Q&A: Supernova Remnants and Neutron Stars

Q:
How bright would this glow be compared to other self luminous and reflective objects (i.e., what magnitude would it appear to be at one AU)?

What how strong would this glow be in different parts of the spectrum (i.e., visible light, IR, etc.)?

A:
A neutron star is born very hot (leftover heat from when the star was still "normal" and undergoing nuclear reactions) and gradually cools over time. For a 1 thousand to 1 million year old neutron star, the surface temperature is about 1 million Kelvin (whereas the Sun is 5800 K).

I will continue to make comparisons to the Sun (one reason is that it is at a distance of 1 AU). To determine it's intrinsic brightness, we need to know the size of the neutron star, which turns out to be about 10 km. The Sun is much bigger (solar radius 7x10⁵ km). The intrinsic brightness or luminosity is proportional to the square of the size and the fourth power of the temperature; the luminosity of a neutron star compared to the Sun is (10/7x10⁵)² x (10⁶/5800)⁴, which is about 1. Therefore, a 1 million Kelvin neutron star is about the same intrinsic brightness as the Sun.

However, because it is much hotter, it is brightest at X-ray wavelengths [whereas the Sun is brightest at visual wavelengths; this is just like a hotter blowtorch is blue (or shorter wavelength), and a cooler one is red.] So if you had X-ray eyes, a neutron star at a distance of 1 AU would appear as bright as the Sun (in visual). On the other hand, a neutron star is quite a bit dimmer at visual wavelengths; it turns out to be about -10th magnitude at visual at a distance of 1 AU, ie a little dimmer than the Moon.