I Distance using Cepheid variables

[Phigla]

Good morning,
I don't understand how the Cepheid variables are used to measure the distance of Stars.
Is a member is patient to explain to me
thanks

 

[Bandersnatch]

When you observe any regular star, you see how bright it looks, but you don't know how much of the observed brightness is due to its intrinsic luminosity, and how much due to being distant.
Cepheids pulsate regularly, with the period of pulsation strongly related to their luminosity. One can measure the period of pulsation, and then derive the luminosity. Having the luminosity, it's then just a matter of measuring the observed brightness to find out how far the star has to be in order to look this bright.

 

[Phigla]

Thanks.
To tell you, I am retired (i'm 70) in China...and Wikipedia and other sites is blocked by the authorities, are so my source of information is limited.
Concerning the Cepheid it is said that all Cepheid with a certain period are assumed to have the same absolute magnitude. Measuring the apparent magnitude allows to determine its distance using period-luminosity relation.
How to measure this apparent magnitude ?
I suppose that if two cepheids have the same period but one is fainter that the other, this one must be further away.
Another things I don't really understand is the difference between luminosity and brightness.
Thanks in advance
Philippe

 

[davenn]

hi there Philippe ( @Phigla )

Welcome to the Physics Forums

I'm going to post some significant sections of the wiki page on Cepheid variable stars
This shouldn't normally be done but since your situation denies you that info, I will do it )

Cepheid variables are divided into two subclasses which exhibit markedly different masses, ages, and evolutionary histories: classical Cepheids and type II Cepheids. Delta Scuti variables are A-type stars on or near the main sequence at the lower end of the instability strip and were originally referred to as dwarf Cepheids. RR Lyrae variables have short periods and lie on the instability strip where it crosses the horizontal branch. Delta Scuti variables and RR Lyrae variables are not generally treated with Cepheid variables although their pulsations originate with the same helium ionisation kappa mechanism.

Classical Cepheids[edit]

Main article: Classical Cepheid variable

Classical Cepheids (also known as Population I Cepheids, type I Cepheids, or Delta Cepheid variables) undergo pulsations with very regular periods on the order of days to months. Classical Cepheids are Population I variable stars which are 4–20 times more massive than the Sun,[9] and up to 100,000 times more luminous.[10] These Cepheids are yellow bright giants and supergiants of spectral class F6 – K2 and their radii change by (~25% for the longer-period I Carinae) millions of kilometers during a pulsation cycle.[11]

Classical Cepheids are used to determine distances to galaxies within the Local Group and beyond, and are a means by which the Hubble constant can be established.[3][4][6][12][13] Classical Cepheids have also been used to clarify many characteristics of our galaxy, such as the Sun's height above the galactic plane and the Galaxy's local spiral structure.[5]

A group of classical Cepheids with small amplitudes and sinusoidal light curves are often separated out as Small Amplitude Cepheids or s-Cepheids, many of them pulsating in the first overtone.

Type II Cepheids[edit]

Main article: Type II Cepheid

Type II Cepheids (also termed Population II Cepheids) are population II variable stars which pulsate with periods typically between 1 and 50 days.[14][15] Type II Cepheids are typically metal-poor, old (~10 Gyr), low mass objects (~half the mass of the Sun). Type II Cepheids are divided into several subgroups by period. Stars with periods between 1 and 4 days are of the BL Her subclass, 10–20 days belong to the W Virginis subclass, and stars with periods greater than 20 days belong to the RV Tauri subclass.[14][15]

Type II Cepheids are used to establish the distance to the Galactic Center, globular clusters, and galaxies.[5][16][17][18][19][20][21]

Anomalous Cepheids[edit]

A group of pulsating stars on the instability strip have periods of less than 2 days, similar to RR Lyrae variables but with higher luminosities. Anomalous Cepheid variables have masses higher than type II Cepheids, RR Lyrae variables, and our sun. It is unclear whether they are young stars on a "turned-back" horizontal branch, blue stragglers formed through mass transfer in binary systems, or a mix of both.[22][23]

Double-mode Cepheids[edit]

A small proportion of Cepheid variables have been observed to pulsate in two modes at the same time, usually the fundamental and first overtone, occasionally the second overtone.[24] A very small number pulsate in three modes, or an unusual combination of modes including higher overtones.[25]

 

[davenn]

another sections...

