling reliable distance measurements up to 5,000 parsecs (16,000 ly) for small numbers of stars. [4] [5] In 2018, Data Release 2 from the Gaia space mission provides similarly accurate distances to most stars brighter than 15th magnitude. [6]

Stars have a velocity relative to the Sun that causes proper motion (transverse across the sky) and radial velocity (motion toward or away from the Sun). The former is determined by plotting the changing position of the stars over many years, while the latter comes from measuring the Doppler shift of the star's spectrum caused by motion along the line of sight. For a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from statistical analysis of the proper motions relative to their radial velocities. This statistical parallax method is useful for measuring the distances of bright stars beyond 50 parsecs and giant variable stars, including Cepheids and the RR Lyrae variables. [7]

The motion of the Sun through space provides a longer baseline that will increase the accuracy of parallax measurements, known as secular parallax. For stars in the Milky Way disk, this corresponds to a mean baseline of 4 AU per year, while for halo stars the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because the relative velocity of observed stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced the uncertainty is inversely proportional to the square root of the sample size. [10]

Moving cluster parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster. Only open clusters are near enough for this technique to be useful. In particular the distance obtained for the Hyades has historically been an important step in the distance ladder.

Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a supernova remnant or planetary nebula, can be observed over time, then an expansion parallax distance to that cloud can be estimated. Those measurements however suffer from uncertainties in the deviation of the object from sphericity. Binary stars which are both visual and spectroscopic binaries also can have their distance estimated by similar means, and don't suffer from the above geometric uncertainty. The common characteristic to these methods is that a measurement of angular motion is combined with a measurement of the absolute velocity (usually obtained via the Doppler effect). The distance estimate comes from computing how far the object must be to make its observed absolute velocity appear with the observed angular motion.

Expansion parallaxes in particular can give fundamental distance estimates for objects that are very far, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio interferometers which can measure very small angular motions. These combine to provide fundamental distance estimates to supernovae in other galaxies. [11] Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.

Almost all astronomical objects used as physical distance indicators belong to a class that has a known brightness. By comparing this known luminosity to an object's observed brightness, the distance to the object can be computed using the inverse-square law. These objects of known brightness are termed standard candles, coined by Henrietta Swan Leavitt. [12]

The brightness of an object can be expressed in terms of its absolute magnitude. This quantity is derived from the logarithm of its luminosity as seen from a distance of 10 parsecs. The apparent magnitude, the magnitude as seen by the observer (an instrument called a bolometer is used), can be measured and used with the absolute magnitude to calculate the distance d to the object in parsecs [13] as follows:

where m is the apparent magnitude, and M the absolute magnitude. For this to be accurate, both magnitudes must be in the same frequency band and there can be no relative motion in the radial direction. Some means of correcting for interstellar extinction, which also makes objects appear fainter and more red, is needed, especially if the object lies within a dusty or gaseous region. [14] The difference between an object's absolute and apparent magnitudes is called its distance modulus, and astronomical distances, especially intergalactic ones, are sometimes tabulated in this way.

Problems Edit

Two problems exist for any class of standard candle. The principal one is calibration, that is the determination of exactly what the absolute magnitude of the candle is. This includes defining the class well enough that members can be recognized, and finding enough members of that class with well-known distances to allow their true absolute magnitude to be determined with enough accuracy. The second problem lies in recognizing members of the class, and not mistakenly using a standard candle calibration on an object which does not belong to the class. At extreme distances, which is where one most wishes to use a distance indicator, this recognition problem can be quite serious.

