CN116413832A - Time sequence data-based space gravitational wave detection sensitivity calculation method and system - Google Patents
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Abstract
The invention relates to the gravitational wave detection field, in particular to a method and a system for calculating the detection sensitivity of a space gravitational wave based on time sequence data. The invention calculates the sensitivity of a spatial gravitational wave detector using mixed noise time sequence data, comprising: acquiring multi-channel mixed noise phase time sequence data; processing the multi-path mixed noise phase time sequence data by using a time delay interferometry technology to generate one-path noise phase time sequence data; converting the noise phase timing data into noise strain timing data; performing Fourier transform on the noise strain time sequence data to calculate noise strain power spectral density; converting the noise strain power spectral density to a noise relative frequency power spectral density; the sensitivity is calculated using the noise versus frequency power spectral density and the transfer function R. The invention realizes the calculation of TDI1.0X combined sensitivity by utilizing the mixed noise time sequence data and the resolved transfer function formula.
Description
Technical Field
The invention relates to the gravitational wave detection field, in particular to a method and a system for calculating the detection sensitivity of a space gravitational wave based on time sequence data.
Background
In the beginning of 2016, the us land laser interference gravitational wave astronomy (LIGO) published results of direct detection of gravitational waves, confirming the prediction of einstein about the existence of gravitational waves one hundred years ago, and opening up a new research direction, gravitational wave astronomy. Unlike electromagnetic waves, gravitational waves will create a completely new window for us to observe the universe. From a large explosion in the universe to a black hole, from a merging of the intermediate stars to a double star of the white dwarf, from a topological defect in the universe to dark energy of a dark substance, and the like.
The ground gravitational wave measurement is limited by the influence of the earth gravitational force and the size of the scale, and the detected gravitational wave range is mainly concentrated at high frequency. Spatial (in space) gravitational wave detection is not an option, as it is understood that a wider range of gravitational waves and wave sources are of a nature. As a representative of the spatial gravitational wave detection items, LISA (Laser Interferometer Space Antenna) describes clear paths and platforms for the spatial gravitational wave detection subjects at the task concept level, provides references for the design of other spatial laser interference gravitational wave detection items such as tai chi plan, tian qin plan and the like in the world, particularly promotes the development of the spatial gravitational wave detection subjects in the aspects of wave source analysis, data processing, relevant wave source astronomy, relative theory itself and the like, and promotes the spatial gravitational wave detection to gradually form a subject research field.
The method is initiated by the institute of science of China in 2008, a plurality of units of the academy of sciences and a plurality of surgical research units of the academy of sciences participate together, so that a space gravitational wave detection demonstration group of the academy of sciences is established, and a development route pattern of space gravitational wave detection of China in the coming decades is planned. Through the pilot pre-research of two-stage Chinese academy, a space gravitational wave detection Taiji plan is provided. In 2014, the university of Zhongshan and the university of Huazhong science and technology jointly propose a Tianqin plan. In 2019, the Taiji team and the Tianqin team successfully launched the technical experimental star Taiji one number and Tianqin one number respectively.
Taking a Taiji plan space gravitational wave detector as an example, the geometry of the Taiji plan space gravitational wave detector is triangular by taking three spacecrafts as vertexes, each spacecraft is provided with two testing quality and two lasers, and each side is an arm. The method has high measurement accuracy requirement, strong coupling of each link and great technical challenge, and the technical scheme and key technology are still in the process of deep research and perfection at present, and comprehensive optimization and verification means of core indexes and the technical scheme are urgently needed in the system level. Because the detection system has strict requirements on microgravity and electromagnetic environment, and is difficult to establish a complete equivalent simulation loop model on the ground to develop system-level function and performance verification, the full-link numerical simulation analysis is an effective means for quickly finding potential problems and risks of tasks, comprehensively optimizing the overall design scheme of the system and assisting in the research, development and verification of key technologies. In order to achieve the purpose, the national center of space science of China academy of sciences constructs a preliminary framework of a space gravitational wave detection full-link simulation system (hereinafter referred to as a simulation system) and has the capabilities of top detection index sensitivity analysis, track and formation design, noise analysis, time sequence signal simulation and the like.
