# Distance of extra-galactic Classical Cepheids

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There have been many questions and answers about finding the distance of a star from the earth. But as I did some research on the net, I found that we have specific approaches for finding the distances of different types of stars.

So, my question is more specific now.

How to determine how far a Classical Cepheid is?

What if the Cepheid is extra-galactic? Is there a good method to finding the solution? Can anybody suggest how to make a start at deriving a relation at finding the distance of a Cepheid from us?

There is this Period-Luminosity-Color relation. Can anyone at least enlist the journal articles where I can make a study to get closer to finding the answer to my question?

Since it seems you don't know the equations, I will try to keep it simple. However, just keep in mind that, in principle, there is no difference between Galactic and extragalactic Cepheids, in this context.

Now, we know that a Period-Luminosity relation holds for the Cepheids:

$Psim L$

Where $P$ is the pulsation period observed from the Cepheid, and $L$ is the observed luminosity.

We also know that:

$Lsim d$

where $d$ is the distance of the source.

Then it is like to write $Psim d$.

This means that, if we observe the pulsation period of a Cepheid, we know its distance, and this allows to know the distance of the host galaxy as well.

Some basic sources:

Cepheid variable

Classical Cepheid variable with some numbers

And some diagrams too

## The Galactic warp’s precession traced by classical Cepheids

The story started more than 3 years ago, when I was a PhD student at Peking University. At that time, I did some work on the period–luminosity relation of classical Cepheid variable stars in the infrared window. Cepheids are primary distance indicators, which make up the astronomical distance ladder from the Local Group of galaxies to cosmological distances. They are irreplaceable because of both their very high luminosities and their exquisite distance accuracy. However, few Cepheids were known in our Milky Way, since our knowledge of them was limited by the heavy extinction and stellar crowding in the Galactic plane. Searching for Milky Way Cepheids in infrared windows and using them to study the Galactic disk’s structure is an active field of research. At the time of my earlier study, Cepheids associated with the Galactic Center and in the disk’s outer flare had been detected, and several Cepheids associated with the spiral arms were also investigated. Nevertheless, the number of known Cepheids was still only around 1,000 and they covered less than 5% of the disk region. So, I got the idea to search for new Cepheids on large scales across our Milky Way as a whole.

An opportunity arose in April 2018 when the Wide-Field Infrared Survey Explorer (WISE) released its fifth year’s photometric catalog, which made it possible to search for periodic variables with periods as long as 10 days. Based on the WISE five-year data, my collaborators and I published an infrared periodic variable catalog containing more than 34,000 new variables – the catalog included 1,312 possible Cepheids. I soon realized its power for studies of the structure of the Milky Way’s disk, and so I collected all known Cepheids in order to trace the Galaxy’s spiral arms. However, my sample pf Cepheids did not obviously agree with the structure of the spiral arms traced by molecular clouds (see Figure 1c). Fortunately, however, I noticed a clear trend in the Cepheid distribution at different heights above and below the Milky Way’s plane. This implied that the Galactic disk is not simply a thin plane. A projection of these Cepheids onto the YZ plane (see Figure 1a) showed an obviously warped disk (see Figure 1b).

Figure 1: a: Three-dimensional map of the Milky Way’s disk traced by Cepheids. b, c: Projections onto the Yz (b) and XY (c) planes. The black upward-pointing triangle is the position of the Sun, and the black solid line denotes the mean LON.

An intuitive 3D map of Milky Way’s disk was established based on the distribution of 1,339 Cepheids (see Figure 1a). My collaborators Licai Deng and Richard de Grijs were all excited when they first saw the morphology of the Cepheid disk. To ensure the highest possible accuracy of the results, contamination such as that caused by eclipsing binary systems and Type II Cepheids were excluded with the aid of Gaia DR2 parallaxes, and a distance accuracy cut of 5% was adopted. The warped and flared structure of the gas and Cepheid disks agree well with each other in terms of their amplitudes. More interestingly, the global line of nodes (LON, it denotes a line that joins the ascending node and the descending node of an orbit) of warp surely deviates from the Galactic Center–Sun direction.

Based on these accurate distances, my collaborator Chao Liu proposed that we might detect the warp’s precession. Indeed, the warp’s LON angle is changing with Galactocentric radius in both the spatial and kinematic maps (Figure 2). A clear increase of the LON is apparent at 12 ≤ R ≤ 15 kpc, advancing in the Milky Way’s rotation direction. This leading spiral pattern warp validates the notion that the origin of the outer disks pattern is predominantly induced by torques associated with the massive inner disk. At even greater distances, R = 15.5 kpc, the LON appears to twist. In addition, within R = 12 kpc, the LON angles decrease with radius. These features support the idea that our Milky Way’s warp follows the rule established for other spiral galaxies (Briggs’ rule).