A significant issue with standard candles is the recurring question of how standard they are. For example, all observations seem to indicate that Type Ia supernovae that are of known distance have the same brightness (corrected by the shape of the light curve). The basis for this closeness in brightness is discussed below however, the possibility exists that the distant Type Ia supernovae have different properties than nearby Type Ia supernovae. The use of Type Ia supernovae is crucial in determining the correct cosmological model. If indeed the properties of Type Ia supernovae are different at large distances, i.e. if the extrapolation of their calibration to arbitrary distances is not valid, ignoring this variation can dangerously bias the reconstruction of the cosmological parameters, in particular the reconstruction of the matter density parameter. [15] [ clarification needed ]

That this is not merely a philosophical issue can be seen from the history of distance measurements using Cepheid variables. In the 1950s, Walter Baade discovered that the nearby Cepheid variables used to calibrate the standard candle were of a different type than the ones used to measure distances to nearby galaxies. The nearby Cepheid variables were population I stars with much higher metal content than the distant population II stars. As a result, the population II stars were actually much brighter than believed, and when corrected, this had the effect of doubling the distances to the globular clusters, the nearby galaxies, and the diameter of the Milky Way.

Gravitational waves originating from the inspiral phase of compact binary systems, such as neutron stars or black holes, have the useful property that energy emitted as gravitational radiation comes exclusively from the orbital energy of the pair, and the resultant shrinking of their orbits is directly observable as an increase in the frequency of the emitted gravitational waves. To leading order, the rate of change of frequency f is given by [16] [17] : 38

By observing the waveform, the chirp mass can be computed and thence the power (rate of energy emission) of the gravitational waves. Thus, such a gravitational wave source is a standard siren of known loudness. [20] [17]

Just as with standard candles, given the emitted and received amplitudes, the inverse-square law determines the distance to the source. There are some differences with standard candles, however. Gravitational waves are not emitted isotropically, but measuring the polarisation of the wave provides enough information to determine the angle of emission. Gravitational wave detectors also have anisotropic antenna patterns, so the position of the source on the sky relative to the detectors is needed to determine the angle of reception. Generally, if a wave is detected by a network of three detectors at different locations, the network will measure enough information to make these corrections and obtain the distance. Also unlike standard candles, gravitational waves need no calibration against other distance measures. The measurement of distance does of course require the calibration of the gravitational wave detectors, but then the distance is fundamentally given as a multiple of the wavelength of the laser light being used in the gravitational wave interferometer.

There are other considerations that limit the accuracy of this distance, besides detector calibration. Fortunately, gravitational waves are not subject to extinction due to an intervening absorbing medium. But they are subject to gravitational lensing, in the same way as light. If a signal is strongly lensed, then it might be received as multiple events, separated in time (the analogue of multiple images of a quasar, for example). Less easy to discern and control for is the effect of weak lensing, where the signal's path through space is affected by many small magnification and demagnification events. This will be important for signals originating at cosmological redshifts greater than 1. Finally, it is difficult for detector networks to measure the polarization of a signal accurately if the binary system is observed nearly face-on [21] such signals suffer significantly larger errors in the distance measurement. Unfortunately, binaries radiate most strongly perpendicular to the orbital plane, so face-on signals are intrinsically stronger and the most commonly observed.

If the binary consists of a pair of neutron stars, their merger will be accompanied by a kilonova/hypernova explosion that may allow the position to be accurately identified by electromagnetic telescopes. In such cases, the redshift of the host galaxy allows a determination of the Hubble constant H 0 > . [19] This was the case for GW170817, which was used to make the first such measurement. [22] Even if no electromagnetic counterpart can be identified for an ensemble of signals, it is possible to use a statistical method to infer the value of H 0 > . [19]

Another class of physical distance indicator is the standard ruler. In 2008, galaxy diameters have been proposed as a possible standard ruler for cosmological parameter determination. [23] More recently the physical scale imprinted by baryon acoustic oscillations (BAO) in the early universe has been used. In the early universe (before recombination) the baryons and photons scatter off each other, and form a tightly-coupled fluid that can support sound waves. The waves are sourced by primordial density perturbations, and travel at speed that can be predicted from the baryon density and other cosmological parameters. The total distance that these sound waves can travel before recombination determines a fixed scale, which simply expands with the universe after recombination. BAO therefore provide a standard ruler that can be measured in galaxy surveys from the effect of baryons on the clustering of galaxies. The method requires an extensive galaxy survey in order to make this scale visible, but has been measured with percent-level precision (see baryon acoustic oscillations). The scale does depend on cosmological parameters like the baryon and matter densities, and the number of neutrinos, so distances based on BAO are more dependent on cosmological model than those based on local measurements.

