Compact binaries through a lens

Summary of work published in Physical Review D and also available on the arXiv.

What are gravitational waves?

Gravitational wave detectors track the oscillations of the spacetime itself, which propagate towards Earth at the speed of light. Unlike light, these ripples of space-time are not absorbed by the many intervening objects between us and the catastrophic event we observed, which may have happened a billion or so years ago. However, their detection is quite challenging because the spacetime is very stiff and can thus only be shaken to a detectable level by very massive events such as the collision of dead stars, which are very dense. Gravitational wave detectors on Earth have seen the merging of black holes or neutron stars or black-hole - neutron star pairs. The observations provide a first map of the stellar graveyard.

Although when black holes collide, the energy they spend that shakes the vacuum of the spacetime is a lot more that they had used to shine as stars they only shake the spacetime a very tiny little bit. By the time these vibrations reach Earth, and we can measure them, they change the arm length of LIGO or Virgo, which are 4 km (or 3 km for Virgo) by less than an electron, which is less than a hair width. So the change is very, very tiny and buried in deep noise. Detecting it is quite challenging, but the LIGO-Virgo-Kagra observatories have a large team of people who do these searches, and make sure the signals are real. In order to find them through the noise, it's crucial to know what we are looking for.

We are looking at the colliding compact objects in the stellar graveyard through a lens, which acts as a magnifying glass. The lens is formed from the material that lies between us and the binary we are observing. The more massive and the closer to the line of sight, the more it affects the signal. In this manuscript, we assumed the lens is a point mass, i.e., can be assumed to be a compact object.

How do lensed waveforms look?

• amplified (e.g., the signal is stronger than the unlensed version), the higher the frequency the more the amplification. The frequency is always highest at merger. Some signals display only amplification.
• a beating pattern may appear with destructive (holes) and constructive interference (brighter spots) of two nearby images produced by the same event. The frequency of the bright spots and holes can be predicted analytically for the point mass lens model.
• separate images/waveforms from the same event appear minutes to months apart if the lens is a galaxy (strong lensing), and less if the lens is smaller (microlensing).

The lensing amplification causes the source's distance from the detector to be underestimated. Not only does it appear to be closer, but it also appears more massive because the redshift is underestimated. A binary at z=3 will appear four times more massive when detected on Earth than it is at the source. So, it's important to know where the source is to be able to accurately predict its mass.

What is the mismatch with unlensed waveforms?

For waveforms that look very similar one might not be able to tell whether they are lensed or not. We compute the match (the number on the white contours is the match) and the signal to noise increase (coloured bar) due to lensing as a function of the mass of the lens that sits between Earth and the merging binary and the source position, y. The smaller the y, the closer to the lens is to the line of sight between the source and Earth. We find that under 20% of all detected events are lensed, and out of those under 5% of events would be detectably lensed with a mismatch greater than 10%. However, our model only includes point masses lenses, and our computation are an upper limit for when all dark matter is formed from these lenses. More realistic studies will include composite lenses between Earth and the binary.

How far could lensed events be?

It depends on the mass of the binary. We see that an event detected at a typical total binary mass that is 60 times more massive than the sun, could be at a redshift z=2. This means the source frame mass would be 3 times less, and thus closer to Xray observations. Similary, if we see an 120 solar mass event, it could be at a redshit z=3, which would make it the detected value 4 times larger that the actual black hole masses.

A redshift of 3, means the signal from the event would have traveled some 11 billion years to reach us, while a z=2 impilies a travel time of 10 billion years. At a z=0.1, the event happened a billion years ago. However, even if the events are lensed, since mismatch to the unlensed template is relatively low, we are likely never know it. The plots of the right shows the distribution of (a) all lensed objects (b) lensed objects with a mismatch of 5% from their unlensed counterparts and (c) lensed objects with a mismatch of 10%. All are are above a threshold SNR of 10 for the estimated O4 noise curve (average expected noise for the current LVK run).

What have we seen to date?

Up to now, we have seen of the order of 100 black hole merger events, two neutron star mergers, and some black-hole neutron star collisions. Ground based detectors are again operational in the US with Virgo soon expected to be joining. However, most black hole binaries detected are unlike any seen in the Milky Way before. There are about more massive than those found in X-ray studies with an average total mass of about 60 solar Masses, while those found in our galaxy are closer in mass to our sun (the pink are the black holes and the yellow the neutron stars).

Are the black holes seen by gravitational waves observatories really different? or do we percieve them as different? Could they be lensed?

It could be that our galaxy is different from the typical galaxies out there. Or it could be that there is something between us and the source that make the black holes appear more massive. We are looking at them through a magnifying glass formed from intervening matter. If that matter is massive enough, it makes them seem more massive than they are. The more distant the event, the more likely it is to be lensed. A lensing pattern has not been observed by the LVK to date. Our results predict that under 5% of events are detectably lensed, which is consistent with observations to date.

