What are Cepheid variable stars, and why are they important?
A Cepheid is a member of a class of very luminous variable stars. The strong direct relationship between a Cepheid variable's luminosity and pulsation period, secures for Cepheids their status as important standard candles for establishing the Galactic and extragalactic distance scales. Cepheid variables are divided into several subclasses which exhibit markedly different masses, ages, and evolutionary histories: Classical Cepheids, Type II Cepheids, Anomalous Cepheids, and Dwarf Cepheids. 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. 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). Initial studies of Cepheid variable distances were complicated by the inadvertent admixture of classical Cepheids and Type II Cepheids. Walter Baade's seminal discovery led to a fourfold increase in the distance to M31, and the extragalactic distance scale. RR Lyrae stars were recognized fairly early (by the 1930s) as being a separate class of variable, due in part to their short periods.
What is the connection between a Cepheid variable star's pulse and its brightness?
The pulsation period of a Cepheid variable is related to its intrinsic luminosity. Hence, measuring the period of light fluctuations allows the object's absolute luminosity to be determined, and its distance then follows through comparison with the observed brightness. Therefore, the Cepheids play an important role as a standard candle in assessing the distance scale in the universe.
Why are Cepheid variable stars good distance indicators?
because they pulse periodically, and this period is related to luminosity. the luminosity and their apparent brightness can be used to work out their distance, and the distance of objects around them, using equations with apparent and absolute magnitude. using cepheid variables allows you to approximate distances much further away than stellar parallax allows.
How do astrophysicists calculate the exact distance of other celestial objects from earth?
There are three basic methods: 1. Parallax. The angle at which the object appears in the sky is very precisely measured at one point in the Earth's orbit, then measured again six months later. Since the Earth is in a different position at these times (186 million miles between the two measurments), the star will appear at slightly different angles, and its distance can then be worked out from these angles using simple trigonometry. 2. Standard candles. Certain types of stars (Cepheid variables, RR lyrae variables), and certain types of stellar events (type Ia supernovae), have luminosities that can be worked out fairly precisely from their intrinsic properties (the variable stars for instance, have a period of variablility that is closely correlated with their luminosity, and the type Ia's luminosity can be worked out by examining its light curve). Since percieved luminosity varies inversely with the square of the distance, and since we konw how much light they put out at the source, we can work out how far away these stars are simply by measuring how bright they are. 3. Redshift. The universe is expanding, and that means that from our perspective, distant galaxies are all moving away from us. This means that the light we recieve from them will be at a lower frequency (that is, redder) than the light they emitted, due to the doppler effect. Edwin hubble discovered that at large scales, the observed redshift is directly proportional to the distance of the object from us. This means that if the object is too far away to measure using parallax and lacks a good standard candle, we can still determine its distance simply by measuring its velocity. Actually doing this is somewhat difficult, and involves looking for patterns in the absorption lines in the object's spectrum to figure out what elements created those lines, and then one you know that you can figure out what the frequency of the light should be. After that, you have to work to filter out as many extraneous sources of redshift as possible, such as the object's gravity, its velocity due to gravitational interactions with other nearby objects (what is called the peculiar velocity), and so forth, to leave just the velocity due to the expansion of the universe - from which the distance is estimated using hubble's law.
How do calculate the distance between galaxies?
If you have a 3-D coordinate for each galaxy, then it is possible to get the distance between them. So the whole trick is to get the 3-D coordinate.It’s fairly easy to get 2 of the 3 coordinates from the position on the sky. This gives you the right ascension (RA) and declination, basically equivalent to longitude and latitude on the sky.What’s trickier is getting the distance to the object. For nearby galaxies it can be possible to use distance indicators like Cepheid variables, a star whose pulsation rate is related to its brightness, and use that intrinsic brightness combined with the apparent brightness on the sky to estimate how far away it is. Other example of so-called “standard candles” are RR Lyrae stars and Type Ia supernovae.But this only works for nearby ones, or the rare galaxy that happens to have a SNIa. There are other distance estimation methods, you can read more about them in Cosmic distance ladder - WikipediaThe last resort is to use the galaxy’s redshift, obtained from a spectrum, and use Hubble’s law to relate the recession velocity to the distance. This “redshift distance” can be inaccurate for a number of reasons, but for very distant galaxies the relative inaccuracies are small.But even getting a spectrum can be expensive if the galaxies are distant or faint. It is much easier just to take a picture. It is possible to get a very rough estimate of the distance based on just images in various different bandpasses, because galaxies have particular features that move in and out of various bands as they get redshifted. So one can estimate the redshift, and hence the distance. This is known as a Photometric redshift - Wikipedia, colloquially known as “photo-z’s”.Photo-z’s are actually an area where machine learning has been extremely useful in astronomy, where ML is used to learn the mapping between bandpasses and redshifts based on all the various galaxy features moving in and out of them.
What important discoveries were made early in this century by using RR Lyrae variables?
In this century - the 21st century? Or do you mean early in the 20th century? If so - RR Lyrae stars are standard candles - that is, their period of variability correlates with brightness, so by seeing how long it takes them to go through one variability cycle, we can find out exactly how bright they really are, and then use how bright they appear to calculate distance. This property allowed them to be used to get the distances to Globular Clusters. Since globular clusters contain ~1 million stars all born close to the same time, they are very important for understanding stellar evolution.
What technique is used to measure the distance of a celestial object from Earth and also of its distance from other celestial objects?
There are two parts of the question - 1. distance of celestial object from earth and 2. distance from other celestial objects.The two have to be treated differentlyThe celestial object in question decides the method of measurement. The method of parallax requires a large baseline. The diameter of the earth serves the purpose for the moon, sun and planets. This baseline will not work for stars; the diameter of the orbit of earth is to be used. However as you try to reach farther, even this will not suffice. Currently HIPPORCOS has provided the parallaxes of stars quite accurately. Other methods include using the variable stars called RR Lyr, Cepheids and the like. They will be of use for distant galaxies too. For very far off galaxies red shift and the brightness of Type I supernovae provide very accurate distance estimates. This is a very brief overview only. There are many more methods.For the relative motion of stars within our Galaxy, the space motion of individual stars are measured. The line of sight velocity is provided by the radial velocity measurements. the movement in the plane perpendicular to line of sight are also measured and the resultant is determined. This gives the motion of the stars relative to each other. That is how the motion of the sun around the center of Galaxy and the spiral arms are established.