Visual binaries and the universal validity of the laws of physics

Visual binaries and the universal validity of the laws of physics [@TaurisvandenHeuvel+2023]

← Physics of Binary Star Evolution

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Visual binaries

• Visual binary $\to$ two in proximity through a telescope

• Physical $\to$ gravitonalty bound orbits

• Optical $\to$ happen to be close together in the sky

• Visual binaries have longer orbits

• the proof of physical binaries (and not just coincidence) was proved in 1767 by John Michell

• Shows that Newton’s law of gravity applied outside just our solar system

Astrometric Binaries

\large Wide binaries

• Binaries where one of the stars is too faint to directly observe
• Can still be detected by the following Proper Motion of the visible component
• Center of mass moves along, star orbits this center, showing a periodic wiggle in its apparent motion (I wonder how this can be muddled with and/or separated from parallax. I’m guessing they are in different planes?? (next graphic helped(it wiggles slightly due to yearly parallax, however, the proper motion is much greater and over a much longer duration, so it sort of just becomes “noise” relative)))

Spectroscopic Binaries

\large Spectroscopic Binaries

• A binary which is determined to be a binary due to its spectra
• double-lined binary (SB2) $\to$ when both sets of spectral lines can be observed redshifting and blueshifting
• single-lined (SB1) $\to$ when only set of spectral lines can be observed redshifting/blueshifting
• this is due to Doppler shifting when one of the binaries is relativistically coming towards us and the other away
• Doppler shift ($\Delta \lambda$) can be related to the radial velocity (the component of the velocity on our line of sight)
• $\frac{\Delta \lambda }{\lambda }=\frac{v_{rad}}{c}$

Eclipsing Binaries

Binaries where one star passes in front of the other at some point during its period

• A partial eclipse will happen if
• $\sin (\varphi )<\sin ({\varphi }_0)=\frac{R_1+R_2}{a}$
• where inclination $i$ is defined as the angle between the orbital plane and the plane of the sky $\to$ $\varphi =90°-i$ and $a$ is the orbital radius
• and a total eclipse will occur if
• $\sin (\varphi )<\sin ({\varphi }_1)=\frac{R_1-R_2}{a}$
• We assume that the angles between line of sight and orbital planes are random, the probability of having an angle between 0 and ${\varphi }_0$ is the fraction of the surface area of the half sphere between the pole and the circle at an angle ${\varphi }_0$ from the pole, which is equal to $2\pi (1-\cos ({\varphi }_0))$. While the area of the half sphere is $2\pi$ (Try this myself and verify that this makes sense). Thus, the probability of having an eclipse is
• ${\mathcal{F}}_{eclipse}=(1-\cos {\varphi }_0)$
• Assuming ${\varphi }_0$ small
• $\sin \varphi \sim eq{\varphi }_0\sim eq\frac{(R_1+R{)}_2}{a}$
• due to series expansion (for sure do this at some point)
• $\cos {\varphi }_0\sim eq1-\frac{(R_1+R_2{)}^2}{2a^2}$
• Thus
• ${\mathcal{F}}_{eclipse}=\frac{(R_1+R_2{)}^2}{2a^2}$
• Because $R_1+R_2<a$, eclipses are most likely for either dwarf stars with a very close orbital radius, or wide binaries where at least one star is a giant

• It is possible for a spinning WDs to show variation (but not pulses) in star brightness
• This is because of the magnetic fields on WDs causing bright spots
• Pulsation can be determined by the density

\large Novae/CVs

• Caused my mass transfer onto a WD
• WD shell goes SN, causing Novae
• Standard candle
• Has a variation called dwarf Novae
• caused by instability in the accretion disk
• much weaker

• Brightest sources of x-rays were found to be CV accreting systems

• The first NS star XrB
• Regular periodicity of with increase of x-ray emission
• Caused by the NS being obscured by the larger star

First BH XrB

• Discovered x-ray source with nearby supergiant
• Falls into two classes
• HMXBs and LMXBs
• determined by the mass of the acceptor with respect to the donor
• x-ray emission called by infilling matter
• $\frac{GMm}{R}=.01m{c}^2$ (Shockingly simple eq)
• much much much more efficient than any fusion reactor on earth
• values as high as $.42m{c}^2$
• Common in Globular clusters

Double NSs & BHs

• Proved by GW detection
• Detections are dominated by DBHs
• DNSs formed through lower mass binaries

MSPs

• Generally remnants of LMXBs
• Systems with MSPs generally have WD partners
• Mass-transfer through evolution, or through orbital momentum loss through or GWR
• The NS is greatly accelerated through accretion
• Old NSs which evolved through this process are called Recycled Pulsars

Results of evolution in binaries

• SNe caused by the death of stars more massive than $\sim 8M_{\odot }$
• SNe types \begin{list}{-}{}
• TI-SNe
• TIb-SNe
• TIc-SNe
• TII-SNe

\item due to the fact that TIb-SNe and TIc-SNe are stripped cores, it is incredibly likely that they result from binary systems \item We may also observe both TIb-SNe and TIc-SNe in WR-star, however, we have not yet \item WD SNe (section WD-SNe) require some sort of mass transfer process \item The companion donor can be either a standard star (SD), or another WD (DD) \end{list}

Weird stars

• Blue stragglers
• Barium