Light echos can be also used as standard rulers, [24] [25] although it is challenging to correctly measure the source geometry. [26] [27]

With few exceptions, distances based on direct measurements are available only out to about a thousand parsecs, which is a modest portion of our own Galaxy. For distances beyond that, measures depend upon physical assumptions, that is, the assertion that one recognizes the object in question, and the class of objects is homogeneous enough that its members can be used for meaningful estimation of distance.

Physical distance indicators, used on progressively larger distance scales, include:

    , uses orbital parameters of visual binaries to measure the mass of the system, and hence use the mass–luminosity relation to determine the luminosity
      — In the last decade, measurement of eclipsing binaries' fundamental parameters has become possible with 8-meter class telescopes. This makes it feasible to use them as indicators of distance. Recently, they have been used to give direct distance estimates to the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), Andromeda Galaxy and Triangulum Galaxy. Eclipsing binaries offer a direct method to gauge the distance to galaxies to a new improved 5% level of accuracy which is feasible with current technology to a distance of around 3 Mpc (3 million parsecs). [28]
      (TRGB) distance indicator. (PNLF) (GCLF) (SBF)

    Main sequence fitting Edit

    When the absolute magnitude for a group of stars is plotted against the spectral classification of the star, in a Hertzsprung–Russell diagram, evolutionary patterns are found that relate to the mass, age and composition of the star. In particular, during their hydrogen burning period, stars lie along a curve in the diagram called the main sequence. By measuring these properties from a star's spectrum, the position of a main sequence star on the H–R diagram can be determined, and thereby the star's absolute magnitude estimated. A comparison of this value with the apparent magnitude allows the approximate distance to be determined, after correcting for interstellar extinction of the luminosity because of gas and dust.

    In a gravitationally-bound star cluster such as the Hyades, the stars formed at approximately the same age and lie at the same distance. This allows relatively accurate main sequence fitting, providing both age and distance determination.

    Extragalactic distance indicators [31]
    Method Uncertainty for Single Galaxy (mag) Distance to Virgo Cluster (Mpc) Range (Mpc)
    Classical Cepheids 0.16 15–25 29
    Novae 0.4 21.1 ± 3.9 20
    Planetary Nebula Luminosity Function 0.3 15.4 ± 1.1 50
    Globular Cluster Luminosity Function 0.4 18.8 ± 3.8 50
    Surface Brightness Fluctuations 0.3 15.9 ± 0.9 50
    Sigma-D relation 0.5 16.8 ± 2.4 > 100
    Type Ia Supernovae 0.10 19.4 ± 5.0 > 1000

    The extragalactic distance scale is a series of techniques used today by astronomers to determine the distance of cosmological bodies beyond our own galaxy, which are not easily obtained with traditional methods. Some procedures utilize properties of these objects, such as stars, globular clusters, nebulae, and galaxies as a whole. Other methods are based more on the statistics and probabilities of things such as entire galaxy clusters.

    Wilson–Bappu effect Edit

    Discovered in 1956 by Olin Wilson and M.K. Vainu Bappu, the Wilson–Bappu effect utilizes the effect known as spectroscopic parallax. Many stars have features in their spectra, such as the calcium K-line, that indicate their absolute magnitude. The distance to the star can then be calculated from its apparent magnitude using the distance modulus.

    There are major limitations to this method for finding stellar distances. The calibration of the spectral line strengths has limited accuracy and it requires a correction for interstellar extinction. Though in theory this method has the ability to provide reliable distance calculations to stars up to 7 megaparsecs (Mpc), it is generally only used for stars at hundreds of kiloparsecs (kpc).

