On a New Method to Estimate the Distance, Reddening, and Metallicity of RR Lyrae Stars Using Optical/Near-infrared (B, V, I, J, H, K) Mean Magnitudes: ω Centauri as a First Test Case (2024)

FAQs

How do astronomers measure the distance to RR Lyrae stars? ›

The period of pulsation of an RR Lyrae variable depends on its mass, luminosity and temperature, while the difference between the measured luminosity and the actual luminosity allows its distance to be determined via the inverse-square law.

The figure to the right shows the variation in the apparent magnitude of the RR Lyrae star VX Her. Note that the average apparent magnitude is about 10.5. Thus, the distance modulus for this stars is (m - M) = 10.5 - 0.5 = 10, which corresponds to a distance of 1000 pc.

Their period is shorter, typically less than one day, sometimes ranging down to seven hours. The relationship between pulsation period and absolute magnitude of RR Lyraes makes them good standard candles for relatively near objects, especially within the Milky Way.

In the H-R diagram, RR Lyrae stars can be found in the narrow region where the horizontal branch intersects the pulsational instability strip.

The RR Lyrae (RR Lyr) stars are identified with a unique stage in the life of a low-mass star, the horizontal branch, helium core burning period of evolution. As such, they show a small range in luminosity, the most variable property being their effective temperature as a function of mass.

Classical Cepheid variables are higher mass population I stars. RR Lyrae variables are much more common than Cepheids, but also much less luminous. The average absolute magnitude of an RR Lyrae star is about +0.75, only 40 or 50 times brighter than the Sun.

The metallicity distribution of the RR Lyrae stars peaks at (Fe/H)_K approximately equals -1.5, and is narrower than that of the Ryan & Norris (1991) subdwarfs, as expected since the most metal-rich and metal-poor progenitors preferentially appear as stable red and blue horizontal branch stars, rather than as RR Lyrae.

This class of stars came to be known as classical Cepheid variables, and by comparing the apparent brightness measured from earth with the known actual brightness of the star, the distance to the star could be calculated with previously unmatched accuracy.

So, RR Lyrae stars make very convenient distance indicators -- but they just aren't luminous enough to be seen in distant galaxies.

The cluster variables -- mostly RR Lyrae stars -- were used as "standard candles" to measure the distances to the globular clusters, and so provided us with a first glimpse of the true size of the Milky Way.

Why are RR Lyrae stars important? ›

RR Lyrae stars are one of the primary distance indicators for old stellar populations such as globular clusters, dwarf galaxies and galaxies.

To calculate this, take 1/2 the value between the brightest and dimmest magnitudes. Remembering that the mean absolute magnitude of an RR Lyrae star is 0.75, calculate the distance to the RR Lyrae star, and thus M4, using the distance-magnitude relation.

The upper right-hand corner of the H-R diagram (marked on Figure 10.14), where these stars are found, is called the red-giant region (and Supergiant region). No red giants are found within 5 pc of the Sun (Figure 10.13), but many of the brightest stars seen in the sky are in fact red giants (Figure 10.14).

Vega is a class A0Va star that's positioned within the main sequence of the Hertzsprung-Russell diagram. It's a nearby star, only 25 light-years distant, and relatively young at 455 million years. This is about 1/10 the age of the Sun.

All Cepheids with a certain period are assumed to have the same absolute magnitude. Measuring the apparent magnitude of a Cepheid then allows us to determine its distance using the period-luminosity relationship. If two Cepheids have the same period but is fainter than the other it must be further away.

Astronomers use an effect called parallax to measure distances to nearby stars. Parallax is the apparent displacement of an object because of a change in the observer's point of view.

All Cepheids with a certain period are assumed to have the same absolute magnitude. Measuring the apparent magnitude of a Cepheid then allows us to determine its distance using the period-luminosity relationship. If two Cepheids have the same period but is fainter than the other it must be further away.

A typical RR Lyrae has a luminosity perhaps 50 times greater than the Sun. That's nice, but it's not powerful enough for us to see these stars in distant galaxies. In fact, we can use RR Lyrae to measure distances only to the very closest galaxies -- members of our own Local Group.

For the same reason, astronomers don't use miles to measure vast distances in space. Instead, they use light-years: the distance that light travels in a year. That makes Proxima Centauri, the closest known star to the Sun, 4.28 light-years away; that's a lot easier than saying 24,000,000,000,000,000 miles.