Taking a census of galaxies? China's sky survey helps resolve the Hubble crisis!

The English version of Science China Physics, Mechanics & Astronomy (SCPMA) published the research results of Zhang Xin's team from Northeastern University as a cover article in the 3rd issue of 2024. The article is titled " Synergy between CSST galaxy survey and gravitational-wave observation: Inferring the Hubble constant from dark standard sirens " [1]. At the same time, a commentary article written by Professor Zhu Zonghong of Wuhan University was published [2].

1 China Space Telescope

Since its launch in 1990, the Hubble Space Telescope (HST) has become one of the most important instruments in the history of astronomy. On December 25, 2021, the James Webb Space Telescope (JWST), the successor to HST, was launched, extending human vision to the more distant and ancient deep space of the universe. When will the Chinese space telescope, which Chinese scientists have been eagerly waiting for, arrive?

The exciting news is that the Chinese Survey Space Telescope (CSST) is scheduled to be launched around 2025, and our own eyes for deep space exploration will soon be available.

Why move telescopes into space?

The main purpose of sending telescopes into space is to avoid the interference of the atmosphere on astronomical observations. Astronomical telescopes observe electromagnetic waves emitted by celestial bodies, and the atmosphere has a great influence on electromagnetic waves in most frequency bands. For example, it is almost impossible to conduct X-ray astronomical observations on the ground. In addition, moving telescopes into space can also avoid interference from artificial light sources. Therefore, space telescopes can see more clearly and farther than ground telescopes of the same caliber.

How powerful is China's space telescope?

Figure 1 shows an imaginary picture of the CSST, which has an aperture of 2 meters, comparable to that of the Hubble Space Telescope HST, but a field of view that is more than 300 times that of the latter (HST is a "precision measurement" telescope, while CSST is a "sky survey" telescope). Therefore, the CSST can very efficiently conduct a "census" of galaxies in the universe. In addition, the upper limit of its observed apparent magnitude is up to 26 magnitude, which is higher than the 23 magnitude of the Hubble Space Telescope. This means that the CSST can observe darker and more distant galaxies in the universe. These advantages allow us to understand the distribution of galaxies in the universe in a more comprehensive and detailed manner, which will help us understand the formation and evolution of galaxies, and even the evolutionary history of the entire universe.

Good design indicators will inevitably lead to high research costs. Referring to the same-level survey telescopes of the same period in the world, such as the Euclid of the European Space Agency (ESA) and the Roman Space Telescope of NASA, the construction cost of CSST is estimated to cost at least several billion yuan. Despite the high cost, its scientific returns are also very huge.

Figure 1: Imaginary image of the China Space Telescope. (Source: CSST official website [3])

2 The third generation of ground-based gravitational wave detectors

On September 14, 2015, humans used the Advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) to directly detect gravitational waves for the first time [4]. aLIGO is an upgraded version of LIGO and is therefore classified as a second-generation gravitational wave detector. In the 2030s, the more ambitious third-generation gravitational wave detectors, the Einstein Telescope (ET) [5] and the Cosmic Explore (CE) [6], will begin operation. Their sensitivity will be an order of magnitude higher than that of the second-generation detectors, and the frequency range of gravitational wave detection will also be wider.

How difficult are gravitational waves to detect?

In fact, more than 100 years ago, in 1916, Einstein predicted the existence of gravitational waves, a type of ripples in spacetime that propagate at the speed of light[7]. If spacetime is likened to a calm surface of water, the generation of gravitational waves is like throwing a stone into the water. The farther away the stone is, the smaller the ripples become. By the time the stone reaches Earth, it is so weak that it took humans 100 years to detect it.

Take aLIGO as an example. Its principle of detecting gravitational waves is simply to use laser interference to measure the tiny length changes caused by gravitational waves on two 4 km long "arms". In 2015, the gravitational waves it first detected had a maximum dimensionless amplitude of about 10-21, which means that the 4 km long "arms" of aLIGO changed by 10-18 m under the influence of gravitational waves. In comparison, the radius of a proton is about 10-15 m, which is hundreds of times the change in the length of aLIGO's arms!

Why detect gravitational waves?

The significance of gravitational wave detection is multifaceted, including verifying the general theory of relativity, studying black holes and neutron stars, detecting the history of cosmic evolution, exploring new physics, etc. Here we will only discuss in detail its measurement of the Hubble constant (H0) to solve the "Hubble crisis". H0 describes the current expansion rate of the universe. It was first proposed by American astronomer Edwin Hubble and can be said to be the first parameter in cosmology [8]. In 1986, Bernard F. Schutz proposed a method to measure H0 using gravitational waves [9]. The core idea is to use a special type of celestial system - a compact binary system (such as binary neutron stars, binary black holes, and a combination of neutron stars and black holes). Under the influence of gravity, they will rotate and gradually approach each other, like two leaves rotating and approaching in a vortex. By analyzing the waveform of the gravitational waves they generate, their absolute distance from us can be obtained. At this time, if their redshift information is obtained through optical observation, the distance-redshift relationship can be established, thereby inferring the expansion history of the universe and measuring the current expansion rate of the universe H0. Analogous to the "standard candle" and "standard ruler" in cosmology, cosmologists named this type of binary star system that is spiraling into merger the gravitational wave "standard whistle."