Figure 2: The precession of Milky Way’s warp.

This new morphology provides a crucial updated map for studies of our galaxy’s stellar motions and the origins of the Milky Way’s disk. In the future, we would like to use a more complete Cepheid sample including objects found at Galactocentric radii R > 15 kpc and behind the Galactic Center, which could reveal an even more accurate and detailed disk structure. Also, other tracers such as stars of certain spectral types or open clusters are expected to trace the evolutionary behavior of our Milky Way’s warp.

## Classical Cepheids as distance indicators and stellar population tracers in the Gaia Era

Giovedì 10 dicembre alle ore 15:00, la dott.ssa Giulia De Somma dell’INAF-Osservatorio Astronomico di Capodimonte e dell’Università Federico II di Napoli terrà il web-seminar dal titolo: Classical Cepheids as distance indicators and stellar population tracers in the Gaia Era.

The modelling of radial pulsating stars, specifically Classical Cepheids, is fundamental to constraining the extragalactic distance scale. The various ingredients entering the theoretical calibration of the Classical Cepheid distance scale can affect the accuracy and reliability of the inferred distances and, as such, cast light on residual systematics in the local determination of the Hubble constant. This topic has known a renewed interest in the last few years in the context of the debate on the so called Hubble Constant tension: the unsolved discrepancy between the value derived by Riess et al (2016, 2018) on the basis of Classical Cepheids, and the Cosmic Microwave Background results.
In the context of my PhD project, I am contributing to the build-up of an updated and accurate set of nonlinear convective pulsation models for Classical Cepheids for the first time homogeneously covering a wide range of stellar parameters, including variations in the assumed Mass-Luminosity relation and super-adiabatic convective efficiency. These models have been used to produce the first theoretical scenario suitable for this class of pulsators in the Gaia DR2 photometric system. From the predicted light curves, mean magnitudes and colors have been obtained and used to derive the first theoretical Period-Luminosity-Color and Period-Wesenheit relations in the Gaia passbands. For each assumption concerning the Mass-Luminosity relation and the efficiency of super-adiabatic convection, the predicted relations have been used to provide individual distances for a sample of Gaia DR2 Cepheids. The comparison between predicted and observed Gaia parallaxes and the implications for the extragalactic distance scale are discussed. By combining our pulsation model results with stellar evolution model predictions, we have also derived new and accurate Period-Age-Color relations in the Gaia bands, then applied them to the selected Gaia DR2 Cepheids. We present and discuss, the distribution of the inferred individual ages as a function of the adopted Mass-Luminosity relation and pulsation mode, as well as the implications of our results for the Galactic star formation history. We conclude with several future perspectives, while waiting for Gaia Data Release 3.

## Distance of extra-galactic Classical Cepheids - Astronomy

Classical Cepheid variable stars (henceforth: Cepheids) are best-known for their crucial role in calibrating the cosmic distance scale, and thus, for investigating dark energy. Yet, Cepheids continue to be objects of high interest for stellar physics and rank among the most-studied types of variable stars.

This talk presents recent observational work aimed at increasing the accuracy of extragalactic distance measurements as well as providing new insights into stellar pulsations via highly precise observations obtained with state-of-the-art instrumentation from the ground and from space. Specifically, I present how high-precision radial velocity measurements of Cepheids a) support unprecedented parallax accuracy, b) reveal systematic uncertainties of Baade-Wesselink-type distances, and c) have enabled the discovery of atmospheric velocity field perturbations that are presently not understood. Related irregular variability patterns discovered via high-precision photometric and interferometric observations are also discussed.

The ongoing ESA mission Gaia is expected to revolutionize stellar astrophysics and provide a highly accurate anchor for the extragalactic distance scale. As this talk shows, high-precision observations can expose secrets of seemingly well-understood stars and play a crucial role for leveraging Gaia’s full potential.