Ok, so you've explained gravitational waves, but what are Xray observations?
Xrays are light of high energy and very short wavelength that can pass through materials that are opaque to visible light. Since different materials absorb light at different lates, they can be used in medicine to show broken bones or in astrophysics to see dying stars (supernova), dead stars with disks (black holes), and merging galaxies.

Our team
Our team is 50% female (me and Helena), while Oleg and Andy represent the other side (males, still 50%). This post is a summary of work published in Physical Review D. The paper is also available on the arXiv. Please read the paper for more details.

Is freedom of speach gone?

Today, I woke up to the news that lawyers in the US are being denied jobs for offering intellectual support to the Palestinian cause.

This is wrong. We should not do this. We are responding with violence to a peaceful act of dissent. This can only escalate the violence. And, when things escalate, terrible things happen.

For example, if one of the students believes the letters of dismissal are wrong, and an act of violence, they may feel entitled to use violence to set things right. It will take a lot of violence (is it an infinite amount? ) to convince a law firm to make a job offer otherwise.

Now, imagine the people in Gaza. Some, perhaps due to intellectual limitations, think that violence is their only way to speak. We do not let them speak otherwise. And, when violence is used to send a message, innocent people die, and it hurts. More violence then follows.

We should allow the ideas of Gazans to be heard in our courts, in our schools and on our television. We should even allow Hamas to speak in our synagogues and temples. We should listen to them, and we should prove that terrorism and violence are wrong. It should be clear to any would be terrorist that they are more welcome to speak in a synagogue than to blow it up. That their arguments can be heard, peacefully, and reasonably.

No matter how absurd it seems to us today, when thousands are willing to die for an idea, no matter how silly it seems, the idea is not without merit. We thus should listen, before the guns come out.

Encouraging logical arguments could give Palestinians an incentive to become educated -- and more able to make logical arguments. Educated people are less inclined towards violence and less likely to want to die for no good reasons, killing other innocents in the process and bringing death, ruin and despair upon their loved ones.

Funding schools, increasing employment rates, allowing for human rights, and open borders are the only way to have peace. This has been shown over and over. Eastern Europeans can travel and work in Western Europe. There was a lot of fear that opening the borders would not work, but it does. Educating people and allowing them to work functions. Many people in the western world are very lonely and old, and the elderly do not receive enough care. They could benefit from interactions with those who still know how to connect with others. People from large families still retain that ability. The US is making the same mistake with its wall with Mexico and with its inner cities, where drugs and guns are prevalent because there is no funding for education.

The world is connected. It should not be so easy to silence all voices as it has been in past wars. Palestinians are at Harvard and Yale, in Scotland, in Barcelona, and in other places. They are not just in Gaza. We should learn from this, and allow for education and employment instead of encouraging guns and the punishment of the wrong people, which has been done and documented by historians over and over and justified by corrupt politicians through the media. The children and women of Gaza have not killed anyone. Neither have those in Israel. They have the right to grow. It should not matter what country they come from.

The leadership needs to change in Israel, Gaza, the US, Russia, China, etc, and countries should unite to fight climate change just as they united in the restrictions against COVID instead of fighting each other and poluting through bombs and destruction of buildings and roads that will have to be rebuilt at a cost to the environment. No country should be allowed to SELL weapons or conduct OR SUPPORT a war without being prepared to pay for the cost to the environment not just for the bombs. Leaders of countries should be changed in the same way we change mayors. They seemed to have little power during COVID. The decisions were uniform. Why are they so powerless to stop genocide yet again? Why is the destruction of a whole country the only way to respond to mass murder like 911 or the massacre in Israel? It's not like the Taliban lost. They have power over Iraq and Afganistan now. So why is Israel supported in repeating the mistake the US made? How far should Hamas extend? West Palestine? Jerusalem?

Gaza and Israel: an evolving tragedy

Hamas, the de facto unelected government of Gaza, achieved the largest single massacre in the history of Israel since the Holocaust. While Hamas has not caused significant damage to Israel, it has clearly demonstrated its ability to repeat the Holocaust -- on a small scale. Under the nose of the Mossad, and paid by Israeli taxes, drinking Israeli water and running on Israeli electricity, a government was born that carried out this massacre. And Israel let it happen -- on a small scale.

Of course, the problem with the other Holocaust was that the government that carried it out was Germany, which was by some accounts, the strongest economy in the world at the time. In Germany, like in Israel today, ordinary people colluded with their hallucinating government and committed despicable crimes that targeted innocent people of a certain kind, i.e., Jews. Then the criminality was forcefully extended to the rest of Europe and to other kinds of people, e.g., after world war two, being educated or owning property was considered a crime worthy of being sent to Siberia for. I still have a letter that identified my grandparents as "poor peasants" and not worthy of being destroyed after they donated all their property to the state. War and bombs never brought peace or justice. They simply brought more attrocities.

Why?

Why don't we have schools to teach our people about government hallucinations, and protect us from a Holocaust? Why do we obey our governments, even when we think they are hallucinating?

What should Israel teach in the schools of Gaza for its people to not fire on civilians when told to do so? And to not join their government in a suicide mission when told to do so? Should Israel teach its own people to not fire on civilians when told to do so?