What is the "Hubble Crisis"?

In recent years, with the improvement of observation accuracy, the measurement of H0 has become inconsistent, triggering a huge cosmological crisis, known as the "Hubble crisis". Specifically, as shown in Figure 2, using the cosmic microwave background (CMB) observations of the early universe, under the standard cosmological model, the inferred H0 value is about 67 pics (uncertainty is 0.8%). The H0 value directly measured in the late universe using the distance ladder method is about 74 pics (uncertainty is about 1.4%).

There is more than 10% inconsistency between the two. From a statistical point of view, the H0 values ​​supported by the two observations are outside the confidence interval of the other's near picture, indicating that the H0 values ​​they point to are contradictory and cannot be true at the same time.

Figure 2: Development of Hubble constant measurements over the past 20 years. Red represents the results obtained using CMB observations (early universe measurements), while blue represents the results of direct measurements using the distance ladder method (late universe measurements). The red and blue shadows represent the uncertainty of the results limited by the two observational methods. The latest results show that the inconsistency of the measurement results has reached 5.3 times the standard deviation. (Source: D'arcy Kenworthy [10])

How to solve the "Hubble Crisis"?

By analyzing the two observation methods, we found that: on the one hand, it is possible that one of the two measurements is wrong, so a third-party cosmological observation is needed to arbitrate the value of H0; on the other hand, if the measurements in the early and late universe are reliable, then there may be a problem with our understanding of the universe, that is, the standard cosmological model is flawed and needs to be expanded. At present, there has been a lot of research work on expanding the standard cosmological model, however, no extended model can both solve the "Hubble crisis" well and match the observational data well.

Research shows that in the future, the gravitational wave "standard whistle" is expected to become a third-party cosmological observation for arbitrating the H0 value. As mentioned above, the "standard whistle" can give the absolute distance of the gravitational wave source. In comparison, in the distance ladder method, the type Ia supernova gives a relative distance, which needs to be calibrated to obtain the absolute distance. The calibration process is widely believed to have unknown systematic errors. Therefore, the gravitational wave standard whistle has a unique advantage in measuring H0.

Why develop the third generation of ground-based gravitational wave detectors?

Although the current second-generation gravitational wave detectors have achieved the transformation of gravitational wave detection from nothing to something, the current observational data still cannot meet the accuracy requirements in cosmology and basic physics research. Taking the measurement of H0 as an example, there is a special type of event in the gravitational wave "standard whistle". They have a coordinated electromagnetic signal (electromagnetic counterpart) that is visible in the electromagnetic band, so they are called "bright whistle". Through the electromagnetic counterpart, we can accurately locate the host galaxy of the "bright whistle" and thus determine the redshift of the gravitational wave source. At present, the only "bright whistle" event GW170817 has achieved independent measurement of H0, with a measurement accuracy of about 14% [11]. Those "standard whistle" events without electromagnetic counterparts are called "dark whistles". To obtain the redshift of the "dark whistle", it is necessary to combine the star catalog provided by the sky survey project (a catalog that records the position, brightness, color and other information of galaxies in the sky).

At present, the measurement accuracy of H0 for 47 "dark whistle" events combined with the GLADE+ star catalog is about 19% [12]. Figure 3 shows the current limitations of H0 imposed by different observations. As can be seen from the figure, the current gravitational wave "standard whistle" observations have not yet reached the accuracy requirements for solving the "Hubble crisis" (the posterior distribution of H0 inferred from the "standard whistle" data spans the limitations of CMB observations and the distance ladder method), so it is very important to develop the next generation of gravitational wave detectors.

Figure 3: Posterior distribution of H0 for various real observational situations. The black line represents the constraint of the only “bright whistle” GW170817. The gray dashed line represents the result of using only the “dark whistle” constraint after fixing the population distribution of gravitational wave events. The blue solid line represents the constraint of using the GLADE+ k-band star catalog in combination with the “dark whistle” and “bright whistle” constraints. The orange solid line represents the constraint of using the GLADE+ k-band star catalog in combination with the “dark whistle” constraints. The pink and green shaded areas represent the 68% confidence regions of H0 under the constraints of Planck’s CMB observations and the SH0ES distance ladder method, respectively. (Source: R. Abbott et al. [12])

3 Strong alliance to resolve crisis

Research shows that the third generation of ground-based gravitational wave detectors will observe millions of gravitational wave events within a decade, with the highest redshift reaching 100. However, limited by the observation of electromagnetic counterparts, the "bright whistle" events account for only about 0.1%, so it is very important to make full use of the huge number of "dark whistle" events for cosmological research. Due to the limitation of observation capabilities, sky survey projects often miss some relatively faint galaxies. The completeness of the GLADE+ star catalog currently used for dark whistle research has dropped to 20% at a redshift of about 0.17 (the lower the completeness of the star catalog, the more galaxies are missed in the star catalog), making it difficult to meet the dark whistle research needs of the next generation of gravitational wave detectors. To this end, we need the star catalog provided by the next generation of sky survey projects that are about to be launched.