    Classical Cepheids Edit

    Beyond the reach of the Wilson–Bappu effect, the next method relies on the period-luminosity relation of classical Cepheid variable stars. The following relation can be used to calculate the distance to Galactic and extragalactic classical Cepheids:

    Several problems complicate the use of Cepheids as standard candles and are actively debated, chief among them are: the nature and linearity of the period-luminosity relation in various passbands and the impact of metallicity on both the zero-point and slope of those relations, and the effects of photometric contamination (blending) and a changing (typically unknown) extinction law on Cepheid distances. [34] [35] [36] [37] [38] [39] [40] [41] [42]

    These unresolved matters have resulted in cited values for the Hubble constant ranging between 60 km/s/Mpc and 80 km/s/Mpc. Resolving this discrepancy is one of the foremost problems in astronomy since some cosmological parameters of the Universe may be constrained significantly better by supplying a precise value of the Hubble constant. [43] [44]

    Cepheid variable stars were the key instrument in Edwin Hubble's 1923 conclusion that M31 (Andromeda) was an external galaxy, as opposed to a smaller nebula within the Milky Way. He was able to calculate the distance of M31 to 285 Kpc, today's value being 770 Kpc.

    As detected thus far, NGC 3370, a spiral galaxy in the constellation Leo, contains the farthest Cepheids yet found at a distance of 29 Mpc. Cepheid variable stars are in no way perfect distance markers: at nearby galaxies they have an error of about 7% and up to a 15% error for the most distant.

    Supernovae Edit

    There are several different methods for which supernovae can be used to measure extragalactic distances.

    Measuring a supernova's photosphere Edit

    We can assume that a supernova expands in a spherically symmetric manner. If the supernova is close enough such that we can measure the angular extent, θ(t), of its photosphere, we can use the equation

    where ω is angular velocity, θ is angular extent. In order to get an accurate measurement, it is necessary to make two observations separated by time Δt. Subsequently, we can use

    where d is the distance to the supernova, Vej is the supernova's ejecta's radial velocity (it can be assumed that Vej equals Vθ if spherically symmetric).

    This method works only if the supernova is close enough to be able to measure accurately the photosphere. Similarly, the expanding shell of gas is in fact not perfectly spherical nor a perfect blackbody. Also interstellar extinction can hinder the accurate measurements of the photosphere. This problem is further exacerbated by core-collapse supernova. All of these factors contribute to the distance error of up to 25%.

    Type Ia light curves Edit

    Type Ia supernovae are some of the best ways to determine extragalactic distances. Ia's occur when a binary white dwarf star begins to accrete matter from its companion star. As the white dwarf gains matter, eventually it reaches its Chandrasekhar limit of 1.4 M ⊙ > .

    Once reached, the star becomes unstable and undergoes a runaway nuclear fusion reaction. Because all Type Ia supernovae explode at about the same mass, their absolute magnitudes are all the same. This makes them very useful as standard candles. All Type Ia supernovae have a standard blue and visual magnitude of

    Therefore, when observing a Type Ia supernova, if it is possible to determine what its peak magnitude was, then its distance can be calculated. It is not intrinsically necessary to capture the supernova directly at its peak magnitude using the multicolor light curve shape method (MLCS), the shape of the light curve (taken at any reasonable time after the initial explosion) is compared to a family of parameterized curves that will determine the absolute magnitude at the maximum brightness. This method also takes into effect interstellar extinction/dimming from dust and gas.

    Similarly, the stretch method fits the particular supernovae magnitude light curves to a template light curve. This template, as opposed to being several light curves at different wavelengths (MLCS) is just a single light curve that has been stretched (or compressed) in time. By using this Stretch Factor, the peak magnitude can be determined. [45]

    Using Type Ia supernovae is one of the most accurate methods, particularly since supernova explosions can be visible at great distances (their luminosities rival that of the galaxy in which they are situated), much farther than Cepheid Variables (500 times farther). Much time has been devoted to the refining of this method. The current uncertainty approaches a mere 5%, corresponding to an uncertainty of just 0.1 magnitudes.