Gaza is 50% children under 18. The adults are 50% non-combatant women. Of the 25 % that are men above 18, not all will be combatants. Some will be bakers, some doctors, some beggars, some gay, some Jews... Among them is the family of our Scottish minister. Many of them are victims of Hamas. Every government has its victims and detractors. Not all Americans voted for Trump. Not everyone in Gaza voted for Hamas. They don't even bother with elections. So, it's important to keep in mind that like all wars, this war affects innocent people. Not Hamas. Hamas thrives on conflict. The people who die or are maimed are innocent. As are those who don't have water, food, medical care, etc.

Israel bombs in response to this massacre. Are they right to bomb them? Or, should they allow them to be educated and civilized instead?

Of course, under the leadership of Hamas, Gaza had the highest fertility rate outside Equatorial Africa until about 2007. If we were to civilize them, their birth rate would drop to align with the rest of the White World. That would decimate them. Far more than bombs ever can.

So... what shall we send? Books to educate them and reduce the babies that are yet to be conceived? Or bombs to set their blood and wombs on fire?

How should Israel respond? Is it reasonable to kill children in Gaza?

Israel has money and technology. Israel will first send in the drones and the tanks and the remote operated land vehicles. Israel will use material assets to "protect" its people.

Hamas is different. Gaza has children, but little tech. Thus, Hamas will hide behind children. Hamas will hide its guns in schools and let the children die before the guns get damaged. Decapitated children look better in press than cheap, old guns destroyed.

Is Israel right to obey Hamas wishes and fire through the bodies of the children of Gaza in order to damage the guns that killed Israeli children? What can Israel do for the children that survive today's carnage in Gaza to not want the Holocaust to happen again, and to not participate in a next Holocaust, if the future gives them the chance?

Half of the population of Gaza is under 18. Half is women. One quarter are men over 18. Many of the children are involved in the war -- either as soldiers of shields. Few of the women fight. They have 6 children each, on average. For them, breastfeeding is more important than shooting. Have these women and children given their valid informed consent to participating in the war?

Surely, the reign of Hamas must be over. Is Israel right to kill people who are involved in a war against their wishes, and without their valid informed consent?

How much money and how many Israeli lives (the lives of soldiers, who, often, are not much older than children) should Israel be willing to lose in order to kill fewer innocent people in Gaza?

Perhaps, the central question, is 'What is Gaza?' Is Gaza a state? Or a jail?

If Gaza is a state, perhaps, we have no business interfering with the internal operations of the state and its Hamas government. We can cordially advice Hamas that Holocaust is not ok, and, should they not obey, we can bomb their children and them into oblivion.

If Gaza is a jail, then it is full of innocent people. Even if we assume all the adults to be guilty of something sufficiently atrocious to warrant keeping them in jail, the children are innocent. The children are half of the population.

If, in this jail, we have a band of criminals -- Hamas and his minions -- who decide to terrorize both Israel and Gaza, it is, perhaps, our responsibility, as custodians and guards of the jail, to protect the inmates from harm caused by Hamas. Not only not harm them, but protect them. If a person is in jail, and they are harmed by another inmate, the prison authority is responsible, as the inmates have not chosen to be there.

What is the effect of the current bombing?

Hamas runs on very little money, compared to the Israel military and state. Hamas runs on people. Many, cheap destitute, desperate men who are willing die for very little reason. Many destitute women who have as many children as they can bear. The bombing of Gaza will make its population more destitute. Their response will be to have more children. Strangely, people have more children in hard times. Gaza and Afghanistan have the largest birth rates in the White World and Israel has the largest birth rate in the Western World.

The many children born in Israel are a reaction to the Holocaust and to terrorism like we have witnessed. Death often acts as a fertilizer for people. The more bombs fall, the closer people feel to death, the more children are born.

The children born in Gaza are the result of the Israeli war. Poverty, destitution, bombs and Hamas have pushed the birth rate of Gaza sky high. It is second only to Afghanistan in the world outside Equatorial Africa.

The more bombs we rain on them, the more children will be born, right next to Israel, where Israeli Arabs will soon outnumber other Israelis.

While governments around the world, from Europe to Asia and the Americas are fighting population collapse with very serious resources, Hamas is getting population growth. Shall, maybe, the people of Japan, Singapore and South Korea go to Gaza and maybe learn some lessons? Can we get some of the growth without the terror and without the bombs? The Amish have high natality while being peaceful. Perhaps smaller communities with leaders that have power locally, and, overall, a simpler life where we give back some of what we take from each other and from nature vs more bombs and more destruction are the solution when we have climate change to fight.

In spite of a warm year with storms, and earthquakes and the longest part over 1.5 C in recorded history, the number of small wars around the world is growing. Gaza has overtaken Ukraine for press coverage of attrocities. There is also unrest in Armenia, Serbia, Hong Kong, etc. Will these conflicts, eventually, unite in a third world-war? How soon? And what will the destruction be? we already have enough problems with climate change without more wars... Will we ever stop bombing innocent people and opt for education instead?