LOG#208. Monsters and LISA.

Posted on by September 1, 2019

Black holes and other astrophysical objects are true monsters. Some interesting tools from web pages to learn about these free catalogues: WATCHDOG and BLACKCAT. Also, the blackhole.org page and the sounds of spacetime for gravitational waves are suitable for you. Furthermore, you can enjoy the BH stardate online encyclopedia.

Two of the biggest and coolest (literally) black holes are quasars. Their names: OJ 287 and 3C 273. Persistent BH sources do emit X-rays, and they are powerful sources of X-rays in our galaxy (and beyond!). Transient BH events are also studied. Beyond X-rays, you study BH accretion and merging, likely BH growing if you are “lucky” or a true believer.

A list of “monsters” (not necessarily BH):

  1. Moon’s magnetic field.
  2. Asteroid with rings. 10199 Chariklo its name.
  3. Sixtail asteroids (not steroids!)
  4. Red storm (Jupiter’s famous biggest spot!).
  5. Hot Jupiter messes.
  6. HD 106906b.
  7. Uranus storms.
  8. KIC2856960.
  9. UV underproduction sources.
  10. Shape of dark matter (DM).
  11. Galaxies with age of billions of years (10 billions or more!).
  12. Iciness Saturn rings.
  13. GR bursts and fast radio bursts.
  14. Cataclysmic variable stars.
  15. Universe smoothness.
  16. Strange structures in the Universe (Multiverse?).

The new born gravitational wave astronomy is going to outer space. LISA (Laser Interferometer Space Antenna) will study a completely different set of sources beyond the ground based gravitational wave observatories. What are they?

  1. WD (White dwarf) binaries.
  2. NS (Neutron Star) binaries.
  3. BH+NS/WD systems (binaries).
  4. BH+BH mergers (supermassive or even intermediate; EMRI and IMRI are expected to be observed). EMRI=Extreme Mass-Ratio Inspirals. IMRI=Intermediate Mass-Ratio Inspirals.

LISA science targets in its timelife (2-10 years):

  1. Hubble constant (after 2 years, by binary inspirals, with accuracy of a few per cent).
  2. Equation of state of dark energy.
  3. EMRI/IMRI sources/observations.
  4. Tests of fundamental physics with gravitational waves.
  5. Ultracompact binaries.
  6. Surprises we have not expected or thought about ;).

By the other hand, beyond GW astronomy, some cool experiments are the HAWC water telescope, Cherenkov telescopes (CTA!), and the AMON network.

Primordial BH are interesting objects. In the window 10^{-16}-10^{-7}M_\odot they offer the option to be ALL the dark matter.

Gravitational wave luminosity (power!) is given for a binary (non-eccentric) system by:

    \[L_{GW}=-\dfrac{dE}{dt}=\left(\dfrac{32}{5c^5}\right)G^{7/3}\left(M_c\pi f_{GW}\right)^{10/3}\]

where the gravitational wave frequency is

    \[f_{GW}=2f_{orb}=\dfrac{1}{\mathbf{\pi}}\sqrt{\dfrac{GM}{r}}\]

and M_c=\mu^{3/5}M^{2/5} is the chirp mass, and the reduced mass \mu=M_1M_2/(M_1+M_2), with M=M_1+M_2. Sometimes, the symmetric mass ratio \eta=\mu/M is used. Non-zero binary eccentricity formula do exist but it will not be considered in this post. GW higher harmonics are useful in GW astronomy. However, for circular orbits, you have

    \[\dot{f}_{GW}=\left(\dfrac{96}{5c^5}\right)G^{5/3}\pi^{8/3}M_c^{5/3}f_{GW}^{11/3}\]

For the strain amplitude, averaging, you get

    \[h=1.5\cdot 10^{-21}\left(\dfrac{f_{GW}}{10^{-3}Hz}\right)^{2/3}\left(\dfrac{M_c}{M_\odot}\right)^{5/3}\left(\dfrac{D}{kpc}\right)^{-1}\]

Remember: the gravitational wave frequency evolution for a binary system from t_0 up to coalescence is twice the orbital frequency:

(1)   \begin{equation*} f_{GW}=2f_{orb}=\dfrac{1}{\pi}\left(\dfrac{GM_c}{c^3}\right)^{-5/8}\left(\dfrac{5}{256(t_0-t)}\right)^{3/8} \end{equation*}

where the chirp mass reads off

(2)   \begin{equation*} M_c=\sqrt[5]{\dfrac{(M_1M_2)^3}{(M_1+M_2)}} \end{equation*}

and the power of the gravitational wave is equal to

(3)   \begin{equation*} P_{GW}=\dfrac{32G}{5c^5}\mu^2\omega^6 r^4 \end{equation*}

with \omega=2\pi f_{GW} and \mu=M_1M_2/M, M=M_1+M_2.

By the way, the maximal frequency on Earth that we can detect from binary black hole mergers is related to the innermost  stable circular orbit (ISCO). Roughly, this orbit corresponds to a radius or separation from the center of mass equal to r=3r_s/2=6GM/c^2. For this orbit, the frequency should be:

(4)   \begin{equation*} f_{max,c}=f_{isco}=\dfrac{c^3}{6^{3/2}\pi GM}\approx 4.4\dfrac{M}{M_\odot} kHz \end{equation*}

Thus, ground bases observatories could catch on mergers of intermediate black holes if sensitive enough. However, they will catch more easily mergers of tens or hundreds of solar masses. What are the biggest monsters? The new created black holes species with more than millions of solar masses: the ultramassive black holes (with more than 10^{10} solar masses). Example: IC 1101, TON 618, NGC 4889, NGC 6166, NGC 1270, and others you can read off from the this wiki-list.

We will learm more about the sounds of spacetime in forthcoming entries! See you in other wonderful blog post…

P.S.: From Orosz et al. and other sources from the arxiv, you get something like this list (several versions included)

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