    Novae in distance determinations Edit

    Novae can be used in much the same way as supernovae to derive extragalactic distances. There is a direct relation between a nova's max magnitude and the time for its visible light to decline by two magnitudes. This relation is shown to be:

    After novae fade, they are about as bright as the most luminous Cepheid variable stars, therefore both these techniques have about the same max distance:

    20 Mpc. The error in this method produces an uncertainty in magnitude of about ±0.4

    Globular cluster luminosity function Edit

    Based on the method of comparing the luminosities of globular clusters (located in galactic halos) from distant galaxies to that of the Virgo Cluster, the globular cluster luminosity function carries an uncertainty of distance of about 20% (or 0.4 magnitudes).

    US astronomer William Alvin Baum first attempted to use globular clusters to measure distant elliptical galaxies. He compared the brightest globular clusters in Virgo A galaxy with those in Andromeda, assuming the luminosities of the clusters were the same in both. Knowing the distance to Andromeda, Baum has assumed a direct correlation and estimated Virgo A's distance.

    Baum used just a single globular cluster, but individual formations are often poor standard candles. Canadian astronomer René Racine assumed the use of the globular cluster luminosity function (GCLF) would lead to a better approximation. The number of globular clusters as a function of magnitude is given by:

    where m0 is the turnover magnitude, M0 is the magnitude of the Virgo cluster, and sigma is the dispersion

    It is important to remember that it is assumed that globular clusters all have roughly the same luminosities within the universe. There is no universal globular cluster luminosity function that applies to all galaxies.

    Planetary nebula luminosity function Edit

    Like the GCLF method, a similar numerical analysis can be used for planetary nebulae (note the use of more than one!) within far off galaxies. The planetary nebula luminosity function (PNLF) was first proposed in the late 1970s by Holland Cole and David Jenner. They suggested that all planetary nebulae might all have similar maximum intrinsic brightness, now calculated to be M = −4.53. This would therefore make them potential standard candles for determining extragalactic distances.

    Astronomer George Howard Jacoby and his colleagues later proposed that the PNLF function equaled:

    Where N(M) is number of planetary nebula, having absolute magnitude M. M* is equal to the nebula with the brightest magnitude.

    Surface brightness fluctuation method Edit

    The following method deals with the overall inherent properties of galaxies. These methods, though with varying error percentages, have the ability to make distance estimates beyond 100 Mpc, though it is usually applied more locally.

    The surface brightness fluctuation (SBF) method takes advantage of the use of CCD cameras on telescopes. Because of spatial fluctuations in a galaxy's surface brightness, some pixels on these cameras will pick up more stars than others. However, as distance increases the picture will become increasingly smoother. Analysis of this describes a magnitude of the pixel-to-pixel variation, which is directly related to a galaxy's distance.

    Sigma-D relation Edit

    The Sigma-D relation (or Σ-D relation), used in elliptical galaxies, relates the angular diameter (D) of the galaxy to its velocity dispersion. It is important to describe exactly what D represents, in order to understand this method. It is, more precisely, the galaxy's angular diameter out to the surface brightness level of 20.75 B-mag arcsec −2 . This surface brightness is independent of the galaxy's actual distance from us. Instead, D is inversely proportional to the galaxy's distance, represented as d. Thus, this relation does not employ standard candles. Rather, D provides a standard ruler. This relation between D and Σ is

    log ⁡ ( D ) = 1.333 log ⁡ ( Σ ) + C

    Where C is a constant which depends on the distance to the galaxy clusters. [46]

    This method has the potential to become one of the strongest methods of galactic distance calculators, perhaps exceeding the range of even the Tully–Fisher method. As of today, however, elliptical galaxies aren't bright enough to provide a calibration for this method through the use of techniques such as Cepheids. Instead, calibration is done using more crude methods.