## Title: The extragalactic distance scale Key Project. III. The discovery of Cepheids and a new distance to M101 using the We report on the discovery of 29 Cepheid variables in the galaxy M101 using the original Wide Field Camera (WFC) and the new Wide Field and Planetary Camera 2 (WFPC2) on the . We observed a field in M101 at 17 independent epochs in (F555W), five epochs in (F785LP/F814W), and one epoch in (F439W), with a time interval baseline of 381 days. We have found Cepheids with periods ranging from 10 to 60 days. The data have been calibrated using WFPC2 observations with zero points derived from Cen, Pal 4, and NGC 2419 observations. This calibration has been verified by using the Medium Deep Survey (MDS) WFC photometric zero points, and ground-based secondary standards in and . The calibrations agree to 0.06 mag, and the calibrations agree to 0.04 mag. We have constructed and period-luminosity (PL) relations and have derived apparent distance moduli based on a distance modulus for the Large Magellanic Cloud (LMC) of 18.50 mag and a reddening of ()=0.10 mag to the LMC Cepheids. Period-residual minimization was used to minimize themore » effects of Malmquist bias on the period-luminosity relation fitting process. Using a Galactic extinction law and the apparent and distance moduli, we have found a mean reddening for the M101 sample of ()=0.03 mag and a true distance modulus to M101 of 29.340.17 mag, corresponding to a distance of 7.40.6 Mpc. The sources of error have been rigorously tracked through an error budget systematic and random errors contribute roughly equally to the quoted error. The mean gas-phase metal abundances in the LMC and in the M101 outer field are similar so we expect metallicity effects to be minimal. (Abstract Truncated) « less Determining the Extragalactic Distance Scale

A number of techniques are required to map the three-dimensional universe. In this lab you will focus on a particular technique that is useful for measuring distances to neighboring galaxies, and the nearest galaxy clusters. You will use actual Hubble Space Telescope (HST) images to find the distance to a galaxy named M100, by looking for a variety of variable stars known as Cepheid variables. (The determination of the extragalactic distance scale was one of the Key Projects for the Hubble Space Telescope). You will then use your newly-determined M100 distance to estimate the age of the universe!

Above: A portion of the Hubble Deep Field (HDF). In December 1995, 10 days of HST observing time were devoted to long exposures, through filters of different colors, of a tiny patch of "blank sky." The long exposures enable us to see very faint, faraway objects. Single-color exposures were combined to produce this multicolor image. The region is filled with galaxies of diverse morphologies and colors! Some of the faintest objects in the HDF are so distant, the light we now see from them was emitted over 10 billion years ago, when our universe was still young! To turn this two-dimensional image into a three-dimensional map, one needs to know the distance to each object in the image. Distances are also needed to determine the physical diameters and intrinsic luminosities of each galaxy. The field shown is approximately 40 by 70 arcseconds of sky. (For comparison, the diameter of the full moon is about 1800 arcseconds.) More images and information on the Hubble Deep Field may be found in the public Web pages of the Space Telescope and Science Institute (STScI). Image credit: Robert Williams and the Hubble Deep Field Team (STScI) and NASA.

## Classical Cepheids as distance indicators and stellar population tracers in the Gaia Era

Giovedì 10 dicembre alle ore 15:00, la dott.ssa Giulia De Somma dell’INAF-Osservatorio Astronomico di Capodimonte e dell’Università Federico II di Napoli terrà il web-seminar dal titolo: Classical Cepheids as distance indicators and stellar population tracers in the Gaia Era.

The modelling of radial pulsating stars, specifically Classical Cepheids, is fundamental to constraining the extragalactic distance scale. The various ingredients entering the theoretical calibration of the Classical Cepheid distance scale can affect the accuracy and reliability of the inferred distances and, as such, cast light on residual systematics in the local determination of the Hubble constant. This topic has known a renewed interest in the last few years in the context of the debate on the so called Hubble Constant tension: the unsolved discrepancy between the value derived by Riess et al (2016, 2018) on the basis of Classical Cepheids, and the Cosmic Microwave Background results.
In the context of my PhD project, I am contributing to the build-up of an updated and accurate set of nonlinear convective pulsation models for Classical Cepheids for the first time homogeneously covering a wide range of stellar parameters, including variations in the assumed Mass-Luminosity relation and super-adiabatic convective efficiency. These models have been used to produce the first theoretical scenario suitable for this class of pulsators in the Gaia DR2 photometric system. From the predicted light curves, mean magnitudes and colors have been obtained and used to derive the first theoretical Period-Luminosity-Color and Period-Wesenheit relations in the Gaia passbands. For each assumption concerning the Mass-Luminosity relation and the efficiency of super-adiabatic convection, the predicted relations have been used to provide individual distances for a sample of Gaia DR2 Cepheids. The comparison between predicted and observed Gaia parallaxes and the implications for the extragalactic distance scale are discussed. By combining our pulsation model results with stellar evolution model predictions, we have also derived new and accurate Period-Age-Color relations in the Gaia bands, then applied them to the selected Gaia DR2 Cepheids. We present and discuss, the distribution of the inferred individual ages as a function of the adopted Mass-Luminosity relation and pulsation mode, as well as the implications of our results for the Galactic star formation history. We conclude with several future perspectives, while waiting for Gaia Data Release 3.