History[edit]

On September 10, 1784, Edward Pigott detected the variability of Eta Aquilae, the first known representative of the class of classical Cepheid variables.[26] However, the eponymous star for classical Cepheids is Delta Cephei, discovered to be variable by John Goodricke a few months later.[27] The number of similar variables grew to several dozen by the end of the 19th century, and they were referred to as a class as Cepheids.[28] Most of the Cepheids were known from the distinctive light curve shapes with the rapid increase in brightness and a hump, but some with more symmetrical light curves were known as Geminids after the prototype ζ Geminorum.[29]

A relationship between the period and luminosity for classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars in the Magellanic Clouds.[30] She published it in 1912 with further evidence.[31]

In 1913, Ejnar Hertzsprung attempted to find distances to 13 Cepheids using the motion through the sky.[32] His research would later require revision, however. In 1915, Harlow Shapley used Cepheids to place initial constraints on the size and shape of the Milky Way, and of the placement of our Sun within it.[citation needed] In 1924, Edwin Hubble established the distance to classical Cepheid variables in the Andromeda Galaxy, until then known as the Andromeda Nebula, and showed that the variables were not members of the Milky Way. Hubble's finding settled the question raised in the "Great Debate" of whether the Milky Way represented the entire Universe or was merely one of numerous galaxies in the Universe.[33]

In 1929, Hubble and Milton L. Humason formulated what is now known as Hubble's Law by combining Cepheid distances to several galaxies with Vesto Slipher's measurements of the speed at which those galaxies recede from us. They discovered that the Universe is expanding (see the expansion of the Universe). However, the expansion of the Universe was posited several years before by Georges Lemaître.[34]

In the mid 20th century, significant problems with the astronomical distance scale were resolved by dividing the Cepheids into different classes with very different properties. In the 1940s, Walter Baade recognized two separate populations of Cepheids (classical and type II). Classical Cepheids are younger and more massive population I stars, whereas type II Cepheids are older fainter Population II stars.[14] Classical Cepheids and type II Cepheids follow different period-luminosity relationships. The luminosity of type II Cepheids is, on average, less than classical Cepheids by about 1.5 magnitudes (but still brighter than RR Lyrae stars). Baade's seminal discovery led to a twofold increase in the distance to M31, and the extragalactic distance scale.[35][36] RR Lyrae stars, then known as Cluster Variables, were recognized fairly early as being a separate class of variable, due in part to their short periods.[37][38]

 

[davenn]

and finally ...

Uncertainties in Cepheid determined distances[edit]

Chief among the uncertainties tied to the classical and type II Cepheid distance scale are: the nature of the period-luminosity relation in various passbands, 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. All these topics are actively debated in the literature.[4][10][12][19][39][40][41][42][43][44][45][46]

These unresolved matters have resulted in cited values for the Hubble constant (established from Classical Cepheids) ranging between 60 km/s/Mpc and 80 km/s/Mpc.[3][4][6][12][13] Resolving this discrepancy is one of the foremost problems in astronomy since the cosmological parameters of the Universe may be constrained by supplying a precise value of the Hubble constant.[6][13] Uncertainties have diminished over the years, due in part to discoveries such as RS Puppis.

Delta Cephei is also of particular importance as a calibrator of the Cepheid period-luminosity relation since its distance is among the most precisely established for a Cepheid, partly because it is a member of a star cluster[47][48] and the availability of precise Hubble Space Telescope/Hipparcos parallaxes.[49] The accuracy of the distance measurements to Cepheid variables and other bodies within 7,500 lightyears is vastly improved by combining images from Hubble taken six months apart when the Earth and Hubble are on opposite sides of the Sun.[50]

Dynamics of the pulsation[edit]

The accepted explanation for the pulsation of Cepheids is called the Eddington valve,[51] or κ-mechanism, where the Greek letter κ (kappa) denotes gas opacity. Helium is the gas thought to be most active in the process. Doubly ionized helium (helium whose atoms are missing both electrons) is more opaque than singly ionized helium. The more helium is heated, the more ionized it becomes. At the dimmest part of a Cepheid's cycle, the ionized gas in the outer layers of the star is opaque, and so is heated by the star's radiation, and due to the increased temperature, begins to expand. As it expands, it cools, and so becomes less ionized and therefore more transparent, allowing the radiation to escape. Then the expansion stops, and reverses due to the star's gravitational attraction. The process then repeats.

The mechanics of the pulsation as a heat-engine was proposed in 1917 by Arthur Stanley Eddington[52] (who wrote at length on the dynamics of Cepheids), but it was not until 1953 that S. A. Zhevakin identified ionized helium[53] as a likely valve for the engine.