In order to determine whether a particular gravitational wave source can be detected by the gravitational wave detector, it is necessary to know the sensitivity limit of the instrument, the detector sensitivity reflecting the sensitivity of the detector to the target signal. The sensitivity of these instruments is typically described by plotting the square root (ASD, amplitude spectral density, amplitude spectral density) of the processed instrument total noise PSD (power spectral density ) versus transfer function ratio. This means that the instrument noise level affects the sensitivity, the smaller the noise level, the higher the sensitivity. "Qianling" medicine for curing common coldThe sensitivity calculation is generally based on two detector noise top-level indexes, namely a displacement noise ASD index and an inertial sensor noise (inertial transmission noise) ASD index. And for convenience, displacement noise only considers the dominant terms shot noise and laser phase noise therein. The laser phase noise of the detector is quite large, and for a ground interferometer, the fixed lengths of the two arms are the same, so that the laser experiences the same delay, and the laser phase noise can be well eliminated. However, for a spatial interferometer, it is not possible to keep the length of each arm constant. This results in lasers in different arms having different delays and residual laser phase noise greatly affects sensitivity. To solve this problem, tinto et al. First, time delay interferometry (TDI, time Delay Interferometry) techniques were proposed to eliminate noise with different measurement data combinations. The laser phase noise is eliminated by using the combination of the X link under TDI1.0, so that only inertial noise and shot noise are considered in calculation, and according to the noise index requirement of Taiji III, the shot noise ASD is 5 multiplied by 10 -12 m/≡Hz, inertial noise ASD of 3×10 -15 ms -2 V Hz, combined with a theoretical formula. The index-based approach obviously does not truly reflect the sensitivity of the detector.
Disclosure of Invention
The invention aims to provide a method for calculating the detection sensitivity of a space gravitational wave based on time sequence data, which can utilize the mixed noise time sequence data simulated by a simulation system to calculate the sensitivity, and can provide a method support for the analysis of the simulation precision of a mixed noise model of the simulation system compared with the sensitivity based on indexes; on the other hand, the method can calculate more real sensitivity by using real detection data obtained by a future space gravitational wave detection formation system.
In order to achieve the above purpose, the present invention is realized by the following technical scheme.
The invention provides a time sequence data-based spatial gravitational wave detection sensitivity calculation method, which is used for calculating the sensitivity of a spatial gravitational wave detector by using mixed noise time sequence data, and comprises the following steps:
s1, acquiring phase time sequence data of multiple paths of mixed noise;
s2, processing the multi-path mixed noise phase time sequence data by using a time delay interferometry technology to generate one-path noise phase time sequence data;
s3, converting the noise phase time sequence data into noise strain time sequence data;
s4, carrying out Fourier transform on the noise strain time sequence data to calculate noise strain power spectral density;
s5, converting the noise strain power spectral density into noise relative frequency power spectral density;
s6, calculating sensitivity by using the noise relative frequency power spectral density and the response function R.
As one of the improvements of the above technical solution, in the step S1, a simulation system is adopted to simulate and obtain multiple paths of mixed noise phase time sequence data, or a transmitted spatial gravitational wave detector is used to obtain multiple paths of mixed noise phase time sequence data.
As one of the improvements of the technical scheme, the space gravitational wave detector comprises three spacecrafts with two lines in a triangle shape;
each spacecraft comprises a master optical bench and a slave optical bench;
each of the master optical bench and the slave optical bench comprises a test quality, a laser and an interferometry device;
each interferometry device includes a scientific interferometer, a test mass interferometer, and a reference interferometer;
the scientific interferometer is used for measuring the distance between corresponding spacecrafts according to the interference of laser emitted by lasers between a main optical bench or a slave optical bench of one of the spacecrafts and a slave optical bench or a main optical bench of other spacecrafts;
the test quality interferometer is used for measuring the distance between the test quality in each spacecraft according to the interference of laser emitted by the laser between the master and slave tables of each spacecraft;
the reference interferometer is used for providing reference phases of laser interference for the scientific interferometer and the quality testing interferometer.
As one of the improvements of the above technical solution, at least 18 paths of mixed noise phase timing data are acquired in the step S1 using all of the scientific interferometer, the test quality interferometer and the reference interferometer.
As one of the improvements of the technical scheme, the noise strain power spectral density generated by S4 is multiplied by (2pi fL/c) 2 Obtaining the relative frequency power spectral density of noise
f is the frequency, L is the distance between any two spacecrafts, and c is the speed of light.
As one of the improvements of the above technical solution, the formula for calculating the sensitivity S (u) in the step S6 is:
wherein T is the observation time.
The invention also provides a space gravitational wave detection sensitivity calculation system based on time sequence data, which comprises:
the noise phase time sequence data input module is used for inputting the multipath mixed noise phase time sequence data acquired by the space gravitational wave detector;
the noise relative frequency power spectrum density module is used for processing the multi-path mixed noise phase time sequence data by utilizing a time delay interferometry technology to generate one-path noise phase time sequence data; the method comprises the steps of converting noise phase time sequence data into noise strain time sequence data, performing Fourier transform on the noise strain time sequence data to calculate noise strain power spectral density, and finally converting the noise strain power spectral density into noise relative frequency power spectral density; and
and the sensitivity calculation module is used for calculating the sensitivity by utilizing the noise relative frequency power spectral density and the response function R.