    A succession of distance indicators, which is the distance ladder, is needed for determining distances to other galaxies. The reason is that objects bright enough to be recognized and measured at such distances are so rare that few or none are present nearby, so there are too few examples close enough with reliable trigonometric parallax to calibrate the indicator. For example, Cepheid variables, one of the best indicators for nearby spiral galaxies, cannot yet be satisfactorily calibrated by parallax alone, though the Gaia space mission can now weigh in on that specific problem. The situation is further complicated by the fact that different stellar populations generally do not have all types of stars in them. Cepheids in particular are massive stars, with short lifetimes, so they will only be found in places where stars have very recently been formed. Consequently, because elliptical galaxies usually have long ceased to have large-scale star formation, they will not have Cepheids. Instead, distance indicators whose origins are in an older stellar population (like novae and RR Lyrae variables) must be used. However, RR Lyrae variables are less luminous than Cepheids, and novae are unpredictable and an intensive monitoring program—and luck during that program—is needed to gather enough novae in the target galaxy for a good distance estimate.

    Because the more distant steps of the cosmic distance ladder depend upon the nearer ones, the more distant steps include the effects of errors in the nearer steps, both systematic and statistical ones. The result of these propagating errors means that distances in astronomy are rarely known to the same level of precision as measurements in the other sciences, and that the precision necessarily is poorer for more distant types of object.

    Another concern, especially for the very brightest standard candles, is their "standardness": how homogeneous the objects are in their true absolute magnitude. For some of these different standard candles, the homogeneity is based on theories about the formation and evolution of stars and galaxies, and is thus also subject to uncertainties in those aspects. For the most luminous of distance indicators, the Type Ia supernovae, this homogeneity is known to be poor [47] [ clarification needed ] however, no other class of object is bright enough to be detected at such large distances, so the class is useful simply because there is no real alternative.

    The observational result of Hubble's Law, the proportional relationship between distance and the speed with which a galaxy is moving away from us (usually referred to as redshift) is a product of the cosmic distance ladder. Edwin Hubble observed that fainter galaxies are more redshifted. Finding the value of the Hubble constant was the result of decades of work by many astronomers, both in amassing the measurements of galaxy redshifts and in calibrating the steps of the distance ladder. Hubble's Law is the primary means we have for estimating the distances of quasars and distant galaxies in which individual distance indicators cannot be seen.


    Title: Measuring the Hubble constant with Type Ia supernovae as near-infrared standard candles

    The most precise local measurements of H0 rely on observations of Type Ia supernovae (SNe Ia) coupled with Cepheid distances to SN Ia host galaxies. Recent results have shown tension comparing H0 to the value inferred from CMB observations assuming ΛCDM, making it important to check for potential systematic uncertainties in either approach. To date, precise local H0 measurements have used SN Ia distances based on optical photometry, with corrections for light curve shape and colour. Here, we analyse SNe Ia as standard candles in the near-infrared (NIR), where luminosity variations in the supernovae and extinction by dust are both reduced relative to the optical. From a combined fit to 9 nearby calibrator SNe with host Cepheid distances from Riess et al. (2016) and 27 SNe in the Hubble flow, we estimate the absolute peak J magnitude MJ = -18.524 ± 0.041 mag and H0 = 72.8 ± 1.6 (statistical) ±2.7 (systematic) km s -1 Mpc -1 . The 2.2% statistical uncertainty demonstrates that the NIR provides a compelling avenue to measuring SN Ia distances, and for our sample the intrinsic (unmodeled) peak J magnitude scatter is just

