add simple example at z=7

%% Cell type:markdown id:f62f241b-275b-43fe-8b6c-079ac7126770 tags:

# Explore AGN lightcurve 1 + z

This notebook explores the AGN lightcurves with and without the (1 + z) term on the structure function. For AGILE DR1 the (1 + z) term was included, which it could be reasoned to omit the term.

Here we aim to quantify the effect of (1 + z) on the structure function in terms of AGN physical parameters and the lightcurve RMS.

%% Cell type:code id:6ee80f74-7bc1-4980-a87c-11e3d016f5a2 tags:

``` python

from lsst_inaf_agile.lightcurve import get_lightcurve_agn

```

%% Cell type:code id:c9d27682-7c1b-4bd4-9d2a-39324edec2c4 tags:

``` python

def lc_mag(*args, **kwargs):

    lc = get_lightcurve_agn(*args, **kwargs)

    return -2.5 * np.log10(lc) + 23.9

```

%% Cell type:code id:0dcc5604-f0e5-4d43-8c02-1c1f33c2a94c tags:

``` python

def calc_stats(mag):

    return {

        "min": mag.min(),

        "max": mag.max(),

        "mean": mag.mean(),

        "rmse": np.sqrt(np.mean((mag - np.mean(mag)) ** 2)),

    }

```

%% Cell type:code id:f4bd35d2-4ffa-423d-8cef-e2af31bb376a tags:

``` python

kwargs = dict(

    mjd0=0,

    mjd=np.arange(365.25 * 10),

    flux=1.0,

    band="lsst-r",

    z=1.0,

    mag_i=-26,

    logMbh=8,

    type2=False,

    seed=2026,

)

```

%% Cell type:markdown id:85339944-a14b-4080-b4d9-699c6abbb307 tags:

# Plot a single lightcurve with and without 1 + z

# Plot a single lightcurve with and without 1 + z at z=1.0

%% Cell type:code id:a2cc1454-efcb-46f9-bba0-634c09291a0e tags:

``` python

plt.figure(dpi=100)

for divide_1z in False, True:

    lc = lc_mag(divide_sf_inf_by_z1=divide_1z, **kwargs)

    stats = calc_stats(lc)

    text = "\n".join(

        [

            f"{divide_1z=}",

        ]

        + [f"{k}: {v:.4f}" for k, v in stats.items()]

    )

    text = "\n".join([f"{divide_1z=}"] + [f"{k}: {v:.4f}" for k, v in stats.items()])

    print(calc_stats(lc))

    plt.plot(lc, label=text)

plt.title(f"z = {kwargs['z']}")

plt.legend(frameon=True)

plt.xlim(0, 4000)

plt.xlabel("mjd")

plt.ylabel("mag")

```

%% Cell type:markdown id:30019c53-ae8b-4190-8b65-3b5223c8ba2a tags:

# Plot a single lightcurve with and without 1 + z at z=7.0

%% Cell type:code id:4bc533a8-5362-4fb3-af83-12e79b69729a tags:

``` python

plt.figure(dpi=100)

for divide_1z in False, True:

    kwargs["z"] = 7.0

    lc = lc_mag(divide_sf_inf_by_z1=divide_1z, **kwargs)

    stats = calc_stats(lc)

    text = "\n".join([f"{divide_1z=}"] + [f"{k}: {v:.4f}" for k, v in stats.items()])

    print(calc_stats(lc))

    plt.plot(lc, label=text)

plt.title(f"z = {kwargs['z']}")

plt.legend(frameon=True)

plt.xlim(0, 4000)

plt.xlabel("mjd")

plt.ylabel("mag")

```

%% Cell type:markdown id:2cbcef2e-0135-4d62-9f27-1e1c7da08a54 tags:

# Plot a differential lightcurve with and without 1 + z

%% Cell type:code id:5be3601c-1b6c-4f5f-aad5-51c8fbc8b21d tags:

``` python

plt.figure(dpi=100)

lc1 = lc_mag(divide_sf_inf_by_z1=True, **kwargs)

lc2 = lc_mag(divide_sf_inf_by_z1=False, **kwargs)

stats = calc_stats(lc1 - lc2)

text = "\n".join([f"{k}: {v:.4f}" for k, v in stats.items()])

print(text)

plt.plot(lc1 - lc2, label=text)

plt.title(f"z = {kwargs['z']}")

plt.xlim(0, 4000)

plt.xlabel("mjd")

plt.ylabel("mag_with - mag_without")

plt.legend()

```

%% Cell type:markdown id:60668bcf-032a-4b49-950d-5ec1b93bee1a tags:

# Plot the redshift-dependence

%% Cell type:code id:e20cbcbb-c347-47de-a852-c5adea52ffad tags:

``` python

plt.figure(dpi=100)

for z in 0.1, 1, 2, 3:

    _kwargs = kwargs.copy()

    _kwargs["z"] = z

    lc = lc_mag(divide_sf_inf_by_z1=True, **_kwargs)

    stats = calc_stats(lc)

    text = "\n".join(

        [

            f"z={_kwargs['z']}",

        ]

        + [f"{k}: {v:.4f}" for k, v in stats.items()]

    )

    print(calc_stats(lc))

    plt.plot(lc, label=text)

plt.legend(frameon=True)

plt.xlim(0, 4000)

plt.xlabel("mjd")

plt.ylabel("mag")

```

%% Cell type:markdown id:a49baef6-8095-4609-9ecc-61ce6f3d6f8e tags:

# Plot a very high redshift example z=0.1 vs. z=7.0

%% Cell type:code id:8320c96e-79b2-4f43-a945-e09681a9cc13 tags:

``` python

plt.figure(dpi=100)

for z in 0.1, 7:

    _kwargs = kwargs.copy()

    _kwargs["z"] = z

    print(_kwargs)

    lc = lc_mag(divide_sf_inf_by_z1=True, **_kwargs)

    stats = calc_stats(lc)

    text = "\n".join(

        [

            f"z={_kwargs['z']}",

        ]

        + [f"{k}: {v:.4f}" for k, v in stats.items()]

    )

    print(calc_stats(lc))

    plt.plot(lc, label=text)

plt.legend(frameon=True)

plt.xlim(0, 4000)

plt.xlabel("mjd")

plt.ylabel("mag")

```

%% Cell type:markdown id:2e55fe1b-0b8d-44e9-ad72-06b4b8efcb4a tags:

# Show scaling with MBH

%% Cell type:code id:1b7a5388-bff5-4f4d-8dc1-ddb8a3965d80 tags:

``` python

plt.figure(dpi=100)

for divide_1z in False, True:

    mbhs = []

    rmses = []

    for logMbh in np.linspace(5, 10):

        _kwargs = kwargs.copy()

        _kwargs["z"] = 1.0

        _kwargs["logMbh"] = logMbh

        lc = lc_mag(divide_sf_inf_by_z1=divide_1z, **_kwargs)

        stats = calc_stats(lc)

        mbhs.append(logMbh)

        rmses.append(stats["rmse"])

    plt.plot(mbhs, rmses, ls="solid" if divide_1z else "dotted", label=f"{divide_1z=}")

plt.title("z = 1")

plt.xlabel("logMBH")

plt.ylabel("RMSE")

plt.legend()

```

%% Cell type:code id:6302eaf8-1c3d-4e8e-a6b2-f63044b25247 tags:

``` python

```