As one of the improvements of the technical scheme, in the noise relative frequency power spectral density module, the noise strain power spectral density generated by S4 is multiplied by (2 pi fL/c) 2 Obtaining noiseThe acoustic relative frequency power spectral density, f is the frequency, L is the distance between any two spacecrafts, and c is the speed of light.
As one of the improvements of the above technical solution, in the sensitivity calculation module, the calculation formula of the sensitivity S (u) is:
wherein T is the observation time.
Compared with the prior art, the invention has the advantages that:
1. the sensitivity of TDI1.0X combination is calculated by combining the mixed noise time sequence data simulated by the simulation system with the analyzed transfer function formula, which is unprecedented;
2. the method can calculate more real sensitivity different from a theoretical value by utilizing real detection data obtained by a future space gravitational wave detection formation system.
Drawings
FIG. 1 is a schematic diagram of a spatial laser interference gravitational wave detection system formation;
FIG. 2 is a PSD of one path of noise timing data after TDI1.0-X combination processing;
FIG. 3 is a flow chart of an embodiment of the present invention;
FIG. 4 is a plot of theoretical sensitivity under TDI1.0X combinations based on noise top level indicators;
FIG. 5 is a plot of sensitivity under TDI1.0X combinations based on several primary noise timing data;
FIG. 6 is a plot of sensitivity under TDI1.0X combinations based on all noise timing data;
FIG. 7 is a plot of sensitivity in TDI1.0X combination with some gravitational wave sources based on all noise timing data;
fig. 8 is a diagram of gravitational wave sources.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and examples.
FIG. 1 is a schematic diagram of a spatial laser interference gravitational wave detector formation; three spacecrafts (SC 1, SC2 and SC 3) of the space gravitational wave detector are triangular, each SC comprises a master optical table and a slave optical table, a testing quality, a laser and an interferometry device are arranged on the optical table, a scientific interferometer link i (i=1, 2 and 3) and a scientific interferometer link is in the figure represent six interference arms corresponding to six scientific interferometers, for example, a scientific interferometer link 1s represents that the laser of the SC1 local laser of the optical table interferes with the laser emitted by the SC3 main optical table laser; similarly, the test quality interferometer links i and is are six interferometer arms corresponding to six test quality interferometers, and the reference interferometer links i and is are six interferometer arms corresponding to six reference interferometers. Each optical platform has a metallic mass thereon, known as the proof mass. According to the generalized relativity theory, when gravitational waves pass, small changes generated by the space-time structure cause the space distance between two tested masses to change, and the laser interference principle is used for measuring the small changes. The scientific interferometer measures the displacement change between two satellites, the interference light intensity is 100pw and 10mw, and the displacement measurement precision is required to be lpm/Hz; the reference interferometer provides reference phases for other interferometers to eliminate noise caused by non-optical platforms, such as optical fibers, frequency modulation devices and the like, and provides phase-locked error signals for weak light phase locking; the test mass interferometer provides inertial sensing, scientific interferometers with positional information of the test mass relative to the optical platform.
The gravitational wave can cause interference arm length change when passing through the detector, and 18 interferometers can measure laser phase change caused by the gravitational wave. In addition, noise also causes laser phase change, and the simulation system simulates 18 paths of phase change time sequence data caused by the gravitational wave and the noise. When simulating, only various noises are simulated, and the simulation system outputs 18 paths of mixed noise time sequence data.
The method for calculating the sensitivity theoretical model based on the noise top-level index TDI1.0X combination (TDI1.0X combination specifically means that the TDI technology eliminates laser phase noise by carrying out phase delay and linear combination on phases measured by a plurality of interferometers, TDI1.0 means that the arm length is fixed without considering spacecraft constellation rotation and scientific interferometer interference arm telescopic bending, and does not change with time and does not distinguish the difference of interference arms when the same arm is shot on and shot off, X combination is also called Michelson combination, and is an important combination mode of the TDI technology), and the method for calculating the sensitivity theoretical model is as follows:
noise index requirements, such as Taiji three, shot noise ASD of 5×10 -12 m/≡Hz, inertial noise ASD of 3×10 -15 ms -2 V Hz, substituting equation (1) to calculate the noise PSD.