    0.10 mag, even without light curve shape or colour corrections. Our results do not varymore » significantly with different sample selection criteria, though photometric calibration in the NIR may be a dominant systematic uncertainty. Our findings suggest that tension in the competing H0 distance ladders is likely not a result of supernova systematics that could be expected to vary between optical and NIR wavelengths, like dust extinction. We anticipate further improvements in H0 with a larger calibrator sample of SNe Ia with Cepheid distances, more Hubble flow SNe Ia with NIR light curves, and better use of the full NIR photometric data set beyond simply the peak J-band magnitude. « less

    1. European Southern Observatory, Garching (Germany) Technische Univ. Munchen, Garching (Germany). Excellence Cluster Universe Technische Univ. Munchen, Garching (Germany). Dept. Physik Stockholm Univ., Stockholm (Sweden). Oskar Klein Centre, Dept. of Physics
    2. Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy
    3. European Southern Observatory, Garching (Germany) Technische Univ. Munchen, Garching (Germany). Excellence Cluster Universe

    Citation Formats

    0.10 mag, even without light curve shape or colour corrections. Our results do not vary significantly with different sample selection criteria, though photometric calibration in the NIR may be a dominant systematic uncertainty. Our findings suggest that tension in the competing H0 distance ladders is likely not a result of supernova systematics that could be expected to vary between optical and NIR wavelengths, like dust extinction. We anticipate further improvements in H0 with a larger calibrator sample of SNe Ia with Cepheid distances, more Hubble flow SNe Ia with NIR light curves, and better use of the full NIR photometric data set beyond simply the peak J-band magnitude.>,
    doi = <10.1051/0004-6361/201731501>,
    journal = ,
    number = ,
    volume = 609,
    place = ,
    year = <2018>,
    month = <1>
    >


    We have obtained 1087 NIR (JHKS) measurements of 21 SNe Ia using PAIRITEL, nearly doubling the number of well-sampled NIR SN la light curves. These data strengthen the evidence that SNe la are excellent standard candles in the NIR, even without correction for optical light-curve shape. We construct fiducial NIR templates for normal SNe la from our sample, excluding only the three known peculiar SNe Ia: SN 2005bl, SN 2005hk, and SN 2005ke. The H-band absolute magnitudes in this sample of 18 SNe la have an intrinsic rms of only 0.15 mag with no correction for light-curve shape. We found a relationship between the H-band extinction and optical color excess of AH = 0.2E(B - V). This variation is as small as the scatter in distance modulus measurements currently used for cosmology based on optical light curves after corrections for light-curve shape. Combining the homogeneous PAIRITEL measurements with 23 SNe la from the literature, these 41 SNe la have standard H-band magnitudes with an rms scatter of 0.16 mag. The good match of our sample with the literature sample suggests there are few systematic problems with the photometry. We present a nearby NIR Hubble diagram that shows no correlation of the residuals from the Hubble line with light-curve properties. Future samples that account for optical and NIR light-curve shapes, absorption, spectroscopic variation, or host-galaxy properties may reveal effective ways to improve the use of SNe la as distance indicators. Since systematic errors due to dust absorption in optical bands remain the leading difficulty in the cosmological use of supemovae, the good behavior of SN Ia NIR light curves and their relative insensitivity to reddening make these objects attractive candidates for future cosmological work.

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    Type Ia supernovae are good standard candles in the near infrared : Evidence from PAIRITEL. / Wood-Vasey, W. Michael Friedman, Andrew S. Bloom, Joshua S. Hicken, Malcolm Modjaz, Maryam Kirshner, Robert P. Starr, Dan L. Blake, Cullen H. Falco, Emilio E. Szentgyorgyi, Andrew H. Challis, Peter Blondin, Stéphane Mandel, Kaisey S. Rest, Armin.

    In: Astrophysical Journal , Vol. 689, No. 1, 10.12.2008, p. 377-390.

    Research output : Contribution to journal › Article › peer-review

    T1 - Type Ia supernovae are good standard candles in the near infrared

    T2 - Evidence from PAIRITEL

    AU - Szentgyorgyi, Andrew H.