## Our Work

Center for Astrophysics | Harvard & Smithsonian scientists refine extragalactic measurements in various ways:

Mapping the structure of the universe by measuring the distances to galaxies. CfA astronomers pioneered this method, from the first redshift survey initiated in 1977 through recent projects like the Two Micron All-Sky Survey (2MASS) Redshift Survey, completed in 2011.
Astronomers Unveil Most Complete 3-D Map of Local Universe

Surveying galaxies using the Baryon Oscillation Spectroscopic Survey (BOSS) to establish the “standard ruler” for extragalactic distances. This ongoing project has mapped tens of thousands of galaxies, and has provided the best measurements astronomers have of the acceleration of the expansion of the universe.
A One-Percent Measure of Galaxies Half the Universe Away

An optical and X-ray image of Kepler's supernova, a type Ia supernova described by Johannes Kepler in 1604. Type Ia supernovas are the explosions of white dwarfs, which astronomers use to measure extragalactic distances and the expansion rate of the universe.

## Standard Bulbs

We discussed in Celestial Distances the great frustration that astronomers felt when they realized that the stars in general were not standard bulbs. If every light bulb in a huge auditorium is a standard 100-watt bulb, then bulbs that look brighter to us must be closer, whereas those that look dimmer must be farther away. If every star were a standard luminosity (or wattage), then we could similarly “read off” their distances based on how bright they appear to us. Alas, as we have learned, neither stars nor galaxies come in one standard-issue luminosity. Nonetheless, astronomers have been searching for objects out there that do act in some way like a standard bulb —that have the same intrinsic (built-in) brightness wherever they are.

A number of suggestions have been made for what sorts of objects might be effective standard bulbs, including the brightest supergiant stars, planetary nebulae (which give off a lot of ultraviolet radiation), and the average globular cluster in a galaxy. One object turns out to be particularly useful: the type Ia supernova. These supernovae involve the explosion of a white dwarf in a binary system (see The Evolution of Binary Star Systems) Observations show that supernovae of this type all reach nearly the same luminosity (about 4.5 × 10 9 LSun) at maximum light. With such tremendous luminosities, these supernovae have been detected out to a distance of more than 8 billion light-years and are therefore especially attractive to astronomers as a way of determining distances on a large scale. An example of such supernova is pictured in Figure 2.

Figure 2. The bright object at the bottom left of centre is a type Ia supernova near its peak intensity. The supernova easily outshines its host galaxy. This extreme increase and luminosity help astronomers use Ia supernova as standard bulbs. (credit: NASA, ESA, A. Riess (STScI))

Several other kinds of standard bulbs visible over great distances have also been suggested, including the overall brightness of, for example, giant ellipticals and the brightest member of a galaxy cluster. Type Ia supernovae, however, have proved to be the most accurate standard bulbs, and they can be seen in more distant galaxies than the other types of calibrators. As we will see in the chapter on The Big Bang, observations of this type of supernova have profoundly changed our understanding of the evolution of the universe.

## Distance of extra-galactic Classical Cepheids - Astronomy

Background material: The distances to galaxies are reliably determined with Cepheid variables. Here is a general introduction to Cepheids and other pulsating stars.

Historical material: Discovery that the spiral nebulae are distant galaxies and cousins to the Milky Way.

In 1920 one of the most important questions in all of science was, What is the size of the Milky Way and the distance to the spiral nebulae?'' This was brought to national prominence in a debate between Harlow Shapley and Heber Curtis, commonly known as The Great Debate. The following paper by Otto Struve shows that the answers of both men were partly correct and partly wrong. Shapley went on to international fame, Curtis remained a quite academic. Their debate framed the beginning of modern extragalactic astrophysics.

The Great Debate was really about two questions,

What were the early (pre 1925) indicators that M31 was a distant, independent stellar system and NOT part of the Milky Way? Several of the papers cited by Hubble are available in the NRAO library, you may want to read them.

Homework: Hubble's variable number 1 has a period of 31 days and a brightness change of 1.2 magnitudes. What is the ratio of its flux at maximum light to that at minimum light?

Current material: The current best determinations of distances to the nearest galaxies using Cepheids and other pulsating stars.

Homework: Using the values of Feast and Walker, what are the distances to the Local Group galaxies in kiloparsecs?