To the left of the equation is the noise PSD (this equation noise PSD is in relative frequency), subscript X 1 Representing TDI1.0X combinations. Right side s of equation a Is inertial noise ASD, s x For shot noise ASD, L is 3000000000m, c is the speed of light 300000000m/s, u is 2pi fL/c, f is the frequency, the frequency band is 0Hz to 1.5Hz, every interval is 1.5X10 -5 Hz takes a frequency bin.
The noise PSD is taken into equation (2) to calculate the sensitivity S.
Wherein T is the observation time 31536000s, R is the average response function of the space gravitational wave detector on the whole celestial sphere obtained by averaging the gravitational wave source position and the polarization angle. Conventionally, sensitivity is typically calculated using an all-celestial average response function. In previous studies, the response function was numerically simulated or semi-resolved, and in recent years, an average response function was derived for resolution, and the TDI1.0 generation X combined resolved response function was used.
The TDI1.0X combined sensitivity theoretical model calculation method based on time sequence data is as follows:
s1, acquiring multi-channel mixed noise phase time sequence data by using a spatial gravitational wave detector;
s2, processing the multi-path mixed noise phase time sequence data by utilizing a time delay interference TDI1.0X combined measurement technology to generate one-path noise phase time sequence data;
s3, converting the noise phase time sequence data into a relation between the noise strain time sequence data phase and strain as shown in a formula (3), wherein h is the strain,
is phase, lambda is laser wavelength, 1064 nm;
s4, carrying out Fourier transform on the noise strain time sequence data to calculate noise strain power spectral density;
s5, multiplying the noise strain power spectral density by (2pi fL/c) 2 Converting into noise relative frequency power spectral density;
s6, calculating the sensitivity by combining the noise relative frequency power spectral density and the transfer function R with the formula (2).
Example 1
The method for calculating the spatial gravitational wave detection sensitivity curve based on time sequence data utilizes one path of noise time sequence data generated by TDI processing of 18 paths of noise time sequence data of an interferometer to calculate noise PSD, and then calculates sensitivity. The noise relative frequency PSD calculated by this method is shown in FIG. 2.
A specific implementation flowchart is shown in fig. 3.
The method specifically comprises the following steps:
s1, acquiring multi-channel mixed noise phase time sequence data by using a spatial gravitational wave detector;
s2, processing the multi-path mixed noise phase time sequence data by utilizing a time delay interference TDI1.0X combined measurement technology to generate one-path noise phase time sequence data;
s3, converting the noise phase time sequence data into a relation between the noise strain time sequence data phase and strain as shown in a formula (3), wherein h is the strain,
is phase, lambda isThe laser wavelength, 1064 nm;
s4, carrying out Fourier transform on the noise strain time sequence data to calculate noise strain power spectral density;
s5, multiplying the noise strain power spectral density by (2pi fL/c) 2 Converting into noise relative frequency power spectral density;
s6, calculating the sensitivity by combining the noise relative frequency power spectral density and the transfer function R with the formula (2).
As fig. 5 shows a sensitivity curve calculated based on several main noise items mixed with noise simulation time sequence data, only shot noise, inertial noise and laser phase noise are considered, and it can be seen from comparison with fig. 4 that the method is basically correct.
Fig. 6 is a sensitivity curve calculated based on all noise term mixed noise simulation timing data, accounting for shot noise, laser frequency noise, laser pointing jitter noise, lead pointing path noise, respiratory angle noise, phase meter noise, inertial total noise, and other noise.
The bottom curve in fig. 7 is a sensitivity curve calculated based on the mixed noise simulation time sequence data of all noise items, and other lines are some wave sources. The gravitational wave source is as shown in fig. 8: wherein J0651+2844 and J0934+4411 are double-white dwarf systems. The wave sources are already marked in the figure.
Example 2
The embodiment 2 of the invention provides a space gravitational wave detection sensitivity calculation system based on time sequence data, and the sensitivity can be obtained after the acquired multipath mixed noise phase time sequence data are input into the system. The system comprises:
the noise phase time sequence data input module is used for inputting multi-path mixed noise phase time sequence data simulated by the simulation system;
the noise phase time sequence data processing module is used for processing the multi-path mixed noise phase time sequence data by utilizing a time delay interference TDI1.0X combination measurement technology to generate one-path noise phase time sequence data;
the noise relative frequency power spectrum density module is used for converting the noise phase time sequence data into noise strain time sequence data, then carrying out Fourier transform on the noise strain time sequence data to calculate noise strain power spectrum density, and finally converting the noise strain power spectrum density into noise relative frequency power spectrum density; and
and the sensitivity calculation module is used for calculating the sensitivity by utilizing the noise relative frequency power spectral density and the transfer function R.