As the next generation of sky survey project, CSST is expected to complete its survey mission around 2035 and provide an advanced star catalog for the third generation of ground-based gravitational wave detectors. Compared with the GLADE+ star catalog, CSST has higher star catalog completeness and lower redshift uncertainty. Figure 4 shows the distribution of the completeness of the CSST simulated star catalog with distance and redshift. It can be seen that the completeness of the CSST star catalog has been significantly improved compared with the GLADE+ star catalog (the completeness at redshifts up to 0.3 is still close to 100%). In addition, studies have shown that the redshift measurement uncertainty of CSST is very low. Among them, photometric surveys can achieve redshift uncertainties of more than 95% of galaxies below 0.05 (1+z), and about 50% of galaxies are within 0.02 (1+z), while seamless spectral surveys can make the redshift uncertainty of galaxies reach 0.002 (1+z) [13,14], which is at least 40% higher than the GLADE+ star catalog. Lower redshift uncertainty can directly improve the measurement accuracy of H0 through the distance-redshift relationship.

So how will the combination of CSST and the third-generation ground-based gravitational wave detector perform in measuring H0? Figure 5 shows the constraint results of different third-generation gravitational wave detectors, including ET, CE, and a network of gravitational wave detectors consisting of one ET and two CEs (ET2CE). We found that for any third-generation gravitational wave detector, only about 300 gravitational wave events located in the 100% completeness region of CSST (redshift less than 0.3) can limit the Hubble constant to less than 1%. In the future, by using reliable statistical methods to eliminate the statistical bias caused by the incompleteness of the star catalog, we hope to take more gravitational wave events into account. By then, the combination of CSST and the third-generation ground-based gravitational wave detectors will provide more accurate results for the constraints on cosmological parameters.

Figure 4: The distribution of the completeness of the star catalog provided by the CSST photometric survey project as a function of photometric distance and redshift. Lines of different colors represent different types of galaxies. The blue solid line represents star-forming galaxies, the orange dashed line represents late-type spiral galaxies, the green dotted horizontal line represents early-type spiral galaxies, and the red dotted line represents bright red galaxies. (Source: Song et al. 2024 [1])

Figure 5: The posterior distribution of the Hubble constant inferred from the CSST combined with the third-generation ground-based gravitational wave detection. (Source: Song et al. 2023 [1])

【References】

[1] JY Song et al., Synergy between CSST galaxy survey and gravitational-wave observation: Inferring the Hubble constant from dark standard sirens, Sci. China-Phys. Mech. Astron. 67, 230411 (2024), doi: 10.1007/s11433-023-2260-2

[2] Z.-H. Zhu, Illuminating dark sirens with CSST, Sci. China-Phys. Mech. Astron. 67, 230431 (2024), doi: 10.1007/s11433-023-2277-5

[3] http://www.bao.ac.cn/csst/

[4] BP Abbott et al., Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, 061102 (2016), doi: 10.1103/PhysRevLett.116.061102

[5] M Punturo et al., The Einstein Telescope: a third-generation gravitational wave observatory, Class. Quantum Grav. 27, 194002 (2010), doi: 10.1088/0264-9381/27/19/194002

[6] BP Abbott et al., Exploring the sensitivity of next generation gravitational wave detectors, Class. Quantum Grav. 34, 044001 (2017), doi: 10.1088/1361-6382/aa51f4

[7] A. Einstein, The field equations of gravitation, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1915, 844-847 (1915)

[8] E. Hubble, A relation between distance and radial velocity among extra-galactic nebulae, Proc. Nat. Acad. Sci. 15, 168 (1929), doi: 10.1073/pnas.15.3.168

[9] Bernard F. Schutz, Determining the Hubble constant from gravitational wave observations, Nature 323, 310-311 (1915), doi:10.1038/323310a0

[10] https://www.aura-astronomy.org/blog/2023/03/06/our-mysterious-universe-still-evades-cosmological-understanding/

[11] BP Abbott et al., A gravitational-wave standard siren measurement of the Hubble constant, Nature 551, 85 (2017), doi: 10.1038/nature24471

[12] R. Abbott et al., Constraints on the cosmic expansion history from GWTC-3, Astrophys. J. 949, 76 (2023), doi: 10.3847/1538-4357/ac74bb

[13] Y. Cao et al., Testing photometric redshift measurements with filter definition of the Chinese Space Station Optical Survey (CSS-OS), Mon. Not. Roy. Astron. Soc. 480, 2178 (2018), doi: 10.1093/mnras/sty1980

[14] Y. Gong, et al., Cosmology from the Chinese Space Station Optical Survey (CSS-OS), Astrophys. J. 883, 203 (2019), doi: 10.3847/1538-4357/ab391e