Gravitational redshift and the pup measuring the mass of sirius b astrobites salary by education level

White dwarfs are fascinating stellar remnants left over at the end of the lifetimes of many stars. Only about the size of Earth, these tiny objects can potentially be more massive than the Sun. And unlike many of the exotic objects we study in astronomy we have one situated right next door to us! Located a mere 8.6 light-years away, Sirius (the brightest star in the night sky), is actually a binary system. Sirius A, the one we see, is a main sequence A-type star, while its invisible companion Sirius B is a white dwarf. (Sirius B is also affectionately called “the Pup” due to Sirius A being known historically as the “Dog Star.”)

Sirius B was discovered on January 31, 1862, and was recognized as a white dwarf in 1915, only the second one to be discovered (after 40 Eridani B, as related in this astrobite).

A year later in 1916 Einstein published his theory of General Relativity, with one of its predictions being that light leaving a star should be affected by gravitational redshift. (This is where light climbing out of a gravitational well loses energy and appears redder.) In 1924 the astronomer Arthur Eddington realized that, since Sirius B was so small and dense, it should show a measurable gravitational redshift. highest level of education attained question This was measured for the first time in 1925 by Walter Adams at the Mt. Wilson Observatory and considered a big success for General Relativity. (Although we now know that both the predicted and measured shift were about four times too low; it’s speculated that the spectra of Sirius B may have been contaminated by light from Sirius A which is very nearby on the sky.)

By measuring the gravitational redshift of a star with a known radius we can also measure its mass, since for a typical stellar object (i.e., not a neutron star or black hole) the gravitational redshift depends only on those two quantities. We can measure the distance to Sirius B using its parallax very well since it’s so nearby, and by measuring its luminosity (based on its brightness and temperature) we can work out its radius. japan education level We can also measure its mass dynamically, by observing how it and Sirius A orbit around their common center of mass and applying Kepler’s laws of orbital motion, but there’s a small problem: estimates of Sirius B’s mass based on measurements of its gravitational redshift have historically differed from its dynamically-measured mass by about 10% (to be clear, this is from new measurements taken after the original ones were realized to be wrong).

To clear up this long-standing confusion, the authors of today’s paper used the Hubble Space Telescope to take spectra of both Sirius A and B in order to perform a differential measurement of the gravitational redshifts of both. Differential measurement is a useful tool as it helps eliminate a lot of systematic errors that might be present in an instrument, since any that exist will affect all observations equally. The gravitational redshift of Sirius A is better known than for Sirius B, so by measuring both, finding the difference between them, and correcting for the known value of Sirius A’s redshift it’s possible to make a more precise and accurate measurement of the gravitational redshift of Sirius B than would be possible by observing it alone. Hubble, Hubble, Toil & Trouble

Gravitational redshift, even for a white dwarf like Sirius B, isn’t a very large effect. In earlier work the gravitational redshift for Sirius B was estimated to be 83 ± 3 km/s. what is secondary level education in australia At the wavelength of hydrogen alpha (Hα) which the authors used to measure the redshift, this corresponds to a shift in wavelength of just 1.81 ångströms (Å, 1×10 −10 m) . what does education level mean Figure 1 shows the four spectra of Sirius B acquired by the HST, showing just how small such a shift is.

Figure 2: The velocity of the Hubble Space Telescope with respect to the Sirius binary system center of mass as a function of time over the time period when the observations used in today’s paper were taken. Blue circles are spectra of Sirius B, green stars of Sirius A. Figure 5 in the paper.

Measuring the redshift of Sirius B required a lot of velocity bookkeeping for the authors: they had to account for the velocity of the HST around Earth (as shown in Figure 2), the velocity of Earth around the Solar System’s center of mass, and the velocities of Sirius A and B around their common center of mass. After correcting for all this they were able to get a measurement of the difference in redshift between Sirius A and B. By correcting for the (previously-calculated) value of the gravitational redshift of Sirius A of 0.759 km/s and comparing it with the differential redshift they found for Sirius B, the authors were able to get an absolute value of the gravitational redshift for Sirius B of 80.65 ± 0.77 km/s.

This measured redshift was then used to compute the mass of Sirius B using a simple model. The value of 1.017 ± 0.025 solar masses from this calculation matches the value obtained by dynamical methods—1.018 ± 0.011 solar masses—almost exactly. And by combining the mass of Sirius B with its radius the authors were able to show that it fits nicely with our models of something called the mass-radius relation for white dwarfs, as shown in Figure 3.

Thanks! To answer your question, white dwarfs are extremely hot when they form (at the level of 150,000 K!), and continue to cool off slowly by emitting electromagnetic radiation for a long time afterwards. This mostly takes the shape of blackbody radiation like you mentioned, since their atmospheres are mostly hydrogen and/or helium which don’t have many spectral lines in the visible region. high school level of education That’s why the authors of the paper used the hydrogen alpha line, as it’s one of the few spectral lines normally visible in white dwarf spectra. And yes, white dwarfs are much fainter than main sequence stars—that’s how they were first noticed, by being much fainter than they “should” be—but they’re still bright enough for us detect quite a lot.

(Some white dwarf spectra show signs of other elements, which means that they must be actively accreting material; their high surface gravity would pull any elements more massive than hydrogen and helium below the surface and out of sight on very short timescales!) Reply