According to the invention, the spatial gravitational wave detection sensitivity curve is calculated based on the noise time sequence data, on one hand, the sensitivity can be calculated by utilizing the mixed noise time sequence data simulated by the simulation system, and compared with the sensitivity based on indexes, the method support is provided for the analysis of the simulation precision of the mixed noise model of the simulation system; on the other hand, method support is provided for calculating more realistic sensitivity for real detection data obtained by utilizing a future space gravitational wave detection formation system.
Finally, it should be noted that the above embodiments are only for illustrating the technical solution of the present invention and are not limiting. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the appended claims.
Claims (9)
1. A method for calculating sensitivity of a spatial gravitational wave detection based on time series data for calculating sensitivity of a spatial gravitational wave detector using mixed noise time series data, the method comprising:
s1, acquiring phase time sequence data of multiple paths of mixed noise;
s2, processing the multi-path mixed noise phase time sequence data by using a time delay interferometry technology to generate one-path noise phase time sequence data;
s3, converting the noise phase time sequence data into noise strain time sequence data;
s4, carrying out Fourier transform on the noise strain time sequence data to calculate noise strain power spectral density;
s5, converting the noise strain power spectral density into noise relative frequency power spectral density;
s6, calculating sensitivity by using the noise relative frequency power spectral density and the response function R.
2. The method according to claim 1, wherein in step S1, the simulation system is adopted to simulate and obtain multiple paths of mixed noise phase time sequence data, or the transmitted spatial gravitational wave detector is used to obtain multiple paths of mixed noise phase time sequence data.
3. The method for calculating the detection sensitivity of the spatial gravitational wave based on time series data according to claim 1, wherein the spatial gravitational wave detector comprises three spacecrafts with two lines in a triangle shape;
each spacecraft comprises a master optical bench and a slave optical bench;
each of the master optical bench and the slave optical bench comprises a test quality, a laser and an interferometry device;
each interferometry device includes a scientific interferometer, a test mass interferometer, and a reference interferometer;
the scientific interferometer is used for measuring the distance between corresponding spacecrafts according to the interference of laser emitted by lasers between a main optical bench or a slave optical bench of one of the spacecrafts and a slave optical bench or a main optical bench of other spacecrafts;
the test quality interferometer is used for measuring the distance between the test quality in each spacecraft according to the interference of laser emitted by the laser between the master and slave tables of each spacecraft;
the reference interferometer is used for providing reference phases of laser interference for the scientific interferometer and the quality testing interferometer.
4. The method for calculating the spatial gravitational wave detection sensitivity based on time series data according to claim 3, wherein said step S1 uses all of the scientific interferometer, the test quality interferometer and the reference interferometer to obtain at least 18 paths of mixed noise phase time series data.
5. The method of calculating sensitivity of spatial gravitational wave detection based on time series data as claimed in claim 3, wherein in said step S5, the noise strain power spectral density generated in S4 is multiplied by (2πfL/c) 2 Obtaining the relative frequency power spectral density of noise
f is the frequency, L is the distance between any two spacecrafts, and c is the speed of light.
6. The method for calculating the sensitivity of spatial gravitational wave detection based on time series data as claimed in claim 5, wherein the formula for calculating the sensitivity S (u) in step S6 is:
wherein T is the observation time.
7. A spatial gravitational wave detection sensitivity calculation system based on time series data, the system comprising:
the noise phase time sequence data input module is used for inputting the multipath mixed noise phase time sequence data acquired by the space gravitational wave detector;
the noise relative frequency power spectrum density module is used for processing the multi-path mixed noise phase time sequence data by utilizing a time delay interferometry technology to generate one-path noise phase time sequence data; the method comprises the steps of converting noise phase time sequence data into noise strain time sequence data, performing Fourier transform on the noise strain time sequence data to calculate noise strain power spectral density, and finally converting the noise strain power spectral density into noise relative frequency power spectral density; and
and the sensitivity calculation module is used for calculating the sensitivity by utilizing the noise relative frequency power spectral density and the response function R.
8. The time series data based spatial gravitational wave detection sensitivity calculation system as claimed in claim 7 wherein in said noise versus frequency power spectral density module, the noise strain power spectral density generated by S4 is multiplied by (2pi fL/c) 2 Obtaining the relative frequency power spectral density of noise
f is the frequency, L is the distance between any two spacecrafts, and c is the speed of light.
9. The time series data based spatial gravitational wave detection sensitivity calculation system of claim 8, wherein in said sensitivity calculation module, the calculation formula of the sensitivity S (u) is:
wherein T is the observation time.
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