    N2 - We have obtained 1087 NIR (JHKS) measurements of 21 SNe Ia using PAIRITEL, nearly doubling the number of well-sampled NIR SN la light curves. These data strengthen the evidence that SNe la are excellent standard candles in the NIR, even without correction for optical light-curve shape. We construct fiducial NIR templates for normal SNe la from our sample, excluding only the three known peculiar SNe Ia: SN 2005bl, SN 2005hk, and SN 2005ke. The H-band absolute magnitudes in this sample of 18 SNe la have an intrinsic rms of only 0.15 mag with no correction for light-curve shape. We found a relationship between the H-band extinction and optical color excess of AH = 0.2E(B - V). This variation is as small as the scatter in distance modulus measurements currently used for cosmology based on optical light curves after corrections for light-curve shape. Combining the homogeneous PAIRITEL measurements with 23 SNe la from the literature, these 41 SNe la have standard H-band magnitudes with an rms scatter of 0.16 mag. The good match of our sample with the literature sample suggests there are few systematic problems with the photometry. We present a nearby NIR Hubble diagram that shows no correlation of the residuals from the Hubble line with light-curve properties. Future samples that account for optical and NIR light-curve shapes, absorption, spectroscopic variation, or host-galaxy properties may reveal effective ways to improve the use of SNe la as distance indicators. Since systematic errors due to dust absorption in optical bands remain the leading difficulty in the cosmological use of supemovae, the good behavior of SN Ia NIR light curves and their relative insensitivity to reddening make these objects attractive candidates for future cosmological work.

    AB - We have obtained 1087 NIR (JHKS) measurements of 21 SNe Ia using PAIRITEL, nearly doubling the number of well-sampled NIR SN la light curves. These data strengthen the evidence that SNe la are excellent standard candles in the NIR, even without correction for optical light-curve shape. We construct fiducial NIR templates for normal SNe la from our sample, excluding only the three known peculiar SNe Ia: SN 2005bl, SN 2005hk, and SN 2005ke. The H-band absolute magnitudes in this sample of 18 SNe la have an intrinsic rms of only 0.15 mag with no correction for light-curve shape. We found a relationship between the H-band extinction and optical color excess of AH = 0.2E(B - V). This variation is as small as the scatter in distance modulus measurements currently used for cosmology based on optical light curves after corrections for light-curve shape. Combining the homogeneous PAIRITEL measurements with 23 SNe la from the literature, these 41 SNe la have standard H-band magnitudes with an rms scatter of 0.16 mag. The good match of our sample with the literature sample suggests there are few systematic problems with the photometry. We present a nearby NIR Hubble diagram that shows no correlation of the residuals from the Hubble line with light-curve properties. Future samples that account for optical and NIR light-curve shapes, absorption, spectroscopic variation, or host-galaxy properties may reveal effective ways to improve the use of SNe la as distance indicators. Since systematic errors due to dust absorption in optical bands remain the leading difficulty in the cosmological use of supemovae, the good behavior of SN Ia NIR light curves and their relative insensitivity to reddening make these objects attractive candidates for future cosmological work.


    A standard candle is an astronomical object that has a known absolute magnitude. They are extremely important to astronomers since by measuring the apparent magnitude of the object we can determine its distance using the formula:

    where m is the apparent magnitude of the object, M is the absolute magnitude of the object, and d is the distance to the object in parsecs.

    The most commonly used standard candles in astronomy are Cepheid Variable stars and RR Lyrae stars. In both cases, the absolute magnitude of the star can be determined from its variability period.

    Type Ia supernovae are also normally classed as standard candles, but in reality they are more standardisible candles since they do not all have the same peak brightness. However, the differences in their peak luminosities are correlated with how quickly the light curve declines after maximum light via the luminosity-decline rate relation, and they can be made into standard candles by correcting for this effect.

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    Watch the video: Astronomy: The Supernova 10 of 10 Type 1A Supernova Used as a Distance Candle (January 2023).