 

[davenn]

Another things I don't really understand is the difference between luminosity and brightness.
Thanks in advance
Philippe

some info on this ( if you cannot access the pages, let me know and I will post sections ) ...

https://www.e-education.psu.edu/astro801/content/l4_p4.htmlhere's a bit of basics from another site ...
https://Earth'sky.org/astronomy-essentials/stellar-luminosity-the-true-brightness-of-stars
Today, when we talk about a star’s brightness, we might mean one of two things: its intrinsic brightness or its apparent brightness. When astronomers speak of the luminosity of a star, they’re speaking of a star’s intrinsic brightness, how bright it really is. A star’s apparent magnitude – its brightness as it appears from Earth – is something different and depends on how far away we are from that star.

For instance, nearly every star that you see with the unaided eye is larger and more luminous than our sun. The vast majority of stars that we see at night with the eye alone are millions – even hundreds of millions – of times farther away than the sun. Regardless, these distant suns can be seen from Earth because they are hundreds or thousands of times more luminous than our local star.That’s not to say that our sun is a lightweight among stars. In fact, the sun is thought to be more luminous than 85% of the stars in our Milky Way galaxy. Yet most of these less luminous stars are too small and faint to see without an optical aid.A star’s luminosity depends on two things:1. Radius measure
2. Surface temperatureRadius measure

Let’s presume a star has the same surface temperature as the sun, but sports a larger radius. In that scenario, the star with the larger radius claims the greater luminosity. In the example below, we’ll say the star’s radius is 4 solar (4 times the sun’s radius) but has the same surface temperature as our sun.

We can calculate the star’s luminosity – relative to the sun’s – with the following equation, whereby L = luminosity and R = radius:

L = R2
L = 42 = 4 x 4 = 16 times the sun’s luminositySurface temperature

Also, if a star has the same radius as the sun but a higher surface temperature, the hotter star exceeds the sun in luminosity. The sun’s surface temperature is somewhere around 5800 Kelvin (9980o Fahrenheit). That’s 5800 degrees above absolute zero, the coldest temperature possible anywhere in the universe. Let’s presume a star is the same size as the sun but that its surface temperature is twice as great in degrees Kelvin (5800 x 2 = 11600 Kelvin).

We use the equation below to solve for the star’s luminosity, relative to the sun’s, where L = luminosity and T = surface temperature, and the surface temperature equals 2 solar.

L = T4
L = 24 = 2 x 2 x 2 x 2 = 16 times the sun’s luminosityLuminosity of Star = R2 x T4

he luminosity of any star is the product of the radius squared times the surface temperature raised to the fourth power. Given a star whose radius is 3 solar and a surface temperature that’s 2 solar, we can figure that star’s luminosity with the equation below, whereby L = luminosity, R = radius and T = surface temperature:L = R2 x T4
L = (3 x 3) x (2 x 2 x 2 x 2)
L = 9 x 16 = 144 times the sun’s luminosity
hopefully the good reading in those several posts helps you out

chers
Dave

 

[Bandersnatch]

And for a short answer:

How to measure this apparent magnitude ?
I suppose that if two cepheids have the same period but one is fainter that the other, this one must be further away.
Another things I don't really understand is the difference between luminosity and brightness.

Apparent magnitude can be obtained with the use of a bolometer, which counts incident radiative flux (power per unit area).
Luminosity is the total power output of a star.
Brightness as used here is just another (non-technical) word for apparent magnitude.
You understanding of how Cepheids are used seems fine.

Btw, see if http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html is blocked where you are or not. You'll find many of these concepts in the astrophysics section. The thought-bubble interface can sometimes be difficult to get it to go where you need it to, so remember you can always use the index.

 

[Phigla]

Dear All,

Thanks a lot for your help, I am sorry to reply so late...the time for me to digest what you sent me.

On the mean time, I have another question not related to Cepheids.

Reading what I can read, I saw that Vega is the star reference for the apparent magnitude (even if it is 0.03) and for the absolute magnitude...so I understand that Vega has the apparent magnitude 0, therefore its Energy density is as well the reference and for a star apparent magnitude 1, this one will have the Energy density of Vega/2.152

But I don't find the value of this Energy density (in Wm^-2) for the overall electromagnetic spectrum.

Is someone will be gentle to give me this value.

Thanks in advance

Philippe